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"Introduction {#Sec1}\n============\n\nSensitive and specific diagnosis of malaria becomes increasingly important as malaria prevalence in many regions continues to decline^[@CR1]^, due to scaling-up of control interventions and improved anti-malarial chemotherapy^[@CR2]^. In many regions, a decline in malaria prevalence results in a transition from *Plasmodium* infections that are predominantly characterised by high parasite density, to those of low parasite density^[@CR3]^. Although the latter are harder to detect, malaria elimination programmes seek to identify all infected individuals, regardless of symptoms or parasite density, to administer anti-malarial drugs and therefore to prevent onwards transmission. ",
"The use of diagnostic tools for malaria is dependent upon the setting, but as the burden of malaria falls disproportionately upon some of the world's poorest populations^[@CR4]^, diagnosis is often constrained by resources. ",
"Current recommendations from the World Health Organisation are that malaria is diagnosed by microscopy and/or rapid diagnostic test (RDT)^[@CR1]^. While microscopy can be a highly sensitive method when conducted proficiently using a thick blood film (for example, by thick film, 10 parasites per μL blood \\[p/μL\\] were detected by a lead microscopist in a reference laboratory in the UK)^[@CR5]^, allowing the operator to screen many blood cells, the sensitivity and precision of this method is dependent upon the microscopist and their level or access to training^[@CR6]^. Although an accepted problem, there is evidence that in some settings standards of malaria diagnostic microscopy may be declining^[@CR7]--[@CR9]^. Rapid diagnostic tests are composed of a plastic or cardboard cassette containing a nitrocellulose strip, on which a band of monoclonal antibodies are visualised if they bind certain *Plasmodium* proteins, set within absorptive padding. ",
"They are widely available, cheap, and easy to use. ",
"However, RDT are less sensitive than microscopy (usually with a limit of detection \\[LOD\\] of approximately 100 p/μL)^[@CR10]--[@CR12]^ and they cannot give a quantitative estimate of the patient's parasite burden. ",
"Further, they cannot be used to confirm parasite clearance following treatment, as circulating *Plasmodium* proteins (e.g. histidine-rich protein-2 (HRP-2)) from recently deceased parasites can continue to indicate positivity^[@CR10],[@CR13]^. Due to these drawbacks, it is recommended by the World Health Organisation (WHO) that microscopy and RDT results are routinely compared in the field^[@CR14]^.\n\nIn recent years, molecular techniques for detecting parasite DNA have been applied to the blood samples that are collected during the process of routine malaria diagnosis. ",
"The first studies of this kind applied polymerase chain reaction (PCR) to Giemsa-stained blood smears used previously for diagnostic microscopy^[@CR15],[@CR16]^. Since then, several studies have recognised the dried blood within used RDT as a valuable source of parasite DNA, and successfully applied molecular analysis to this template. ",
"The advantages of this are multiple: RDT are widely deployed across all malaria endemic settings, the volume of blood required is generally small (e.g. 5 µL), minimising discomfort and inconvenience to the patient, there are minimal storage requirements, and DNA amplification from the blood inside used RDT (RDT~DNA~) has repeatedly been shown to be successful up to one year post-collection^[@CR17]--[@CR20]^. Further, there is very little possibility of cross-contamination since blood is contained within the RDT cassette, and retrospective clinical and research studies can be undertaken where whole blood or dried blood spot samples for DNA extraction were not specifically collected. ",
"While initial studies of PCR from RDT~DNA~ focussed on proof of principle and quality assessment of the PCR result^[@CR18],[@CR21]^, it is now acknowledged that extraction and amplification of parasite DNA from RDT~DNA~ can allow more in-depth molecular analysis, including parasite genotyping to identify emerging resistance or important polymorphisms including HRP-2 deletions^[@CR22]^, better monitoring of the progress of malaria control strategies and studies of parasite genetic diversity^[@CR18],[@CR20]^. The identification of different infecting *Plasmodium* species, and indeed mixed-species infections, has also been demonstrated^[@CR21],[@CR23]^. Further, the use of such methods under different epidemiological and environmental settings has now been established, with an expanding evidence base that includes studies in French Guiana^[@CR17]^, Tanzania^[@CR18]^, Zanzibar^[@CR19]^, Mali^[@CR20]^ and the Comores^[@CR23]^. Methods of DNA extraction from RDT~DNA~ have been optimised in terms of the extraction procedures themselves^[@CR17],[@CR19]^, and importantly have also identified the optimal internal RDT component for targeted DNA extraction^[@CR21]^, whilst accounting for possible variability according to the specific brand of RDT. ",
"However, to our knowledge, the quantification of patient parasite density based on RDT~DNA~ has not previously been demonstrated.",
"\n\nThe objective of this study was therefore to determine *Plasmodium* parasite burden in patients by duplex quantitative PCR (qPCR) based on RDT~DNA~. We validated this parasite quantification through comparison to that calculated using a simultaneously sampled dried blood spot on Whatman filter paper (DBS~DNA~). ",
"External validation is particularly critical in the context of RDT~DNA~ because the nitrocellulose membrane that has been shown to best harbour good quality parasite DNA^[@CR21]^ is nonetheless not designed to this end. ",
"In addition, as it is recognised that the advantages of RDT~DNA~ include minimal long-term storage requirements, parasite quantification data after various storage times are needed to validate these conditions.",
"\n\nResults {#Sec2}\n=======\n\nValidation of robotic DNA extraction {#Sec3}\n------------------------------------\n\nWe validated the quality of *P*. *",
"falciparum* DNA derived from artificial dried blood spots (DBS) made with Dd2 and 3D7 cultures, by using a robotic extraction system (QIAsymphony, QIAGEN, Germany) with two different reagent and column kits from the Manufacturer (designated \"Investigator\" and \"Blood\"), in parallel with a manual (Chelex)^[@CR24],[@CR25]^ extraction system. ",
"We then genotyped the extracted DNA using the commonly used *pfcrt* qPCR assay^[@CR26]^. Both the manual and robotic extractions gave comparable results (Fig.",
" [1](#Fig1){ref-type=\"fig\"}), although the latter was slightly more efficient, exhibiting a lower average cycle threshold (CT) value compared to the former (manual 30.16 ± 5.86; automatic \"Investigator\" 29.37 ± 5.95; automatic \"Blood\", 29.56 ± 5.96 \\[mean CT ± standard deviation\\]). ",
"Both extraction methods detected the two *pfcrt* haplotypes (CVMNK and CVIET in 3D7 and Dd2 parasites respectively) with a sensitivity as low as five parasites per microliter. ",
"The coefficient of variation (CV) at the lowest parasitaemia was 5.10% and 5.20% for \"Blood\" and \"Investigator\" kits respectively using the CVMNK probe and 5.10% and 5.12% respectively for the kits using the CVIET probe. ",
"We observed no difference in mean CT value between QIAGEN \"Blood\" kit and QIAGEN \"Investigator\" kit at the lowest parasitaemia (the latter is recommended for DNA extraction from DBS) (*P* = 0.51, paired t-test, SED = 2.4, DF = 5; Table [1](#Tab1){ref-type=\"table\"}), when used in the robotic system.",
"Figure 1Comparison of the performance of the manual (chelex, solid lines) and automatic (QIAsymphony, dashed lines) systems for DNA extraction prior to qPCR genotyping of the pfcrt gene. (**",
"A**) Extraction from the *P*. *",
"falciparum* 3D7 pfcrt haplotype CVMNK, and (**B**) extraction from the *P*. *",
"falciparum* Dd2 pfcrt haplotype CVIET. ",
"NTC is no template control.",
"Table 1Cycle threshold (CT) values obtained during qPCR of the pfcrt haplotypes CVMNK and CVIET in the 3D7 and Dd2 *P*. *",
"falciparum* strains, respectively), following manual (chelex) or robotic (QIAsymphony) extraction.",
"FormatMethod\\*DNA dilution (p/μL)3D7 CVMNKDd2 CVIETMean CtCt STDCt CIMean CtCt STDCt CIManualChelex1:1 (50000)22.860.3422.58--23.1423.100.2822.87--23.331:10 (5000)25.910.7425.31--26.5125.610.5625.15--26.071:100 (500)27.920.3627.63--28.2127.450.3427.17--27.731:1000 (50)30.280.2630.07--30.4930.350.3130.10--30.601:5000 (5)35.940.4735.56--36.3236.210.5335.78--36.641:10000 (1)38.022.0036.39--39.6538.601.8937.06--40.14AutomaticInvestigator1:1 (50000)21.80.3021.56--22.0422.720.4922.32--23.121:10 (5000)25.280.0225.26--25.3026.790.1026.71--26.871:100 (500)26.30.4225.96--26.6429.760.4729.38--30.141:1000 (50)30.611.1429.68--31.5429.600.3729.30--29.901:5000 (5)35.510.5235.09--35.9335.210.2635.00--35.421:10000 (1)36.721.9135.16--38.2836.801.8635.28--38.32Blood1:1 (50000)21.20.1121.11--21.2922.500.1222.40--22.601:10 (5000)25.280.1725.14--25.4226.510.2426.31--26.711:100 (500)27.990.0927.92--28.0629.600.4629.22--29.981:1000 (50)30.750.0930.68--30.8229.620.2329.43--29.811:5000 (5)35.390.7834.75--36.0335.310.8134.65--35.971:10000 (1)36.721.9135.16--38.2836.401.8634.88--37.92\\*The robotic system was tested with two kits, \"Blood\" and \"Investigator\", that latter being specifically recommended for use in DBS extraction.",
"\n\nCorrelation in parasite densities obtained in qPCR using two DNA templates {#Sec4}\n--------------------------------------------------------------------------\n\nAll blood samples used in this study were RDT and filter paper finger prick samples collected in parallel from participants in a malaria odour study (described elsewhere, Supplementary Fig.",
" [S1](#MOESM1){ref-type=\"media\"})^[@CR27]^. *Plasmodium* parasite density, quantified by duplex qPCR, was correlated across the 141 RDT~DNA~ and DBS~DNA~ paired samples (*r* = 0.78, *P* \\< 0.001, F = 208.77), with no difference between the parasite densities obtained by either method (Wilcoxon Matched-Pairs test z = 0.475, *P = *0.635, *N* = 141, Figs [2](#Fig2){ref-type=\"fig\"} and [3A](#Fig3){ref-type=\"fig\"}). ",
"When only including pairs in which both the RDT and DBS sample was positive for parasite DNA (and both repeats of each sample), a good correlation remained (*r* = 0.53, *P* \\< 0.001, F = 15.41, *n* = 41, Fig.",
" [3B](#Fig3){ref-type=\"fig\"}) and no difference was observed between the values obtained from either method (Wilcoxon Matched-Pairs test z = −0.279, *P* = 0.781, *n* = 41). ",
"Although paired samples were only marginally different, there was a trend for the DBS~DNA~ sample to give higher parasite densities across most of the range of parasite densities (deviation from 1:1 correlation, Fig.",
" [3A](#Fig3){ref-type=\"fig\"}).Figure 2Parasite density measured by duplex qPCR, from a DNA template based on RDT~DNA~ (blue bars) or DBS~DNA~ (pink bars) (*n* = 108). ",
"Ordered by (**A**) RDT~DNA~ value, (**B**) DBS~DNA~ value (samples for which both results were zero are not shown, *n* = 33). ",
"Multiple values at 1.43 (0.93 + 0.5) p/μL represent 'inconclusive' samples (those that gave one positive and one negative repeat, which were universally allocated the median positive value for such samples, 0.93).Figure 3Parasite density measured by duplex qPCR, based on RDT~DNA~ or DBS~DNA~. There was a good correlation between parasite density in these paired samples across the whole dataset (**A**) (*r* = 0.78, *P* \\< 0.001, F = 208.77, *N* = 141), and when considering only paired samples that were both positive (**B**) (*r* = 0.53, *P* \\< 0.001, F = 15.41, *n* = 41). ",
"Both correlations (dashed lines) are however different from a 1:1 relationship ((**A**) *P* \\< 0.001, t-test; (**B**) *P* = 0.026, t-test. ",
"Data points of value 1.03 in (**A**) are missing from (**B**) as samples with one positive and one negative PCR repeat are omitted (median parasitaemia = 1.03 \\[0.93 + 0.1\\], see methods 'Parasite quantification').",
"\n\nPerformance of templates for DNA storage and amplification {#Sec5}\n----------------------------------------------------------\n\nParasite density was estimated by qPCR from one RDT~DNA~ sample to be 0.05 p/μL, with both repeats positive, suggesting a low limit of detection for this assay based on a RDT~DNA~ template. ",
"Further, given the correlation in parasite density obtained here between these two templates, and accepted ability of Whatman filter paper to preserve DNA, we deduce that storage of RDT~DNA~ for over a year (14 months: sample collection 15/05/2014--10/07/2014, first DNA extraction 28/09/2015) did not lead to DNA degradation.",
"\n\nWe used the recovery of human DNA (*HumTuBB*) to perform an exploratory analysis, comparing the amount of DNA recovered from the two template types. ",
"By taking advantage of the within-PCR-plate normalisation of *HumTuBB* amplification CT value to the international standard (i.e. delta CT)^[@CR28]^, we observed a difference between RDT and DBS sample pairs (*P* \\< 0.001, N = 141, Sign test), despite total surface area of the two template types available for extraction being approximately equal. ",
"A non-zero, positive median ratio of RDT:DBS delta CT values (median = 2.64, IQR: 0.83--7.67) indicated that RDT delta CT was more often a higher value, indicating a lower recovery of detectable human DNA.",
"\n\nImmunochromatographic test outcome vs. qPCR parasite quantification on two templates {#Sec6}\n------------------------------------------------------------------------------------\n\nApproximately one third of all samples with a positive RDT test result were found to be negative by qPCR (RDT~DNA~ or DBS~DNA~), although there was not clear agreement on which samples were truly negative between the two PCR templates (Supplementary Table [S1](#MOESM1){ref-type=\"media\"}). ",
"Further, several samples yielded a negative RDT test result, were qPCR RDT~DNA~ positive or 'inconclusive', but qPCR DBS~DNA~ negative, indicating probable false positivity by qPCR RDT~DNA~ (Supplementary Table [S1](#MOESM1){ref-type=\"media\"}). ",
"Samples were collected from participants over three timepoints, at zero, seven and 21 days (Supplementary Fig.",
" [S1](#MOESM1){ref-type=\"media\"}). ",
"Rapid diagnostic test positivity and qPCR negativity was disproportionately observed in timepoint two, at seven days (RDT result positive, qPCR result 'inconclusive' or negative: timepoint 1, qPCR RDT~DNA~ 32.3%, qPCR DBS~DNA~ 25.8%; timepoint 2, qPCR RDT~DNA~ 66.7%, qPCR DBS~DNA~ 73.3%; timepoint 3, qPCR RDT~DNA~ 29.2%, qPCR DBS~DNA~ 33.3%).",
"\n\nDiscussion {#Sec7}\n==========\n\nDuplex qPCR was successfully used to quantify parasite density in paired samples, comprising used RDTs and dried blood spots on Whatman filter paper. ",
"Despite weak evidence of higher values derived from qPCR DBS~DNA~, no statistical difference in estimated parasite density was found between the paired samples. ",
"For this analysis, we successfully validated a robotic extraction system for extracting DNA derived from dried blood spots. ",
"Lower CT values, indicating more rapid DNA amplification, were observed in qPCR assays based on robotically extracted template. ",
"This can be interpreted as improved extraction performance by the robotic system relative to the manual system and may reflect the superiority in DNA quality generated by the robotic system. ",
"Similarly, lower CT values for the human gene were observed in qPCR assays based on DBS template relative to used RDT template in the paired field samples. ",
"This, and the skew towards higher parasitaemia values derived from qPCR DBS~DNA~, may be indicative of superior DNA quality derived from the Whatman filter paper dried blood spots relative to the used RDT.",
"\n\nAs in previous studies that compared RDT results with qPCR amplification on the same sample, a proportion (approximately one third) were found to be negative by qPCR while the RDT result was positive^[@CR18],[@CR20],[@CR21],[@CR23]^. Circulating parasite antigen following anti-malarial chemotherapy would lead to this, because of continued antigen detection by RDT. ",
"Indeed, we observed this disproportionately in the second sampling timepoint, where individuals were likely to have received anti-malarial chemotherapy. ",
"As the third timepoint was 21 days after the first timepoint and 14 days after the second, the drug effect on parasite density is less likely to be observed.",
"\n\nA high proportion of qPCR 'inconclusive' samples (one positive and one negative repeat) in the RDT negative samples was probably due to the prevalence of low-density infections often found in this endemic setting^[@CR29],[@CR30]^. For such samples these discrepancies are more common. ",
"As the qPCR limit of detection, estimated from duplex qPCR assays to be approximately 0.05 parasites/μL, is considerably lower than that of a standard RDT (100--200 p/μL)^[@CR10]^, these samples most likely represent infections in which the parasite density fluctuates around the qPCR limit of detection. ",
"At such densities, stochastic effects can dictate whether parasite DNA is detected in the sample, in terms of the random likelihood of parasites in that particular blood aliquot, the randomness in the location of the parasites on the blood template, and the likelihood of that specific area of template being tested. ",
"Also contributing to the mismatch between RDT and qPCR results is the presence of *P*. *",
"falciparum hrp2* and *hrp3* gene deletions, known to affect the functionality of HRP-2-based RDT, and reported elsewhere from this study cohort^[@CR22]^. Of these RDT negative qPCR positive samples, there was some disagreement between RDT~DNA~ and DBS~DNA~ template qPCR results. ",
"Again, this is most simply explained by the relatively high prevalence of low-density infections in this cohort, where parasite numbers fluctuate around the point of qPCR detection and stochasticity exists in sampling.",
"\n\nBy using a duplex qPCR that normalises parasite DNA quantification relative to the quantity of a human gene (*HumTuBB*), our assay circumvents two possible problems in the use of RDT~DNA~ as a quantitative DNA template: that the blood spot in an RDT is an imprecise volume, and that the nitrocellulose membrane was not designed to bind and store DNA and (as is suggested by our data) may do so with less efficiency than other substrates. ",
"Here, the amplification of *HumTuBB* constitutes an internal control, although poor amplification of *HumTuBB* should be identified and interpreted with caution, as this could lead to artificially raised estimates of *Plasmodium* parasite density. ",
"We used a pan-genus qPCR test with a target sequence (*pgmet* tRNA gene) that is 100% identical in nucleotide sequence in all human-infecting *Plasmodium* species^[@CR28]^. Our approach would be equally effective with a duplexed qPCR test with a species-specific target for *Plasmodium falciparum*, as this is the species represented in the International Standard (INT)^[@CR31]^.\n\nIn finding that the stored blood deposit within used rapid diagnostic tests presents opportunities for future molecular analysis of the *Plasmodium* parasite population, we support the findings of other studies^[@CR17]--[@CR20],[@CR23],[@CR32]^. We further build on this finding by demonstrating that *Plasmodium* parasite densities can be estimated by qPCR from RDT~DNA~ templates, with similar results as obtained from standard Whatman filter paper dried blood templates. ",
"This finding is of interest across a range of clinical and research settings, where in-depth retrospective molecular analysis of parasite populations can be undertaken following appropriate, minimal requirement, storage of RDT~DNA~. This study provides further evidence that the long-term storage (up to 14 months at −20 °C) of such RDT~DNA~ has no effect on the outcome of retrospective molecular assays, as previously shown^[@CR17]--[@CR20]^. This is in keeping with studies that suggest storage of DBS blood samples at −20 °C averts loss of assay sensitivity over time^[@CR33]^, and that this is not affected by a limited number of freeze-thaw cycles, as experienced by our samples during shipment. ",
"Further, other studies have successfully amplified parasite DNA from used rapid diagnostic tests that had been stored at ambient temperature for one^[@CR18],[@CR21]^, three^[@CR18]^ or 14 months^[@CR20]^. It would be interesting to compare parasite quantification from used RDT among different RDT cassettes/brands. ",
"Parasite detection from used RDT from 12 RDT brands was previously reported, and variable Ct values were demonstrated^[@CR21]^. Therefore, the correlation between parasites densities obtained from DBS~DNA~ and RDT~DNA~ as described in the current paper may not be of similar strength to that obtained when using alternative RDT types.",
"\n\nIn this study, rapid diagnostic tests previously used for malaria diagnosis in a cohort of 141 five- to 12-year-old children in Western Kenya were shown to provide a DNA template for *Plasmodium* parasite quantification of equal functionality to Whatman filter paper. ",
"This study further bolsters the literature indicating that rapid diagnostic tests, with adequate storage, can reliably be used for retrospective quantitative molecular studies of *Plasmodium* parasite population dynamics some months to years after original use.",
"\n\nMethods {#Sec8}\n=======\n\nEthics {#Sec9}\n------\n\nFive- to 12-year-old, male and female school children were recruited to a 'malaria odour' study^[@CR27]^ after informed consent was obtained from their parent or legal guardian. ",
"The study protocol (NON SSC 389) was approved by the Scientific and Ethical Review Committee of the Kenya Medical Research Institute (KEMRI) (KEMRI/RES/7/3/1). ",
"Subsequent analyses of the blood samples were conducted at the London School of Hygiene & Tropical Medicine (LSHTM) under the ethics reference 8510. ",
"All research was performed in accordance with relevant guidelines and regulations.",
"\n\nStudy site and population {#Sec10}\n-------------------------\n\nParticipants were recruited at four schools less than 10 km from the Thomas Odhiambo Campus of the International Centre of Insect Physiology and Ecology (ICIPE) in Western Kenya (0°25′48.1″S, 34°12′24.5″E), in Suba District, Homa Bay County. ",
"In this area, community livelihoods depend upon fishing, small-scale trading or subsistence farming, and the dominant ethnic group is Luo. ",
"Malaria is endemic and transmission peaks late in the rainy season (March to August). ",
"Parasite prevalence on the nearby Rusinga island, on Lake Victoria, at this time was estimated to be 30% across the whole population^[@CR34]^.\n\nStudy design and sampling procedures {#Sec11}\n------------------------------------\n\nTo inform sampling in the malaria odour study, participants were tested in the field for their *Plasmodium* parasite status using point-of-care methods (thick and thin blood film microscopy, and RDT \\[One Step malaria HRPII and pLDH antigen rapid test, SD BIOLINE, Cat no 05FK60\\]). ",
"Individuals who were odour-sampled were followed up at two further time-points, approximately seven (R2) and 21 (R3) days later, as described previously^[@CR27]^. Repeat sampling was intrinsic to the odour study but arbitrary to this study^[@CR27]^ of parasite quantification methods. ",
"At each time-point, *Plasmodium* diagnosis was repeated, and positive individuals were treated with weight-dosed artemether-lumefantrine (AL) according to manufacturer's instructions. ",
"Throughout the entire sampling period (January--July 2014), whole blood was stored for 18S and QT-NASBA molecular assays (reported elsewhere)^[@CR27]^, and RDT~DNA~ cassettes were stored for later analysis by bench-top air-drying for 24 hours, followed by storage in bundles in sealed plastic bags containing the desiccant silica gel (silicon dioxide). ",
"Between May and July, dried blood spots of approximately 5 mm were additionally collected onto Whatman No. ",
"3 filter paper (DBS~DNA~). ",
"The latter samples provided a suitable comparator for RDT~DNA~ as a qPCR DNA template. ",
"After air-drying, filter paper samples (RDT~DNA~ and DBS~DNA~) were stored at −18 °C, other than when in transit from Kenya to London.",
"\n\nRobotic extraction validation {#Sec12}\n-----------------------------\n\nTo validate the extraction of DNA using a robotic system, we used culture-adapted 3D7 and Dd2 strains of *Plasmodium falciparum* parasites. ",
"Strains were serially diluted in blood (five-fold, starting at 1% parasitaemia) to determine the sensitivity and limit of detection of DNA extraction using both a manual (Chelex) and robotic extraction system (QIAsymphony QIAGEN, Germany), across a range of parasite densities.",
"\n\nRobotic DNA extraction was performed according to the manufacturer's instructions in a deep well plate using a robotic extraction system (QIAsymphony QIAGEN, Germany), using either of two kits: \"Investigator\" kit (recommended for extraction of DNA from filter paper) and \"Blood\" kit (recommended for extraction from whole blood). ",
"Details of the procedure can be found elsewhere^[@CR22]^. Manual DNA extraction for comparison was performed using the Chelex method^[@CR24]^.\n\nSample processing and extraction {#Sec13}\n--------------------------------\n\nUsed RDT cassettes were opened laterally and the nitrocellulose strip was removed from inside. ",
"A central section of the nitrocellulose strip was cut out using a sterile scalpel blade and then into 1--3 small pieces of approximately 2 mm length^[@CR21]^. All RDT~DNA~ nitrocellulose pieces, per sample, were extracted together. ",
"A three mm diameter circle was punched from each DBS~DNA~ using a sterile hole punch, giving a total surface area for extraction of approximately 7.07 mm^2^. Both template types were extracted using the robotic extraction system, with the QIAsymphony DSP DNA mini kit (QIAGEN, Germany) and according to the manufacturer's instructions. ",
"In brief, buffer ATL (180 μL) and proteinase K (20 μL) were added to each well and mixed by thermomixer at 900 rpm at 560C for 15 minutes. ",
"The deep-well plate was then placed directly into the sample compartment of the QIAsymphony for DNA extraction.",
"\n\nParasite quantification {#Sec14}\n-----------------------\n\nParasite density was measured by a duplex qPCR as described previously^[@CR28]^ and used previously in western Kenya^[@CR35]^. This assay is designed to enable parasite quantification when the volume of blood in the sample is unknown, by normalisation against human signal. ",
"Briefly, fragments of the *Plasmodium* methionine tRNA gene and the human beta tubulin exon 4 gene (*HumTuBB*) were amplified simultaneously and detected by hydrolysis probes detected on separate fluorescent channels, allowing internal normalisation for DNA extraction efficiency. ",
"DNA extract from either RDT~DNA~ or DBS~DNA~ template (5 μL) was added to the qPCR reaction, with no-template and positive control reactions set up per PCR plate in duplicate, the latter being the INT for *P*. *",
"falciparum* DNA^[@CR31]^. Amplification assays were performed using probe-based quantitative PCR on RG3000 and RG6000 thermo-cyclers, with cycle conditions as described previously^[@CR28]^. Positive samples were defined as those that crossed a pre-determined threshold of 0.025, and the cycle threshold (CT) value was taken to be the cycle number at which the amplification curve crossed this threshold. ",
"Ct values for the parasite probe fluorescence of each sample, including INT, were normalised to the *HumTuBB* gene probe fluorescence and parasite density calculated as described previously^[@CR28]^. Specifically, the WHO INT DNA standard for *P*. *",
"falciparum* comprises lyophilised blood from a hyper-parasitaemic patient who underwent exchange transfusion with an estimated parasite density pre-freezing of 4.9 × 10^5^ parasites per μL whole blood^[@CR31]^. When reconstituted with 500 μL of water as the final reagent, each vial contains 500 million International Units (IU) of *P*. *",
"falciparum* DNA. ",
"This represents 250 million parasite genome equivalents (i.e. 500 μL of human blood carrying 4.9 × 10^5^ parasites per μL), and so 1IU approximates 0.5 parasite genome equivalents, using our qPCR method.",
"\n\nAll samples were amplified in duplicate and the average parasite density was obtained per sample. ",
"If the two repeats were positive and negative, an overall parasite density of 0.93 p/μL was assigned (median parasite density of all the positive samples in this category, across the entire malaria odour study, *n* = 71), and these samples termed 'inconclusive'.",
"\n\nStatistical analysis {#Sec15}\n--------------------\n\nWe compared limit of detection of the pfcrt qPCR assay on DNA extracted using two Qiagen kits (investigator and blood). ",
"The difference in mean CT value over the different dilutions was compared using a paired t-test (*n* = 6, analyses performed in Stata \\[v. ",
"15, StatCorp\\]). ",
"We analysed qPCR data using Rotor-Gene Q software (version 2.3.1, Qiagen), before comparing parasite densities obtained using RDT~DNA~ or DBS~DNA~ template by application of the Wilcoxon Matched Pairs Test. ",
"Quantities of DNA for RDT and DBS sample pairs were compared using the Sign test. ",
"Pearson correlations (*r*) between parasite densities from the two templates were tested using the F-test having first transformed the data using a natural logarithm with an adjustment (0.1) to allow for zero observations (analyses performed in Stata \\[v. ",
"15, StatCorp\\]).",
"\n\nSupplementary information\n=========================\n\n {#Sec16}\n\nSupplementary Information\n\n**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.",
"\n\nSupplementary information\n=========================\n\n**Supplementary information** accompanies this paper at 10.1038/s41598-019-41438-0.",
"\n\nThe authors thank all of the volunteers and their families for participating in this study. ",
"We are very grateful to David John Odoyo and Geoffrey Omondi Olweru, the field team/nurses, and to Dr. Patrick Sawa (St. Jude's Clinic, ICIPE) and the Minister for Education, Mbita district, who assisted in enabling the fieldwork. ",
"We thank Donelly van Schalkwyk for providing cultured *P*. *",
"falciparum* parasites. ",
"This work was supported by the Netherlands Organization for Health Research and Development (ZonMW TOPGrant 91211038, to Willem Takken and Renate C. Smallegange). ",
"T.B. is further supported by a grant from The Netherlands Organization for Scientific Research (Vidi fellow-ship; NWO Project 016.158.306). ",
"K.B.B. and J.K.M. are supported by the UNITAID-funded Access-SMC project, and C.J.S. by Public Health England.",
"\n\nA.R., K.B.B., C.J.S. and J.G.d.",
"B. designed research; W.T. and J.G.L. obtained funding, A.R., A.O.B., J.K.M., T.B., D.K.M., K.B.B. and J.G.d.",
"B. performed or facilitated research; A.R., S.J.P., K.B.B. and C.J.S. analysed data, A.R., K.B.B. and C.J.S. wrote the paper.",
"\n\nThe datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.",
"\n\nCompeting Interests {#FPar1}\n===================\n\nThe authors declare no competing interests.",
"\n"
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"We are so proud of the fact that each year, the world’s top storytellers in the film industry rely on Avid to bring to life some of the most beloved characters and soundtracks for moviegoers around the world. ",
"Many film editors, song composers and sound editors who used Avid’s Media Composer®, Pro Tools® and Sibelius® solutions took home awards, including: Argo for Best Picture and Best Editing, Zero Dark Thirty and Skyfall for Sound Editing, Les Misérables for Sound Mixing, Life of Pi for Original Score, and Skyfall for Original Song.",
"\n\nAvid solutions were also used by other Oscar winners, including: Django Unchained for Original Screenplay and Actor in a Supporting Role, Amour for Foreign Language Film, Lincoln for Production Design and Actor in a Leading Role, and Silver Linings Playbook for Actress in a Leading Role. ",
"Oscar-nominated film Beasts of the Southern Wild was also created with Avid solutions. ",
"We’re so excited to see these talented and creative people receive this prestigious recognition.",
"\n\nTo keep you going throughout your Monday, we’ve put together an Oscar®-inspired playlist featuring some of our customer’s top original songs from your favorite movie sound tracks, including “Skyfall” by Adele and “The Bathtub” by Dan Romer and Benh Zeitlin (featuring The Lost Bayou Ramblers)."
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"Beyond the Mist (Lotte Anker album)\n\nBeyond the Mist is the debut album by a quartet co-led by two Danish jazz musicians: saxophonist Lotte Anker and pianist Mette Petersen, which was recorded in 1989 and released on the Danish Stunt label.",
"\n\nReception\n\nThe Penguin Guide to Jazz notes that the album \"is well worth searching out, not least for the interplay between two of the most interesting female performers in European free jazz. ",
"The improvisations here are well centred and almost earthy in impact, contrary to any false impression ´mist' may have given.\"",
"\n\nIn a review for Wondering Sound, Charles Farrell says \"Beyond the Mist is genuinely interactive quartet music: The players are all integral to its success, contributing to the common language. ",
"Each also manages to establish a strong individual voice along the way.\"",
"\n\nTrack listing\n \"Beyond the Mist\" (Lotte Anker/Mette Petersen) – 2:56\n \"Guardian\" (Mette Petersen) – 6:36\n \"Månegal\" (Mette Petersen) – 8:06\n \"Februar\" (Lotte Anker) – 4:58\n \"Syeeda's Song Flute\" (John Coltrane)– 8:44\n \"Flossing\" (Lotte Anker) – 8:24\n \"Pieces of My Master's Pieces\" (Mette Petersen) – 5:19\n\nPersonnel\nLotte Anker – soprano sax\nMette Petersen – piano\nJesper Lundgaard – bass\nJens Jefsen – bass on 7\nJesper Elén – drums\n\nReferences\n\nCategory:1989 albums\nCategory:Lotte Anker albums"
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"Q:\n\nggplot individual densities with mean density\n\nI would like to plot densities from two different categories as lines and then the mean density of each category overlaid as alpha. ",
"Below is code to show the 'mean' densities only summarised over disease and treatment. ",
"How can I overlay this with lines representing the density for each individual (preferably red for disease = 1 and blue for disease = 2)? ",
"i.e. a line per disease, treatment combination in the example:\n# Initialise data frame in melted form\n # 2 disease categories\n # 10 people from each disease\n # 2 treatments given to each individual\n # 25 variables with measured values per person/treatment combination\nset.seed(6737334)\ndf <- data.frame(id = 1:(2*10*2*25), var = rep(1:25, times=2*10), \n val = rnorm(2*10*2*25),\n disease = as.factor(rep(1:2, each=2*10*25)),\n treat = as.factor(rep(1:2, times=10, each=25)))\n\nplot <- ggplot(df, aes(x=val, fill=disease)) + geom_density(alpha=.3) +\n facet_grid(treat ~ .)",
"\n\nprint(plot)\n\n################## EDIT\n\nThis code is very very close to my desired solution. ",
"How can I make the lines, currently black, match the colour of the disease category?",
"\n# Initialise data frame in melted form\n # 2 disease categories\n # 10 people from each disease\n # 2 treatments given to each individual\n # 25 variables with measured values per person/treatment combination\nset.seed(6737334)\ndf <- data.frame(id = 1:(2*10*2*25), var = rep(1:25, times=2*10),\n test = as.factor(rep(1:(2*10), each=25)),\n val = rnorm(2*10*2*25),\n disease = as.factor(rep(1:2, each=2*10*25)),\n treat = as.factor(rep(1:2, times=10, each=25)))\n\nggplot(df) + \n geom_density(aes(x=val, group=test, color=disease)) +\n geom_density(aes(x=val, fill=disease), color=NA, alpha=.5) +\n facet_grid(treat ~ .)",
"\n\nA:\n\nThe method turned out to be to utilise the group option of aes() with interaction. ",
"See full example below. ",
"Thank you to @Jaap above and this question for pointing in the right direction.",
"\n# Initialise data frame in melted form\n # 2 disease categories\n # 10 people from each disease\n # 2 treatments given to each individual\n # 25 variables with measured values per person/treatment combination\nset.seed(6737334)\ndf <- data.frame(id = 1:(2*10*2*25), var = rep(1:25, times=2*10),\n test = as.factor(rep(1:(2*10), each=25)),\n val = rnorm(2*10*2*25),\n disease = as.factor(rep(1:2, each=2*10*25)),\n treat = as.factor(rep(1:2, times=10, each=25)))\n\nggplot(df) + \n geom_density(aes(x=val, group=interaction(test,disease), colour=disease)) +\n geom_density(aes(x=val, fill=disease), alpha=.5) +\n guides(fill=guide_legend(title=\"mean\")) + # else legend title 'NA'\n facet_grid(treat ~ .)",
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"Similarly, some families with a high incidence of cancer throughout the family j(cancer families) sometimes display chromosome instability in clinically normal members as well as affected individuals. ",
"These associations suggest that chromosome instability may be a visible manifestation of genetic susceptibility of neoplastic development. ",
"We propose to study the cytogenetics of MCT in the members of a large kindred with this disease. ",
"We plan to search for a specific chromosome abnormality, chromosome instability and/or segregational errors of chromosomes (SEC), which precede chromosome instability, that may be associated with MCT. ",
"This will require the use of a variety of cytogenetic techniques, e.g. scoring of metaphase preparations for structural and numerical aberrations, metaphase and prometaphase/prophase banding analyses and SEC analyses. ",
"Positive cytogenetic findings will be correlated with the presence of disease, as defined by histological examination or positive tests of calcitonin stimulation. ",
"The overall goal is the development of a simple, definitive cytogenetic test which will identify individuals with the MCT gene in childhood. ",
"Affected individuals could then be followed closely and treated promptly (total thyroid-ectomy at an early stage is curative). ",
"Non-affected individuals would be spared years of anxiety plus the cost and discomfort of yearly calcitonin stimulation tests. ",
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"Owensboro (Ky.) Apollo offensive lineman Hunter Bivin made a trip to the Big House for the Wovlerines' 28-7 victory over San Diego State. ",
"Though it was just his first time in Ann Arbor, it piqued his interest in the Wolverines. ",
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"PM: Public anger against gang-rape 'genuine, justified'\n\nDecember 23, 2012 23:06 IST\n\nBreaking his silence on the Delhi gang-rape issue amid continuing protests, Prime Minister Manmohan Singh said on Sunday night that the public anger is \"genuine\" and \"justified\" but appealed for peace while promising all steps to ensure safety of women in the country.",
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"\n\n\"We are all joined in our concern for the young woman who was the victim of a heinous crime in Delhi. ",
"There is genuine and justified anger and anguish at this ghastly incident. ",
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"\n\nHe said, \"I feel deeply sad at the turn of events leading to clashes between protesters and police forces. ",
"I appeal to all concerned citizens to maintain peace and calm.\"",
"\n\nHis statement came as protests continued for the sixth day on Sunday and turned violent.",
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"The creators of Plague, Inc. have announced they are working on a new mode for the pandemic strategy sim \"which lets players save the world from a deadly disease outbreak.\" ",
"The mode is being developed \"with the help of experts from the World Health Organisation, the Global Outbreak Alert and Response Network and more.\"",
"\n\nThe new mode will be free for all players, though a release date hasn't yet been announced.",
"\n\nAs we noted back in January, the spread of coronavirus sparked a renewed interest in Plague, Inc. which saw record-high numbers of concurrent players on Steam. ",
"At the time, the developers warned that Plague, Inc. was not a scientific model, though it was designed to be as realistic and informative as possible.",
"\n\nThe makers of Plague, Inc. have also made a generous $250,000 donation to aid in the fight against coronavirus, Ndemic Creations announced yesterday. ",
"The donation is being split between two organizations: CEPI, the Coalition of Epidemic Preparedness Innovations, and the World Health Organisation’s COVID-19 Solidarity Response Fund.",
"\n\n\"Eight years ago, I never imagined the real world would come to resemble a game of Plague Inc. or that so many players would be using Plague Inc. to help them get through an actual pandemic,\" said creator James Vaughan. \"",
"We are proud to be able to help support the vital work of the WHO and CEPI as they work towards finding a vaccine for COVID-19.\"",
"\n\nCEPI is \"a global alliance financing and coordinating the development of vaccines against emerging infectious diseases.\" ",
"The WHO's COVID-19 Solidarity Response Fund is attempting to raise $675 million to fund the Strategic Preparedness and Response Plan to track the coronavirus, buy and ship protective gear for medical workers, and accelerate efforts to develop tests and vaccines."
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"//Copyright (c) 2018 Yardi Technology Limited. ",
"Http://www.kooboo.com \n//All rights reserved.",
"\nusing System;\nusing System.",
"Collections.",
"Generic;\nusing System.",
"Linq;\nusing System.",
"Text;\nusing System.",
"Threading.",
"Tasks;\n\nnamespace Kooboo.",
"IndexedDB.Query\n{\n public class FilterItem\n {\n public string FieldOrProperty { get; set; }\n\n public byte[] Value\n {\n get;\n set;\n }\n\n public Type FieldType { get; set; }\n\n public int Length { get; set; }\n\n public Comparer Compare { get; set; }\n\n public DateTimeScope TimeScope { get; set; }\n\n }\n}\n"
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"\nGap-junction channels (GJCs) are formed by head-to-head association of two hemichannels (HCs, connexin hexamers). ",
"HCs and GJCs are permeable to ions and hydrophilic molecules of up to Mr ~1 kDa. ",
"Hearing impairment of genetic origin is common, and mutations of connexin 26 (Cx26) are its major cause. ",
"We recently identified two novel Cx26 mutations in hearing-impaired subjects, L10P and G109V. L10P forms functional GJCs with slightly altered voltage dependence and HCs with decrease ATP/cationic dye selectivity. ",
"G109V does not form functional GJCs, but forms functional HCs with enhanced extracellular Ca(2+) sensitivity and subtle alterations in voltage dependence and ATP/cationic dye selectivity. ",
"Deafness associated with G109V could result from decreased GJCs activity, whereas deafness associated to L10P may have a more complex mechanism that involves changes in HC permeability."
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"Q:\n\nSuggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages\n\nI am interested in analyzing full length songs for general features of the track which are not otherwise apparent. ",
"For e.g., I want to look at various parts of the song with time-frequency plots/wavelets/other signal processing tools for, lets say - How does the frequency content of the song during the guitar solo compare to the part when only vocals are on? ",
"What is the frequency with which the guitar solo starts? ",
"What is its peak? ..",
"and so forth.",
"\nAlthough I use FFT often for research, this is something I am fascinated by.... Any suggestions where to start?",
"\nAt this point I have got WAV files for MATLAB analysis, since they have almost no loss. ",
"Where do I go from here? ",
"Any references to concepts/open source codes/literature etc. ",
"would be greatly appreciated. ",
"\nAlso, I am not into audio engineering or anything similar. ",
"Its just for my own interest.",
"\n\nA:\n\nMy favorite is Sonic Visualiser. ",
"It is free and fast. ",
"In combination with the Vamp Plugins you can analyze low level features up to high level features like onsets, pitches, chords and so on. ",
"It has also an nice spectrum and spectrogram fea\n\n"
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"Viets' Tavern\n\nViets' Tavern is an 18th-century tavern on Newgate Road, directly across the street from the Old Newgate Prison State Historical Site in East Granby, Connecticut. ",
" This 18th-century building was home for many years to the prison warden, who also operated it as a tavern. ",
" It was listed on the National Register of Historic Places in 1972.",
"\n\nDescription and history\nViets' Tavern is located in a rural setting of northern East Granby, set close to the east side of Newgate Road opposite the former prison complex, now a state-run historic site. ",
" It is a two-story wood frame L-shaped structure, with a cross gabled roof and clapboarded exterior. ",
" The crook of the L is filled by a two-story frame addition, also with a gabled roof. ",
" Its main facade faces south, and is five bays wide. ",
" The bays are slightly asymmetrical in their placement, with the main entrance roughly at the center, framed by simple moulding. ",
" A secondary entrance is located at the north end of the four-bay street-facing facade. ",
" The interior includes several original fireplaces, as well as evidence of a ballroom space with cove ceiling on the second floor.",
"\n\nThe date of the construction of this building is not known, but there are multiple references to a tavern at this location in historical records. ",
"In 1712, Dr. John Viets was granted a license by the town of Turkey Hills (now East Granby) to \"keep a house of public entertainment.\" ",
"His son John also had a tavernkeepers licenses, and served as warden at the prison until his death by smallpox in 1777. ",
" Luke Viets, John's son, continued to operate the tavern until 1834, and it continued to be the site of traveler accommodations into the late 19th century. ",
"The Connecticut Historical Society has a photograph of an early 19th-century sign at the location with the date 1790, although the sign was destroyed in a 1904 fire.",
"\n\nDuring the prison's active period, the tavern was popular, not only with prison officials and visitors, but also some of the convicts.",
"\n\nSee also\nNational Register of Historic Places listings in Hartford County, Connecticut\n\nReferences\n\nCategory:National Register of Historic Places in Hartford County, Connecticut\nCategory:Commercial buildings completed in 1763\nCategory:Buildings and structures in Hartford County, Connecticut\nCategory:East Granby, Connecticut"
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"FileNotFoundException: /var/log/syslog (Permission denied)\n\nwhen run as a background service\nsudo start server\n\nbut succeeds when run as a foreground task \nexec bin/server.sh\n\nThe file exists:\nniru@node2:~$ ls -l /var/log/syslog\n-rw-r----- 1 syslog adm 616642 Sep 6 15:59 /var/log/syslog\n\nThe niru userid has read access to the file:\n niru@node2:~$ id -a niru\n uid=2001(niru) gid=2001(niru) groups=2001(niru),4(adm),27(sudo)\n niru@node2:~$ head -3 /var/log/syslog\n Aug 1 15:47:57 node kernel: imklog 5.8.6, log source = /proc/kmsg started.",
"\n Aug 1 15:47:57 node rsyslogd: [origin software=\"rsyslogd\" swVersion=\"5.8.6\" x-pid=\"535\" x-info=\"http://www.rsyslog.com\"] start\n Aug 1 15:47:57 node rsyslogd: rsyslogd's groupid changed to 103\n\nCan anyone let me know what would be the reason for this?",
"\n\nA:\n\nThis permissions issue because the credentials of the user running the service on a Debian distro are not the same as the credentials of the user.",
"\nFor example, when logged in as the 'niru' userid, the 'id -a' command returns this output:\nniru@node2:~$ id -a\nuid=2001(niru) gid=2001(niru) groups=2001(niru),4(adm),27(sudo)\n\nIn the context of the service process, the same 'id -a' command returns:\nuid=2001(niru) gid=2001(niru) groups=2001(niru)\n\nSo, in the service context, the niru userid does not have permissions to read the /var/log/syslog file.",
"\nThis bug in Upstart is documented here: https://bugs.launchpad.net/upstart/+bug/812870\n\nAdding the setgid parameter to the service startup file resolved the issue.",
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"Dela via: Facebook\n\nTwitter\n\nLinkedIn\n\nSamma oärlighet går igen hela tiden. ",
"Idag publicerade Aftonbladet en artikel om Greta Thunberg, där en Helena Iles förnekar att det finns en PR-byrå bakom Greta Thunberg.",
"\n\nKritiken från i höstas vad gäller PR rör för övrigt det faktum att Ingemar Rentzhog från We don’t have time tidigare drev en finansiell PR-byrå och därför besitter mycket goda PR-kunskaper. ",
"Hon fick hans hjälp i höstas, det har han själv medgett i intervjuer. ",
"Hjälp att få uppmärksamhet i media och online första veckan av strejken och hjälp att få kontakt med miljöorganisationer som bl a gav henne sin slot att tala i Katowice,\n\nAnnika Strandhäll, som alltid har en sällsynt fingertoppskänsla just kring vad som är sant och osant (hon tenderar att fokusera på det senare), publicerade en slags verbal spya på sin Facebook precis:\n\nFör Helena Iles påstår ju som synes att hon inte alls sysslar med PR. ",
"Märkligt då att hennes byrå heter Iles PR.",
"\n\nOch består av tre PR-konsulter.",
"\n\nOch allt hon säljer är exakt det som en traditionell PR-byrå säljer, som textproduktion, press, mediehantering, krishantering etc.",
"\n\nPå Twitter beskriver sig Iles som “PR-ballerina”.",
"\n\nMen jag tänker att man får vanan inne att påstå att en spade inte är en spade när man som Helena Iles varit pressansvarig på just statliga mediebolaget Sverige Radio innan.",
"\n\nSå vi kan alltså konstatera att det redan är fastlagt att Greta Thunberg först fick pro bono-hjälp av Ingemar Rentzhog, som själv ägt och drivit en PR-byrå innan han blev aspirant på Klimat-Jesus inom sociala medier, och att hon idag har PR-hjälp av självaste fd pressansvarig på SR och sedan 2010 PR-byråägare – Helena Iles.",
"\n\nOm Iles hade säg drivit en skrädderifirma eller ett tvätteri hade man absolut kunnat tänka sig att hon helt ideellt bokat pressförfrågningar åt Greta Thunberg. ",
"Utan något egenintresse.",
"\n\nMen det klingar ju inte så lite falskt när ett pressproffs från statlig media som äger en egen PR-byrå hävdar att hon gör det på sin fritid. ",
"Vilket fritid då undrar jag? ",
"Den tiden som inte ägnas åt exakt de saker hon hjälper Thunberg med som hon ändå spenderar dagarna med?",
"\n\nJag tror absolut att Iles gör det utan ersättning. ",
"Just nu. ",
"Men om Greta börjar tjäna pengar på det hela lär den ideella delen ersättas av fakturor från antingen denna PR-byrå eller någon annan. ",
"Pro bono-hjälp av ett PR-proffs till en klimataktivist, och det tänker inte jag ifrågasätta alls. ",
"Alla är fria att donera sin expertis bäst de vill, jag har till exempel hjälpt GAPF.",
"\n\nAtt hjälpa Thunberg pro bono innebär dessutom värdefulla kontakter med bland annat miljörörelsen för Iles, potentiella uppdragsgivare. ",
"Hon kan skriva upp kostnaden på sitt eget sälj-konto.",
"\n\nMen det är faktiskt lögn att påstå att det inte finns en PR-byrå bakom Greta Thunberg idag.",
"\n\nDet finns det. ",
"Den heter Iles PR.",
"\n\nAtt de inte tar betalt är irrelevant. ",
"Det är något mellan klient och företag och berör transaktion, inte innehåll i tjänsten. ",
"Iles levererar exakt samma tjänst till Thunberg som till andra kunder.",
"\n\n…………………\n\nUppdatering 26 april kl 10:\n\nDet visar sig att Iles PR har en lång relation med just Greta Thunbergs mamma Malena Ernman.",
"\n\nDe var nämligen PR-byrå för Malena Ernmans och Svante Thunbergs gemensamma uppsättning av Xerxes 2014.",
"\n\nIles PR var även PR-byrå för en julkonsert Malena Ernman hade med Loa Falkman i december 2014.",
"\n\nHelena Iles har för övrigt en diger lista kändisar på sin kundlista. ",
"Allt ifrån Jonas Gardell, Fredrik Lindström och Henrik Schyffert till Özz Nujen och Soran Ismail.",
"\n\nUppdatering kl 12.49\n\nHelena Iles samarbetar sedan 2017 med bokförlaget Polaris.",
"\n\nSamma förlag som gav ut Malena Ernmans klimatbok…..\n\n……………………..\n\nBli en Patreon – välj valfri summa från 1 dollar per månad och ingen bindningstid\n\nSwish: 0762096244"
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"---\nabstract: 'Kummer’s Conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. ",
"We extend Kummer’s Conjecture to cyclotomic fields of conductor $n$, where $n$ is any natural number. ",
"We show that the Elliott-Halberstam Conjecture implies that this Generalised Kummer’s Conjecture is true for almost all $n$ but is false for infinitely many $n$.'\naddress: 'Department of Mathematics and Statistics, Calvin College, Grand Rapids, Michigan 49546, USA'\nauthor:\n- MJR Myers\ntitle: 'A Generalised Kummer’s Conjecture'\n---\n\nIntroduction\n============\n\nLet $\\Q (\\zeta_m) $ be the $m$th cyclotomic field, where $\\zeta_m$ is a primitive $m$th root of unity for an integer $m \\geq 1$. Let $h_m$ denote the class number of $\\Q (\\zeta_m)$ and $h_m^+$ be the class number of its maximal real subfield $\\Q (\\zeta_m + \\zeta_m^{-1})$.\n\nKummer proved that the relative class number $h^-_{m} = h_{m} / h^+_{m} $ is an integer, and in 1851 he claimed ([@ku], pg. ",
"473) that the rule for the asymptotic growth of $h_p^-$ as the prime $p \\to \\infty$ is given by the formula $$\\frac {p^{(p+3)/4}} {2^{(p-3)/2} \\pi^{(p-1)/2}} =: G(p). ",
"\\eqno (1)$$ Kummer never published a proof of his claim, and the modern, rigourous reading of Kummer’s assertion, that $$\\lim_{p \\to \\infty} \\frac{h_p^-}{G(p)} =1$$ has become well-known as “Kummer’s Conjecture”.",
"\n\nAs it stands, Kummer’s Conjecture remains unproven; however, Ankeny and Chowla [@ac] showed that $$\\log (h^-_p / G(p)) = o(\\log p )$$ as $p \\to \\infty.$ Murty and Petridis [@mp] proved what they called the Weak Kummer’s Conjecture. ",
"They showed that\n\nthere exists a positive constant $c$ such that $$c^{-1} \\leq \\frac {h^-_p} {G(p)} \\leq c$$ holds for a sequence of primes $p_i$, where the number of primes $p_i \\leq x$ is asymptotic to $x / \\log{x}$ as $x \\to \\infty$. With the additional assumption of the Elliott-Halberstam Conjecture, they were able to prove a stronger result. ",
"Recall that this conjecture says\n\n\\[eh\\] For any $\\delta >0$ and any $A>0$, $$\\sum_{k < x^{1 - \\delta}} \\max_{(l,k)=1} \\max_{y \\leq x} \n\\left| \\pi (y, k, l) - \\frac{\\li y}{\\phi (k)} \\right| \\ll_{\\delta, A}\n\\frac{x}{\\log^A x}$$ where $\\pi (y, k, l)$ equals the number of primes $p \\leq y$ such that $p \\equiv l \\mod k $, and $\\li y = \\int_2^y \\frac{dt}{\\log t}$.\n\nMurty and Petridis showed that the Elliott-Halberstam Conjecture implies that for every $\\epsilon > 0$ there exists an $x_{\\epsilon}$ such that $$1 - \\epsilon < \\frac{h^-_p}{G(p)} < 1 + \\epsilon$$ holds for all primes $x_{\\epsilon} < p \\leq x$, with the exception of a set $P(\\epsilon)$ such that $$| \\{ p \\in P(\\epsilon): x_\\epsilon < p \\leq x \\} | =o(\\pi(x)) \\text{.}$$\n\nHence Kummer’s Conjecture concerning class numbers of cyclotomic fields is related to the density of primes in arithmetic progressions. ",
"Kummer’s Conjecture is also related to pairs of primes. ",
"The Hardy-Littlewood Conjecture posits the existence of $\\gg x / \\log^2 x $ primes $p \\leq x$ such that $2p+1$ is also prime; in 1990 Granville [@gr] proved that the Elliott-Halberstam Conjecture and the Hardy-Littlewood Conjecture together imply that Kummer’s Conjecture is false. ",
"In that same paper Granville offered heuristic reasoning for believing that for all primes $p$ $$(\\log \\log p )^{-1/2 +o(1)} \\leq h_p^- /G(p) \\leq (\\log \\log p )^{1/2 +o(1)},$$ and that these bounds are the best possible.",
"\n\nMore recently, Lu and Zhang [@lz] proved that for any fixed $\\epsilon >0$, there is a positive number $Q$ depending only on $\\epsilon$ such that for all primes $p \\geq Q$, $$e^{-1.4} p^{-\\epsilon} (\\log p)^{-1/3} \\leq h_p^- / G(p) \\leq e^{0.84} p^{\\epsilon} (\\log p)^{1/6} .$$\n\nIn this paper we extend Kummer’s Conjecture to composite numbers; that is, for natural numbers $n$ and a suitable function $G(n)$ (see (\\[Gofn\\])), the Generalised Kummer’s Conjecture predicts that $\\lim_{n \\to \\infty} h_n^- / G(n) = 1$. We prove a composite moduli analogue of Murty and Petridis’ Weak Kummer’s Conjecture:\n\n\\[nnwkcuv\\] Let $\\omega (n)$ the number of distinct prime divisors of $n$. Then $$e^{- \\omega (n)} \\ll \\frac{h_n^-}{G(n)} \\ll e^{ \\omega (n)}$$ holds for all but $o (x)$ natural numbers $n \\leq x$.\n\nMoreover, assuming the Elliott-Halberstam Conjecture, the Generalised Kummer’s Conjecture is true for almost all $n$ and is false for infinitely many $n$. More precisely we have the following two results.",
"\n\n\\[nnwkccv\\] Assume the Elliott-Halberstam Conjecture. ",
"Then for every $\\epsilon > 0$ there exists an $x_{\\epsilon}$ such that $$1 - \\epsilon < \\frac{h_n^-}{G(n)} < 1 + \\epsilon$$ holds for all natural numbers $n \\geq x_{\\epsilon}$ with the exception of $ o(x) $ natural numbers $n<x$.\n\n\\[gkcf\\] Assume the Elliott-Halberstam Conjecture. ",
"Then the Generalized Kummer’s Conjecture fails for infinitely many natural numbers $n$.\n\nGeneralised Kummer’s Conjecture\n===============================\n\nFor the cyclotomic field $\\Q(\\zeta_n)$, one may obtain the formula (see pg. ",
"42 of [@wa]): $$\\label{poleratio}\nh_n^- = \\frac{Q w \\sqrt{|d_n / d_n^+|}}{\\pi^{\\phi (n) /2} 2^{ \\phi (n)/2}} \n\\prod_{\\substack{\\chi \\ \\mod n \\\\ \\chi \\ \\text{odd} }} L(1, \\chi ).$$ Here $d_n$ is the discriminant of $\\Q(\\zeta_n)$ and $d_n^+$ is the discriminant of $\\Q (\\zeta_n + \\zeta_n^{-1})$. Also, $w$ is the number of roots of unity in $\\Q(\\zeta_n)$, and $Q=1$ if $n$ is a prime power $p^r$ and $Q= 2$ otherwise.",
"\n\nBy Proposition 2.7 in [@wa], $$\\label{wa 2.7}\nd_n = (-1)^{\\phi (n) /2} \\frac{n^{\\phi (n)}}{\\prod_{p|n} p^{\\phi (n) / (p-1)}},$$ and by Lemma 4.19 in [@wa], $$\\label{wa 4.19}\nd_n = \\begin{cases}\n\\ \\ p(d_n^+)^2 & \\text{if $n = p^r$ with $p \\ne 2$},\\\\\n\\ \\ 4(d_n^+)^2 & \\text{if $n = 2^r$},\\\\\n\\ \\ (d_n^+)^2 & \\text{otherwise.}",
"\n\\end{cases}$$\n\nHence we see that $$h_n^- = \na_n \\left( \\frac{1}{2 \\pi} \\sqrt{ \\frac{n}{\\prod_{p | n}p}} \\right)^{\\phi(n) /2}\n\\prod_{\\substack{\\chi \\ \\text{odd} \\\\ \\chi \\mod n }} L(1, \\chi ),$$ with $$a_n = \\begin{cases}\n\\ \\ 2p^{r +1/4} & \\text{if $n = p^r$ with $p \\ne 2$},\\\\\n\\ \\ 2^{r+ 1/2} & \\text{if $n = 2^r$},\\\\\n\\ \\ 4n & \\text{if odd $n \\ne p^r$ }, \\\\\n\\ \\ 2n & \\text{if even $n\\ne 2^r$ .}",
"\n\\end{cases}$$ Let $$\\label{Gofn}\nG(n) = a_n \\left( \\frac{1}{2 \\pi} \\sqrt{ \\frac{n}{\\prod_{p | n} p}} \\right)^{\\phi(n) /2}.$$ Then the composite moduli form of Kummer’s Conjecture may be stated as follows.",
"\n\n\\[gkc\\] $$h_n^- \\sim G(n)$$ as the natural number $n \\to \\infty$.\n\nAs in [@mjrm1], we can rewrite the product of $L$-functions in (\\[poleratio\\]) as $$\\prod_{\\substack{\\chi \\ \\mod n \\\\ \\chi \\ \\text{odd} }} L(1, \\chi ) =\n\\exp \\left( \\frac{\\phi (n)}{2} f_n \\right),$$ where $f_n = \\lim_{x \\to \\infty} f_n (x)$ and $f_n (x)$ is the finite sum $$f_n (x) = \\sum_{r \\leq x} \\frac{c_n (r)}{r}$$ with $$c_{n} (r) = \\begin{cases}\n\\ \\ 1 & \\text{if $r = q^m \\equiv 1 \\mod n$},\\\\\n-1 & \\text{if $r= q^m \\equiv -1 \\mod n$},\\\\\n\\ \\ 0 & \\text{otherwise}\n\\end{cases}$$ where $q$ is a prime and $m \\geq 1$.\n\nClearly the Generalized Kummer’s Conjecture is true if and only if $f_n = o\\left( \\frac{1}{\\phi (n)} \\right).$\n\nLemmas\n======\n\nWe will need the following theorems which are also used in [@mp].",
"\n\n\\[sw\\] For any constant $A>0$, there is a constant $c(A) > 0$ so that uniformly for $x \\geq 3$, $1 \\leq k \\leq (\\log x)^A, \n(k, l)=1$, we have $$\\pi (x, k, l) = \\frac{ \\li x}{ \\phi (k)} + O \\left( x e^{-c(A) \\sqrt{\\log x}} \\right).$$\n\n\\[bv\\] Assume $x \\geq 2$. For any $A > 0$ there exists $B= B(A) > 0$ such that $$\\sum_{k < \\frac{x^{1/2}}{\\log^B x }} E(x, k) \\ll_A \\frac{x}{\\log^A x}$$ where $$E(x, k) := \\max_{y \\leq x} \\max_{(k,l) = 1} \\left| \\pi (y, k, l) - \\frac{\\li y}{\\phi (k)} \\right|.$$\n\n\\[bt\\] For $k<x$, $(k,l) = 1$, $$\\pi (x, k, l) < \\frac{2x}{\\phi (k) \\log (x/k)} .$$\n\n\\[hooley\\] Let $l$ be a fixed, non-zero integer, and $ \\epsilon , A, B$ positive real numbers where $A > B +30$. Then for any numbers $x$ and $X$ such that $x^{1/2} < X < x \\log^{-A} x$ and $x> x_0 (\\epsilon, B)$, we have $$\\pi (x, k, l) \\leq \\frac{(4 + \\epsilon )x}{\\phi (k) \\log X}$$ for every $k$ such that $X \\leq k \\leq 2X $, and $(l, k)=1$, except for at most $X \\log^{-B} x$ exceptional values of $k$.\n\n\\[mp 2.3\\] Fix $l$ and $k$, $(l, k) =1$. The number of primes $x < p \\le 2x$ such that $kp+l$ is also prime is $$\\ll \\prod_{p_i | kl} \\left( 1- \\frac{1}{p_i} \\right)^{-1} \\frac{x}{\\log^2 x}$$ uniformly for $k<x^2$.\n\n\\[mp 2.4\\] There is a constant $c$ such that, as $T \\to \\infty$, $$\\sum_{k \\leq T} \\prod_{p_i |k} \\left( 1- \\frac{1}{p_i} \\right)^{-1} \\sim cT.$$\n\n\\[[@mjrm1], Corollary 3.6\\] \\[murty cong cor\\] The number of solutions $\\mod n$ to $ x^m \\equiv 1 \\mod n$ (or to $ x^m \\equiv -1 \\mod n$) is at most $2m^{\\omega (n)}$, where $\\omega (n) $ is the number of distinct prime divisors of $n$.\n\nLet $A$ be some constant greater than or equal to $e$. A slight modification of Hardy and Ramanujan’s original proof in [@hr2] of the normal order of $\\omega (n)$ shows that the number of $n \\leq x$ such that $\\omega (n) > A \\log \\log x$ is $o\\left(\\frac{x}{\\log x}\\right)$. More specifically, we have\n\n\\[hr lemma\\] For any constant $A \\geq e$, $$|\\{ n \\leq x : \\omega (n) > A \\log \\log x \\}| \\ll \\frac{x}{(\\log x)^{1 + A \\log A - A}(\\log \\log x)^{1/2}}.$$\n\nLet $$\\pi (x, k) = \\sum_{\\substack {n \\leq x \\\\ \\omega(n) = k} } 1 \\ \\ \\text{ and } \\ \\ S = \\sum_{k \\geq A \\log \\log x} \\pi (x, k+1).$$ Lemma B of [@hr2] gives us the uniform upper bound $$\\pi (x, k+1) < \\frac{Lx}{\\log x} \\ \\frac{(\\log \\log x +D)^{k}}{k!},$$ where $L$ and $D$ are absolute constants. ",
"Clearly, then $$S < \\frac{Lx}{\\log x} \\ \\sum_{k \\geq A \\log \\log x} \\frac{(\\log \\log x +D)^{k}}{k!}.$$\n\nWrite $\\xi = \\log \\log x +D$ and let $k_1$ be the smallest integer greater than $A\\xi$. Then $$\\begin{aligned}\n \\sum_{k \\geq A \\xi} \\frac{\\xi^k}{k!}",
"\n&<& \\ \\frac{\\xi^{k_1}}{k_1!} ",
"\\left[ 1+\\frac{\\xi}{k_1 + 1} +\\frac{\\xi^2}{ (k_1+1)(k_1+2)} + \\cdots \\right] \\\\\n&<& \\frac{\\xi^{k_1}}{k_1!} ",
"\\left[ 1+\\frac{1}{A} + \\frac{1}{ A^2 } + \\cdots \\right] \n = \\ \\frac{ \\xi^{k_1}}{k_1!} ",
"\\left[ \\frac{A}{A-1} \\right] \\\\\n&\\ll& \\frac{e^{k_1(\\log \\xi - \\log k_1 + 1)}}{\\sqrt{k_1}} \\end{aligned}$$ by Stirling’s formula. ",
"It follows, then, that $$\\sum_{k \\geq A \\xi} \\frac{\\xi^k}{k!} \\",
"\n \\ll \\ \\frac{e^{(A - A\\log A)\\xi}}{\\sqrt{\\xi}} \\ \\ll \\ (\\log x)^{A-A\\log A} (\\log \\log x)^{-1/2}.$$ Thus the number of $n \\leq x$ such that $\\omega (n) > A \\log \\log x$ is $$\\ll \\frac{x}{(\\log x)^{1 + A \\log A - A}(\\log \\log x)^{1/2}},$$ as required.",
"\n\nUnconditional Composite Moduli Weak Kummer’s Conjecture\n=======================================================\n\nIn this section we will prove Theorem \\[nnwkcuv\\], the Weak Kummer’s Conjecture for composite moduli. ",
"To remove the contributions of the prime powers $q^m$ with $m \\geq 2$ from the sum $f_n$, we will use the following lemma:\n\n\\[chuck powers 2\\] $$\\sum_{q \\text{ prime}} \\sum_{m \\geq 2 } \\frac{c_{n} (q^m)}{mq^m}\n= O\\left( \\frac{\\omega (n)}{n} \\right).$$\n\nWrite $ S = \\sum_{q \\text{ prime}} \\sum_{m \\geq 2 } \\ \\ \\frac{c_{n} (q^m)}{mq^m}$. Then clearly $$| S | \\leq \\sum_{q \\text{ prime} } \\sum_{\\substack{ m \\geq 2 \\\\ q^m \\equiv \\pm 1 (n) }} \\frac{1}{mq^m} \n= S_1 + S_2$$ where $$\\begin{aligned}\nS_1 = \\sum_{\\substack {q \\text{ prime} \\\\ q < n }} \\sum_{\\substack{ m \\geq 2 \\\\ q^m \\equiv \\pm 1 (n) }} \\frac{1}{mq^m} \n& \\text{ and } &\nS_2 = \\sum_{\\substack {q \\text{ prime} \\\\ q > n }} \\sum_{\\substack{ m \\geq 2 \\\\ q^m \\equiv \\pm 1 (n) }} \\frac{1}{mq^m}.\\end{aligned}$$\n\nRecall that $\\pi (x)$ is the number of primes $p \\leq x$. By the prime number theorem, we have $$\\begin{aligned}\n|S_2| & \\leq & \\sum_{\\substack {q > n \\\\ q \\ \\text{prime}}} \\sum_{m \\geq 2 } q^{-m} \n \\ll \\sum_{\\substack {q > n \\\\ q \\ \\text{prime}}} q^{-2} \\\\ \n& \\ll & \\lim_{x \\to \\infty} \\left[ \\frac{\\pi (t)}{t^2} \\right]_{n}^{x} + \\int_n^x \\frac{\\pi(t)}{t^3}dt \\\\ \n& \\ll & \\frac{1}{n \\log n} + \\int_n^{\\infty} \\frac{1}{t^2 \\log t}dt \\\\\n& \\ll & \\frac{1}{n \\log n} = o \\left( \\frac{1}{n} \\right) .\\end{aligned}$$ We now consider $S_1 = S_3 + S_4$ with $$\\begin{aligned}\nS_3 = \\sum_{m \\geq 2 } \\sum_{\\substack{q < n \\\\ q^m \\equiv 1 (n) }} \\frac{1}{mq^m}\n & \\text{and} &\nS_4 = \\sum_{m \\geq 2 } \\sum_{\\substack{q < n \\\\ q^m \\equiv -1 (n) } } \\frac{1}{mq^m}.\\end{aligned}$$\n\nFor a fixed $n$, let $C(m)$ denote the number of solutions $x<n$ to the congruence $x^m \\equiv 1 \\mod n$. By Lemma \\[murty cong cor\\] $ C(m) \\leq 2m^{\\omega (n)}$, where $\\omega (n)$ is the number of distinct prime divisors of $n$. This gives us the upper bound $$\\left| \\bigcup_{i=2}^m \\{x<n : x^i \\equiv 1 \\mod n \\}\\right| \\leq \\sum_{i=2}^m C(i) \\leq \\sum_{i=2}^m 2i^{\\omega (n)} =:B(m).$$ Observe that $B(m) \\ll m^{\\omega (n) +1}$.\n\nNow for each solution $x<n$ to $x^m \\equiv 1 \\mod n$, write $x^m = u_i n+1$, where each $u_i$ is a distinct positive integer for $i = A(m), \\dots, A(m) + C(m) - 1$. Here $A(2) = 1$, and for $m \\geq 3$, $A(m) = B(m-1) + 1$. Then $$S_3 = \\sum_{m \\geq 2 } \\frac{1}{m} \\sum_{\\substack{q < n \\\\ q^m \\equiv 1 (n)}} \\frac{1}{q^m} \n= \\sum_{m \\geq 2} \\frac{1}{m} \\left( \\sum_{a= A(m)}^{B(m)} \\frac{\\theta_a}{ u_a n +1} \\right),$$ where for $ A(m) \\leq a \\leq A(m) +C(m) - 1$, $$\\theta_a = \\begin{cases}\n\\ \\ 1 & \\text{if $\\sqrt[m]{u_a n + 1} $ is a prime},\\\\\n\\ \\ 0 & \\text{otherwise.}",
"\n\\end{cases}$$ For any $ A(m) + C(m) \\leq a \\leq B(m)$, let $\\theta_a = 0$ and $ u_a = 1$. Thus $$S_3 < \\frac{1}{n} \\sum_{m \\geq 2} \\frac{1}{m} \n\\left( \\sum_{a= A(m)}^{B(m)} \\frac{\\theta _a}{ u_a} \\right).$$\n\nLet $d_m$ be the inner sum $ \\sum_{a= A(m)}^{B(m)} \\frac{\\theta _a}{ u_a}$, and write the partial sums $$D_2 = d_2, D_3 = d_2 + d_3, D_4 = d_2 + d_3 + d_4, \\dots .$$ Notice that for any two indices $a \\not= a'$ such that $\\theta_a$ and $\\theta_{a'}$ are both nonzero, we must have $u_a \\not= u_{a'}$, which implies that $D_r \\leq \\sum_{a=1}^{B(r)} a^{-1}$.\n\nNow, $$\\sum_{m=2}^x \\frac{d_m}{m} = \\frac{D_x}{x} + \\sum_{r=2}^{x-1} \\frac{D_r}{r(r+1)},$$ and we get $$\\begin{aligned}\n0 < S_3 %& < & n^{-1} \\sum_{m \\geq 2} \\frac{d_m}{m} \n& = & \\frac{1}{n} \\sum_{m \\geq 2} \\frac{D_m}{m(m+1)} \\\\\n%& \\leq & \\frac{1}{n} \\sum_{m \\geq 2} \\frac{1}{m(m+1)} \\left( \\sum_{a=1}^{B(r)} \\frac{1}{a} \\right) \\\\\n& \\ll & \\frac{1}{n} \\sum_{m \\geq 2} \\frac{1}{m(m+1)} \\left( \\sum_{a=1}^{m^{\\omega (n) +1}} \\frac{1}{a} \\right) \\\\\n& \\ll & \\frac{\\omega (n)}{n} \\sum_{m \\geq 2} \\frac{\\log (m)}{m(m+1)} \n = O \\left( \\frac{\\omega (n)}{n} \\right).\\end{aligned}$$\n\nSimilarly we can express the sum $S_4 = \\sum_{m \\geq 2} \\frac{1}{m} \\left( \\sum_{a= A(m)}^{B(m)} \\frac{\\phi_a}{ v_a n -1} \\right)$ where the $v_a$’s are positive integers and $\\phi_a = 1$ or $0$. Since $$\\sum_{a= A(m)}^{B(m)} \\frac{\\phi_a}{ v_a n -1} = \\sum_{a= A(m)}^{B(m)} \\frac{\\phi_a}{ v_a n +1}\n+ O(n^{-2}),$$ it follows that $S_4 \\ll \\frac{\\omega (n)}{n}$ as well.",
"\n\nDefine the sum $$g_{n}(x) = \\sum_{ \\substack {q \\ \\text{prime } \\\\ q \\leq x }} \\frac{c_{n} (q)}{q},$$ and $$g_{n} = \\lim_{x \\to \\infty} g_{n} (x).$$ By Lemma \\[chuck powers 2\\], $f_n = g_n + O(\\frac{\\omega (n)}{n})$. An application of the Siegel-Walfisz Theorem (Lemma \\[sw\\]) reduces the infinite sum $g_n$ to a finite one.",
"\n\n$$g_{n} = g_{n} (2^{n}) + O (n^{-2}).$$ \\[sw lemma 2\\]\n\nFor $x \\geq y \\geq 3$, Riemann-Stieltjes integration gives $$\\label{rsi}\ng_{n} (x) -g_{n} (y) = \\sum_{y < q \\leq x} \\frac{c_{n} (q)}{q} \n= \\left[ \\frac{A_{n} (t)}{t} \\right]_y^x + \\int_y^x \\frac{A_{n} (t)}{t^2} dt,$$ where $A_{n} (t) = \\pi (t, n, 1) - \\pi (t, n, -1) $. ",
"Using the Siegel-Walfisz Theorem and taking $x > 2^{n}$, we obtain $A_{n} (x) \\ll \\frac{x}{n \\log^2 x}\n$ and so $$\\begin{aligned}\n| g_{n}(x) - g_{n}(2^{n}) | \n& \\ll & \\left[ \\frac{A_{n} (t)}{t} \\right]_{2^{n}}^x + \\int_{2^{n}}^x \\frac{A_{n} (t)}{t^2} dt \\\\\n& \\ll & \\frac{1}{n \\log^2 x} - \\frac{1}{n (\\log 2^{n})^2} \n+ \\frac{1}{n} \\left[ \\frac{1}{\\log t} \\right]_{2^{n}}^x \\\\\n& \\ll & \\frac{1}{n^{2}}.\\end{aligned}$$\n\nWe have shown $$f_n = g_n +O \\left( \\frac{\\omega (n)}{n} \\right) = g_n (2^n) + O \\left( \\frac{\\omega (n)}{n} \\right)$$ and have reduced the problem to one of studying the finite sum $$g_{n}(2^n) = \\sum_{\\substack {q \\ \\text{prime, } \\\\ q \\leq 2^n }} \\frac{c_{n} (q)}{q}.$$ We will now find bounds on $g_n (2^n)$ by using (\\[rsi\\]) to partition this sum into terms on which we may apply our various estimates for $\\pi (t, n, 1) - \\pi (t, n, -1) $. ",
"We are now in a position to prove Theorem \\[nnwkcuv\\].",
"\n\nNote that $$| A_{n} (t)|= |\\pi (t, n, 1) - \\pi (t, n, -1) | \\leq 2 E(t, n)$$ as defined in Lemma \\[bv\\], the conditions of which are satisfied for $x < n \\leq 2x$ and $n^{2} \\log ^{2B} n < q < 2^{n}$. Hence, $$\\begin{aligned}\n%\\begin{split}\n\\sum_{x < n \\leq 2x} \\sum_{ n^2 \\log^{2B} n < q < 2^{n}} \\frac{c_{n} (q)}{q}\n%& \\ll \\left[ \\frac{\\sum_{x < n \\leq 2x} E(t, n)}{t} \\right]_{n^{2} \\log^{2B} n}^{2^{n}} \\\\\n%& \\quad \\quad \\quad + \\int_{n^{2} \\log^{2B} n}^{2^{n}} \\frac{\\sum_{x < n \\leq 2x} E(t, n)}{t^2} dt\\\\\n& \\ll & \\left[ \\frac{\\sum_{x < n \\leq 2x} E(t, n)}{t} \\right]_{n^2 \\log^{2B}n}^{2^{n}} \n+ \\int_{n^2 \\log^{2B}n}^{2^{n}} \\frac{\\sum_{x < n \\leq 2x} E(t, n)}{t^2} dt \\\\\n& \\ll & \\left[ \\frac{1}{\\log^A t} \\right]_{x^2 \\log^{2B} x}^{\\infty} \n+ \\int_{x^2 \\log^{2B} x}^{\\infty} \\frac{1}{t \\log^A t} dt \\\\\n&\\ll & \\log^{-A+1} x.\n%\\end{split}\\end{aligned}$$ If we set $D(n) = g_{n} (2^{n}) - g_{n} (n^2 \\log^{2B} n)$, then we have shown $$\\sum_{x< n < 2x} |D(n) | \\ll \\frac{1}{\\log^{A-1} x}.$$ Thus for any constant $c > 0$, $$\\begin{aligned}\n\\# \\left\\{ x < n \\leq 2x \\ : \\ |D(n)| > \\frac{c}{n} \\right\\} \n%& \\leq & \\# \\left\\{ x < n \\leq 2x \\ : \\ |D(n)| > \\frac{\\text{const}}{2x} \\right\\} \\\\\n& \\ll & \\frac{x}{\\log^{A-1} x}.\\end{aligned}$$ Take $A > 3$ in Lemma \\[bv\\].",
"\n\nBy dyadic decomposition we discard at most $x \\log^{-A+1} x$ natural numbers and we now restrict our attention to primes $q$ in the range $ n^2/4 < q \\leq n^{2} \\log^{2B} n $. ",
"By Lemma \\[bt\\], $$\\begin{aligned}\n\\sum_{ n^{2}/4 < q \\leq n^{2} \\log^{2B} n } \\frac{c_{n} (q)}{q} \n%& = & \\left[\\frac{A_{n} (t)}{t} \\right]_{n^{2}/4}^{n^{2} \\log^{2B} n } \n% + \\int_{n^{2}/4}^{ n^{2} \\log^{2B} n } \\frac{A_{n} (t)}{t^2} dt. \\\\",
"\n& \\ll & \\frac{1}{\\phi (n) \\log n} + \n \\int_{n^{2}/4}^{n^{2} \\log^{2B} n } \\frac{1}{t \\phi(n) \\log (t/ n) } dt \\\\\n%& \\ll& \\frac{1}{\\phi (n) \\log (\\frac{n^{2} \\log^{2B} n}{n})} + \\frac{1}{\\phi (n) \\log (\\frac{n^{2}/4}{n})} \\\\\n& \\ll & %\\frac{1}{\\phi (n) \\log n} + \n \\frac{1}{\\phi(n)} \\log \\left( 1 + \\frac{\\log ( \\log^{2B} n )}{\\log (n /4)} \\right) \\\\\n& = & o \\left(\\frac{1}{\\phi (n)} \\right).\\end{aligned}$$ That is, $g_{n} (n^{2} \\log^{2B} n) - g_{n} (n^{2}/4) = o(1/n)$, and we now consider the range $ 2^A n \\log^A n < q \\leq n^{2}/4$.\n\nTake $X < n < 2X$ and let $2^A n \\log^A n < t < n^{2}/4$. The conditions of Lemma \\[hooley\\] are satisfied in this range, and so $$\\begin{aligned}\n\\sum_{2^A n \\log^A n < q \\leq n^{2}/4 } \\frac{c_{n} (q)}{q} \n%& = & \\left[\\frac{A_{n} (t)}{t} \\right]_{2^A n \\log^A n }^{ n^{2}/4} \n%+ \\int_{2^A n \\log^A n }^{ n^{2}/4} \\frac{A_{n} (t)}{t^2} dt. \\\\",
"\n&\\ll & \\frac{1}{\\phi (n) \\log n} + \\frac{1}{\\phi (n) } \\int_{2^A n \\log^A n }^{ n^{2}/4} \\frac{1}{t \\log t} dt \\\\\n& \\ll & \\frac{1}{\\phi (n)}.\\end{aligned}$$ This holds for all natural numbers $X < n < 2X$ with the exception of a set of size $\\ll \\frac{X}{\\log^B X}$. Using dyadic decomposition, we see the number of exceptional $n<x$ is $ \\ll \\frac{x}{\\log^B x}$.\n\nTo estimate $g_n(2^A n \\log^A n) - g_n ( n \\log n) $, we apply Lemma \\[bt\\] again to get $$\\begin{aligned}\n\\sum_{ n \\log n < q \\leq 2^A n \\log^A n } \\frac{c_{n} (q)}{q}\n%& = & \\left[\\frac{A_{n} (t)}{t} \\right]_{n \\log n}^{2^A n \\log^A n} + \\int_{n \\log n}^{2^A n \\log^A n} \\frac{A_{n} (t)}{t^2} dt \\\\ \n& \\ll & \\frac{1}{\\phi (n)} \\left[ \\log \\left( \\log \\frac{t}{n} \\right) \\right]_{n \\log n}^{2^A n \\log^A n} \\\\\n& \\ll & % \\frac{1}{\\phi (n) \\log \\log n} + \n \\frac{1}{\\phi (n)} \\log \\left( 1 + \\frac{\\log (2^A \\log^{A-1} n) }{\\log (\\log n ) } \\right) \\\\\n& \\ll & \\frac{1}{\\phi (n)} .\\end{aligned}$$\n\nUsing Lemma \\[bt\\] one more time:\n\n$$\\begin{aligned}\n\\sum_{\\epsilon n \\log n / \\log \\log n < q < n \\log n } \\frac{c_n(q)}{q}\n& \\ll & %\\sum_{\\epsilon n \\log n / \\log \\log n < q \\leq n \\log n} \n\\int_{\\epsilon n \\log n / \\log \\log n}^{n \\log n} \n\\frac{dt}{ \\phi (n) t \\log (t/n)} \\\\\n& \\ll & \\frac{1}{\\phi (n)} \\log \\left( \\frac{\\log (\\log n)}{\\log ( \\log n / \\log \\log n ) } \\right) \n%& \\ll & \\frac{\\log \\log \\log n}{ \\phi (n) \\log \\log n}\n = o \\left( \\frac{1}{\\phi (n)} \\right).\\end{aligned}$$\n\nFinally, we need to analyse the sum $$g_n ( \\epsilon n \\log n / \\log \\log n ) = \\sum_{n < q < \\epsilon n \\log n / \\log \\log n} \\frac{c_n (q)}{q}.$$ This sum is $\\neq 0$ when there are summands; that is, when at least one of $\nn \\pm 1, 2n \\pm 1, \\dots , kn \\pm 1 \n$ is prime for $k < \\epsilon \\log x / \\log \\log x $. ",
"Hence we use the Prime Number Theorem for arithmetic progressions and we see $$\\begin{aligned}\n\\sum_{k < \\frac{\\epsilon \\log x}{ \\log \\log x}} \\frac{k}{\\phi (k)} \\frac{x}{\\log x}\n& \\ll & \\frac{x}{\\log x} \\cdot \\frac{\\epsilon \\log x}{ \\log \\log x} \n \\ll \\frac{\\epsilon x}{ \\log \\log x} = o(x).\\end{aligned}$$ The number of $ n \\leq x$ such that $g_n ( \\epsilon n \\log n / \\log \\log n ) \\neq 0$ is $o(x)$, and Theorem \\[nnwkcuv\\] has been proved.",
"\n\nConditional Composite Moduli Weak Kummer’s Conjecture\n=====================================================\n\nWe now prove Theorem \\[nnwkccv\\] that Kummer’s Conjecture holds for almost all $n$. We will need natural numbers analogues of Propositions 1 and 2 from [@gr].",
"\n\n\\[grprop1nn\\] $$\\sum_{m \\geq 2} \\frac{1}{m} \\sum_{\\substack{q^m \\equiv \\pm 1 \\mod n \\\\ q \\text{ prime} }} \\frac{1}{q^m} = o \\left( \\frac{1}{n} \\right)$$ for all but $o\\left( \\frac{x}{\\log x} \\right)$ natural numbers $n \\leq x$.\n\nFor any prime $q> n$, $$\\begin{aligned}\n\\sum_{m \\geq 2} \\frac{1}{mq^m} \n& \\leq & \\frac{1}{2} \\left( \\frac{1}{q^2} + \\frac{1}{q^3} + \\cdots \\right) \n%& = & \\frac{1}{2q^2} \\left( 1+ \\frac{1}{q} + \\frac{1}{q^2} + \\cdots \\right) \n\\leq \\frac{1}{q^2}.\\end{aligned}$$ Also, for any prime $q < n$, $$\\sum_{m \\geq 2} \\frac{1}{mq^m} \n\\leq \\frac{1}{2n^{2}} \\left( 1+ \\frac{1}{q} + \\frac{1}{q^2} + \\cdots \\right)\n\\leq \\frac{1}{n^{2}}.$$ Thus if we list the primes $q_i$ in order so that $ q_k < n < q_{k+1}$, $$\\begin{aligned}\n\\sum_{m \\geq 2} \\frac{1}{m} \\sum_{\\substack{q^m \\equiv \\pm1 \\mod n \\\\ q^m > n^{2} }} \\frac{1}{q^m} \n& \\leq & \\sum_{m \\geq 2} \\frac{1}{m q_1^m} + \\cdots + \\sum_{m \\geq 2} \\frac{1}{m q_k^m} \n+ \\sum_{m \\geq 2} \\frac{1}{m q_{k+1}^m} + \\sum_{m \\geq 2} \\frac{1}{m q_{k+2}^m} + \\cdots \\\\\n& \\leq & \\frac{1}{n^2} + \\cdots \\frac{1}{n^2}\n+ \\frac{1}{q_{k+1}^2} + \\frac{1}{q_{k+2}^2} + \\cdots \\\\\n&=& O \\left( \\frac{1}{n^2} \\cdot \\frac{n}{\\log n} \\right) = O \\left( \\frac{1}{n \\log n} \\right) \\end{aligned}$$ by the Prime Number Theorem.",
"\n\nAgain using Lemma \\[murty cong cor\\], we have $\\leq 4(2)^{\\omega (n)}$ solutions mod $n$ of the congruence $x^m \\equiv \\pm 1 \\mod n$. Also, by Lemma \\[hr lemma\\], the number of $n \\leq x$ such that $\\omega (n) > A \\log \\log x$ is $o\\left(\\frac{x}{\\log x}\\right)$. (Here we choose $ e \\leq A < 2 / \\log 2$.)\n\nHence $$\\label{damn it}\n\\frac{1}{2}\\sum_{\\substack{q^2 \\equiv \\pm1 \\mod n \\\\ n \\log^2 n < q^2 \\leq n^2 }} \\frac{1}{q^2} \\ \n\\leq \\frac{1}{2n\\log^2 n} \\sum_{\\substack{q^4 \\equiv 1 \\mod n \\\\ q \\leq n }} 1 \\\n\\leq \\ \\frac{2(2^{\\omega (n)})}{n \\log^2 n} \\ = \\ o \\left( \\frac{1}{n} \\right)$$ for all but $o\\left(\\frac{x}{\\log x}\\right)$ numbers $n \\leq x$.\n\nNow if $q^m \\leq n^2$, then $m < 4 \\log n$. Let $$S_{n} = \\sum_{3 \\leq m \\leq 4\\log n} \\frac{1}{m} \n\\sum_{\\substack{q^m \\equiv \\pm 1 \\mod n \\\\ q^m \\leq n \\log^2 n} } \\frac{1}{q^m}.$$ Then $$\\begin{aligned}\n\\sum_{x <n <2x} S_{n} & \\ll & \\sum_{3 < m < \\log n} \\frac{1}{m} \\sum_{x \\log^2 x < q^m < x^2 } \\frac{1}{q^m} \n \\sum_{ \\substack{ x<n<2x \\\\ n| q^m \\pm 1 }} 1 \\\\\n& \\ll & \\sum_{3 < m < \\log n} \\frac{1}{m} \\sum_{\\substack{q < x^{2/m} \\\\ q \\text{ prime} }} \\frac{1}{x \\log^2 x} \\cdot x^{\\delta} \\\\\n& \\ll & \\log \\log x \\cdot \\frac{x^{2/3}}{\\log (x^{2/3})} \\cdot \\frac{1}{x^{1-\\delta} \\log^2 x} \\\\\n& \\ll & \\frac{\\log \\log x}{\\sqrt[4]{x} \\log^3 x},\\end{aligned}$$ because the number of divisors of $q^m + 1$ or of $q^m - 1$ is $o(x^{\\delta})$ for any $\\delta >0$ (see [@ap], pg. ",
"296).",
"\n\nThe number of $ x < S_n < 2x$ such that $S_n > \\epsilon /n$ is $\\ll x^{3/4}$, since otherwise $$\\sum_{x <n <2x} S_{n} \\gg \\frac{1}{x} \\cdot x^{3/4} = \\frac{1}{\\sqrt[4]{x}}.$$ By dyadic decomposition together with (\\[damn it\\]), we see that $$\\sum_{m \\geq 2} \\frac{1}{m} \n\\sum_{\\substack{q^m \\equiv \\pm 1 \\mod n \\\\ n \\log^2 n \\leq q^m \\leq n^2 } } \\frac{1}{q^m} = o (1/n)$$ for all but $o(x/\\log x) $ natural numbers $n \\leq x$. It now suffices to show that $$s_{n} = \\sum_{m \\geq 2} \\frac{1}{m} \n\\sum_{\\substack{q^m \\equiv \\pm 1 \\mod n \\\\ q^m < n \\log^2 n } } \\frac{1}{q^m} = o (1/n)$$ for all but $o(x/\\log x)$ numbers $n \\leq x$.\n\nNote that\n\n$$\\begin{aligned}\n\\sum_{x <n <2x} s_{n} & \\ll & \\sum_{m \\geq 2} \\frac{1}{m} \\sum_{x < q^m < x \\log^2 x} \\frac{1}{q^m} \n \\sum_{ \\substack{ x<n<2x \\\\ q^{m}= \\pm 1 + kn }} 1 \\\\\n& \\ll & \\sum_{m \\geq 2} \\frac{1}{m} \\sum_{x < q^m < x \\log^2 x} \\frac{\\log^2 x}{q^m} \\\\\n%& \\ll & \\sum_{m \\geq 2} \\sum_{x< q^m < x \\log^2 x} \\frac{\\log^2}{q^m} \\\\\n& \\ll & \\sum_{\\substack{q \\ \\text{prime} \\\\ q < x^{1/2} \\log x }} \\frac{\\log^2 x}{x} \\\\\n& \\ll & \\frac{\\log^2 x}{x} \\cdot \\frac{x^{1/2} \\log x }{ \\log (x^{1/2} \\log x )} \n \\ll \\frac{\\log^2 x}{x^{1/2}} \\end{aligned}$$\n\nby the Prime Number Theorem.",
"\n\nThus if $s_{n} > \\epsilon / n$ for $ \\gg x^{1/2} \\log^3 x$ natural numbers $x < n \\leq 2x$, then $$\\sum_{x< n < 2x} s_{n} \\gg \\frac{1}{x} (x^{1/2} \\log^3 x) = \\frac{\\log^3 x}{x^{1/2}} ,$$ a contradiction. ",
"By dyadic decomposition, $s_{n} = o(1/n)$ holds for $\\ll x^{1/2} \\log^3 x = o(x/ \\log x)$ numbers $n \\leq x$.\n\nRecall $g_{n} = \\lim_{x \\to \\infty} g_{n} (x)$, where $$g_{n}(x) = \\sum_{\\substack{q \\ \\text{prime} \\\\ q \\leq x \\\\ q \\equiv 1 \\mod n }} \\frac{1}{q} \\ \n- \\sum_{\\substack{q \\ \\text{prime} \\\\ q \\leq x \\\\ q \\equiv -1 \\mod n }} \\frac{1}{q}.$$ Then by Proposition \\[grprop1nn\\] we have $f_n = g_n + o(1/n)$ for all but $o(x/\\log x)$ numbers $n \\leq x$.\n\n\\[grprop2nn\\] Assume the Elliott-Halberstam Conjecture is true, and fix $ \\delta > 0$. For a constant $C \\geq 3$, the equation $g_{n} - g_{n} (n^{1 + \\delta}) = o(1/n) $ holds for all but $\\ll x / \\log^C x$ natural numbers $n \\leq x$.\n\nSet $S(t, x) = \\sum_{x <n< 2x} | \\pi (t, n, 1) - \\pi (t, n, -1) |$; then the Elliott-Halberstam Conjecture gives $$\\begin{aligned}\n\\sum_{x< n < 2x} |g_{n} - g_{n} (n^{1 + \\delta})| \n& \\ll & \\left[ \\frac{S(t, x)}{t} \\right]_{x^{1+ \\delta}}^{\\infty} \n + \\int_{x^{1+ \\delta}}^{\\infty} \\frac{S(t, x)}{t^2} dt \\\\\n& \\ll & \\frac{1}{\\log^5 x} + \\int_{x^{1+ \\delta}}^{\\infty} \\frac{dt}{t \\log^5 t}\n%\\ \\ \\ \\ \\ \\text{ Take $A \\geq 5$ in \\ref{eh}.} ",
" \n \\ll \\frac{1}{\\log^{A-1} x}. ",
"\\end{aligned}$$ Take $A \\geq 3$ in the Elliott-Halberstam Conjecture.",
"\n\nIf the inequality $$\\sum_{x< n < 2x} |g_{n} - g_{n} (n^{1 + \\delta})| > \\frac{\\epsilon}{n}$$ holds for $ \\gg x / \\log^{A-2} x$ numbers $x < n \\leq 2x$, then $$\\sum_{x< n < 2x} |g_{n} - g_{n} (n^{1 + \\delta})| \\gg\n\\frac{1}{x} \\cdot \\frac{x}{\\log^{A-2} x} = \\frac{1}{\\log^{A-2} x},$$ a contradiction. ",
"The result follows by dyadic decomposition.",
"\n\n\\[grcor1nn\\] Assume the Elliott-Halberstam Conjecture. ",
"Then for any $\\delta >0$ and $C\\geq 3$, $$f_{n} = g_{n}(n^{1 + \\delta }) + o(1/n)$$ for all but $o(x / \\log x)$ numbers $n \\leq x$.\n\nThis follows from Propositions \\[grprop1nn\\] and \\[grprop2nn\\].",
"\n\nWe will also need the following result.",
"\n\nLet $g$ be a natural number, and let $a_i$, $b_i (1 = 1, \\dots , g)$ be integers satisfying $$E:= \\prod_{i=1}^g a_i \\prod_{1 \\leq r < s \\leq g} (a_r b_s - a_s b_r) \\neq 0.$$ Let $\\rho (p)$ denote the number of solutions of $$\\prod_{i=1}^g (a_i n +b_i) \\equiv 0 \\mod p,$$ and suppose that $\\rho (p) < p$ for all $p$. Let $y$ and $x$ be real numbers satisfying $1 < y \\leq x$. Then $$| \\{n: x-y <n \\leq x, a_i n +b_i \\ \\text{prime for} \\ i=1, \\dots, g \\}|$$ $$\\leq 2^g g! ",
"\\prod_p \\left( 1 - \\frac{\\rho (p) - 1}{p-1} \\right) \\left( 1- \\frac{1}{p} \\right)^{-g+1} \\frac{y}{\\log ^g y}$$ $$\\times \\left\\{ 1 + O \\left( \\frac{\\log \\log 3y + \\log \\log 3|E|}{\\log y} \\right) \\right\\},$$ where the implied constant depends at most on $g$. \\[halberstam 5.7\\]\n\nWe are now ready to prove Theorem \\[nnwkccv\\].",
"\n\nWe are left to deal with the finite sum $$g_n (n^{1+\\delta}) = \\sum_{q < n^{1+\\delta}} \\frac{c_n (q) }{q} \n= \\sum_{q <(1+ \\delta) n \\log^2 n} \\frac{c_n (q) }{ q}\n+\\sum_{ (1+ \\delta) n \\log^2 n <q < n^{1+\\delta}} \\frac{c_n (q) }{q}.$$\n\nFor $ X < n < 2X$, and $(1 + \\delta )^A n \\log ^A n < x < n^{1+ \\delta }$, the conditions of Lemma \\[hooley\\] are satisfied, and $$\\begin{aligned}\n\\sum_{ (1+ \\delta )^A n \\log^A n <q < n^{1+\\delta}} \\frac{c_n (q) }{ q} \n& \\ll & \\int_{(1 + \\delta )^A n \\log ^A n}^{n^{1+ \\delta }} \\frac{t}{\\phi (n) \\log n} \\ \\frac{dt}{t^2} \\\\ \n%& \\ll & \\frac{1}{\\phi (n) \\log n} \\int_{(1 + \\delta )^A n \\log ^A n}^{n^{1+ \\delta }} \\frac{dt}{t} \\\\\n& \\ll & \\frac{1}{\\phi (n) \\log n} [\\delta \\log n - A \\log (1+ \\delta ) - A \\log n ] \\\\\n& \\ll & \\frac{\\delta }{\\phi (n)}.\\end{aligned}$$\n\nNow we put bounds on the sum $$\\sum_{q <(1+ \\delta)^A n \\log^A n} \\frac{c_n (q) }{ q} \n% = \\sum_{q < \\epsilon n \\log n} \\frac{c_n (q) }{ q} +\n% \\sum_{ \\substack{ \\epsilon n \\log n < q \\\\ <(1+ \\delta) n \\log^2 n}} \\frac{c_n (q) }{ q}\n.$$\n\nFor the range $(1+ \\delta) n \\log^2 n < q <(1+ \\delta)^A n \\log^A n$, we use the Brun-Titchmarsh Theorem. ",
"$$\\begin{aligned}\n\\sum_{\\substack{ (1+ \\delta) n \\log^2 n < q \\\\ <(1+ \\delta)^A n \\log^A n}} \\frac{c_n (q) }{ q} \n& \\ll & \\int _{(1+ \\delta) n \\log^2 n}^{(1+ \\delta)^A n \\log^A n} \\frac{dt}{\\phi (n) t \\log (t/n)} \n%& \\ll & \\frac{1}{\\phi (n) \\log \\log n} \\int _{(1+ \\delta) n \\log^2 n}^{(1+ \\delta)^A n \\log^A n} \\frac{dt}{t}\n\\ll \\frac{1}{\\phi (n)}.\\end{aligned}$$\n\nFor $\\epsilon n \\log n < q < (1+ \\delta) n \\log^2 n$, $$\\begin{aligned}\n\\sum_{ \\substack{ \\epsilon n \\log n < q \\\\ < (1+ \\delta) n \\log^2 n}} \\frac{c_n (q) }{q}\n& \\ll & \\sum_{\\substack{ \\epsilon n < t < (1+ \\delta ) \\log^2 n, \\\\ nt \\pm 1 \\ \\text{prime} }} \\frac{1}{nt} .",
"\n% \\\\ & \\ll & \\frac{t}{\\phi (n)} \\frac{x}{\\log x} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\text{by \\ref{halberstam 5.7}.} ",
"\\end{aligned}$$ On average, $$\\begin{aligned}\n\\sum_{x<n<2x} \\ \\ \\sum_{\\substack{ \\epsilon \\log n < t < (1+ \\delta )\\log^2 n, \\\\ nt \\pm 1 \\ \\text{prime} }} \\frac{1}{nt} \n& \\ll & \\sum_{\\epsilon \\log x < t < (1+ \\delta ) \\log^2 x } \\frac{1}{tx} \n \\sum_{\\substack{ x<n<2x, \\\\ nt \\pm 1 \\ \\text{prime}}} 1 \\\\\n& \\leq & \\sum_{\\epsilon \\log x < t < (1+ \\delta ) \\log^2 x } \\frac{1}{tx} \\frac{x}{\\phi (t) \\log x} \\\\ \n& \\ll & \\frac{\\log \\log x} {\\log x}.\\end{aligned}$$ Therefore the number of $ n \\leq x $ such that $$\\sum_{\\substack{ \\epsilon \\log n < t < \\log^2 n, \\\\ nt \\pm 1 \\ \\text{prime} }} \\frac{1}{nt} > \\frac{\\epsilon}{n}$$ is $\\ll \\frac{x \\log \\log x}{ \\log x} = o (x).$ That is $|g_n(\\epsilon n \\log n) - g_n((1+ \\delta) n \\log^2 n) | = o(n) $ for all but $o(x)$ natural numbers $n \\leq x$.\n\nFinally, for the range $q < \\epsilon n \\log n$, we will use Lemma \\[halberstam 5.7\\]. ",
"Fix some $t < \\epsilon \\log x$. Then the number of $ n < x$ such that $nt +1$ or $nt -1$ is a prime is $\\leq x / \\log x +O (\\frac{x \\log \\log x} {\\log ^2 x})$, and so $$\\sum_{t <\\epsilon \\log x} \\# \\{n < x : \\ nt \\pm 1 \\ \\text{prime} \\} \\leq \\epsilon x + O \\left( \\frac{x \\log \\log x}{\\log x} \\right).$$\n\nSo the number of $n < x$ for which $$\\sum_{q < \\epsilon n \\log n} \\frac{c_n (q) }{q} \\neq 0$$ is $o(x)$, and we may assume $g_n(\\epsilon n \\log n) = 0 $ for almost all $n$, and the proof of Theorem \\[nnwkccv\\] is complete.",
"\n\nConditional Disproof of Generalised Kummer’s Conjecture\n=======================================================\n\nRecall that $$h_n^- = G(n) \\exp \\left( \\frac{\\phi (n)}{2} f_n \\right)$$ and that the Generalized Kummer’s Conjecture predicts that $h_n^- \\sim G(n)$ as $n \\to \\infty$. In this section, we will prove Theorem \\[gkcf\\], that the Elliott-Halberstam Conjecture implies that the Generalized Kummer’s Conjecture fails for infinitely many natural numbers $n$. Here we wish to show that $ f_n = o (1/\\phi (n))$ fails for infinitely many $n$.\n\nBy Corollary \\[grcor1nn\\], the Elliott-Halberstam Conjecture implies that for any $\\delta >0$ and $C\\geq 3$, $$f_n = g_n(n^{1+\\delta}) + o (1/n)$$ for all but $o(x / \\log x)$ numbers $n \\leq x$. We wish to find bounds on $g_n(n^{1 + \\delta } ) - \\frac{1}{n+1}$ and so estimate the contribution of the primes $q$ of the form $n+1$.\n\n\\[gkcflem1\\] Fix $\\lambda > 0$ and $\\epsilon > 0$. There exists some $\\delta >0$ such that for all sufficiently large values of $x$, there are $\\leq \\frac{\\lambda x}{\\log x} $ natural numbers $n \\leq x$ such that $n+1$ is prime and $$\\left|g_n(n^{1 + \\delta } ) - \\frac{1}{n+1} \\right| \\geq \\frac{\\epsilon }{2n} .$$\n\nDefine $$%\\label{N_k}\nN_k^{\\pm} (x) = | \\left\\{ x<n \\leq 2x : n+1 \\text{ and } kn \\pm 1 \\ \\text{both prime} \\right\\} | .$$ Then for $k \\geq 2$, $$\\label{N_k^+}\nN_k^+ (x) \\ll \\left( \\prod_{p | k(k-1)} \\frac{p}{p-1} \\right) \\frac{x}{\\log^2 x}$$ and $$\\label{N_k^-}\nN_k^- (x) \\ll \\left( \\prod_{p | k(k+1)} \\frac{p}{p-1} \\right) \\frac{x}{\\log^2 x}$$ by Theorem \\[mp 2.3\\].",
"\n\nThus $$\\begin{aligned}\n\\sum_{\\substack{x<n \\leq 2x \\\\ n+1 \\ \\text{prime}}} n \\left|g_n(n^{1 + \\delta } ) - \\frac{1}{n+1} \\right| \n& \\ll & \\sum_{\\substack{ x<n \\leq 2x \\\\ n+1 \\ \\text{prime} }} \n \\sum_{\\substack{ q \\equiv \\pm 1 \\mod n \\\\ q \\leq n^{1+ \\delta} \\\\ q \\ \\text{prime}, \\ q \\neq n+1 }} \n \\frac{n}{q \\mp 1} \\\\\n& \\ll & \\sum_{k=2}^{(2x)^{\\delta}} \\frac{N_k^+}{k} + \\sum_{k=2}^{(2x)^{\\delta}} \\frac{N_k^-}{k} \\\\\n& \\ll & \\frac{x}{\\log^2 x} \\sum_{k=2}^{(2x)^{\\delta}} \\left( \\frac{1}{k} \\prod_{p | k(k-1)} \\frac{p}{p-1} \\right) \n + \\frac{x}{\\log^2 x} \\sum_{k=2}^{(2x)^{\\delta}} \\left( \\frac{1}{k} \\prod_{p | k(k+1)} \\frac{p}{p-1} \\right) \\\\\n& \\ll & \\frac{x}{\\log^2 x} \\cdot \\delta \\log x = \\frac{\\delta x}{\\log x} \\end{aligned}$$ by Lemmas \\[mp 2.3\\] and \\[mp 2.4\\].",
"\n\nHence there exists a constant $c_1 >0$ such that $$\\sum_{\\substack {x<n \\leq 2x \\\\ n+1 \\ \\text{prime}}} \\left|g_n(n^{1 + \\delta } ) - \\frac{1}{n+1} \\right| \n\\leq \\frac{1}{n} c_1 \\delta \\frac{x}{\\log x} = \\frac{\\epsilon }{2n} \\cdot \\frac{\\lambda x}{\\log x}$$ for $\\delta = \\frac{\\epsilon \\lambda}{2 c_1}.$ By dyadic decomposition, there exists $\\leq \\frac{\\lambda x}{\\log x} $ numbers $n \\leq x$ such that $n+1$ is prime and $$\\left|g_n(n^{1 + \\delta } ) - \\frac{1}{n+1} \\right| \\geq \\frac{\\epsilon }{2n} ,$$ as required.",
"\n\n\\[gkcfprop1\\] Suppose the Elliott-Halberstam Conjecture is true. ",
"Then for a fixed $\\epsilon > 0$ there exist $\\gg x / \\log x$ natural numbers $ n \\leq x$ such that $f_n = (1 \\pm \\epsilon) \\frac{1}{n}$.\n\nBy the Prime Number Theorem, there are $\\geq c_2 x / \\log x $ numbers $n \\leq x$ such that $n+1$ is prime. ",
"Fix $\\epsilon >0$ and let $\\lambda =c_2 / 2$ in Lemma \\[gkcflem1\\]. ",
"Then there exist $\\geq c_2 x / 2 \\log x$ numbers $n \\leq x$ such that $n+1$ is prime and $$\\left|g_n(n^{1 + \\delta } ) - \\frac{1}{n+1} \\right| < \\frac{\\epsilon }{2n}.$$\n\nBy Corollary \\[grcor1nn\\], there exist $\\geq c_2 x / 2 \\log x$ numbers $n \\leq x$ such that $n+1$ is prime and $$\\left| f_n - \\frac{1}{n} \\right| < \\frac{\\epsilon}{n}.$$\n\nWe have shown that with the assumption of the Elliott-Halberstam Conjecture, $$\\frac{h_n^-}{G(n)} = \\exp \\left( \\frac{\\phi (n)}{2} f_n \\right)\n= \\exp \\left( \\frac{\\phi (n)}{4n} (1 \\pm \\epsilon) \\right)$$ for $\\gg \\frac{x}{\\log x}$ numbers $n \\leq x$. We now wish to prove that for infinitely many of these $n$, $\\frac{\\phi (n)}{n}$ is bounded away from $0$. This must be verified, of course, because $\\liminf_{n \\to \\infty} \\frac{\\phi (n)}{n} =0$.\n\n\\[murtylem1\\] $$\\sum_{\\substack{ n \\leq x \\\\ 2n+1 \\ \\text{prime} }} \\frac{\\phi (n)}{n}\n\\sim \\frac{c x}{\\log x}, \\ \\ \\ \\text { as $x \\to \\infty $, }$$ where $c= \\frac{3}{2}\\prod_{p \\ \\text{odd}} \\left( 1 - \\frac{1}{p(p-1)} \\right) \\neq 0$.\n\nSince $$\\frac{\\phi(n)}{n} = \\sum_{d|n} \\frac{\\mu (d)}{d} ,$$ we have $$\\sum_{\\substack{ n \\leq x \\\\ 2n+1 \\ \\text{prime} }} \\frac{\\phi (n)}{n} \\ \\ =\n \\sum_{\\substack{ n \\leq x \\\\ 2n+1 \\ \\text{prime} }} \\sum_{d|n} \\frac{\\mu (d)}{d} \\ \\ = \\ \\\n\\sum_{d \\leq x} \\frac{\\mu (d)}{d} \\sum_{\\substack{ t \\leq x/d \\\\ 2dt+1 \\ \\text{prime} }} 1 .$$ The inner sum is $\\pi (2x+1, 2d, 1)$.\n\nThus we need to evaluate $$\\sum_{d \\leq x} \\frac{\\mu (d)}{d} \\pi(2x+1, 2d, 1) = \n\\sum_{d < \\log^A x} \\frac{\\mu (d)}{d} \\pi(2x+1, 2d, 1) + \\sum_{\\log^A x \\leq d \\leq x} \\frac{\\mu (d)}{d} \\pi(2x+1, 2d, 1).$$ For the second sum, we have the estimate $$\\sum_{\\log^A x \\leq d \\leq x} \\frac{\\mu (d)}{d} \\pi(2x+1, 2d, 1)\n\\ll \\sum_{d \\geq \\log^A x} \\frac{x}{d^2} \\ll \\frac{x}{\\log^A x} .$$ For the first sum, we use the Siegel-Walfisz Theorem \\[sw\\] to get $$\\sum_{d < \\log^A x} \\frac{\\mu (d)}{d} \\pi(2x+1, 2d, 1) \\ll \\sum_{d \\leq \\log^A x} \\frac{\\mu (d)}{d \\phi (d)} \\li 2x + O \\left( \\frac{x}{\\log^A x} \\right).$$ The first term is $$(\\li 2x) \\left( \\sum_{d=1}^{\\infty} \\frac{\\mu (d) }{ d \\phi (2d) } + O \\left( \\frac{1}{\\log^{A-1} x} \\right) \\right).$$ Since $$\\begin{aligned}\n\\sum_{d=1}^{\\infty} \\frac{\\mu (d)}{d \\phi (d) } \n& = & \\sum_{\\substack{d= 2d_1 \\\\ d_1 \\ \\text{odd} }} \\frac{\\mu (d)}{d \\phi (2d) } \n + \\sum_{d \\ \\text{odd} } \\frac{\\mu (d)}{d \\phi (2d) } \\\\\n& = & \\sum_{d \\ \\text{odd} } \\frac{\\mu (2d)}{2d 2\\phi (d) } +\\sum_{d \\ \\text{odd} } \\frac{\\mu (d)}{d \\phi (d) } \n\\ = \\ - \\frac{1}{4} \\sum_{d \\ \\text{odd} } \\frac{\\mu (d)}{d \\phi (d) } +\\sum_{d \\ \\text{odd} } \\frac{\\mu (d)}{d \\phi (d) } \\\\\n& = & \\frac{3}{4} \\sum_{d \\ \\text{odd} } \\frac{\\mu (d)}{d \\phi (2d) } \n\\ = \\ \\frac{3}{4} \\sum_{d \\ \\text{odd}} \\mu (d) \\prod_{p|d} \\left( \\frac{p}{p-1} \\right) \\frac{1}{d^2} \\\\\n& = & \\frac{3}{4} \\prod_{p \\ \\text{odd}} \\left( 1 - \\frac{1}{p(p-1)} \\right)\n%Dirichlet series, f(n) = 0 if in is even, blah otherwise. ",
"Let s=2, use euler product.\\end{aligned}$$ and $$\\li 2x \\sim \\frac{2x}{\\log x},$$ this completes the proof of the lemma.",
"\n\n\\[murtylem2\\] Let $\\delta > 0$ and $x \\geq 1$. Then $$\\label{crazy sum} \n\\sum_{\\substack{ n \\leq x \\\\ n+1 \\ \\text{prime} \\\\ kn \\pm 1 \\ \\text{both prime for some} \n\\\\ 2 \\leq k \\leq \\delta \\log x }}\n\\frac{\\phi (n)}{n}\n\\ll \\frac{\\delta x}{\\log x},$$ where the implied constant is absolute.",
"\n\nSince $\\frac{\\phi(n)}{n} \\leq 1$, we have that the sum in (\\[crazy sum\\]) is bounded by $$\\sum_{2 \\leq k \\leq \\delta \\log x} N_k^{\\pm} (x)$$ where $$\\begin{aligned}\nN_k^{\\pm} (x) & = & | \\left\\{ n \\leq x : n +1 \\ \\text{ and }\nkn \\pm 1 \\ \\text{both prime} \\right\\}|. ",
"\n%& \\ll & \\frac{x}{\\log^2 x} \\prod_{\\substack{p|k \\\\ p \\neq 2}} \\left( 1- \\frac{1}{p-1} \\right)^{-1}.\\end{aligned}$$ By dyadic decomposition and equations (\\[N\\_k\\^+\\]) and (\\[N\\_k\\^-\\]), $$N_k^+ (x) \\ll \\left( \\prod_{p | k(k-1)} \\frac{p}{p-1} \\right) \\frac{x}{\\log^2 x}$$ and $$N_k^- (x) \\ll \\left( \\prod_{p | k(k+1)} \\frac{p}{p-1} \\right) \\frac{x}{\\log^2 x}.$$ Inserting this estimate into the sum, we get the sum is $\n\\ll \\frac{\\delta x}{\\log x}, \n$ as claimed.",
"\n\nWe now prove Theorem \\[gkcf\\].",
"\n\nBy Proposition \\[gkcfprop1\\], the Elliott-Halberstam Conjecture implies that $$\\frac{h_n^-}{G(n)} = \\exp \\left( \\frac{\\phi (n)}{2} f_n \\right)\n= \\exp \\left( \\frac{\\phi (n)}{2n} (1 \\pm \\epsilon) \\right)$$ for $\\gg \\frac{x}{\\log x}$ numbers $n \\leq x$. By Lemmas \\[murtylem1\\] and \\[murtylem2\\], for a sufficiently small $\\delta$ we have $$\\sum_{\\substack{ \\frac{x}{2} \\leq n \\leq x \\\\ n+1 \\ \\text{prime} \\\\ \\text{neither } kn \\pm 1 \\ \\text{is prime for any} \n\\\\ 2 \\leq k \\leq \\delta \\log x } } \n\\frac{\\phi (n)}{n} \\gg \\frac{x}{\\log x}.$$ From this we deduce that there are infinitely many $n$ such that $$\\frac{h_n^-}{G(n)} \\geq \\exp (\\eta)$$ for some fixed $\\eta > 0$. Thus if the Elliott-Halberstam Conjecture is true, then the Generalized Kummer’s Conjecture (\\[gkc\\]) fails for infinitely many natural numbers.",
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"\n"
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"Down Payment Assistance Options\n\nOne of the largest misconceptions about purchasing a house is that you need at least 20% to purchase a house. ",
"Mountain West Financial is a leader in affordable housing solutions, from down payment assistance grants to interest-free second mortgages and other special mortgage programs, there is a growing number of options for people who want to buy a home without a down payment.",
"\n\nMountain West Financial is approved with over 140 different Down Payment Assistance Programs.",
"\n\nDeferred payment silent seconds, tax deductions, and grants are all different forms that Down Payment Assistance can be found in\n\nPrograms can be used for down payment, closing cost assistance and more"
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"Switzerland Air Blog\n\nWe’re in the middle of winter now in Texas, but think back to summer—pool parties, barbecues, clear blue skies and… AC trouble? ",
"If you had any problems with your air conditioning system this past year then it’s time to contact a technician from our team. ",
"We know that it might seem a little early to address problems with your air conditioning system, but you can really never be too early. ",
"Summer comes pretty early here in Texas. ",
"If you need AC repair in Clute, TX then make sure to contact our team. ",
"Our technicians are extensively trained and NATE-certified. ",
"We understand what it takes to keep your Brazoria County home cool.",
"\n\nWhen people think of harsh winters, their mind’s eye probably takes them to a Boston snow day or the bitter chill of a Seattle morning. ",
"Just because we’re not notorious for our winter weather conditions here in Clute doesn’t mean that they’re anything to scoff at. ",
"If you’ve lived in this part of Texas for even one winter, you know how surprisingly cold our conditions can get. ",
"The last thing you need is to turn your heater on one evening and realize your heater gave out.",
"\n\nWe realize that many homeowners run into these dire situations because they didn’t pick up on the warning signs of their heater going out. ",
"If you need heater repair in Clute, TX, make sure you contact our team. ",
"We ensure that all our technicians are capable and conscientious through extensive training. ",
"If you’d like to know the signs that you should call, keep reading below.",
"\n\nAre your heating bills a little too high this winter? ",
"This is a common problem here in Texas. ",
"We don’t necessarily experience the coldest possible winters across the nation, but we do sometimes have quite cold temperatures here. ",
"When your heater is battling against these low temperatures to keep your home comfortable, it’s common to run into high bills.",
"\n\nLuckily, we can help you avoid these problems. ",
"When you need heater service in Freeport, TX then make sure you contact Switzerland Air. ",
"We work alongside all the best brands like Aprilaire and Daikin and all our technicians are NATE-certified and extensively trained. ",
"Make sure you choose our team.",
"\n\nWe know it’s winter here in Freeport, but think back to a few months ago when the weather was warm and the daylight hours were long. ",
"Now, were you having trouble with your air conditioning? ",
"It’s easy to romanticize the past, but any problems you had like short cycling, odd noises, or troublesome operation is something you should address sooner rather than later. ",
"Winter is a great time to do this with your system because you don’t have to worry about using your air conditioner during this time. ",
"If you need AC repair in Freeport, TX, we’re the team for the job. ",
"We’re reliable, conscientious, and always punctual when you need our services. ",
"Contact our team today.",
"\n\nAre you looking to boost your heating in a simple way? ",
"Upgrading your thermostat is the best way to get the most out of your heating system this winter. ",
"If you only take one thing away from this article, remember that a thermostat is one of the most important aspects of your heating system. ",
"So many homeowners upgrade their heating system throughout their lifetime because they understand that HVAC technology is ever-evolving. ",
"But they neglect to spread this mindset to their thermostat. ",
"Your thermostat needs to be upgraded too. ",
"If you’re thinking of upgrading to a smart thermostat in Freeport, TX, please read more below.",
"\n\nThere are a lot of heating systems out there, and choosing the right one for your home can be tricky. ",
"A qualified technician can help you select the right system for your home’s specific needs. ",
"If you are considering a radiant heating system for your household comfort, there are some things that we would like you to know.",
"\n\nThe last thing you want during this winter in Lake Jackson is a faulty furnace system. ",
"Furnace breakdowns are incredibly inconvenient especially now that we’re getting to the coldest part of the year. ",
"Furnace problems may seem inevitable—your heater incurs wear and tear over time, right? ",
"While time is a strain against your furnace, you don’t have to helplessly watch your system wither away. ",
"There are many things you can do to avoid furnace problems this winter. ",
"If you need furnace repair in Lake Jackson, TX then contact our team. ",
"If you’d like to know what furnace problems are common here in Texas and how you can avoid a repair charge, then keep reading below.",
"\n\nIs your boiler making a sound like an overgrown tea kettle boiling over? ",
"If so, you have a bit of a problem. ",
"That sound is called kettling, and it is a symptom of a serious issue afflicting a boiler system. ",
"We highly recommend that you call on a professional technician for a repair appointment as soon as you notice this sound coming from your boiler. ",
"But while you’re waiting for your technician to arrive and fix the problem, read on to find out why kettling is such a big threat to the health of your boiler system.",
"\n\nBefore too long, you’re going to be relying on your furnace to keep your home warm from day to day. ",
"Most people prepare for the added strain that this will put on their system by scheduling preventive maintenance for it before heating season starts. ",
"For some systems, though, maintenance won’t be enough to get them through the winter. ",
"If your furnace is not up to the task of getting you through the next few months, it’s best that you replace it now rather than midway through the season. ",
"The best way to determine whether or not your furnace needs replacement is to contact a professional and have them examine it for you. ",
"Before that happens, you can also take a look at the symptoms below to help you determine whether or not it’s time to consider replacement.",
"\n\nSure, it’s still pretty hot out most days. ",
"Summer is coming to an end sooner than you think, however, which means you should be thinking about the kind of preparations you should be making for the fall and winter seasons. ",
"If you take these steps now, you won’t have to scramble to get them done when the weather starts to cool off. ",
"Check out the following tips to help get your home ready for heating season."
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"The drugs related to the patient symptoms were nonsteroidal anti-inflammatory drugs (70%), antiplatelet agents (19%) and oestroprogestinic agents (11%). ",
"Colonoscopy was normal in 30% of patients and abnormal in 70%. ",
"Histology showed low content of inflammatory cells and normal crypt architecture in-patients with endoscopy similar to inflammatory bowel diseases. ",
"The eosinophil score was significantly higher in the left side of the colon in the patient group compared with controls. ",
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"The SCOR Program does not try to address all of the basic and clinical issues related to sepsis-induced acute lung injury. ",
"The specific focus and rationale for the SCOR Program is as follows. ",
"During gram-sepsis, endotoxin and bacterial DNA are released and stimulate macrophages to release TNF. ",
"Cell wall products of gram + organisms mimic the effects of endotoxin on macrophages. ",
"TNF can trigger organ and cellular dysfunction (decreased surfactant production) and/or injury (by apoptosis). ",
"The SCOR Program recognizes that other types of cells release mediators (including TNF) during sepsis and that mediators, other than TNF, are important for the pathogenesis of acute lung injury. ",
"We further realize that surfactant abnormalities are only one of the manifestations of organ dysfunction during acute lung injury and that injury to tissues can occur by mechanisms that do not involve apoptosis. ",
"This paradigm is only presented tot illustrate the focus and interrelationships in the SCOR Program. ",
"Projects 11 and 12 evaluate the regulation of cytokine genes (including TNF) in human alveolar macrophages and liver. ",
"Project 11 evaluates the role of MAPK' and Project 12 evaluates redox regulation of Nfkappab. ",
"T- cells regulate the sensitivity of macrophages to endotoxin via the secretion of pro-inflammatory mediators (like the TH-1 cytokine, interferon gamma) or anti-inflammatory mediators (like the TH-2 cytokines). ",
"The regulation of TH-1 and TH-2 populations of T-cells by CD95 ligands is evaluated in Project 13. ",
"Various tissues, like lung, may also protect themselves from invading T-cells or neutrophils during inflammation by expressing CD95 ligand. ",
"This is also explored in Project 13. ",
"Injury to tissues can also be triggered by expression of CD95 ligand and its receptor, as explored in Project 13. ",
"Project 14 explores TNF- induces suppression of surfactant lipid production. ",
"Surfactant abnormalities are a major manifestation of acute lung injury. ",
"The Clinical Core determines if bacterial DNA (a surrogate marker for infection) in blood or lung predicts continued inflammation and patient outcome in acute lung injury. ",
"The Clinical Core also provides human tissues and biometry support for each of the projects. ",
"This is a highly integrated program with many scientific interactions between the projects and cores. ",
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"Session.",
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"More than half of that acreage total came from just one fire. ",
"The Montana Stockgrowers Association tells Drovers Cattle Network Dot Com that cattle losses from the fires have been limited. ",
"29 fires are currently active in Montana, with the bulk of them burning in the western part of the state where cattle numbers are more limited. ",
"The biggest fire is the Lodgepole Complex fire in eastern Montana. “",
"Most of the people affected by the Lodgepole fire are getting a better handle on things,” says Jay Bodner, Director of Natural Resources for the Montana Stockgrowers Association. “",
"Luckily, we did see minimal cattle losses from the fire.” ",
"So far, there haven’t been any reports of major cattle losses from the fires. ",
"Some cattle were unfortunately electrocuted by power lines when a power pole burned down. ",
"Bonder says he doesn’t think the cattle death toll will be as widespread as the fires that ravaged the southern plains in March. ",
"The latest drought monitor shows almost 12 percent of Montana is listed under the most extreme category of drought."
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"5 rules of wealth mindset to run an E-commerce business\n\nEcommerce Marketing Apprenticeship 2015 FREE Training\nIn This FREE training,local Singaporean Internet Millionaire,his will enveil the secrets to GENERATING Constast Sales in his First year of running an ONLINE business…\nHe will hand-pick new apprentices under his wing to be trained to run his online business together.",
"\nCan work any time and any where in the World\nCan work as Part Time or Full Time\nLocals or Foreigners all are welcome\nAs this is only a FREE training to teach how to use “ 5 Rules of Wealth to earn passive income” and done out of good will and spare time.",
"\nIt could be a last chance to get first hand experience in learning personally from a local Millionaire who created wealth from the INTERNET\nTo ensure that you get a SEAT,Fill up the form for reservation.",
"\nhttp://goo.gl/forms/hE5SWdq62a\nsee you there !!"
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"Immunostaining of growth hormone and prolactin in paraffin-embedded and stored or previously stained materials.",
"\nIn attempts to evaluate immunocytochemically autopsy and biopsy material previously obtained and processed for conventional histologic staining, we had to resort to immunostaining of tissues embedded years ago or even sections already stained with hematoxylin-eosin or aldehyde thionin-PAS-orange G. Hypophysial growth hormone and prolactin proved remarkably resistant to such prior treatment with regard to their antigenic properties, and could be readily immunostained in tissue embedded in paraffin 3-4 years earlier, and after destaining of sections prepared up to 7 years earlier. ",
"The results of such \"retrospective\" immunocytochemical evaluation of autopsy and biopsy materail is illustrated with the staining of \"pregnancy cells\" for prolactin in the hypophysis of a woman postpartum, the immunostaining for prolactin in the cells of adenomas associated with marked hyperprolactinemia, the staining for growth hormone in adenomas removed from children with gigantism, and the immunostaining for prolactin, growth hormone or both in several adenomas that were discovered at autopsy and not associated with a known clinical history of endocrine aberrations."
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"Search Results for: add table to schema\n\nMydumper is known as the faster (much faster) mysqldump alternative. ",
"So, if you take a logical backup you will choose Mydumper instead of mysqldump. ",
"But what about the restore? ",
"Well, who needs to restore a logical backup? ",
"It takes ages! ",
"Even with Myloader. ",
"But this could change just a bit if we are able to take […]\n\nPeople using OpenStack Trove instances can hit a common issue in the MySQL world: how to perform schema change operations while minimizing the impact on the database server? ",
"Let’s explore the options that can allow online schema changes. ",
"Summary With MySQL 5.5, pt-online-schema-change from Percona Toolkit is your best option for large tables while regular […]\n\nMySQL table alterations can interrupt production traffic causing bad customer experience or in worst cases, loss of revenue. ",
"Not all DBAs, developers, syadmins know MySQL well enough to avoid this pitfall. ",
"DBAs usually encounter these kinds of production interruptions when working with upgrade scripts that touch both application and database or if an inexperienced admin/dev […]\n\nStarting with MySQL 5.6 there is an INNODB_METRICS table available in INFORMATION_SCHEMA which contains some additional information than provided in the SHOW GLOBAL STATUS output – yet might be more lightweight than PERFORMANCE_SCHEMA. ",
"Too bad INNODB_METRICS was designed during the Oracle-Sun split under MySQL leadership and so it covers only InnoDB counters. ",
"I think this […]\n\nI recently encountered a situation in which after running Percona Toolkit’s pt-table-checksum on a customer system, 95% of the table on the MySQL master was different on the MySQL slave. ",
"Although this table was not a critical part of the infrastructure, from time to time, writes to the table from the master would break replication. […]",
"\n\nI recently worked on a case where one node of a Galera cluster had its schema desynchronized with the other nodes. ",
"And that was although Total Order Isolation method was in effect to perform the schema changes. ",
"Let’s see what happened. ",
"Background For those of you who are not familiar with how Galera can perform […]\n\nWe are using Percona Server + TokuDB engine extensively in Percona Cloud Tools and getting real usage operational experience with this engine. ",
"So I want to share some findings we came across, in hope it may help someone in their work with TokuDB. ",
"So, one problem I faced is that SELECT * FROM INFORMATION_SCHEMA.TABLES is […]\n\nHosting a shared MySQL instance for your internal or external clients (“multi-tenant”) was always a challenge. ",
"Multi-tenants approach or a “schema-per-customer” approach is pretty common nowadays to host multiple clients on the same MySQL sever. ",
"One of issues of this approach, however, is the lack of visibility: it is hard to tell how many resources (queries, disk, […]\n\nSome of us Perconians are at OpenStack summit this week in Atlanta. ",
"Matt Griffin, our director of product management, tweeted about the turbo-hipster CI talk about their experience of ALTER TABLEs running faster on Percona Server. ",
"Oracle’s Morgan Tocker then tweeted in response, asking why this was the case. ",
"I decided that the simplest way to […]"
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"Q:\n\nHow can I use sscanf to analyze string data?",
"\n\nHow do I split a string into two strings (array name, index number) only if the string is matching the following string structure: \"ArrayName[index]\".",
"\nThe array name can be 31 characters at most and the index 3 at most. ",
"\nI found the following example which suppose to work with \"Matrix[index1][index2]\". ",
"I really couldn't understand how it does it in order to take apart the part I need to get my strings. ",
"\nsscanf(inputString, \"%32[^[]%*[[]%3[^]]%*[^[]%*[[]%3[^]]\", matrixName, index1,index2) == 3\n\nThis try over here wasn't a success, what am I missing? ",
"\nsscanf(inputString, \"%32[^[]%*[[]%3[^]]\", arrayName, index) == 2\n\nA:\n\nHow do I split a string into two strings (array name, index number) only if the string is matching the following string structure: \"ArrayName[index]\".",
"\n\nWith sscanf, you don't. ",
" Not if you mean that you can rely on nothing being modified in the event that the input does not match the pattern. ",
" This is because sscanf, like the rest of the scanf family, processes its input and format linearly, without backtracking, and by design it fills input fields as they are successfully matched. ",
" Thus, if you scan with a format that assigns multiple fields or has trailing literal characters then it is possible for results to be stored for some fields despite a matching failure occurring.",
"\nBut if that's ok with you then @gsamaras's answer provides a nearly-correct approach to parsing and validating a string according to your specified format, using sscanf. ",
" That answer also presents a nice explanation of the meaning of the format string. ",
" The problem with it is that it provides no way to distinguish between the input fully matching the format and the input failing to match at the final ], or including additional characters after.",
"\nHere is a variation on that code that accounts for those tail-end issues, too:\n char array_name[32] = {0}, idx[4] = {0}, c = 0;\n int n;\n\n if (sscanf(str, \"%31[^[][%3[^]]%c%n\", array_name, idx, &c, &n) >= 3\n && c == ']' && str[n] == '\\0')\n printf(\"arrayName = %s\\nindex = %s\\n\", array_name, idx);\n else\n printf(\"Not in the expected format \\\"ArrayName[idx]\\\"\\n\");\n\nThe difference in the format is the replacement of the literal terminating ] with a %c directive, which matches any one character, and the addition of a %n directive, which causes the number of characters of input read so far to be stored, without itself consuming any input.",
"\nWith that, if the return value is at least 3 then we know that the whole format was matched (a %n never produces a matching failure, but docs are unclear and behavior is inconsistent on whether it contributes to the returned field count). ",
" In that event, we examine variable c to determine whether there was a closing ] where we expected to find one, and we use the character count recorded in n to verify that all characters of the string were parsed (so that str[n] refers to a string terminator).",
"\nYou may at this point be wondering at how complicated and cryptic that all is. ",
" And you would be right to do so. ",
" Parsing structured input is a complicated and tricky proposition, for one thing, but also the scanf family functions are pretty difficult to use. ",
" You would be better off with a regex matcher for cases like yours, or maybe with a machine-generated lexical analyzer (see lex), possibly augmented by machine-generated parser (see yacc). ",
" Even a hand-written parser that works through the input string with string functions and character comparisons might be an improvement. ",
" It's still complicated any way around, but those tools can at least make it less cryptic.",
"\nNote: the above assumes that the index can be any string of up to three characters. ",
" If you meant that it must be numeric, perhaps specifically a decimal number, perhaps specifically non-negative, then the format can be adjusted to serve that purpose.",
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"Kahlestan\n\nKahlestan (, also Romanized as Kahlestān; also known as Kūlestān) is a village in Lat Leyl Rural District, Otaqvar District, Langarud County, Gilan Province, Iran. ",
"At the 2006 census, its population was 532, in 149 families.",
"\n\nReferences \n\nCategory:Populated places in Langarud County"
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"It’s also got some bad ones. ",
"That’s understandable, but a couple in particular have frustrated me – because they’re attacking the book for having a LGBT character.",
"\n\nI won’t apologize for that. ",
"Far from it, in fact. ",
"I wish I’d done more with it; I didn’t put in as much content on the subject as I wish I had. ",
"I should have explored it in more detail to make it feel more authentic and help the characters be more accessible to LGBT readers who might be interested.",
"\n\nI’ll try to learn from this experience and include more LGBT content in my future books. ",
"People of all genders and sexual orientations deserve positive representation.",
"\n\nBrett, thanks for the link. ",
"That’s very similar to my own situation. ",
"My intent was definitely to be low-key about it since the character’s sexuality is not integral to the plot, but I think some people will definitely find it upsetting regardless of which approach is taken.",
"\n\nI picked up this book on Amazon after only reading the summary. ",
"I was pleasantly surprised to find out it had LGBT content since besides Urban Paranormal and Fantasy, LGBTQ fiction is my preferred genre. ",
"I haven’t finished the book yet, but I’m looking forward to seeing how the story plays out and I can’t wait to purchase and read the next book in the series to find out more about the Attunement systems and the other spires, as well as seeing more LGBTQ content! ",
"(^_^)\nSincerely,\nAndre’\n\nLoved the book, didn’t too much care for the LGBT aspects, but they were understated enough I didn’t mind them. ",
"That said, it’s your story to tell as you like, but I’m afraid if you start shoe-horning more into the next stories just for the sake of having more, I won’t be choosing to follow. ",
"No, I’m not homophobic, I don’t hate people who have those attractions, but as much as I enjoy your writing, it’s not a subject I care for. ",
"In case you like feed back from fans with different points of view…\n\nSome of my characters happen to prefer people of the same sex – or just don’t care about the sex of their romantic interests. ",
"I’m not going to change that.",
"\n\nThis means that you’ll still end up seeing more LGBT content here and there. ",
"There are also characters that prefer the opposite sex, so hopefully you’ll enjoy that content more.",
"\n\nI don’t intend for romance to be the primary focus of my books in general. ",
"It’s just one type of relationship that I intend to explore. ",
"That said, there definitely will still be some scenes with LGBT romantic content here and there.",
"\n\nIf just having LGBT content in the story hurts your interest, I hope you still find elements you enjoy in the story. ",
"If not, there are plenty of other great novels out there and I hope you find ones that cater to your own interests.",
"\n\nI feel that I must echo Kobin’s sentiment. ",
"I also don’t prefer to read about LGBT relationships and since you intend to include them in your future books, I will need to hold off on reading those future books. ",
"When I read a book, I of course visualize the character’s, the scenes, etc. ",
"Since LGBT interactions are not ones I wish to visualize, I will sadly need to stick to only book one, which was an excellent read.",
"\n\nEven if you don’t read my own books in the future, I appreciate that you were willing to give Sufficiently Advanced Magic a shot.",
"\n\nI would encourage you to consider reading other books with LGBT content in the future and challenge yourself – there are a lot of great books out there that have LGBT characters, and I think you’re doing yourself a disservice if you exclude anything that has any hint of that sort of content.",
"\n\nThat is, of course, entirely up to you. ",
"Everyone has things they like and dislike in fiction, and I understand that people have different comfort levels with styles of relationships that differ from their own.",
"\n\nI just finished “Sufficiently Advanced Magic (SAM),” and was visiting your blog to learn more about the sequel. ",
"The book was a fun read, and I gave it four stars on Amazon.",
"\n\nThanks for including a LGBTQ character. ",
"How surprising as most authors are not that courageous, and for the main character to be, well that was great. ",
"It’s fun to have a character of my sexual orientation. ",
"Corin’s reaction to being asked to be ball was very realistic too.",
"\n\nI’m looking forward to reading your other books, and especially to the SAM sequel.",
"\n\nI can’t say that I noticed excessive use of dashes in SAM; sometimes editors have to complain about something. ",
"I’m sure they said Hemingway was too laconic.",
"\n\nThank you for the kind words. ",
"I’m glad you appreciated the inclusion of an LGBT character, and that you felt Corin’s reaction was realistic. ",
"I’m glad I kept that scene in the book, and I’m looking forward to writing the aftermath in the sequel.",
"\n\nI find the LGBT themes in the book very subtle, i don’t see how anyone would find it worth complaint\n\nso the LGBT characters are Corin, Jin and Keras? ",
"right?",
"\n\ni think Corin is only slightly Bi ( Mostly because i ship him with Marissa) his reactions show that his is really open minded (or that their society is open minded), but his reaction at the end of the book made me think he never had any attraction or feelings for Jin\n\nJin seems he could be Gay or Bi\n\nKeras sounded Gay, but it could be he is really sexually open.",
"\n\nThe book was great, but the Attunement cliffhanger for one year will kill me.",
"\n\nI agree that they were definitely pretty subtle in the first book, but I guess that was enough that some people were upset.",
"\n\nThus far, those are the only characters I’ve called out as being LGBT. ",
"There may be others.",
"\n\nCorin is asexual, but he’s panromatic, meaning he can be romantically attracted to anyone regardless of their sex or gender. ",
"Even more specifically, he tends toward being sapioromantic, meaning that he’s most interested in people who he finds intellectually stimulating.",
"\n\nMarissa is absolutely a valid ship for Corin; the chemistry between the two of them was deliberate. ",
"I won’t say if that ship will ever sail, but I agree that they make a good pair option.",
"\n\nI don’t want to say too much about the details of the interests of other characters since they haven’t been clearly addressed in the story yet.",
"\n\nI’m glad you enjoyed the book. ",
"I’ll try to get the sequel out earlier if I can do so without hurting the quality. ",
"=)\n\nGreetings! ",
"First, your book here is not the normal genre I read, BUT….you got my attention. ",
"At the very least I finished the book, which is more than I can say for the other book I read today. ",
"40% through, I just quit and deleted it from my library. ",
"Just a bad story. ",
"I might be straight as an arrow, but I also have an open mind. ",
"Don’t let the people with the closed minds stop you, please.",
"\n\nSo, I don’t have any problem at all with the LGBT content, wish more authors had the courage to do it. ",
"It adds more dimension to the story for one thing, and is a bit more realistic in this day and age…..(sorry for the cliche there). ",
"You have inticated that Corrin is, well, lets say unsure about his sexuality? ",
"Well, nothing wrong with him going both ways right…I mean its a better ballgame if you can switch hit? ",
"I agree with previous post about Marissa though. ",
"I got the impression at some point in the story that she has the hots for him, but I also got something else at some point, and I can’t figure out where it happened. ",
"Mostly it’s like a voice whispered in my ear ” She’s his Guardian….” ",
"and I said,”well hell I know that…..”wait…I did know that….how the hell did I know that? ",
"lol Really I think she might have a bad case of “I’m the one meant to protect you-ism”….lol. ",
"She might be the right ship indeed, could she not also end up being his retainer? ",
"Also, seems he’s screwed now for a date to the ball, he could ask Derrek right? ",
"Anyway, I actually really love the world build here, and the structure you built for magic. ",
"Attunements? ",
"hell yeah, where can I get one of those? ",
"Well written story and I love pretty much all the characters. ",
"one thing though…..I’m really hoping that at some point something is going to happen to Corrin that will really raise his power and abilities.(maybe it already has, that unknown attunement he just received?)",
"\nI would like to see him change the way people (read that as “the world”) see Enchanters…and most of all, I want something to happen that will cause his father to have to eat a very large plate of crow, followed by an ample serving of humble pie.",
"\n\nNice work, really nice, Gonna hit amazon and grab one of your other books and see what’s what. ",
"Even if I don’t like that story, I will be reading the next in this series, really want to see where you take this. ",
"Thanks for holding my attention and granting me a really great ride.",
"\n\nA bit late on this topic… but Corin seemed not very interested is physical contact or sex, going so far as to mention that fact numerous times. ",
"As I read the Jin interaction, I read Corin to be more gender neutral, he liked Jin, trusted him, found him attractive, “why not go to the dance”. ",
"To me it was more him considering an aspect of growing up he hadn’t considered before and gender wasn’t a defining consideration.",
"\n\nJust finished, and really enjoyed, “Sufficiently Advanced Magic”. ",
"Looking forward to the next one… my soul make the sound of absolute suffering when I saw 2018 though 🙂\n\nLGBT elements in a book are neither a plus or minus to me when handled well. ",
"Only a negative when handled “poorly”. ",
"Sometimes it feels like its just a checkbox to have such elements and they can be easily overplayed or stereotyped. ",
"To me, the elements in your book blended in seamlessly into the story.",
"\n\nAfter reading a whole mess of urban fantasy lately that devolved from sex being part of life to being the only thing that drives all the main characters and the predominant theme of the book, I really liked having an asexual lead. ",
"When I realized Corin was essentially heading off to college, I had worries the book would become more about their sex lives than anything else.",
"\n\nSalutations,\nI just finished SAM! ",
"I enjoyed the book immensely, being a dnd/anime/fantasy junkie I found the gaming/magic/tower elements you included really refreshing as a ‘read’ rather than a ‘watch’ or ‘play’……and I may have just used my entire forward slash allotment there…but on to the meat of the message:\n\nI saw your post, and in the face of those bad remarks, I really wanted to echo some of the other comments about your handling of Corin’s love life:\n\nThank you.",
"\n\nCorin is a delightful breath of fresh air, and I find his outlook and encounters ring far truer to me than most any given awkward teen romance in fiction. ",
"I enjoy seeing Corin establish new connections in tune with the thoughtful, witty, and introverted character I read him to be. ",
"Not being sexual fits him to a tee, and it’s fun to watch him puzzle his way through being outside his head with people. ",
"I’ll admit though, being incidentally LGBT-oriented myself, I was warmly (like, warm and fuzzy) surprised at your inclusion and handling of Jin and Corin’s date invite – that is to say that the scenario happened at all, and that it wasn’t made into a big deal in the book (beyond Corin’s own rather charming mental gear change; Corin being ‘asked out’ by anyone). ",
"It’s the kind of situation I wish I’d read more of as a misunderstood melodramatic misanthropic teenager, and I still hope to see more of its kind in the genres I love – so again, thank you.",
"\n\nJin was a bit of a surprise and disappointment but not because of the same sex aspect. ",
"I saw Corin as almost asexual- he describes himself as simply having no interest. ",
"Not liking or wanting to be touched, etc…ect..\n\nTo me Marissa seemed like a great potential relationship (not because if sexual orientation) because they could grow together, especially after her early experiences. ",
"They both seem a bit damaged had a past they would need to overcome to be able to have a real relationship. ",
"That and he was attracted by her strength and ability, not looks. ",
"Also, I’m a sucker for breaking class, race, and cultural barriers.",
"\n\nThat said, this book no more requires a “LGBT” tag than it does a “Romance” tag- A romantic scene does not make a book a Romance and neither does a innocent same sex attraction/exploration scene make a book LGBT.",
"\n\nIMHO write the full gamut of the often confusing, conflicted, human experience-\n\nCorin is, in fact, asexual – but he’s not aromantic. ",
"He’s not fully aware of this distinction himself yet; he’s still a teenager who is learning about his own interests. ",
"Thus, he could potentially have romantic engagements, he simply wouldn’t be interested in sex.",
"\n\nThere are a lot of people who saw chemistry between Marissa and Corin for the same reasons you did. ",
"I’m not saying I’m going to do anything with that in the future, but it’s not off the table. ",
"They’re skill teenagers; Jin asking Corin out on a date isn’t likely to be the only romantic involvement he has in his lifetime.",
"\n\nAgree with you about the tags completely. ",
"There’s not enough content for me to justify the LGBT tag, at least in the first book.",
"\n\nDefinitely planning to write a lot about the human experience in general, although I think tackling *all* of it might be a bit too ambitious. ",
"We have a lot going on. ",
"=D\n\nReading my post, I realized that I jumped right into the topic with saying. ",
"Fun book to read, which I enjoyed\n\nAlso disappointed was too strong a term- it’s not what I actually felt, more surprised. ",
"Perhaps because of the young lady he was avoiding from before his father pulled him out if school- I assumed some awkward romance attempt by one of them. ",
"I now realize that was binary thinking, this or that. ",
"Rather than focusing on the attributes he might find intriguing- funny, now matter how progressive we think we are, we often default to gender preferences as the first.",
"\n\nIt’s very easy to slip into binary thinking. ",
"Many fantasy novels encourage this sort of thinking, too, with clear good vs. evil and that sort of thing.",
"\n\nI’ll clarify the whole thing with the girl he’s been avoiding soon enough – that’s a pretty significant plot point, and a lot of people read it the same way you did. ",
"It’s been interesting to see how many people came to that conclusion.",
"\n\nI absolutely love that Corin is ace and Jin was okay with it. ",
"I feel like it’s so hard to get decent books with asexual characters because it always ends up being trivialized or “changed” because they’ve found their “one true love”. ",
"Corin not liking to be touched and just not thinking about romance really added that extra dimension to his character for me. ",
"I could really relate to him, and that made the book so much better.",
"\nJin-Corin is definitely my OTP though. ",
"I don’t think I’ve shipped anyone this hard, ever. ",
"When Jin asked Corin to the ball, my heart just about exploded. ",
"Thank you so much for that.",
"\nI mean, Marissa is nice and all, but SHE didn’t ask Corin to the ball. ",
"And Jin always manages to be next to/supporting Corin. ",
"I really hope they “kiss and make-up” eventually (haha, see what i did there?).",
"\nAs for Cecily, I thought there would be some past related to his father there. ",
"Like, they were both molested or something equally horrible. ",
"But that’s probably just me. ",
"Looking forward to how that turns out though.",
"\nEnough from me. ",
"I wish you all the best with your writing endeavors. ",
"Of course, that would be to my and any other of your readers’ benefit because we’d have more books to read available sooner. ",
"Nonetheless, please don’t break your hands. (",
"I assume you don’t type with your elbows…)\n\nP.S. The flirting between Derek and Keras was such a nice note to end the book on. ",
"BUT. ",
"THE. ",
"TWIST! ",
"I don’t think i would have seen that coming in a million years…\nAnyways, it made for an interesting cocktail of emotions to remember the book by.",
"\n\nSo, I read and really liked the book (discovered through amazon unlimited). ",
"One of the things I liked about it was the LGBT main character. ",
"Not because I can identify with him, but because it was a refreshing change of pace from the normal. ",
"And seriously, kudos for being the first author that I know of to have a LGBT main character in a fantasy book. ",
"I almost wrote about it and how I thought it was great but was worried about it attracting negative attention.",
"\n\nThanks for writing Sufficiently Advanced Magic as I enjoyed it immensely!",
"\n\nNow, to the whole Bi/Homosexual aspect to the book the only real problem I had with it was that it was more of a surprise than anything else… almost misleading in a way. ",
"So I can see why some people would take issue with that whether they are homophobic or not, it certainly made me pause while reading the book. ",
"I paused mainly because I was surprised and it made wonder if I should keep reading because authors usually bomb the romance angle in books regardless of the genders involved, unless its a romance or G.R.R.Martin novel and they usually just go overboard in those cases ( 😛 ). ",
"I kept reading because I really liked the novel up to that point and I wanted moar! ",
"But people do like to read about (or with) a MC that is similar to them irregardless(?) ",
"of other characters or relationships in the book.",
"\n\nTo be honest, I bet if people knew ahead of time that the MC was bi would have toned down the response from *most* people. ",
"There is no pleasing everyone! ",
"😛\n\nI understand being surprised, but I don’t feel there was anything misleading in the text. ",
"Certainly there was nothing deliberately so; Corin’s preferences were not intended to be a “twist”. ",
"The reveal was treated as ordinary because it is intended to come across as ordinary and not a big deal, which is appropriate for the culture the story takes place in.",
"\n\nTo be clear, Corin is not homosexual or bisexual. ",
"He’s asexual, but he’s not aromantic. ",
"As a teenager, he’s not exactly clear on all this yet himself, which is something that he’s going to need to figure out as the story progresses – but it’s not something I consider a major part of the plot.",
"\n\nConsequently, that’s why there’s no LGBT tag on the book – I don’t feel there’s enough LGBT content to justify that, in my opinion, and I wouldn’t want a LGBT reader to pick it up expecting a LGBT romance and be disappointed by the light amount.",
"\n\nYou’re absolutely right that there’s no pleasing everyone, and I’m glad you liked the book in spite of your surprise at the protagonist’s preferences. ",
"I hope we reach a point where a character can prefer any sex (or no sex) without it being a “twist” or “reveal”.",
"\n\nAndrew, am currently listening to Sufficiently Advanced Magic and had no idea it had LGBTQIA content as I try to go into books blind without reading the summary – thank you so much for presenting a positive LGBTQIA character in fantasy fiction. ",
"I’m so tired of being represented as the villain or a single paragraph token character who never appears again – hopefully this will show young LGBTQIA people they don’t have to be entirely unrepresented in mainstream fiction. ",
"Also love the setting, magic system as characters!",
"\n\nHello Andrew,\nas many other here i just finished SAM and really liked it. ",
"I really looking forward to hear the second “Audiobook” to come out. ",
"Sadly in my language there are not much “RPG”/”Game” like storys so im lucky to try yours out.",
"\n\nTo be honest, the LGBT parts are nothing i like to read/hear, because it is not my way of thinking and feeling. ",
"I even don´t “read” storys with female MP because i dont like to see storys that feel strange to me. ",
"I´m maybe in your perspective to simple minded. ",
"Theres no way i can prove you wrong. ",
"In short. ",
"I stoped hearing as the date between Jin and Corin where arranget.",
"\n\nIt is indeed very importend that there is content for people who like LGBT. ",
"And to be honest, is just a normal, other than mine, but normal! ",
"way of sexuality.",
"\n\nFor the Twist… i finished it anyway because the world, your humor, the asexuality (that dont bother me in any way, i rather have nothing than even a bad hetero part… and to be honest… i don´t have read many good sex parts in books anyway… i like it when its as less as possible because its to often akward) and especially your attunements. ",
"I love shounen (who have thougt so..) and you a little bit promised something like that (that he will become more powerfull) so i can´t let the secont book unheard… or so…\n\nThe LGBT parts in this book are so light that even i could ignored them. ",
"I feel lucky that the parts where so light. ",
"I would be very sad if i have`t missed souch a good book because of that. ",
"I have perceived that the second book will not be so light… i hope it will still be not toooo much of it so it´ll be able for me to hear it.",
"\n\nThank you very much\nHeiko\n\nPS. ",
"for the real twist…. ",
"it get me good. ",
"Haven´t see it coming so i appreciate it.",
"\n\nI’m glad you finished the book even if you didn’t like that particular scene. ",
"I hope that you can find a way to empathize with the characters in future books even if they don’t have the same sexuality that you do.",
"\n\nSir. ",
"I am currently reading SAM and must say that I was enjoying the book more than any book I’ve read in recent history. ",
"And then shocker, the homosexual element was introduced. ",
"I have read other series with homosexual characters and never really enjoyed the way it was thrust into the limelight, kind of forced into the reader. ",
"I love the interaction between a man and a woman. ",
"That romance is one of the reasons I read.",
"\n\nThat being said, this is the first time I’ve felt compelled to write a review because of it. ",
"Here is the issue: this series has the potential of being one of my favorite fantasy series of all time. ",
"It is right now (40% of book one) running along side Brent Weeks Night angle Trilogy and that is incredible company to be in. ",
"I so hope this LBGT theme doesn’t distract and or detract from this series. ",
"Please realize that you have fans that are not LGBT and we have value too.",
"\n\nI advocate for Lgbt community. ",
"I am extremely liberal in my views. ",
"Live and let live. ",
"But I have trouble reading a book from the perspective of a gay character. ",
"I guess some would say I have growing to do there. ",
"I am the guy that fiercely fights for gay rights but would be deeply disappointed if my children turn out to be homosexual.",
"\n\nI love the world you have created Andrew. ",
"I love the magic system and I love the intelligence of Corrin. ",
"I honestly was enjoying the lack of love interest for him. ",
"I believe that he hasn’t met his true interest yet. ",
"His visions seem to hint at a much grander love interest with the goddess or someone from one of the other provinces. ",
"The main conflict hasn’t even been revealed imo. ",
"At this point, he is just scrambling to get acquainted with magic and demonstrating that his craftiness is as effective as the more widely accepted powers. ",
"Perhaps this is one of the underlying themes of your series: to assume is to be proven wrong; or, to have prejudice is to miss out on something worthwhile? ",
"Just rambling at this point. ",
"I will carry on and read the rest of this book regardless. ",
"I hope that the series continues to develop as needed and the homosexual themes do not become the dominant theme simply to appease one of your reader groups. ",
"If it is needed, so be it. ",
"But my fear is that because so many in the LBGT community need representation and have embraced this book and your introduction of a possible gay bi main character…then you will feel compelled to push him all the way there to appease them.",
"\n\nThere will continue to be LGBT+ content in my books. ",
"I’m sorry that detracts from the experience for you, but I’m not going to change elements of the setting (or the preferences of the characters) because they make some people uncomfortable.",
"\n\nI would also hope that for liberal readers like yourself, maybe reading about a society where LGBT+ people aren’t as overtly persecuted might help you consider why you have your own biases, and if those biases are fair. ",
"I had a hard time reading about LGBT+ relationships myself when I was younger, because I’d internalized a lot of what popular culture, religious groups, and political groups had told me – and it took me many years to work through those biases.",
"\n\nI would have not enjoyed reading about Corin and Jin’s relationship when I was younger, and to me, that’s a big part of why it’s important. ",
"I want people who have biases like I myself did to be able to read that and question their own views.",
"\n\nI also want people who are used to being persecuted for their own sexualities (or, in Corin’s case, lack thereof) to have examples in literature they can read and enjoy. ",
"There are *very* few asexual protagonists, and I’ve seen how important representation can be to marginalized groups.",
"\n\nIf it’s simply that you’d like to see some heterosexual relationships in addition to LGBT+ ones, well, there will be some of those in there (including with the narrators of other books in the same universe). ",
"For example, I’ll be writing a book from Keras’ perspective in the future, and it’s likely that most (or all) of his love interests will be female.",
"\n\nThat all being said, romance will never be the primary driving force behind any of these books. ",
"In terms of relationships, this series is much more about the bonds between friends than romance.",
"\n\nJust listened to the audiobook of the first one. ",
"I loved it. ",
"It was one of the only books I have left a review for on goodreads and I have suggested it to all of my friends. ",
"I’m actually just starting the second one and am stoked to see the development of the story and characters.",
"\n\nCorin is me. ",
"I am obsessed with this character. ",
"He approaches the magic system in the same way I see myself approaching it if I were to have an attunement. ",
"I love hearing his thoughts on everything and how interested he is in the mechanics of the world around him.",
"\n\nWhen I was first reading, I got the hunch that Corin was asexual, but I figured it was too good to be true. ",
"Then sure enough, he gets all twitterpated when Jin asks him to the dance and I thought “Oh darn. ",
"Here it goes again. ",
"Another potential asexual character turns out to be gay.” ",
"I have nothing against gay characters, but as an asexual living in a world of sexuals, it’s easy to feel left behind or misunderstood when every character you read about ends up finding someone eventually. ",
"Sexuals often assume that asexuals just haven’t found the right person yet and that maybe they just need to explore other avenues (like try out men instead of women) and then surely they will find someone. ",
"Even in the show Sense8, which was directed by a transgender woman, they tried extremely hard to represent all sides of the LBGT community really well, but as an asexual I felt completely forgotten.",
"\n\nReading here, however, that Corin is ace makes me SO happy. ",
"I thought he would end up being gay and so I just moved on, but now I am completely elated. ",
"I know sexuality can be fluid, so I get that anything can happen, but I’m really hoping that Corin STAYS asexual. ",
"Meaning, I’m kind of hoping he doesn’t “finally meet that special someone” and fall in love, but rather his life ahead of him is focused on relationships in general and forming meaningful bonds in ways that work for him.",
"\n\nThere is an ocean of almost exclusively asexual experiences that sexuals that I would love to see him go through. ",
"Like the frustration of seeing everyone around him finding someone and feel a bit left behind or unneeded and having to learn how to cope with that. ",
"Or maybe having people very interested in him, and him trying to make it work but understanding that something is not working in him that seems to work naturally in others. ",
"Or after he understands what he is, he apologetically tells them he’s asexual but they don’t understand it and try to pressure him into trying something out with them and the ensuing anxiety and confusion that results is difficult for him. ",
"Or maybe see him get irritated at his friends because of their attempts to get him to admit that he is gay, but in their attempts to support him, they end up just frustrating him because they can’t seem to wrap their minds around the idea that he just isn’t attracted to anyone. “",
"Corin, we love you and you can tell us anything! ",
"It’s okay if you’re gay.” “",
"I’ve told you already, that’s not it…” “Okay, well, just know that we don’t care, and we love you no matter who you love.” “",
"I get it. ",
"I just don’t think you guys get that I’m not hiding anything.”",
"\n\nAgain, I don’t know what will happen with Corin, and it is your story. ",
"If you feel that Corin’s path is different than these, I am excited to see what that will be. ",
"I just feel like I am Corin’s spirit animal and this is maybe the first time I’ve felt any hope at seeing a character that I can finally relate with on a sexual level (or lack thereof).",
"\n\nWow, didn’t mean to write that much… sorry. ",
"I just love this and I am excited to see what happens, that’s all.",
"\n\nThanks for the heartfelt comment. ",
"I absolutely see where you’re coming from. ",
"I understand how rare it is to see asexuality represented in fantasy, and I’m glad that you were able to empathize with the character.",
"\n\nI really appreciate your suggestions, and I’ll see if I can incorporate some of those suggestions in ways that make sense for the setting. ",
"There are some similar things in book 2 already, and I’m curious what you’ll think of that.",
"\n\nI definitely intend for Corin to remain asexual, and I intend to make it clear that there’s nothing wrong with that. ",
"I do want to make sure it’s clear that I make a distinction between asexual and aromantic, though, and he may have romantic interests that are not sexual in nature. (",
"These are still going to be minor elements, but I think asexual characters who aren’t aromantic are important to represent, too.)",
"\n\nI will most likely have some characters that are both aromantic and asexual in the future, too.",
"\n\nI love your book! ",
"I’m glad I ordered it on Amazon and I have the next book coming in the mail!",
"\nFor me it has rivalled some of the great books that I have read, Eragon, Amulet of Samarkans, etc. ",
"It even came close to being my favorite book, Name of the wind!",
"\nI shipped Corin and Jin before Jin asked Corin to the ball and the feeling I got from their relationship is inexplicably exuberating!",
"\nI have resolved to put more LGBTQ+ characters in my D&D sessions."
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"Patients' experiences of the recovery period 12 months after upper gastrointestinal surgery.",
"\nThe aim of this study was to describe and explore participants' experiences of their recovery from upper gastrointestinal surgery and being recovered or not 12 months following their operations. ",
"A hermeneutic approach was used to understand participants' experiences and situations. ",
"Fifteen participants were interviewed at 12 months postoperatively. ",
"According to participants, the year that had passed was experienced as being \"pale and gray.\" ",
"Themes that were identified included feelings of doubtfulness, others' concern, and disappointment; never feeling quite well and having to adapt to new circumstances; feelings of being changed; and feelings of becoming free from illness and regaining strength. ",
"Being trapped in suffering meant that participants' lives had lost meaningful values. ",
"They felt disappointed because of physical discomforts and thoughts about disease and death. ",
"Recovery was felt when their physical discomforts decreased, and they felt free from doubts and \"difficult\" thoughts about illness and death. ",
"The recovery process can be understood as a movement between darkness and light."
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"The present invention relates to a method for making alkylhalosilanes. ",
"More particularly, the present invention relates to a process involving the reaction of methyl chloride and powdered silicon in the presence of a copper-zinc-tin catalyst.",
"\nPrior to the present invention, methylchlorosilanes were made by effecting reaction between powdered silicon and methyl chloride in the presence of a copper catalyst, as shown by U.S. Pat. ",
"No. ",
"2,380,995, Rochow, assigned to the same assignee as the present invention. ",
"Improved results were achieved by utilizing a fluidized bed reactor, as shown by Reed et al, U.S. Pat. ",
"No. ",
"2,389,931, also assigned to the same assignee as the present invention. ",
"Further improvements in the production of particular methylchlorosilanes were achieved when zinc was used in combination with copper catalyst as a promoter as shown by Gilliam, U.S. Pat. ",
"No. ",
"2,464,033. ",
"Gilliam teaches that a proportion of from about 2 to about 50% by weight of copper in elemental form or as the halide or oxide, and preferably 5 to 20% and from about 0.03 to about 0.75% by weight of zinc in the form of zinc halide, zinc oxide, or zinc metal, or mixture thereof, where the weight of copper and zinc are based on the weight of silicon, can be used as a promoter for making dialkyl substituted dihalogenosilanes, such as dimethyldichlorosilane in the direct reaction between silicon powder and methyl chloride.",
"\nSubsequent to the investigation made by Gilliam, Radosavlyevich et al, found that micro quantities of silver added to contact masses resulting from the reaction of powdered silicon and methyl chloride in the presence of cuprous chloride decreased the yield of methylchlorosilanes, while tin and calcium chloride increased the rate of formation of methylchlorosilanes as reported in \"Influence of Some Admixtures on the Activity of Contact Masses for Direct Synthesis of Methylchlorosilanes\", Institute of Inorganic Chemistry, Belgrade, Yugoslavia, (1965).",
"\nAs utilized hereinafter, the term \"methylchlorosilanes\" includes dimethyldichlorosilane, which is the preferred methylchlorosilane, and a variety of other silanes such as tetramethylsilane, trimethylchlorosilane, methyltrichlorosilane, silicon tetrachloride, trichlorosilane, methyldichlorosilane and dimethylchlorosilane.",
"\nIn addition to the above methylchlorosilanes, \"residue\" is also formed during the production of methylchlorosilane crude. ",
"Residue means products in the methylchlorosilane crude having a boiling point >70.degree. ",
"C. at atmospheric pressure. ",
"Residue consists of such materials as disilanes, for example, symmetrical 1,1,2,2-tetrachlorodimethyldisilane, 1,1,2-trichlorotrimethyldisilane, disiloxanes, disilmethylenes and other higher boiling species, for example, trisilanes, trisiloxanes, trisilmethylenes, etc. ",
"In addition to residue, those skilled in the art also are interested in T/D weight ratio of the methylchlorosilane crude. ",
"The T/D ratio is the ratio of methyltrichlorosilane to dimethyldichlorosilane in the crude methylchlorosilane reaction product. ",
"Accordingly, an increase in the T/D ratio indicates that there is a decrease in the production of the preferred dimethyldichlorosilane.",
"\nAlthough as taught by the prior art, while zinc or tin can be valuable promoters for copper catalyst, or copper-silicon contact mass in the reaction between powdered silicon and methyl chloride, it has been found that the rate of crude methylchlorosilane formation and the T/D ratio are often unsatisfactory.",
"\nWhen defining a rate constant for crude methylchlorosilane formation, the term \"K.sub.p \", or \"reaction rate constant for methylchlorosilane product\" is often used by those skilled in the art. ",
"A more detailed derivation of K.sub.p, is shown below immediately prior to the examples.",
"\nK.sub.p values can be obtained using an apparatus as shown by FIG. ",
"2. ",
"On a relative scale, when a mixture of copper and powdered silicon containing 5% by weight of copper is used to make methylchlorosilane, a \"K.sub.p 38 (grams silane/grams silicon, hr) having a numerical value of about 13 can be obtained. ",
"A K.sub.p of 16 can be obtained from a mixture of powdered silicon containing 5% by weight copper and 0.5% by weight zinc. ",
"A K.sub.p of 45 can be obtained when a mixture of powdered silicon containing 5% weight copper and 0.005% by weight tin is reacted with methyl chloride.",
"\nAlthough the above K.sub.p values indicate that tin promoted copper catalyst can provide a superior methylchlorosilane formation rate when used with powdered silicon and methyl chloride, it has been found that the selectivity of tin promoted copper catalyst can be inferior to zinc promoted copper catalyst.",
"\nAs defined hereinafter, the term \"selectivity\" means the ability of a catalyst to maximize the production of dimethyldichlorosilane, as shown for example by a reduction in the value of the T/D ratio and a reduction in the % residue. ",
"It is found, for example, that although a higher K.sub.p can be obtained when tin is utilized with copper to catalyze the reaction between powdered silicon and methyl chloride, a significant increase in the T/D ratio is also effected, as compared to the use of a copper catalyst promoted with zinc.",
"\nThe present invention is based on the surprising discovery that direct method reactions between powdered silicon and methyl chloride in the presence of an effective amount of a copper-zinc-tin catalyst as defined hereinafter, can provide K.sub.p values about twice that shown for tin promoted copper catalyst as discussed above, while simultaneously substantially improving the selectivity over zinc promoted copper catalyst and over tin promoted copper catalyst. ",
"More particularly, optimum selectivity and maximum K.sub.p values can be obtained by practicing the direct method with a mixture of powdered silicon, copper, tin and zinc containing 0.5-10% by weight of copper, based on the weight of silicon, where the copper can be in the free state or in the form of a copper compound as defined hereinafter, with 0.01 to 0.5 part of zinc, per part of copper and 200-3,000 ppm of tin relative to copper, where both zinc and tin are also expressed in terms of weight of metal, although optionally employed as a zinc compound or a tin compound, as defined hereinafter."
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"Why do I love Finn and Rachel? ",
"I love them because they've cultivated this bond and relationship where they're the other's only true friend. ",
"I love that Finn loves every part of Rachel, right down to her sequined leg warmers. ",
"I love how Rachel finds Finn's naivete endearing. ",
"I love that Finn is always rooting for Rachel. ",
"I love their banter. ",
"I love the hallway chats. ",
"I love the fact that they like each other because of their quirks, not in spite of them. ",
"Most of all? ",
"I love the chemistry between Lea and Cory that makes the pairing of Finn and Rachel so endearing and real.",
"ManoloChoo (Nicole)\n\nThe first time I watched Glee, I fell in love with Finn and Rachel. ",
"It was inevitable, really—Finn being the hot male lead and Rachel the stunning young ingénue everyone roots for. ",
"Their chemistry in undeniable, and their developing friendship is beautiful. ",
"I have never been inspired by something as much as I have been by their relationship—I think 20-something fics is proof of that The ups and downs of their relationship, as well as the struggles they face individually, make me want to root for them, and I think it’s clear that their story is one that will continue for a long time to come. ",
"For me, Glee would not work without Finn and Rachel, because they bring out the best in each other. ",
"Finn grounds Rachel when she has the tendency to get out of hand, while Rachel builds Finn up when he needs support. ",
"They are each other’s checks and balances, and to put it simply, they work perfectly. ",
"They may seem like complete opposites at first, but when it comes down to it, they both want the same thing: to be the best that they can be, and together, they can do that.alifab (Ali)\n\nThe first time I saw Finn and Rachel in the same scene, I instantly fell in love. ",
"Maybe it was the height difference or Rachel's crazy eyes or Finn's wtf face, but everything about them was perfect to me. ",
"They each have their flaws and imperfections, but what one lacks the other has, and vice versa. ",
"They teach each other to be better people and from each other they've learned to love, to laugh, to be themselves.. because the real Finn is the Finn Rachel loves and the real Rachel is the Rachel Finn loves. ",
"We've only been given 13 episodes, but I'm excited to see where they both go in the future.hotairballoon (Victoria)\n\nFinn isn’t the sharpest tool in the shed and sometimes doesn’t understand the words Rachel uses, but never once has that bugged her and she has never put him down for it. ",
"She’s a bit of a diva that’s never had a real friend or someone to believe in her, but he likes her for who she is and he roots for her. ",
"She encourages him to follow his dreams despite what everyone else tells him. ",
"He likes her for who she is despite what other people think of her. ",
"I could go on forever about why I love them, because what’s not to love about them? ",
"Lea and Cory have amazing chemistry and always bring their best in their scenes. ",
"They have many more wonderful moments ahead of them and I can’t wait to see what this show has in store for them.ordinaryday (Jen)\n\nI love how Finn was scared of Rachel at first, but then he learned to love her craziness, and how they started fast, kissing in the second episode, but then developed this friendship, and how they support each other and how, even in an age when people are still trying to figure out what they are, instead of trying to change each other, they both accept and like each other exactly the way they are. ",
"And I love how they say weird things to each other, and it's hilarious and adorable at the same time. ",
"They can make me laugh histerically, melt completely or cry like a baby. ",
"They are magic and I just love everything about them.",
"AmanditaSininho (Amanda)\n\nI love Finn and Rachel together because, well lets face it they would be perfect for each other. ",
"I think they would compliment each other well because Rachel is organized, smart, dedicated. ",
"She really knows what she wants and wont stop until she gets it. ",
"I think Finn needs someone like that in his life because he seems like a laid back kind of guy and some of her traits could rub off on him. ",
"Also you have to admit just looking at them you know they would make such a cute couple.",
"David'sgirl12 (Krystal)\n\nFrom the moment I watched the Pilot in May, I thought wow how many episodes until Finn and Rachel get together? ",
"They are amazing together, there is a reason they were established as the main couple of the show by RM. ",
"They have great chemistry and are the only true friend either one of them has most of the time. ",
"They each understand that the other has interesting quirks but instead of disliking or trying to change those, they embrace them. ",
"They are truly a couple that is a great example of what a couple should be.",
"Slexie4ever (Whitney)\n\nWhat I love about Finn and Rachel, aside from their amazing chemistry, is that they love and understand what is already so great about the other person. ",
"Finn not only likes Rachel, but he likes the things that make Rachel Rachel, like her sequined leg warmers. ",
"Rachel knows that Finn's not the brightest, but she never dumbs things down for him, and never calls him a moron. ",
"Instead she encourages him... they encourage each other because they see their potential. ",
"And, at the end of the day, they are there for each other. ",
"Their height difference is also adorable.",
"Kyls (Kylie)\n\nTo me Finn and Rachel are like the perfect match. ",
"Finn is that quiet, not-so-smart guy, who is supposed to be a leader but is rather a follower, because he doesn't really believe in himself and just tries to please everyone around him. ",
"Rachel is quite the opposite as she is loud and smart, wants to be a leader, believes in herself and her talent and tries to get her way depite what everyone else wants or says, but isn't accepted by everyone around her because of her diva-like attitude. ",
"Both of them are looking for someone who takes them for who they really are despite all of their faults. ",
"Therefore I think they complete each other in a way that no one else around them could.k_1234 (Kiki)\n\nFinn and Rachel are an unconventional couple in that he's the popular jock with tons of friends, while she is the talented outcast who doesn't seem to belong anywhere and has no friends. ",
"I love them as friends and a potential couple because they are both completely honest with each other. ",
"Rachel never hides that she has feelings for him and even calls him out when he tries to back down from her. ",
"She's a strong, hard-headed woman who is fighting to become the star she knows she can be. ",
"But even with this goal to strive for, she still wants a leading man to share the spotlight with. ",
"Finn is sweet, caring, and even when he doesn't quite understand what she's saying, he appreciates her for who she is no matter what others say or think about her. ",
"When the truth about Quinn's baby is revealed, Finn is left devastated and hurt and in the end the only person who is honest with him is Rachel. ",
"Throughout the season we see Rachel get let down by Finn for choosing his popularity and reputation over Glee, but in the end, when it really matters and when there's almost no hope, he finally comes through for her. ",
"The moment he steps into the room at Sectionals, Rachel's face lights up and the hope that she had almost lost is returned to her the second he hands her that sheet of music. ",
"I'm looking forward to the rest of the season to see their friendship grow and develop into more because they would be an amazing couple.neonbliss (Kat)\n\nI love Rachel&Finn because they're extremely cute, when they share a scene together it's so visible that they would want that moment to last forever and they would want to say things they feel but can't for some reason, I feel them so much on that!Their duets are just LOVE, they've got such a chemistry that makes it all so intense, everything they do makes clear what they feel for each other, and I can't help it but love them more and more! ",
"<3Leyton4ever (Carmen)\n\nWhy I love Rachel/Finn.. They are the Classic Couple that I love to love, There shy, Honest, Silly, Real with each other. ",
"In my opinion they are mean to be. ",
"Finn can be himself with Rachel and Finn see’s something in Rachel that scares him, in a good way. ",
"Rachel has always felt something for Finn but when she heard him sing she fell in love now Finn is slowly but surely falling in love with her too. ",
"These two are my OTP come to life in opinion.",
"Smile_xD (Amy Louise)\n\nI love Finn and Rachel because they are like that song playing on the radio that gets stuck in your head, once its there is never leaves. ",
"Once you ship FR, you can never stop. ",
"They just have this ability to be cute and sexy at the same time. ",
"They understand one another on a level that none of the other characters do and on top of that they support one another. ",
"You will never hear Finn call Rachel a “diva” or Rachel tell Finn he is “stupid“. ",
"Sometimes one of them will make a mistake but its ok because the other one will be still be standing right by their side. ",
"In the simplest words, Finn and Rachel may not be perfect people, but they are perfect for one another.",
"Squeegee Beckenhiem (Sam)\n\nFinn and Rachel just click. ",
"They understand each other and share a special bond. ",
"As Lea Michele has stated, Rachel sees Finn for who he really is and that is one of the main reasons I adore this couple. ",
"They are so beautiful together and Lea and Cory bring out the best in each other.haydensgirl (Jess)\n\nBasically, the make me smile. ",
"The have a sweetness about them that appeals to the hopeless romantic in me. ",
"They also have flaws and aren't cookie cutter cutouts. ",
"To be so sweet and unassuming, they have scorching hot chemistry. ",
"I think Cory said it best when he said that Rachel represents what HE wants out of life and not what other people expect out from him. ",
"I think they both bring out the best in each other. ",
"shelleylovinu (Carmen)\n\nI love Finn and Rachel because of the way they look at each other and are there for each other no matter what. ",
"They always forgive each other, and help each other out. ",
"Rachel doesn’t belittle Finn for being less-intelligent than her, and Finn doesn’t belittle Rachel for not being popular. ",
"They respect and admire what the other does and believes in, and they balance each other out so well. ",
"They are the focal point and the “Couple Extraodinaire” of Glee, and I can’t wait for them to be together forever.",
"EdieRose (Edie)\n\nFrom the start I knew that Finn and Rachel will have a connection and sparks will fly when they sing together. ",
"As the show goes on, I see their chemistry growing. ",
"Both their characters are so cute and adorable. ",
"Finn and Rachel are perfect together and together their love is like a song.jules! (",
"Jules)\n\nThere's just something about them. ",
"I can't quite put my finger on it, and I never really can when it comes to my favourite couples on TV. ",
"There's just that undeniable spark and connection that draws me in. ",
"Finn and Rachel make my heart fill with joy and they also break it into a million pieces. ",
"Their relationship has been filled with so many ups and downs, but my faith in them has never wavered, and their faith in each other, ultimately, didn't either. ",
"They need each other, they complete one another. ",
"Because of him, she has become a little more grounded. ",
"Because of her, he grew confidence and courage. ",
"They belong together, and it's as simple as that.mslat92\n\nI love Rachel/Finn as a couple because they are both dysfunctional, crazy teenagers who screw up all the time but still manage to find their way back to each other in the end. ",
"You can see that Rachel loves Finn and Finn loves Rachel and despite all the mixes that can come up on the show, they’re still a constant and in the end they’ll be together. ",
"Finn is delightfully dorky and the opposite to Rachel’s quick mind but she’s forever patient with him and loves him even though he messes things up occasionally and is like a hundred feet taller than her. ",
"And I love Finchel because you can’t help but fall in love with them. ",
"iana.costa (Iana)\n\nHe's the boy that likes her for everything she is, including the parts that even she doesn't like! \"",
"I like you\"..\"I actually like the way you usually dress..squinted leg warmers and stuff\". ",
"Since the first episode, it was so clear that these two were meant to be together, one of those couples you can define as epic. ",
"They are my second favorite couple on this show, and I've always supported them. ",
"Right down the line, it's been him and her! ",
"They are taking us on this amazing Journey, and I can't wait to see where it takes them and us.||michelle|| (Michelle)\n\nI love Finn/Rachel for many reasons but I ship them mainly based on the idea that they \"carry each other\" and help each other when it comes to their weaknesses, thus making the perfect combination that will lead them both to success. ",
"Finn's always there to help Rachel when she's down or not feeling loved, he always compliments her, and he’s her biggest fan. ",
"When everyone treats her badly and she feels unloved, he's there to tell her things like “I like you” or “I appreciate you” or “I’m rooting for you” or “you’re cool Rachel” or “there’s so many awesome things about you.” ",
"Also, he's the only person that can make her smile or laugh when she's upset. ",
"And he will always be there to tell her to be herself and not change anything about her because he loves her for who she is, as he did in Hairography. ",
"Rachel can also do many things for Finn. ",
"She can raise his ambition and help him fulfill his life long dreams. ",
"He gets his leader drive from Rachel, who will tell him things like “you’re really talented” or “you can't keep worrying about what people think, you’re better than all of them” or “you’re a leader Finn.” ",
"She pushes him to carry on. ",
"In addition, Rachel never makes fun of Finn for being stupid. ",
"Instead she helps him, like in the scene where he pointed his heart to the wrong side, she showed him the way rather than roll her eyes, laugh, and call him names. ",
"So I truly believe Rachel is Finn’s savior and can push and motivate him to do great things in the future. ",
"That is why I ship them, they're the perfect combination even if they are not the same person, they carry each other and that's what makes them one.foreveralways21 (Leyla)\n\nSince the very first preview for the pilot Finn and Rachel have been destined for each other. ",
"They are completley different people but at the center they're very much the same. ",
"Their souls match :] When you see them on screen or in a photograph it doesn't matter who else is there, your eyes are drawn straight to them. ",
"Their chemistry is unlike anything I've ever seen and the way that they can convey so much and tell such an amazing story with just a shared look is nothing short of amazing. ",
"They see each other for who they really are and not the fabricated images that they're pressured in to conforming. ",
"They see what's real and they genuinely like what makes each other unique. ",
"I am literally not able to comprehend why anyone would like them with anyone but each other, I don't get it. ",
"Finn and Rachel are exactly what Glee has been about from the beginning: being who you are and liking that person and embracing your differences with pride. ",
"To say that they are my OTP is the understatement of the century. ",
"Finn and Rachel are destiny and anything less than true love is simply an insult to them.nhlpfan (Lauren)\n\nDespite the fact I hated Finn when I first saw him, I quickly changed my mind. ",
"I was convinced he'd leave Quinn for Rachel and if it wasn't for Quinn lying to him he would have. ",
"I love how Finn several times told Rachel that he liked her. ",
"He was the first person to accept her with all her flaws. ",
"That's what made me fall in love with their dynamic. ",
"It might be cliché to some people, but nevertheless I'm rooting for Finn and Rachel to be together. ",
"They love each other and accept each other and no matter what they're there for each other. ",
"It always makes me smile to see them on screen. ",
"It makes me happy to see a love unfolding between two teenagers despite all the troubles they have to go through. ",
"Finn and Rachel bot captured my heart and I will always root for them to be together.",
"Blondezilla90 (Kathy)\n\nI'm not very good with words, especially if I have to explain my love for a ship, but I'll try nevertheless. ",
"Rachel&Finn are special, they touch me in a way not many ships do, when they sing together I get gooseflesh, I could watch them sing for hours. ",
"I love the fact that despite being an obvious OTP they never had it easy; every moment, every little thing was earned and not easily. ",
"I love how they can crack me up with a single line, or how they can make me cry when they fight, how they can make me squee when they share a romantic scene. ",
"I love the fact that they're the right mix between comedy & drama, bewteen insanity & seriousness, between heart & brain. ",
"They're simply the right mix, the right pair.ale-la-pazza1 (Alessia)\n\nWhy I like Finn & Rachel? ",
"Because they compliment each other and they bring out the best in the other. ",
"she has the drive where he lacks confidence and decisivness and he broadens her focus from just singing. ",
"he is mellow where she is intense, she is focused where he is distracted. ",
"she wont let him quit and he wont let her either.carly-hope (Carly)\n\nThere really aren't enough words to describe my love for Finchel, and I'm not sure that this paragraph properly articulates what I'm trying to say, but here goes. ",
"The thing about Finn & Rachel is that even when they are apart, they're together... because neither of them can ever truley be with someone else as long as they continue to keep one eye on the other. ",
"They're so connected and I just adore that aspect of their relationship. ",
"Simply put? ",
"I love everything about Finn & Rachel. ",
"Some claim they are totally cliche, but that's not true; not at all. ",
"Rachel isn't the perfect girl that just makes the dumb jock become a better person when he's with her. ",
"That would be cliche. ",
"Instead, they ballance each other out, and that is one of my most favorite things about them. ",
"Not only does Rachel make Finn a better version of himself, but Finn makes Rachel better as well. ",
"She has helped him to realize that there are more important things than ones reputation; that he shouldn't care so much about what other people think about him, and that there more important things than throwing eggs at people and letting others influence the things that you do in life. ",
"In return, he's the one person who can sort of tame the crazy in Rachel. ",
"He balances out all of Rachel's little quirks. ",
"When she's getting all overbearing and out of control, he's there to tell her she's being completely crazy. ",
"There's a mutual give-take ballance between the two that isn't at all one-sided. ",
"Also, I just love how adorable they are together - I don't think there will ever be a couple that could possibly be more cute than these two. ",
"Not only do they look amazingly good together, but they have chemistry in every aspect that could literally set the atlantic ocean on fire. ",
"They understand and get each other - and they've given each other their hearts. ",
"They make each other smile, and in return, it makes me smile too.",
"Stefani (Steph)\n\nEPIC: is the one word that decribes the amazingness of Finchel. ",
"CUTENESS: is LC who are adorably cute when they are around each other. ",
"And, AMAZING is what I decribe as the 300th threads of adorkable duets and adorable LC fantasies. ",
"I can't believe we hit 300 threads and let's hope for 300 more.",
"\n\nFinchel and LC, ever since becoming a fan of Glee I thought that these two made the show and it made me continue to watch and see what happens with them. ",
"During season 1, I became a big fan of Finn and thought he was the cutest thing ever on TV and some time later after that I became a fan of Rachel too. ",
"I enjoy them the most on the show cause they are the most entertaining and they don't bore me like some other pairings. ",
"And LC, Monchele I love them so much now because they are such fun off screen and I love how close they are as friends (I would like more than friends) but I don't think that will happen. ",
"Anyway, my love for Finchel and LC is huge and it's just getting bigger and bigger as the episodes and seasons pass on.ღRose♦Nylundღ (Shari)\n\nLea: Basically, I bring light and joy into Cory's life everyday.",
"Cory: Every single day, when she's not around, I think, 'My life will get better soon'.",
"\n\nCory: When the Glee audition came around, my manager literally had to talk me into it. ",
"I was petrified to sing in front of anyone.",
"Lea: Fast-forward two years, he's on stage at Radio City, singing live in front of 6,000 people and, like, loving it.",
"Cory: Loving it.",
"Lea: He's a rock star.",
"\n\nLea: I love working with Cory, and i love pretending like he’s my boyfriend. ",
"It’s so fun.",
"\n\nLea: (On cast romances) I mean, for me, if it was going to happen with anybody it would have happened with Cory. ",
"The moment I saw him, I thought ‘This boy is very cute.’",
"\n\nLea: We're such good friends that we've passed that level of weirdness. ",
"Cory farts in front of me.",
"\n\nCory: And Lea’s best trait is that she’s very inspiring. ",
"And incredibly talented. ",
"And hot.",
"\n\nLea: Cory is amazing and I love working with him. ",
"He's great and he makes me laugh. ",
"He's fantastic.",
"\n\nCory: I work opposite Lea Michele and there's no finer teacher.",
"\n\nLea: Working with Cory is such a joy. ",
"He is committed, focused and so much fun. ",
"His story to success is so inspirational, he truly deserves all of this.",
"\n\nCory: It’s speculation. ",
"I can’t blame them for thinking that. ",
"I mean, we’re very close. ",
"We go out in public and we’re very like this [grabs reporter close to him].",
"\n\nLea: What they don’t know is that Cory and I are taking pictures for the ‘Save the Date’s’ for our wedding.",
"Cory: Save the date for our wedding.",
"\n\n\"The show is simply more fun to watch when Finn and Rachel are together, don't you agree?\" ",
"-TVF\n\"I don't care about Puck! ",
"I don't care about anybody but you!\"",
"\n\"I don't want to talk about Quinn, I want to talk about you.\"",
"\n\"Just because I can't be with you doesn't mean I don't believe in you.\"",
"\n\"She's prettier than me.\" \"",
"Would you stop? ",
"You're beautiful.\"",
"\n\"You’re a real star, and you need to shine.\"",
"\n\"I love working with Cory. ",
"And I love pretending like he's my boyfriend. ",
"It's so fun.\" - ",
"Lea\n\"Rachel and Finn all the way!\" - ",
"JU\nBecause Lea LOVES working with Cory, and we love it too.",
"\nBecause Lea is happy as long as she has scenes with Cory\nBecause when describing his perfect woman Cory described Lea.",
"\nBecause we aren't the sinking ship, we are the life boats that stay afloat after the wreck.",
"\n\"They have a very serious love\" - Lea on Finn and Rachel\nYou're the one who keeps me up at night, thinking about how we'd look together in the future\nI smile a lot these days. ",
"And everybody knows it's because of you. ",
"Everyone knows it but you.",
"\nIt's not being in love that makes me happy. ",
"It's been in love with you that makes me happy.",
"\nPeople say happiness is a choice. ",
"I think happiness is you.",
"\nThe happiest feeling ever is knowing that he could be with any other girl in the world, but he chooses to be with you.",
"\nAt first I loved your smile. ",
"Then I loved your laugh. ",
"After that I loved your humor. ",
"But in the end I realized I just love you.",
"\nEveryone says you only fall in love once. ",
"That's not true because every time I see you, I fall in love all over again.",
"\nBecause Cory's favourite episodes are Duets and Showmance and his favourite Glee Tour performance is Faithfully."
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"More from SI\n\nNCAA announces bracketing rules changes for NCAA tournament\n\nWith these latest rules changes, the NCAA is hoping to keep teams closer to their true seed once they're placed in the bracket.",
"\n\nOn Thursday afternoon, the NCAA revealed the approved changes to bracketing rules for the NCAA tournament, starting with this coming spring's event. ",
"Overall, the new approach seems to make sense, with the goal to keep teams closer to true seed once they're placed in the bracket by relaxing conference and regular-season rematch restrictions. ",
"In a media conference call following the release, Wake Forest athletic director and selection committee chairman Ron Wellman said that 90 percent of the seed-line moves in the last three NCAA tournaments would have been eliminated under these new procedures.",
"\n\nHere are the main rules changes coming in 2014.",
"\n\n* How early conference rivals can meet in the tournament will now be based on how many times they have already played prior to the tournament. ",
"If teams only have played once previously, they can be bracketed to meet as early as the \"third round\" (i.e. Round of 32). ",
"If they have played twice, they can't meet before the Sweet 16. ",
"If they already have played three times, they can't have a potential matchup until the Elite Eight.",
"\n\n* The rule that required the top three seeds from a particular conference to be put into different regions has been changed. ",
"Now, the top four teams from a league will be separated only if they all land within the top four seed lines (i.e. top 16 teams on the 1-68 seed list).",
"\n\n\"It is important we avoid the top teams from leagues receiving multiple bids to the tournament from playing one another when they are seeded in the first quadrant,\" said Wellman in the NCAA release. \"",
"But after those first four lines are seeded, we want to remain as true to the seed lines as possible.\"",
"\n\n* The committee will avoid regular-season nonconference rematches in the First Four, and also in the Round of 64, if possible. ",
"If two teams from the same conference are in the First Four, any of the rules can be relaxed to help accommodate that scenario.",
"\n\nGenerally speaking, these rules changes seem to make sense on first glance. ",
"Relaxing the rule that required the top three teams from a league to be placed into different conferences is a big plus. ",
"That will allow the committee to stay closer to real seeds and not punish teams, especially those from slightly smaller conferences, where the best team from a league previously could be squeezed out of a preferred region due to conference conflicts elsewhere. ",
"It also will diminish the number of situations like last season, where Indiana was perceived to be \"playing for Indianapolis\" against Michigan and other Big Ten contenders. ",
"In theory, both of those teams could now be in the same region (as the 1 and 2) as long as there weren't four Big Ten teams in the top four seed lines (as there were last season).",
"\n\nIt also probably will mean that one-bid conferences and other non-major conference champs won't be as much of \"bracket free agents\" in the sense that they get plugged in last after the major-conference conflicts were addressed. ",
"That was a large factor in a lot of the \"mid-on-mid violence\" you saw in previous year's events, as teams could only slide into certain spots based on conference membership.",
"\n\nAs much as these rules may make bracket projections a little harder to do by hand, they look like guidelines that will help the tournament going forward. ",
"I hope the committee also spends more of its gathering time on the bracket placement process, to help create the fairest and most interesting tournament possible. ",
"On the call, Wellman said that the committee would be establishing timing benchmarks for the five-day process, trying to allot a specific amount of time for the actual bracketing of the event.",
"\n\nNow if they would just address the ridiculousness of referring to the play-in games as the first round, creating a second round where 60 teams are playing for the first time, we'll be on to something..."
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"Now I've never worked with databases or web servers before, but after reading a bunch of tutorials and a few days of hacking away I managed to get a node.js server with mongodb up and running on the openshift platform.",
"\nRight now anyone can interact with the database just by sending a GET request or even just pulling up the url in a browser. ",
"Is there a way to prevent that by happening or would I have to maybe encrypt the data myself before storing it?",
"\n\nA:\n\nYou describe a typical web application using REST APIs. ",
" To secure it, do two things:\n\nDeploy your REST APIs (or the entire site) using HTTPS instead of HTTP. ",
" This provides end to end encryption so your sensitive data cannot be viewed while in transit\nAdd an authentication and authorization mechanism, so that only authenticated endpoints can access your REST APIs.",
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"Leopard Pro and Yamaha Senior to compete for up to $6,700 cash purse at New Castle Motorsports Park on June 7-9\n\nShare this story:\n\nFollowing its inaugural event in Mooresville, North Carolina, the United States Pro Kart Series – presented by Bridgestone, FranklinKart.com, and L&T Manufacturing – is ready to host its second event of the 2013 season. ",
"The new series will travel to the New Castle Motorsports Park on June 7-9 for stop number two, sponsored by DRT Racing and Ribtect3. ",
"The event will continue to feature the $3,100 cash purse for the Leopard Pro category for the weekend, and will now include a $2,100 purse for the Yamaha Senior class on Sunday.",
"\n\nThe New Castle Motorsports Park/Comet Kart Sales Yamaha Pro Challenge will take place Sunday of the June 7-9 weekend within the Yamaha Senior category. ",
"Racers will compete for a $600 first place prize, with second through fifth earning $500 to $200 in cash along with another $100 going to the fast lap of the main event for a total of $2,100.",
"\n\nThe Leopard Pro division will continue racing for another $3,100 on the weekend, with $1,550 in cash handed out after both finals. ",
"Austin Wayne Self and Mike Giessen each took home a check for $750 for their first place prize. ",
"The $500 bonus for the same driver to win both main events on the weekend from Mooresville has grown to $1,000 by the series, with HYTORC offering an additional $500 bonus to the driver to win both days. ",
"In total, up to $6,700 in cash could be handed out during the USPKS New Castle event.",
"\n\nYamaha Senior drivers will race for ,100 on Sunday of the United States Pro Kart Series event at New Castle(Photo: eKartingNews.com)\n\nA number of drivers have positioned themselves in the title chase for the inaugural United States Pro Kart Series season, with the New Castle events to shape up the contenders even more. ",
"The Leopard Pro division saw two drivers earn inaugural wins, both in the rain. ",
"Self was the top driver in Saturday’s main event while veteran Giessen showed the way on Sunday. ",
"The two are locked up at the top of the point standings with Saturday runner-up Mason Chelootz trailing by 35 points. ",
"Dustin Stross and Austin McCusker split the wins in Leopard Semi-Pro. ",
"Stross was the ‘rainmaster’ on Saturday while McCusker came through with the victory on Sunday. ",
"Both ran runner-up to each other while Mike McAndrews was third both days and trails by 65 points in the standings. ",
"Chuck Gafrarar left the inaugural USPKS event leading the Leopard Masters. ",
"Gafrarar swept Saturday’s action but ran third on Sunday. ",
"Brian McHattie earned victory in round two, and trails by 15 points in the standings. ",
"Brian McEvoy was runner-up Sunday and third Saturday to sit 25 points behind Gafrarar while Chuck Tate and Tim Shutt remain within 85 points.",
"\n\nJoel Jens was dominant in the Yamaha Senior division, sweeping the weekend and securing an 85-point lead over Sam Cate in the championship. ",
"Anthony Gangi Jr. fought strong in his Yamaha Junior debut, placing runner-up both days of competition. ",
"His consolation prize is leading the championship, holding a 10-point advantage over Saturday winner Zach Holden with Sunday winner Gresham Wagner another 60 points behind. ",
"Yamaha Cadet was a great battle all weekend at the Mooresville Motorplex with Neil Verhagen and Austin Schaff each earning a main event victory. ",
"They are tied for the championship lead following the first two rounds with Sam Mayer and Alex Verhagen both within 35 points of the top two. ",
"Mark Fineis leads the standings in the Yamaha Rookie point standings. ",
"The Sunday main event winner leads Nic Sheppard – the Saturday round winner – by 45 points.",
"\n\nFriday evening, June 7, McLaughlin Motorsports will be hosting a cookout following the practice on track in New Castle. ",
"During that time, a 3-on-3 basketball tournament will be held at the NCMP facility, right on pit lane. ",
"The event is open to all ages and is presented by eKartingNews.com. ",
"When racing action begins Saturday, June 8, EKN will be providing its ‘Trackside Live’ once again through qualifying to the final checkered flag, allowing those unable to attend New Castle in person to feel like they are along the fence line. ",
"Friends, family and fans can listen in at http://www.ekartingnews.com/live on the weekend to view live timing and live race call from USPKS announcer Randy Kugler. ",
"Those companies interested in supporting this weekend’s broadcast may contact EKN via email sales@ekartingnews.com .",
"\n\nThe pre-entry form for the United States Pro Kart Series at New Castle Motorsports Park can be found at the following link (http://www.uspks.com/files/formNCMP.pdf) and must be turned into the series no later than May 31. ",
"Pit reservations are to be submitted to the New Castle staff by calling 765-987-8090. ",
"Hotel information for the NCMP facility along with more information about the second stop of the USPKS program can be found at http://www.uspks.com . ",
"Be sure to ‘Like’ them at Facebook.com/UnitedStatesProKartSeriesUspks"
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"Emphasis is laid on the description of the indications underlying the investigation and on the hysteroscopic and histological findings in the cases examined. ",
"The sample was also subdivided into two groups depending on the fertility or postmenopausal status of the patients. ",
"In the sample of 284, 89 (31.3%) patients were subjected to local anaesthesia with paracervical block, while the remaining 195 (68.7%) did not receive any form of anaestetic. ",
"The hysteroscopies were generally carried out in day surgery, using the commonest and most tried and tested hysteroscopic optic systems and carbon dioxide as a means for distending the uterine cavity. ",
"None of the hysteroscopies gave rise to important complications. ",
"In both the group of patients in fertile age and in the group of post-menopause patients, the main indication for hysteroscopy was anomalous uterine bleeding (AUB) for which a total of 159/284 hysteroscopies (56%) were carried out, of which 68 (42.8%) in patients in fertile age and 91 (57.2%) in post-menopause patients. ",
"In the group of post-menopause patients hysteroscopy was carried out for this indication in 73.4% of cases (91/124) while in fertile age it was performed in 42.5% of cases (68/160). ",
"Underlying AUB in the post-menopause patient endometrial hypo-atrophy was evidenced in 59 of 91 patients examined (64.9%), while in fertile age most of the 68 cases of AUB proved to be of dysfunctional nature: hystological examination showed a proliferative endometrium in 29 cases, secretory in 7 and hyperplastic in 12 cases (11 cases of simple endometrial hyperplasia with atypia and 1 of complex hyperplasia with atypia). ",
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"\n\nDe acuerdo con reportes policiacos, los hechos ocurrieron alrededor de las 9:00 horas sobre la carretera federal número 95, cerca de la Escuela Primaria Silvino Añorve Dávila, cuando Martínez Rodríguez se dirigía al Ayuntamiento y fue atacado por un comando.",
"\n\nSe informó que aunque los uniformados lograron repeler el ataque, los agresores huyeron del lugar en un automóvil compacto color gris.",
"\n\nDe acuerdo con los reportes de prensa, Martínez Rodríguez ya había sido atacado en dos ocasiones, y había denunciado amenazas de muerte en su contra.",
"\n\n“No le hago daño a nadie, he agarrado a muchos rateros y mañosos, si esto me cuesta la vida, la voy a dar peleando […] Yo no fumo, no tomo, yo no traigo compromiso con nadie, ni con malandrines, ni con nadie”, dijo Honorio Martínez tras ser atacado en noviembre de 2013."
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"Related Articles\n\nJames posted a photo of himself in a Cavaliers uniform on Instagram and Twitter with the phrase \"I'm coming home\" and the Cavaliers logo.",
"\n\n\"We're not ready right now. ",
"No way. ",
"It will be a long process, much longer than it was in 2010. ",
"My patience will get tested.\"",
"\n\nAdvertisement\n\nJames leaves behind a veteran Miami club with teammates Dwyane Wade and Chris Bosh and joins a young squad with new coach Dave Blatt, star guard Kyrie Irving and this year's top NBA draft pick, guard Andrew Wiggins, that could be a contender for many years to come.",
"\n\nYou will now receive updates fromSport Newsletter\n\nSport Newsletter\n\n\"I'm going into a situation with a young team and a new coach. ",
"I will be the old head,\" James said. \"",
"But I get a thrill out of bringing a group together and helping them reach a place they didn't know they could go.\"",
"\n\nThe wait for James to make his decision shut down most other major free agency decisions in the league and kept fans in Miami and Cleveland spellbound to US sports television networks that provided non-stop coverage of his every move.",
"\n\nJames was selected by Cleveland as the top pick of the 2003 NBA draft and won Rookie of the Year honours. ",
"He guided the Cavaliers to their only NBA Finals in 2007, where they were swept by the San Antonio Spurs.",
"\n\nIn 2010, James became a free agent and staged a television show on ESPN called The Decision on which he announced he was leaving for Miami, a much-criticised move that prompted Cleveland fans to burn his jerseys in anger.",
"\n\n\"I always believed that I'd return to Cleveland and finish my career there. ",
"I just didn't know when,\" James said.",
"\n\nAll is now forgiven .. a Cleveland Cavaliers fan holds a sign and yells as Miami Heat's LeBron James is introduced before a game against Cleveland in 2012. ",
"Photo: AP\n\nJames, 29, whose endorsement partners include Nike, Coca-Cola and McDonald's, can receive a four-year contract with a starting salary of about $US20.7 million ($22.06 million). ",
"Separately, he reaped about $US30 million ($31.98 million) for his stake in Beats Electronics, which last month was acquired by Apple for $US3 billion ($3.2 billion).",
"\n\nJames, according to Sports Illustrated, is the second- highest-earning athlete this year behind boxer Floyd Mayweather, taking in $US57 million ($60.75 million) in salary and endorsements. ",
"His marketing company, LRMR, represents Browns quarterback Johnny Manziel.",
"\n\n\"It means more to the franchise than any normal player transaction because he means so much to the city,\" Estis said of James, who unlike many highly compensated athlete endorsers has shown a willingness to address controversial topics.",
"\n\nNot since the 1964 Cleveland Browns won the National Football League crown has the city known a major sports champion.",
"\n\nDan Gilbert, the Cavaliers owner who called James a coward for leaving and joked about his \"King James\" nickname, praised James on Twitter shortly after the return was confirmed.",
"\n\n\"Welcome Home @kingjames. ",
"I am excited for the fans and people of Cleveland and Ohio. ",
"No fans and people deserve a winner more than them,\" Gilbert said.",
"\n\nMy 8-year-old: \"Daddy, does this mean I can finally wear my Lebron jersey, again?\"...Yes it does, son. ",
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"Theophano Martinakia\n\nTheophano Martinakia (; died 10 November 897) was a Byzantine Empress by marriage to Leo VI the Wise. ",
"She is venerated as a saint by the Eastern Orthodox Church.",
"\n\nFamily \nBorn in , she was a daughter of Constantine Martinakios and Anna. ",
"Her family, the Martinakioi, were related to the Amorian dynasty, which ruled the Byzantine Empire from 820–867. ",
"Theophanes Continuatus, a continuation of the chronicle of Theophanes the Confessor by writers active during the reign of Constantine VII, records the story of a possible ancestor during the reign of Theophilos (reigned 829–842).",
"\n\nAccording to said story, there was an elder Martinakios related by marriage to Theophilos. ",
"A prophecy circulated at the time predicted that the family of Martinakios would come to rule the Byzantine Empire. ",
"In reaction Theophilos forced his kinsman to become a monk and convert his personal house into a monastery.",
"\n\nChristian Settipani has suggested the Martinakioi family could share common ancestry with the Phrygian Dynasty, allowing descendants some claim to the throne. ",
"He has suggested the relation may be through one of the sisters of dynasty founder Michael II. ",
"The origins of the dynasty are poorly recorded.",
"\n\nEmpress \nThe chronicle of Symeon Metaphrastes places the marriage of Leo VI and Theophano in the sixteenth year of the reign of Basil I (c. 883). ",
"Basil was the official father of Leo VI by Eudokia Ingerina. ",
"However Eudokia was the mistress of his predecessor Michael III who was suspected to be the natural father of the prince.",
"\n\nIn any case the marriage was arranged by Basil I and forced on Leo VI. ",
"The poor relation of father and son may have played a part in the eventual failure of this marriage. ",
"Basil died on 29 August, 886. ",
"Leo succeeded him to the throne and Theophano became his empress.",
"\n\nShe was an educated and deeply religious woman. ",
"According to the Byzantine tradition of hagiography about her, Theophano devoted most of her days to prayers, psalms and hymns to God. ",
"She was reportedly the builder or patron of the Monastery of Saint Anastasia the Protector from Potions (Hagia Anastasia Pharmacolytria) in Chalkidiki.",
"\n\nSymeon records Leo falling in love with Zoe Zaoutzaina in the third year of his reign, placing their meeting c. 889. ",
"Zoe became his mistress and replaced Theophano in his affections.",
"\n\nMonastic life \n\nIn the seventh year of his reign (c. 893), Theophano retired to a monastery in the Blachernae suburb of Constantinople. ",
"Theophano is considered particularly devoted to the church throughout her life. ",
"Whether her retirement was voluntary is left vague by both Theophanes and Symeon. ",
"Zoe replaced her in the palace and court life.",
"\n\nThere is a contradiction on her particular status from c. 893 to 897. ",
"According to Symeon, the marriage of Leo VI to Theophano was officially void. ",
"Allowing Leo and Zoe to marry within the year. ",
"According to Theophanes, the original marriage was still valid and Zoe remained the royal mistress.",
"\n\nDeath and canonization\nTheophano died in her monastery on 10 November, 897. ",
"According to Theophanes, Leo and Zoe proceeded to marry at this point. ",
"Both Symeon and Theophanes agree that Zoe was only crowned Augusta following the death of her predecessor.",
"\n\nTheophano was glorified (canonized a saint) by the Orthodox Church following her death. ",
"Her feast day is 16 December of the Eastern Orthodox Church calendar. ",
"After her death, her husband built a church, intending to dedicate it to her. ",
"When he was forbidden to do so, he decided to dedicate it to \"All Saints,\" so that if his wife were in fact one of the righteous, she would also be honored whenever its feast day was celebrated. ",
"According to tradition, it was Leo who expanded the celebration on the Sunday following Pentecost from a commemoration of All Martyrs to a general commemoration of All Saints, whether martyrs or not.",
"\n\nChildren \nAccording to De Ceremoniis by Constantine VII, Leo VI and Theophano only had one daughter, Eudokia, considered to have died young. ",
"Eudokia is buried in the Church of the Holy Apostles along with her father and mother.",
"\n\nReferences\n\nSources\n\nExternal links\n in Charles Cawley's \"Medlands\"\nListing and brief biography among other Orthodox saints by the Dailyreadings Listserver of the Greek Orthodox Archiochese of America\n\nCategory:9th-century births\nCategory:897 deaths\nCategory:Byzantine empresses\nCategory:Macedonian dynasty\nCategory:Byzantine saints of the Eastern Orthodox Church\nCategory:Eastern Orthodox royal saints\nCategory:9th-century Byzantine people\nCategory:9th-century Byzantine women\nCategory:Burials at the Church of the Holy Apostles\nCategory:9th-century Christian saints"
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"Regency Technologies Announces New CRT Glass Recycling Facility\n\nPost Time：Feb 16,2012Classify:Company NewsView：217\n\nRegency Technologies, a leader in IT asset recycling, is proud to announce its new operation in conjunction with Dlubak Glass Company, America's largest recycler of TV and PC monitor CRT (cathode ray tube) glass.",
"\n\nRegency Technologies' new location in Upper Sandusky, Ohio, adjacent to Dlubak Glass, allows for the complete breakdown, dismantling, and recycling of any device that contains CRT glass safely and responsibly without polluting the environment. ",
"As experts in electronic scrap recycling, Regency Technologies' thorough dismantling process takes TVs and PC monitors and breaks them down to separate recyclable materials including CRT glass, plastic, wire, metals, and more.",
"\n\nDlubak Glass receives the separated CRT glass and recycles it into environmentally safe furnace ready cullet which is reused in many applications including road surface paving material, building construction, and aggregate products.",
"\n\nAbout Regency Technologies\n\nRegency Technologies, certified to RIOS/R2 as well as ISO 9001/2008 and ISO 14001:2004, serves Fortune 500 companies, small businesses, and consumers with all aspects of IT asset management and asset recycling. ",
"From asset recovery to remarketing and recycling, hundreds of thousands of units annually pass through their 500,000+ square feet of facilities in Cleveland, Upper Sandusky, Atlanta, and Chicago.",
"\n\nRegency Technologies is affiliated with Reserve Management Group (RMG), a family of related businesses involved in recycling, scrap metal processing, and more. ",
"Formed in 1991, RMG consists of 500+ employees in 6 states with annual sales in excess of $475 million.",
"\n\nAbout Dlubak Glass Company\n\nFounded in 1932, the Dlubak Glass Company has grown to be one of the largest recyclers and processors of glass in the United States. ",
"Dlubak supplies a majority of \"furnace ready cullet\" to glass manufacturers in the automotive, lighting, plate, CRT, container, fiberglass, and aggregate industries. ",
"Based in Upper Sandusky, Ohio, Dlubak Glass employs 200+ people and has 5 additional plants located in Pennsylvania, Kentucky, Texas, Oklahoma, and Arizona. ",
"All 6 plants are fully licensed for glass recycling and serve customers worldwide, recycling over 600,000 tons of glass per year."
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[
"Q:\n\nfopen pass variables to remote servers\n\nI'm using fopen to allow webmasters to access data directly from my web servers soon. ",
"The problem is my server doesn't see a few things it normally see's when its loading through JavaScript. ",
"\nSo I want to pass a few variables using fopen or file_get_contents depending which is quicker performance once I do so benchmarks.",
"\nI'm using the example code below\n$file = 'http://example.com/get.php?var1=foo&var2=foo';\n$fp = fopen($file, 'rb');\nfpassthru($fp);\n\nbut it doesn't pass the get variables through. ",
"I don't want to use cURL just encase they don't have it installed and it seems to be slow also. ",
"I'm trying to make it very simple for the webmasters. ",
"How would I go about passing the variables through?",
"\nUpdate\nI found if you have a space in the variable it stops sending the rest of the variable string. ",
"How do I allow spaces without it interrupting the rest of the variables? ",
"It also real buggy using multiple variables as it doesn't send them all for me.",
"\n\nA:\n\nOn updated question - perhaps URL encoding the spaces in the variables - replace space with %20 may help.",
"\n\n"
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[
"from collections import OrderedDict\n\nfrom django.utils.functional import cached_property\nfrom rest_framework.decorators import detail_route\nfrom rest_framework.response import Response\nfrom rest_framework.status import HTTP_200_OK, HTTP_201_CREATED\nfrom six import iteritems\n\nfrom portia_orm.models import Project\nfrom storage import get_storage_class\nfrom storage.backends import InvalidFilename\nfrom .route import (JsonApiRoute, JsonApiModelRoute, CreateModelMixin,\n ListModelMixin, RetrieveModelMixin)\nfrom .response import FileResponse\nfrom ..jsonapi.exceptions import (JsonApiFeatureNotAvailableError,\n JsonApiBadRequestError,\n JsonApiNotFoundError,\n JsonApiConflictError)\nfrom ..utils.download import ProjectArchiver, CodeProjectArchiver\nfrom ..utils.copy import ModelCopier, MissingModelException\n\nfrom ..utils.deploy import ProjectDeployer\n\nclass ProjectDownloadMixin(object):\n @detail_route(methods=['get'])\n def download(self, *args, **kwargs):\n fmt = self.query.get('format', 'spec')\n version = self.query.get('version', None)\n branch = self.query.get('branch', None)\n spider_id = self.kwargs.get('spider_id', None)\n spiders = [spider_id] if spider_id is not None else None\n try:\n self.project\n except InvalidFilename as e:\n raise JsonApiNotFoundError(str(e))\n if hasattr(self.storage, 'checkout') and (version or branch):\n try:\n self.storage.checkout(version, branch)\n except IOError:\n pass\n except ValueError as e:\n raise JsonApiNotFoundError(str(e))\n archiver = CodeProjectArchiver if fmt == u'code' else ProjectArchiver\n try:\n content = archiver(self.storage).archive(spiders)\n except IOError as e:\n raise JsonApiNotFoundError(str(e))\n return FileResponse('{}.zip'.format(self.project.name), content,\n status=HTTP_200_OK)\n\n\nclass BaseProjectRoute(JsonApiRoute):\n @cached_property\n def projects(self):\n storage_class = get_storage_class()\n return storage_class.get_projects(self.request.user)\n\n @cached_property\n def project(self):\n project_id = self.kwargs.get('project_id')\n try:\n name = self.projects[project_id]\n return Project(self.storage, id=project_id, name=name)\n except KeyError:\n raise JsonApiNotFoundError()\n\n\nclass BaseProjectModelRoute(BaseProjectRoute, JsonApiModelRoute):\n pass\n\n\nclass ProjectRoute(ProjectDownloadMixin, BaseProjectRoute,\n ListModelMixin, RetrieveModelMixin, CreateModelMixin):\n lookup_url_kwarg = 'project_id'\n default_model = Project\n\n class FakeStorage(object):\n def exists(self, *args, **kwargs):\n return False\n\n def listdir(self, *args, **kwargs):\n return [], []\n\n def create(self, request):\n \"\"\"Create a new project from the provided attributes\"\"\"\n try:\n name = self.data['data']['attributes']['name']\n except KeyError:\n raise JsonApiBadRequestError('No `name` provided')\n self.kwargs['project_id'] = name\n\n projects = self.projects\n if not self.storage.is_valid_filename(name) or '.' ",
"in name:\n raise JsonApiBadRequestError(\n '\"{}\" is not a valid project name,\\nProject names may only '\n 'contain letters and numbers'.format(name))\n if name in projects:\n raise JsonApiBadRequestError(\n 'A project with the name \"{}\" already exists'.format(name))\n\n # Bootstrap project\n storage = self.storage\n storage.commit()\n\n project = Project(storage, id=name, name=name)\n serializer = self.get_serializer(project, storage=storage)\n data = serializer.data\n headers = self.get_success_headers(data)\n return Response(data, status=HTTP_201_CREATED, headers=headers)\n\n # def update(self):\n # \"\"\"Update an exiting project with the provided attributes\"\"\"\n\n # def destroy(self):\n # \"\"\"Delete the requested project\"\"\"\n\n @detail_route(methods=['get'])\n def status(self, *args, **kwargs):\n response = self.retrieve()\n data = OrderedDict()\n data.update({\n 'meta': {\n 'changes': self.get_project_changes()\n }\n })\n data.update(response.data)\n return Response(data, status=HTTP_200_OK)\n\n @detail_route(methods=['put', 'patch', 'post'])\n def publish(self, *args, **kwargs):\n if not self.storage.version_control and hasattr(self.storage, 'repo'):\n raise JsonApiFeatureNotAvailableError()\n\n if not self.get_project_changes():\n raise JsonApiBadRequestError('You have no changes to publish')\n\n force = self.query.get('force', False)\n branch = self.storage.branch\n published = self.storage.repo.publish_branch(branch, force=force)\n if not published:\n raise JsonApiConflictError(\n 'A conflict occurred when publishing your changes.'",
"\n 'You must resolve the conflict before the project can be '\n 'published.')",
"\n self.deploy()\n self.storage.repo.delete_branch(branch)\n response = self.retrieve()\n return Response(response.data, status=HTTP_200_OK)\n\n @detail_route(methods=['put', 'patch', 'post'])\n def reset(self, *args, **kwargs):\n if not self.storage.version_control and hasattr(self.storage, 'repo'):\n raise JsonApiFeatureNotAvailableError()\n branch = self.storage.branch\n master = self.storage.repo.refs['refs/heads/master']\n self.storage.repo.refs['refs/heads/%s' % branch] = master\n return self.retrieve()\n\n @detail_route(methods=['post'])\n def copy(self, *args, **kwargs):\n from_project_id = self.query.get('from') or self.data.get('from')\n if not from_project_id:\n raise JsonApiBadRequestError('`from` parameter must be provided.')",
"\n try:\n self.projects[from_project_id]\n except KeyError:\n raise JsonApiNotFoundError(\n 'No project exists with the id \"{}\"'.format(from_project_id))\n models = self.data.get('data', [])\n if not models:\n raise JsonApiBadRequestError('No models provided to copy.')",
"\n\n try:\n copier = ModelCopier(self.project, self.storage, from_project_id)\n copier.copy(models)\n except MissingModelException as e:\n raise JsonApiBadRequestError(\n 'Could not find the following ids \"{}\" in the project.",
"'.format(\n '\", \"'.join(e.args[0])))\n response = self.retrieve()\n return Response(response.data, status=HTTP_201_CREATED)\n\n def get_instance(self):\n return self.project\n\n def get_collection(self):\n storage = self.",
"FakeStorage()\n return Project.collection(\n Project(storage, id=project_id, name=name)\n for project_id, name in iteritems(self.projects))\n\n def get_detail_kwargs(self):\n return {\n 'include_data': [\n 'spiders',\n 'schemas',\n ],\n 'fields_map': {\n 'spiders': [\n 'project',\n ],\n 'schemas': [\n 'name',\n 'default',\n 'project',\n ],\n },\n 'exclude_map': {\n 'projects': [\n 'extractors',\n ],\n }\n }\n\n def get_list_kwargs(self):\n return {\n 'fields_map': {\n 'projects': [\n 'name',\n ],\n }\n }\n\n def get_project_changes(self):\n storage = self.storage\n if not storage.version_control:\n raise JsonApiFeatureNotAvailableError()\n return [{'type': type_, 'path': path, 'old_path': old_path}\n for type_, path, old_path\n in storage.changed_files()]\n\n @detail_route(methods=['put', 'post'])\n def deploy(self, *args, **kwargs):\n deployer = ProjectDeployer(self.project, self.storage)\n response = deployer.deploy()\n\n #response = self.retrieve()\n data = OrderedDict()\n #data.update(response)\n data.setdefault('meta', {})['deployed'] = response\n\n return Response(data, status=HTTP_200_OK)\n\n"
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"The Grand (Baltimore, Maryland)\n\nThe Grand is a Masonic temple located in Baltimore, Maryland. ",
"Constructed in 1866 by the Freemasons as the Grand Lodge of Maryland Masonic Temple, the building was the headquarters for the Maryland Freemasons for over 130 years. ",
"Edmund G. Lind was commissioned to design a new Masonic Temple. ",
"The French and Italian Renaissance-inspired property is a 7-story, 90,000 square foot building in downtown Baltimore. ",
" Among its ten main meeting rooms are Edinburgh Hall, modeled after the Tudor-style Rosslyn Chapel in Scotland, and another which resembles an Egyptian temple. ",
" The building features ornate plaster moldings, a marble staircase, stained glass windows and Rococo chandeliers.",
"\n\nIn 1822, the Masons dedicated their first Grand Lodge of Maryland on St. Paul Street and Lexington Avenue. ",
" During the Civil War years, the Grand Lodge served as a federal court house for U.S. Supreme Court Chief Justice Roger B. Taney. ",
" After the war ended, Baltimore's economy returned to its economic focus and continued to expand. ",
" Later on, the City of Baltimore acquired the Grand Lodge for a permanent extension of the Court House, and the Masons began construction on their second Grand Lodge. ",
" On November 20, 1866, the cornerstone was laid for the new Grand Lodge on Charles Street. ",
" A fire destroyed the interior in 1890, and a second fire again gutted the building in 1900, also destroying the upper stories. ",
"Repairs were completed in 1909, according to designs by Joseph Evans Sperry. ",
"It was Sperry who added the Beaux Arts sixth story and attic, as well as the elaborate ornamentation around the entryway.",
"\n\nIts first floor was partially used for retail and its headquarters was there until 1994, when the Lodge moved to the suburbs. ",
"After the 1987 Bicentennial Celebration of the founding of the Maryland Freemasons, the Masons decided to make use of a large parcel of land they owned north of the city for a new Grand Lodge. ",
" In 1993, construction of a new complex in Cockeysville, Maryland began, and the new Grand Lodge of Maryland was dedicated there in 1996.",
"\n\nAttracted by its beauty and recognizing the possibilities for other uses, the owners of the neighboring Tremont Suites Hotel purchased the Lodge from the Masons in 1998. ",
" The firm began planning a renovation of the structure which would honor its grace and historical significance while using it for meeting space and social functions. ",
" City of Baltimore officials were unaware of plans for restoration, and condemned the building in order to erect a much needed parking structure on the land. ",
" Working with the City, the hotel's owners crafted an agreement which would save the building and add a parking structure directly behind it. ",
" Thanks to that agreement, restoration of the magnificent structure began. ",
" A team of architects, designers, restoration specialists and world class craftsmen was assembled to restore the original interiors and replicate what they could. ",
" After years of work, the doors of the lodge, newly named Tremont Grand, were opened in September 2005. ",
" The project’s scope of work involved restoration and cleaning of exterior and all interior finishes; a new addition providing elevator and lobby access for floors 2 through 5; and a connector to The Tremont Plaza Hotel. ",
"Nearly 140 years after its original cornerstone was laid as the Grand Lodge of Maryland, the Tremont Grand was returned to a graceful and elegant state, and a piece of Baltimore's history. ",
"When the hotel was renamed Embassy Suites Baltimore Inner Harbor the building was renamed Grand Historic Venue. ",
"Then in 2015 the building was renamed \"The Grand\".",
"\n\nSee also\nList of tallest buildings in Baltimore\n\nReferences\n\nExternal links\nOfficial website\n\nCategory:Buildings and structures completed in 1967\nCategory:Former Masonic buildings in the United States\nCategory:Skyscrapers in Baltimore\nCategory:Former buildings and structures in Maryland\nCategory:Skyscrapers in Maryland"
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"Within the opening few minutes she’d seen not one but both of the team’s cars slide into the gravel – and an underlying aerodynamic issue has now been identified as the cause.",
"\n\nLance Stroll was the first of the Williams drivers to hit trouble, spinning off at the end of the Wellington Straight and beaching his FW41 in the gravel, necessitating a red flag. ",
"The session had barely got going again when Sergey Sirotkin repeated the trick at Stowe in the sister car, and though he was able to get going again, both drivers were eliminated in the opening stage for the sixth time this season.",
"\n\nHaving investigated what happened, Williams were quick to rule out driver error, saying both spins were caused by a new aerodynamic ‘phenomenon’.",
"\n\n“We have a phenomenon which we have not seen all year, or indeed ever before, whereby the DRS activation intermittently causes a complete loss of aerodynamic floor loading which does not recover at the entry to the subsequent corner,” explained Chief Technical Officer Paddy Lowe.",
"\n\n“In the case of both spins, the cars entered the corner with no load in the floor which had obvious consequences. ",
"We came to this event with a number of new bodywork items which we evaluated during FP1 and FP2.",
"\n\n“This new DRS-related phenomenon was seen only once in FP1 on one of the cars but was incorrectly diagnosed to be related to a particular configuration which we chose not to carry forward into FP2 and for qualifying and the race. ",
"We must now understand exactly what change in the cars caused this phenomenon which is entirely related to the use of DRS.”"
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"Q:\n\nShuffling algorithm for a \"guess that tune\" game\n\nI'm making a \"guess that tune\" game in Visual Basic 6 that is supposed to play each song in a random order:\n' from frmGuessGame.frm\nPrivate Sub Swap(ByRef Value1 As Variant, ByRef Value2 As Variant)\nDim Temporary As Variant\nTemporary = Value1\nValue1 = Value2\nValue2 = Temporary\nEnd Sub\n\nPrivate Sub ShuffleList()\nDim LoopCtr As Integer, SwapWith As Integer\nFor LoopCtr = LBound(InnerPlaylist) To UBound(InnerPlaylist)\nSwapWith = (Rnd * (UBound(InnerPlaylist) - LBound(InnerPlaylist))) + LBound(InnerPlaylist)\nSwap InnerPlaylist(LoopCtr), InnerPlaylist(SwapWith)\nNext\nEnd Sub\n\nMy initialization function does include the Randomize statement, so it should be a good, even shuffle.",
"\n' from mdiMain.frm\nPrivate Sub MDIForm_Load()\n'initialize pseudo-random number generator\nRandomize\nfrmMusiguess.",
"Show\nfrmSplash.",
"Show\nEnd Sub\n\nI'm not sure, however, that this is the best way to do it. ",
"Am I on the right track?",
"\n\nA:\n\nNo. ",
"Your shuffle will not be random. ",
"You are stepping through each card and swapping it with another random card. ",
"This is a common bug found in many shuffling algorithms. ",
"\nTo illustrate why your shuffle is not random, let's assume you are shuffling three songs (1, 2, 3). ",
"There are six combinations of three song (123, 132, 213, 231, 321, 312). ",
"If your shuffle was random, each of these combinations should appear with equal probability. ",
"So if you run your shuffle algorithm 600,000 times, each combination should appear roughly 100,000 times each.",
"\nBut it doesn't. ",
"When you run your shuffle algorithm 600,000 times (as written), you will see results similar to this: \n\nTo understand why your implementation produces biased results, read this article on Coding Horror: The Danger of Naïveté.",
"\nWhat you want is a Fisher-Yates shuffle where you swap the current card with any of the remaining cards (or itself). ",
"\nHere it is in pseudo code for an in-place shuffle:\nTo shuffle an array a of n elements:\n for i from n − 1 downto 1 do\n j ← random integer with 0 ≤ j ≤ i\n exchange a[j] and a[i]\n\nThere are other types of Fisher-Yates shuffles listed here: Wikipedia: Fisher–Yates shuffle.",
"\n\nA:\n\nI would probably do something like this:\nI don't know VB so this is pseudo code.",
"\nPrivate Function Shuffle(playlist) as Playlist\n{\n Dim PlayList as NewPlayList\n Dim RandomIndex as Integer\n\n while(playlist has elements)\n {\n RandomIndex = (Random number between lowerbound and upperbound)\n\n remove song at RemoveIndex from playlist\n add removed song to NewPlaylist\n }\n\n return NewPlayList\n}\n\nThe issue I have with the way you did it is that there is ample opportunity to undo the shuffle. ",
"For example, Suppose you are at index 1 and the random number is 2. ",
"You swap 1 and 2. ",
"Now suppose you are at index 2 and the random number is 1. ",
"Now you just undid the shuffle that you preformed in the previous iteration. ",
"Also, I don't like the use of the global variable InnerPlaylist. ",
"\n\n"
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"1. ",
"Field of the Invention\nThis invention relates generally to a portable bulk product melt system and, more specifically, to a portable bulk product melt system having a bulk product mixing system which receives a bulk product from a bulk product source vessel, wherein the bulk product is offloaded then treated to form a melted product mixture and then discharged back into the bulk product source vessel.",
"\n2. ",
"Description of Prior Art\nMany conventional bulk product melt systems require bulk product to be deliver in a container, such as a truck tanker, railroad car tank, or temporary storage tank, to a factory or off-site building having a mixing station or system. ",
"The bulk product is transferred into the mixing station or system and mixed with various ingredients or materials to produce or process a mixture. ",
"The mixture is than transferred into a second container, such as a second truck tanker or second railroad car tank, for storage and/or transporting the mixture to another location. ",
"This process may include costly and unnecessary movement and handling of the bulk product.",
"\nTherefore, there exists a need for a portable bulk product melt system that is transportable to and positionable with respect to a bulk product source.",
"\nThere exists a need for a portable bulk product melt system that can process a bulk product received from a bulk product source vessel into a treated product mixture and discharge the treated product mixture back into the bulk product source vessel."
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"\nNeuropathic pain (NP) is a main feature of Fabry disease (FD) as consequence of small fiber neuropathy. ",
"Restless legs syndrome (RLS) in FD was not described, but it is an important feature in other small fiber neuropathies, i.e., diabetes. ",
"The aim of this study was to assess the prevalence of RLS in patients with FD, and its association with neuropathy. ",
"We investigated the occurrence of RLS in four families of classical FD, diagnosed in accordance with the criteria of the International RLS Study Group. ",
"Eleven patients, 6 hemicigote and 5 heterocigote, ages among 19 to 32 years old for males and 45 to 56 years old for females, were studied. ",
"The 6 hemizigote and 2 heterozigote patients were on enzyme therapy with agalsidase beta. ",
"One heterocigote patient had not clinical NP and the other 10 patients had small fiber sensory neuropathy with symptoms: burning and painful feet. ",
"RLS was present in 3/6 hemicigote and 1/5 heterocigote patients (36%). ",
"In these four patients, RLS was associated with dysesthesias or pain crisis and it was characterized to be a desire to move the low extremities as crisis of motor restlessness. ",
"RLS was characterized for worsening of symptoms with rest without diurnal changes. ",
"Patients have to uncover the feet for improving burning or sometimes they have to get out of bed in the night looking for relief. ",
"Both NP and RLS improved after 3 years of enzyme replacement therapy. ",
"Our data shows that RLS is associated to NP as a treatable manifestation of small fiber involvement in the course of FD."
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"\nMacroamylasemia (MA) is a rare condition characterized by an active macromolecular complex formed by normal amylase with abnormal proteins; to our knowledge, it has not been previously described in Mexico. ",
"The size of the macromolecular complex precludes its renal excretion; thus MA is characterized by high levels of amylase in serum with normal amylasuria. ",
"We report a 53-year-old male with abdominal pain and hyperamylasemia who was erroneously diagnosed as pancreatitis. ",
"Amylase in urine was normal and a protein electrophoresis demonstrated hyperglobulinemia. ",
"Several months after the initial work-up, the diagnosis of non-Hodgkin's lymphoma was established. ",
"Serum pancreatic amylase was again found elevated with normal urinary amylase. ",
"Precipitation of amylase with polyethylene-glycol was of 81% (normal: less than 70%). ",
"This established the diagnosis of MA associated to non-Hodgkin's lymphoma. ",
"After chemotherapy, the abnormal macroamylasemia and hyperglobulinemia disappeared."
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"• Have students make credit card payments online through a third party and pay the convenience fee. ",
"Savings: $350,000\n\nSource: The Board of Trustees' Committee on Effectiveness and Efficiency for the Future\n\nTurning off lights and computers when not in use, reducing the number of picnics for faculty and staff and making students pay the fees for credit-card tuition payments.",
"\n\nAll are tactics public universities and colleges across the state are considering as available funds decrease.",
"\n\n\"It makes us very mindful of what we do all the time and why we do what we do,\" said Deborah Arfken, director of university planning at the University of Tennessee at Chattanooga.",
"\n\nThe August commencement ceremony was the last one UTC will hold for students completing their degrees over the summer. ",
"The university will save about $20,000 by holding only two commencement ceremonies each year, one in December and one in May.\n\nTo save an estimated $1.7 million, UTC is implementing 12 measures such as using electronic billing statements, turning off unused lights and computers and resetting thermostats in some buildings.",
"\n\nThe UT board of trustees' committee on effectiveness and efficiency for the future identified 132 initiatives it said could save up to $52 million.",
"\n\nUniversity of Tennessee system President Joe DiPietro.",
"\n\nUniversity of Tennessee system President Joe DiPietro.",
"\n\n\"As the economy continues to be unpredictable, it is crucial for the university to remain in a cost-conscious mode,\" UT President Joe DiPietro said in a news release.",
"\n\nHe said UT began the fiscal year on July 1 down $112 million in state funding from 2008.",
"\n\nUTC's state appropriations for the current fiscal year were cut $779,400, or 2 percent. ",
"The school also lost about $25 million in federal stimulus funding.",
"\n\nIn 2008, UTC also created an efficiency and effectiveness committee to look at possible cost-cutting measures, said Arfken, who served as chairwoman.",
"\n\nAbout 160 suggestions were submitted, ranging from changing to a different athletic conference to cutting back on travel costs and personal computers, she said.",
"\n\nThe committee chose several measures, including discontinuing the two annual picnics for faculty and staff, Arfken said, although one was later reinstated. ",
"The picnics, meant to foster campus community, cost $9,000 to $10,000, she said.",
"\n\n\"These are challenging economic times and I think that UTC has managed very well,\" said Richard Brown, vice chancellor for finance and operations.",
"\n\n\"We've made some strategic decisions in regards to how to financially re-balance the institution and put us in a good position to move forward.\"",
"\n\nOne of the most challenging decisions was eliminating positions as enrollment continues to grow, said Brown.",
"\n\nUTC also upped its tuition by 9.9 percent this year, to $6,718 annually for full-time students.",
"\n\nAnd this year it enrolled more students, a 6 percent increase to 11,429 students, up from 10,781 last year.",
"\n\nThe school eliminated 23 full-time staff and 14 full-time faculty positions in fiscal 2010 to save about $2 million. ",
"It also eliminated more than $1 million set aside to pay adjunct faculty.",
"\n\nFor 2011, 22 full-time staff jobs and one faculty position were eliminated for a total savings of $631,211.",
"\n\nMany of the cuts came from unfilled vacancies, said Arfken.",
"\n\n\"We were very careful to not let people go,\" she said. \"",
"We worked really hard to prevent that.\"",
"\n\nBut the result has been a higher student-teacher ratio in some classes, she said.",
"\n\nBrown said enrollment growth has helped with some of the financial challenges.",
"\n\nHowever, he added, \"moving forward we really need to keep our eye on the financial ball in the next one to two years.\""
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"Britain’s trade figures released by the ONS last week have provided further evidence of how the nation’s trading future lies outside the EU.",
"\n\nThe UK’s trade deficit with the EU rose to an all-time high of £89 billion -- a figure which fully demonstrates the importance of Britain as the EU’s biggest single trade market. ",
"For those who have argued Britain would be prevented from securing a favourable trade deal following Brexit, the figures make humbling reading.",
"\n\nBritish importers and consumers have been propping up the economies of struggling eurozone countries -- including Spain and Italy -- alongside being vital markets for the economic heavyweights of France and Italy. ",
"This major imbalance should greatly strengthen the negotiating position of the UK post-Brexit, as the British Prime Minister could have simply threatened to walk away if he was not offered a good enough deal.",
"\n\nSuch a decision would be disastrous for major European producers and manufacturers, such as German car manufactures, who would demand their respective governments offer Britain a better deal – despite the latest threats from Brussels they will make it hard for Britain with huge trade tarriffs. ",
"This is unlikely to happen, as they want to sell more to us then the other way around.",
"\n\nIt is a shame Cameron instead decided to go into the negotiations shutting the proverbial door behind him, with his fellow EU leaders well aware he wants to keep Britain inside the EU -- at any cost. ",
"Instead of putting forward the deal he promised Britain in his famous Bloomberg speech, and being prepared to walk away if he did not succeed -- Cameron bottled it, abandoning any attempt to bring necessary reform to the EU.",
"\n\nWhat is undeniable is the EU is in decline as an economic force. ",
"In 2003 its share of the world economy was 30.7 percent. ",
"This has fallen to 23.7 percent and looks to drop below 20 percent by the end of the decade. ",
"Leaving would allow Britain to sign trade deals with countries like China and India, whose economies will dominate the 21st century.",
"\n\nThe ONS figures for 2015 support this, revealing how UK sales to EU countries lagged behind its exports to the rest of the world, for a second year in a row. ",
"For 2015 the EU accounted for 47 percent of British exports -- a major decline from the 62 percent of 10 years ago. ",
"Indeed current projections place exports to the EU as low as 40% by 2019 -- further evidence of the EU’s declining importance to UK businesses.",
"\n\nThose who attempt to scare us into remaining will claim Britain is no longer economically powerful enough to secure important trade deals without the EU. ",
"This is a complete fallacy. ",
"An examination of the Trans-Pacific Partnership reveals how New Zealand -- a country 54th in world economic rankings -- has secured trading access to nearly 40 percent of global GDP. ",
"All this was achieved without the need for any political union.",
"\n\nWe could ask why we should be sacrificing so much of our national sovereignty to gain access to such a small proportion of world trade. ",
"We should not permit the UK to be left behind in a declining Europe whilst the rest of the world speeds past us.",
"\n\nNew Zealand and other TPP nations are signing vast trade deals, while the EU is instead focussing on maintaining its deeply flawed policies such as the borderless Schengen Zone. ",
"The federalists have hailed this as one of the EU’s landmark projects, yet we have seen its gradual demise as Brussels struggles to deal with the political and economic destabilisation which comes with unchecked migration flows.",
"\n\nThe EU is at its heart protectionist. ",
"It’s more interested in protecting French farmers, Spanish fishermen and Italian designers, than securing trade deals with the rest of the world.",
"\n\nAs the new ONS trade statistics demonstrate, Britain’s future looks rosier outside of the Union. ",
"If the world truly has reached Cold War levels of risk -- as the World Economic Forum suggests -- it makes no sense for our politicians to attach ourselves to the hip of a declining and stagnant economic entity, determined to secure political union at all costs.",
"\n\nTo avoid further risk to Britain’s future, we must Get Britain Out.",
"\n\nChris Carter is a Research Executive at Get Britain Out"
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"/**\n *\n */\n\n\"use strict\";\n\n\nvar Blink1 = require('node-blink1');\n\nvar tinycolor = require('tinycolor2');\n\nvar config = require('../configuration');\n\nvar log = require('../logger');\nvar utils = require('../utils');\n\nvar Eventer = require('../eventer');\n\n// some globals because we are a singleton\n\n/**\n * Maximum support blink(1) devices for this service. ",
"GUI supports up to 8 I think\n */\nvar maxBlink1s = 4;\n/**\n * Number of individual LEDs allowed in a blink(1) device. ",
" Max is 18, 2 for dev\n */\nvar maxLEDsPerBlink1 = 2; // 18\n\nvar listeners = []; // callback listeners\n\n/**\n * blink1 devices currently opened.",
"\n * This is a global because this is true across entire Node process\n * One entry per blink1, with always at least one entry.",
"\n * Entry 0 is 'default' entry when no blink1 is plugged in.",
"\n * Format:\n * { serial: '12345678',\n * device: new Blink1()\n * }\n * @type {Array}\n */\nvar blink1s = []; // collection of opened blink1s\nvar currentBlink1Id = ''; // current blink1 (as set by colorpicker)\n\nvar defaultPatternStr = // as close as possible as the default firmware pattern\n \"0,\" + // forever\n \"#ff0000,0.5,1,#ff0000,0.5,2,#000000,0.5,0,\" + // red A, red B, off\n \"#00ff00,0.5,1,#00ff00,0.5,2,#000000,0.5,0,\" + // grn A, grn B, off\n \"#0000ff,0.5,1,#0000ff,0.5,2,#000000,0.5,0,\" + // blu A, blu B, off\n \"#808080,1.0,0,#000000,1.0,0,\" + // white 50% A+B, off\n \"#ffffff,0.5,1,#000000,0.5,1,\" + // white 100% A, off\n \"#ffffff,0.5,2,#000000,1.0,2,\" + // white 100% B, off\n \"#000000,1.0,0\" // everybooy off\n\n/**\n * Current color state of all blink1s and their last used millis & ledns,\n * with at least one entry.",
"\n * Entry 0 is 'default' entry when no blink1 is present.",
"\n * Supports 8 blink1s currently.",
"\n * @type Array\n */\nvar currentState = [];\nfor( var i=0; i< maxBlink1s; i++ ) {\n var cs = new Array( maxLEDsPerBlink1);\n cs.fill( tinycolor('#10100'+i));\n currentState.push( {\n colors: cs,\n millis: 100,\n ledn:0\n }\n );\n}\n\nvar Blink1Service = {\n deviceScanner: null,\n // toyEnable: false,\n // toyTimer:null,\n // toyMode:'off',\n // toyValue:0,\n defaultPatternStr: defaultPatternStr,\n\n // settings for toy button commands\n toy: {\n enable: false,\n timer: null,\n interval: 0,\n mode: 'off',\n value: 0,\n },\n conf: {},\n start: function() {\n listeners = []; // erase previous listeners\n this.reloadConfig();\n },\n reloadConfig: function() {\n log.msg(\"Blink1Service.reloadConfig\");\n this.conf = config.readSettings('blink1Service') || {};\n Blink1Service._removeAllDevices();\n Blink1Service.scanForDevices();\n },\n scanForDevices: function() {\n log.msg(\"Blink1Service.scanForDevices\");\n // initial population of any already-plugged in devices\n var serials = Blink1.devices();\n serials.sort();\n serials.reverse(); // newest blink1s first\n serials.map( function(s) {\n Blink1Service._addDevice(s);\n });\n\n // log.msg(\"Blink1Service.scanForDevices: done. ",
"serials:\", serials);\n if( serials.length === 0 ) { // no blink1s, look for insertion events\n if( this.conf.deviceRescan ) {\n if( this.deviceScanner ) {\n clearTimeout( this.deviceScanner );\n }\n this.deviceScanner = setTimeout( this.scanForDevices.bind(this), 5000); // look again in 5 secs\n }\n }\n },\n /**\n * Add a blink1 to the device list.",
"\n * @constructor\n * @param {string} serialnumber - serialnumber of blink1 to add\n */\n _addDevice: function(serialnumber) {\n log.msg(\"Blink1Service._addDevice:\", serialnumber);\n var olddev = blink1s.find( (blink1) => blink1.serial===serialnumber );\n if( !",
"olddev ) {\n log.msg(\"Blink1Service._addDevice: new serial \", serialnumber);\n blink1s.push( { serial: serialnumber, device: null } );\n }\n // set up all devices at once\n // we wait 500msec because it was failing without it (USB HID delay?)",
"\n setTimeout(() => {\n this._setupFoundDevices();\n }, 500);\n },\n _setupFoundDevices: function() {\n var self = this;\n log.msg(\"Blink1Service._setupFoundDevices\", blink1s, \"conf: \", self.conf);\n blink1s.map( function(b1) {\n if( !",
"b1.device ) {\n log.msg(\"Blink1Service._setupFoundDevices: opening \",b1.serial);\n b1.device = new Blink1(b1.serial);\n }\n });\n\n Eventer.emit('deviceUpdated');\n\n Blink1Service.notifyChange();\n },\n /**\n * Remove a blink1 from the device list. ",
" Triggers a scanForDevices()\n * @method function\n * @param {string} serialnumber serial number of blink1 to remove\n */\n _removeDevice: function(serialnumber) {\n log.msg(\"Blink1Service._removeDevice: current devices:\", blink1s);\n blink1s = blink1s.filter( (blink1) => {\n if( blink1.serial === serialnumber ) {\n if( blink1.device ) { blink1.device.close(); blink1.device==null; }\n return false; // remove it\n }\n return true; // keep it\n } );\n // var olds = lodash.remove( blink1s, {serial:serialnumber} );\n // olds.forEach( function(b1) {\n // if( b1.device ) {\n // b1.device.close();\n // b1.device = null;\n // }\n // });\n // if( currentBlink1Id === serialnumber ) {\n // log.msg(\"FORGETTING OLD BLINK1!!!!\");",
"\n // currentBlink1Id = 0;\n // }\n\n Blink1Service.notifyChange(); // FIXME: need to think about this\n\n setTimeout( this.scanForDevices.bind(this), 5000);\n },\n _removeAllDevices: function() {\n log.msg(\"Blink1Service._removeAllDevices\");\n blink1s.forEach( function(b1) {\n if( b1.device ) {\n b1.device.close();\n b1.device = null;\n }\n });\n blink1s = [ ]; //{serial: '', device: null } ]; // startup state\n log.msg(\"Blink1Service._removeAllDevices: done\");\n // FIXME: notify? ",
"nah, because scanForDevices always called after\n },\n\n /**\n * Fade to an RGB color over time, on particular LED and blink1 device.",
"\n * Private function, accesses hardware.",
"\n * assumes good & defined blink1idx, ledn, r,g,b, millis\n * blink1idx is index into blink1s array\n * @param {number} millis milliseconds to fade\n * @param {Color} color tinycolor object\n * @param {number} ledn which led, 0=all, 1-18\n * @param {number} blink1idx index into blink1s array\n */\n _fadeToRGB: function( millis, color, ledn, blink1idx ) {\n // if the device exists\n if( blink1s[blink1idx] && blink1s[blink1idx].device ) {\n var crgb = color.toRgb();\n try {\n var b1 = blink1s[blink1idx].device;\n if( this.conf.enableGamma !",
"== undefined ) { // i.e. if defined\n b1.enableDegamma = this.conf.enableGamma; // FIXME: fix this in node-blink1?",
"\n }\n else { b1.enableDegamma = false; }\n b1.fadeToRGB( millis, crgb.r, crgb.g, crgb.b, ledn );\n } catch(err) {\n log.error('Blink1Service._fadeToRGB: error', err);\n this._removeDevice( blink1s[blink1idx].serial );\n currentBlink1Id = 0; // FIXME: is this the correct response to this error?",
"\n }\n }\n },\n\n // begin public functions\n\n /**\n * Return array of all blink1 serialnumbers\n * @return {Array} array of blink1 serialnumbers\n */\n getAllSerials: function() {\n return blink1s.map(function(b1) { return b1.serial; });\n },\n // FIXME: support multiple blink1s\n /**\n * Returns true if connected, really returns number of devices connected\n * @return {Number} return number of devices connected\n */\n isConnected: function() {\n // return (blink1serials.length > 0);\n var cnt = 0;\n blink1s.map( function(b1) {\n if( b1.device ) { cnt++; }\n });\n return cnt;\n },\n getStatusString: function() {\n //return Blink1Service.isConnected() ? \"",
"connected\" : \"not connected\",\n var cnt = this.isConnected();\n return (cnt>1) ? ",
"cnt + \" devices connected\" : (cnt) ? \"",
"device connected\" : \"no device connected\";\n },\n // FIXME: support multiple blink1s\n serialNumber: function() {\n if( this.isConnected() ) {\n return blink1s[0].serial;\n }\n return '';\n },\n // FIXME: support multiple blink1s\n serialNumberForDisplay: function() {\n return (this.isConnected()) ? ",
"this.serialNumber() : '-';\n },\n // FIXME: fix and call this blink1Id or something\n getIftttKey: function() { // FIXME:\n // console.log(\"IFTTT KEY:\",this.serialNumber());\n var s = this.serialNumber() || '00000000';\n var k = this.getHostId() + s;\n return k;\n },\n getHostId: function() {\n var id = config.readSettings('hostId');\n if( !",
"id ) {\n id = utils.generateRandomHostId();\n this.setHostId(id);\n }\n return id;\n },\n /**\n * Sets HostId, an 8-digit hexadecimal\n * @method setHostId\n * @param {String} id new HostId value\n * @returns true if hostId is valid format, false if not\n */\n setHostId: function(id) {\n id = id.toUpperCase();\n if( ! ",
"/^[0-9A-F]{8}$/.test(id) ) {\n return false;\n }\n config.saveSettings( 'hostId', id);\n this.notifyChange();\n return true;\n },\n\n setCurrentBlink1Id(id) {\n log.msg(\"setCurrentBlink1Id: \",id);\n currentBlink1Id = id;\n this.notifyChange();\n },\n getCurrentBlink1Id() {\n return currentBlink1Id;\n },\n\n setCurrentLedN: function(n,blink1id) {\n var blink1idx = this.idToBlink1Index(blink1id);\n currentState[blink1idx].ledn = n;\n this.notifyChange();\n },\n\n getCurrentLedN: function(blink1id) {\n var blink1idx = this.idToBlink1Index(blink1id);\n // blink1idx = blink1idx || 0;\n return currentState[blink1idx].ledn;\n },\n\n setCurrentMillis: function(m,blink1id) {\n var blink1idx = this.idToBlink1Index(blink1id);\n currentState[blink1idx].millis = m;\n this.notifyChange();\n },\n getCurrentMillis: function(blink1id) {\n var blink1idx = this.idToBlink1Index(blink1id);\n return currentState[blink1idx].millis;\n },\n // FIXME: this seems overly complex\n getCurrentColorOld: function(blink1id) { // FIXME\n var blink1idx = this.idToBlink1Index(blink1id);\n // log.msg(\"getCurrentColor: idx\", blink1idx, \"currentState:\", currentState);\n var curledn = currentState[blink1idx].ledn;\n curledn = (curledn>0) ? ",
"curledn-1 : curledn; // 0 = all LEDs in a blink1, so shift or use 0th element as rep\n return currentState[blink1idx].colors[ curledn ];\n },\n getCurrentColor: function(blink1id,ledn) {\n var blink1idx = this.idToBlink1Index(blink1id);\n if(ledn===undefined) {\n ledn = currentState[blink1idx].ledn;\n ledn = (ledn>0) ? ",
"ledn-1 : ledn; // 0 = all LEDs in a blink1, so shift or use 0th element as rep\n }\n var color = currentState[blink1idx].colors[ ledn ];\n if( color === undefined ) {\n color = tinycolor('#000000');\n }\n return color;\n },\n\n // FIXME: this is confusing\n getCurrentColors: function(blink1id) {\n var blink1idx = this.idToBlink1Index(blink1id);\n // blink1idx = blink1idx || 0;\n return currentState[blink1idx].colors;\n },\n /**\n * Lookup blink1id (blink1 serial number) and map to an index in blink1s array\n * If 'blink1ToUse' is set, and blink1id is undefined or 0, use blink1ToUse\n * FIXME: Should use conf.blink1Service.blink1ToUse\n * FIXME: should convert serial to index\n * @param {number|String} blink1id array id (0-maxblink1s) or 8-digit blink1serial\n * @return {number} known-good index into blink1s array or 0\n */\n idToBlink1Index: function(blink1id) {\n var blink1idx = 0; // default to first blink1\n if( blink1id === undefined || blink1id === '' ) {\n if( this.conf.blink1ToUse ) {\n blink1id = this.conf.blink1ToUse;\n } else {\n blink1id = (currentBlink1Id) ? ",
"currentBlink1Id : 0; // 0 = common case\n }\n }\n // it's an array index (also early-exist for common 0 case)\n if( blink1id >= 0 && blink1id < blink1s.length ) {\n return blink1id;\n }\n // otherwise it's a blink1 serialnumber, so search for it\n blink1id = blink1id.toString().toUpperCase();\n blink1s.map( function(b,idx) {\n if( blink1id === b.serial ) {\n blink1idx = idx;\n }\n });\n return blink1idx;\n },\n // debug only\n dumpCurrentState: function() {\n var str = '';\n currentState.map( function(b1state, i) {\n var colorsstr = b1state.colors.reduce( function(prev,curr) { return prev +','+ curr.toHexString(); });\n str += 'blink1Idx:'+i+ ': ledn:'+b1state.ledn+ ', millis:'+b1state.millis+ ', colors:'+colorsstr + ';\\n';\n });\n return str;\n },\n /**\n * Main entry point for this service, sets currentColor & currentLedN\n * 'color' arg is a tinycolor() color or hextring ('#ff00ff')\n * if color is a hexstring, it will get converted to tinycolor\n * ledn is 1-index into color array, and ledn=0 means \"all leds\"\n * blink1_id is index into blink1s array (but should also be by serialnumber)\n * FIXME: currentState[0] will be currentState[blink1idx]\n *\n * @param {[type]} millis [description]\n * @param {[type]} color [description]\n * @param {[type]} ledn [description]\n * @param {[type]} blink1_id [description]\n * @return {[type]} [description]\n */\n fadeToColor: function( millis, color, ledn, blink1_id) {\n // var startmillis = new Date().getTime()\n // console.log(\"Blink1Service.fadeToColor: start \" + startmillis);\n ledn = ledn || 0; // 0 == all LEDs\n if( typeof color === 'string' ) {\n color = tinycolor( color ); // FIXME: must be better way\n }\n // convert blink1_id to array index\n var blink1Idx = this.idToBlink1Index(blink1_id);\n\n // FIXME: how to make sure 'color' is a tinycolor object? ",
"color.isValid?",
"\n // log.msg('Blink1Service.fadeToColor: blink1Idx:',blink1Idx,' msec:',millis,' ledn:',ledn,\n // \t' c:',color.toHexString(), \"currentState:\\n\"+ this.dumpCurrentState()); // JSON.stringify(currentState,null,2));\n\n var colors = currentState[blink1Idx].colors;\n // handle special meaning: ledn=0 -> all LEDs\n if( ledn === 0 ) { colors = colors.fill( color ); }\n else { colors[ledn-1] = color; }\n\n // FIXME: do we need these states and the blink1s struct?",
"\n // lastState[blink1idx] = currentState[blink1idx];\n currentState[blink1Idx] = { ledn: ledn, millis: millis, colors: colors };\n\n this.notifyChange();\n\n // divide currentMillis by two to make it appear more responsive\n // by having blink1 be at destination color for half the time\n millis = millis/2;\n // color, ledn, & blink1idx is known-good at this point\n this._fadeToRGB( millis, color, ledn, blink1Idx);\n\n // console.log(\"Blink1Service.fadeToColor: end \" + (new Date().getTime() - startmillis));\n },\n\n /**\n * Turn off everything, or for just a specific blink1\n * @method function\n * @param {String} blink1id blink1 serial number or id or nothing\n * @return {[type]} [description]\n */\n off: function(blink1id) {\n var self = this;\n self.toyStop();\n if( blink1id === undefined && blink1s.length > 0 ) {\n blink1s.map( function(serial,idx) {\n // console.log(\"POOP\");\n self.fadeToColor(100, '#000000', 0, idx);\n });\n } else {\n self.fadeToColor(100, '#000000', 0, blink1id); // 0 = all leds\n }\n },\n\n /**\n * Write a color pattern to a blink1\n *\n * @param {Object} pattern a pattern from PatternsService\n * @param {boolean} fill whether or not to fill-out the pattern with last pattern line\n * @param {String} blink1id blink1 serial number or id or nothing to use first blink1\n * @return error message, if any\n */\n writePatternToBlink1: function(pattern, fill, blink1id) {\n log.msg(\"writePatternToBlink1: \")\n var blink1idx = this.idToBlink1Index(blink1id);\n var colors = pattern.colors;\n if( !",
"colors ) {\n return \"no colors in pattern\";\n }\n var pattlen = colors.length;\n if( pattlen < 32 ) { // extend out pattern to fill\n for( var i=0; i< 32-pattlen; i++) {\n var c = {rgb:'#000000',time:0,ledn:0};\n colors.push( (fill) ? ",
"colors[i] : c );\n }\n }\n // if the device exists\n if( blink1s[blink1idx] && blink1s[blink1idx].device ) {\n var blink1dev = blink1s[blink1idx].device;\n for(var i=0; i<colors.length; i++) {\n var color = tinycolor(colors[i].rgb);\n var crgb = color.toRgb();\n var millis = colors[i].time * 1000;\n var ledn = colors[i].ledn;\n log.msg(\"Blink1Service.writePatternLine:\",i,\",crgb:\",crgb,\", millis:\",millis,\",ledn:\",ledn);\n try {\n // blink1dev.fadeToRGB( millis, crgb.r, crgb.g, crgb.b, ledn );\n blink1dev.setLedN( ledn );\n blink1dev.writePatternLine( millis, crgb.r, crgb.g, crgb.b, i );\n } catch(err) {\n log.error('Blink1Service.writePatternToBlink1: error', err);\n }\n }\n try {\n blink1dev.savePattern();\n } catch(err) { // this fails for some blink(1) devices\n log.msg(\"Blink1Service.writePatternLine: savePattern exception (expected)\");\n }\n }\n else {\n log.msg(\"Blink1Service.writePatternToBlink1: no blink1 device\");\n return \"no blink1 device\"\n }\n },\n\n /**\n * Stop the toy engine\n * @param {String} mode Toy mode: 'moodlight', 'colorcycle', 'strobe'\n */\n toyStop: function() {\n this.toy.mode = '';\n this.toy.enable = false;\n if( this.toy.timer ) { clearTimeout( this.toy.timer ); }\n },\n /**\n * Start up the toy engine\n * @param {String} mode Toy mode: 'moodlight', 'colorcycle', 'strobe'\n */\n toyStart: function(mode) {\n if( mode === 'moodlight' ) {\n this.toy.interval = 5000;\n }\n else if( mode === 'colorcycle' ) {\n this.toy.interval = 30;\n this.toy.value = Math.floor( Math.random() * 360 );\n }\n else if( mode === 'party' ) {\n this.toy.interval = 100;\n // this.toy.value = '#FFFFFF';\n }\n else if( mode === 'strobe' ) {\n this.toy.interval = 100;\n this.toy.value = '#FFFFFF';\n }\n else {\n log.msg(\"Blink1Service: unknown toy mode: \",mode);\n return;\n }\n this.toy.mode = mode;\n this.toy.enable = true;\n this.toyDo();\n },\n /**\n * Actually do the toy in question\n */\n toyDo: function() {\n var rledn = Math.floor( Math.random() * 2 ) + 1;\n var rhue = Math.floor( Math.random() * 360 );\n var rcolor;\n if( !",
"this.toy.enable ) { return; }\n if( this.toy.mode === 'moodlight' ) {\n rcolor = tinycolor( {h:rhue, s:1, v:0.75} );\n this.fadeToColor( this.toy.interval*2, rcolor, rledn );\n }\n else if( this.toy.mode === 'colorcycle' ) {\n this.toy.value += 2;\n this.toy.value = (this.toy.value>360) ? ",
"0 : this.toy.value;\n var color = tinycolor({h:this.toy.value, s:1, v:1});\n this.fadeToColor( 100, color, 0 );\n }\n else if( this.toy.mode === 'party' ) {\n rcolor = tinycolor({h:rhue, s:1, v:1});\n this.fadeToColor( this.toy.interval, rcolor, rledn);\n }\n else if( this.toy.mode === 'strobe' ) {\n this.toy.value = (this.toy.value==='#000000') ? '#",
"FFFFFF' : '#000000' ;\n this.fadeToColor( this.toy.interval, this.toy.value, 0 );\n }\n this.toy.timer = setTimeout(this.toyDo.bind(this), this.toy.interval);\n },\n\n addChangeListener: function(callback, name) {\n listeners.push( {name, callback} );\n log.msg(\"Blink1Service: addChangelistener\", listeners );\n },\n removeChangeListener: function(name) {\n listeners = listeners.filter( (listener) => listener.name !",
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"Gay Couple Recovering from Broken Bones After Attack at Seattle Pride\n\nPatrick Dettling and Scott Briggs said a group of three men punched and kicked their heads during a pride celebration after yelling a homophobic slur.",
"\n\nA gay couple is recovering from facial injuries after enduring what they believe was a hate-motivated attack during Seattle Pride, reports Seattle's KOMO-TV.",
"\n\nSteven Briggs and Patrick Dettling said they traveled from Olympia to Seattle Sunday to celebrate Pride at Capitol Hill and had enjoyed a morning full of fun and laughter. ",
"But when the couple sat down to eat lunch, they told KOMO a group of three men and two women stopped behind them. ",
"Dettling, who was seated and holding his hands behind his back to stretch, said one man hit his hand hard.",
"\n\n\"I said, Why did you do that?'\" ",
"Dettling recalled. \"",
"And he was like, 'I was just high-fiving you.' ",
"And I said, 'That wasn't a high-five.' ",
"And that's when things escalated.\"",
"\n\nDettling told KOMO his attacker punched him in the face several times as another yelled a homophobic slur. ",
"Briggs tackled that assailant to the ground but then the two other men kicked and punched him in the head. ",
"By the time he could stand up again, the group had made a run for it and Briggs could not keep up.",
"\n\nDettling and Briggs said they spent the next 5 hours in the hospital. ",
"Dettling suffered a broken nose, cuts, bruises, and a left leg injury that has made it difficult for him to walk. ",
"Briggs suffered a broken right ring finger and had half of a front tooth knocked out. ",
"Dettling snapped a picture of the worst of his injuries for evidence.",
"\n\nThe couple — together for 8 years and moving to a new home next week — told KOMO they were concerned they would now have to miss several days of work and pay thousands of dollars in medical bills as they recover from the attack.",
"\n\nDespite this, Briggs and Dettling couldn't be kept from from attending the rest of Pride. ",
"Briggs, who works as a crime victim advocate, convinced Dettling to return to the celebration, saying, \"No, we shouldn't let them get to us. ",
"We should come up here and do what we originally planned, which was to enjoy Pride,\" according to Dettling.",
"\n\nBut Dettling said he's still shaken. \"",
"It's kinda made me regress back a bit ... regress backwards in my progress of feeling comfortable with who I am. ",
"I feel like I've been pushed back a step,\" he explained to the station.",
"\n\n\"People have this idea now that same-sex marriage has been legalized, they think with marriage comes everything,\" he added. \"",
"You know, that all the ignorance and intolerance goes away — and it doesn't.\"",
"\n\nIn the wake of Friday's decision by the Supreme Court to legalize same-sex marriage nationwide, several LGBT groups have expressed concern that anti-gay violence might rise in a backlash.",
"\n\nFear rose over the weekend when a San Francisco Pride attendee was shot and wounded Saturday evening, but police say the gunfire stemmed from a disagreement unrelated to the event. ",
"Yesterday, a North Carolina man was arrested for assaulting a Charlotte bar owner several times as he yelled angrily about the ruling.",
"\n\nSeattle police have not yet identified Dettling and Briggs's attackers, but are investigating the alleged assault. ",
"It remains unclear whether hate crime charges will be filed.",
"\n\nLearn more in the KOMO report below."
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"---\nabstract: 'This paper reviews recent advances in the study or circumstellar masers and masers found toward supernova remnants. ",
"The review is organized by science focus area, including the astrophysics of extended stellar atmospheres, stellar mass-loss processes and outflows, late-type evolved stellar evolution, stellar maser excitation and chemistry, and the use of stellar masers as independent distance estimators. ",
"Masers toward supernova remnants are covered separately. ",
"Recent advances and open future questions in this field are explored.'",
"\nauthor:\n- 'Athol J. Kemball'\ntitle: 'Stellar masers, circumstellar envelopes, and supernova remnants'\n---\n\nIntroduction\n============\n\nThis review concerns circumstellar masers and the masers associated with supernova remnants. ",
"The material covered focuses primarily on results published since the last maser symposium, IAU 206 [@Mig02], but avoids those areas covered separately by other papers in these proceedings.",
"\n\nIn considering circumstellar masers, it is appropriate to start by first examining the host stars and the basic properties of the most common masers found in their circumstellar shells. ",
"The late-type evolved stars that host circumstellar masers are either red supergiants or large-amplitude long-period variables (LALPV), such as thermally-pulsing asymptotic giant branch (TP-AGB) stars. ",
"These stars are astrophysically important for well-known, but still important, reasons [@Hab96]:\n\n1. ",
" [Through their mass-loss they enrich the chemical and dust composition of the interstellar medium from which new stars form.]{}",
"\n\n2. ",
" [They are high-luminosity tracers of faint and obscured stellar populations and their main sequence progenitors; intermediate mass stars, for example, achieve their highest brightness at the tip of the AGB.]{}",
"\n\n3. ",
" [They highlight an important short-lived stage of stellar evolution in the transition from the AGB to planetary nebulae.]{}",
"\n\nThe key properties of the most common circumstellar maser transitions are summarized in Table \\[tab:masers\\]. ",
"Numerical values in this table are approximate only; representative temperatures and densities are drawn from @Rei02. ",
"In the most basic model of circumstellar masers, the maser species enumerated in Table \\[tab:masers\\] are assumed concentrically distributed about the central star, at radii broadly correlated with the transition excitation temperature.",
"\n\n \n\n SiO H$_2$O OH\n ------------------- ----------------------------------- ------------------- ---------------------------------------------------\n Transition ${v=0,1,2,3,..; \\triangle J=1}$ $6_{16} - 5_{23}$ ${}^2\\Pi_{3/2}, J=3/2, \\triangle F=\\{0,1\\}~~~$\n Radius (AU) $\\sim$ 3-6 $\\sim 100$ $\\sim 1000$\n $n_H$ (cm$^{-3}$) $5.10^{10}$ $10^8$ $10^7$\n Temperature (K) 1500 750 450\n Pumping mechanism Radiative or Collisional Radiative\n collisional \n\n : Common masers in late-type, evolved stars[]{data-label=\"tab:masers\"}\n\nGiven the late-type evolved stars and the basic properties of circumstellar masers they host, it is appropriate to ask the broader question of what larger astrophysical questions can be explored by stellar maser studies. ",
"We can answer this in part by noting first that masers are unique probes of obscured circumstellar astrophysics due to both their high brightness temperature and compact spatial structure. ",
"As such, they give us unique insights into the extended stellar atmosphere, the region between the photosphere and dust formation point. ",
"They also allow the study of the mass-loss process both near the star and in the outflow at larger radii. ",
"The masers allow an exploration of circumstellar excitation and pumping conditions as well as circumstellar chemistry. ",
"They also allow independent methods of stellar astrometry and distance measurement. ",
"We consider each of these scientific areas in more detail below.",
"\n\nIn addition to the topics listed here, stellar masers provide insights into stellar magnetic fields, basic maser theory, surveys for galactic population and dynamical studies, and are also used in specialized galactic center dynamics studies. ",
"Though each is extremely important, these issues are not included further in this review as they are covered by separate papers in these proceedings. ",
"Masers toward supernova remnants are covered in Section 7 below.",
"\n\nExtended atmosphere\n===================\n\nThe near-circumstellar environment is shown schematically in Figure \\[fig:reid02\\], taken from @Rei02. ",
"This region is dominated by mass-loss, shocks from the centrally-pulsating star, and is expected to have a complex kinematic and dynamical structure [@Eli92]. ",
"High-resolution imaging of this region is essentially only provided by SiO maser observations; a capability unmatched by contemporary telescopes in other wave-bands.",
"\n\n![",
"Schematic representation of the circumstellar envelope of a stellar maser from the inner envelope out to the dust formation zone; Figure 3 from @Rei02[]{data-label=\"fig:reid02\"}](Reid_2002B.eps){height=\"3.072in\" width=\"4in\"}\n\nA number of astrophysical sub-themes are of interest and importance in studies of the extended atmosphere. ",
"These can be broadly categorized as issues of kinematics, dynamics, and the physical conditions supporting individual maser transitions. ",
"In kinematics, there are open questions concerning localized flows, their connection to the central star and convective envelope, the nature and extent of any global asymmetry established at the base of the mass-loss process, and the matching of gas kinematics in this region to pulsation hydrodynamic models. ",
"The dynamical issues concern the nature of any shaping forces, and the magnitude and dynamical influence of local or global stellar magnetic fields. ",
"Physical conditions cover issues of excitation and chemistry.",
"\n\nKnowledge of the convective stellar envelope is limited primarily to numerical simulation studies [@Fre02; @Por97]. ",
"In the 3-D heat convection study of a red-giant atmosphere by @Por97, in which heat was supplied steadily to the central core to drive the convection, two unexpected behaviors arose, namely pulsation and large-scale convective flows. ",
"Complex convective structures and phenomena in the stellar envelope are likely to have a significant impact on the extended atmosphere.",
"\n\nThe extended atmosphere can be studied uniquely using VLBI observations of SiO masers, which act as ultra-compact astrophysical probes of this region. ",
"Their importance as probes of this inner CSE was realized soon after their first detection in the 1970s but early imaging studies faced difficult technical challenges [@Mor79; @Gen79], primarily due to the low sensitivity of millimeter-wavelength VLBI arrays. ",
"The advent of improved VLBI sensitivity enabled new observations [@Col92; @Miy94]; in particular, the commissioning of the VLBA[^1], a little over ten years ago, provided dramatically-improved imaging capabilities compared to the challenges faces by the earliest observations [@Dia94; @Gre95].",
"\n\nA particularly important result in the last several years has been the conduct of simultaneous near-infrared (NIR) interferometry and radio interferometry imaging campaigns of stellar SiO maser sources using the VLBA both in conjunction with the VLTI[^2] [@Bob05; @Wit05] and with IOTA/FLUOR[^3] [@Cot04; @Cot06]. ",
"These observations have allowed the unambiguous co-location of photospheric and SiO radii at ${R_{SiO}\\over{R_*}} \\sim 1.5-3.0$, without having to rely on model-based photospheric diameter estimates. ",
"The monitoring campaign reported by Cotton et al. (",
"2004) also hints at a possible relationship between the relative location of the 3.6 $\\mu m$ photosphere and a dependence of the SiO maser radius on the relative 3.6 to 2.2 $\\mu m$ photospheric radii. ",
"Those stars in this monitoring sample with higher 3.6 $\\mu m$ opacity in the molecular photosphere also appear to have large dust condensation radii.",
"\n\nAt longer IR wavelengths, the ISI[^4] has recently reported an important direct measurement of radial pulsation in the diameter of Mira at 11 $\\mu m$, showing a fluctuation in the continuum photosphere of +11% between stellar pulsation phase $\\phi=-0.08$ to 0.15 [@Wei03], in good agreement with theoretical models for Mira-class pulsation.",
"\n\nPulsation affects the extended atmosphere directly, driving periodic shocks into the near-circumstellar environment (NCSE) [@Ber85]. ",
"The shock emerges at pre-maximum, accelerating gas outwards, which subsequently falls back under the influence of gravity [@Hin82; @Hin97; @Alv00]. ",
"This produces a double-lined S-shaped velocity profile in photospheric infrared lines such as 1.6 $\\mu m$ CO $\\triangle \\nu=3$ absorption [@Hin82]. ",
"The shocks levitate material above the the hydrostatic atmosphere and subsequent radiation pressure on dust couples to the gas and carries it further outwards. ",
"Shock formation in the NCSE is studied in a number of spherically-symmetric, piston-driven hydrodynamic models of the stellar atmosphere [@bow88; @Bes96; @Hum02]. ",
"Shock propagation through the NCSE in these models leads to a saw-tooth velocity profile with radius. ",
"The models also accurately predict a net mass-loss of material to the outer circumstellar environment over time and a complex interaction between accelerating and decelerating gas from successive pulsation cycles.",
"\n\nIn the time since the last maser conference in 2001, the number of synoptic imaging campaigns of stellar SiO masers has increased significantly and yielded new results. ",
"These imaging campaigns are enabled by the technical advances in VLBI imaging at this wavelength, as noted above. ",
"Cotton and collaborators are monitoring a small LALPV sample in a snapshot imaging campaign [@Cot04; @Cot06]. ",
"Synoptic imaging of the Mira variable TX Cam has also continued both at short-spacing in pulsation phase [@Dia03; @Gon05], and over longer phase increments [@Yi05]. ",
"@Gon05 has shown that the median SiO maser component lifetime in TX Cam is approximately 150-200 days, a substantial fraction of the 557 day stellar pulsation period. ",
"This permits detailed proper motion studies, as reported by @Dia03 [@Gon05]. ",
"A global proper motion analysis shows outer components falling back from earlier pulsation cycles simultaneously with outflow during the current pulsation cycle. ",
"This is consistent with the saw-tooth velocity profile discussed above; however, there are significant local departures from a globally ordered flow in the measured proper motions in NSEW quadrants of the projected shell [@Dia03]. ",
"The mean velocities are broadly consistent with shock damping in the radio photosphere however, as deduced from upper limits to radio continuum stellar variability by @Rei97.",
"\n\nAn important astrophysical question in this area is the degree of agreement between measured mean global radial motions and the predictions of pulsation hydrodynamic models of the type discussed above. ",
"Recent reported mean global motions are summarized in Table \\[tab:prop\\] against the pulsation phase interval $\\triangle\n\\phi$, and whether the outflow was generally contracting, expanding, or neither. ",
"This table show that there are disagreements between individual stars in the same pulsation phase range (e.g. R Aqr, TX Cam, and VX Sgr), where both expansion and contraction are variously reported. ",
"However, note that this is comparing a known binary, a Mira variable, and a supergiant. ",
"Some authors [@Cot04; @Cot06] have also reported no systematic motions with pulsation phase for their sample. ",
"However, it is clear that this picture is likely more complex. ",
"If we examine TX Cam over multiple pulsation periods we can argue for inter-cycle variability and possible interaction between two competing time-scales, the pulsation period and the free-fall gravitational time-scale, possibly causing a non-strictly repeating pattern of global motions. ",
"We also note that there are systematic measurement effects that need to be carefully addressed. ",
"The inner shell is not circular and robust estimators are needed to determine the mean inner radius [@Dia03]. ",
"For at least one pulsation phase interval of TX Cam, there is clear evidence for ballistic deceleration with physically reasonable parameter values [@Dia03]. ",
"It is not true for all pulsation phase cycles however.",
"\n\n \n\n[llccl]{} Reference & Sources & $\\triangle \\phi$ & Projected & Outflow or\\\n& & & velocity (kms$^{-1}$) & infall\\\nBoboltz [et al.",
" ]{} (1997) & R Aqr & 0.78-1.04 & -4.2 & Contraction\\\n@Dia03 & TX Cam & 0.7-1.5 & +7 & Expansion\\\n@Cot04 & See below$^1$ & Various & & No pattern\\\n@Yi05 & TX Cam & 0.60-1.05 & & Slowing expansion\\\n@Gon05 & TX Cam & 1.5-2.7 & & Both\\\n@Cot06 & See below$^2$ & Various & & No pattern\\\n@Che06 & VX Sgr & 0.75-0.80 & -4 & Contraction\\\n\\\n\\\n\nThe issue of rotation in the extended atmosphere is also important from a kinematic and evolutionary perspective. ",
"Two detections of SiO maser shell rotation, including differential rotation, have been reported since the last maser meeting, namely for R Aqr [@Hol01] and Mira [@Cot06], both known binaries. ",
"This is, however, not common for other sources, as evident in the sector-averaged velocity plots reported by @Cot06 for their LALPV sample. ",
"Substantial rotation is difficult to explain in evolved late-type stars that are not part of multiple star systems.",
"\n\nThe expanded range of SiO imaging studies, such as those enumerated in Table \\[tab:prop\\], continue to reveal clear evidence for spatially-coherent arcs and filaments in the SiO maser region [@Kem97]. ",
"These local features have recently been argued by @Yi05 to be from spokes of SiO flows with line-of-sight velocities either slightly red- or blue-shifted with respect to the systemic stellar velocity. ",
"This kinematic structure maximizes the line-of-sight velocity coherence. ",
"The radial spokes are especially visible in several TX Cam image epochs reported by @Yi05, one of which is reproduced here as Figure \\[fig:yi2005\\].",
"\n\n![",
"VLBI maps of $v=1, J=1-0$ SiO maser emission toward TX Cam, summed over all channels of emission. ",
"The bar shows the flux scale in Jy/beam (Figure 3 from @Yi05).[]{data-label=\"fig:yi2005\"}](Yi_2005.eps){height=\"3.16in\" width=\"3in\"}\n\nOutflows\n========\n\nThe water and hydroxyl masers probe intermediate and outer circumstellar radii [@Cha86; @Boo81]. ",
"These masers trace the mass-loss process beyond the dust formation point; in this region, the flow is driven by radiation pressure on dust. ",
"The astrophysical sub-themes that are relevant to this region of the outflow include the kinematic structure of the mass-loss, including the degree of asymmetry on local and global scales, and the connection of this kinematic pattern to the inner NCSE. ",
"For cases where a dominant kinematic pattern is clear, the science issue becomes that of identifying any shaping processes. ",
"This is also a particularly important area of the outflow in which to explore the evolutionary onset of more extreme asymmetry related to post-AGB evolution, including stellar jets.",
"\n\nSome of these science questions have been explored in recent MERLIN[^5] observations of stellar water masers; @Bai03 report the first connected-element resolution of individual maser spots, and derive important parameters relating to the water maser region surrounding four LALPV stars: IK Tau, U Ori, RT Vir, and U Her. ",
"They report significant departures from spherical symmetry in tori that have an inner radius of 6-16 AU and an outer radius of 24-54 AU. ",
"Individual maser components are resolved out at 2-4 AU, and are found to be density-bounded $(\\sim 10^{1-2}$ times ambient), with a volume filling factor $< 0.5\\%$. In related MERLIN observations of the red-supergiant, VX Sgr, @Mur03 have performed a proper motion study of the water maser emission toward this source over a five year interval. ",
"A bi-conical outflow is used to describe the water maser kinematics. ",
"A similar over-density of maser components and a comparable extrapolated cloud size at the stellar surface of $\\sim 0.07 R_*$ is reported, relative to that given by @Bai03 for the sample of low-mass AGB stars. ",
"Both observations confirm an accelerating flow across the water maser region, with a logarithmic velocity gradient of $0.5 \\leq \\epsilon \\leq 1$.\n\nConcerning the role of water maser studies as a probe of early-onset post-AGB asymmetry, a particularly important result in recent years has been the discovery and exploration of a rare sub-class of AGB stars showing highly-collimated stellar jets [@Ima04; @Vle06]. ",
"The dynamical age of the jets is very young ($< 35-100$ years) and only a handful of such sources are known, consistent with this dynamical age. ",
"This rare class of “water fountain” sources is described in separate review papers in these proceedings by Imai and Vlemmings.",
"\n\nA particularly unusual and rare source studied by @Bab06 [@Szc06] presents water masers in a warped disk around a companion to the SiC star V778 Cyg.",
"\n\nOH observations of the supergiant NML Cyg are also reported by @Eto04. ",
"In this source, they present evidence for two shells, an older spherical shell, presumed from an earlier mass-loss phase, and a younger asymmetric flow.",
"\n\nLate-type stellar evolution\n===========================\n\nIn this section, we consider the issue of post-AGB evolution, and how stellar masers can inform our understanding of this phase of stellar evolution. ",
"Planetary nebulae (PNe) show a rich diversity of point- and axi-symmetric structure [@Bal02]. ",
"The immediate post-AGB (PAGB) evolution is heavily shrouded and masers provide a powerful method to study this transition phase, complementary to imaging studies in other wave-bands, such as infrared.",
"\n\nThe astrophysical sub-themes that are important in this area concern how to explain the prevalence of point- and axi-symmetry in PNe. ",
"Four major shaping mechanisms have been proposed including binarity, equatorial density enhancement, a globally-acting magnetic field and sculpting by highly-collimated stellar jets [@Mor03]. ",
"It is of significant interest to determine when the shaping mechanism is activated on the AGB.",
"\n\nAn over-arching issue in this area is also how to identify and select post-AGB objects in samples of OH-IR stars, such as the complete 1612 MHz OH survey conducted by @Sev97a [@Sev97b; @Sev01]. ",
"PAGB identification in such surveys is considered by @Sev02 based on clustering in color-color IR plots, using both IRAS and MSX data. ",
"Follow-up observations of candidate PAGB stars in the Sevenster survey are presented by @Dea04; their observations show a significantly higher incidence of asphericity in the candidate PAGB sample and further strengthen the IR color-color selection analysis by @Sev02.",
"\n\nKinematic models for OH outflow sources are presented by @Zij01 using a two component model, consisting of a shell/torus (20-25 kms$^{-1}$) and higher-velocity linear outflow (10-80 kms$^{-1}$).",
"\n\nMasers are particularly rare in young PNe, and only a handful of such sources are known although they are very important. ",
"These sources are discussed by Gómez (these proceedings).",
"\n\nExcitation and chemistry\n========================\n\nThe question of maser excitation, pumping, and circumstellar chemistry cuts across both theory and observation. ",
"It is needed to understand physical conditions in the masing regions and most importantly to properly interpret observations. ",
"In addition, these issues are central to predicting new masing transitions that may be accessible using future telescopes.",
"\n\nBoth collisional [@Loc91] and radiative [@Deg76] mechanisms have been proposed for SiO maser pumping. ",
"There are observational discriminants between the two pumping mechanisms, primarily the relative spatial location of v=1 and v=2 masers, variability studies, and linear polarization morphology. ",
"There have been important recent observational results in this area, but conclusions drawn in the literature remain mixed. ",
"Based on the location of the v=1 and v=2 J=1-0 masers toward TX Cam, @Yi05 cite evidence for collisional pumping. ",
"However, @Sor04 draw the opposite conclusion from v=1 and v=2 J=1-0 imaging of the SiO masers toward IRC+10011 and $\\chi$ Cyg. ",
"In recent variability studies, @Par04 reports finding a zero phase lag between IR and SiO flux density over an 11-year short time-spacing monitoring campaign, and @McI06 finds no time-lag between several vibrationally-excited J=1-0 transitions toward Mira. ",
"Both authors argue for radiative SiO pumping as a result. ",
"@Ase05 consider the effect of anisotropic radiative pumping and the Hanle effect on the linear polarization morphology of SiO stellar masers.",
"\n\nStudies of the relative location of different rotational transitions in the same vibrational state, primarily J=2-1 relative to J=1-0, have shown perplexing results [@Sor04; @Phi03]. ",
"In the handful of sources imaged so far, the morphology is significantly different, contrary to basic theoretical expectations. ",
"Line overlaps may strongly influence the theoretical predictions about spatial location however, as discussed by @Sor04.",
"\n\nAnother important recent result in SiO maser excitation has been the imaging of v=0, J=1-0 SiO maser emission towards a sample of late-type, evolved stars by @Bob04. ",
"A predominance of weak masers is confirmed and one source was found to have thermal emission. ",
"Although their spatial resolution is limited, they propose that v=0 is found at twice the radius of the v=1 emission.",
"\n\nSeveral new possible masers have been reported toward C-stars since our last meeting, including new HCN lines toward a sample of carbon stars [@Bie01], and a possible weak OH maser detection toward IRC+10216 [@For03].",
"\n\n@Men06 also report the possible new detection of maser action in the H$_2$O $v_2=1,6_{61}-7_{52}$ line at 294 GHz toward VY CMa. ",
"In addition, @Tho03 report weak maser emission in the J=9 $l$-type HCN transition toward CRL 618.",
"\n\nIndependent distance estimates\n==============================\n\nStellar masers can also be used to provide independent stellar distances. ",
"This technique, demonstrated by @vLa00, is based on the assumption that the compact, blue-shifted maser emission is assumed coincident with the central star. ",
"The technique was applied to further AGB stars by @Vle03.",
"\n\nOH stellar astrometry is likely limited to distances less than 1 kpc [@Vle03]; astrometry using H$_2$O and SiO masers can reach larger distances. ",
"Recently, @Kur05 demonstrated stellar water maser astrometry in observations of UX Cyg. ",
"@Vle02 also showed positional coincidence between the brightest water maser feature toward U Her and the stellar Hipparcos position.",
"\n\n1720 MHz OH masers toward supernova remnants\n============================================\n\nOH 1720 MHz masers, shock-excited toward supernova remnants (SNR), were first detected by @Gos68. ",
"Their phenomenology is now well-known and a sound theoretical basis has been established for their modeling and pumping [@Gre02].",
"\n\nThey are an important probe of SNR shock interactions with molecular clouds, and are also found in the galactic center circumnuclear disk. ",
"They are considered in more detail in separate invited papers in these proceedings by Brogan, Yusef-Zadeh, and Hewitt.",
"\n\nThe future\n==========\n\nThere remain important open astrophysical problems in the area of circumstellar and SNR masers, requiring advances in both observation and theory. ",
"An integrated model for the kinematics and dynamics of the mass-loss process from the convective stellar envelope, through the extended atmosphere to the outer circumstellar shell will require further detailed observations, and more complex numerical hydrodynamic models in order to explain the observed local and global asymmetries and to identify the underlying shaping forces. ",
"This is particularly important in so far as it concerns stellar magnetic fields of late-type, evolved stars. ",
"Recent detections of stellar jets in water maser emission also open new windows on post-AGB evolution. ",
"The theory of astrophysical masers continues to remain central to this field, and recent observations have posed new theoretical questions, particularly in the area of SiO excitation, that are vital to proper interpretation of observations. ",
"We are also on the cusp of major new observational advances in this field, driven by the commissioning of VERA[^6], ALMA[^7], and the eVLA[^8] and look forward to significant future results from these instruments.",
"\n\nThe author would like to gratefully acknowledge the support of the National Science Foundation under grant NSF AST 05-07473.",
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"The invention concerns a device for attaching an essentially vertical guide for a submersible mixer in a liquid tank.",
"\nMixers are often used in tanks for holding liquids containing amounts of solid bodies to prevent sedimentation and to keep the liquid homogeneous. ",
"A type of mixer often used today is a submersible machine comprising an electric motor which may be provided with a gearbox, and an impeller. ",
"The machine is then normally arranged to be lowered along a vertical guide which is attached within the tank in a suitable way. ",
"One way of attaching the guide in the tank is by mounting one end of the guide for pivotal movement near the opening in the tank. ",
"This is described in co-pending application of Hjalmar Fries-Roland Narholm Bengt Thomaeus, Ser. ",
"No. ",
"847,809, filed Apr. 3, 1986, entitled \"A Method and a Device for Installation of a Mixer\". ",
"The advantage of a submersible machine/vertical guide arrangement is, above all, that the mixer may be easily raised for service and in addition is very easy to adjust in various directions.",
"\nThe central and important part in the plant is, in addition to the mixer itself, the guide used to lower the machine down to its operating position. ",
"The guide must be easy to attach in tanks already in use. ",
"It is also important that the attaching devices are not obstacles when the machine is moved along the guide. ",
"The attaching devices must also be suitable for attaching to horizontal, vertical as well as sloping surfaces. ",
"In order to provide an inexpensive solution, the same type of device should be used for all types of surfaces. ",
"Finally, the attaching means must be so designed that the guide can be rotated in both directions. ",
"This rotation is necessary to make possible various directions of the mixer, and the guide must also be turned when the mixer is lifted and taken away from the tank."
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"Arbon District\n\nArbon District is one of the five districts of the canton of Thurgau in Switzerland. ",
"It has a population of (as of ).Its capital is the town of Arbon.",
"\n\nThe district contains the following municipalities:\n\nReferences\n\nCategory:Districts of Thurgau"
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"Q:\n\nWhat is the standard order to develop software features in?",
"\n\nFor a beginner hobbyist, it seems fairly common to create everything in the order it will be viewed by the user, regardless of its importance, and to intertwine back-end and front-end development.",
"\nObviously, this isn't the most efficient method and would probably be avoided by more experienced developers. ",
"I've been exploring different ways to order software development, but I'd like to know if there's a standard that's widely accepted or recommended by the industry.",
"\n\nA:\n\nThat is what software development processes are for.",
"\nThing is: there are many different processes; thus there are many different answers to your question.",
"\nIn 2017, most organisations use processes around the \"agile\" mindset (or they try to get there), thus your first stop could be Agile software development.",
"\nAnd to give a direct answer to your question:\n\nwhen you start an agile project, you simply don't know about \"all the things the user will view\"\ninstead, you collect requirements\nyou translate requirements into \"user stories\"\nthen the development team and the users (or user representatives) decide on the priority of those user stories\nand then, during the development iterations (sprints) a subset of the \"most important\" user stories is implemented\n\nThe key part here: requirements and their priorities are subject to change. ",
"The idea to collect everything upfront, to then define an order over all items is simply rejected nowadays. ",
"\n\n"
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"Q:\n\nDouble integral - finding the region\n\nI need to find the volume of an object bounded by the following planes:\n$$z=y+4$$\n$$x^{2}+y^{2}=4$$\n$$z=0$$\nIs this true that the region of interest on the XY plane is the whole circle drew by the second formula above?",
"\n\nA:\n\nIf you do a little sketch, you get\n$$-2\\le x\\le 2\\;,\\;\\;-\\sqrt{4-x^2}\\le y\\le\\sqrt{4-x^2}\\;,\\;\\;0\\le z\\le y+4\\implies$$\n$$\\int\\limits_{-2}^2dx\\int\\limits_{-\\sqrt{4-x^2}}^{\\sqrt{4-x^2}}dy\\int\\limits_0^{y+4}dz=\\int\\limits_{-2}^2dx\\int\\limits_{-\\sqrt{4-x^2}}^{\\sqrt{4-x^2}}(y+4)dy=$$\n$$=\\int\\limits_{-2}^2 8\\sqrt{4-x^2}=16\\int\\limits_{-2}^2\\sqrt{1-\\left(\\frac x2\\right)^2}\\;dx=32\\int\\limits_{-\\pi/2}^{\\pi/2}\\cos^2t\\,dt$$\nThe last equality following from the substitution\n$$\\frac x2=\\sin t\\;,\\;\\;dx=2\\cos t\\,dt\\;,\\;\\;\\text{ so }$$\n$$32\\int\\limits_{-\\pi/2}^{\\pi/2}\\cos^2t\\,dt=\\left.32\\frac{t+\\sin t\\cos t}2\\right|_{-\\pi/2}^{\\pi/2}=16\\pi$$\n\n"
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"1. ",
"Technical Field\nThe present invention generally relates to a computer comprising a storage function for storing data of a storage device, and particularly relates to a computer comprising a data replication function or remote copy function (hereinafter referred to as the “remote copy function”) for transferring data of the storage device to an external storage controller.",
"\n2. ",
"Description of the Related Art\nA client-use computer such as a personal computer to be used by a user for running application programs such as document processing is basically configured the same as a server-use computer such as a web server or an email server that executes application programs for providing service to a plurality of users, and is configured from computer resources such as a CPU, a memory, a hard disk, a network connection and the like.",
"\nA client-use computer generally has limited computational resources in comparison to a server-use computer. ",
"In addition, when the client-use computer is a portable computer such as a laptop (notebook) computer, there are many cases where the client-use computer is subject to physical shock and damaged while it is being carried around.",
"\nA computer stores an operating system, application programs and user data in a storage device such as a hard disk, and the operating system reads application programs and user data from the storage device into a memory, updates the user data and the like, and writes the same into the storage device according to instructions from the user.",
"\nAs technology for preserving this kind of data, for example, RAID (Redundant Arrays of Inexpensive Disks) technology for collectively managing a plurality of hard disks as a single hard disk is well known, and it is primarily implemented in a server-use computer.",
"\nIn light of the failure rate of client-use computers, it is also necessary to take measures for reliably preserving data as with server-use computers, but since the foregoing RAID technology requires a plurality of hard disks, it is inappropriate for use in client-use computers with limited computational resources.",
"\nThus, technology has been disclosed for using a bitmap table corresponding to the data area of a storage apparatus and transferring the data of a first storage to a second storage (e.g., US Patent Application Publication No. ",
"2005/0071589).",
"\nAlso disclosed is technology of acquiring write data from a first storage and transferring such write data to a second storage (e.g., US Patent Application Publication No. ",
"2004/0078630)"
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[
"1. ",
"Introduction {#sec0005}\n===============\n\nModern sectors like health care, agriculture, environmental monitoring, forensic diagnosis, food safety, and industrial applications depend heavily on low-cost, point-of-care tests (POCT) \\[[@bib0005], [@bib0010], [@bib0015], [@bib0020]\\]. ",
"Across all areas, a variety of technologies and hybrid devices have been extensively reported, indicating the rapid improvement and spread of the point-of-care (POC) analysis. ",
"To this end, it is now possible to perform rapid, efficient, inexpensive, and easy analyses almost anywhere and at any time \\[[@bib0025], [@bib0030], [@bib0035], [@bib0040], [@bib0045]\\]. ",
"Over the past few decades, lateral flow immunoassay strips (LFIS) have become an increasingly popular diagnostic tool for use in POCT because of their use-friendliness, rapidity, inexpensive nature, and specificity \\[[@bib0050], [@bib0055], [@bib0060], [@bib0065], [@bib0070]\\]. ",
"Currently, LFIS are considered to be one of the easiest methods to commercialize for use as a POC diagnostic tool.",
"\n\nGiven this, different signal material have been developed to meet different detection requirements, including ones containing colloidal gold \\[[@bib0075]\\], magnetic nanoparticles \\[[@bib0080]\\], quantum dots \\[[@bib0085]\\], fluorescence \\[[@bib0090]\\], biological enzyme \\[[@bib0095]\\], Raman enhancement probe \\[[@bib0100]\\] and nano-enzyme \\[[@bib0105]\\], etc. ",
"In addition, different types of LFISs have been developed through conjunction with different technologies to enable the detection of different analytes, such as barcodes lateral flow strip \\[[@bib0110],[@bib0115]\\], biochemical-immunological hybrid biosensor \\[[@bib0095]\\], etc. ",
"Despite this variety, AuNPs-LFIS are one of the most common types of LFIS due to its inexpensive cost of production, ease of manufacture, stability, and simple readout. ",
"However, classic AuNPs-LFIS detection uses the naked eye, only providing a \"yes/no‿ result. ",
"If quantitative analysis is needed, professional image analysis software and commercial instruments would be required. ",
"This limits the wide application of AuNPs-LFIS in homes or in on-site testing in resource-poor areas \\[[@bib0120]\\]. ",
"Therefore, a simple, inexpensive, user friendly, and pocket-sized reader would be an extremely useful tool to further advance the usability of the AuNPs-LFIS analytic technique.",
"\n\nOver the past decade, mobile phones have seen rapid development and gained ever-increasing levels of computational power. ",
"Globally, there are more than 5 billion mobile phone subscriptions, which is largely due to their ease of use and wide functionality. ",
"Critically, this popularity provides a development opportunity for their use in portable detection \\[[@bib0125],[@bib0130]\\]. ",
"Due to their multifunctional capacities (e.g. permanent, built-in physical sensors, multi-core processors, digital cameras, USB ports, audio jacks, wireless transmission devices, and application software), smartphones have potential application in a wide variety of biosensor platforms \\[[@bib0135],[@bib0140]\\]. ",
"In addition, the wireless telecommunication technologies incorporated within them allows for data upload to the internet. ",
"This could then help establish a ubiquitous platform for real-time, on-site monitoring \\[[@bib0145]\\]. ",
"Given this, coupling smartphones with LFIS could provide a portable, equipment-free, rapid, low-cost, and user-friendly POCT platform. ",
"To this end, Mudanyali et al. ",
"designed a cellphone-based reader platform that could work with various LFISs and get instrument similar tests to sense the presence of target analyte in samples. ",
"This platform could detect malaria, tuberculosis and HIV RDTs by installing it on both Android-based smartphones and iPhones \\[[@bib0150]\\]. ",
"Ling et al. ",
"reported a lateral flow-through strip for use with a smartphone camera that could quantitatively detect alkaline phosphatase activity in milk \\[[@bib0155]\\]. ",
"Hou et al. ",
"developed a smartphone-based, dual-modality imaging system that quantitatively detected either color or fluorescent LFIS \\[[@bib0160]\\]. ",
"In previous reports, smartphone-based LFIS readers were used directly with smartphone cameras to capture images of the LFIS test results. ",
"The data from these images were digitally processed using software. ",
"However, this approach has limits to its accuracy, resulting from the different pixilation and focal lengths between different smartphone's cameras. ",
"To this end, the ambient light sensor on a given smartphone is sensitive and accurate and offers a more consistent starting point to develop a biosensor readout system. ",
"A microplate reader based on smartphone's ambient light sensor to measures transmitted light intensities of liquid assay have been developed in our laboratory \\[[@bib0165], [@bib0170], [@bib0175], [@bib0180]\\]. ",
"The results were consistent with those obtained from a professional microplate reader and demonstrated its potential use in a variety of detection strategies for different targets.",
"\n\nHere, we have developed a LFIS reader based on the ambient light sensor of a smartphone and have extended our initial approach to now allow for the direct quantification of AuNPs-LFIS. ",
"The analytical system comprised a smartphone with ambient light sensor and an accessory (height 42 mm; width 30 mm; length 66 mm; weight 30 g) made by a 3D-printer. ",
"The principle behind this approach is as follows: (1) AuNPs accumulate at the testing zone positions, which decrease light transmittance through the NC membrane. (",
"2) When the reader\\'s switch is opened, the light emitted from the light-emitting diode (LED) projects over the testing zone positions and is then recorded by the ambient light sensor. (",
"3) The light intensity signal is displayed on the smartphone's screen using an app specifically designed to measure illuminance. (",
"4) Light intensity relies on the degree of AuNPs coloration, AuNPs coloration is dependent on the concentration of the measured substance. ",
"Given this relationship, the light transmittance intensity can be used to directly quantify the tested sample ([Fig. ",
"1](#fig0005){ref-type=\"fig\"} ). ",
"We then analyzed three different analytes (cadmium ion (Cd^2+^), clenbuterol (CL), and porcine epidemic diarrhea virus (PEDV)) to validate our newly developed smartphone-based colloidal gold LFIS reader. ",
"Readout results were consistent with those obtained from traditional approaches, demonstrating that our smartphone based-reader could accurately quantify AuNPs-LFIS.Fig. ",
"1AuNPs-LFIS and plastic housing schematic representations for the SPALS-based reading system: (a) LFIS section; (b) Plastic housing.",
"Fig. ",
"1\n\n2. ",
"Materials and methods {#sec0010}\n========================\n\n2.1. ",
"Material {#sec0015}\n-------------\n\nGoat anti-mouse immunoglobulins G (IgG) were obtained from Sun gene Biotech Co., Ltd (Tianjin, China). ",
"Nitrocellulose (NC) membranes were purchased from Millipore (Shanghai, China). ",
"Plastic backing and absorbent pads, conjugation pads, and sample pads were obtained from JN Bio Co., Ltd (Shanghai, China). ",
"Chloroauric acid (HAuCl4), Bovine serum albumin (BSA), Trisodium citrate (99.8%), polyethylene glycol (PEG, MW, 2000), polyvinylpyrrolidone (PVP, MW 40,000), and S-17 (Rhoda surf ON-870) were all purchased from Sigma-Aldrich. ",
"Isothiocyanate benzyl-EDTA (iEDTA) was purchased from Dojindo Laboratories (Kumamoto, Japan). ",
"All aqueous solutions were prepared with double-distilled water (Milli-Q, Millipore). ",
"Cadmium chloride (99.99%) was purchased from Aldrich Chemical (Milwaukee, WI, USA). ",
"All other metal ions were purchased from Merck Chemical (Darmstadt, Germany). ",
"All other chemicals were of analytical grade and used without any further purification. ",
"The anti-Cd^2+^-EDTA monoclonal antibody(mAb)and the coating antigen BSA-Cd^2+^-EDTA were provided by our laboratory. ",
"The complete clenbuterol antigen (CL-BSA) and anti-CL monoclonal antibody(mAb)was purchased from Fapon Biotech Inc. (Shenzhen, China). ",
"The pierce TM BCA protein assay kit was purchased from Thermo Scientific (Rockford, USA). ",
"The PED Ag test kit was purchased from BioNote, Inc. (Gyeonggi-do, Korea). ",
"PEDV solution (106 TCID50/ml) was isolated, identified, and provided by Guangdong HAId Group Co., Ltd. LEDs (510 nm) were purchased from Shenzhen OCtai Co., Ltd. A battery (3 V) was purchased from VSAI while resistor (30,000 Ω), switch, and wires were collected from a local store.",
"\n\n2.2. ",
"Design of SPALS-based LFIS reader {#sec0020}\n--------------------------------------\n\nThe auxiliary device consisted of a switch, a 30,000 Ω resistor, three batteries (3 v), and a 520 nm LED. ",
"All of these electrical and optical elements were consolidated into a 3D printed, fixed structure (66 × 30 × 42 mm^3^) weighing approximately 30 g. The 3D printed, fixed structure was designed by SolidWorks 2016 software and fabricated using an EinStart-S 3D printer (SHINING 3D Technology Co., LTD). ",
"The printing material was thermoplastic black butadiene styrene (ABS) polymers, and was purchased from SHINING 3D Technology Co., LTD (Hangzhou, China).",
"\n\n2.3. ",
"AuNPs-LFISs preparation for use with SPALS-based reader {#sec0025}\n------------------------------------------------------------\n\nThe AuNPs-LFIS structure was slightly altered when compared with conventional LFIS for use specifically with the SPALS-based reading system. ",
"Briefly, the bottom of the board was hollowed under the T/C-lines ([Fig. ",
"1](#fig0005){ref-type=\"fig\"}a). ",
"The plastic housing was specially modified and equipped with a light transparent hole in the bottom ([Fig. ",
"1](#fig0005){ref-type=\"fig\"}b). ",
"These modifications were necessary to allow for light transmission. ",
"Additional information regarding the preparation and fabrication process for the model AuNPs-LFIS, Cd^2+^-LFIS, CL-LFIS, and PEDV-LFIS are provided in Supplementary Information.",
"\n\n2.4. ",
"Quantitative reading of LFIS using both the SPALS-based reader and traditional image analysis method {#sec0030}\n---------------------------------------------------------------------------------------------------------\n\nBriefly, the procedure for using the SPALS-based reader to assess LFIS results was as follows: First, samples were added to sample orifice. ",
"After the immunoreaction was completed, LFIS were placed into the SPALS-based reader and the resulting, transmitted light intensities were measured using the Light Meter App. ",
"Simultaneous to light intensity measurements, a picture of the LFIS was obtained using the smartphone's camera. ",
"Images were then analyzed using the free image analysis software Image J (NIH). ",
"Additional details regarding these experiments are provided in Supplementary information.",
"\n\n3. ",
"Results and discussion {#sec0035}\n=========================\n\n3.1. ",
"Work principle behind the SPALS-based LFIS reader {#sec0040}\n------------------------------------------------------\n\nIn this study, we developed a battery powered, 3D-printed attachment that could be connected to a smartphone's ambient light sensor (SPALS). ",
"This could then be used to quantitatively read the results of colloidal gold lateral flow immunoassay strips ([Fig. ",
"2](#fig0010){ref-type=\"fig\"} a). ",
"Here, we chose an Android-based phone as the baseline smartphone for fabricating the reader. ",
"However, the SPSLS-based LFIS reader is easily adaptable to different mobile phones with minor modifications to the accessory (e.g. XIAOMI Note or HUAWEI P10). ",
"The attachment module included the LED, batteries, resistors, switch, wires, and a 3D-printed structure ([Fig. ",
"2](#fig0010){ref-type=\"fig\"}b). ",
"LED wavelengths were specifically matched with the maximum absorption spectra of the AuNPs. ",
"The resistor (30,000 Ω) was used to regulate the intensity of the excitation light. ",
"Three batteries (3 V) was used to power the LED. ",
"The switch allowed the reader to turn on and off while the wires were used to connect all of the electronic components. ",
"The 3D-printed accessory held two light transparent holes of 2 mm diameter: The top hole was connected to the LFIS's light transparent hole, the following hole was connected to the ambient light sensor. ",
"The 3D-printed accessory was equipped with a holder cartridge (64 × 21 × 7 mm^3^) as well as a holder slot (49 × 30 × 8.4 mm^3^), which were used to place the LFIS and fix the accessory in the cell phone, respectively. ",
"The holder slot is easily modifiable to fit any smartphone. ",
"The smartphone application for light intensity signal acquisition and data display was a free android app, Light Meter App. ",
"Collectively, the SPALS-based reader accessory weighed approximately 30 g, was manufactured in 2 h, and only cost \\$1.30 (Table S1).Fig. ",
"2Schematic illustration of the smartphone based AuNPs-LFIS reading system: (a) Three-dimensional structure of the AuNPs-LFIS reader installed on an Android-based smartphone and placed LFIS; (b) Design of the smartphone-based AuNPs-LFIS reader.",
"Fig. ",
"2\n\n3.2. ",
"Work principle behind the SPALS-based LFIS reader {#sec0045}\n------------------------------------------------------\n\nThe working principle behind the SPALS-based LFIS readers is diagrammed and displayed in [Fig. ",
"3](#fig0015){ref-type=\"fig\"} . ",
"The immunoreaction on the NC membrane was completed by the sample, AuNPs-immunoreagents, and T-line's immunoreagents. ",
"AuNPs-colored bands were formed since the label accumulated at specific positions on the NC membrane. ",
"The degree of the analyte concentration was then displayed as its corresponding color intensity. ",
"AuNPs have specific optical properties; as such, AuNPs color can decrease light transmittance through the NC membrane. ",
"When the LFIS assay was completed, the LFIS was put into the SPALS-based LFIS reader. ",
"The reader's switch was opened and the light emitted by the LED was projected over the NC membrane. ",
"This was then measured by the ambient light sensor of the smartphone. ",
"The light intensity signals were displayed on the smartphone's screen using the Light Meter app. ",
"When AuNPs concentration on the NC membrane was low, measured transmitted light intensity was high. ",
"Conversely, when AuNPs concentration on the NC membrane was high, measured transmitted light intensity was low. ",
"Given this relationship, it is clear that the transmitted light intensity depends on AuNPs concentration.",
"Fig. ",
"3SPALS-based AuNPs-LFIS reading system schematic: (a) Image of the actual optical reader installed on the smartphone HUAWEI P10; (b) Work principle behind the smartphone-based AuNPs-LFIS reading system. ",
"Light emitted by the LED was projected over the T-line of the strip, which was then record by the smartphone's ambient light sensor; (c) When AuNPs concentration on the NC membrane was high, transmitted light intensity as measured by the SPALS-based AuNPs-LFIS reader was low; (d) When AuNPs concentration on the NC membrane was low, intensities of measured light transmittance by the SPALS-based AuNPs-LFIS reader was high.",
"Fig. ",
"3\n\nIn order to study the accuracy of the smart phone based LFIS reader, we prepared a simple AuNPs-LFIS model. ",
"When the goat anti-mouse IgG-AuNPs and mouse IgG immunoreactions are performed on the T-line, the AuNPs colored bands will result. ",
"The transmitted light intensities of the LFIS were then record by the SPALS-based reader. ",
"Simultaneous to this, color images were obtained by the smartphone's camera and were analyzed using the image analysis software Image J. As shown in [Fig. ",
"4](#fig0020){ref-type=\"fig\"} a and b, increasing AuNPs concentrations resulted in decreasing transmitted light intensities. ",
"To quantitatively determine the agreement between our SPALS-based reader and more conventional image analysis, we then performed a linear correlation. ",
"Results between the SPALS-based reader and image analysis showed strong agreement (R^2^ = 0.992, [Fig. ",
"4](#fig0020){ref-type=\"fig\"}c). ",
"Transmitted light intensities were obtained from 10 runs of the quantitative AuNPs LFISs assays and each had nearly identical results ([Fig. ",
"4](#fig0020){ref-type=\"fig\"}d). ",
"Taken together, these findings demonstrate the smartphone-based LFIS reader's feasible and stability.",
"Fig. ",
"4Performance of SPALS-based AuNPs-LFIS reader: a. Photograph of the quantitative AuNPs-LFISs for detecting different AuNPs concentration; b. Smartphone images of assays for detecting different AuNPs concentration; c. Agreement between detected results obtained by the SPALS-based reader and image analysis; d. Stability of the SPALS-based reader. ",
"Each value represents the mean of three independent experiments (n = 3).Fig. ",
"4\n\n3.3. ",
"Performance of the SPALS-based LFIS reader for quantitative detection of Cd^2+^ and CL {#sec0050}\n-------------------------------------------------------------------------------------------\n\nSmall analytes are one of the most commonly used indicators to test for environmental pollution, pesticide residue, food safety, and drug inspection \\[[@bib0185]\\]. ",
"Due to their smaller molecular mass and single antigenic determinant, competitive format lateral flow assay has been widely employed for testing for the presence of small analytes. ",
"Cadmium (Cd^2+^) and clenbuterol (CL) have been important testing targets for both environmental pollutants and food safety, respectively. ",
"As established by the World Health Organization (WHO), the maximum contaminant level (MCL) for Cd^2+^ in drinking water is 3 ng/mL \\[[@bib0190],[@bib0195]\\]. ",
"Detecting Cd^2+^ in either drinking water or agricultural irrigation water has been shown to be a very effective way to reduce cadmium pollution. ",
"Clenbuterol (CL) is a synthesized β2-agonist/antagonist and is used to promote animal growth and decrease fat synthesis. ",
"Poisoning symptoms can occur in individuals who consume food containing CL residues. ",
"Although many countries have banned the use CL in livestock, CL poisoning has been frequently reported \\[[@bib0070],[@bib0200],[@bib0205]\\].",
"\n\nAs shown in [Fig. ",
"5](#fig0025){ref-type=\"fig\"} a and d, we conducted an analysis for Cd^2+^ and CL levels using our SPALS-based reader. ",
"Results indicated that increasing Cd^2+^ analyte concentration corresponded to increasing transmitted light intensities, with a strong linear correlation between the two (R^2^ = 0.989). ",
"Cd^2+^ concentrations were found to be within the range of 0.1953--50 ng/mL and the limit of detection (LOD) was 0.16 ng/mL. To detect CL, results indicated a good linear correlation (R^2^ = 0.978) between the transmitted light intensities and CL concentration. ",
"The range obtained was 0.0625--1 ng/mL and the LOD for the CL assay was 0.046 ng/mL. As shown in [Fig. ",
"5](#fig0025){ref-type=\"fig\"}b and e, the two reading methods for Cd^2+^-LIFS and CL-LIFS showed excellent correlations. ",
"We next validated the feasibility of using the SPALS-based reader for the analysis of spiked Cd^2+^ tap water samples and separate samples from the Pearl River (Guangzhou, China, see [Fig. ",
"5](#fig0025){ref-type=\"fig\"}d). ",
"CL in swine urine samples was measured using LFIS and result were read using the SPALS-based reader ([Fig. ",
"5](#fig0025){ref-type=\"fig\"}f). ",
"These results indicated that the SPALS reader had a high reliability and could successfully determine LFIS in water and urine samples.",
"Fig. ",
"5Evaluation of SPALS-based AuNPs-LFIS reader for quantitative detection of Cd^2+^ and CL: (a) AuNPs-LIFS transmitted light intensities for quantitative detection of different Cd^2+^ concentrations; (b) Agreement between Cd^2+^ results obtained by both the SPALS-based reader and image analysis; (c) Cd^2+^ results from spiked samples obtained using the SPALS-based AuNPs-LFIS reader; (d) AuNPs-LIFS transmitted light intensities for quantitative detection of different CL concentrations; (e) Agreement between CL results obtained by both the SPALS-based reader and image analysis; (f) CL results in spiked samples obtained by the SPALS-based AuNPs-LFIS reader. ",
"Each value represents the mean of three independent experiments (n = 3).Fig. ",
"5\n\n3.4. ",
"Performance of SPSLS-based LFIS reader for quantitative detection of PEDV {#sec0055}\n------------------------------------------------------------------------------\n\nLarge analytes are one of the most common testing markers used in health care, including enzymes, protein markers, bacteria, and viruses. ",
"Due to their large molecular mass and multiple antigenic determinants, double antibody sandwich LFIS has been widely employed in testing for the presence of large analytes \\[[@bib0185]\\]. ",
"Porcine epidemic diarrhoea virus (PEDV) is a member of the coronavirus family that destroys that epithelial cells of the small intestine. ",
"This results in the development of an acute intestinal infectious disease in piglets and fattening pigs known as porcine epidemic diarrhoea (PED). ",
"A diagnosis of PED is conclusively made by detecting PEDV in pig waste \\[[@bib0210],[@bib0215]\\]. ",
"Currently, the colloidal gold LFIS is one of the most common, qualitative detection methods used in veterinary diagnostics for on-site PEDV detection.",
"\n\nHere, quantitative analyte of PEDV-LFIS was obtained using both the conventional image analysis approach and our newly developed SPALS-based reader. ",
"The results from these two methods are shown in Fi. ",
"6a and 6b. ",
"The image analysis system enabled discrimination of PEDV over a linear range of 0.078--20 μg/mL with a LOD of 0.062 μg/mL. The linear detection range for CL-LIFS using the SPALS-based reader was 0.078--20 μg/mL with a LOD of 0.055 μg/mL. As shown in [Fig. ",
"6](#fig0030){ref-type=\"fig\"} c, the results from these two methods had good agreement. ",
"The swine faecal samples were then spiked with different concentrations of PEDV and detected using the PEDV-LFIS. ",
"These results were then measured using the SPALS-based reader ([Fig. ",
"6](#fig0030){ref-type=\"fig\"}d). ",
"Taken together, these results demonstrate the feasibility of using our smartphone reader in clinical samples.",
"Fig. ",
"6Performance of SPALS-based AuNPs-LFIS reader for the quantitative detecting of PEDV: (a) AuNPs-LIFS PEDV results obtained by image analysis; (b) AuNPs-LIFS PEDV results obtained using the SPALS-based reader; (c) Agreement between the detected results obtained by the SPALS-based reader and image analysis; (d) Detected results of PEDV in spiked samples obtained using the SPALS-based AuNPs-LFIS reader. ",
"Each value represents the mean of three independent experiments (n = 3).Fig. ",
"6\n\n4. ",
"Conclusions {#sec0060}\n==============\n\nIn summary, we have development a novel SPALS-based detection device that can quantitatively read colloidal gold lateral flow immunoassay strips (AuNPs-LFIS). ",
"We illustrated the performance of the SPALS-based AuNPs-LFIS reader by quantifying the detected AuNPs concentrations on the NC membrane. ",
"First, the linearity results for the AuNP quantification showed good correlation (R^2^ = 0.992) between transmitted light intensity analysis and the image analysis, indicating the device was validated with good sensitivity and stability. ",
"In addition, our technological evaluation analyzed three types AuNPs-LFIS and showed good agreement between the SPALS-based AuNPs-LFIS reader and the traditional image analysis method (Table S5). ",
"Additional evaluation the device with spiked samples revealed excellent recovery rates (Table S2,3 and 4). ",
"Compared with the conventional analysis system, our reading system has following advantages: 1) our reader operated more easily, the result could be directly obtained did not required additional data analysis; 2) our approach can be implemented on different smartphones and would only require an adjustment to the size of the holder slot for better fixation of the accessory; 3) our device is favored since ambient sensors do not require a focal adjustment; 4) the ambient light sensors do not require a large dark field, thus minimizing the size of accessory (height 42 mm; width 30 mm; length 66 mm; weight 30 g), even it can be put it in pocket; 5) our device doesn't require expensive optical component to improve the performance of the sensor, thus the production cost of the instrument are cheaper (about 1.3 \\$, Table S1). ",
"Taken together, our new smartphone-based device provides a quantitative analysis tool for AuNPs-LFIS and enhances the applied range of AuNPs-LFIS. ",
"This approach will have wide-ranging applications prospect s, including in environmental testing, public health monitoring, and disease prevention. ",
"In future studies, to reduce fabrication difficulty of the LFIS, more advanced materials and manufactures is essential, such as transparent bottom board. ",
"On the side, a higher resolution smartphone application should be used to improve the accuracy and stability of SPALS-based detection device.",
"\n\n**Wei Xiao** presently is a PhD student at Jinan University. ",
"His research interests are in the area of biosensors and analytical chemistry.",
"\n\n**Caihong Huang** is currently enrolled in the Department of Bioengineering at Jinan University. ",
"She is studying for his Master\\'s degree. ",
"His current research interest focuses on biosensors.",
"\n\n**Fei Xu** is currently studying for her Master\\'s degree in the Department of Bioengineering, Jinan University. ",
"Her current research interest focuses on lateral-flow immunochromatographic strip.",
"\n\n**Junjie Yan** is currently studying for his Master\\'s degree in the Department of Bioengineering, Jinan University. ",
"His current research interest focuses on monoclonal antibody preparation.",
"\n\n**Hongfen Bian** is currently studying for her Master\\'s degree in the Department of Bioengineering, Jinan University. ",
"Her current research interest focuses on antigen purification and monoclonal antibody preparation.",
"\n\n**Qiangqiang Fu** Has gotten his Doctor\\'s degree in the Department of Bioengineering, Jinan University. ",
"His current research interest focuses on biosensors and analytical chemistry.",
"\n\n**Kaixin Xie** is currently enrolled in the Department of Bioengineering at Jinan University. ",
"He is studying for his Master\\'s degree. ",
"His current research interest focuses on biosensors.",
"\n\n**Lei Wang** currently is a master\\'s student at Jinan university. ",
"His current research interest focuses on preparation and purification of antibodies.",
"\n\n**Yong Tang** is a professor of the Department of Bioengineering, Jinan University, PR China. ",
"He spends most of his time in preparation of monoclonal antibodies and biosensor analytical tools.",
"\n\nAppendix A. Supplementary data {#sec0070}\n==============================\n\nThe following is Supplementary data to this article:\n\nThis work was supported by the National Key Research and Development Program of China (2016YFD0500600) and the Technology Research Program of Guangzhou City (201508020100).",
"\n\nSupplementary data associated with this article can be found, in the online version, at <https://doi.org/10.1016/j.snb.2018.03.110>.",
"\n"
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"HTC Announces Key Executive Promotions\n\nJason Mackenzie takes on global executive role; André Lönne assumes leadership of HTC Americas region\n\nTAIPEI, Taiwan, Jan. 22, 2016 /PRNewswire/ -- HTC Corporation today announced the promotions of Jason Mackenzie to global Executive Vice President and André Lönne, his successor as President of HTC Americas. ",
"The promotions come as HTC expands its businesses beyond traditional smartphones into new innovative opportunities like virtual reality and IOT.",
"\n\nIn Mackenzie's new role, he will report to the CEO and help build and lead new strategic partnerships while strengthening existing ones. \"",
"Jason Mackenzie is one of HTC's strongest senior executives and it was important for us to promote our senior talent and take advantage of his leadership as HTC moves forward,\" said Cher Wang, Chairman and CEO of HTC.",
"\n\nAs a founding member of HTC America, Mackenzie built a respected team and customer-first culture that helped HTC gain many industry firsts in the Americas, including the first 4G smartphone at every major US mobile operator. ",
"Under Mackenzie's leadership, HTC America pioneered several customer-focused initiatives that were adopted by HTC in other markets and globally.",
"\n\nAndré Lönne succeeds Mackenzie as president of HTC America and will oversee the company's business operations across the Americas, which includes the United States, Canada, and Latin America. ",
"Lönne has held several leadership roles at HTC, including country manager of Germany, and vice president of sales for HTC EMEA and, most recently, of HTC America.",
"\n\n\"André has had a significant impact on HTC's businesses across Europe and most recently in North America and with this new role will lead our HTC Americas team to continue our strategic growth in the region,\" said Chialin Chang, Global President of Sales for HTC."
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"Q:\n\nIs it a subspace or not?",
"\n\nIs $$\\mathscr{S_1}=\\lbrace(a,b,c)\\in\\mathbb{R}^3:a^3=b^3\\rbrace$$ subspace of R^3?",
"\nmy try:: $a^3=b^3\\iff a=b$ in $\\mathbb{R}$. So $\\mathscr{S_1}=\\lbrace(a,a,c)\\in\\mathbb{R}^3\\rbrace$ this is a plane going through the origin so it is a subspace\nIs $$\\mathscr{S_2}=\\lbrace(a,b,c)\\in\\mathbb{C}^3:a^3=b^3\\rbrace$$ subspace of C^3?",
"\nmy try:: $a^3=b^3\\iff a=b$ or $a=(-b+\\sqrt{-3b^2})/2=b*\\rho_1$ or $a=(-b-\\sqrt{-3b^2})/2=b*\\rho_2$ where $\\rho_1=\\frac{-1+\\sqrt{-3}}2$ and $\\rho_2=\\frac{-1-\\sqrt{-3}}2$ .... at the end i get it is a subspace, is my try right? ",
"if not why not?",
"\n\nA:\n\nHint\nLook at the axioms. ",
"Obviously $0\\in\\mathcal S_2$ and $\\lambda x\\in\\mathcal S_2$ for $\\lambda\\in\\mathbb C$ and $x\\in \\mathcal S_2$. What will blow up is that\n$$x,y\\in\\mathcal S_2 \\not\\Rightarrow x+y\\in\\mathcal S_2$$\nTry to find a counter-example for that, it's not hard ;)\n\n"
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"Gmina Wymiarki\n\n__NOTOC__\nGmina Wymiarki is a rural gmina (administrative district) in Żagań County, Lubusz Voivodeship, in western Poland. ",
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"\n\nNeighbouring gminas\nGmina Wymiarki is bordered by the gminas of Iłowa, Przewóz and Żary.",
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"Ricardo Güiraldes\n\nRicardo Güiraldes (13 February 1886 — 8 October 1927) was an Argentine novelist and poet, one of the most significant Argentine writers of his era, particularly known for his 1926 novel Don Segundo Sombra, set amongst the gauchos.",
"\n\nLife\nGüiraldes was born in Buenos Aires, the second son of a wealthy family of the old landowning aristocracy. ",
"His mother was Dolores Goñi, descendant of Ruiz de Arellano, who founded the village of San Antonio de Areco in 1730. ",
"Manuel Güiraldes, his father, later intendente (governmentally appointed mayor) of Buenos Aires, was a cultured, educated man, interested in art. ",
"Ricardo inherited that predilection; in his youth he sketched rural scenes and painted in oils.",
"\n\nWhen Güiraldes was one year old, he travelled with his family to Europe, living for four years in Paris near the Rue Saint-Claude. ",
"By the age of six, he spoke not only Spanish but French and German. ",
"Indeed, French was his first language, and French-language literature would leave a strong mark on his literary style and tastes.",
"\n\nGüiraldes's childhood and youth were divided between the family ranch, La Porteña in San Antonio de Areco, and Buenos Aires. ",
"In San Antonio he came into contact with the world of the gauchos, which would figure prominently in his novels Raucho and Don Segundo Sombra; there, too, he met Segundo Ramírez, upon whom he based the title character of the latter work. ",
"He loved the country life, but suffered from asthma that sometimes limited his own physical activity, though he generally presented an image of physical vigor.",
"\n\nHe was educated by several female teachers and, later, by a Mexican engineer, Lorenzo Ceballos, who recognized and encouraged his literary ambitions. ",
"He studied in various institutes and completed his bachillerato at the age of 16. ",
"Güiraldes was not a brilliant student; at the Colegio Lacordaire, the Vertiz Institute and the Instituto Libre de Segunda Enseñanza, he studied both architecture and law, but never practiced either one. ",
"He did make several attempts at business, all unsuccessful. ",
"He traveled to Europe in 1910 in the company of his friend Roberto Leviller, then travelled with another friend, his future brother-in-law Adán Deihl, with whom he visited Italy, Greece, Constantinople, Egypt, Japan, China, Russia, India, Ceylon, and Germany before settling in Paris, where (after his father decided he had had enough of paying the costs of his son's idleness) he stayed with the sculptor (to whom he later dedicated Xaimaca), and where he decided to become a writer.",
"\n\nDespite that decision, Güiraldes threw himself into the French capital's social whirl, practically abandoning his literary ambitions. ",
"But one day he unpacked some draft stories he had written about rural Argentina and set to work; these would eventually become his Cuentos de muerte y de sangre (\"Stories of death and of blood\").",
"\n\nHe read the stories to friends, who encouraged him to publish them. ",
"Even the early drafts already showed a distinct, individual style.",
"\n\nFinally truly committed to literature, he returned to Buenos Aires in 1912, becoming part of the circle of Alejandro Bustillo. ",
"On October 13, 1913 he married Adelina del Carril, also from one of the city's leading families, whom he had first met in 1905. ",
"In 1913–1914, he published several stories in the magazine Caras y Caretas; in 1915, these and others were published as Cuentos de muerte y de sangre; earlier that year he had published a book of poetry, El cencerro de cristal. ",
"He was encouraged in his writing by his wife and by Leopoldo Lugones, but when these early works did not meet with a receptive public, Güiraldes withdrew them from circulation, gathered up the unsold copies, and threw them into a well. ",
"His wife managed to rescue some; these surviving, water-damaged copies are now prized by book collectors.",
"\n\nAt the end of 1916, the couple traveled to the Pacific Ocean, to Cuba, and to Jamaica, where he wrote a \"theatrical caprice\" called El reloj (\"The clock\", never published). ",
"These travels would eventually lead to his 1923 novel Xaimaca, but long before that, in 1917, came his first novel Raucho, followed in 1918 by a short novel Un idilio de estación (\"A Season's Idyll\") in Horacio Quiroga's magazine El cuento ilustrado; this would eventually be revised and published as a well-received book in 1922, with the new title Rosaura.",
"\n\nIn 1919, with his wife, Güiraldes again traveled to Europe. ",
"In Paris he established contact with many French writers and frequented literary salons and bookstores; there, too, he began Don Segundo Sombra. ",
"He has been described as particularly influenced by his friend Valéry Larbaud, but Güiraldes's English-language translator Harriet de Onís believes that influence to have been overstated. ",
" Güiraldes returned to Argentina, then went back to Europe in 1922, where besides returning to Paris he passed some time in Puerto de Pollensa, Majorca, where he rented a house.",
"\n\nIn this period he underwent an intellectual and spiritual change. ",
"He became interested in theosophy and Eastern philosophy, seeking spiritual peace; this is strongly reflected in his late poetry.",
"\n\nAt the same time, Güiraldes's writing became more accepted in his native Buenos Aires, where he became a supporter of new avant-garde writers; he was something of an elder and teacher to the Florida group. ",
"In 1924, along with Alfredo Brandán Caraffa (1898-1978), Jorge Luis Borges, and Pablo Rojas Paz he founded the short-lived magazine Proa, which was not particularly successful in its home city but met with a better reception elsewhere in Latin America. ",
" Güiraldes also co-founded the Frente Ứnico, opposed to pompierismo (the use of dry or pompous academic language in writing), and collaborated in the publication of the magazine Martín Fierro.",
"\n\nAfter closing down the magazine, Güiraldes focused on finishing Don Segundo Sombra, which he completed in March 1926.",
"\n\nIn 1927, intending to head back to India because of his increasing interest in Hinduism, Güiraldes traveled once more to France. ",
"He went first to Arcachon, but it developed that he was sick with Hodgkin's disease. ",
"He was brought to Paris by ambulance, was met there by his wife, and died in the house of his friend, the painter Alfredo González Garaño (1886-1969). ",
"Güiraldes's body was brought back to Buenos Aires and finally entombed in San Antonio de Areco.",
"\n\nWorks\n\nEach year links to its corresponding \"[year] in literature\" or \"[year] in poetry\" article:\n 1915: El cencerro de cristal (poetry)\n 1915: Cuentos de muerte y sangre (short stories)\n Aventuras grotescas (short stories)\n Trilogía cristiana (short stories)\n 1917: Raucho (novel)\n 1917: Un idilio de estación, later revised as Rosaura (1922), published in Rosaura y siete cuentos. ",
"Short novel.",
"\n 1923: Xaimaca (fictionalized travel story).",
"\n 1926: Don Segundo Sombra (novel)\n 1928: Poemas místicos (posthumously published, poems)\n 1928: Poemas solitarios (posthumously published poems)\n 1929: Seis relatos (posthumously published short stories)\n 1932: El sendero (posthumously published)\n 1936: El libro bravo (posthumously published poems)\n 1954: Pampa (posthumously published)\n 1952: El pájaro blanco (poem)\n\nFurther reading \nJ.P. Spicer-Escalante, Ricardo Güiraldes’s Américas: Reappropriation and Reacculturation in Xaimaca (1923). ",
"Studies in Travel Writing 7.1: 9-28.",
"\nJ.P. Spicer, Don Segundo Sombra: en busca del otro. ",
"Revista de Crítica Literaria Latinoamericana 38.2: 361-73.",
"\nRicardo Güiraldes and Don Segundo Sombra; life and works / Giovanni Previtali, 1963\nLanguage, humor, and myth in the frontier novels of the Americas : Wister, Güiraldes, and Amado / Nina M Scott, 1983\nMartín Fierro, Don Segundo Sombra, ambassadors of the New World / Edward Larocque Tinker, 1958\nRicardo Güiraldes : argentino (1886-1927) / Harry Weiss, 1955\n\nReferences\n\n Harriet de Onís, afterword (p. 215–222) to her 1935 translation of Don Segundo Sombra; Signet, 1966.",
"\n Accessed 13 September 2006.",
"\n Johannes Beilharz, Ricardo Güiraldes on jbeilharz.de. ",
"Undated. ",
"Accessed 14 September 2006.",
"\n Ricardo Güiraldes, undated, on Todo-Argentina.net. ",
"Accessed 14 September 2006.",
"\n Ricardo Güiraldes. ",
"Part of La Literatura en Argentina, Escuela Normal Superior de Chascomús; site dated 1997. ",
"Accessed 14 September 2006.",
"\n Carlos Galliani, Delia del Carril: Neruda's wife was born in Saladillo, undated, on the official site of the city of Saladillo, Argentina. ",
"Accessed 28 February 2007.",
"\n\nExternal links\n Ricardo Güiraldes works online on Portal Academia Argentina de Letras\n\nCategory:Argentine male novelists\nCategory:20th-century Argentine poets\nCategory:20th-century Argentine male writers\nCategory:Argentine male poets\nCategory:Argentine writers in French\nCategory:Argentine writers in German\nCategory:1886 births\nCategory:1927 deaths\nCategory:People from Buenos Aires\nCategory:20th-century Argentine novelists"
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[
"/**\n ******************************************************************************\n * @file stm32f4xx.h\n * @author MCD Application Team\n * @version V2.1.0\n * @date 19-June-2014\n * @brief CMSIS STM32F4xx Device Peripheral Access Layer Header File. ",
" \n * \n * The file is the unique include file that the application programmer\n * is using in the C source code, usually in main.c. ",
"This file contains:\n * - Configuration section that allows to select:\n * - The STM32F4xx device used in the target application\n * - To use or not the peripheral’s drivers in application code(i.e. ",
"\n * code will be based on direct access to peripheral’s registers \n * rather than drivers API), this option is controlled by \n * \"#define USE_HAL_DRIVER\"\n * \n ******************************************************************************\n * @attention\n *\n * <h2><center>© COPYRIGHT(c) 2014 STMicroelectronics</center></h2>\n *\n * Redistribution and use in source and binary forms, with or without modification,\n * are permitted provided that the following conditions are met:\n * 1. ",
"Redistributions of source code must retain the above copyright notice,\n * this list of conditions and the following disclaimer.",
"\n * 2. ",
"Redistributions in binary form must reproduce the above copyright notice,\n * this list of conditions and the following disclaimer in the documentation\n * and/or other materials provided with the distribution.",
"\n * 3. ",
"Neither the name of STMicroelectronics nor the names of its contributors\n * may be used to endorse or promote products derived from this software\n * without specific prior written permission.",
"\n *\n * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n * DISCLAIMED. ",
"IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\n * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\n * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\n * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\n * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\n * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.",
"\n *\n ******************************************************************************\n */\n\n/** @addtogroup CMSIS\n * @{\n */\n\n/** @addtogroup stm32f4xx\n * @{\n */\n \n#ifndef __STM32F4xx_H\n#define __STM32F4xx_H\n\n#ifdef __cplusplus\n extern \"C\" {\n#endif /* __cplusplus */\n \n/** @addtogroup Library_configuration_section\n * @{\n */\n\n/* Uncomment the line below according to the target STM32 device used in your\n application \n */\n#if !",
"defined (STM32F405xx) && !",
"defined (STM32F415xx) && !",
"defined (STM32F407xx) && !",
"defined (STM32F417xx) && \\\n !",
"defined (STM32F427xx) && !",
"defined (STM32F437xx) && !",
"defined (STM32F429xx) && !",
"defined (STM32F439xx) && \\\n !",
"defined (STM32F401xC) && !",
"defined (STM32F401xE) && !",
"defined (STM32F411xE)\n /* #define STM32F405xx */ /*!",
"< STM32F405RG, STM32F405VG and STM32F405ZG Devices */\n /* #define STM32F415xx */ /*!",
"< STM32F415RG, STM32F415VG and STM32F415ZG Devices */\n /* #define STM32F407xx */ /*!",
"< STM32F407VG, STM32F407VE, STM32F407ZG, STM32F407ZE, STM32F407IG and STM32F407IE Devices */\n /* #define STM32F417xx */ /*!",
"< STM32F417VG, STM32F417VE, STM32F417ZG, STM32F417ZE, STM32F417IG and STM32F417IE Devices */\n /* #define STM32F427xx */ /*!",
"< STM32F427VG, STM32F427VI, STM32F427ZG, STM32F427ZI, STM32F427IG and STM32F427II Devices */\n /* #define STM32F437xx */ /*!",
"< STM32F437VG, STM32F437VI, STM32F437ZG, STM32F437ZI, STM32F437IG and STM32F437II Devices */\n /* #define STM32F429xx */ /*!",
"< STM32F429VG, STM32F429VI, STM32F429ZG, STM32F429ZI, STM32F429BG, STM32F429BI, STM32F429NG, \n STM32F439NI, STM32F429IG and STM32F429II Devices */\n /* #define STM32F439xx */ /*!",
"< STM32F439VG, STM32F439VI, STM32F439ZG, STM32F439ZI, STM32F439BG, STM32F439BI, STM32F439NG, \n STM32F439NI, STM32F439IG and STM32F439II Devices */\n /* #define STM32F401xC */ /*!",
"< STM32F401CB, STM32F401CC, STM32F401RB, STM32F401RC, STM32F401VB and STM32F401VC Devices */\n /* #define STM32F401xE */ /*!",
"< STM32F401CD, STM32F401RD, STM32F401VD, STM32F401CE, STM32F401RE and STM32F401VE Devices */\n#define STM32F411xE /*!",
"< STM32F411CD, STM32F411RD, STM32F411VD, STM32F411CE, STM32F411RE and STM32F411VE Devices */ \n#endif\n \n/* Tip: To avoid modifying this file each time you need to switch between these\n devices, you can define the device in your toolchain compiler preprocessor.",
"\n */\n#if !",
"defined (USE_HAL_DRIVER)\n/**\n * @brief Comment the line below if you will not use the peripherals drivers.",
"\n In this case, these drivers will not be included and the application code will \n be based on direct access to peripherals registers \n */\n#define USE_HAL_DRIVER\n#endif /* USE_HAL_DRIVER */\n\n/**\n * @brief CMSIS Device version number V2.1.0\n */\n#define __STM32F4xx_CMSIS_DEVICE_VERSION_MAIN (0x02) /*!",
"< [31:24] main version */ \n#define __STM32F4xx_CMSIS_DEVICE_VERSION_SUB1 (0x01) /*!",
"< [23:16] sub1 version */\n#define __STM32F4xx_CMSIS_DEVICE_VERSION_SUB2 (0x00) /*!",
"< [15:8] sub2 version */\n#define __STM32F4xx_CMSIS_DEVICE_VERSION_RC (0x00) /*!",
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"General Description of the Research Core Facility. ",
"The RI-INBRE core facility was inaugurated in July 2003. ",
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"Financial support is provided by the RI-INBRE grant and by all seven institutions that are participating in the network. ",
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"The core facility is located on the fourth floor, and occupies 3,220 sq. ",
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"which represents a 70% expansion over the previous space (Figure 3.2 in Section 3.5). ",
"Included in the space are separate rooms for cell culture, microscopes, radioactive counters, as well as space for the staff. ",
"There are two chemical fume hoods, which are certified for the use of toxic chemicals. ",
"In addition, there is provision for both short-term and longer-term back-up power for critical equipment. ",
"The facility staff provide research and training support to RI-INBRE participants as well as other scientists affiliated with the network institutions throughout the state. ",
"The facility services are also extended to Rl's non?profit research organizations and private companies on a fee-for-service basis. ",
"Both basic and advanced analytical instrumentation required for biomedical, pharmaceutical, and biotechnological research are available for shared usage. ",
"Rl's geographic compactness facilitates user access. ",
"All network institutions are within 35 miles of the site. ",
"The access is further enhanced through the core facility website (www.uri.edu/inbre/corelab), which allows participants to reserve major equipment online on a first-come, first-served basis. ",
"A user-fee structure has been placed in effect starting June 2013 to ensure future sustainability of the facility. ",
"The core facility has proven to be a major factor in enhancing existing research and forging new collaborative initiatives within Rl's research community. ",
"At the state level, the facility is listed on a searchable website of the Rl STAC maintained by the Rl Research Alliance (http://stac.ri.gov/alliance/), a statewide platform for promoting collaboration across COBRE, INBRE, EPSCoR, and other research networks. ",
"It is also listed on Brown's shared resource facilities website (://biomed.brown.edu/research/facilities) and searchable website (www.CoresRI.org ). ",
"At the national level, the facility is listed on the Vermont Genetics Network (Vermont INBRE) website (www.vgn.uvm.edu/corefacilities/)."
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"Share this story\n\nSenate Democrats pushed ahead with President Barack Obama’s vision of health reform Saturday night – but at the same time, exposed significant divides in the party that make it all but impossible to complete work on a plan by year’s end.",
"\n\nDemocrats voted strictly along party lines, 60 to 39, to send an $848 billion health care bill to the floor after Thanksgiving, but not before a clutch of moderates served notice that they couldn’t back the bill in its current form.",
"\n\nPress Secretary Robert Gibbs's statement on the vote:\n\n“The President is gratified that the Senate has acted to begin consideration of health insurance reform legislation. ",
"Tonight’s historic vote brings us one step closer to ending insurance company abuses, reining in spiraling health care costs, providing stability and security to those with health insurance, and extending quality health coverage to those who lack it. ",
"The President looks forward to a thorough and productive debate.”",
"\n\nShare this story\n\nAfter an afternoon of golf at Andrews Air Force Base, POTUS made a quick stop at the White House before heading out again at 6 p.m,. ",
"for what pool is told is a birthday dinner for senior adviser Valerie Jarrett, at her condo in Georgetown. ",
"The rest of the first family will also be arriving separately for the b’day bash. (",
"7:02 p.m.).",
"\n\nShare this story\n\nIncoming White House communications director Dan Pfeiffer just posted a blog item comparing health reform legislation to the Medicare prescription drug benefit passed under Republicans. ",
"For instance, he writes, the drug benefit increased the deficit by $395 billion while the reform cuts the deficit by $130 billion:\n\n“Opponents of health insurance reform have spent hours on the Senate floor today attacking the Senate's efforts to provide stability and security for those with insurance, affordable coverage for those without, and lower costs for families, small businesses and the government. ",
"To provide a little perspective on these attacks, let’s compare today's legislation with the 2003 Medicare Part D effort, which many of these same critics supported.” –",
"Chris Frates (4:35 p.m.).",
"\n\nShare this story\n\nAs the Senate begins its debate on Obama’s top legislative priority, the president is at Andrews Air Force Base for a Saturday golf game. ",
"So far no word on who’s on the links with the golfer-in-chief. (",
"1:20 p.m.) .",
"\n\nShare this story\n\nPresident Obama saved one last message from his eight-day trip to Asia, telling Americans that he “will go anywhere” in pursuit of economic growth and jobs.",
"\n\n“Hi. ",
"I’m recording this message from Seoul, South Korea, as I finish up my first presidential trip to Asia,” Obama begins his weekly radio and internet address. “",
"As we emerge from the worst recession in generations, there is nothing more important than to do everything we can to get our economy moving again and put Americans back to work, and I will go anywhere to pursue that goal.”"
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"Introduction {#s1}\n============\n\nApproximately 1.1--1.9 million youth sustain concussions annually ([@B1]), and up to 30% have persistent symptoms such as headache, fatigue, and difficulty concentrating for weeks or months ([@B2]--[@B5]). ",
"Persistent concussive symptoms can impact social development, cognitive function, and academic success, and result in greater utilization of sub-specialty care ([@B6]). ",
"A recent consensus statement called for research into treatments for persistent concussive symptoms ([@B7]), as the extant literature provides little guidance. ",
"One promising approach is the use of rehabilitative exercise. ",
"Individuals who sustain concussions have increased symptoms with exercise, and exercising at a \"sub-symptom threshold\" level appears to help them return to function more quickly ([@B8], [@B9]). ",
"A few studies have reported benefit for such an approach, but have required weekly in-person visits ([@B8]--[@B16]). ",
"Currently no exercise treatments have been designed for concussion that could be completed with minimal in-person visits and therefore be more easily disseminated. ",
"We proposed to address this gap, adapting a pre-existing exercise intervention for concussion to be delivered with only two in-person visits, and utilizing weekly check-ins via phone contact with the youth, as has been used effectively in previous studies ([@B17]).",
"\n\nDebate also exists regarding how sub-threshold exercise might produce benefit in patients with persistent concussive symptoms. ",
"Some have posited ([@B8], [@B9], [@B12]) that exercise improves cerebrovascular autoregulation, which appears to be impaired following brain injury. ",
"Participating in daily exercise at a level below that which exacerbates symptoms could assist with rehabilitation of neurologic adaptations to exercise, thus decreasing exercise-related symptoms occurring secondary to transmission of systemic pressure into the cerebrovascular space.",
"\n\nWe conceptualized that exercise interventions for concussion might also have effects on \"fear-avoidance\" ([@B18]--[@B22]). ",
"The fear-avoidance model is a prominent theoretical model applied to adults and youth to understand processes through which an acute pain experience can become chronic ([@B18]--[@B22]), According to this model, individuals who perceive pain as threatening and place a catastrophic meaning on the pain experience (e.g., rumination and worry that pain will not go away), develop pain-related anxiety that maintains avoidance, leading to functional disability, depression, and persistence of pain. ",
"Pediatric specific models of fear-avoidance include the important role of parent behavioral and psychological responses to the child\\'s pain experience, recognizing that the child\\'s own experiences develop within the familial context ([@B23], [@B24]).",
"\n\nA few authors ([@B25]--[@B27]) have suggested a role for fear-avoidance in the persistence of concussive symptoms, and we theorized that fear-avoidance might be impacted by sub-threshold exercise programs post-concussion ([Figure 1](#F1){ref-type=\"fig\"}). ",
"Patients with acute concussion are initially instructed not to exercise, given concerns about the vulnerability of the injured brain. ",
"When symptoms worsen during exercise, concussed patients may fear such increases indicate greater injury. ",
"This fear leads them to become anxious about participating in exercise and avoid exercise, bolstering their fear, and generating a cycle of disability. ",
"Rehabilitative exercise challenges catastrophic assumptions about exercise, thus decreasing anxiety and avoidance of exercise, and improving function ([@B28]). ",
"Function in chronic illness states is often conceptualized as health-related quality of life (HRQoL), which can be measured using the Pediatric Quality of Life scale (PedsQL) ([@B29]). ",
"Prior research has suggested that youth with PPCS have deficits in function that can be measured with the PedsQL ([@B30], [@B31]), and that these deficits can improve with intervention ([@B32]).",
"\n\n![",
"Conceptual model of Fear-avoidance ([@B19]), adapted for concussion.](fneur-10-00623-g0001){#F1}\n\nWe conducted a pilot randomized controlled trial (RCT) of a 6-week rehabilitative exercise program requiring minimal in-person visits for youth with persistent concussive symptoms, the Sub-Threshold Exercise Program (STEP). ",
"Our goals were to: (a) assess feasibility and acceptability of this approach, (b) collect pilot data regarding the effect of STEP on trajectory of concussive symptoms, and variation by demographic and injury factors (sex, age, prior concussion, time since injury), and (c) explore impact of the intervention on objectively measured moderate-vigorous physical activity (MVPA), standardized measures of fear-avoidance of pain, and health-related quality of life over time.",
"\n\nMethods {#s2}\n=======\n\nRecruitment\n-----------\n\nWe recruited youth 12--18 years old from concussion clinics at Seattle Children\\'s Hospital and an on-line portal over a period of \\~9 months. ",
"The on-line portal consisted of a website with information about the study and targeted advertisements on social media platforms. ",
"Inclusion criteria included: (1) diagnosis of sports-related concussion consistent with Zurich definition by a clinician experienced with concussion management ([@B33]), (2) at least two concussive symptoms, (3) duration of symptoms 3 weeks−6 months after concussion, (4) no contraindication to performing physical activity, and (5) not currently receiving physical therapy to increase physical activity. ",
"Subjects completed a baseline exercise tolerance test (a modified Buffalo Concussion Treadmill Test) ([@B8]) and were eligible for the study if symptoms worsened during this test, consistent with prior studies ([@B8], [@B9], [@B14]). ",
"Subjects continued to receive usual care from their referring concussion clinician during the study. ",
"We did not collect information about other treatments pursued by subjects during the study. ",
"The study was approved by the Seattle Children\\'s Hospital Institutional Review Board and registered at Clinicaltrials.gov, NCT02673112. ",
"All youth and parents completed written informed consent.",
"\n\nProcedures\n----------\n\nAll subjects completed in-person assessments at study entry (baseline) and 6 weeks later (post-intervention). ",
"Subjects were examined by a study physical therapist at baseline to ensure they had no concerning cervical spine or vestibular issues that would preclude exercise. ",
"The remainder of the assessments were completed online, including weekly assessments of concussion symptoms during intervention, and surveys at 3 and 6 month follow up. ",
"Accelerometer assessments were completed for 5--7 days at baseline and 6 weeks to measure moderate-vigorous physical activity (MVPA) in an objective manner. ",
"Youth and parents were provided incentives for completing accelerometry measurements and surveys using gift cards.",
"\n\nRandomization\n-------------\n\nRandomization was conducted by the study analyst (K.W.) using random number generation in blocks of four, stratified by age (11--13 and 14--18) and sex. ",
"Allocation was weighted 2:1: toward the intervention arm to provide maximum data for feasibility and acceptability. ",
"Study arm allocation details were placed into opaque envelopes and chosen sequentially.",
"\n\nParticipants\n------------\n\nTwo hundred thirty youth were screened, but 69% did not meet inclusion criteria as concussion symptoms had resolved by the time of recruitment contact or they were already receiving physical therapy ([Figure 2](#F2){ref-type=\"fig\"}). ",
"Of the 72 patients who met criteria for participation, 45 were initially interested, 10 of whom did not have an increase in symptoms with the treadmill test, and three of whom later declined participation. ",
"Thirty-two individuals enrolled and were randomized to intervention or control. ",
"Only one of the enrolled participants came from the on-line portal, the remainder were patients at Seattle Children\\'s Hospital. ",
"Two subjects discontinued participation in the study, both in the first week of the study, leaving 30 total subjects, 11 control, and 19 intervention.",
"\n\n{#F2}\n\nExperimental Arms\n-----------------\n\na. **Stretching (Control)**: Individuals randomized to control were given a home stretching program and provided a handout with color illustrations. ",
"Stretches required 5--10 min to complete and were completed daily (see [Supplementary Material](#SM1){ref-type=\"supplementary-material\"}). ",
"Research assistants (RAs) called subjects weekly to ensure they were tolerating the exercises.",
"\n\nb. **Sub-Threshold Exercise Program (STEP) (Intervention):** Individuals randomized to the intervention were given a 6 week daily home aerobic exercise program. ",
"The exercise prescription for participants included specifications for frequency, duration, and intensity as recommended by Howell et al. ([",
"@B34]) Frequency was set at daily, with the understanding that youth might miss 1--2 days per week due to scheduling conflicts. ",
"Duration of exercise was started at 5--10 min per day greater than MVPA at baseline measured with accelerometry, and increased weekly by 5--10 minutes per/day via phone contact with the RA (for a goal of 60 min/day). ",
"Intensity was set at 80% of the heart rate that produced symptoms during the modified Buffalo Concussion Treadmill Test (i.e., \"sub-threshold\") ([@B8], [@B9]). ",
"Measuring MVPA using actigraphy provided information about quantity of physical activity at baseline, to ensure that the intervention was an increase from a participant\\'s baseline. ",
"Utilizing the treadmill test provided information about the intensity of exercise a participant could tolerate, to ensure that the intervention would not provoke symptoms. ",
"If symptoms worsened during exercise, HR goal was decreased by 10%. ",
"Subjects were provided a wrist-based HR monitor to track heart rate. ",
"Participants were instructed to exercise in whatever manner they chose, and most utilized either exercise bike, treadmill, fast walking up an incline/stairs, or calisthenics. ",
"Exercise type was allowed to shift during the intervention to adapt to participant preferences and lifestyle.",
"\n\nBlinding\n--------\n\nPhysical therapists conducting the modified Buffalo Concussion Treadmill Test were blinded to randomization status. ",
"Aside from accelerometry, all other assessments were completed via self-report.",
"\n\nDemographics, Past Medical History, and Family History\n------------------------------------------------------\n\nYouth and parents were interviewed together at baseline regarding: (a) date of injury, (b) mechanism, and (c) prior concussion. ",
"Parents completed surveys regarding (a) demographics (age, race, socioeconomic status) and (b) past medical history.",
"\n\nBaseline Exercise Tolerance\n---------------------------\n\nThe Buffalo Concussion Treadmill Test ([@B35]) is a graded treadmill test used to determine heart rate threshold for concussive symptoms. ",
"The test was administered in accordance with prior studies ([@B8], [@B9]), beginning with a treadmill speed of 3.3 mph with 0% incline. ",
"After 1 min, the grade was increased to 2.0%. ",
"At the start of the 3rd min and each minute thereafter, the grade was increased by 1%. ",
"The same speed was maintained throughout. ",
"The test was stopped when the subject self-reported worsening of concussive symptoms, when they reached HR max for age or at 20 min, and HR was recorded using pulse oximetry. ",
"Participants who reached either the HR max for age or completed 20 min on the treadmill were excluded from the study. ",
"For the remaining participants, the HR at which they reported worsening was defined as the threshold HR and used to guide the intensity of exercise for the intervention arm.",
"\n\nOutcome Assessment\n------------------\n\n### Feasibility and Acceptability\n\n1. ",
" **Enrollment:** Recorded numbers of patients screened, eligible, and enrolled.",
"\n\n2. ",
" **Retention/attrition:** Tracked rates of participant withdrawal and loss to follow up. ",
"Recorded reasons for withdrawal, and tracked adverse events.",
"\n\n3. ",
" **Engagement:** Recorded visit completion rates, and rates of completion of surveys and other procedures.",
"\n\n4. ",
" **Satisfaction:** Subjects completed an end of study interview regarding satisfaction with study procedures and suggestions for improvement.",
"\n\n5. ",
" **Safety:** RA called subjects weekly to track exercise tolerance and any adverse events.",
"\n\nPreliminary Efficacy Outcomes\n-----------------------------\n\n**Trajectory of concussive symptoms, measured using the Health behavior inventory** ([@B5], [@B36])**:** The HBI is a 20-item instrument assessing post-concussive symptoms on a four-point Likert scale with higher scores indicating greater severity. ",
"This scale has demonstrated validity and reliability among adolescents with mild traumatic brain injury (mTBI) ([@B36], [@B37]). ",
"The HBI was measured at nine time points: Baseline, weekly during the intervention (weeks 1--6), 3 months, and 6 months.",
"\n\nExploratory Outcomes\n--------------------\n\n1. ",
" **Trajectory of Health-related quality of life, measured using the Pediatric Quality of Life Inventory (youth and parent report):** PedsQL© is a 23-item five point questionnaire that assesses physical, emotional, social, and school functioning, with established validity and reliability ([@B29], [@B38]). ",
"PedsQL was measured at four time points: Baseline, 6 weeks, 3 months, and 6 months.",
"\n\n2. ",
" **Change in physical activity, measured using accelerometry**: Physical activity was measured pre- and post-intervention (baseline and 6 weeks) in both experimental arms using a hip-mounted ActiGraph GT3X (ActiGraph LLC, Pensacola, FL). ",
"The GT3X accelerometers collect data at a frequency of 30 Hz, and data was processed into 1 s epochs ([@B39]--[@B41]). ",
"Participants wore the accelerometer for 1 week at baseline and in the last week of the intervention. ",
"We used the accelerometer data quality standards by Troiano et al. ([",
"@B42]), including criteria for wear time and valid days (4--7 days, eight or more hours of accelerometer wear/day) ([@B42]). ",
"We used the accelerometer cut-points for moderate-to-vigorous physical activity (MVPA) developed by Evenson et al. ([",
"@B43]), which has the highest classification accuracy ([@B44]). ",
"Total minutes above the threshold was divided by number of valid days to obtain minutes of MVPA per day pre- and post-intervention.",
"\n\n3. ",
" **Trajectory of Fear-avoidance, measured using the Fear of pain questionnaire** ([@B45]): The FOPQ-C and FOPQ-P are 24- and 23-item child and parent proxy versions of the Fear Of Pain Questionnaire, and have been shown to reliably and validly measure pain-related fear and pain-related avoidance of activities in youth (Cronbach\\'s alpha 0.92) ([@B23], [@B45]). ",
"Fear-avoidance was measured at four time points: Baseline, 6 weeks, 3 months, and 6 months.",
"\n\nAnalysis\n--------\n\n### Descriptive\n\nParticipant characteristics, including sociodemographic characteristics, were summarized overall and compared by study arm using chi-square. ",
"Continuous measures were summarized via means and standard deviations, or median and interquartile range for asymmetrically distributed variables, and were compared by Student\\'s *T*-tests and Wilcoxon rank sum, respectively.",
"\n\n### Feasibility and Acceptability\n\nFeasibility and acceptability measures were descriptively summarized. ",
"Satisfaction was measured qualitatively and themes were summarized.",
"\n\n### Preliminary Efficacy Outcome\n\nWe collected pilot data regarding trajectory of concussive symptoms (HBI), hypothesizing that intervention youth would have a more rapid decline in concussive symptoms than control youth. ",
"Our previous work ([@B13]) has suggested that injury recovery follows an exponential curve with a rapid rate of decline initially after injury, and thus we modeled trajectory of concussive symptoms using an exponential decay framework which fit well with the data.",
"\n\nH\n\nB\n\nI\n\n(\n\nt\n\n)\n\n=\n\nN\n\nb\n\nl\n\n\\*\n\ne\n\n\\-\n\nλ\n\nt\n\nIn this model, N~BL~ represents mean HBI at study baseline, estimated as a linear function of random intercept (HBI at the time of injury, N~0~) and covariates (duration of symptoms at entry into the study, age at concussion, and sex):\n\nN\n\nB\n\nL\n\n=\n\nN\n\n0\n\n\\+\n\nβ\n\nX\n\n.",
"\n\nWe modeled intercept as a random effect, modified based on factors that might impact concussive symptoms at study baseline (sex, age, prior concussion, and duration of symptoms). ",
"Rate of exponential decay (non-linear slope) was modified based on covariates expected to impact rate of symptom resolution (prior concussion, duration of symptoms). ",
"Rate of change at time t weeks from study baseline, denoted by -λ~t~, was estimated as a linear function of study arm and covariates:\n\nλ\n\nt\n\n=\n\nγ\n\n0\n\n\\+\n\nγ\n\n1\n\n(\n\nI\n\nn\n\nt\n\ne\n\nr\n\nv\n\ne\n\nn\n\nt\n\ni\n\no\n\nn\n\n)\n\n\\+\n\nγ\n\nX\n\n.",
"\n\nA statistically significant intervention effect (λ~1~) therefore denotes a difference in the rate of symptom resolution, accounting for duration of symptoms at entry into the study, age, sex, and prior concussion.",
"\n\nExploratory Outcomes (MVPA, Fear-Avoidance and Health-Related Quality of Life)\n------------------------------------------------------------------------------\n\nGiven skewness in MVPA data, we examined this outcome categorically, assessing the proportion in each group who achieved a minimum of 15 min per day of MVPA at 6 weeks with logistic regression. ",
"Fear-avoidance (FOPQ) and health-related quality of life (PedsQL©), were entered into separate linear mixed models. ",
"Models were covariate-adjusted for duration of symptoms at entry into the study, age, sex, and prior concussion. ",
"Within participant correlation was modeled via an autoregressive covariance structure.",
"\n\nResults {#s3}\n=======\n\nSample Description\n------------------\n\nHalf of the participants were female, with average age 15.5 years (SD 1.6, [Table 1](#T1){ref-type=\"table\"}). ",
"Approximately half the sample reported a prior concussion. ",
"Duration of concussion symptoms at the start of the study averaged about 2 months, but was quite skewed (median 48.5 days, IQR 33, 64). ",
"Concussions occurred from a wide range of sports ([Table 1](#T1){ref-type=\"table\"}). ",
"The majority of youth (70%) reported headaches \"often\" at study entry. ",
"Approximately 40% had difficulty with concentrating and being tired. ",
"Only 17% reported history of chronic pain, but 73% had pain in the week before starting the study, all of whom had headaches. ",
"A smaller proportion reported neck pain (33%), back pain (23%), or pain in other locations (17%). ",
"Half the subjects reported family history of chronic headaches, 60% back or neck pain, and 47% other joint pain.",
"\n\n###### \n\nDemographic characteristics of concussed youth participating in Sub-Threshold Exercise Program (STEP) study, Seattle WA 2016--17.",
"\n\n **Control (*n* = 11) *Mean (SD) or N (%)*** **Intervention (*n* = 19) *Mean (SD) or N (%)*** **Total (*n* = 30) *Mean (SD) or N (%)***\n ---------------------------------------------------------------------------- --------------------------------------------- -------------------------------------------------- -------------------------------------------\n Female 6 (54.6) 12 (63.2) 17 (56.7)\n Age at baseline (years) 15.8 (1.1) 15.4 (1.8) 15.5 (1.6)\n **Race** [^**a**^](#TN1-1){ref-type=\"table-fn\"} \n White 7 (63.7) 17 (89.5) 24 (82.8)\n African-American/Black 2 (18.2) -- 2 (6.6)\n Asian -- 2 (10.5) 2 (6.6)\n Missing 2 (18.2) -- 2 (6.6)\n **Ethnicity** \n Hispanic -- 1 (5.2) 1 (2.9)\n Non-hispanic 10 (90.9) 17 (89.5) 31 (88.6)\n Missing 1 (9.1) 1 (5.3) 2 (6.7)\n **Household income** \n \\$0--60,000/year 3 (27.3) 3 (15.8) 6 (20.0)\n History of prior concussion 7 (63.6) 8 (42.1) 15 (50.0)\n Duration of symptoms at baseline (days) [^b^](#TN1-2){ref-type=\"table-fn\"} 75.9 (49.4) Range 22--202 48.8 (32.2) Range 21--175 58.8 (41.1) Range 21--202\n Mechanism of injury \n Football 1 (09.1) 4 (21.1) 5 (16.7)\n Soccer 2 (18.2) 3 (15.8) 5 (16.7)\n Basketball 3 (27.3) 1 (5.2) 4 (13.3)\n Wrestling 1 (9.1) 2 (10.5) 3 (10.0)\n Swimming -- 2 (10.5) 2 (6.7)\n Volleyball -- 2 (10.5) 2 (6.7)\n Softball 1 (9.1) 1 (5.2) 2 (6.7)\n Lacrosse 1 (9.1) -- 2 (6.7)\n Tennis 1 (9.1) -- 1 (3.3)\n Hockey -- 1 (5.2) 1 (3.3)\n Ultimate frisbee 1 (9.1) -- 1 (3.3)\n Gymnastics -- 1 (5.2) 1 (3.3)\n Dance -- 1 (5.2) 1 (3.3)\n\n*Chi-square, p = 0.06*.",
"\n\n*Wilcoxon rank sum, p = 0.02*.",
"\n\n### Feasibility and Acceptability\n\nTwo participants discontinued the study after randomization but prior to starting the intervention as their symptoms had already resolved. ",
"Retention was excellent for participants who began the intervention, with 90% of youth and 83% of parents who began the intervention completing 6 month follow up. ",
"During interviews with parents and youth, 100% reported they would recommend the study to a friend. ",
"Other themes included: (1) enjoyment of the study (particularly incentives, weekly RA check-ins and use of wrist-based heart rate monitors) (2) appreciation of structure and organization, and (3) appreciation of minimal in-person study visits. ",
"Symptoms during exercise were reported by 2/11 subjects in the control group (18.2%) and 7/19 (36.8%) subjects in the intervention group, but were managed effectively by decreasing intensity of exercise, and no subjects chose to leave the study due to symptom exacerbations. ",
"Most symptom exacerbations occurred in the first few weeks of the study. ",
"Two individuals in the intervention group had symptoms exacerbate in later weeks, both of which were associated with participants engaging in a longer duration of exercise than was prescribed. ",
"No adverse events occurred during the study. ",
"We did not inquire as to whether participants were able to return to sporting activities.",
"\n\nQuantitative Outcomes\n---------------------\n\nThe exponential decay model revealed a significant effect of the intervention on rate of decline of concussive symptoms (HBI, *p* = 0.02, [Table 2](#T2){ref-type=\"table\"} and [Figure 3](#F3){ref-type=\"fig\"}), after controlling for age, sex, and prior concussion. ",
"Rate of concussion symptom improvement was slower among youth with chronic symptoms (9--22 weeks, and \\>22 weeks) compared to those with acute symptoms (\\<9 weeks) in both intervention and control groups. ",
"However, the intervention effect (i.e., the difference in rates between intervention and control youth) was also most pronounced in youth with chronic symptoms. ",
"All subjects completed the pre-intervention accelerometry as it was a requirement for starting the study. ",
"Most subjects (26/30, 87%) completed the post-intervention accelerometry. ",
"The proportion of youth achieving a minimum of 15 min/day of MVPA was not significantly different by study arm. ",
"Parent-reported health-related quality of life (PedsQL©) was significantly improved in intervention compared to control youth (β = 0.56, *p* = 0.05; [Table 3](#T3){ref-type=\"table\"}). ",
"Child-reported PedsQL© improved overall (β = 0.75, *p* = 0.0045; [Table 3](#T3){ref-type=\"table\"}), but was not significantly affected by the intervention (β = 0.19, *p* = 0.47; [Table 3](#T3){ref-type=\"table\"}). ",
"Parental fear-avoidance (FOPQ-P) significantly declined overall (*p* = 0.0096), but was not different by treatment group (β = −0.0031, *p* = 0.99, [Table 3](#T3){ref-type=\"table\"}; [Figure 4](#F4){ref-type=\"fig\"}). ",
"Child fear-avoidance (FOPQ-C) was not significantly different by treatment group (β = −0.29, *p* = 0.23, [Table 3](#T3){ref-type=\"table\"}; [Figure 4](#F4){ref-type=\"fig\"}).",
"\n\n###### \n\nExponential decay model examining the effect of the Sub-Threshold Exercise Program (STEP) on concussive symptoms over time (Health Behavior Inventory, or HBI), adjusted for age, sex, duration of time since injury and history of concussion, Seattle WA 2016--17.",
"\n\n **Estimate** **95% Confidence limits** ***p*-value** \n ------------------------ ---- -------------- --------------------------- --------------- ------------\n Intercept mu 24.48 −27.60 76.56 0.36\n Age (continuous) c1 0.69 −2.63 4.01 0.69\n Female c2 −4.68 −15.55 6.19 0.40\n Duration of symptoms \n \\<9 weeks (referent) -- \n 9--22 weeks (int) b2 −8.24 −12.85 −3.62 **0.0005**\n \\>22 weeks (int) b3 −3.97 −11.65 3.71 0.31\n Rate g0 0.12 0.05 0.19 **0.0009**\n Duration of symptoms \n \\<9 weeks (referent) -- \n 9--22 weeks (rate) g2 −0.07 −0.14 0.00 **0.048**\n \\>22 weeks (rate) g3 −0.03 −0.06 −0.01 **0.01**\n Prior concussion (y/n) c3 −0.01 −0.03 0.01 0.25\n Intervention g1 0.02 0.00 0.04 **0.02**\n\n*Bold values indicate the highlighted results that are significant with p values \\<0.05*.",
"\n\n{#F3}\n\n###### \n\nLinear mixed model examining the impact of the Sub-Threshold Exercise Program (STEP) intervention on concussed youth on outcomes of fear avoidance of pain and health-related quality of life, adjusted for age, sex, duration of symptoms, and prior concussion, Seattle WA 2016--17.",
"\n\n FOPQ[^a^](#TN3-1){ref-type=\"table-fn\"} (Child) FOPQ[^a^](#TN3-1){ref-type=\"table-fn\"} (Parent) PEDsQL© [^b^](#TN3-2){ref-type=\"table-fn\"} (Child) PEDsQL© [^b^](#TN3-2){ref-type=\"table-fn\"} (Parent) \n ------------------------ ------------------------------------------------ ------------------------------------------------- ---------------------------------------------------- ----------------------------------------------------- --------- ------------ -------- --------- -------------- ------- --------- ------------\n Mean \n Intercept −24.54 (28.54) 0.40 20.80 (28.80) 0.48 71.90 (22.91) 0.0044 57.97 (24.22) 0.02\n Age (continuous) 3.24 (1.88) 0.10 1.03 (1.90) 0.59 −0.10 (1.51) 0.95 −0.06 (1.60) 0.97\n Female 13.64 (5.45) **0.02** 9.58 (5.42) 0.59 −6.49 (4.35) 0.15 −1.21 (4.53) 0.79\n Prior concussion −8.79 (6.02) 0.16 −9.02 (6.03) 0.15 −1.18 (4.84) 0.81 7.73 (5.12) 0.14)\n Duration of symptoms \n *\\<9 weeks (referent)* -- -- -- -- -- -- -- -- -- -- -- --\n *9--22 weeks* −7.26 (4.73) 0.13 −5.83 (4.49) 0.20 15.46 (3.04) **\\<0.0001** 11.42 (3.49) **0.0016**\n *\\>22 weeks* 4.31 (3.62) 0.24 6.35 (3.33) 0.06 −11.46 (3.95) **0.0048** −0.82 (4.49) 0.86\n Slope \n Week −0.40 (0.26) 0.13 −0.63 (0.24) **0.0096** 0.75 (0.26) **0.0045** 0.22 (0.29) 0.44\n Week x Intervention −0.29 (0.25) 0.23 −0.0031 (0.23) 0.99 0.19 (0.25) 0.47 0.56 (0.29) **0.05**\n\n*Fear of Pain Questionnaire, a measure of fear-avoidance of pain*.",
"\n\n*Pediatric Quality of Life Inventory, a measure of health-related quality of life.*.",
"\n\n*Bold values indicate the highlighted results that are significant with p values \\<0.05*.",
"\n\n{#F4}\n\nDiscussion {#s4}\n==========\n\nWhile previous studies utilized sub-threshold exercise to treat youth with persistent concussion, this is the first study to measure MVPA using accelerometry, and the first to examine an intervention requiring minimal in-person visits. ",
"This is also the first study to explore the impact of exercise on fear-avoidance of pain in youth with concussion. ",
"We found the Sub-Threshold Exercise Program (STEP) was feasible and acceptable for youth with concussive symptoms. ",
"Youth reported enjoying the structure and support provided, and preferred the minimal visits. ",
"Preliminary data suggested potential benefit of this approach, as youth who received STEP had more rapid improvement in concussion symptoms compared to youth in a stretching control, and improvement was maintained at 6 months. ",
"Health-related quality of life improved significantly for all subjects and fear-avoidance of pain declined significantly for all subjects, but neither was significantly different by intervention group.",
"\n\nOur findings are in line with prior studies of exercise interventions for concussed youth, all of which report benefit ([@B8]--[@B15]). ",
"Much of our methodology was similar to prior studies: (a) utilizing the Buffalo Concussion Treadmill Test to determine HR threshold, (b) setting exercise goals at 80% of the HR threshold ([@B8], [@B9]), and (c) asking participants to exercise for 6 weeks ([@B8]--[@B15]). ",
"However, previous studies of sub-threshold exercise required weekly in-person visits, which present greater barriers for access and are difficult to scale. ",
"Instead, we utilized RAs as health coaches, phoning youth weekly to advance exercise goals, and required only two in-person visits, which we felt was a more scalable approach. ",
"We also provided youth with wrist-mounted HR monitors, to allow them to self-monitor HR goals. ",
"In addition, we objectively measured MVPA using hip-mounted accelerometers pre- and post-intervention, which allowed us to tailor the intervention to activity level, ensuring that the intervention was an increase from baseline MVPA. ",
"Utilizing accelerometry also allowed us to quantify changes in MVPA. ",
"Despite the impact of the intervention on concussive symptoms, it did not significantly change MVPA compared to controls in this pilot study.",
"\n\nFinding no significant change in MVPA and yet a positive effect of the intervention on rate of decline of concussive symptoms poses a new question---how can an aerobic exercise intervention be efficacious if it does not increase MVPA? ",
"We suggest caution in examining these MVPA data, given the relatively small sample size. ",
"In addition, accelerometry is an imperfect measure of MVPA, and certain types of physical activity such as swimming and cycling are not well-captured. ",
"The intervention and control groups also had differences in amount of MVPA at baseline, which makes it challenging to measure improvement. ",
"The lack of differences in MVPA does suggest we should consider other factors. ",
"In planning this study, we felt it would be beneficial to examine concepts from the chronic pain literature, given the prevalence of headache as a chronic symptom of concussion. ",
"One prevalent theory regarding the development of chronic pain is fear-avoidance of pain ([@B18]--[@B22]).",
"\n\nPrior studies ([@B25]--[@B27]) have measured high levels of fear-avoidance of pain and fear of physical activity (\"kinesiophobia\") in patients with persistent concussive symptoms. ",
"However, this is the first study to report decreases in fear-avoidance of pain in patients undergoing two different exercise treatments for concussion, and this finding deserves further study. ",
"Clearly further work needs to be done to examine the relationship between fear-avoidance and concussion symptom resolution longitudinally, as there are possible bidirectional relationships. ",
"In addition, \"fear-avoidance\" contains multiple concepts---pain-catastrophizing, fear of pain, and avoidance of activities that might result in pain. ",
"Future studies should disentangle these concepts, and better understand potential predictive relationships between children\\'s psychological and behavioral response to concussion and their subsequent symptom experience using mediation analyses. ",
"It is of note that the intervention was most efficacious for youth with persistent symptoms (\\>9 weeks), fitting with a chronic pain model ([@B18]--[@B22]). ",
"Additional research is needed to explore whether mediators of exercise treatment effects vary with chronicity of symptoms.",
"\n\nIt is notable that more than half of the youth in our study had parents who reported chronic pain. ",
"Parents play an important role in contextualizing pain and other negative symptoms for their children ([@B23], [@B46]--[@B48]). ",
"If a parent expresses fear about a child\\'s pain, their child is more likely to be concerned about potential danger. ",
"Intervening with parents to decrease pain catastrophizing, pain fears and avoidance of potentially painful activities has proven beneficial for youth with chronic pain ([@B49]--[@B51]). ",
"While the STEP intervention included parents at the baseline visit, parents did not receive tailored education and were not significantly involved in weekly calls. ",
"Future studies might consider greater engagement with parents to help them support their child\\'s exercise and lessen fear of concussive symptoms.",
"\n\nThis study was limited by a lack of diversity, which affects the ability to generalize to other populations. ",
"We also had a small sample size and thus lacked the power to conduct a definitive assessment of efficacy or true mediation analysis regarding fear-avoidance of pain and MVPA, and future studies are needed to explore both of these areas. ",
"Hip-mounted accelerometry is also an imperfect measure of MVPA, and does not accurately capture a full range of activities such as swimming and cycling. ",
"Accelerometers are also relatively burdensome to wear, and must be used for brief periods of time, resulting in activity bias. ",
"We attempted to defray such issues through standardized methods including recommendations regarding wear time, but the data remain imperfect. ",
"Finally, we had no direct measure of adherence such as a daily log, which would allow us to better estimate compliance with the exercise intervention.",
"\n\nIn conclusion, this study found that a Sub-threshold Exercise Program (STEP) for youth with persistent concussive symptoms was feasible, and may increase the rate of improvement in concussive symptoms. ",
"The STEP intervention was acceptable to subjects even with a small number of in-person visits, and treatment benefits were maintained at 6 month follow-up. ",
"Future studies are needed to examine this type of intervention in a larger sample powered to assess efficacy and mediation of treatment effects.",
"\n\nData Availability {#s5}\n=================\n\nThe datasets generated for this study are available on request to the corresponding author.",
"\n\nAuthor Contributions {#s6}\n====================\n\nSC conceptualized and designed the study, oversaw data analysis, drafted the initial manuscript and incorporated all revisions and comments. ",
"KW conducted data analysis, prepared the figures and reviewed and revised the manuscript. ",
"JM and FR assisted with conceptualization and design of the study, provided input regarding analysis, and critically reviewed the manuscript for important intellectual content. ",
"MB assisted with conceptualization and design of the study, and reviewed and revised the final manuscript. ",
"ES assisted with conceptualization and design of the study, assisted with data collection and reviewed and revised the final manuscript. ",
"AH and LF assisted with data collection and analysis, and reviewed and revised the final manuscript. ",
"TP provided input regarding analysis, and critically reviewed the manuscript for important intellectual content. ",
"All authors approved the final manuscript as submitted and agree to be accountable for all aspects of the work.",
"\n\nConflict of Interest Statement\n------------------------------\n\nThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.",
"\n\nThe authors wish to thank the patients and families who participated in this study and their providers who referred them as without them this research could not have been possible.",
"\n\n**Funding.** ",
"Research was supported by a grant from the Seattle Pediatric Concussion Research Consortium.",
"\n\nSupplementary Material {#s7}\n======================\n\nThe Supplementary Material for this article can be found online at: <https://www.frontiersin.org/articles/10.3389/fneur.2019.00623/full#supplementary-material>\n\n###### \n\nClick here for additional data file.",
"\n\n[^1]: Edited by: Noah D. Silverberg, University of British Columbia, Canada\n\n[^2]: Reviewed by: John Leddy, University at Buffalo, United States; Kelly Russell, University of Manitoba, Canada\n\n[^3]: This article was submitted to Neurorehabilitation, a section of the journal Frontiers in Neurology\n\n[^4]: †Present address: Ellie Somers, Sisu Sports Performance, Seattle, WA, United States\n"
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"This essay focuses on one of the best known patterns, the daily oscillation of body temperature (Tb), and the possibility of its difference between genders. ",
"From human and animal studies globally considered, the tentative conclusion is reached that differences in Tb circadian pattern between genders are very small and probably limited to the timing of the rhythm, not to its amplitude. ",
"Such similarity between genders, despite the differences in hormonal systems, presumably testifies to the importance that the Tb circadian pattern plays in the economy of the organism and its survival against environmental challenges. ",
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"In adult rats hypoxia (10.5% O2 for three days) caused a profound drop of the Tb daily oscillations; by day 3 they were 55% (♀) and 22% (♂) of the normoxic amplitudes, with a statistically significant gender difference. ",
"In pre-puberty rats (26-day old) hypoxia caused a major disruption of the circadian pattern qualitatively similar to the adults but not different between genders. ",
"Hence, on the basis of this preliminary set of data, it seems that sex-hormones may be a factor in how the Tb daily pattern responds to hypoxia. ",
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"When I’m 62\n\nWe misssed Paul McCartney’s birthday this past Friday when he turned 62. ",
"Today Brian Wilson turns 62 as well. ",
"Below are the brief notices we posted in their honor last year.",
"\nAs an addled teenager, I studied political philosophy at the feet of John Lennon. ",
"But the team of Lennon/McCartney — as singers, songwriters, and instinctive harmonists — was the organic entity that made the Beatles.",
"\nWe celebrate Paul McCartney’s birthday. ",
"Bring to mind any one of his tough, beautiful, moving songs — “Things We Said Today,” “We Can Work It Out,” “What You’re Doing,” “I’m Looking Through You,” “Penny Lane,” “Blackbird,” your own personal favorite. ",
"Recall the closing words of his throwaway rocker off the “White Album” — “I’m glad it’s your birthday/Happy birthday to you.”",
"\nUnlike McCartney, whose genius was sustained in a musical partnership with John Lennon, Brian Wilson was the lone musical genius who created the sound and the best songs of the Beach Boys.",
"\nIn mid-60’s singles like “Don’t Worry Baby” and “Good Vibrations” and at greater length on albums like “Summer Days (and Summer Nights)” and “The Beach Boys Today,” Wilson explored the possibilities of group harmony in pop music. ",
"Both albums are full of breathtakingly beautiful, impossibly romantic pop songs. ",
"The productions are so wonderully crafted, you can feel the perfectionism that (combined with an abusive father and hallucinogenic drugs) fueled his subsequent nervous breakdown.",
"\nBefore the breakdown, however, came the full flowering of Wilson’s genius in “Pet Sounds,” the consummate Beach Boys album that powerfully expressed (with help from Tony Asher on the lyrics) Wilson’s deepest yearnings with a moving spiritual twist. ",
"It was the album that gave Paul McCartney the idea to have the Beatles create an album around a theme — the album that became “Sgt. ",
"Pepper’s Lonely Hearts Club Band.” ",
"Happy birthday to Brian."
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[
"Вице-премьер Ольга Голодец обнаружила у нас такое явление, как «работающие бедные». ",
"Назвав его уникальным. ",
"А Росстат (его НИИ) выдал: 75% наемных работников находится у черты бедности. ",
"Некоторым едва хватает на еду. ",
"Работающим! ",
"На еду!",
"\n\nВидимо, это и станет «последним ура» Росстата как независимого статистического ведомства. ",
"После передачи Минэкономразвития он, надо полагать, не станет обнародовать то, что констатирует провал экономической политики эпохи «вставания с колен».",
"\n\nНа мой взгляд, откровения Голодец и Росстата заслуживают того, чтобы по этому поводу собрать заседание не только правительства, но и Совета безопасности.",
"\n\nПоскольку это прямо относится и к национальной безопасности, если под ней в том числе понимать ответ и на такой вопрос: имеет ли страна будущее? ",
"А получив вполне предсказуемый ответ, можно хотя бы частично передислоцировать ресурсы с победоносных внешнеполитических фронтов на те фронты внутри страны, где мы оказались на грани поражения.",
"\n\nОбъявление войны с бедностью могло бы стать главным месседжем президентской кампании Путина, который начали искать ответственные за это дело люди, но почему-то не удосужились посмотреть «под фонарем».",
"\n\nСтесняться тут совершенно нечего. ",
"Пора.",
"\n\nКонечно, Росстат считает по официальной зарплате. ",
"По таким подсчетам, примерно 10% наемных работников — нищие, еще под треть — «просто бедные», у 37% заработок выше черты бедности. ",
"При том что так называемая официальная черта бедности в нашей стране, скажем мягко, сильно занижена. ",
"И почти не имеет отношения к выработке социальной политики реальной помощи этим людям, а нужна лишь для разных минфиновских вычислений, в том числе размеров штрафов. ",
"Под определение «средний класс» по доходам попадет из числа наемных работников лишь процентов двенадцать, несколько лет назад таковых было на 3–4% больше.",
"\n\nЕсли же использовать термин «малоимущие», то им можно наградить две трети населения страны. ",
"Подавляющее большинство этих людей каждый день ходят на работу и проводят там полный рабочий день.",
"\n\nДобавление заработков в теневой экономике, в малом бизнесе (который одной ногой точно в тени), от воровства, доходы от натурального хозяйства и перераспределение между родственниками, заменяющее современную систему соцобеспечения, вряд ли сильно улучшит картину.",
"\n\nПри этом Голодец, говоря об уникальности явления работающих бедных, не права дважды. ",
"Во-первых, это явление отечественные социологи начали публично изучать еще в 90-х годах, когда рухнул привычный советский уклад жизни. ",
"Непублично они это стали изучать — и докладывать ЦК КПСС — примерно с конца 50-х годов, что позволило, кстати, определить вполне адекватно прожиточный минимум, который в 70-х годах позволял не едва выживать (как сейчас), а скромно жить-поживать на 40 рублей в месяц. ",
"Но, видимо, апеллировать к исследованиям «проклятых» 90-х годов Голодец не захотела.",
"\n\nВо-вторых, термин «работающие бедные» уже несколько десятилетий используется в западных исследованиях. ",
"Которые, в свою очередь, стали продолжением ранних споров между левыми и правыми. ",
"Первые винили в бедности «несправедливость системы», а вторые — в большей степени самих работников, за их леность, пагубные привычки, нежелание вырваться из порочного круга и т.д. ",
"Мол, общество равных возможностей дало тебе удочку, так начни уже ловить рыбу.",
"\n\nА вот кого и что сегодня винить у нас? ",
"Людскую лень или все же систему?",
"\n\nНа Западе все чаще говорят о ряде объективных явлений, способствующих умножению числа «работающих бедных». ",
"Там все меньше склонны винить только их леность в их положении (хотя иждивенцев, поколениями живущих на пособие, стало многовато). ",
"Появился термин «прекариат». ",
"Нестабильный (ключевое слово) класс наемных работников, постоянно имеющих нестабильную работу и заработки. ",
"Эти люди работают на местах с гибкой занятостью. ",
"Они — и совместители на двух-трех работах, и фрилансеры с никем не гарантированной занятостью, граничащей с бесправием.",
"\n\nПри том что профсоюзы загибаются по всему миру, крепнущая на бумаге (в законодательстве) социальная защищенность работников в жизни опрокидывается этой самой «гибкостью», работой по договору, совместительством, где все может накрыться разом в любой момент и без выходного пособия и т.д. ",
"Развитию прекариата способствует переход к «экономике услуг» от «экономики производства». ",
"И на Западе представители этой самой уязвимой категории наемных работников — в большей степени как раз работники сферы услуг, низкооплачиваемые и неквалифицированные.",
"\n\nВ развитых странах число таких наемных работников иногда доходит до 40% наемной рабочей силы. ",
"Но! ",
"Во-первых, при гораздо более высоком, чем у нас, уровне общего благосостояния. ",
"Во-вторых, при обеспечивающей реальный прожиточный минимум системе социального обеспечения. «",
"Зачинщиком» которой был в ХХ веке Советский Союз, но теперь его наследники все в этом плане развалили. ",
"Осталось доразвалить медицину и образование, где вымещение бесплатных функций платными идет стремительными темпами.",
"\n\nЛюдские ресурсы становятся еще более уязвимы по части здоровья и получения стартовых возможностей (образовательных) для продвижения вверх по социальной лестнице. ",
"В том числе — с целью выбраться из бедности и нищеты.",
"\n\nПо американским меркам, «работающие бедные» — это люди, занятые не менее 27 недель в году (то есть и временно безработные тоже), чей доход ниже официальной черты бедности. ",
"На 2017 год это примерно в 12 тыс. ",
"долл. ",
"в год на человека (с «шагом» около 4 тыс. ",
"на каждого дополнительного члена семьи) для 48 штатов, от 15 тыс. ",
"для Аляски и от 13,6 тыс. ",
"для Гавайев.",
"\n\nТри четверти «работающих бедных» работают лишь часть времени в году, лишь 25% работают более 50 недель. ",
"Основные представители таких бедных — нацменьшинства. ",
"Среди белых — лишь 5,5% «работающих бедных», при том что эта этническая группа — самая крупная в Америке. ",
"Среди черных — более 11% (как и «латинос»), при том что черные составляют 12% населения страны. ",
"18% «работающих бедных» имеют образование не выше среднего. ",
"Лишь у 2% уровень бакалавра или выше. ",
"Так что встретить в роли «работающего бедного» представителя высококвалифицированной профессии с высшим образованием невозможно. ",
"Если только это не опустившийся наркоман.",
"\n\nТеперь посмотрим на наши цифры. ",
"К социально тревожной группе «прекариата» российские социологи относят лишь 6–7% работников. ",
"Казалось бы, и возрадоваться. ",
"К тому же подчас наши фрилансеры живут относительно неплохо, получая еще и прибавку оттого, что крутятся в теневой экономике, не платя налогов. ",
"Однако радоваться особо нечему — отсылаем к вышеприведенным цифрам НИИ Росстата. ",
"Настоящая катастрофа в другом.",
"\n\nК униженной и оскорбленной категории «работающих бедных» относится не менее половины постоянно (более 48–50 недель в году) работающих россиян, если не две трети наемных работников. ",
"Среди них много работников, имеющих образование высшее или среднее специальное.",
"\n\nНаши «работающие бедные» — это учителя и врачи, инженеры и преподаватели вузов. ",
"Это отчасти работники низшего звена государственных или муниципальных структур.",
"\n\nТо есть люди, от которых критическим образом зависит будущее страны, ее технический и научный прогресс, здоровье нации, качество исполнения государственных решений на местах. ",
"Вот в чем настоящая катастрофа.",
"\n\nСреди отраслей с повышенной долей людей с заработком на уровне малообеспеченности — система образования (87% работников, заработок на уровне нищеты получают миллион преподавателей), здравоохранения (85%, «нищие» — каждый седьмой медработник), предоставление коммунальных, социальных услуг, включая культуру и спорт (вот почему мы все больше будем отставать по медалям и забитым голам) — 83%.",
"\n\nО «культуре бедности» написаны горы исследований. ",
"Это люди со специфическим горизонтом планирования. ",
"С особой системой ценностей и методами решения жизненных проблем. ",
"Они никогда не уверены в завтрашнем дне и забиты днем сегодняшним. ",
"Они не носители «социального оптимизма» (разве что в форме «идеологии гопоты»), но забитого, зависимого от воли властей, вплоть до отдельных самодуров, патернализма.",
"\n\nЭтих людей заставляют быть убогими в желаниях и потребностях. ",
"Они боятся возвысить свой голос в защиту своих даже самих элементарных прав, укрепляя тем самым социальные основы авторитаризма на всех уровнях. ",
"Они — пассивные потребители навязываемой им информационной жвачки, но не искатели альтернативных взглядов и жизненных путей. ",
"Они баранами пойдут на «митинг по разнарядке» и на «карусель голосования». ",
"Их взгляд на мир сжат до предела давлением невыносимости быта. ",
"Они все более погружаются в болото постоянной бедности, будучи все менее способным вырваться из него — в новую жизнь, на новый социальный уровень и на новое место жительства, в новую более перспективную профессию, включая риск начать свое дело.",
"\n\nЭти люди превращаются в общероссийское «гетто», рассадник социальных болезней. ",
"Идеологически и технологически с преобладанием таких людей в обществе страна обречена на сползание в архаику, культурное мракобесие и технологическую деградацию. ",
"У нее нет будущего.",
"\n\nИ даже огороженные трехметровыми заборами «золотые бантустаны» богатой элиты (т.н. ",
"элитные коттеджные поселки) не спасут ни ее, ни страну от цивилизационного краха.",
"\n\nЕсли говорить сугубо об экономических последствиях, то это не только сжатие внутреннего рынка сбыта (и стимулов развития экономики), но и стагнация целого ряда отраслей — начиная от банковской, строительной, автомобильной и кончая телекоммуникационной, информационной и даже оборонной. ",
"По поводу последней должно ведь понятно: бедные люди не могут качественно добросовестно собирать ракетный двигатель «Протон», придуманный десятилетия назад.",
"\n\nПроблема наличия огромного числа «работающих бедных» если и упомянута мимоходом, то не признана в качестве требующей неотложного решения. ",
"Данью признания этой проблемы можно считать, впрочем, известные майские указы Путина. ",
"Однако в значительной мере их выполнение происходит за счет манипулирования статистикой зарплаты по регионам и оптимизации числа работников школ и больниц.",
"\n\nВозможно, пора законодательно ввести минимальную почасовую ставку оплаты труда. ",
"Вместо «виртуальной» месячной. ",
"Во многих странах эта мера давно признана важной формой борьбы с «работающей бедностью». ",
"Могут быть и иные меры. ",
"Не надо выдумывать велосипед — все уже придумано до нас. ",
"От страхования по безработице до сокращения наличного оборота.",
"\n\nДля начала надо признать само наличие массовой бедности среди работающих полный рабочий день, в том числе квалифицированных работников, — как самой актуальной и опасной для страны.",
"\n\nГотов ли правящий класс к этому? ",
"Готов ли он к войне с бедностью? ",
"Или это «не его война»?",
"\n\nОна будет посложнее, чем война в далекой Сирии. ",
"Но пока нет впечатления готовности. ",
"Правящий класс живет в совсем иных условиях. ",
"С «низами» он почти не пересекается. ",
"В том числе — не пересекается в форме реального (а не постановочного) диалога на выборах. ",
"Посему проблемы «инопланетян» его мало волнуют. ",
"Пока от «инопланетян» туда к ним наверх не прилетит."
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"Irish Whiskey\n\nIrish whiskeys are often thought to be smooth, fruity, and triple distilled and many of them are, but this isn't the full story. ",
"The Irish are widely credited as being the first to distil whiskey, though this is strictly contested by the Scots. ",
"The Bushmills distillery, for example, is the world’s oldest licensed distillery, founded in 1608. ",
"The Irish are unique in their pure pot still whiskey. ",
"Irish single pot still whiskey is a mix of barley, malted and otherwise, distilled in a pot still. ",
"The unmalted barley proffers a spicy freshness that one associates with Irish whiskey. ",
"Some of the Irish blends are global successes with Bushmills Original and Jameson both being notable examples. ",
"There's also a healthy selection of single malt expressions, including the majority of the Bushmills range, Tyrconnell and Connemara.",
"\nIn the last 20 or so years we've seen the re-introduction of double distilled single malts and peated malts, as well as a reinvigorated and now thriving single pot still Irish whiskey style. ",
"There are also many new distilleries being constructed as Irish whiskey continues to be the fastest growing spirits category in the world!",
"\n\nYou must be at least 21 years of age to purchase wine or spirits. ",
"By placing an order through our website, you are representing yourself to us as at least 21 years of age and that the person to whom it is being shipped is at least 21 years of age. ",
"We reserve the right to ask for proof of identity before processing an order.",
"Do you agree?"
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"Dear White People is coming to television. ",
"Netflix has given a 10-episode order to a half-hour comedy series based on Justin Simien’s acclaimed debut indie feature. ",
"Simien is writing the series adaptation and will direct the first episode. ",
"The series, which will begin filming later this year for a 2017 debut, will be produced by Lionsgate, whose sister company Roadside Attractions released the original film in 2014.",
"\n\nPrimetime-Panic Your Complete Guide to Pilots and Straight-to-Series orders See All\n\nSet among a diverse group of students of color as they navigate a predominantly white Ivy League college where racial tensions are often swept under the rug, Dear White People is a send up of “post-racial” America that also weaves a universal story about forging one’s own unique path.",
"\n\nPhoto by Rick Proctor\n\n“Justin is a gifted storyteller whose bold, unique vision is perfectly suited to Netflix,” said Cindy Holland, VP of Original Content at Netflix. “",
"His original film Dear White People announced the arrival of a fresh, creative voice that had everyone talking, and we’re excited to have Justin create this new series for our members worldwide.”",
"\n\nThe Dear White People movie satire, which Simien wrote, directed and produced, originated with a concept trailer for his then-unproduced script that Simien made using his tax refund. ",
"The trailer went viral on YouTube, garnering over a million views and $50,000 in donations from fans around the world. ",
"The crowd funded movie went on to win Simien the Special Jury Award for Breakthrough Talent at Sundance and an Independent Spirit award for Best First Screenplay. (",
"Watch the film’s trailer below)\n\nIn interviews surrounding the movie’s 2014 release, Simien had spoken of his desire to continue Dear White People as a TV series in the vein of A Different World, an idea he pursued in the past year and a half as the themes in the film became even more relevant.",
"\n\n“During the film’s release, I had the pleasure to speak with hundreds of students and faculty across a variety of college campuses dealing with these very issues in real time,” Simien said. “",
"I’m so grateful to have this platform – not only to give a voice to those too often unheard in our culture, but to also tell great stories from new points of views.”",
"\n\nSimien executive produces the series with Devon Shepard (House of Lies) and the original movie’s Stephanie Allain Bray and Julia Lebedev.",
"\n\n“We’re proud to expand our partnership with our friends at Netflix on a comedy that tackles racial themes with a combination of intelligence, honesty, irreverence and wit,” said Chris Selak, EVP, Television, Lionsgate TV. “",
"Our original film with Roadside Attractions catapulted Dear White People into the national conversation about race, and Justin and the rest of the creative team have an opportunity to expand this world and bring its timely and universal themes to a global television audience.”",
"\n\nDear White People is Lionsgate’s second original series for Netflix, joining hit Orange Is The New Black, which returns for its fourth season on June 17."
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"Medicine’s New Tools: Algorithms\n\nBuilding and sharing software to probe the genetic secrets of the immune system.",
"\n\nBy Vita Staff\n08 Aug 2019\n\nData scientist Wei Shi received support from CSL through a Walter and Eliza Hall Institute Centenary Fellowship to conduct research at the Melbourne, Australia, institute. (",
"Photo courtesy: Walter and Eliza Hall Institute)\n\nThis is the first article in a three-part series about data scientists.",
"\n\nWe are in the midst of a revolution in medical research. ",
"Your genetic code can help scientists understand how the unique variations in your genes affect your risk of diseases such as cancer, and your body’s ability to fight back. ",
"But genomic medicine generates mountains of data. ",
"Wei Shi is creating the tools to enable researchers to climb those mountains.",
"\n\nIn his lab at Melbourne’s Walter and Eliza Hall Institute, Wei studies the genetic secrets of the immune system using software tools he built and has given away to hundreds of thousands of researchers around the world.",
"\n\nCSL is supporting his research through a Walter and Eliza Hall Institute Centenary Fellowship.",
"\n\n“My work is at the crossroads of computer science and biology,” Shi says. “",
"I develop algorithms for analyzing genomic data, and I help biologists make sense of that data,” Shi says.",
"\n\nGrowing up in Dalian in north-eastern China, Shi had a passion for both biology and computer science. ",
"While studying at Harbin Institute of Technology, he had to choose between the two—and ended up with a Ph.D. in computer science.",
"\n\nShi moved to Australia in 2003 to take up a postdoctoral position in high performance computing at Deakin University in Melbourne, Australia. ",
"While there, he began to revisit his interest in biology.",
"\n\n“Even when the human genome was first sequenced in 2001, I realized that computers would play a big part in understanding all that data,” he says.",
"\n\nBut once Shi started to look into how his knowledge of computing and data could be used in biology, he realized he would need to learn from experts who had a deep understanding of biology, immunology and genetics.",
"\n\nSo, when the opportunity arose to move to the Walter and Eliza Hall Institute to work with Gordon Smyth, a world-renowned bioinformatics expert, Shi didn’t hesitate.",
"\n\nIn 2013, with Gordon Smyth and Yang Liao, he developed an algorithm for analyzing genetic sequencing data called Subread that has become indispensable in labs around the world.",
"\n\nSubread solves a problem created by the avalanche of data that \"next-generation sequencing\" technologies have unleashed.",
"\n\nDNA and RNA sequencing is now much faster and cheaper than in the past, which means that sequencing of individual patients’ genomes and transcriptomes is a possibility, opening the way for treatments to be more precisely targeted. ",
"It’s also possible to see which genes are switched on—producing proteins in the body—and which are switched off.",
"\n\nHowever, understanding the results of the sequencing can be like completing an enormously complex jigsaw puzzle.",
"\n\nThe human genome is some three billion bases long, but to be read it must first be broken up into chunks of at most a couple of hundred bases. ",
"These chunks must then be reassembled into their original order by aligning them with a map of the human genome.",
"\n\nThis process of alignment is what Shi’s Subread algorithm does, which in turn lets researchers see how active each gene is and what the differences in genetic activity are between a healthy and a sick person. ",
"Analyzing these differences can reveal what genes or mutations are involved in immune disorders and cancers.",
"\n\nReleased on an open-source basis, Subread is free for anyone to use and adapt. ",
"Each year it is downloaded around 60,000 times, and the paper explaining how it works is cited in around 1,000 papers by other researchers, earning Shi a spot in the Clarivate highly cited researchers list in 2018.",
"\n\n“I’m very proud of that,” he says.",
"\n\nNow Shi is using this technology to study how the immune system responds to threats.",
"\n\nHe wants to understand how the body produces immune cells, and what genes are switched on and switched off to produce different types of immune cells.",
"\n\nWorking with immunologists, Shi and his team have sequenced immune cells as they change from one type to another, and have discovered a signature of 300 genes that are highly active in plasma cells that produce antibodies to attack invaders. ",
"These genes are potential targets for improving vaccines or other treatment.",
"\n\nRelated News\n\nTurning Promising Ideas Into Reality\n\nPhiladelphia's University City Science Center helps innovators go from idea to IPO."
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"---\nabstract: |\n We consider the inverse problem of determining the unknown function $\\alpha: \\mathbb{R} \\rightarrow \\mathbb{R}$ from the DN map associated to the operator $\\mbox{div}(A(x',\\alpha (x_3))\\nabla \\cdot)$ acting in the infinite straight cylindrical waveguide $\\Omega =\\omega \\times \\mathbb{R}$, where $\\omega$ is a bounded domain of $\\mathbb{R}^2$. Here $A=(A_{ij}(x))$, $x=(x',x_3) \\in \\Omega$, is a matrix-valued metric on $\\Omega$ obtained by straightening a twisted waveguide. ",
"This inverse anisotropic conductivity problem remains generally open, unless the unknown function $\\alpha$ is assumed to be constant. ",
"In this case we prove Lipschitz stability in the determination of $\\alpha$ from the corresponding DN map. ",
"The same result remains valid upon substituting a suitable approximation of the DN map, provided the function $\\alpha$ is sufficiently close to some [*a priori*]{} fixed constant.",
"\n\n [**Key words:**]{} Dirichlet Laplacian, twisted infinite cylindrical domain, inverse anisotropic conductivity problem, DN map, stability estimate.",
"\n\n [**AMS subject classifications:**]{} 35R30.",
"\naddress:\n- 'Institut Élie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine, Ile du Saulcy, F-57045 Metz cedex 1, France'\n- 'Centre de Physique Théorique, UMR CNRS 7332, Université d’Aix-Marseille, Université du Sud-Toulon-Var, CNRS-Luminy, F-13288 Marseille, France'\nauthor:\n- Mourad Choulli\n- Eric Soccorsi\ndate:\n- \n- \ntitle: Some inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain\n---\n\nIntroduction\n============\n\nIn the present paper we consider an inverse conductivity problem in an anisotropic medium arising from the twisting of a homogeneous infinite straight cylindrical waveguide. ",
"Generically the inverse conductivity problem in an arbitrary domain $\\Omega \\subset \\mathbb{R}^n$, $n \\geq 1$, is to determine a symmetric, positive definite matrix $A=A(x)$, $x \\in \\Omega$, representing the conductivity tensor of $\\Omega$, from the Dirichlet-to-Neumann (abbreviated to DN in the following) map associated to $A$: $$\\Lambda_A: u_{| \\partial \\Omega} \\mapsto A \\nabla u \\cdot \\nu.$$ Here $u$ is the solution to the elliptic equation $\\mbox{div} (A \\nabla u) =0$ in $\\Omega$ and $\\nu$ denotes the unit outward normal vector to the boundary $\\partial \\Omega$ of $\\Omega$.\n\nIf $A$ is isotropic (i.e. $A$ is the identity matrix of $\\mathbb{R}^n$ up to some multiplicative scalar -unknown- function of $x \\in \\Omega$) Silvester and Uhlmann [@SU] proved that the conductivity is uniquenely determined from the knowledge of $\\Lambda_A$. Similar results were derived by Lionheart in [@L] upon substituting a suitable given matrix $A_0(x)$ for the identity. ",
"For a conductivity of the form $A(x)=A_0(x,\\alpha(x))$ where $A_0$ is given and $\\alpha$ is an unknown scalar function, Alessandrini and Gaburro [@AG1; @AG2] obtained uniqueness and stability under the monotonicity assumption $$\\label{monotone}\n\\partial_t A_0(x,t) \\geq c I,\\ x \\in \\Omega,\\ t \\in \\mathbb{R}.$$ Here $c$ is some positive constant and $I$ stands for the identity of $\\mathbb{R}^n$. The case $A(x)=A_0(\\alpha(x))$ was treated earlier by Alessandrini in [@A] under the same kind of monotonicity condition.",
"\n\nAll the above mentioned results were obtained in a bounded domain of $\\mathbb{R}^n$. In this paper we will rather consider an infinite cylindrical straight waveguide $\\Omega = \\omega \\times \\mathbb{R}$, where $\\omega$ is a bounded domain of $\\mathbb{R}^2$. To $\\theta \\in C^1(\\mathbb{R})$ we then associate the twisted waveguide $$\\Omega _\\theta =\\left\\{ (R_{\\theta (x_3)}x',x_3);\\; x'=(x_1,x_2)\\in \\omega ,\\; x_3\\in \\mathbb{R}\\right\\},$$ where $R_\\xi$ denotes the rotation in $\\mathbb{R}^2$ of angle $\\xi\\in \\mathbb{R}$. Twisted waveguides modeled by $\\Omega_\\theta$ exhibit interesting propagation properties such as the occurence of propagating modes with phase velocities slower than those of similar modes in a straight waveguide. ",
"This explains why these peculiar structures are at the center of the attention of many theoretical and applied physicists (see e.g. [@Kang; @DMR; @KF; @NZG; @Sh; @Wi; @YM]). ",
"From a mathematical viewpoint twisted waveguides are the source of challenging spectral and PDE problems, some of them having been extensively studied in the mathematical literature (see e.g. [@BKRS; @EKK; @KK; @KS; @KZ1; @KZ2]). ",
"Moreover the cylindrical geometry is well suited to the construction of complex geometrical optics solutions [@DKSU; @CKS], which motivates for the analysis of inverse problems occuring in waveguides.",
"\n\nWe consider the following boundary value problem (abbreviated to BVP) for the Laplacian in $\\Omega_\\theta$: $$\\label{1}\n\\left\\{\n\\begin{array}{ll}\n\\Delta v(y)=0,\\ y \\in \\Omega_\\theta,\n\\\\\nv(y)=g(y),\\ y \\in \\partial \\Omega_\\theta.",
"\n\\end{array}\n\\right.$$ Upon straightening $\\Omega_\\theta$, may be brought into an equivalent BVP stated in $\\Omega$. This can be seen by introducing $$T_\\xi =\n\\begin{pmatrix}\nR_\\xi &0\n\\\\\n0&1\n\\end{pmatrix},$$ putting $u(x)=v(T_{\\theta (x_3)}(x',x_3))$, $x=(x',x_3)\\in \\Omega$, and performing the change of variable $y=T_{\\theta (x_3)}(x',x_3)$. We get using direct calculation that $u$ is solution to the following elliptic BVP in the divergence form $$\\label{2}\n\\left\\{\n\\begin{array}{ll}\n{{\\mathrm{div}}}\\big(A_0(x',\\alpha (x_3))\\nabla u\\big)=0,\\ x \\in \\Omega,\n\\\\\nu(x)=f(x),\\ x \\in \\partial \\Omega,\n\\end{array}\n\\right.$$ where $\\alpha =\\theta'$, $f(x)=g(T_{\\theta (x_3)}(x',x_3))$ for $x\\in \\partial \\Omega$, and the matrix $A_0$ is given by $$A_0(x',t)=\n \\begin{pmatrix}\n1+x_2^2t^2 & -x_2x_1t^2 &-x_2t\n\\\\\n-x_2x_1t^2 & 1+x_1^2t^2 & x_1t\n\\\\\n-x_2t & x_1t &1\n \\end{pmatrix},\\;\\; x'\\in \\omega ,\\; t\\in \\mathbb{R}.$$ At this point it is worth stressing out that the BVP is stated on the straight waveguide $\\Omega$ and not on the twisted waveguide $\\Omega_\\theta$ itself. ",
"Nevertheless we notice that the geometry of $\\Omega_\\theta$ is expressed in through the metric $A=(A_{ij}(x))=A_0(x',\\alpha(x_3))$.\n\nThe problem we examine in this paper is to know whether the unknown function $\\alpha$ can be determined from the DN map $$\\Lambda_\\alpha : f \\mapsto A\\nabla u \\cdot \\nu .$$ This is the same kind of inverse anisotropic conductivity problem, but stated here in the unbounded straight waveguide $\\Omega$, as the one studied in [@A; @AG1; @AG2; @GL] in a bounded domain. ",
"However, it turns out that the usual monotonicity assumption (\\[monotone\\]) on the conductivity, which is essential to the identification of $A$ from the DN map in this approach, is not verified in our framework. ",
"This explains why the inverse problem associated to is still open for general unknown functions $\\alpha \\in C({\\mathbb R})$. However, if $\\alpha$ is sufficiently close to some [*a priori*]{} fixed constant we prove in Theorem \\[thm-aconstant\\] that this unknown function may well be determined from the knowledge of some suitable approximation of the DN map (see ). ",
"Moreover, in the particular case where $\\alpha$ is known to be constant so the conductivity matrix $A$ is invariant w.r.t. ",
"the infinite variable $x_3$, the original problem is equivalent to some inverse anisotropic conductivity problem stated in $\\omega$. The corresponding conductivity matrix satisfies a weak monotonicity condition in this case implying Lipschitz stability in the determination of $\\alpha$ from $\\Lambda_\\alpha$ (see Theorem \\[theorem2\\]).",
"\n\nThe paper is organized as follows. ",
"Section 2 gathers the definition and the main properties of $\\Lambda_\\alpha$. In the first part of section 3 we adapt the method developped by Alessandrini and Gaburro in [@AG1; @AG2] to determine the conductivity in a bounded anisotropic medium from the DN map, to the particular framework of an infinite cylindrical waveguide under consideration in this text. ",
"Although this technique does not allow for the identification of general unknown functions $\\alpha$, we prove stability in the determination of $\\alpha$ from some suitable approximation of the DN map, provided $\\alpha$ is sufficiently close to some arbitrarily fixed constant. ",
"The case of constant unknown functions is examined in section 4 and we prove Lipschitz stability in the determination of $\\alpha$ from the knowledge of $\\Lambda_\\alpha$ in this case. ",
"Finally, for the sake of completness, we gather several properties (which are not directly useful for the analysis of the inverse problem under study) of the DN map $\\Lambda_\\alpha$ in Appendix.",
"\n\n[**Acknowledgments.**]{} ",
"We thank Gunther Uhlmann for valuable suggestions and comments during the completion of this work.",
"\n\nThe DN map $\\Lambda_\\alpha$\n===========================\n\n[**Solution to the BVP .**]{} ",
"As we are dealing with an infinitely extended domain $\\Omega$, we start by defining the Sobolev spaces on $\\partial \\Omega$ required by our analysis. ",
"Let $s$ be either $1/2$ or $3/2$. Since the trace operator $$\\begin{aligned}\n\\tau : C_0^\\infty (\\mathbb{R}, H^{s+1/2}(\\omega ))&\\longrightarrow L^2(\\mathbb{R}, H^s(\\partial \\omega ))\n\\\\\nG&\\mapsto \\left[t\\in \\mathbb{R}\\mapsto G(t,\\cdot )_{|\\partial \\omega}\\right]\\end{aligned}$$ extends to a bounded operator, still denoted by $\\tau$, from $L^2(\\mathbb{R},H^{s+1/2}(\\omega ))$ into $L^2(\\mathbb{R}, H^s(\\partial \\omega ))$, we put $$\\label{hs}\n\\widetilde{H}^{s}(\\partial \\Omega )=\\left\\{g\\in L^2(\\mathbb{R},H^{s}(\\partial \\omega ));\\; \\mbox{there exists}\\; G\\in H^{s+1/2}(\\Omega )\\; \\mbox{such that}\\; \\tau G=g\\right\\}.$$ The space $\\widetilde{H}^{s}(\\partial \\Omega )$ is Hilbertian for the quotient norm $$\\label{hsn}\n\\|g\\|_{\\widetilde{H}^{s}(\\partial \\Omega )}=\\inf \\left\\{\\|G\\|_{H^{s+1/2}(\\Omega )};\\ G \\in H^{s+1/2}(\\Omega )\\ \\mbox{is such that}\\ \\tau G=g\\right\\}.$$ For the sake of simplicity we write $G=g$ on $\\partial \\Omega$ instead of $\\tau G=g$ in the sequel.",
"\n\nThe definition in [@LM]\\[Chap. ",
"1\\] of fractional Sobolev spaces $H^s(\\partial \\Omega )$, $s \\in \\mathbb{Q}$, on compact manifolds without boundary, may as well be adapted to the manifold $\\partial \\Omega = \\partial \\omega \\times \\mathbb{R}$ and it is not hard to check that the two spaces $H^s(\\partial \\Omega )$ and $\\widetilde{H}^{s}(\\partial \\Omega )$ then coincide both algebraically and topologically in this case.",
"\n\nAs a direct consequence of (\\[hs\\])-(\\[hsn\\]) we have the following extension lemma:\n\n\\[lemma1bis\\] Let $g\\in \\widetilde{H}^{s}(\\partial \\Omega )$ for $s \\in \\{ 1 /2 , 3/2 \\}$. Then there exists $G\\in H^{s+1/2}(\\Omega )$ such that $G=g$ on $\\partial \\Omega$ and $$\\label{10}\n \\|G\\|_{H^{s+1/2}(\\Omega )}\\leq 2\\|g\\|_{\\widetilde{H}^{s}(\\partial \\Omega )}.$$\n\nThe main ingredient in the analysis of the BVP is the uniform ellipticity of $A$, where $A$ denotes either $A(x',t)$ or $A_0(x',\\alpha (x_3))$, as defined in section 1. ",
"Indeed, for all $\\zeta \\in \\mathbb{R}^3$ we have $$\\begin{aligned}\nA(x',t)\\zeta \\cdot \\zeta &=\\zeta _1^2+\\zeta _2^2+\\zeta_3^2-2tx_2\\zeta _1\\zeta _3+2tx_1\\zeta _2\\zeta _3+t^2(x_2\\zeta_1 -x_1\\zeta _2)^2\n\\\\\n&=\\zeta _1^2+\\zeta _2^2+(\\zeta_3 +t(x_2\\zeta_1 -x_1\\zeta _2))^2,\\ x'=(x_1,x_2) \\in \\omega,\\, t \\in {\\mathbb R},\\end{aligned}$$ by straightforward computations, which entails that $A(x',t)\\zeta \\cdot \\zeta=0$ if and only if $\\zeta =0$. Since $\\overline{\\omega} \\times [\\underline{t},\\overline{t}]$ is compact for all real numbers $\\underline{t}<\\overline{t}$, there is thus $\\lambda \\geq 1$, depending on $\\omega$, $\\underline{t}$ and $\\overline{t}$, such that we have $$\\label{8}\n\\lambda ^{-1}|\\zeta |^2\\leq A(x',t)\\zeta \\cdot \\zeta \\leq\\lambda |\\zeta |^2\\; \\textrm{for all}\\; x'\\in \\omega ,\\; t\\in [\\underline{t},\\overline{t}],\\; \\zeta \\in \\mathbb{R}^3.$$ We turn now to studying the direct problem associated to . ",
"We pick $f\\in \\widetilde{H}^{1/2}(\\partial \\Omega )$ and $F\\in H^1(\\Omega)$ such that $F=f$ on $\\partial \\Omega$. In light of and the Lax-Milgram lemma, there exists a unique $v\\in H^1_0(\\Omega)$ solving the variational problem $$\\label{25}\n\\int_\\Omega A\\nabla v\\cdot \\nabla w dx =-\\int_\\Omega A\\nabla F\\cdot \\nabla w dx,\\ \\textrm{for all}\\ w\\in H_0^1(\\Omega ).$$ Hence $u=v+F$ is the unique weak solution to the BVP . ",
"That is, $u$ satisfies the first equation in in the distributional sense and the second equation in the trace sense. ",
"By taking $w=v$ in , we get $\\|v\\|_{H^1(\\Omega )}\\leq C \\|F\\|_{H^1(\\Omega )}$ from and Poincaré’s inequality[^1][,]{} whence $$\\|u\\|_{H^1(\\Omega )}\\leq C\\|F\\|_{H^1(\\Omega )},$$ where $C$ denotes some generic positive constant depending on $\\omega$. Finally, by choosing $F \\in H^1(\\Omega)$ in accordance with Lemma \\[lemma1bis\\] so that $\\| F \\|_{H^1(\\Omega)} \\leq 2 \\| f \\|_{\\tilde{H}^{1 \\slash 2}(\\partial \\Omega)}$, we find out that $$\\label{26}\n \\|u\\|_{H^1(\\Omega )}\\leq C\\|f\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )}.$$\n\n[**Definition of the DN map.**]{} ",
"Let us first introduce the following $H(\\textrm{div})$-type space, $$H({{\\mathrm{div}}}_A,\\Omega )=\\{ P\\in L^2(\\Omega )^3;\\; {{\\mathrm{div}}}(AP)\\in L^2(\\Omega )\\},$$ and prove that $P\\in C_0^\\infty (\\overline{\\Omega})\\mapsto AP \\cdot \\nu \\in C^\\infty (\\partial \\Omega )$ may be extended to a bounded operator from $H({{\\mathrm{div}}}_A,\\Omega )$ into the space $\\widetilde{H}^{-1/2}(\\partial \\Omega )$ dual of $\\widetilde{H}^{1/2}(\\partial \\Omega )$.",
"\n\n\\[proposition1\\] Let $P\\in H({{\\mathrm{div}}}_A,\\Omega )$. ",
"Then $AP\\cdot \\nu \\in \\widetilde{H}^{-1/2}(\\partial \\Omega )$ and we have $$\\label{24}\n \\|AP\\cdot \\nu \\|_{\\widetilde{H}^{-1/2}(\\partial \\Omega )}\\leq C\\big( \\|P\\|_{L^2(\\Omega )}+\\|{{\\mathrm{div}}}(AP)\\|_{L^2(\\Omega )}\\big),$$ for some constant $C=C(\\omega,\\theta)>0$. In addition, the following identity $$\\label{27}\n \\langle AP\\cdot \\nu ,g \\rangle = \\int_\\Omega G {{\\mathrm{div}}}(AP) dx+\\int_\\Omega A\\nabla G\\cdot P dx,$$ holds for $g\\in \\widetilde{H}^{1/2}(\\partial \\Omega )$ and $G\\in H^1(\\Omega)$ such that $G=g$ on $\\partial \\Omega$. Here $\\langle \\cdot ,\\cdot \\rangle$ denotes the duality pairing between $\\widetilde{H}^{1/2}(\\partial \\Omega )$ and its dual $\\widetilde{H}^{-1/2}(\\partial \\Omega )$.",
"\n\nWe first consider the case of $P\\in C_0^\\infty (\\overline{\\Omega})^3$. Fix $g\\in \\widetilde{H}^{1/2}(\\partial \\Omega )$ and choose $G \\in H^1(\\Omega)$ such that $G=g$ on $\\partial \\Omega$. Since $P$ has a compact support, we have $$\\label{28}\n \\int_\\Omega G{{\\mathrm{div}}}(AP)dx=-\\int_\\Omega A\\nabla G\\cdot Pdx+\\int_{\\partial \\Omega}gAP\\cdot \\nu d \\sigma,$$ by Green’s formula, whence $$\\Big|\\int_{\\partial \\Omega}gAP\\cdot \\nu d\\sigma \\Big|\\leq C\\|G\\|_{H^1(\\Omega )}\\big( \\|P\\|_{L^2(\\Omega )}+\\|{{\\mathrm{div}}}(AP)\\|_{L^2(\\Omega )}\\big).$$ Taking the infimum over $\\{ G\\in H^1(\\Omega),\\ G=g\\ \\mathrm{on}\\ \\partial \\Omega \\}$ in the right hand side of above estimate, we find that holds true for every $P \\in C_0^\\infty (\\overline{\\Omega})^3$.\n\nFurther, we pick $P \\in H({{\\mathrm{div}}}_A,\\Omega )$. ",
"The set $C_0^\\infty (\\overline{\\Omega})^3$ being dense in $H({{\\mathrm{div}}}_A,\\Omega )$, as can be seen by mimmicking the proof of [@GR]\\[Theorem 2.4\\], we may find a sequence $(P_k)_k$ in $C_0^\\infty (\\overline{\\Omega})^3$ converging to $P$ in $H({{\\mathrm{div}}}_A,\\Omega )$. ",
"Moreover, $(AP_k\\cdot \\nu )_k$ being a Cauchy sequence in $\\widetilde{H}^{-1/2}(\\partial \\Omega )$ by , then $(AP_k\\cdot \\nu )_k$ admits a limit, denoted by $AP\\cdot \\nu$, in $\\widetilde{H}^{-1/2}(\\partial \\Omega )$. ",
"Now follows readily from this and .",
"\n\nLet $u$ be the $H^1(\\Omega)$-solution to . ",
"Applying Proposition \\[proposition1\\] to $P=\\nabla u$, we deduce from that $$\\Lambda _\\alpha :f \\mapsto A\\nabla u\\cdot \\nu$$ is well defined as a bounded operator from $\\widetilde{H}^{1/2}(\\partial \\Omega )$ into $\\widetilde{H}^{-1/2}(\\partial \\Omega )$. ",
"Moreover the following identity $$\\label{29}\n \\langle \\Lambda _\\alpha f,g\\rangle =\\int_\\Omega A\\nabla u\\cdot \\nabla G dx,$$ holds for all $g\\in \\widetilde{H}^{1/2}(\\partial \\Omega )$ and $G\\in H^1(\\Omega)$ such that $G=g$ on $\\partial \\Omega$.\n\nFurther, by taking $G=v$ in , where $v$ is the solution to with $f$ replaced by $g$, we find out that $$\\langle \\Lambda _\\alpha f,g\\rangle =\\int_\\Omega A\\nabla u\\cdot \\nabla v dx=\\int_\\Omega \\nabla u\\cdot A\\nabla v dx,$$ entailing $$\\label{30}\n \\langle \\Lambda _\\alpha f,g\\rangle =\\langle f, \\Lambda _\\alpha g\\rangle ,\\; \\textrm{for all}\\; f,g\\in \\widetilde{H}^{1/2}(\\partial \\Omega ).$$ This proves that $\\Lambda _\\alpha ^\\ast{ _{\\big|\\widetilde{H}^{1/2}(\\partial \\Omega )}}=\\Lambda _\\alpha$, where $\\widetilde{H}^{1/2}(\\partial \\Omega )$ is identified with a subspace of its bidual space.",
"\n\nFinally, for $i=1,2$, we put $A_i=A(x',\\alpha _i(x_3))$ and $\\Lambda _i=\\Lambda_{\\alpha _i}$, and let $u_i\\in H^1(\\Omega )$ denote a weak solution to the equation $${{\\mathrm{div}}}(A_i\\nabla u_i)=0\\; \\textrm{in}\\; \\Omega .$$ Applying to $f=u_i{_{\\big|\\partial \\Omega}}$ and $g=u_{3-i}{_{\\big|\\partial \\Omega}}$, we thus get $$\\langle \\Lambda _1 u_1,u_2\\rangle =\\int_\\Omega A_1\\nabla u_1\\cdot \\nabla u_2 dx\\ \\mathrm{and}\\\n\\langle \\Lambda _2 u_2,u_1\\rangle =\\int_\\Omega A_2\\nabla u_2\\cdot \\nabla u_1 dx.$$ which finally yields $$\\label{31}\n\\langle (\\Lambda _1 -\\Lambda _2)u_1,u_2\\rangle =\\int_\\Omega (A_1-A_2)\\nabla u_1\\cdot \\nabla u_2 dx,$$ according to .",
"\n\nCan we determine the unknown function $\\alpha$ from $\\Lambda_\\alpha$?",
"\n=====================================================================\n\nIn this section we examine the inverse problem of identifying $\\alpha$ from the knowledge of $\\Lambda_{\\alpha}$.\n\n[**Analysis of the problem for general unknown functions.**]{} ",
"Let $\\gamma$ be a nonempty open subset of $\\partial \\omega$. We put $\\Gamma =\\gamma \\times (-2L,2L)$ for some fixed $L>0$, and define the functional space $$\\label{eq1a}\n\\widetilde{H}^{1/2}_\\Gamma (\\partial \\Omega )=\\{f\\in \\widetilde{H}^{1/2}(\\partial \\Omega );\\; \\textrm{supp} f\\subset \\Gamma \\}.$$ For $\\alpha _i\\in W^{1,\\infty}(\\mathbb{R})$, $i=1,2$, we note $A_i=A(x',\\alpha_i'(x_3))$ and $\\Lambda_i=\\Lambda_{\\alpha _i}$. In light of , we have $$\\label{32}\n\\langle (\\Lambda _1 -\\Lambda _2)u_1,u_2\\rangle =\\int_\\Omega (A_1-A_2)\\nabla u_1\\cdot \\nabla u_2 dx,$$ for any function $u_i \\in H^1(\\Omega)$ which is a weak solution to the equation $${{\\mathrm{div}}}(A_i\\nabla u_i)=0\\ \\mbox{in}\\ \\Omega,\\ i=1,2.$$ Putting $\\Omega^L=\\omega \\times (-L,L)$ and assuming that $$\\label{eq1b}\n\\alpha _1(x_3)=\\alpha _2(x_3),\\ |x_3|>L,$$ we may rewrite as $$\\label{33}\n\\langle (\\Lambda _1 -\\Lambda _2)u_1,u_2\\rangle =\\int_{\\Omega^L}(A_1-A_2)\\nabla u_1\\cdot \\nabla u_2 dx.$$ The following analysis is essentially based on the method built in [@AG2] for bounded domains, that will be adapted to the case of the infinite waveguide $\\Omega$ under consideration. ",
"To this purpose we set $$\\Gamma _\\rho =\\{ x\\in \\Gamma ;\\; \\textrm{dist}(x,\\partial \\Gamma )>\\rho \\}\\ \\textrm{and}\\\nU_\\rho=\\{ x\\in \\mathbb{R}^3 ;\\; \\textrm{dist}(x,\\Gamma _\\rho )<\\rho /4 \\},$$ for all $\\rho \\in (0, \\rho _0]$, where $\\rho _0$ is some characteristic constant depending only on $\\omega$ and $L$, which is defined in [@AG2]. ",
"Upon eventually shortening $\\rho_0$, we can assume without loss of generality that $\\Gamma _0=\\gamma _0\\times [-L,L]\\subset \\Gamma _\\rho$ for some $\\gamma _0 \\Subset \\gamma$. In view of [@AG2], we thus may find a Lipschitz domain $\\Omega _\\rho$ satisfying simultaneously: $$\\Omega \\subset \\Omega _\\rho,\\; \\Gamma _0\\subset\\partial \\Omega \\cap \\Omega _\\rho \\Subset \\Gamma\\; \\mathrm{and}\\\n\\textrm{dist}(x,\\partial \\Omega _\\rho)\\geq \\rho /2\\; \\textrm{for all}\\; x\\in U_\\rho.$$ Moreover we know from [@AG1]\\[Section 3\\] that there is a unitary $C^\\infty$ vector field $\\tilde{\\nu}$, defined in some suitable neighborhood of $\\partial \\omega\\times (-2L,2L)$, which is non tangential to $\\partial \\Omega$ and points to the exterior of $\\Omega$. For $x^0\\in \\overline{\\Gamma _\\rho}$, the point $z_\\tau = x^0+\\tau \\tilde{\\nu}$ obeys $C \\tau \\leq \\textrm{dist}(z_{\\tau},\\partial \\Omega) \\leq \\tau$ for all $0 < \\tau \\leq \\tau_0$, according to [@AG1]\\[Lemma 3.3\\]. ",
"Here $C$ and $\\tau_0$ are two positive constants depending only on $\\Omega$ and $\\lambda$, $\\underline{t}$ and $\\overline{t}$ are the same as in .",
"\n\nIn light of [@HK], the operator ${{\\mathrm{div}}}(A_i\\nabla \\cdot\\, )$, $i=1,2$, has a Dirichlet Green function $G_i=G_i(x,y)$ on $\\Omega _\\rho$. More specifically, $G_i(x)=G_i(x,z_\\tau )$ is the solution to the BVP $$\\label{equation1}\n\\left\\{\n\\begin{array}{ll}\n{{\\mathrm{div}}}(A_i\\nabla G_i)=-\\delta (x-z_\\tau )\\;\\; &\\textrm{in}\\;\\; \\mathscr{D}'(\\Omega _\\rho)\n\\\\\nG_i=0 &\\textrm{on}\\;\\; \\partial \\Omega _\\rho,\n\\end{array}\n\\right.\\ i=1,2,$$ and we will see in the coming lemma that the claim of [@AG2]\\[Corollary 3.4\\] remains essentially unchanged for the unbounded domain $\\Omega _\\rho$ arising in this framework.",
"\n\n\\[lemma1\\] There are two constants $\\tau _0=\\tau _0(\\Omega ,\\rho) >0$ and $C=C(\\Omega ,\\lambda ,\\underline{t},\\overline{t})$ such that the restriction $G_i(.,z_\\tau)$ to $\\Omega$, $i=1,2$, belongs to $H^1(\\Omega )$, and satisfies $$\\label{equation2}\n\\|G_i(\\cdot ,z_\\tau )\\|_{H^1(\\Omega )}\\leq C\\tau ^{-1/2},\\;\\; 0<\\tau \\leq \\tau _0.$$\n\nLet the space $Y^{2,1}(\\Omega )=\\{u\\in L^6(\\Omega );\\; \\nabla u\\in L^2(\\Omega )^3\\}$ be endowed with the norm $\\| v \\|_{Y^{2,1}(\\Omega )}=\\| v \\|_{L^6(\\Omega)} + \\| \\nabla v \\|_{L^2(\\Omega)^3}$ and choose $\\tau_0=\\tau_0(\\Omega,\\rho)$ so small relative to $\\rho$ that $\\textrm{dist}(z_\\tau,\\partial \\Omega_\\rho)>\\tau$ for all $\\tau \\in (0,\\tau_0]$. Since the ball $B_{\\tau \\slash 3}(z_\\tau)$ centered at $z_\\tau$ with radius $\\tau \\slash 3$, is embedded in $\\Omega_\\rho \\setminus \\overline{\\Omega}$, we have $$\\label{equ3}\n\\|G_i(\\cdot ,z_\\tau )\\|_{Y^{2,1}(\\Omega )}\\leq \\| G_i(\\cdot,z_{\\tau}) \\|_{Y^{2,1}(\\Omega_\\rho \\setminus B_{\\tau \\slash 3}(z_\\tau))} \\leq C\\tau ^{-1/2},\\;\\; 0<\\tau \\leq \\tau _0,$$ directly from [@HK]\\[Formula (4.45)\\]. ",
"Here $C$ is some positive constant depending only on $\\Omega$, $\\lambda$, $\\underline{t}$ and $\\overline{t}$.\n\nFinally, the domain $\\Omega$ having the Poincaré inequality property since $\\omega$ is bounded, we may deduce (\\[equation2\\]) from (\\[equ3\\]).",
"\n\nFurther, as a Green function is a Levi function, it behaves locally like a parametrix. ",
"Hence, by applying [@M]\\[Formula (8.4)\\], $G_i$ can be brought into the form $$\\label{e1}\nG_i(x)=C(\\textrm{det}\\, (A_i(z_\\tau )))^{-1/2}\\big(A(z_\\tau )^{-1}(x-z_\\tau )\\cdot (x-z_\\tau )\\big)^{-1/2}+R_i(x),\\ i=1,2,$$ where $C>0$ is a constant and the reminder $R_i$ obeys the condition: $$\\exists (r_0,\\alpha) \\in \\mathbb{R}_+^* \\times (0,1),\\ |R_i(x)|+|x-z_\\tau|\\, |\\nabla R_i|\\leq C|x-z_\\tau|^{-1+\\alpha},\\\nx \\in \\Omega _\\rho, |x-z_\\tau|\\leq r_0.$$ On the other hand it holds true that ${{\\mathrm{div}}}(A_i\\nabla G_i)=0$ in the weak sense in $\\Omega$ for $i=1,2$, so entails $$\\langle (\\Lambda _1 -\\Lambda _2)G_1,G_2\\rangle =\\int_{\\Omega^L}(A_1-A_2)\\nabla G_1\\cdot \\nabla G_2dx.$$ Taking into account that $G_i{_{\\big |\\partial \\Omega}}\\in \\widetilde{H}^{1/2}(\\partial \\Omega )$, this yields $$\\int_{\\Omega^L}(A_1-A_2)\\nabla G_1\\cdot \\nabla G_2dx\\leq \\|\\Lambda _1 ^\\Gamma -\\Lambda _2 ^\\Gamma \\| \\| G_1\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )} \\|G_2 \\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )},$$ where $\\Lambda _i ^\\Gamma$ is the restriction of $\\Lambda _i$ to the closed subspace $\\widetilde{H}^{1/2}_\\Gamma (\\partial \\Omega )$, and consequently $$\\label{e2}\n \\int_{\\Omega^L}(A_1-A_2)\\nabla G_1\\cdot \\nabla G_2dx\\leq C \\|\\Lambda _1 ^\\Gamma -\\Lambda _2 ^\\Gamma \\| \\| G_1\\|_{H^1( \\Omega )} \\|G _2\\|_{H^1(\\Omega )}.$$\n\nThe next step involves picking $x^0 \\in \\Gamma _0$ such that $|\\alpha_1(x_3^0)-\\alpha '_2(x_3^0)|=\\|\\alpha_1-\\alpha _2\\|_{L^\\infty (-L,L)}$. We may actually assume without loss of generality that $|\\alpha_1(x_3^0)-\\alpha_2(x_3^0)|=\\alpha_1(x_3^0)-\\alpha_2(x_3^0)$. In view of and [@AG2]\\[Formula (4.2)\\], the main term in the left hand side of has the following expression $$\\int_{B(z_\\tau ,\\rho )\\cap \\Omega }\\frac{\\left[A^{-1}((x^0)',t_0)-A^{-1}((x^0)',s_0)\\right](x-z_\\tau )\\cdot (x-z_\\tau )}{\\left[P_0(x-z_\\tau )\\cdot (x-z_\\tau )\\right]^{3/2}\\left[Q_0(x-z_\\tau )\\cdot (x-z_\\tau )\\right]^{3/2}}dx,$$ with $t_0=\\alpha_1(x_3^0)$, $s_0=\\alpha_2(x_3^0)$, $P_0=A^{-1}(z_\\tau' ,t_0)$ and $Q_0=A^{-1}(z_\\tau' ,s_0)$, where we recall that $z_{\\tau}=x^0+\\tau \\tilde{\\nu}$ for some $\\tau \\in \\mathbb{R}_+^*$. The main ingredient in the analysis developped in [@AG2] is the ellipticity condition [@AG2]\\[Formula (2.5)\\] imposed on $\\partial _tA(x',t)$, implying $$\\label{e3}\n\\int_{B(z_\\tau ,\\rho )\\cap \\Omega }\\frac{\\left[A^{-1}((x^0)',t_0)-A^{-1}((x^0)',s_0)\\right](x-z_\\tau )\\cdot (x-z_\\tau )}{\\left[P_0(x-z_\\tau )\\cdot (x-z_\\tau )\\right]^{3/2}\\left[Q_0(x-z_\\tau )\\cdot (x-z_\\tau )\\right]^{3/2}}dx\\geq C\\tau (t_0-s_0),$$ for some constant $C>0$, which leads ultimately to the desired result.",
"\n\nUnfortunately, this condition is not fulfilled by $\\partial_t A(x',t)$ in this framework. ",
"This can be seen from the following explicit expression $$\\begin{aligned}\n&\\lambda _1=0,\n\\\\\n&\\lambda _2= |x'|^2t-\\sqrt{|x'|^4t^2+|x'|^2},\n\\\\\n&\\lambda _3=|x'|^2t+\\sqrt{|x'|^4t^2+|x'|^2},\\end{aligned}$$ of the eigenvalues of $\\partial_t A(x',t)$, showing that the spectrum of $\\partial_t A(x',t)$ has a negative component for $x' \\in \\partial \\omega$. Moreover, due to the occurence of this negative eigenvalue, the weak monotonicity assumption [@AG1]\\[Formula (5.7)\\] is not satisfied by the conductivity matrix under consideration either. ",
"Therefore, the approach developped in [@AG2] does not apply to the inverse problem of determining $\\alpha$ from the knowledge of $\\Lambda_\\alpha$, which remains open in the general case.",
"\n\nNevertheless, we will see in section \\[sec-constant\\] that this is not the case for constant unknown functions anymore. ",
"But, prior to examining this peculiar framework, we will now deduce from the above reasoning, upon substituting a suitable matrix $A^\\bullet$ for $A$, that unknown functions $\\alpha$ which are close to some [*a priori*]{} fixed constant value may well be identified from the associated DN map.\\\n[**The case of unknown functions close to a constant value.**]{} ",
"Put $$A^\\bullet (x',t)=t\n \\begin{pmatrix}\n1+x_2^2 & -x_2x_1 &-x_2\n\\\\\n-x_2x_1 & 1+x_1^2 & x_1\n\\\\\n-x_2& x_1 &1\n \\end{pmatrix},\\ x'\\in \\omega ,\\ t\\in \\mathbb{R},$$ and denote by $\\Lambda _\\alpha ^\\bullet$ the DN map $\\Lambda_{\\alpha}$ where $A^\\bullet (x',\\alpha (x_3))$ is substituted for $A(x',\\alpha (x_3))$. Then, by arguing as in the derivation of , we obtain that $$\\label{51}\n\\langle (\\Lambda _\\alpha -\\Lambda _\\alpha ^\\bullet )u,u^\\bullet \\rangle =\\int_\\Omega (A(x',\\alpha (x_3) )-A^\\bullet (x',\\alpha (x_3))\\nabla u\\cdot \\nabla u^\\bullet dx,$$ for all $u, u^{\\bullet} \\in H^1(\\Omega )$ satisfying ${{\\mathrm{div}}}(A(x',\\alpha (x_3) )\\nabla u)={{\\mathrm{div}}}(A^\\bullet (x',\\alpha (x_3) )\\nabla u^\\bullet )=0$ in the weak sense in $\\Omega$. For $f$ (resp. ",
"$g$) in $\\tilde{H}^{1 \\slash 2}(\\partial \\Omega)$ let $u$ (resp. ",
"$u^\\bullet$) be the solution to (resp. ",
"where $(A^\\bullet,g)$ is substituted to $(A,f)$). ",
"Thus, applying we get that $| \\langle (\\Lambda _\\alpha -\\Lambda _\\alpha^\\bullet )f, g \\rangle | \\leq \\| \\alpha - 1 \\|_{\\infty} \\| u \\|_{H^1(\\Omega)} \\| u^\\bullet \\|_{H^1(\\Omega)}$. This entails $| \\langle (\\Lambda _\\alpha -\\Lambda _\\alpha ^\\bullet )f, g \\rangle | \\leq C \\| \\alpha - 1 \\|_{\\infty}\n\\| f \\|_{\\tilde{H}^{1 \\slash 2}(\\partial \\Omega)} \\| g \\|_{\\tilde{H}^{1 \\slash 2}(\\partial \\Omega)}$, by , where $C=C(\\omega)$ is some positive constant. ",
"As a consequence we have $$\\label{eq-approx}\n\\|\\Lambda _\\alpha -\\Lambda ^\\bullet _\\alpha \\|_{\\mathscr{L}(\\widetilde{H}^{1/2}(\\partial \\Omega ),\\widetilde{H}^{-1/2}(\\partial \\Omega )) }\\leq C\\|\\alpha -1\\|_\\infty,$$ showing that $\\Lambda_{\\alpha}^{\\bullet}$ is a suitable approximation of $\\Lambda_{\\alpha}$ provided $\\alpha$ is sufficiently close to $1$.[^2] Actually, the main benefit of dealing with $\\Lambda_{\\alpha}^{\\bullet}$ instead of $\\Lambda_{\\alpha}$ in the inverse problem of determining $\\alpha$ from $\\Lambda_{\\alpha}$, boils down to the following identity $$\\partial _tA^\\bullet (x',t)=A^\\bullet (x',1)=A(x',1),\\ {\\rm for\\ all}\\ x' \\in \\omega\\ {\\rm and}\\ t \\in {\\mathbb R},$$ ensuring that the ellipticity condition [@AG2]\\[Formula (2.5)\\] required by the method presented in [@AG2], is verified by $A^{\\bullet}$. Now, in light of the reasoning developped in the first part of this section, arguing as in the proof of [@AG2]\\[Theorem 2.2\\] we derive the:\n\n\\[thm-aconstant\\] Let $L>0$ and $M>0$. Assume that $\\alpha_i \\in W^{1,\\infty}(\\mathbb{R})$, $i=1,2$, obey and are such that $$\\|\\alpha_i\\|_{W^{1,\\infty }(\\mathbb{R})} \\leq M.$$ Then there exists a constant $C>0$ depending only on $\\omega$, $M$ and $L$, such that we have $$\\| \\alpha_1-\\alpha_2\\|_{L^\\infty (\\mathbb{R})}\\leq C\n\\|(\\Lambda ^\\bullet _{\\alpha _1})^\\Gamma -(\\Lambda ^\\bullet _{\\alpha _2})^\\Gamma \\|_{\\mathscr{L}(\\widetilde{H}^{1/2}(\\partial \\Omega ),\\widetilde{H}^{-1/2}(\\partial \\Omega )) },\n$$ where $(\\Lambda ^\\bullet _{\\alpha _i})^\\Gamma=(\\Lambda ^\\bullet _{\\alpha _i})_{| \\widetilde{H}^{1/2}_\\Gamma (\\partial \\Omega )}$ for $i=1,2$, the space $\\widetilde{H}^{1/2}_\\Gamma (\\partial \\Omega )$ being the same as in .",
"\n\nThe case of constant unknown functions {#sec-constant}\n======================================\n\nIn this section we address the case of affine twisting functions $\\theta$, that is constant functions $\\alpha$, by means of the partial Fourier transform $\\mathcal{F}_{x_3}$ with respect to the variable $x_3$. This is suggested by the translational invariance of the system under consideration in the infinite direction $x_3$, arising from the fact that the matrix $A(x',\\alpha (x_3))$ appearing in does not depend on $x_3$ in this peculiar case.",
"\n\nIn the sequel, we note $\\xi$ the Fourier variable associated to $x_3$ and we write $\\widehat{w}$ instead of ${\\mathcal F}_{x_3} w$ for every function $w=w(x',x_3)$: $$\\widehat{w}(x',\\xi)=({\\mathcal F}_{x_3} w)(x',\\xi),\\ x' \\in \\omega,\\ \\xi \\in \\mathbb{R}.$$ The first step of the method is to re-express the system in the Fourier plane $\\{ (x',\\xi),\\ x' \\in \\omega, \\xi \\in \\mathbb{R} \\}$.\\\n[**Rewriting the BVP in the Fourier variables.**]{} ",
"We start with two useful technical lemmas.",
"\n\n\\[lemma2\\] For every $w\\in H^1(\\Omega)$ the identity $\\widehat{\\partial _{x_j}w}=\\partial _{x_j}\\widehat{w}$ holds for $j=1,2$.\n\nFix $j=1,2$. For every $\\varphi \\in C_0^\\infty (\\omega )$ and $\\psi \\in \\mathcal{S}(\\mathbb{R})$, we have $$\\int_\\omega \\varphi (x') \\left( \\int_\\mathbb{R}\\partial _{x_j}w(x',x_3)\\widehat{\\psi}(x_3)dx_3 \\right) dx'=\\int_\\mathbb{R}\\widehat{\\psi}(x_3) \\left( \\int_\\omega \\partial _{x_j}w(x',x_3)\\varphi (x')dx' \\right) dx_3,$$ from Fubini’s theorem. ",
"By integrating by parts in the last integral, we obtain $$\\int_\\omega \\partial _{x_j}w(x',x_3)\\varphi (x')dx'=-\\int_\\omega w(x',x_3)\\partial _{x_j}\\varphi (x')dx',\\; \\textrm{a.e.}\\; x_3\\in \\mathbb{R},$$ so we get $$\\begin{aligned}\n\\int_\\omega \\varphi (x') \\left( \\int_\\mathbb{R}\\partial _{x_j}w(x',x_3)\\widehat{\\psi}(x_3)dx_3 \\right) dx'& = & -\\int_\\mathbb{R}\\widehat{\\psi}(x_3) \\left( \\int_\\omega w(x',x_3)\\partial _{x_j}\\varphi (x')dx'\\right) dx_3 \\\\\n& = & \n- \\int_\\omega \\partial _{x_j}\\varphi (x') \\left( \\int_\\mathbb{R}w(x',x_3)\\widehat{\\psi}(x_3)dx_3 \\right) dx'.\\end{aligned}$$ Further, the operator $\\mathcal{F}_{x_3}$ being selfadjoint in $L^2(\\mathbb{R})$, it is true that $$\\int_\\mathbb{R}w(x',x_3)\\widehat{\\psi}(x_3)dx_3=\\int_\\mathbb{R}\\widehat{w}(x',\\xi ) \\psi (\\xi )d\\xi,\\; \\textrm{a.e.}\\; x'\\in \\omega,$$ whence $$\\begin{aligned}\n\\int_\\omega \\varphi (x') \\left( \\int_\\mathbb{R}\\partial _{x_j}w(x',x_3)\\widehat{\\psi}(x_3)dx_3 \\right) dx'&=-\\int_\\omega \\partial _{x_j}\\varphi (x') \\left( \\int_\\mathbb{R}\\widehat{w}(x',\\xi ) \\psi (\\xi )d\\xi \\right) dx'\\\\ &= \\int_\\omega \\varphi (x') \\left( \\int_\\mathbb{R}\\partial _{x_j}\\widehat{w}(x',\\xi ) \\psi (\\xi )d\\xi \\right) dx',\\end{aligned}$$ by integrating by parts. ",
"From the density of $C_0^{\\infty}(\\omega)$ in $L^2(\\omega)$, the above identity entails that $$\\int_\\mathbb{R}\\partial _{x_j}w(x',x_3)\\widehat{\\psi}(x_3)dx_3=\\int_\\mathbb{R}\\partial _{x_j}\\widehat{w}(x',\\xi ) \\psi (\\xi )d\\xi,\\; \\textrm{a.e.}\\; x'\\in \\omega,$$ for every $\\psi \\in \\mathcal{S}(\\mathbb{R})$. From this, the selfadjointness of $\\mathcal{F}_{x_3}$ and the density of $\\mathcal{S}(\\mathbb{R})$ in $L^2(\\mathbb{R})$, then follows that $\\widehat{\\partial _{x_j}w}=\\partial _{x_j}\\widehat{w}$.\n\n\\[lemma3\\] Let $C=(C_{kl})_{1 \\leq k,l \\leq 3} \\in W^{1,\\infty}(\\omega )^{3\\times 3}$ be such that $(C_{kl}(x'))_{1 \\leq k,l \\leq 3}$ is symmetric for all $x'\\in \\omega$. Then every $w\\in H^1(\\Omega )$ obeying $$\\label{34}\n\\int_\\Omega C\\nabla w\\cdot \\nabla v dx =0\\ \\textrm{for all}\\ v\\in H_0^1(\\Omega ),$$ satisfies the equation $$\\label{eqdiv}\n-{{\\mathrm{div}}}_{x'} (\\widetilde{C}(x')\\nabla _{x'}\\widehat{w})+P(x',\\xi )\\cdot \\nabla _{x'}\\widehat{w}+q(x',\\xi )\\widehat{w}=0\\;\\; \\textrm{in}\\; \\mathcal{D}'(\\Omega ),$$ with $$\\begin{aligned}\n&\\widetilde{C}(x')=(C_{ij}(x'))_{1\\leq i,j \\leq 2}\n\\\\\n&P(x',\\xi )=-i2\\xi\n \\begin{pmatrix}\n C_{31}(x') \\\\ C_{32}(x') \n \\end{pmatrix}\n \\\\\n&q(x',\\xi )=-i\\xi {{\\mathrm{div}}}_{x'} \\begin{pmatrix}\n C_{31}(x') \\\\ C_{32}(x') \n \\end{pmatrix} +\\xi ^2C_{33}(x'),\\ (x',\\xi) \\in \\Omega.\\end{aligned}$$ Moreover, if $w\\in H^2(\\Omega )$ is solution to then holds for a.e. ",
"$(x',\\xi) \\in \\Omega$.\n\nChoose $v=\\varphi \\otimes \\widehat{\\psi}$ in , with $\\varphi \\in C_0^\\infty (\\omega )$ and $\\psi \\in \\mathcal{S}(\\mathbb{R})$, so we have: $$\\label{35}\n\\sum_{k,l=1,2,3}\\int_\\Omega C_{kl}(x')\\partial_{x_k}w(x',x_3)\\partial _{x_l}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3=0.$$ For $1 \\leq k, l \\leq 2$, we notice that $$\\begin{aligned}\n\\int_\\Omega C_{kl}(x')\\partial_{x_l}w(x',x_3)\\partial _{x_k}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3\n& = \\int_\\omega C_{kl}(x')\\partial _{x_k}\\varphi (x') \\left( \\int_\\mathbb{R}\\partial_{x_l} w(x',x_3)\\widehat{\\psi}(x_3) dx_3 \\right) dx' \\nonumber \\\\\n& = \\int_\\Omega C_{kl}(x')\\partial_{x_l}\\widehat{w}(x',\\xi )\\partial _{x_k}(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi, \\label{36}\\end{aligned}$$ directly from Lemma \\[lemma2\\]. ",
"Further, the identity $$\\begin{aligned}\n\\int_\\Omega C_{3l}(x')\\partial_{x_l}w(x',x_3)\\partial _{x_3}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3 &=\\int_\\omega C_{3j}(x')\\varphi (x') \\left( \\int_\\mathbb{R}\\partial_{x_l}w(x',x_3)\\widehat{\\psi}'(x_3)dx_3 \\right) dx'\n\\\\ \n&=\\int_\\omega C_{3l}(x')\\varphi (x') \\left( \\int_\\mathbb{R}\\partial_{x_l}w(x',x_3)\\widehat{(-i\\xi )\\psi}(x_3)dx_3 \\right) dx',\\end{aligned}$$ holds for $l=1,2$, so we have $$\\label{37}\n\\int_\\Omega C_{3l}(x')\\partial_{x_l}w(x',x_3)\\partial _{x_3}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3=\\int_\\Omega C_{3l}(x')(-i\\xi )\\partial_{x_l}\\widehat{w}(x',\\xi )(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi .$$ Next, since $$\\begin{aligned}\n\\int_\\Omega C_{k3}(x')\\partial_{x_3}w(x',x_3)\\partial _{x_k}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3\n& = \\int_\\omega C_{k3}(x')\\partial_{x_k}\\varphi (x') \\left( \\int_\\mathbb{R}\\partial_{x_3}w(x',x_3)\\widehat{\\psi}(x_3)dx_3 \\right) dx' \\\\\n& = - \\int_\\omega C_{k3}(x')\\partial_{x_k}\\varphi (x') \\left( \\int_\\mathbb{R}w(x',x_3)\\widehat{\\psi}'(x_3)dx_3 \\right)\ndx',\\end{aligned}$$ for each $k=1,2$, with $$\\int_\\mathbb{R}w(x',x_3)\\widehat{\\psi}'(x_3)dx_3\n=-\\int_\\mathbb{R}w(x',x_3)\\widehat{(i \\xi) \\psi}(x_3)dx_3 = -\\int_\\mathbb{R} (i \\xi) \\widehat{w}(x',\\xi) \\psi(\\xi)d \\xi,$$ then $$\\int_\\Omega C_{k3}(x')\\partial_{x_3}w(x',x_3)\\partial _{x_k}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3=\\int_\\Omega C_{k3}(x')(i\\xi )\\widehat{w}(x',\\xi )\\partial_{x_k}(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi .$$ Integrating by parts in the right hand side of the above identity we get $$\\begin{aligned}\n\\label{38}\n\\int_\\Omega C_{k3}(x')\\partial_{x_3}w(x',x_3)\\partial _{x_k}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3&=\\int_\\Omega C_{k3}(x')(-i\\xi )\\partial_{x_k}\\widehat{w}(x',\\xi )(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi \\nonumber\n\\\\\n&+\\int_\\Omega \\partial_{x_k}C_{k3}(x')(-i\\xi )\\widehat{w}(x',\\xi )(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi .\\end{aligned}$$ Further, bearing in mind that $\\partial _{x_3}(\\varphi \\otimes \\widehat{\\psi})=\\varphi \\otimes \\widehat{(-i \\xi) \\psi}$ and noticing that $$\\int_{\\mathbb{R}} \\partial_{x_3}w(x',x_3) \\widehat{(-i \\xi)\\psi}(x_3) dx_3\n= - \\int_{\\mathbb{R}} w(x',x_3) \\widehat{(-i \\xi)^2\\psi}(x_3) dx_3\n= - \\int_{\\mathbb{R}} \\widehat{w}(x',\\xi) (-i \\xi)^2 \\psi(\\xi) d \\xi,$$ we find out that $$\\label{39}\n\\int_\\Omega C_{33}(x')\\partial_{x_3}w(x',x_3)\\partial _{x_3}(\\varphi \\otimes \\widehat{\\psi})(x',x_3)dx'dx_3=\\int_\\Omega C_{33}(x')(-i\\xi )^2\\widehat{w}(x',\\xi )(\\varphi \\otimes \\psi)(x',\\xi )dx'd\\xi.$$ Finally, putting - together, we end up getting that $$\\langle -{{\\mathrm{div}}}_{x'} (\\widetilde{C}(x')\\nabla _{x'}\\widehat{w})+P(x',\\xi )\\cdot \\nabla _{x'}\\widehat{w}+q(x',\\xi )\\widehat{w},\\Phi \\rangle = 0,\\;\\; \\Phi \\in C_0^\\infty (\\omega )\\otimes C_0^\\infty (\\mathbb{R}),$$ where $\\langle \\cdot ,\\cdot \\rangle$ denotes the duality pairing between $C_0^\\infty (\\Omega )$ and $\\mathcal{D}'(\\Omega )$. ",
"From this and the density of $C_0^\\infty (\\omega )\\otimes C_0^\\infty (\\mathbb{R})$ in $C_0^\\infty (\\Omega )$ then follows that $$-{{\\mathrm{div}}}_{x'} (\\widetilde{C}(x')\\nabla _{x'}\\widehat{w})+P(x',\\xi )\\cdot \\nabla _{x'}\\widehat{w}+q(x',\\xi )\\widehat{w}=0\\;\\; \\textrm{in}\\; \\mathcal{D}'(\\Omega ),$$ which completes the proof.",
"\n\nLet $a \\in \\mathbb{R}$ be fixed. ",
"We assume in the remaining of this section that $\\alpha (x_3)=a$ for all $x_3 \\in \\mathbb{R}$. For notational simplicity we write $A_a(x')$ instead of $A(x',\\alpha (x_3))$. With the help of Lemma \\[lemma3\\] we will first re-express in the Fourier plane.",
"\n\nFor $g\\in H^1(\\mathbb{R})\\cap L^1(\\mathbb{R})$ such that $\\int_\\mathbb{R}g(x_3)dx_3=1$ and for $h \\in H^{1 \\slash 2}(\\partial \\omega)$, we consider the $H^1(\\Omega)$-solution $u$ to , with $$f(x',x_3)= g(x_3) h(x'),\\ x' \\in \\partial \\omega,\\ x_3 \\in \\mathbb{R}.$$ Since $u$ is solution to with $C=A_a \\in W^{1,\\infty}(\\omega)^{3 \\times 3}$, we deduce from Lemma \\[lemma3\\] that $\\widehat{u}\\in L^2(\\mathbb{R};H^1(\\omega ))$ is solution to the system $$\\label{41}\n\\left\\{\n\\begin{array}{ll}\n-{{\\mathrm{div}}}_{x'}\\big(\\widetilde{A}_a(x')\\nabla_{x'} \\widehat{u}(x',\\xi )\\big)-2ia\\xi x'{^\\bot} \\cdot \\nabla _{x'}\\widehat{u}+\\xi ^2\\widehat{u}=0\\;\\; &\\textrm{in}\\;\\; \\mathcal{D}'(\\Omega ), \n\\\\\n\\widehat{u}(\\cdot ,\\xi)= \\widehat{g}(\\xi )f &\\textrm{on}\\;\\; \\partial \\omega ,\\; \\textrm{for all}\\; \\xi \\in \\mathbb{R},\n\\end{array}\n\\right.$$ where $$x'{^\\bot}=(-x_2,x_1)\\ {\\rm and}\\\n\\widetilde{A}_a(x')=\n \\begin{pmatrix}\n1+x_2^2a^2 & -x_2x_1a^2 \n\\\\\n-x_2x_1a^2 & 1+x_1^2a^2 \n \\end{pmatrix}.$$ We turn now to examining .\\\n[**Analysis of the variational problem associated to .**]{} ",
"Let us consider the bilinear form $$\\begin{aligned}\n\\mathcal{A}_\\xi[(v,w),(\\varphi ,\\psi)]&= \\int_\\omega \\widetilde{A}_a\\nabla v\\cdot \\nabla \\varphi dx' -2a\\xi \\int_\\omega x'{^\\bot}\\cdot \\nabla w \\varphi dx'+\\xi ^2\\int_\\omega v\\varphi dx'\n\\\\\n&\\; +\\int_\\omega \\widetilde{A}_a\\nabla w\\cdot \\nabla \\psi dx' +2a\\xi \\int_\\omega x'{^\\bot}\\cdot \\nabla v \\psi dx'+\\xi ^2\\int_\\omega w\\psi dx',\\ (v,w),(\\varphi ,\\psi) \\in \\mathcal{H},\\end{aligned}$$ defined on the Hilbert space $\\mathcal{H}=H_0^1(\\omega )\\times H_0^1(\\omega )$ endowed with the norm $$\\|(v,w)\\|_{\\mathcal{H}}=\\big(\\| \\nabla v\\|_{L^2(\\omega )}^2+\\| \\nabla w\\|_{L^2(\\omega )}^2\\big)^{1/2}.$$ Taking into account that $$\\widetilde{A}_a(x')\\zeta \\cdot \\zeta \\geq |\\zeta |^2,\\; \\textrm{for all}\\; \\zeta \\in \\mathbb{R}^2\\; \\textrm{and}\\; x'\\in \\omega,$$ and that $$2a|\\xi |\\int_\\omega \\Big|x'{^\\bot} \\cdot \\nabla v w\\Big|dx'\\leq a^2\\delta ^2\\int_\\omega |\\nabla v|^2 dx'+\\xi ^2\\int_\\omega w^2dx',\\ (v,w) \\in \\mathcal{H},$$ where $\\delta=\\max_{x' \\in \\omega} |x'| < \\infty$, it is easy to see that $$\\label{42}\n\\mathcal{A}_\\xi[(v,w),(v,w)]\\geq (1-a^2\\delta ^2)\\|(v,w)\\|_{\\mathcal{H}}^2.$$ Let us fix $a_0>0$ so small that $\\alpha=1-a_0^2\\delta ^2>0$. In light of the above estimate, the bilinear form $\\mathcal{A}_\\xi$ is $\\alpha$-elliptic for every $\\xi \\in \\mathbb{R}$, provided we have $|a| \\leq a_0$. For each $\\Phi \\in C(\\mathbb{R}; \\mathcal{H}')$ and every $\\xi \\in \\mathbb{R}$, there is thus a unique $(v(\\xi ), w(\\xi ))\\in \\mathcal{H}$ satisfying $$\\label{43}\n\\mathcal{A}_\\xi[(v(\\xi),w(\\xi)),(\\varphi ,\\psi )]=\\langle \\Phi (\\xi ), (\\varphi ,\\psi)\\rangle \\;\\; \\textrm{for all}\\;\\; (\\varphi ,\\psi)\\in \\mathcal{H},$$ by Lax-Milgram’s lemma. ",
"From this then follows that $$\\begin{aligned}\n& & \\mathcal{A}_{\\xi +\\eta}[(v(\\xi +\\eta )-v(\\xi ) ,w(\\xi +\\eta )-w(\\xi )),(\\varphi ,\\psi )] \\nonumber \\\\\n&=& \\mathcal{A}_\\xi [(v(\\xi ) ,w(\\xi )),(\\varphi ,\\psi )]-\\mathcal{A}_{\\xi +\\eta}[(v(\\xi ),w(\\xi )),(\\varphi ,\\psi )]\n+ \\langle\\Phi (\\xi +\\eta )-\\Phi (\\xi ), (\\varphi,\\psi) \\rangle,\n\\label{44}\\end{aligned}$$ for each $\\xi, \\eta \\in \\mathbb{R}$ and $(\\varphi ,\\psi)\\in \\mathcal{H}$. Further, by noticing through elementary computations that $$\\mathcal{A}_{\\xi+\\eta}[(v,w),(\\varphi ,\\psi )]\n=\\mathcal{A}_{\\xi+\\eta}[(v,w),(\\varphi ,\\psi )] - 2 a \\eta \\int_{\\omega} x'^{\\perp} \\cdot ( \\varphi \\nabla_{x'} w - \\psi \\nabla_{x'} v) dx'+ \\eta (2 \\xi +\\eta) \\int_{\\omega} (v \\varphi + w \\psi) dx',$$ for every $(v,w), (\\varphi,\\psi) \\in \\mathcal{H}$, we deduce from and Poincaré’s inequality that there exists a constant $C=C(\\xi ,\\omega ,a_0)>0$ satisfying $$\\begin{aligned}\n& & \\mathcal{A}_\\xi [(v(\\xi ) ,w(\\xi )),(v(\\xi +\\eta )-v(\\xi ),w(\\xi +\\eta )-w(\\xi ))] \\nonumber \\\\\n& - & \\mathcal{A}_{\\xi +\\eta}[(v(\\xi ),w(\\xi )),(v(\\xi +\\eta )-v(\\xi ) ,w(\\xi +\\eta )-w(\\xi ))] \\nonumber \\\\\n& \\leq & C |\\eta | \\|(v(\\xi ) ,w(\\xi ))\\|_{\\mathcal{H}} \\|(v(\\xi +\\eta )-v(\\xi ),w(\\xi +\\eta )-w(\\xi ))\\|_{\\mathcal{H}},\n\\label{45}\\end{aligned}$$ for all $\\xi \\in \\mathbb{R}$ and $\\eta \\in [-1,1]$. In light of , written with $(\\varphi ,\\psi )=(v(\\xi +\\eta )-v(\\xi ),w(\\xi +\\eta )-w(\\xi ))$ and , we thus find out that $$\\alpha \\|(v(\\xi +\\eta )-v(\\xi ),w(\\xi +\\eta )-w(\\xi ))\\|_{\\mathcal{H}}\\leq C|\\eta | \\|(v(\\xi ) ,w(\\xi ))\\|_{\\mathcal{H}}+\\|\\Phi (\\xi +\\eta )-\\Phi (\\xi )\\|_{\\mathcal{H}'}.$$ This proves that $(v,w)\\in C(\\mathbb{R};\\mathcal{H})$. Moreover, we obtain $$\\label{46}\n\\|(v(\\xi ),w(\\xi )) \\|_{\\mathcal{H}}\\leq (1/\\alpha )\\|\\Phi (\\xi )\\|_{\\mathcal{H}'},\\;\\; \\xi \\in \\mathbb{R},$$ directly from -. ",
"Further, it is easy to check for $\\Phi \\in C^1(\\mathbb{R};\\mathcal{H}')$ that $(v'(\\xi ),w'(\\xi )) \\in C(\\mathbb{R},\\mathcal{H})$ is the solution to the variational problem $$\\mathcal{A}_{\\xi}[((v'(\\xi ),w'(\\xi )),(\\varphi ,\\psi)]=\\langle \\Phi_0(\\xi ),(\\varphi ,\\psi)\\rangle +\\langle \\Phi '(\\xi ),(\\varphi ,\\psi)\\rangle \\;\\; \\textrm{for all}\\;\\; \n(\\varphi ,\\psi)\\in \\mathcal{H},$$ where $$\\langle \\Phi_0(\\xi ),(\\varphi ,\\psi)\\rangle =2a \\int_\\omega x'{^\\bot}\\cdot ( \\varphi \\nabla_{x'} w(\\xi ) - \\psi \\nabla_{x'} v(\\xi) ) dx'+2 \\xi \\int_\\omega (v(\\xi )\\varphi + w(\\xi )\\psi) dx' .$$ Using and noting $\\langle \\xi \\rangle=(1+|\\xi |^2)^{1/2}$, we deduce from the above estimate that $$\\| (v'(\\xi ),w'(\\xi ))\\|_{\\mathcal{H}}\\leq C\\big( \\langle \\xi \\rangle \\|\\Phi (\\xi )\\|_{\\mathcal{H}'}+\\|\\Phi '(\\xi )\\|_{\\mathcal{H}'}\\big),\\;\\; \\xi \\in \\mathbb{R},$$ for some constant $C=C(a_0,\\omega )>0$. Similarly, if $\\Phi \\in C^2(\\mathbb{R};\\mathcal{H}')$ then the same reasoning shows that $(v,w)\\in C^2(\\mathbb{R},\\mathcal{H})$ verifies $$\\| (v''(\\xi ),w''(\\xi ))\\|_{\\mathcal{H}}\\leq C\\big(\\langle \\xi \\rangle ^2\\|\\Phi (\\xi )\\|_{\\mathcal{H}'}+ \\langle \\xi \\rangle \\|\\Phi '(\\xi )\\|_{\\mathcal{H}'}+\\|\\Phi ''(\\xi )\\|_{\\mathcal{H}'}\\big),\\;\\; \\xi \\in \\mathbb{R}.$$ Summing up we obtain the:\n\n\\[proposition2\\] Let $a_0 \\in (0,(\\max_{x' \\in \\omega} |x'|)^{-1 \\slash 2})$, pick $a \\in [-a_0,a_0]$ and assume that $\\alpha(x_3)=a$ for all $x_3 \\in \\mathbb{R}$. Then for every $\\Phi \\in H^2(\\mathbb{R},\\mathcal{H}')$ such that $\\langle \\xi \\rangle ^{2-j} \\Phi^{(j)} \\in L^2(\\mathbb{R},\\mathcal{H}')$, $j=0,1$, the variational problem admits a unique solution $(v,w)\\in H^2(\\mathbb{R};\\mathcal{H})$ satisfying $$\\label{47}\n\\| (v,w)\\|_{H^2(\\mathbb{R};\\mathcal{H})}\\leq C\\Big(\\sum_{j=0}^2\\| \\langle \\xi \\rangle ^{2-j}\\Phi ^{(j)}\\|_{L^2(\\mathbb{R};\\mathcal{H}')}\\Big),$$ for some constant $C=C(\\omega ,a_0)>0$. The above assumptions on $\\Phi$ are actually satisfied whenever $\\Phi =\\widehat{\\Psi}$ for some $\\Psi \\in H^2(\\mathbb{R}; \\mathcal{H}')$ such that $x_3\\Psi \\in H^1(\\mathbb{R}; \\mathcal{H}')$ and $x_3^2\\Psi \\in L^2(\\mathbb{R}; \\mathcal{H}')$. Moreover, the estimate reads $$\\label{48}\n\\| (v,w)\\|_{H^2(\\mathbb{R};\\mathcal{H})}\\leq C\\Big(\\sum_{j=0}^2\\| x_3^{j}\\Psi\\|_{H^{2-j}(\\mathbb{R};\\mathcal{H}')}\\Big),$$ in this case.",
"\n\nArmed with Proposition \\[proposition2\\] we may now tackle the analysis of the solution to .\\\n[**Some useful properties of the solution to .**]{} ",
"Pick $F\\in H^1(\\omega )$ such that $F=f$ on $\\partial \\omega$ and $\\|F\\|_{H^1(\\omega )}\\leq C(\\omega )\\|f\\|_{H^{1/2}(\\partial \\omega )}$. ",
"Let $\\widetilde{u}^r$ (resp. ",
"$\\widetilde{u}^i$) denote the real (resp. ",
"imaginary) part of $\\widetilde{u}=\\widehat{u}-\\widehat{g}(\\xi )F=\\widetilde{u}^r+i\\widetilde{u}^i$. Since the Fourier transform $\\widehat{u}$ of the $H^1(\\Omega)$-solution $u$ to is actually solution to , we get by direct calculation that $(\\widetilde{u}^r,\\widetilde{u}^i)$ is solution to the variational problem , with $$\\label{48b}\n\\langle \\Phi (\\xi ), (\\varphi ,\\psi )\\rangle =-\\mathcal{A}_\\xi [(\\widehat{g}^rF,\\widehat{g}^iF), (\\varphi ,\\psi )],$$ and where $\\widehat{g}^r$ (resp. ",
"$\\widehat{g}^i$) stands for the real (resp. ",
"imaginary) part of $\\widehat{g}$. In light of we check out using elementary computations that $$\\begin{aligned}\n\\|\\Phi (\\xi )\\|_{\\mathcal{H}'} & \\leq & C\\langle \\xi \\rangle ^2|\\widehat{g}(\\xi )|\\|f\\|_{H^{1/2}(\\partial \\omega )}\n\\label{48c1} \\\\\n\\|\\Phi '(\\xi )\\|_{\\mathcal{H}'} & \\leq & C\\big(\\langle \\xi \\rangle ^2|\\widehat{g}'(\\xi )|+\\langle \\xi \\rangle |\\widehat{g}(\\xi )|\\big)|\\|f\\|_{H^{1/2}(\\partial \\omega )}\n\\label{48c2} \\\\\n\\|\\Phi ''(\\xi )\\|_{\\mathcal{H}'} & \\leq & C\\big(\\langle \\xi \\rangle ^2|\\widehat{g}''(\\xi )|+\\langle \\xi \\rangle |\\widehat{g}'(\\xi )|+|\\widehat{g}(\\xi )|\\big)\\|f\\|_{H^{1/2}(\\partial \\omega )}, \\label{48c3}\\end{aligned}$$ for some constant $C=C(a_0,\\omega )>0$. Therefore we have $\\langle \\xi \\rangle^j \\Phi^{(2-j)} \\in L^2(\\mathbb{R})$ for $j=0,1,2$, provided $\\langle \\xi \\rangle^{4-j} \\widehat{g}^{j} \\in L^2(\\mathbb{R})$, which is actually the case if $x_3^j g \\in H^{4-j}(\\mathbb{R})$. From this and Proposition \\[proposition2\\] then follows the:\n\n\\[corollary1\\] Let $a$ and $\\alpha$ be the same as in Proposition \\[proposition2\\] and assume that $g\\in H^4(\\mathbb{R})$ verifies $x_3g\\in H^3(\\mathbb{R})$, $x_3^2g\\in H^2(\\mathbb{R})$ and $\\int_\\mathbb{R}g(x_3)dx_3=1$. Then we have $\\widehat{u}\\in H^2(\\mathbb{R};H^1(\\omega ))$, $u\\in L^1(\\mathbb{R};H^1(\\omega ))$ and $U=\\widehat{u}(\\cdot ,0)=\\int_\\mathbb{R}u(\\cdot ,x_3)dx_3\\in H^1(\\omega )$ is the variational solution to the BVP $$\\left\\{\n\\begin{array}{ll}\n{{\\mathrm{div}}}_{x'} \\big(\\widetilde{A}_a \\nabla_{x'} U\\big)=0\\;\\; &\\textrm{in}\\; \\omega \n\\\\\nU= f &\\textrm{on}\\; \\partial \\omega.",
"\n\\end{array}\n\\right.$$\n\nIn view of and , we deduce from - that $$\\begin{aligned}\n&\\| {{\\mathrm{div}}}_{x'}\\big(\\widetilde{A}_a \\nabla _{x'}\\widehat{u}(\\cdot ,\\xi )\\big) \\|_{L^2(\\omega)}\\leq C\\langle \\xi \\rangle ^4|\\widehat{g}(\\xi )|\\|f\\|_{H^{1/2}(\\partial \\omega )}\n\\\\\n&\\|\\partial _\\xi{{\\mathrm{div}}}_{x'}\\big(\\widetilde{A}_a \\nabla _{x'}\\widehat{u}(\\cdot ,\\xi )\\big) \\|_{L^2(\\omega)}\\leq C\\big(\\langle \\xi \\rangle ^5|\\widehat{g}'(\\xi )|+\\langle \\xi \\rangle ^4|\\widehat{g}(\\xi )|\\big)|\\|f\\|_{H^{1/2}(\\partial \\omega )}\n\\\\\n&\\|\\partial _\\xi ^2{{\\mathrm{div}}}_{x'}\\big(\\widetilde{A}_a \\nabla_{x'} \\widehat{u}(\\cdot ,\\xi )\\big)\\|_{L^2(\\omega)}\\leq C\\big(\\langle \\xi \\rangle ^6|\\widehat{g}(\\xi )|+\\langle \\xi \\rangle ^5|\\widehat{g}'(\\xi )|+\\langle \\xi \\rangle ^4|\\widehat{g}''(\\xi )|\\big)\\|f\\|_{H^{1/2}(\\partial \\omega )},\\end{aligned}$$ for some positive constant $C$ depending only on $a_0$ and $\\omega$. This combined with Corollary \\[corollary1\\] yields the:\n\n\\[proposition3\\] Let $a$ and $\\alpha$ be as in Proposition \\[proposition2\\]. ",
"Let $g\\in H^6(\\mathbb{R})$ verify $x_3g\\in H^5(\\mathbb{R})$, $x_3^2g\\in H^4(\\mathbb{R})$ and $\\int_\\mathbb{R}g(x_3)dx_3=1$. Then we have $\\widetilde{A}_a \\nabla _{x'} \\widehat{u} \\cdot \\nu (x')\\in H^2(\\mathbb{R};H^{-1/2}(\\partial \\omega))$ and thus $A_a\\nabla u\\cdot \\nu (x)\\in L^1(\\mathbb{R};H^{-1/2}(\\partial \\omega))$, with $$\\widetilde{A}_a \\nabla_{x'} U\\cdot \\nu (x')=\\widetilde{A}_a \\nabla_{x'} \\widehat{u}(\\cdot ,0)\\cdot \\nu (x')=\\int_\\mathbb{R}A_a\\nabla u(\\cdot ,x_3)\\cdot \\nu (x') d x_3 \\in H^{-1/2}(\\partial \\omega ).$$\n\nIn light of Proposition \\[proposition3\\] it is natural to define the two following DN maps: $$\\begin{aligned}\n&\\Lambda _a : f\\in H^{1/2}(\\partial \\omega )\\mapsto A_a\\nabla u(\\cdot ,x_3)\\cdot \\nu (x)\\in L^1(\\mathbb{R};H^{-1/2}(\\partial \\omega ))\n\\\\\n&\\widetilde{\\Lambda}_a:f\\in H^{1/2}(\\partial \\omega )\\mapsto \\widetilde{A}_a \\nabla_{x'}U\\cdot \\nu (x')\\in H^{-1/2}(\\partial \\omega ).\\end{aligned}$$ These two operators are bounded, and they satisfy the estimate $$\\label{49}\n\\|\\widetilde{\\Lambda}_1-\\widetilde{\\Lambda}_2\\|_{\\mathscr{L}(H^{1/2}(\\partial \\omega ),H^{-1/2}(\\partial \\omega ))}\\leq \\|\\Lambda _1-\\Lambda _2\\|_{\\mathscr{L}\\big(H^{1/2}(\\partial \\omega ),L^1(\\mathbb{R};H^{-1/2}(\\partial \\omega ))\\big)},$$ where, for simplicity, we write $\\Lambda _j$ (resp. ",
"$\\widetilde{\\Lambda}_j$) for $\\Lambda _{a_j}$ (resp. ",
"$\\widetilde{\\Lambda}_{a_j}$), $j=1,2$.\n\nFinally, since the matrix $\\partial_a \\widetilde{A}(x',a)$ has two eigenvalues $\\lambda _0=0$ and $\\lambda _1=|x'|^2$, we derive the following result by mimmicking the proof of [@AG1]\\[CLAIM, page 169\\].",
"\n\n\\[theorem2\\] Let $a_0$ be the same as in Proposition \\[proposition2\\], let $a_j \\in \\mathbb{R}$, $j=1,2$, and assume that $\\alpha_j(x_3)=a_j$ for all $x_3 \\in \\mathbb{R}$. Then there exists a constant $C>0$, depending only on $a_0$ and $\\omega$, such that the following stability estimate $$|a_1-a_2|\\leq C \\|\\Lambda _1-\\Lambda _2\\|_{\\mathscr{L}\\big(H^{1/2}(\\partial \\omega ),L^1(\\mathbb{R};H^{-1/2}(\\partial \\omega ))\\big)},$$ holds true whenever $|a_1|,\\ |a_2|\\leq a_0$.\n\nAppendix: more on $\\Lambda_\\alpha$\n==================================\n\n[**Appendix 1: Restriction to $\\widetilde{H}^{3/2}(\\partial \\Omega )$.**]{} ",
"In this subsection we exhibit sufficient conditions on $\\omega$ and $\\alpha$ ensuring that the restriction of $\\Lambda_\\alpha$ to $\\widetilde{H}^{3/2}(\\partial \\Omega )$ is a bounded operator into $L^2(\\mathbb{R}; H^{1/2}(\\partial \\omega ))$. ",
"We assume for this purpose that $\\Omega_1= \\omega \\times (-1,1)$ has $H^2$-regularity property. ",
"That is, for every $F\\in L^2(\\Omega )$ and any matrix-valued function $C=(C_{ij}(x))_{1 \\leq i,j \\leq 3}$ with coefficients in $W^{1,\\infty}(\\Omega _1)$ verifying the ellipticity condition $$\\exists \\alpha >0,\\ C(x)\\xi \\cdot \\xi \\geq \\alpha |\\zeta |^2,\\ \\textrm{for all}\\; \\zeta \\in \\mathbb{C}^3,\\; x\\in \\Omega_1,$$ the following BVP $$\\left\\{\n\\begin{array}{ll}\n{{\\mathrm{div}}}(C\\nabla w)=F\\;\\; &\\textrm{in}\\;\\; \\Omega _1,\n\\\\\nw=0 &\\textrm{on}\\;\\; \\partial \\Omega _1,\n\\end{array}\n\\right.$$ has a unique solution $w\\in H^2(\\Omega _1)$ obeying $$\\|w\\|_{H^2(\\Omega _1)}\\leq C(\\alpha , M)\\|F\\|_{L^2(\\Omega _1)},$$ for some constant $C(\\alpha ,M)>0$ depending only on $\\alpha$, $M=\\max_{1 \\leq i,j \\leq 3}\\|C_{ij}\\|_{W^{1,\\infty}(\\Omega _1)}$ and $\\omega$.\n\nNotice that $\\Omega_1$ has $H^2$-regularity property if and only if this is the case for $\\Omega _a=\\omega \\times (-a,a)$ and some $a>0$. Moreover we recall from [@G] that $\\Omega_1$ has $H^2$-regularity property provided $\\omega$ is convex.",
"\n\nWe turn now to establishing the following result, which is our main tool for the analysis of the restriction of $\\Lambda_\\alpha$ to $\\tilde{H}^{3 \\slash 2}(\\partial \\Omega )$.",
"\n\n\\[theorem1\\] Assume that $\\alpha \\in C^{0,1}(\\mathbb{R})$ and that $\\Omega _1$ has $H^2$-regularity property. ",
"Then for any $f\\in \\widetilde{H}^{3/2}(\\partial \\Omega )$, the BVP admits a unique solution $u\\in H^2(\\Omega )$. ",
"Moreover there is a constant $C>0$, depending only on $\\|\\alpha \\|_{C^{0,1}(\\mathbb{R})}$ and $\\omega$, such that we have: $$\\label{17}\n\\|u\\|_{H^2(\\Omega )}\\leq C \\|f\\|_{\\widetilde{H}^{3/2}(\\partial \\Omega )}.$$\n\nSince $f\\in \\widetilde{H}^{3/2}(\\partial \\Omega )$ we may choose $F\\in H^2(\\Omega )$ in accordance with Lemma \\[lemma1bis\\] so that $F=f$ on $\\partial \\Omega$ and $$\\label{18}\n \\|F\\|_{H^2(\\Omega )}\\leq 2\\|f\\|_{\\widetilde{H}^{3/2}(\\partial \\Omega )}.$$ Putting $\\Psi ={{\\mathrm{div}}}(A\\nabla F)$ we next refer to and define the unique vector $u_0\\in H_0^1(\\Omega )$ satisfying simultaneously $$\\label{19}\n\\int_\\Omega A\\nabla u_0\\cdot \\nabla v dx=\\int_\\Omega \\Psi v dx,\\; \\textrm{for all}\\; v\\in H_0^1(\\Omega ),$$ and $$\\label{20}\n\\|u_0\\|_{H^1(\\Omega )}\\leq C_0 \\|\\Psi \\|_{L^2(\\Omega )},$$ for some constant $C_0>0$ depending on $\\omega$ and $M=\\|\\alpha \\|_{C^{0,1}(\\mathbb{R})}$.\n\nFurther, for all $n \\geq 1$, we consider $\\xi _n\\in C_0^\\infty (-(n+1),n+1)$ such that $\\xi _n=1$ in $[-n,n]$, $\\|\\xi_n'\\|_{\\infty} \\leq 1 \\slash 2$ and $\\|\\xi_n'' \\|_{\\infty} \\leq 1 \\slash 2$. For every $v\\in H_0^1(\\Omega )$, we get $$\\int_\\Omega A\\nabla (\\xi _n u_0)\\cdot \\nabla v dx=\\int_\\Omega A\\nabla u_0\\cdot \\nabla (\\xi _nv) dx-\\int_\\Omega (A\\nabla u_0\\cdot \\nabla \\xi _n) v dx+\\int_\\Omega (A\\nabla \\xi _n \\cdot \\nabla v) u_0 dx,$$ by direct calculation. ",
"An integration by parts in the last term of this identity providing $$\\int_\\Omega (A\\nabla \\xi _n \\cdot \\nabla v) u_0 dx= -\\int_\\Omega (A\\nabla \\xi _n \\cdot \\nabla u_0) v dx-\\int_\\Omega {{\\mathrm{div}}}(A\\nabla \\xi_n) u_0 v dx,$$ we find out that $$\\int_\\Omega A\\nabla (\\xi _n u_0)\\cdot \\nabla v dx=\\int_\\Omega A\\nabla u_0\\cdot \\nabla (\\xi _nv) dx -\\int_\\Omega ( A\\nabla u_0\\cdot \\nabla \\xi _n ) v dx -\\int_\\Omega (A\\nabla \\xi _n \\cdot \\nabla u_0) v dx-\\int_\\Omega {{\\mathrm{div}}}(A\\nabla \\xi _n)u_0 v dx.$$ Since $A$ is symmetric, it follows from this and that $$\\int_\\Omega A\\nabla (\\xi _n u_0)\\cdot \\nabla v dx=\\int_\\Omega \\Psi \\xi _nv dx-2\\int_\\Omega ( A\\nabla \\xi _n \\cdot \\nabla u_0) v dx-\\int_\\Omega {{\\mathrm{div}}}(A\\nabla \\xi _n)u_0 v dx,\\ \\textrm{for all}\\ v \\in H_0^1(\\Omega ).$$ Therefore, bearing in mind that $\\Omega_a=\\omega \\times (-a,a)$ for any $a>0$, the $\\xi_n u_0 \\in H_0^1(\\Omega _{n+1})$ is thus solution to the variational problem $$\\label{21}\n\\int_{\\Omega _{n+1}}A\\nabla (\\xi _nu_0)\\cdot \\nabla v dx=\\int_{\\Omega _{n+1}}\\widetilde{\\Psi}v dx,\\; \\textrm{for all}\\; v\\in H_0^1(\\Omega _{n+1}),$$ with $$\\widetilde{\\Psi}= \\Psi \\xi _n-2A\\nabla \\xi _n \\cdot \\nabla u_0-{{\\mathrm{div}}}(A\\nabla \\xi _n)u_0.$$ The next step of the proof is to make the change of variables $(x',x_3)\\in \\Omega _{n+1}\\mapsto (x', y_3)=(x',1/(n+1)x_3) \\in \\Omega _1$ in . ",
"Putting $$J_n= \\left( \\begin{array}{ccc} 1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1 \\slash n \\end{array} \\right),\\ n \\geq 1,$$ and $$\\begin{aligned}\n&\\underline{A}(x',y_3)=1/(n+1)J_{n+1}A(x', (n+1)y_3)J_{n+1},\n\\\\\n&\\underline{\\xi}(y_3)=\\xi _n((n+1)y_3),\n\\\\\n& \\underline{u}(x',y_3)=u_0(x',(n+1)y_3),\n\\\\\n& w_n(x',y_3)=\\xi _n((n+1)y_3)u_0(x',(n+1)y_3),\n\\\\\n& \\underline{{{\\mathrm{div}}}} (P(x',y_3))= \\partial _{x_1}P_1(x',y_3)+\\partial _{x_2}P_2(x',y_3)+1/(n+1)\\partial _{y_3}P_3(x',y_3),\n\\\\\n& \\underline{\\Psi}(x',y_3)=1/(n+1)\\Big[\\Psi (x',(n+1)y_3)-2J_{n+1}A(x', (n+1)y_3)J_{n+1}\\nabla \\underline{\\xi}(y_3)\\cdot \\nabla \\underline{u}(x',y_3)\n\\\\\n& \\hskip 3.5cm -\\underline{{{\\mathrm{div}}}} \\big( A(x', (n+1)y_3) J_{n+1} \\nabla \\underline{\\xi}(y_3) \\big)\\underline{u}(x',y_3)\\Big],\\end{aligned}$$ for $(x',y_3) \\in \\Omega_1$, we find out by direct computations that $w_n \\in H_0^1(\\Omega _1)$ is solution to $$\\int_{\\Omega _1}\\underline{A}\\nabla w_n\\cdot \\nabla v dx=\\int_{\\Omega _1}\\underline{\\Psi}v dx,\\; \\textrm{for all}\\; v\\in H_0^1(\\Omega _1).$$ Since $\\|\\underline{\\Psi}\\|_{L^2(\\Omega _1)}\\leq (n+1)^{-3/2}C(\\omega,M )\\|\\Psi \\|_{L^2(\\Omega )}$ by , where $C=C(\\omega,M)$ denotes some generic positive constant depending only on $\\omega$ and $M$, it holds true that $\\|w_n\\|_{H^2(\\Omega _1)}\\leq (n+1)^{-3/2}C(\\omega, M )\\|\\Psi \\|_{L^2(\\Omega )}$. ",
"Here we used the estimate $\\|w_n\\|_{H^2(\\Omega _1)}\\leq C(\\omega, M )\\|\\underline{\\Psi}\\|_{L^2(\\Omega _1)}$, arising from the $H^2$-regularity property imposed on $\\Omega_1$. As a consequence we have $$\\label{23}\n\\|\\xi _nu_0\\|_{H^2(\\Omega )}\\leq C(\\omega,M )\\|\\Psi \\|_{L^2(\\Omega )}.$$ Therefore, upon eventually extracting a subsequence of $(\\xi _n u_0)_n$, we may assume that it converges weakly to $\\widetilde{u}$ in $H^2(\\Omega )$. ",
"On the other hand since $(\\xi _n u_0)_n$ converges to $u_0$ in $L^2(\\Omega )$ it is true that $u_0\\in H^2(\\Omega )$ so $(\\xi _nu_0)_n$ converges weakly to $u_0$ in $H^2(\\Omega )$. ",
"Further, the norm $\\|\\cdot \\|_{H^2(\\Omega )}$ being lower semi-continuous, we have $$\\label{23b}\n\\|u_0\\|_{H^2(\\Omega )}\\leq \\liminf_n \\|\\xi _nu_0\\|_{H^2(\\Omega )}\\leq C(\\omega,M )\\|\\Psi \\|_{L^2(\\Omega )},$$ by . ",
"Bearing in mind that $\\|\\Psi \\|_{L^2(\\Omega )}\\leq C(\\omega,M )\\|F\\|_{H^2(\\Omega )}$ and $\\|F\\|_{H^2(\\Omega )}\\leq 2\\|f\\|_{\\widetilde{H}^{3/2}(\\partial \\Omega )}$, and then yield $$\\|u_0\\|_{H^2(\\Omega )}\\leq C(\\omega, M )\\|f\\|_{\\widetilde{H}^{3/2}(\\partial \\Omega )}.$$ Now the desired result follows from this by taking into account that $u=u_0+F\\in H^2(\\Omega )$ is the unique solution to .",
"\n\nFor all $\\Omega$ and $\\alpha$ fulfilling the assumptions of Theorem \\[theorem1\\], the mapping $$\\Lambda _\\alpha : f\\in \\widetilde{H}^{3/2}(\\partial \\Omega ) \\mapsto \\partial _\\nu u\\in L^2(\\mathbb{R}; H^{1/2}(\\partial \\omega )),$$ where $u$ denotes the unique $H^2(\\Omega)$-solution to , is well defined by Theorem \\[theorem1\\]. ",
"Further, since $C_0^\\infty (\\mathbb{R};H^2(\\omega ))$ is dense in $H^2(\\Omega )$, then the trace operator $$\\widetilde{\\tau} : w\\in H^2(\\Omega )\\mapsto \\partial _\\nu w\\in L^2(\\mathbb{R}; H^{1/2}(\\partial \\omega )),$$ is easily seen to be bounded. ",
"From this and then follows that $\\|\\Lambda _\\alpha \\|\\leq C$ as a linear bounded operator from $\\widetilde{H}^{3/2}(\\partial \\Omega )$ into $L^2(\\mathbb{R}; H^{1/2}(\\partial \\omega ))$, where the constant $C>0$ depends only on $\\omega$ and $\\| \\alpha \\|_{C^{0,1}(\\mathbb{R})}$.\\\n[**Appendix 2: Linking $\\Lambda_\\alpha$ to the DN map associated with $\\Omega_{\\theta}$.**]{} \\[sec-DNO\\] In this subsection we define the DN map $\\widetilde{\\Lambda}_\\theta$ associated to the BVP , which is stated on the twisted domain $\\Omega_\\theta$, and establish the link between $\\widetilde{\\Lambda}_\\theta$ and $\\Lambda_\\alpha$, where we recall that $\\alpha=\\theta'$. Of course, it turns out that $\\widetilde{\\Lambda}_\\theta$ is not directly relevant for the analysis of the inverse problem under consideration in this text, but since the BVP was derived from , it is plainly natural to link the operator $\\Lambda_\\alpha$ we used in the preceding sections to $\\widetilde{\\Lambda}_\\theta$.\n\nWe start by defining the trace space for functions in $H^1(\\Omega _\\theta )$. ",
"We set for all $L>0$, $$\\Omega _\\theta ^L=\\{ (R_{\\theta (x_3)}x',x_3);\\; x'=(x_1,x_2)\\in \\omega ,\\; x_3\\in (-L,L)\\} = \\{ x \\in \\Omega_\\theta,\\ | x_3 | < L \\}$$ and $$\\Gamma _\\theta ^L=\\{ (R_{\\theta (x_3)}x',x_3);\\; x'=(x_1,x_2)\\in \\partial \\omega ,\\; x_3\\in [-L,L]\\} = \\{ x \\in \\partial \\Omega_\\theta,\\ | x_3 | < L \\}.$$ Let $>0$ be fixed. ",
"For every $u\\in H^1(\\Omega _\\theta )$ we have $u_{|\\Omega _\\theta ^L} \\in H^1(\\Omega _\\theta ^L)$ hence $u_{|\\partial \\Omega _\\theta ^L}\\in H^{1/2}(\\partial \\Omega _\\theta ^L)$. Thus, putting $$H^{1/2}(\\Gamma _\\theta ^L)=\\{ h=g_{|\\Gamma _\\theta ^L}\\ \\textrm{in}\\ L^2(\\Gamma _\\theta ^L);\\ g\\in H^{1/2}(\\partial \\Omega _\\theta ^L) \\},$$ it holds true that $u_{| \\Gamma_\\theta^L} \\in H^{1/2}(\\Gamma _\\theta ^L)$. Here the space $H^{1/2}(\\Gamma _\\theta ^L)$ is equipped with its natural quotient norm $$\\|h\\|_{H^{1/2}(\\Gamma _\\theta ^L)}=\\inf \\{ \\|g\\|_{H^{1/2}(\\partial \\Omega _\\theta ^L)};\\; g_{|\\Gamma _\\theta ^L}=h \\}.$$ Further we define $$H_{\\textrm{loc}}^{1/2}(\\partial \\Omega _\\theta )=\\{h\\in L^2_{\\textrm{loc}}(\\partial \\Omega _\\theta );\\;\\; h_{|\\Gamma _\\theta ^L}\\in H^{1/2}(\\Gamma _\\theta ^L)\\; \\textrm{for all}\\ L>0 \\},$$ and then introduce the following subspace $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )=\\{ h\\in H_{\\textrm{loc}}^{1/2}(\\partial \\Omega _\\theta );\\; \\textrm{there exists}\\; v\\in H^1(\\Omega _\\theta )\\; \\textrm{such that}\\; v_{|\\partial \\Omega _\\theta}=h\\}$ of $H_{\\textrm{loc}}^{1/2}(\\partial \\Omega _\\theta )$. ",
"Here and henceforth $v_{|\\partial \\Omega _\\theta}=h$ means that the identity $v_{|\\Gamma _\\theta ^L}=h_{|\\Gamma _\\theta ^L}$ holds in the trace sense for every $L>0$. It is not hard to see that $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$ is a Banach space for the quotient norm: $$\\| h\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )}=\\inf\\{\\|v\\|_{H^1(\\Omega _\\theta )};\\; v_{|\\partial \\Omega _\\theta}=h\\}.$$\n\nWe introduce the mapping $$\\begin{aligned}\nI_\\theta : C_0^1(\\partial \\Omega _\\theta )&\\longrightarrow C_0^1(\\partial \\Omega )\n\\\\\ng &\\mapsto f=g\\circ \\varphi _\\theta ,\\end{aligned}$$ where, for shortness sake, we note $\\varphi _\\theta (x)=T_{\\theta (x_3)}(x',x_3)$ for $x \\in \\overline{\\Omega}$. Pick $g$ in $C_0^1(\\partial \\Omega_\\theta )$ and choose $v\\in C_0^1(\\mathbb{R}^3)$ such that $v_{|\\partial \\Omega _\\theta}=g$. Since $v_{| \\Omega_{\\theta}} \\in H^1(\\Omega_{\\theta})$ we get that $g \\in \\tilde{H}^{1 \\slash 2}(\\partial \\Omega_\\theta)$. Moreover for all $v \\in H^1(\\Omega_{\\theta})$ obeying $v_{|\\partial \\Omega _\\theta}=g$ the function $u=v_{|\\Omega _\\theta}\\circ \\varphi _\\theta$ belongs to $H^1(\\Omega)$ by [@Bre]\\[Proposition 9.6\\], and $$\\|I_\\theta g\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )}\\leq \\|u\\|_{H^1(\\Omega )}\\leq C(\\omega ,\\theta )\\| v\\|_{H^1(\\Omega _\\theta )}.$$ As a consequence we have $$\\label{50}\n\\|I_\\theta g\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )}\\leq C(\\omega ,\\theta )\\|g\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )}\\;\\; \\textrm{for any}\\; g\\in C_0^1(\\partial \\Omega _\\theta ).$$\n\nLet us now consider $g\\in \\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$ and $v\\in H^1(\\Omega _\\theta )$ such that $v_{|\\partial \\Omega _\\theta}=g$. For any sequence $(v_n)_n \\in C_0^1(\\mathbb{R}^3)$ such that $v_n{_{|\\Omega _\\theta}} \\mapsto v$ in $H^1(\\Omega _\\theta)$ as $n \\rightarrow +\\infty$, it is clear that $$\\| g-g_n\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )}\\leq \\|v-v_n\\|_{H^1(\\Omega _\\theta )},$$ provided $g_n={v_n}_{|\\partial \\Omega _\\theta}$. Hence $(g_n)_n$ converges to $g$ in $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$.",
"\n\nFor all $n \\geq 1$, put $f_n=I_\\theta g_n=g_n\\circ \\varphi _\\theta$ and $u_n=v_n\\circ \\varphi _\\theta$. Since $f_n=u_n{_{|\\partial \\Omega}}$, we see that $$\\|f_n-f_m\\|_{\\widetilde{H}^{1/2}(\\partial \\Omega )}\\leq \\|u_n-u_m\\|_{H^1(\\Omega )}\\leq C(\\omega ,\\theta )\\|v_n-v_m\\|_{H^1(\\Omega _\\theta)}.$$ Therefore $(f_n)_n$ is a Cauchy sequence in $\\widetilde{H}^{1/2}(\\partial \\Omega )$ and $f=\\lim_n f_n \\in \\widetilde{H}^{1/2}(\\partial \\Omega )$. ",
"Set $f=I_\\theta g$. Then, in view of , $I_\\theta$ extends to a bounded operator, still denoted by $I_\\theta$, from $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$ into $\\widetilde{H}^{1/2}(\\partial \\Omega )$.",
"\n\nArguing as above, we thus find out that the mapping $$\\begin{aligned}\nJ_\\theta : C_0^1(\\partial \\Omega )&\\longrightarrow C_0^1(\\partial \\Omega _\\theta)\n\\\\\nf &\\mapsto g=f\\circ \\psi _\\theta ,\\end{aligned}$$ where $\\psi_{\\theta}=\\varphi_{\\theta}^{-1}$, extends to a bounded operator, which is still called $J_\\theta$, from $\\widetilde{H}^{1/2}(\\partial \\Omega )$ into $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$.",
"\n\nEvidently, $I_\\theta J_\\theta f=f$ for all $f\\in C_0^1(\\partial \\Omega )$ and $J_\\theta I_\\theta g=g$ for all $g\\in C_0^1(\\partial \\Omega _\\theta)$. Therefore we have$J_\\theta =I_\\theta ^{-1}$ from the density of $C_0^1(\\partial \\Omega)$ (resp. ",
"$C_0^1(\\partial \\Omega _\\theta)$) in $\\tilde{H}^{1 \\slash 2}(\\partial \\Omega)$ (resp. ",
"$\\tilde{H}^{1 \\slash 2}(\\partial \\Omega_\\theta)$).",
"\n\nNext, by reasoning in the same way as in the derivation of , we prove with the help of the Lax-Milgram lemma that the BVP has a unique solution $v\\in H^1(\\Omega _\\theta )$ for every $g\\in \\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$. ",
"Moreover the operator $$\\widetilde{\\Lambda}_\\theta : g\\mapsto v$$ is well defined as a bounded operator from $\\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$ into its dual space $\\widetilde{H}^{-1/2}(\\partial \\Omega _\\theta )$. ",
"Similarly to $\\Lambda _\\theta$, it can be checked that $\\widetilde{\\Lambda}_\\theta$ is characterized by the following identity $$\\langle \\widetilde{\\Lambda}_\\theta g,h\\rangle =\\int_{\\Omega _\\theta}\\nabla v \\cdot \\nabla H dy,$$ which holds true for all $h\\in \\widetilde{H}^{1/2}(\\partial \\Omega _\\theta )$ and all $H\\in H^1(\\Omega _\\theta )$ such that $H_{|\\partial \\Omega _\\theta}=h$. By performing the change of variable $y=\\varphi _\\theta (x)$ in the last integral, we thus get that $$\\langle \\widetilde{\\Lambda}_\\theta g,h\\rangle =\\int_\\Omega A\\nabla u \\cdot \\nabla (H\\circ \\varphi _\\theta ) dx,$$ where $u$ denotes the solution to the BVP with $f=I_\\theta g$. Therefore we have $$\\langle \\widetilde{\\Lambda}_\\theta g,h\\rangle =\\langle \\Lambda _{\\theta '}I_\\theta g, I_\\theta h \\rangle,$$ which means that $\\widetilde{\\Lambda}_\\theta= I_\\theta ^* \\Lambda _{\\theta '} I_\\theta$, or equivalently that $\\Lambda _{\\theta '}=J_\\theta ^* \\widetilde{\\Lambda}_\\theta J_\\theta$, where $\\Lambda_{\\theta'}$ stands for $\\Lambda_\\alpha$.\n\n[CS2]{}\n\n, [*Singular solutions of elliptic equations and the determination of conductivity by boundary measurements*]{}, J. Differ. ",
"Equat. ",
"84 (2) (1990), 252-272.",
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"\n\n[^1]: Which holds true for $\\Omega$ since $\\omega$ is bounded.",
"\n\n[^2]: Note that $1$ can be replaced by any constant $\\mu$ by only substituting $\\mu A^*$ for the matrix $A^*$ in the above reasoning.",
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"\n\nServices we provide\n\nDJs\n\nMobile Discos\n\nAddress\n\nHU8 8HR\n\nAbout Twinspin Mobile DJ Services\n\nIf you choose to book my services for your event I will always provide you with a full disco with lighting, a high quality P.A system, an elegant starlight DJ booth, and myself as your DJ for the whole day or evenings entertainment. ",
"There are no hidden costs whatsoever, and your booking will be signed in a legally binding agreement so you won’t be let down.",
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"Lateral collateral ligament = worse if injured. ",
"This is because the medial tibial plateau forms a deeper and more stable socket with the femoral condyle than the lateral plateau.",
"\n\nWhat’s the unhappy triad?",
"\n\nResults from a strong force applied to the lateral aspect of the knee.",
"\n\n18\n\nWhere to the anterior and posterior cruciate ligament extend from?",
"\n\nExtend from the intercondylar eminence of the tibia to the intercondylar notch of the distal femur\n\nACL attaches to posterior aspect of femoral notch and the anterior intercondylar region of the tibia.",
"\n\nPCL goes from medial edge of lateral femoral condyle and the roof of the intercondylar notch. ",
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"\n\nACL resists anterior translation and medial rotation of the tibia in relation to the femur\n\nPCL prevents posterior dislocation of the tibia on the femur\n\n20\n\nHow is the ACL usually torn and what does the patient feel?",
"\n\nAs a result of quick deceleration, hyperextension or rotational injury The tibia can slide anteriorly under the femur Usually feel a popping sensation in the knee.",
"\n\n21\n\nHow is the PCL damaged?",
"\n\nDashboard injury = flexion of the knee and a force placed on the upper tibia, displacing it posteriorly\n\nAlso during football when a player falls on a flexed knee when their ankle plantar flexed\n\n22\n\nWhat’s prepatella bursitis and how will patients present?",
"\n\nInflammation of the prepatella bursa. ",
"A superficial bursa between the skin and patella.",
"\n\nInflammation causes increase in fluid.",
"Patient has pain and swelling, cant kneel on affected knee and cant walk due to pain. ",
"Usually a history of repetitive trauma to the bursa e.g kneeling on the ground to scrub = housemaids knee.",
"\n\n23\n\nWhat is infrapatella bursitis and how does it occur?",
"\n\nTwo bursa - one below the knee cap and one deep between the patella tendon and tibial bone (shin).",
"\n\nUsually superficial one is inflammed\n\nOccurs due to repeated micro trauma e.g repeated kneeling. ",
"Clergymans knee = common nickname and reflects upright position of kneeling.",
"\n\n24\n\nWhat’s suprapatella bursitis\n\nSwelling within the suprapatellar pouch presents with a knee effusion.",
"\n\nIt’s usually a sign of pathology in the knee. ",
"Causes can be osteoarthritis or rheumatoid arthritis, gout, infection, repetitive microtrauma, ect.",
"\n\n25\n\nWhat’s osgood schlatters disease and what do patients complain of?",
"\n\nInflammation of the patellar ligament at its insertion into the tibial tuberosity. ",
"Commonly occours in teenagers who play sport.",
"\n\nComplain of intense knee pain during running, jumping, squatting, ascending and descending stairs and during kneeling. ",
"Resolves with rest and ice.",
"\n\n26\n\nWhat are the symptoms of osteoarthritis in the knee?",
"\n\nPain comes and goes at varying levels of intensityPain precipitated by activities e.g bending, kneeling, squatting or climbing stairs Pain is worse after prolonged inactivity or rest e.g getting out of bed in the morning. ",
"Knees may buckle when going downstairs due to weakness of quads causing instability\n\nLoss of articular cartilage = bone rubs on bone = firiction can be felt as crepitus. ",
"An effusion may develop.",
"\n\n27\n\nWhat are the risk factors with OA and what will you see on an X-ray?",
"\n\nRisk factors- gender (female)- age- other conditions effecting the joint- previous trauma to the joint- family history\n\nX ray- osteophytes- narrow joint space\n\n28\n\nWhat is septic arthritis of the knee joint and what is the most common cause?",
"\n\nInflammation caused by the invasion of micro organisms in the joint space\n\nWhat are the risk factors for septic arthritis?",
"\n\nProsthetic joint replacement also. ",
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"Pirenzepine binding, which can discriminate muscarinic receptor subtypes, showed the presence of a single population of low affinity sites (M2) before and after synaptogenesis. ",
"The change in agonist binding was not due to the late development of receptor function; tests for receptor-stimulated phosphatidylinositol turnover and for modulation of agonist binding by guanylylimidodiphosphate showed functional coupling to be present several days prior to the onset of synapse formation. ",
"However, detergent-solubilization of membranes eliminated differences in agonist binding between receptors from embryos and hatched chicks, suggesting a developmental change in interactions of the receptor with functionally related membrane components. ",
"A possible basis for altered interactions was obtained from isoelectric point data showing that the muscarinic receptor population underwent a transition from a predominantly low pI form (4.25) in 13 day embryos to a predominantly high pI form (4.50) in newly hatched chicks. ",
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"I have done a bunch of different stuff within fishing, but I would put this guiding related work I am doing with John Quinlan over in Kerry right up there as one of the most rewarding things I have ever been involved with. ",
"The chance to work with John and his wife Lynn in such an outrageously special part of the world and help anglers/clients with their fishing is beyond thrilling for me, seriously, and John and I have been bashing emails and phone calls back and forth to work out some trips for this year that coincided with good tides and different seasons to take advantage of a lot that Kerry has to offer - which is a hell of a lot..............\n\nIt goes without saying that when I say \"guiding\", I am of course working with one of the most experienced and competent bass guides around. ",
"John Quinlan knows his local waters frighteningly well, and with this joint venture I get to work with John at putting our anglers/clients onto various fish, helping out with various methods and techniques, and I will also shoot a bunch of photos of each trip so that everybody has a proper visual record of their time in Kerry - these are intense trips where we pack as much into every day as weather and conditions allow, and the emphasis of course is on catching fish, learning plenty, and simply having a load of fun. ",
"Here's some feedback from one of our clients last year which says far more than I can really :\n\n\"Henry, having just completed half of my journey home from a week with you and John, I find myself sitting on the ferry pondering what just happened over the past five days. ",
"Did I ever imagine that such a trip could be so much fun, give me so much satisfaction? ",
"I don't even remember what my expectations were before arriving at Thatch Cottage, were they even realistic I wonder. ",
"Whatever they were, they could not have come anywhere near close to what I have just experienced. ",
"Alas the real world for this weary but merry angler now kicks back in, but I cannot help but sit here full of mixed emotions, trying to pick through the highlights, the best fish, the best locations, the best laughs. ",
"But most importantly, what I have learnt. ",
"Your resolution to not take a rod and fill your boots with hard fighting fish which we clients heaped on you, together with the big fat cheshire cat grin you wore whilst we toiled with them is enough for anyone to see how much enjoyment you get out of the guiding business. ",
"What people won't see though, unless they take this trip of course, is the sheer hard work and constant effort you both put in (not to mention John's fabulous wife) to make this experience one to be both appreciated and well remembered. ",
"It was like having one's best mates besides us, all crowding for those fish, constantly working it out, sharing the joy and frustration together. ",
"But is the guiding really about the fish? ",
"How can it be? ",
"It has to be so much more. ",
"Yes the fish may be primary, but holy cow, what about that location, the challenges, the variety, the constant searching, and the satisfaction of taking willing participants beyond anything they have experienced before? ",
"So when the fish do come along in those hard to get to places it makes it worth it for all, not just the anglers and that could be felt in skip loads. ",
"I would urge any readers who are in two minds or not to take this trip to jump in with both feet and an open mind, however experienced or not they may be. ",
"Driving away from Thatch Cottage this afternoon with my car full of moist soaking kit was difficult to say the least, I could have stayed forever.....maybe I will after next years visit because I WILL be back. ",
"So save a date for me please\". ",
"Crumbs, thank you.",
"\n\nI'll be honest with you here - I find it a tough to be entirely subjective about these trips and of course Ireland. ",
"If you hadn't guessed, I am in love with Ireland anyway (really?), ",
"and John and Lynn's Thatch Cottage Ireland setup just happens to be situated in what in my opinion is truly one of the most special places on earth. ",
"It's inspiring just being there, let alone fishing. ",
"Having photographed John's operation in the past and now co-guided etc. ",
"with him, I also know that as an angler and lure/bass fishing nut especially I would be doing whatever I could to do a trip like this. ",
"See? ",
"I can't be subjective when I so want to be on these trips anyway, almost regardless of the fact that it's a work thing for me. ",
"But heh, what's wrong with loving your work?",
"\n\nJohn and I have put various dates aside for 2015, so please do get in touch either with me here, or with John and Lynn here - for this blog post though, I wanted to tell you mainly about a spring bass fishing trip that revolves around arriving at Thatch Cottage Ireland on Wednesday 29th April, then fishing Thursday 30th, Friday 1st May, Saturday 2nd May and Sunday 3rd May - departing on Monday 4th May. These dates are designed around tides rather than weekends etc. ",
"Spring bass fishing in Kerry can be some pretty special stuff, revolving a lot around soft plastics, shallow water, perhaps a chance to sight-fish to bass which can concentrate in potentially serious numbers, and of course being spring it's a good excuse to nail some early season fish and banish those winter blues. ",
"If conditions are ok then there is also a chance to lure fish for sea trout in saltwater as well, plus early seasonish wrasse and pollack etc.",
"\n\nWe have various other dates available, so if the idea of coming to Ireland and fishing with John and me appeals, please do get in touch (here and here) and we will sort it out. ",
"As well as the spring fishing, we have dates in August and October, again all coinciding with good tides. ",
"Check out a bunch of photos from our 2014 spring trip here, and our 2014 August trip here, and then imagine yourself in a place like that. ",
"Hope to see some of you in Ireland this year, and in the meantime, have a good weekend."
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"14 August 2013.",
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[
"153*h**2 + 4\nLet s(d) be the second derivative of 5*d**3/6 + 30*d + 12. ",
"Let y(c) = -1566*c**2. ",
"Determine y(s(m)).",
"\n-39150*m**2\nLet i be -2 + (0 - (-235)/(-5))*1. ",
"Let c(b) = 10*b**2 - 4*b + 4. ",
"Let j(f) = -119*f**2 + 49*f - 49. ",
"Let y(p) = i*c(p) - 4*j(p). ",
"Let a(m) = m**2. ",
"What is y(a(l))?",
"\n-14*l**4\nLet s(w) = -2754*w**2 - 5. ",
"Let x(g) = -307*g. ",
"Determine x(s(v)).",
"\n845478*v**2 + 1535\nLet x(b) = 10 + 4 + 5*b**2 - 14 - 9*b**2. ",
"Let g(z) = 468*z**2. ",
"Determine g(x(h)).",
"\n7488*h**4\nLet t(u) = 2*u**2. ",
"Let h(c) = -13716202*c. ",
"What is h(t(o))?",
"\n-27432404*o**2\nLet z(x) = 10251*x**2. ",
"Let f(t) = 118*t**2. ",
"What is z(f(h))?",
"\n142734924*h**4\nLet z(s) = -15*s - 88552. ",
"Let t(w) = -4*w**2. ",
"What is z(t(r))?",
"\n60*r**2 - 88552\nLet j(k) = 4 - 3*k - 4. ",
"Suppose 13 = 5*o - 47. ",
"Let d(v) = -355 + 355 - o*v. ",
"Give d(j(l)).",
"\n36*l\nLet t(c) = -c. ",
"Let x(m) = -1163*m - 80. ",
"Let s(y) = -3033103*y - 208620. ",
"Let a(r) = 4*s(r) - 10431*x(r). ",
"What is t(a(w))?",
"\n1159*w\nLet u(o) = -8 + 5 + o**2 + 3 + 0. ",
"Let m(x) = 35*x - 5. ",
"Determine u(m(t)).",
"\n1225*t**2 - 350*t + 25\nLet g = 29 + -27. ",
"Let d(j) = -j - g - 47 + j + j. Let r(i) be the third derivative of i**4/24 - 2*i**2. ",
"Determine d(r(k)).",
"\nk - 49\nLet a(k) be the first derivative of 2 + 0*k + 0*k**2 + 1/3*k**3. ",
"Let y(f) = -34*f - 2. ",
"Let s(h) = -47*h - 3. ",
"Let z(n) = 3*s(n) - 5*y(n). ",
"Give a(z(b)).",
"\n841*b**2 + 58*b + 1\nLet m be (-68)/5*(1 + 4). ",
"Let i = m - -255. ",
"Let f(x) = -x**2 - 187*x + i*x. ",
"Let q(j) = 12*j**2 + 5*j. ",
"Determine q(f(w)).",
"\n12*w**4 - 5*w**2\nLet l(x) = 160*x**2. ",
"Let s(n) be the third derivative of -n**6/720 + 2*n**4 + 23*n**2 - 1. ",
"Let w(g) be the second derivative of s(g). ",
"Determine w(l(z)).",
"\n-160*z**2\nLet o(y) = -2*y. ",
"Let c be 1884/360 - 0 - (9/(-15))/1. ",
"Let t(u) be the second derivative of -c*u**3 + 0*u**2 + 0 - 17*u. ",
"Calculate o(t(s)).",
"\n70*s\nLet h(i) = -6*i - 5. ",
"Let j(q) = 7*q + 6. ",
"Let m(t) = 6*h(t) + 5*j(t). ",
"Let g(p) be the third derivative of -p**5/20 - 327*p**2. ",
"What is g(m(d))?",
"\n-3*d**2\nLet r(u) = -18*u**2 - 13*u**2 + 29*u**2. ",
"Let g(j) = 119*j**2. ",
"Determine g(r(k)).",
"\n476*k**4\nLet x(q) = -13234970*q. ",
"Let s(j) = -j**2. ",
"Calculate x(s(g)).",
"\n13234970*g**2\nLet i(m) = -2*m**2 - 22*m - 22. ",
"Let f(t) = -t - 1. ",
"Let s(v) = 88*f(v) - 4*i(v). ",
"Suppose -94 = -2*b + 32. ",
"Let p(q) = b*q - 59*q - 5 + 5. ",
"What is s(p(w))?",
"\n128*w**2\nLet g(y) = y. Let a(j) = -5269*j**2 + 78857*j + 2. ",
"Calculate g(a(d)).",
"\n-5269*d**2 + 78857*d + 2\nLet k = 56 + -9. ",
"Let a = k - 41. ",
"Let p(j) = -a*j + 2*j - 2*j. ",
"Let c(o) = 2*o. ",
"Give p(c(l)).",
"\n-12*l\nLet h(r) = -25*r. ",
"Suppose 0 = -2*s + 4*a - 10 + 2, 0 = s + a + 4. ",
"Let q be (0 + s)*(-3 - -2). ",
"Let w(o) = -o + 4*o - q*o. ",
"Give h(w(u)).",
"\n25*u\nLet l(n) = 8*n**2. ",
"Let c(o) = -80886*o - 1. ",
"What is c(l(t))?",
"\n-647088*t**2 - 1\nLet b(r) = 3*r. ",
"Suppose -2*n = 4*n - 24. ",
"Let f(u) = -13*u**2 - 8 + 12 - n. Calculate b(f(k)).",
"\n-39*k**2\nLet w(t) = 2*t. ",
"Let d(c) = -10588*c - 1032. ",
"What is w(d(u))?",
"\n-21176*u - 2064\nLet l(f) = 38*f**2 + 4*f - 18. ",
"Let o(g) = 7*g. ",
"What is o(l(a))?",
"\n266*a**2 + 28*a - 126\nLet r(y) = -1 - 6 + y**2 - 60*y + 53*y. ",
"Let z(i) = -i**2 + 6*i + 6. ",
"Let h(x) = 6*r(x) + 7*z(x). ",
"Let a(w) = 24*w. ",
"What is h(a(f))?",
"\n-576*f**2\nLet c(y) = 6*y**2. ",
"Let k(j) = 438*j - 56. ",
"Let x be k(7). ",
"Let o(h) = -x + 3010 - h**2. ",
"Give c(o(p)).",
"\n6*p**4\nLet h(u) = -74 + 37 + 41 - 7*u + u + 9*u. ",
"Let j(o) = -25*o**2. ",
"Give h(j(l)).",
"\n-75*l**2 + 4\nLet h(b) be the first derivative of -2*b**2 + 114. ",
"Let g(x) = -3*x - 115. ",
"Calculate g(h(m)).",
"\n12*m - 115\nLet z(d) = -8*d**2. ",
"Let i(s) be the first derivative of 2*s**2 - s**2 - 53 - 3*s**2. ",
"What is i(z(c))?",
"\n32*c**2\nLet l(u) = -63*u**2 - 15*u + 15. ",
"Let t(g) = 4*g**2 + g - 1. ",
"Let i(s) = l(s) + 15*t(s). ",
"Suppose z + 2*z - 6 = 0. ",
"Let v(f) = f - f - z*f. ",
"Calculate i(v(d)).",
"\n-12*d**2\nLet c(k) = 50. ",
"Let n(b) = -2*b - 60. ",
"Let z(m) = -6*c(m) - 5*n(m). ",
"Let v(d) be the third derivative of -d**5/30 - 4*d**2. ",
"Give z(v(a)).",
"\n-20*a**2\nLet x(w) = 435*w**2 - 367*w**2 - 18*w - 39*w**2. ",
"Let o(h) = 2*h**2. ",
"Give x(o(t)).",
"\n116*t**4 - 36*t**2\nLet l(v) = 21*v - 297. ",
"Let z(g) = 19*g - 264. ",
"Let i(m) = 8*l(m) - 9*z(m). ",
"Let k(x) = 1607*x. ",
"Give k(i(c)).",
"\n-4821*c\nLet v(n) be the first derivative of -n**2 - 4254. ",
"Let r(q) be the second derivative of -37*q**4/4 + 2*q. ",
"Calculate v(r(f)).",
"\n222*f**2\nLet j(s) = 20*s. ",
"Let u(a) be the second derivative of 19*a**4/12 + 11*a**3/6 + 3*a**2 + 27*a. ",
"Let o be u(-3). ",
"Let d(c) = -144 + c + o + c. Give j(d(f)).",
"\n40*f\nLet l(i) = i**2. ",
"Suppose 0*q = 2*q - 20. ",
"Let z(v) = v**3 - 11*v**2 + 12*v + 9. ",
"Let h be z(q). ",
"Let n(f) = 29*f + 2*f**2 + 0*f**2 - h*f. ",
"What is n(l(g))?",
"\n2*g**4\nLet f(l) = 2*l. ",
"Let n = -33 - -38. ",
"Let g(a) = n*a + 4*a - 2*a - 2 - 14*a. ",
"Determine f(g(k)).",
"\n-14*k - 4\nLet f be (36 - (-2 - -2))*2/(-4). ",
"Let u be (-153)/f + (-2)/(-4). ",
"Let o(n) = -3 - n - u + 12. ",
"Let b(a) = 2*a**2. ",
"Determine b(o(s)).",
"\n2*s**2\nLet v(p) = 10378828*p. ",
"Let u(w) = -3*w**2. ",
"Give v(u(n)).",
"\n-31136484*n**2\nLet u(m) = 25*m**2 - 71*m**2 + 45*m**2. ",
"Let x(l) = 921*l**2. ",
"Determine u(x(a)).",
"\n-848241*a**4\nLet i(w) be the first derivative of 49*w**2 - 40. ",
"Let v(u) = 19 - u - 19 + 3*u. ",
"What is i(v(b))?",
"\n196*b\nLet y(f) = -4*f. ",
"Let k(v) = 84074*v - 4445. ",
"Let n(i) = -284*i + 15. ",
"Let r(t) = 3*k(t) + 889*n(t). ",
"Determine y(r(c)).",
"\n1016*c\nLet s(l) be the first derivative of -10*l**3/3 + l**2 + 4*l + 38. ",
"Let t(q) = -19*q**2 + 5*q + 10. ",
"Let u(o) = 5*s(o) - 2*t(o). ",
"Let c(n) = 5*n. ",
"Give u(c(z)).",
"\n-300*z**2\nLet a(g) be the second derivative of -160*g**3/3 - 1316*g. ",
"Let f(i) = 2*i**2. ",
"Give a(f(r)).",
"\n-640*r**2\nLet q(w) = -15*w**2. ",
"Let z(g) = -758929*g. ",
"Calculate q(z(t)).",
"\n-8639598405615*t**2\nLet c(i) = -2*i. ",
"Let a(o) be the second derivative of -1055*o**4/12 + 26*o + 58. ",
"Calculate a(c(b)).",
"\n-4220*b**2\nLet c(r) = -1705*r**2 + 2. ",
"Let u(m) = -6985*m**2. ",
"Calculate c(u(f)).",
"\n-83187333625*f**4 + 2\nLet r(j) be the third derivative of 5*j**4/24 - 1029*j**2 - 2. ",
"Let q(z) = 1233*z**2. ",
"Calculate r(q(i)).",
"\n6165*i**2\nLet y(b) = -3*b + 3*b - 5*b + 0*b. ",
"Let d(q) be the first derivative of -19*q**2 + 3. ",
"Determine y(d(v)).",
"\n190*v\nLet q(c) = -438*c. ",
"Let m(w) be the third derivative of w**4/12 - 77*w**2 - 6*w + 2. ",
"Give m(q(g)).",
"\n-876*g\nLet b be (5/(-15))/((-2)/24). ",
"Let j(x) = -b*x - 11*x + 23*x. ",
"Let h(w) = 3*w**2 + 5*w. ",
"Let i(a) = -2*a**2 - 3*a. ",
"Let s(o) = 3*h(o) + 5*i(o). ",
"Give s(j(g)).",
"\n-64*g**2\nLet a(q) = -235*q + 10. ",
"Let c(p) be the second derivative of -p**3/6 + 2366*p. ",
"What is a(c(k))?",
"\n235*k + 10\nLet q(i) = 2*i. ",
"Let t(r) be the second derivative of -2881*r**3/6 - 339*r - 2. ",
"What is t(q(k))?",
"\n-5762*k\nLet u(g) = 303*g**2. ",
"Let b(k) be the second derivative of k**4/3 - 6*k - 22. ",
"Give b(u(a)).",
"\n367236*a**4\nLet z(o) = -11*o. ",
"Let n(u) = -42*u**2 + 18994. ",
"What is n(z(q))?",
"\n-5082*q**2 + 18994\nLet v(z) = 3*z + 978. ",
"Let j(k) = 39*k + 12. ",
"Determine v(j(t)).",
"\n117*t + 1014\nLet w(n) = 2*n. ",
"Suppose 6*h = -4*m + h - 17, -5*m = -2*h + 13. ",
"Let q be (m - 469/(-14))*(-8)/(-2). ",
"Let d(b) = 2*b**2 - 122*b + q*b - 3*b**2. ",
"What is w(d(f))?",
"\n-2*f**2\nLet u(a) = 76736631*a**2. ",
"Let n(x) = -2*x**2. ",
"Give u(n(m)).",
"\n306946524*m**4\nLet k(i) = -4*i - 32. ",
"Let u(t) = 387*t**2 - 177*t**2 - 195*t**2. ",
"Determine k(u(g)).",
"\n-60*g**2 - 32\nLet v(c) be the third derivative of c**8/20160 - c**5/6 - 5*c**3/6 - c**2. ",
"Let y(k) be the third derivative of v(k). ",
"Let l(g) = -2*g - 3 + 3. ",
"Calculate y(l(a)).",
"\n4*a**2\nLet y(w) be the second derivative of w**3/3 - w. Let t(p) be the second derivative of -95*p**3/2 + 252*p + 4. ",
"Calculate t(y(k)).",
"\n-570*k\nLet k(d) = -400860*d**2 + 2*d + 1. ",
"Let m(w) = -3*w. ",
"Calculate k(m(q)).",
"\n-3607740*q**2 - 6*q + 1\nLet g = -43 + 26. ",
"Let i = g - -25. ",
"Let y(q) = q - 10*q + 3*q - i*q. ",
"Let d(w) = -2*w**2. ",
"Give d(y(p)).",
"\n-392*p**2\nLet h(p) be the second derivative of 7*p**3/2 + 33*p - 67. ",
"Let f(c) = -c - 2. ",
"Give h(f(r)).",
"\n-21*r - 42\nLet v(q) = -142341351*q. ",
"Let g(i) = -2*i. ",
"Calculate g(v(y)).",
"\n284682702*y\nLet c(x) be the third derivative of 0*x + 1/15*x**5 + 0*x**3 + 82*x**2 + 0 + 0*x**4. ",
"Let s(a) be the first derivative of -a**3/3 - 1. ",
"Give s(c(y)).",
"\n-16*y**4\nLet k(d) = -2996 - 2998 + 45*d + 5994 - 47*d. ",
"Let r(f) = 88*f + 5. ",
"Let l(v) = 4399*v + 249. ",
"Let w(j) = -5*l(j) + 249*r(j). ",
"What is w(k(h))?",
"\n166*h\nLet z(n) = 1382*n - 32. ",
"Let d(f) = 43*f**2 - 4*f. ",
"What is z(d(w))?",
"\n59426*w**2 - 5528*w - 32\nLet n(c) be the first derivative of 0*c**2 + 0*c - 2/3*c**3 + 100. ",
"Let p(k) = 18*k**2 + k. What is p(n(d))?",
"\n72*d**4 - 2*d**2\nLet c(f) = 19*f - 2. ",
"Let z(g) = 1 + 292*g**2 + 297"
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[
"Q:\n\nИдентификатор \"ch\" не определён. ",
"В чём ошибка?",
"\n\nПо-моему, код должен работать, но visual studio считает иначе\nint main()\n{\n do\n {\n int shift;\n string word, originalWord;\n char ch;\n\n system(\"cls\");\n\n cout << \"Enter your word, that you are wont to encrypt: \" << endl;\n cin >> originalWord;\n\n cout << \"1 - cipher of Caesar (russian version (doesn't work correctly))\" << endl;\n cout << \"2 - cipher of Caesar (english version)\" << endl;\n cout << \"3 - exchange 'begin - the end' (russian version (doesn't work correctly))\" << endl;\n cout << \"4 - exchange 'begin - the end' (english version)\" << endl;\n\n ch = _getch();\n\n switch (ch)\n {\n case 49: cipherOfCaesarRussian(word, shift); break;\n case 50: cipherOfCaesarRussian(word, shift); break;\n //case 51: cipherExchangeBeginToTheEndRussian(word); break;\n //case 52: cipherExchangeBeginToTheEndEnglish(word); break;\n }\n\n cout << \"Continue?\" ",
"<< endl << endl << \"Yes - press 'Enter'\" << endl << \"No - press 'Esc'\";\n\n ch = _getch();\n } while (ch !",
"= 27); // Пока не нажата клавиша Esc\n\n _getch();\n\n return 0;\n}\n\nПосле строки while (ch !",
"= 27) компилятор выдаёт \n\n\"идентификатор \"ch\" не определён\"\n\nA:\n\nНу правильно - он определен в теле цикла, и на скобке } перед while его область видимости и заканчивается...\nТак что прав Visual Studio...\n\nA:\n\nПросто объявите ch до цикла, в начале функции main например, тогда ваша переменная будет видна во всех последующих (не факт) блоках функции main и на запись и на чтение.",
"\n\n"
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[
"13) to base 8\n71335\nConvert c2b (base 15) to base 6.",
"\n20405\nWhat is -13a39 (base 15) in base 4?",
"\n-33121032\n2129 (base 13) to base 15\n1568\n-32264 (base 8) to base 2\n-11010010110100\nConvert 143 (base 11) to base 5.",
"\n1133\n-21d1 (base 15) to base 16\n-1c03\nConvert -23304 (base 9) to base 2.",
"\n-11110011000100\n-5831 (base 9) to base 8\n-10341\n-144300 (base 5) to base 13\n-2a8c\nConvert 15b1 (base 12) to base 9.",
"\n3477\n-954 (base 13) to base 12\n-b06\nWhat is -88dd (base 16) in base 13?",
"\n-12c42\nConvert -4244 (base 5) to base 4.",
"\n-20332\n5a5 (base 11) to base 2\n1011010000\n-1b7 (base 14) to base 2\n-101100101\nWhat is 114332 (base 9) in base 16?",
"\n10cbe\nWhat is 1015 (base 14) in base 6?",
"\n20443\n-151152 (base 7) to base 15\n-89e6\n-46 (base 12) to base 3\n-2000\nWhat is -2aa (base 11) in base 9?",
"\n-442\nConvert -214034 (base 5) to base 8.",
"\n-16342\nConvert 22122021 (base 3) to base 5.",
"\n200143\nWhat is 343 (base 14) in base 5?",
"\n10042\nWhat is 31763 (base 9) in base 15?",
"\n6376\n39b5 (base 16) to base 12\n8671\nConvert 1819 (base 11) to base 10.",
"\n2319\nWhat is -2871 (base 16) in base 9?",
"\n-15173\nConvert 10202201 (base 3) to base 10.",
"\n2746\nConvert 18390 (base 12) to base 5.",
"\n2110400\n100001110011100 (base 2) to base 6\n212044\nWhat is -3716 (base 11) in base 15?",
"\n-168c\nConvert -3472 (base 8) to base 14.",
"\n-962\nConvert 512 (base 7) to base 10.",
"\n254\n4693 (base 16) to base 9\n26704\n-b41 (base 12) to base 7\n-4522\nConvert -1624 (base 9) to base 10.",
"\n-1237\nConvert 2527 (base 8) to base 5.",
"\n20432\nWhat is -109 (base 12) in base 15?",
"\n-a3\n-11219 (base 10) to base 15\n-34ce\nConvert -21054 (base 7) to base 3.",
"\n-21010000\nWhat is 101101100110011 (base 2) in base 12?",
"\n11617\nWhat is 2002311 (base 4) in base 3?",
"\n102111010\n957 (base 11) to base 10\n1151\nWhat is 10333 (base 5) in base 14?",
"\n394\nConvert 3331221 (base 5) to base 6.",
"\n1125543\nConvert 15250 (base 8) to base 7.",
"\n25616\nConvert -162 (base 13) to base 8.",
"\n-371\n10000111010110 (base 2) to base 4\n2013112\nConvert -13202 (base 7) to base 2.",
"\n-110111001010\nWhat is 7362 (base 8) in base 11?",
"\n2969\n113013 (base 6) to base 11\n7345\nWhat is -104402 (base 6) in base 16?",
"\n-2252\n16d (base 14) to base 9\n355\nWhat is 1661 (base 11) in base 4?",
"\n201030\nWhat is 110011011001110 (base 2) in base 14?",
"\n983c\n-4551 (base 13) to base 11\n-7318\nWhat is 1011100001110011 (base 2) in base 5?",
"\n3002334\nWhat is -10010100110011 (base 2) in base 14?",
"\n-3683\n-5250 (base 6) to base 7\n-3306\nConvert -32101 (base 5) to base 13.",
"\n-c96\nConvert -1541 (base 6) to base 3.",
"\n-120121\nWhat is -88f (base 16) in base 10?",
"\n-2191\n-101010110110 (base 2) to base 8\n-5266\n-2252 (base 9) to base 14\n-871\nConvert -18d9b (base 15) to base 8.",
"\n-235470\n-1854 (base 11) to base 12\n-1446\n-541 (base 9) to base 2\n-110111010\nConvert -1110001001 (base 2) to base 4.",
"\n-32021\n33765 (base 8) to base 16\n37f5\nWhat is -86 (base 16) in base 2?",
"\n-10000110\nWhat is -7962 (base 16) in base 14?",
"\n-b478\nWhat is -247 (base 12) in base 3?",
"\n-110201\nWhat is -3254 (base 6) in base 4?",
"\n-23302\nWhat is -280 (base 14) in base 7?",
"\n-1320\n36d (base 15) to base 11\n648\n5831 (base 13) to base 5\n344002\nConvert 11102010 (base 3) to base 12.",
"\n1a40\n714 (base 13) to base 3\n1122110\nConvert 298 (base 16) to base 10.",
"\n664\nWhat is 21023002 (base 4) in base 14?",
"\nd998\nConvert -43242 (base 5) to base 4.",
"\n-232003\nWhat is -1071 (base 10) in base 15?",
"\n-4b6\n28ca (base 13) to base 8\n13430\n21102111 (base 3) to base 16\n1525\nWhat is 411 (base 14) in base 10?",
"\n799\nConvert 121100112 (base 3) to base 13.",
"\n5570\nWhat is 814 (base 11) in base 9?",
"\n1312\nConvert 10212111012 (base 3) to base 13.",
"\n28895\nConvert -13130320 (base 4) to base 6.",
"\n-353144\n8410 (base 11) to base 16\n2b87\n-22f (base 16) to base 12\n-3a7\nWhat is -10010121 (base 3) in base 8?",
"\n-4354\nConvert -6275 (base 9) to base 8.",
"\n-10774\nWhat is 496 (base 14) in base 8?",
"\n1624\n4405 (base 7) to base 9\n2137\n1033233 (base 4) to base 3\n21000000\n2442 (base 6) to base 14\n310\nWhat is 2051 (base 6) in base 13?",
"\n298\nWhat is -201002 (base 3) in base 16?",
"\n-203\nConvert -211022 (base 3) to base 14.",
"\n-310\nWhat is -212330 (base 6) in base 15?",
"\n-5256\n-1784 (base 16) to base 12\n-3598\n-14 (base 5) to base 12\n-9\nConvert 22132 (base 8) to base 10.",
"\n9306\nWhat is -408 (base 9) in base 13?",
"\n-1c7\n-486 (base 13) to base 9\n-1063\nConvert 1144 (base 9) to base 15.",
"\n3ba\nConvert 1860 (base 9) to base 13.",
"\n861\nWhat is -1201101 (base 3) in base 7?",
"\n-3436\n33115 (base 6) to base 10\n4583\n-7bb (base 13) to base 14\n-6b7\n4167 (base 9) to base 14\n1186\nConvert -1034314 (base 5) to base 9.",
"\n-26723\nConvert -144 (base 11) to base 12.",
"\n-121\nConvert -94db (base 15) to base 8.",
"\n-75371\nConvert 21200120 (base 3) to base 7.",
"\n22224\nConvert -222110221 (base 3) to base 8.",
"\n-45547\nWhat is 3320444 (base 5) in base 7?",
"\n330000\nWhat is -1705 (base 10) in base 8?",
"\n-3251\nWhat is 118 (base 16) in base 11?",
"\n235\nConvert 1452 (base 12) to base 3.",
"\n10020122\n101221 (base 3) to base 8\n447\n-11101010110 (base 2) to base 9\n-2516\nConvert -113040 (base 6) to base 15.",
"\n-2d49\nWhat is 52632 (base 8) in base 6?",
"\n245242\nWhat is 480 (base 15) in base 6?",
"\n4420\nConvert -1 (base 9) to base 8.",
"\n-1\nWhat is 1561 (base 7) in base 11?",
"\n524\nConvert -3002 (base 6) to base 4.",
"\n-22022\nConvert -100000011 (base 2) to base 4.",
"\n-10003\n1005 (base 12) to base 13\na34\nWhat is -5864 (base 12) in base 7?",
"\n-40525\n20302132 (base 4) to base 15\na9ed\nConvert -647 (base 12) to base 11.",
"\n-766\n-110404 (base 9) to base 3\n-10100110011\n2332 (base 10) to base 12\n1424\nWhat is -1111000001 (base 2) in base 12?",
"\n-681\nConvert -290 (base 12) to base 10.",
"\n-396\nConvert 6941 (base 15) to base 11.",
"\n15866\nWhat is 864 (base 9) in base 10?",
"\n706\nWhat is -315620 (base 7) in base 8?",
"\n-153075\n-9a8 (base 11) to base 8\n-2267\nWhat is be76 (base 16) in base 10?",
"\n48758\nWhat is 8d7 (base 16) in base 6?",
"\n14251\n-67b0 (base 13) to base 6\n-151100\n544 (base 8) to base 13\n215\nWhat is 56a6 (base 11) in base 12?",
"\n4409\nWhat is 2543b (base 12) in base 8?",
"\n143057\nConvert -1120220200 (base 3) to base 11.",
"\n-21560\nWhat is 60301 (base 7) in base 15?",
"\n44a4\n-640 (base 15) to base 4\n-112002\n-508 (base 11) to base 6\n-2501\n100001101001101 (base 2) to base 8\n41515\n-21014 (base 6) to base 2\n-101100000010\nWhat is -102122110 (base 3) in base 16?",
"\n-212a\n32431 (base 5) to base 8\n4301\nWhat is -8273 (base 11) in base 2?",
"\n-10101011011010\nConvert -101540 (base 8) to base 13.",
"\n-12401\nConvert 559 (base 16) to base 7.",
"\n3664\n-12316 (base 7) to base 10\n-3247\nConvert 53 (base 16) to base 7.",
"\n146\nConvert 31231 (base 5) to base 4.",
"\n200102\nConvert -2111000 (base 3) to base 8.",
"\n-3421\nWhat is 1421 (base 6) in base 11?",
"\n30a\nWhat is -2341421 (base 5) in base 10?",
"\n-43361\nConvert 1030331 (base 4) to base 7.",
"\n20234\nConvert -32032 (base 5) to base 6.",
"\n-13530\nWhat is -ada3 (base 15) in base 12?",
"\n-19390\nWhat is 13660 (base 12) in base 7?",
"\n141204\nConvert 2922 (base 12) to base 2.",
"\n1001010101010\nWhat is -1001101101 (base 2) in base 5?",
"\n-4441\nWhat is 203626 (base 7) in base 10?",
"\n34957\nConvert -100000111110 (base 2) to base 8.",
"\n-4076\nConvert 1149 (base 13) to base 12.",
"\n14a3\n-101011 (base 2) to base 16\n-2b\nConvert 160 (base 8) to base 9.",
"\n134\nWhat is 23103 (base 4) in base 9?",
"\n883\nWhat is 12ab (base 12) in base 10?",
"\n2147\n451431 (base 6) to base 16\n944b\nConvert -111 (base 3) to base 13.",
"\n-10\nWhat is 2010000 (base 3) in base 5?",
"\n22124\n-101f (base 16) to base 4\n-1000133\nWhat is 177 (base 13) in base 4?",
"\n10023\nWhat is -4405 (base 10) in base 7?",
"\n-15562\nWhat is 458 (base 14) in base 11?",
"\n714\nWhat is 1020132 (base 4) in base 14?",
"\n1994\nConvert 31a (base 15) to base 3.",
"\n221221\nConvert -1750 (base 13) to base 11.",
"\n-2652\nWhat is -310300 (base 5) in base 12?",
"\n-59b7\nWhat is 1000101111100 (base 2) in base 12?",
"\n2710\n956a (base 12) to base 16\n3fe2\nWhat is 501 (base 12) in base 16?",
"\n2d1\nConvert -2b65 (base 16) to base 7.",
"\n-44250\nConvert -1011323 (base 4) to base 15.",
"\n-14d5\nWhat is -22020 (base 3) in base 15?",
"\n-ec\nWhat is 104 (base 16) in base 3?",
"\n100122\nConvert 532 (base 8) to base 7.",
"\n1003\n534 (base 7) to base 14\n154\nWhat is 106130 (base 7) in base 2?",
"\n100100111110111\n13714 (base 13) to base 8\n107000\nWhat is 73 (base 13) in base 3?",
"\n10111\n673 (base 11) to base 6\n3422\nConvert 25012 (base 9) to base 16.",
"\n418a\n2404 (base 6) to base 4\n21010\nConvert -1727 (base 12) to base 7.",
"\n-11032\n-2213431 (base 5) to base 10\n-38616\n1113321 (base 4) to base 10\n5625\n5461 (base 7) to base 13\nb74\nWhat is b8 (base 15) in base 8?",
"\n255\nConvert 67a9 (base 12) to base 7.",
"\n45354\n154b (base "
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"If you are unable to show one of these cards after purchasing online, you will have to pay a surcharge.",
"\n\nCinema card holders Holders of a kinokarte.ch, ArenaCard and Filmpodium’s GA or Half Fare Card can purchase ZFF Cards for a reduced price.",
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"Boe, Borghild Collection\n\nThe Borghild Boe Collection, available at the Center for Western Studies, contains papers on Borghild's personal history, as well as family history, and items related to her work with the Family Service Association of America in Beloit, Wisconsin. ",
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"\n\nThe Borghild Boe Collection, available at the Center for Western Studies, contains papers on Borghild's personal history, as well as family history, and items related to her work with the Family Service Association of America in Beloit, Wisconsin. ",
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"Plán práce: viz zápis\nJean-Pierre Audy\n(FR) Vážený pane předsedo, rád bych se ujal slova na základě článku č. ",
"16 Smlouvy o Evropské unii. ",
"Tento týden byl na popud francouzského prezidenta Nicolase Sarkozyho, který prokázal velkou vnímavost ke společenství, předložen návrh na svolání výjimečné schůzky Evropské rady, která by se měla konat v pátek.",
"\nPodle smluv připravuje schůzky obvykle Rada pro obecné záležitosti. ",
"Avšak na programu na tento týden jsem si žádné schůze Rady pro obecné záležitosti, která by byla věnována přípravě této výjimečné schůzky Evropské rady, nevšiml. ",
"Domnívám se, že v době, kdy jsme svědky významných demokratických změn, by občané měli být spolu se svými prezidenty zahrnuti do rozhodnutí, které Evropa v oblasti těchto klíčových otázek podniká.",
"\nPředsedající\nDěkuji vám za vaši poznámku. ",
"Pošlu vám písemnou odpověď.",
"\n"
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"For indispensable reporting on the coronavirus crisis, the election, and more, subscribe to the Mother Jones Daily newsletter.",
"\n\n\n\n\n\nAccording to the 2012 and 2016 exit polls, Hillary Clinton did six points worse than Barack Obama among Latinos, receiving only 66 percent of the Latino vote. ",
"Donald Trump did one point better than Romney, receiving 28 percent of the Latino vote. ",
"Ever since, a group called Latino Decisions has been insisting that the exit polls are all wrong, and Clinton actually received a much larger percentage of the Latino vote. ",
"Today they highlighted a new study in the Nevada Independent that examines voting by precinct and then compares the results to 2012. ",
"Here’s what it looks like for Nevada:\n\nThe authors say that Trump seems to have gotten about the same vote share as Romney: “It is therefore extremely unlikely that more than one in four (28 percent) Latinos in Nevada turned out for Trump, as purported by the exit poll. ",
"Instead, it is likely that Clinton won just under 9 out of 10 Latino voters, leaving 1 in 10 to Trump.”",
"\n\nThere are all sorts of criticisms to make of this approach, the biggest of which is that the authors’ own chart suggests that Clinton got fewer Latino votes in Nevada than Obama. ",
"If Obama got 71 percent in Nevada, that sure doesn’t gibe with Clinton getting 88 percent. ",
"But let’s put that aside. ",
"I have a different question. ",
"First, though, let’s leave Nevada and take a look at the national vote. ",
"Here’s a reminder of what the exit polls look like for 2012 and 2016:\n\nTrump received 46 percent of the popular vote in 2016 compared to 47 percent for Romney in 2012. ",
"That’s a loss of one percentage point. ",
"However, the exit poll for the white vote is based on a large, widely distributed sample, so it’s pretty reliable—and it shows that Trump lost two points of the white vote compared to Romney. ",
"This means that Trump must have gained roughly one point among all the other groups in order to come out only one point behind in the overall vote.",
"\n\nSo if Trump gained one point among the non-white vote, the only way he could have done substantially worse than 28 percent among Latinos is if he did substantially better among blacks and Asians. ",
"It’s the only way the arithmetic works. ",
"How likely is that?",
"\n\nThis is why I think the exit polls are probably right about the Latino vote. ",
"If they’re off by a lot, you have to come up with a plausible recount of all the other racial groups that adds up to the right total number. ",
"I don’t see how you can do that."
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"Q:\n\nMagento 2: How to Solve Defer parsing of JavaScript on CDN?",
"\n\nMy website in Production Mode & I set Javascript to be Merged. ",
"So we have only one JS file.",
"\nOn Speed related website it keep saying F grade on Defer Parsing of Javascript. ",
"I'm using CDN.",
"\n<script type=\"text/javascript\" src=\"cdn.domain.com/pub/static/_cache/merged/0285dfa79816d33a235c33875d3d2e57.min.js\"></script>\n\nHow to achieve mostly A Grade in this?",
"\nNeed to add async in Script Tag but How & Where?",
"\nAlready followed Defer parsing of JavaScript in Magento\n\nA:\n\nIn Observer method \n $response = $observer->getEvent()->getData('response');\n if (!",
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"锘? ",
"When you think about Custom Fitting Your Golf Clubs adidas yeezy boost 350 v2 noir , what do you think of first? ",
"Which aspects of Golf Clubs are important, which are essential, and which ones can you take or leave? ",
"You be the judge.",
"\n\nOnce you begin to move beyond basic background information, you begin to realize that there's more to Custom Fitting Your Golf Clubs than you may have first thought.",
"\n\nEvery golfer's physical capability and swing is distinctive. ",
"Many of today's best golf clubs can be custom fit for lie angle adidas yeezy boost 350 femme , shaft type and length, grip type and size. ",
"Custom fitting golf clubs involves several easy measurements and a quick self-assessment of your game. ",
"This custom golf club has become more than a fad that even not so professional golfers test its waters.",
"\n\nCustom fitting is the process for tailoring a golf club to suit your personal swing.",
"\n\nWhatever your level, with a custom golf club the aim is to ensure that if you do make a good swing, the club will be square at impact and should produce a straight shot.",
"\n\nCustom Golf Club How To's:\n\nTo custom fit your golf clubs adidas superstar 80s noir , you need to know: your gender (male or female); your height in your stockings or socks; the distance from your wrist (where it bends) to the floor with your shoes off; your age; your handicap or skill level; how fast you swing a golf club; what club you use at the 150 yard marker.",
"\n\nGender is used to put you into the correct fitting scale for custom golf clubs. ",
"The golf industry uses different definitions of \"standard length\" for men and women.",
"\n\nYour height and the distance in inches from your wrist to the floor are used together to determine the length of a custom golf club that is appropriate for you. ",
"The starting point for club length can vary up to 3 -inch ranging from ladies to men plus 1 -inch. ",
"A tall person with long arms can very easily require shorter clubs than an average height person with short arms. ",
"About 80 percent of golfers are standard length.",
"\n\nYour age, handicap (if you happen to have one), self-assessed skill level, estimated golf swing speed and club you use at the 150 yard marker are all combined to determined the custom golf club's shaft flex that is appropriate for you.",
"\n\nCustom fitting can fix your slice. ",
"If you slice the ball it means that the toe of the club is leading into the ball which opens the face of the club. ",
"That may be down to a swing fault adidas superstar 2 noir homme , but it could be because the club is too flat. ",
"So as part of the custom fitting process you can make the custom golf club more upright to help with this. ",
"This will mean that the toe of the club will be slightly off the ground at address to compensate.",
"\n\nThere are different methods of fitting according to custom golf club manufacturers but ultimately they are all trying to improve your game. ",
"To begin with simple measurements such as wrist-to-floor, height and hand size are taken and will point you to the right size club and at what angle it should be to the ground. ",
"Then you will take a club and hit some balls. ",
"One method is to place impact tape on the bottom of the custom golf club and an impact board on the floor.",
"\n\nAs you hit the ball the board will leave a mark on the tape showing whether the heel or the toe of the custom golf club is striking the floor first. ",
"The resulting mark will show whether the club face needs to be flatter or more upright. ",
"Then things get a bit more advanced. ",
"Analysis equipment can measure everything from your club speed to the side spin of the ball so that you can get maximum distance from your shot. ",
"You can also measure the launch angle of the ball, how much backspin you generate and impact efficiency - all which affect distance. ",
"The angle in which the custom golf club approaches the ball and the sidespin of it can help fix your game too.",
"\n\nRather than bringing down your old clubs, it might be better to start from scratch. ",
"It's a big misconception that custom fitting is only for good golfers. ",
"Anyone can benefit. ",
"That said adidas superstar pride pack pas cher , if you plan to upgrade a new set of clubs with the same manufacturer they may be able to adjust your old set to become custom golf clubs.",
"\n\nCustom fitting won't cure all your bad shots. ",
"Coaching will sort that out. ",
"But if you do make a good swing, then the custom golf club will arrive correctly at impact and should produce a straight shot at your target. ",
"That alone will save shots during a round.",
"\n\nLastly, custom fitting is often free of charge. ",
"But it is usually on the condition that you buy some clubs once you've been fitted. ",
"So it really depends on what your budget is. ",
"If you're prepared to buy a new set of clubs it's definitely worth getting fitted.",
"\n\nTake time to consider the points presented above. ",
"What you learn may help you overcome your hesitation to take action.",
"\nAuthor's Resource Box\n\nAuthor J. Brian Keith is a proud contributing author for\nGolf Equipment,\nExercise Equipment and enjoys writing about\nmany different topics. ",
"Please visit my other web sites\nfor Golf Articles and\nPicture Sharing.",
"\n\nArticle Source:\n\nRewards of internet game playing Parraz Cly\nSubmitted 2014-01-04 08:43:20\n\nWith internet book of ra adidas superstar w noir , players don't simply play this game to be able to win as it offers avid gamers an incomparable online gaming encounter. ",
"The internet edition of this game is available in different types and gamers can easily access the game and revel in. ",
"Most of the web casinos if not all of them provide this game that players may play but before a person sign up at any site, ."
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"/*\n * Copyright Amazon.com, Inc. or its affiliates. ",
"All Rights Reserved.",
"\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\").",
"\n * You may not use this file except in compliance with the License.",
"\n * A copy of the License is located at\n *\n * http://aws.amazon.com/apache2.0\n *\n * or in the \"license\" file accompanying this file. ",
"This file is distributed\n * on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either\n * express or implied. ",
"See the License for the specific language governing\n * permissions and limitations under the License.",
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"This has caused a few issues:\n *\n * ## GUARD in a function returning integer types\n *\n * There is no compiler error if `GUARD(nested_call());` is used in a function\n * that is meant to return integer type - not a error signal.",
"\n *\n * ```c\n * uint8_t s2n_answer_to_the_ultimate_question() {\n * GUARD(s2n_sleep_for_years(7500000));\n * return 42;\n * }\n * ```\n *\n * In this function we intended to return a `uint8_t` but used a\n * `GUARD` which will return -1 if the call fails. ",
"This can lead to\n * very subtle bugs.",
"\n *\n * ## `GUARD`ing a function returning any integer type\n *\n * There is no compiler error if `GUARD(nested_call());` is used\n * on a function that doesn't actually return an error signal\n *\n * ```c\n * int s2n_deep_thought() {\n * GUARD(s2n_answer_to_the_ultimate_question());\n * return 0;\n * }\n * ```\n *\n * In this function we intended guard against a failure of\n * `s2n_answer_to_the_ultimate_question` but that function doesn't\n * actually return an error signal. ",
"Again, this can lead to sublte\n * bugs.",
"\n *\n * ## Ignored error signals\n *\n * Without the `warn_unused_result` function attribute, the compiler\n * provides no warning when forgetting to `GUARD` a function. ",
"Missing\n * a `GUARD` can lead to subtle bugs.",
"\n *\n * ```c\n * int s2n_answer_to_the_ultimate_question() {\n * s2n_sleep_for_years(7500000); // <- THIS SHOULD BE GUARDED!!!",
"\n * return 42;\n * }\n * ```\n *\n * # Solution\n *\n * s2n_result provides a newtype declaration, which is popular in\n * languages like [Haskell](https://wiki.haskell.org/Newtype) and\n * [Rust](https://doc.rust-lang.org/rust-by-example/generics/new_types.html).",
"\n *\n * Functions that return S2N_RESULT are automatically marked with the\n * `warn_unused_result` attribute, which ensures they are GUARDed.",
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"Before fixing anything, you have to let go of your ego and acknowledge that your baby is ugly.",
"\nAfter launching a landing page optimization project, you inevitably will find chinks in the armor of your beautiful and perfect creations. ",
"Before fixing anything, you have to let go of your ego and acknowledge that your baby is ugly.",
"\n0 Comments"
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