bluuebunny/crossref_metadata_2025 huggingface dataset:
Hot embossing of discrete microparts
Authors: Kuduva‐Raman‐Thanumoorthy Ramasubramani , Yao Donggang
Published: May 2009

The hot embossing process has so far been developed mainly for replication of surface structures on thermoplastic substrates. Because of the lack of a through‐thickness action, fabrication of discrete microparts such as microgears is considered difficult. In this study, embossing molds having multiple microcavities were used in a through‐thickness embossing process with a rubber‐assisted ejection mechanism. Microparts made of HDPE and ABS with each part weighing approximately 1 and 1.4 mg, respectively, were produced. When in the mold, embossed microparts were intermittently connected to each other through thin residual films of a thickness approximately 20 μm. The residual films were detached from the microparts during a rubber‐assisted ejection stage. Because no resin delivery paths, e.g., runners and gates, are needed for microcavities on the multicavity embossing mold, this micropart fabrication process could replace micro injection molding in many applications. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers
X‐ray crystallographic studies of RNase A variants engineered at the most destabilizing positions of the main hydrophobic core: Further insight into protein stability
Authors: Kurpiewska Katarzyna , Font Josep , Ribó Marc , Vilanova Maria , Lewiński Krzysztof
Published: May 2009

To investigate the structural origin of decreased pressure and temperature stability, the crystal structure of bovine pancreatic ribonuclease A variants V47A, V54A, V57A, I81A, I106A, and V108A was solved at 1.4–2.0 Å resolution and compared with the structure of wild‐type protein. The introduced mutations had only minor influence on the global structure of ribonuclease A. The structural changes had individual character that depends on the localization of mutated residue, however, they seemed to expand from mutation site to the rest of the structure. Several different parameters have been evaluated to find correlation with decrease of free energy of unfolding ΔΔGT, and the most significant correlation was found for main cavity volume change. Analysis of the difference distance matrices revealed that the ribonuclease A molecule is organized into five relatively rigid subdomains with individual response to mutation. This behavior consistent with results of unfolding experiments is an intrinsic feature of ribonuclease A that might be surviving remnants of folding intermediates and reflects the dynamic nature of the molecule. Proteins 2009. © 2009 Wiley‐Liss, Inc.
Leaching behaviour of azoxystrobin and metabolites in soil columns
Authors: Ghosh Rakesh Kumar , Singh Neera
Published: May 2009

BACKGROUND: Azoxystrobin [methyl (E)‐2‐{2‐[6‐(2‐cyanophenoxy)pyrimidin‐4‐yloxy]phenyl}‐3‐methoxyacrylate], a strobilurin fungicide, is a broad‐spectrum, systemic and soil‐applied fungicide. Azoxystrobin has been registered for rice cultivation in India, but no information is available on its leaching behaviour in Indian soils. Therefore, leaching behaviour of azoxystrobin was studied in packed and intact soil columns under different irrigation regimes.

RESULTS: Azoxystrobin did not leach out of the 300 mm long columns after 126 and 362 mm rainfall. After percolating water equivalent to 362 mm rainfall, azoxystrobin leached down to 10–15 cm (packed columns) and 15–20 cm (intact columns) depth. Azoxystrobin was not detected in the leachate from the packed column leached with 94.5 mL water every week (140 mm rainfall per month) during the 28 weeks of the study period. However, azoxystrobin acid, formed by azoxystrobin degradation, was detected in the leachate after 18 weeks. At the end of the study, azoxystrobin had leached down to 5–10 cm depth, and only 60% of initially applied azoxystrobin was recovered from the soil.

CONCLUSION: The results indicate that azoxystrobin is fairly immobile in sandy loam soil, but azoxystrobin acid, a major metabolite of azoxystrobin, is quite mobile and may pose a threat of soil and groundwater contamination. Copyright © 2009 Society of Chemical Industry
Effect of deposition temperature on the microstructure and dielectric properties of Ba0.6Sr0.4TiO3 thin film deposited by radio‐frequency magnetron sputtering
Authors: Feng Zuyong , Chen Wei , Tan Ooi Kiang
Published: May 2009

Ba0.6Sr0.4TiO3 (BST) thin films with the thickness of 300 nm were deposited on Pt/SiO2/Si substrates at various deposition temperatures by RF magnetron sputtering technique, and their electric properties were investigated. Due to the high temperature annealing process at substrate temperature of 600 °C, well‐crystallized BST film was deposited. The dielectric constant and dielectric loss of the film deposited at 600 °C are 300 and 0.033 at 100 kHz, respectively. Due to the good crystallinity of the BST films deposited by RF magnetron sputtering, high dielectric tunability up to 39.2% is achieved at a low applied voltage of 5 V. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the experimental evidence for a departure from first‐order photochemical kinetics in bistable photochromic materials
Authors: Perciante César D. , Ferrari José A.
Published: May 2009

We discuss the apparent discrepancy between experimental results and the mono‐exponential decay law (which is characteristic of first‐order kinetics) for two‐state photochromic materials during activation and bleaching. Although deviations from first‐order kinetics could be expected for realistic samples, we show that the experimental data presented are actually compatible with a mono‐exponential decay law, and that the apparent discrepancy is attributable to an inappropriate description of the photo‐stationary state. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Private computing on public platforms: portable application security
Authors: Morris Thomas H. , Nair V. S. S.
Published: May 2009

As cellular telephones and high capacity memory sticks emerge as users' primary repository for data and applications, users will often run applications and display data on remote hosts. The biggest challenge in supporting this mobile data, mobile applications, stationary platform model is ensuring the security and privacy of user applications and data during execution on the remote platforms. Private computing on public platforms (PCPP) is a new application security approach which isolates applications to allow for secure and private execution on third party systems. This paper introduces PCPP and details its five basic building blocks which together ensure that the PCPP protected application's executable code, context, and data remain unaltered, unmonitored, and unrecorded before, during, and after exposure to the remote platform. Copyright © 2009 John Wiley & Sons, Ltd.
Lévy base correlation
Authors: Garcia João , Goossens Serge , Masol Viktoriya , Schoutens Wim
Published: May 2009

In this paper we investigate one‐factor models that extend the classical Gaussian copula model for pricing tranches of CDOs. We introduce Lévy base correlation and compare it to the classical Gaussian copula. The results of a historical study of both models on the iTraxx Europe Main dataset are presented. Our focus is on the base correlation surface and on the deltas of the tranches with respect to the index. We observe that the Lévy base correlation curve is much flatter than the corresponding Gaussian one. With respect to the deltas we conclude that the Lévy model produces larger deltas for the equity tranche and smaller deltas for the senior tranches. Copyright © 2009 Wilmott Magazine Ltd
Neutral Hexacoordinate Mixed Trichelate Silicon Complexes, Structure and Stereodynamics
Authors: Kertsnus‐Banchik Evgenia , Sela Einat , Wagler Jörg , Kalikhman Inna , Kost Daniel
Published: May 2009

Neutral hexacoordinate silicon trichelates have been synthesized by transsilylation, using two approaches: (i) The reaction of a dichloro‐monocyclic silane [2,5‐diphenyl‐2,5‐diazasilolidine] with two mol‐equivalents of O‐(trimethylsilyl)imidates. (ii) A dichloro‐dichelate reacted with one mol‐equivalent of the trimethylsilyl bidentate ligand precursor, bis(trimethylsilyl)benzhydroxamic acid imidate. The former group of complexes underwent inversion of configuration observed by the temperature dependence of the 1H NMR spectra and coalescence of signals due to diastereotopic N‐methyl‐ and CH2 groups, presumably by exchange of hydrazido chelate rings through a bicapped tetrahedral intermediate or transition state. The activation free energies range between 13.8 and 14.7 kcal·mol–1. Similar exchange in the hydroxamic acid derived complexes was not observed, because of much shorter and stronger dative N–Si bonds.
Use of Leukoreduced Blood Does Not Reduce Infection, Organ Failure, or Mortality Following Trauma
Authors: Englehart Michael S. , Cho S. David , Morris Melanie S. , Gee Arvin C. , Riha Gordon , Underwood Samantha J. , Differding Jerome A. , Luem Nick D. , Wiesberg Tracy T. , Boshkov Lynn K. , Schreiber Martin A.
Published: May 2009

Background

Leukoreduced (LR) blood has been demonstrated to reduce morbidity and mortality in high‐risk surgical patients, but not in trauma patients. The objective of the present study was to determine the effect of LR blood on morbidity and mortality. We hypothesized that the use of LR blood does not improve outcome in trauma patients.

Methods

This study was a retrospective cohort analysis of trauma patients transfused at a level 1 Trauma Center from 2001 to 2004. Between 2002 and 2003, LR blood was transfused. Prior to that time and subsequent to it, non‐leukoreduced (NLR) blood was transfused. This created two historical comparison groups. Data collected included patient demographics, units of blood transfused, intensive care unit (ICU) and hospital days, ventilator days, injury severity score (ISS), mortality, presence of acute respiratory distress syndrome (ARDS), and infectious complications. A multiple organ dysfunction syndrome (MODS) score was calculated.

Results

The distribution of patients was as follows: 284 patients received only NLR blood, 153 received only LR blood, and 58 received at least one unit of each. The mean ISS was similar (NLR: 26, LR: 24; P > 0.1). No differences were seen between groups in units transfused (6.2 vs. 5.5), number of ICU days (8.2 vs. 9.0), number of hospital days (16.9 vs. 18.6), number of ventilator days (6.1 vs. 5.7), incidence of ARDS (8.3% vs. 8.5%), MODS score (5.5 vs. 5.9), mortality rate (15.1% vs. 15.7%), or infection rate (36% vs. 30%) (P > 0.1).

Conclusions

This study represents the largest series comparing trauma patients who received either LR or standard blood transfusions. The use of LR blood does not improve outcome in trauma patients.
A Comparative Analysis of Ethical and Professional Challenges Experienced by Australian and U.S. Genetic Counselors
Authors: Alliman Sarah , McCarthy Veach Patricia , Bartels Dianne M. , Lian Fengqin , James Carolyn , LeRoy Bonnie S.
Published: May 2009

Ethical issues are an inevitable part of genetic counseling practice. Prior research identified 16 domains of ethical and professional challenges encountered by practitioners in the United States. In order to further validate these domains, the present study surveyed Australian genetic counselors. Sixty‐three respondents rated the frequency with which they encountered each domain, and 39 individuals also provided personal anecdotes detailing their most challenging ethical and professional dilemmas. Every domain reportedly was experienced by the Australian sample. However, there were some differences between Australian respondents and U.S. genetic counselors in frequencies of domain occurrence, and in strategies recommended for resolving them. Several anecdotes illustrate challenging situations due to Australia's geography, universal healthcare system, and the genetic counseling profession's evolution in that country. The results generally validate domains identified for U.S. genetic counselors. They further suggest that certain ethical issues may manifest in ways unique to a given country, and therefore they must be addressed in a culturally‐appropriate manner.
A Simplified Method to Distinguish Farmed (Salmo salar) from Wild Salmon: Fatty Acid Ratios Versus Astaxanthin Chiral Isomers
Authors: Megdal Peter Andrew , Craft Neal A. , Handelman Garry J.
Published: May 2009

Mislabeling of farmed and wild salmon sold in markets has been reported. Since the fatty acid content of fish may influence human health and thus consumer behavior, a simplified method to identify wild and farmed salmon is necessary. Several studies have demonstrated differences in lipid profiles between farmed and wild salmon but no data exists validating these differences with government‐approved methods to accurately identify the origin of these fish. Current methods are both expensive and complicated, using highly specialized equipment not commonly available. Therefore, we developed a testing protocol using gas chromatography (GC), to determine the origin of salmon using fatty acid profiles. We also compared the GC method with the currently approved FDA (United States Food and Drug Administration) technique that uses analysis of carotenoid optical isomers and found 100% agreement. Statistical validation (n = 30) was obtained showing elevated 18:2n‐6 (z = 4.56; P = 0.0001) and decreased 20:1n‐9 (z = 1.79; P = 0.07) in farmed samples. The method is suitable for wide adaptation because fatty acid methyl ester analysis is a well‐established procedure in labs that conduct analysis of lipid composition and food constituents. GC analysis for determining the origin of North American salmon compared favorably with the astaxanthin isomer technique used by the FDA and showed that the fatty acid 18:2n‐6 was the key indicator associated with the origin of these salmon.
Effect of ALA‐Enriched Food Supply on Cardiovascular Risk Factors in Males
Authors: Sioen Isabelle , Hacquebard Mirjam , Hick Gaëlle , Maindiaux Veronique , Larondelle Yvan , Carpentier Yvon A. , De Henauw Stefaan
Published: May 2009

The outcome of a total dietary approach using a wide range of n‐3 polyunsaturated fatty acids (PUFA) enriched food items on cardiovascular diseases called for further investigation. The study objective was to assess the effect of an ALA‐enriched food supply on cardiovascular risk factors in healthy males. A dietary intervention (single‐blind field trial with pre‐ and post‐measurements) was performed with 59 healthy males in a Belgian prison. Over a period of 12 weeks they were supplied with an n‐3 enriched diet (containing 6.5 g n‐3 PUFA/day compared to 4 g n‐3 PUFA/day in the standard diet) that was substituted for their regular diet, increasing mainly the α‐linolenic acid intake (from 2.8 to around 5 g/day). The results indicated no impact on subjects waist circumference, weight and BMI or systolic blood pressure. In contrast, the diastolic blood pressure significantly decreased during the intervention period (from 74.6 ± 8.2 to 71.7 ± 10.1 mmHg; P < 0.02). Moreover, the HDL‐cholesterol level increased in non‐smoking participants (from 0.97 ± 0.25 to 1.06 ± 0.23 mmol/l; P < 0.03). In summary, the study demonstrated that enrichment of commonly eaten food items with n‐3 fatty acids provides the opportunity to increase the n‐3 fatty acid intake and to decrease the n‐6/n‐3 ratio which results in a decreasing diastolic blood pressure and an increase of HDL‐cholesterol (in non‐smokers).
Differences in Sterol Composition between Male and Female Gonads of Dominant Limpet Species
Authors: Kawashima Hideki , Ohnishi Masao , Ogawa Satoshi
Published: May 2009

The present study demonstrated here for the first time that there are statistically significant differences in sterol composition between male and female gonads of the dominant limpets Cellana grata and Cellana toreuma, which are intertidal gastropods. Among 11 different sterols identified in this study, unusually high levels (11.2–19.8% of total sterols) of the Δ8‐sterols 5α‐cholest‐8‐en‐3β‐ol (zymostenol) and 5α‐cholesta‐8,24‐dien‐3β‐ol (zymosterol), which have never been reported in aquatic invertebrate gonads, were present in only the male gonads.
A late Holocene paleoclimatic history of Lake Tanganyika, East Africa
Authors: Stager J. Curt , Cocquyt Christine , Bonnefille Raymonde , Weyhenmeyer Constanze , Bowerman Nicole
Published: May 2009

A nearshore core (LT03-05) from the north basin of Lake Tanganyika provides diatom, pollen, and sedimentary time series covering the last ca. 3800 yr at 15–36 yr resolution. A chronology supported by 21 AMS dates on terrestrial and lacustrine materials allows us to account for ancient carbon effects on14C ages and to propose refinements of the region's climatic history. Conditions drier than those of today were followed after ca. 3.30 ka by an overall wetting trend. Several century-scale climate variations were superimposed upon that trend, with exceptionally rainy conditions occurring 1.70–1.40 ka, 1.15–0.90 ka, 0.70–0.55 ka, and 0.35–0.20 ka. Around 0.55–0.35 ka, during the Spörer sunspot minimum, drier conditions developed in the northern Tanganyika basin while more humid conditions were registered at Lakes Victoria and Naivasha. This indicates significant variability in the nature and distribution of near-equatorial rainfall anomalies during much of the Little Ice Age.
The effects of a low-sodium base-producing diet including red meat compared with a high-carbohydrate, low-fat diet on bone turnover markers in women aged 45–75 years
Authors: Nowson Caryl A. , Patchett Annabelle , Wattanapenpaiboon Naiyana
Published: May 2009

A randomised, parallel-design dietary intervention study was conducted in women (aged 45–75 years) with prehypertension or stage 1 hypertension. The aim was to compare the effects on bone turnover of a low-Na base-producing (LNAB) Dietary Approaches to Stop Hypertension (DASH)-type diet (including six serves lean red meat/week) with a high-carbohydrate low-fat (HCLF) diet with a higher acid load (both >800 mg dietary Ca/d). Fasting serum bone markers (baseline and week 14) and 24 h urinary electrolyte excretion (baseline, weeks 4, 8, 12 and 14) were measured. After the intervention period, the LNAB group (n46) had a fall of 26 (sem6) % (P < 0·0001) in urinary Na, an increase in K excretion (6·8 (sem3·6) mmol/d;P = 0·07) and, compared with the HCLF group (n49), a greater reduction in urinary Ca excretion by 0·7 (sem0·3) mmol/d. Serum 25-hydroxyvitamin D, intact parathyroid hormone and osteocalcin did not change, and both groups had a similar increase of 23 (sem5) % (P < 0·0001) in C-terminal telopeptide of type I collagen. The HCLF group had an 11 (sem4) % increase (P = 0·003) in N-terminal propeptide, type I procollagen, which could indicate an increased rate of bone turnover. The fall in urinary Ca with the lower-Na lower-acid load diet is likely to have long-term beneficial effects on bone. As bone resorption was not different between the two dietary patterns with relatively high Ca intake, the effect on bone health of a dietary pattern with a lower acid load warrants further study on a lower Ca intake.
Growth and nutrient intake among very-low-birth-weight infants fed fortified human milk during hospitalisation
Authors: Henriksen Christine , Westerberg Ane C. , Rønnestad Arild , Nakstad Britt , Veierød Marit B. , Drevon Christian A. , Iversen Per O.
Published: May 2009

Postnatal growth failure in preterm infants is due to interactions between genetic and environmental factors, which are not fully understood. We assessed dietary supply of nutrients in very-low-birth-weight (VLBW, < 1500 g) infants fed fortified human milk, and examined the association between nutrient intake, medical factors and growth during hospitalisation lasting on average 70 d. We studied 127 VLBW infants during the early neonatal period. Data were obtained from medical records on nutrient intake, growth and growth-related factors. Extra-uterine growth restriction was defined as body weight < 10th percentile of the predicted value at discharge. Using logistic regression, we evaluated nutrient intake and other relevant factors associated with extra-uterine growth restriction in the subgroup of VLBW infants with adequate weight for gestational age at birth. The proportion of growth restriction was 33 % at birth and increased to 58 % at discharge from hospital. Recommended values for energy intake (>500 kJ/kg per d) and intra-uterine growth rate (15 g/kg per d) were not met, neither in the period from birth to 28 weeks post-conceptional age (PCA), nor from 37 weeks PCA to discharge. Factors negatively associated with growth restriction were energy intake (Ptrend = 0·002), non-Caucasian ethnicity (P = 0·04) and weight/predicted birth weight at birth (Ptrend = 0·004). Extra-uterine growth restriction is common in VLBW infants fed primarily fortified human milk. Currently recommended energy and nutrient intake for growing preterm infants was not achieved. Reduced energy supply and non-Caucasian ethnicity were risk factors for growth restriction at discharge from hospital.
Late Cretaceous–Early Eocene tectonic development of the Tethyan suture zone in the Erzincan area, Eastern Pontides, Turkey
Authors: RICE SAMUEL P. , ROBERTSON ALASTAIR H. F. , USTAÖMER TIMUR , İNAN NURDAN , TASLI KEMAL
Published: May 2009

Six individual tectonostratigraphic units are identified within the İzmir–Ankara–Erzincan Suture Zone in the critical Erzincan area of the Eastern Pontides. The Ayıkayası Formation of Campanian–Maastrichtian age is composed of bedded pelagic limestones intercalated with polymict, massive conglomerates. The Ayıkayası Formation conformably overlies the Tauride passive margin sequence in the Munzur Mountains to the south and is interpreted as an underfilled foredeep basin. The Refahiye Complex, of possible Late Cretaceous age, is a partial ophiolite composed of ~75% (by volume) serpentinized peridotite (mainly harzburgite), ~20% diabase and minor amounts of gabbro and plagiogranite. The complex is interpreted as oceanic lithosphere that formed by spreading above a subduction zone. Unusual screens of metamorphic rocks (e.g. marble and schist) locally occur between sheeted diabase dykes. The Upper Cretaceous Karayaprak Mélange exhibits two lithological associations: (1) the basalt + radiolarite + serpentinite association, including depleted arc-type basalts; (2) the massive neritic limestone + lava + volcaniclastic association that includes fractionated, intermediate-composition lavas, and is interpreted as accreted Neotethyan seamount(s). The several-kilometre-thick Karadağ Formation, of Campanian–Maastrichtian age, is composed of greenschist-facies volcanogenic rocks of mainly basaltic to andesitic composition, and is interpreted as an emplaced Upper Cretaceous volcanic arc. The Campanian–Early Eocene Sütpınar Formation (~1500 m thick) is a coarsening-upward succession of turbiditic calcarenite, sandstone, laminated mudrock, volcaniclastic sedimentary rocks that includes rare andesitic lava, and is interpreted as a regressive forearc basin. The Late Paleocene–Eocene Sipikör Formation is a laterally varied succession of shallow-marine carbonate and siliciclastic lithofacies that overlies deformed Upper Cretaceous units with an angular unconformity. Structural study indicates that the assembled accretionary prism, supra-subduction zone-type oceanic lithosphere and volcanic arc units were emplaced northwards onto the Eurasian margin and also southwards onto the Tauride (Gondwana-related) margin during Campanian–Maastrichtian time. Further, mainly southward thrusting took place during the Eocene in this area, related to final closure of Tethys. Our preferred tectonic model involves northward subduction, supra-subduction zone ophiolite genesis and arc magmatism near the northerly, Eurasian margin of the Mesozoic Tethys.
Proof of a conjecture of Ramanujan
Authors: Atkin A. O. L.
Published: May 2009

We write

and

so thatp(n) is the number of unrestricted partitions ofn. Ramanujan [1] conjectured in 1919 that ifq= 5, 7, or 11, and 24m≡ 1 (modqn), then p(m) ≡ 0 (modqn). He proved his conecture forn= 1 and 2†, but it was not until 1938 that Watson [4] proved the conjecture forq= 5 and alln, and a suitably modified form forq= 7 and alln. (Chowla [5] had previously observed that the conjecture failed forq= 7 andn= 3.) Watson's method of modular equations, while theoretically available for the caseq= 11, does not seem to be so in practice even with the help of present-day computers. Lehner [6, 7] has developed an essentially different method, which, while not as powerful as Watson's in the cases where Γ0(q) has genus zero, is applicable in principle to all primesqwithout prohibitive calculation. In particular he proved the conjecture forq= 11 andn= 3 in [7]. Here I shall prove the conjecture forq= 11 and alln, following Lehner's approach rather than Watson's. I also prove the analogous and essentially simpler result forc(m), the Fourier coefficient‡ of Klein's modular invariantj(τ) as
Compact linear operators from an algebraic standpoint
Authors: Bonsall F. F.
Published: May 2009

Let B(X) denote the Banach algebra of all bounded linear operators on a Banach space X. Let t be an element of B(X), and let edenote the identity operator on X. Since the earliest days of the theory of Banach algebras, ithas been understood that the natural setting within which to study spectral properties of t is the Banach algebra B(X), or perhaps a closed subalgebra of B(X) containing t and e. The effective application of this method to a given class of operators depends upon first translating the data into terms involving only the Banach algebra structure of B(X) without reference to the underlying space X. In particular, the appropriate topology is the norm topology in B(X) given by the usual operator norm. Theorem 1 carries out this translation for the class of compact operators t. It is proved that if t is compact, then multiplication by t is a compact linear operator on the closed subalgebra of B(X) consisting of operators that commute with t.
A new class of Hadamard matrices
Authors: Spence E.
Published: May 2009

A Hadamard matrixHis an orthogonal square matrix of ordermall the entries of which are either + 1 or - 1; i. e.

whereH′denotes the transpose ofHandImis the identity matrix of orderm. For such a matrix to exist it is necessary [1] that

It has been conjectured, but not yet proved, that this condition is also sufficient. However, many values ofmhave been found for which a Hadamard matrix of ordermcan be constructed. The following is a list of suchm(pdenotes an odd prime).
On Riemann surfaces with maximal automorphism groups
Authors: Lehner Joseph , Newman Morris
Published: May 2009

Let S be a closed Riemann surface of genus

g > 1,

so that Ŝ, the universal covering surface of S, is hyperbolic. We can then uniformize S by a discrete, nonabelian group Γ1 of Möbius transformations of the upper half-plane ℋ. It follows that N1 = NΩ(Γ1) is discrete; here N1is the normalizer of Γ in Ω, the group of (conformal) automorphisms of ℋ. An automorphism of S can be lifted to a coset of Nl/Γl. Hence C(S), the group of automorphisms of S, is isomorphic to Nl/Γ1. The order of C = C(S) equals the index of Γ1 in N1, which in turn equals ⃒Γ1⃒ / ⃒Nl⃒, where ⃒Nl⃒ is the hyperbolic area of a fundamental region of Nl. Since Γ1 uniformizes a surface, we have ⃒Γ1⃒ = 4π(g – 1), while, by Siegel's results [7], ⃒N1 ⃒ ≧ π/21 and N1 can only be the triangle group (2, 3, 7). Hence in all cases the order of C(S) is at most 84(g–1), an old result of Hurwitz [1]. The surfaces that permit a maximal automorphism group (= automorphism group of maximum order) can therefore be obtained by studying the finite factor groups of (2, 3, 7). Such a treatment, purely algebraic in nature, has been promised by Macbeath [5].
The translational hull of a completely 0-simple semigroup
Authors: Petrich Mario
Published: May 2009

The translational hull Ω(S) of a semigroupSplays an important role in the theory of ideal extensions of semigroups. In fact, every ideal extension ofSby a semigroupTwith zero can be constructed using a certain partial homomorphism ofT\0into Ω(S); a particular case of interest is whenSis weakly reductive (see §4.4 of [3], [2], [7]). A theorem of Gluskin [6, 1.7.1] states that ifSis a weakly reductive semigroup and a densely embedded ideal of a semigroupQ, thenQand Ω(S) are isomorphic. A number of papers of Soviet mathematicians deal with the abstract characteristic (abstract semigroup, satisfying certain conditions, isomorphic to the given semigroup) of various classes of (partial) transformation semigroups in terms of densely embedded ideals (see, e.g., [4]). In many of the cases studied, the densely embedded ideal in question is a completely 0-simple semigroup, so that Gluskin's theorem mentioned above applies. This enhances the importance of the translational hull of a weakly reductive, and in particular of a completely 0-simple semigroup. Gluskin [5] applied the theory of densely embedded ideals (which are completely 0-simple semigroups) also to semigroups and rings of endomorphisms of a linear manifold and to certain classes of abstract rings.
An identity for certain Dirichlet series
Authors: Berndt B. C.
Published: May 2009

In deriving the approximate functional equation for certain Dirichlet series, one first establishes an identity for the function in terms of a partial sum of the series (e.g. see [1] and [2]). It is the purpose of this note to give a short proof of this identity for Hecke's Dirichlet series [1]. The proof is valid with only a few minor changes for the identity given by Chandrasekharan and Narasimhan [2, Lemma 2] for a much larger class of Dirichlet series. However, the brevity of the paper would be lost if we introduced the necessary terminology and notation.
Residuation theory and matrix multiplication on orthomodular lattices
Authors: Bevis J. H. , Martin C. K.
Published: May 2009

In this paper we consider mappings induced by matrix multiplication which are defined on lattices of matrices whose coordinates come from a fixed orthomodular lattice L (i.e. a lattice with an orthocomplementation denoted by ′ in which a ≦ b ⇒ a ∨ (a′ ∧ b) = b). will denote the set of all m × n matrices over L with partial order and lattice operations defined coordinatewise. For conformal matrices A and B the (i,j)th coordinate of the matrix product AB is defined to be (AB)ij = Vk(Aik ∧ BkJ). We assume familiarity with the notation and results of [1]. is an orthomodular lattice and the (lattice) centre of is defined as , where we say that A commutes with B and write . In § 1 it is shown that mappings from into characterized by right multiplication X → XP (P ∈ ) are residuated if and only if p ∈ ℘ (). (Similarly for left multiplication.) This result is used to show the existence of residuated pairs. Hence, in § 2 we are able to extend a result of Blyth [3] which relates invertible and cancellable matrices (see Theorem 3 and its corollaries). Finally, for right (left) multiplication mappings, characterizations are given in § 3 for closure operators, quantifiers, range closed mappings, and Sasaki projections.
On the loci |f(z)| = R, f(z) Entire
Authors: Hejhal Dennis A.
Published: May 2009

The following result is found quite widely. Suppose f(z) is a non-constant entire function such that |f(z)| = 1 along |z| = 1. Then, f (z) has form czm, |c| = 1, m ≧ 1. See Ahlfors [1, p. 172, exercise 3], Dienes [4, p. 172, exercise 23], Hille [6, p. 317, exercise 2]. It is natural to inquire about a generalization of this result.
Lattice subgroups of free congruence groups
Authors: Mason A. W.
Published: May 2009

Let Г(1) denote the homogeneous modular group of 2 × 2 matrices with integral entries and determinant 1. Let (1) be the inhomogeneous modular group of 2 × 2 integral matrices of determinant 1 in which a matrix is identified with its negative. (N), the principal congruence subgroup of level N, is the subgroup of (1) consisting of all T ∈ (1) for which T ≡ ± I (mod N), where N is a positive integer and I is the identity matrix. A subgroup of (1) is said to be a congruence group of level N if contains (N) and N is the least such integer. Similarly, we denote by Г(N) the principal congruence subgroup of level N of Г(1), consisting of those T∈(1) for which T ≡ I (mod N), and we say that a sub group of Г(1) is a congruence group of level N if contains Г (N) and N is minimal with respect to this property. In a recent paper [9] Rankin considered lattice subgroups of a free congruence subgroup of rank n of (1). By a lattice subgroup of we mean a subgroup of which contains the commutator group . In particular, he showed that, if is a congruence group of level N and if is a lattice congruence subgroup of of level qr, where r is the largest divisor of qr prime to N, then N divides q and r divides 12. He then posed the problem of finding an upper bound for the factor q. It is the purpose of this paper to find such an upper bound for q. We also consider bounds for the factor r.
Remarks on the asymptotic behaviour of perturbed linear systems
Authors: Wong James S. W.
Published: May 2009

We are here concerned with following result of Trench:

Theorem. (Trench [5]). Let v1 and v2 be two linearly independent solutions of the differential equation

where a(t) is continuous on [0, ∞), and let b(t) be a continuous function of t for t ≧ 0 satisfying

where m(t) = max {|v1(t)|2, |v2(t)|2}. Then, if α1and α2are two arbitrary constants, there exists a solution u of

which can be written in the form

,

with

fori = 1, 2.
Some triple trigonometrical series
Authors: Tranter C. J.
Published: May 2009

This paper considers the determination of the coefficients in two sets of triple trigonometrical series and shows that these can be obtained in closed form. The series considered are special cases of some triple series in Jacobi polynomials studied by K. N. Srivastava [1]. Srivastava, however, shows that the problem for the more general series can be reduced to the solution of a Fredholm integral equation of the second kind and he does not discuss special cases which may lead to closed form solutions.
A variance method in combinatorial number theory
Authors: Anderson Ian
Published: May 2009

Let s = s(a1, a2,...., ar) denote the number of integer solutions of the equation

subject to the conditions

the ai being given positive integers, and square brackets denoting the integral part. Clearly s (a1,..., ar) is also the number s = s(m) of divisors of which contain exactly λ prime factors counted according to multiplicity, and is therefore, as is proved in [1], the cardinality of the largest possible set of divisors of m, no one of which divides another.
Some arithmetical functions in finite fields
Authors: Cohen Stephen D.
Published: May 2009

In this paper, we investigate various “arithmetical” functions associated with the factorisation of polynomials in GF[q, X1, …, Xk], where k ≥ 1 and GF[q]is the finite field of order q. We shall assume throughout that all polynomials discussed are non-zero and have been normalised by selecting one polynomial from each equivalence class with respect to multiplication by non-zero elements of GF[q]. The constant polynomial will be denoted by 1. With this normalisation, GF[q, X1, …, Xk] becomes a unique factorisation domain. When k = 1, normalisation is achieved by considering only monic polynomials. By the degree of a polynomial A(X1, …, Xk) will be understood the ordered set (m1, …, mk), where m1 is the degree of A(X1, …, Xk) in X1,(i = 1, …, k).
On the order of the Sylow subgroups of the automorphism group of a finite group
Authors: Hyde K. H.
Published: May 2009

Given any finite groupG, we wish to determine a relationship between the highest power of a primepdividing the order ofG, denoted by |G|p, and |A(G)|p, whereA(G)is the automorphism group ofG. It was shown by Herstein and Adney [8] that |A(G)|p≧ p whenever|G|p= ≧P2. Later Scott [16] showed thatA(G)p≧P2. For the special case whereGis abelian, Hilton [9] proved that Adney [1] showed that this result holds if a Sylow p-subgroup ofGis abelian, and gave an example where|G|p= p4and|A(G)|P=p2. We are able to show in Theorem 4.5 that, if|G|p= ≧ p5, then|A(G)| = ≧ p3.
The number of irreducible tournaments
Authors: Wright E. M.
Published: May 2009

An n-tournament is a set of n labelled points, each pair A, B of which is joined either by the oriented line AB or by the oriented line BA. There are N = n(n –1)/2 such pairs and so Fn different n-tournaments, where Fn = 2N. A tournament is reducible if the points can be separated into two non-empty subsets and ℬ, such that every line joining a point in to a point in ℬ is directed towards the point in ℬ. Rado [3] showed that an irreducible tournamentis strongly connected; i.e. for every ordered pair of points A, B, there is a sequence of correctly oriented lines AC1, C1C2, …, ChB in the tournament, and conversely that a strongly connected tournament is irreducible.
On univalent polynomials
Authors: Brannan David A.
Published: May 2009

Let Pn be the class of normalised polynomials of the form

of degree n which are univalent in U = {|z| < 1}. In this note we discuss the coefficients of polynomials in Pn and in some of its subclasses.
Note on a partition theorem
Authors: Andrews George E.
Published: May 2009

In [1, p. 130] the following partition theorem was deduced from a general theorem concerning the limit of a recurrent sequence.
The wave, Laplace, and heat equations and related transforms
Authors: Dettman J. W.
Published: May 2009

This paper is concerned with three basic transforms

The first of these has been studied by Widder [1], who points out that f(t) can be interpreted as the temperature u(0, t) on the time axis, where u(x, t) is the solution of the heat equation withsymmetric initial temperature u(x, 0) = g(|x|). The second has also been studied by Widder [2], where it is pointed out that f(t) can be interpreted as the value of the harmonic function u(x, t) on the t-axis arising from the boundary data u(x, 0) = g(|x|).
A note on Köthe spaces
Authors: Các Nguyen Phuong
Published: May 2009

LetEbe a locally compact space which can be expressed as the union of an increasing sequence of compact subsetsKn(n=1, 2, …) and let μ be a positive Radon measure onE. Ω is the space of equivalence classes of locally integrable functions onE. We denote the equivalence class of a function f byand ifis an equivalence class then f denotes any function belonging to f. Provided with the topology defined by the sequence of seminorms

Ω is a Fréchet space. The dual of Ω is the space φ of equivalence classes of measurable, p.p. bounded functions vanishing outside a compact subset ofE. For a subset Γ of Ω, the collection Λ of all∊Ω, such that for eachg∊Γ the productfgis integrable, is called a Köthe space and Γ is said to be the denning set of Λ. The Köthe space Λxwhich has Λ as a denning set is called the associated Kothe space of Λ. Λ and Λxare put into duality by the bilinear form
Concerning intrinsic topologies on Boolean algebras and certain bicompactly generated lattices
Authors: Atherton C. R.
Published: May 2009

This paper may be regarded as a continuation of the investigations begun in [2]; certain intrinsic lattice topologies are studied, especially the order and ideal topologies in Boolean algebras, bicompactly generated lattices, and other more general structures. The results of [1], [2], and [3] are shown to be closely related. It is proved that the ideal topology on any Boolean algebra has a closed subbase consisting of all sublattices, whereas the order topology on an atomic Boolean algebra has a closed subbase consisting of all sub-complete lattices. It is also shown that the order topology on an atomic Boolean algebra is autouniformizable (in the sense defined by Rema [3]) and, if the ground set is infinite, strictly coarser than the ideal topology. The conditions Cl and C3 on a lattice, introduced by Kent [1], are shown to be slightly stronger than the condition “ bicompactly generated ”, and in complete lattices, where these conditions are satisfied, the order topology is shown to be coarser than the ideal topology.
The quotient semigroup of a semigroup that is a semilattice of groups
Authors: McMorris F. R.
Published: May 2009

Let Q(S) denote the maximal right quotient semigroup of the semigroup S as defined in [4]. In this paper, we initiate a study of Q(S) when S is a semilattice of groups. A structure theorem for such semigroups is given by Theorem 4.11 of [2].
Conditioning maps on orthomodular lattices
Authors: Foulis D. J. , Randall C. H.
Published: May 2009

Let (χ Σ, μ) be a probability space, so that X is a non-empty set, Σ is a Boolean a-algebra of subsets of X, and μ is a probability measure defined on Σ. If D Ε S is such that μ(D)≠0, then one traditionally associates with D a new probability measure μD, called the conditional probability measure determined by D, and defined by μD(E)= μ(D∩E)/μ(D), for all EΕΣ.
Automorphisms of compact non-orientable Riemann surfaces
Authors: Singerman D.
Published: May 2009

Using the definition of a Riemann surface, as given for example by Ahlfors and Sario, one can prove that all Riemann surfaces are orientable. However by modifying their definition one can obtain structures on non-orientable surfaces. In fact nonorientable Riemann surfaces have been considered by Klein and Teichmüller amongst others. The problem we consider here is to look for the largest possible groups of automorphisms of compact non-orientable Riemann surfaces and we find that this throws light on the corresponding problem for orientable Riemann surfaces, which was first considered by Hurwitz [1]. He showed that the order of a group of automorphisms of a compact orientable Riemann surface of genus g cannot be bigger than 84(g – 1). This bound he knew to be attained because Klein had exhibited a surface of genus 3 which admitted PSL (2, 7) as its automorphism group, and the order of PSL(2, 7) is 168 = 84(3–1). More recently Macbeath [5, 3] and Lehner and Newman [2] have found infinite families of compact orientable surfaces for which the Hurwitz bound is attained, and in this paper we shall exhibit some new families.
Crack-like imperfections in a spherical shell
Authors: Sih G. C. , Dobreff P. S.
Published: May 2009

In structures having high strength-to-weight ratios such as those used in aerospace applications, the presence of mechanical imperfections can reduce the capability of the structure to perform as intended. Thus, it becomes essential to account for the localized intensification of the stresses around through or surface cracks, which might trigger fracture under applied loads. This type of study is currently receiving great research emphasis.
Kleinian groups with unbounded limit sets
Authors: Beardon A. F.
Published: May 2009

The easiest way to construct automorphic functions is by means of the Poincaré series. If G is a Kleinian group with ∞ an ordinary point of G and if k ≧ 4, then

where Vz=(az+b)/(cz+d) and ad-bc=1. The convergence of this series is the crucial step in showing that the Poincaré series converges and is an automorphic form on G If ∞ is a limit point of ∞ the series in (1) may diverge and one can derive automorphic forms on ∞ from the Poincaré series of some conjugate group. These constructions are described in greater detail in /3, pp. 155–165].
On the locally antisimple radical
Authors: Stewart Patrick N.
Published: May 2009

In this paper we presuppose a familiarity with the terminology and the basic results of radical theory, all of which can be found in Divinsky [2].
A note on the radical of row-finite matrices
Authors: Slover Rebecca
Published: May 2009

Let Rbe an associative ring, Jan infinite index set, and Rj the ring of all J × J row-finite matrices over R. The Jacobson radical of Rwill be denoted by Γ(R).
On the spectrum of a linear operator
Authors: Dollinger Michael B. , Oberai Kirti K.
Published: May 2009

In the definition of the spectrum of a linear operator, it is customary to assume that the underlying space is complete. However there are occasions for which it is neither desirable nor necessary to assume completeness in order to obtain a spectral theory for an operator; for example, completeness is not needed in the Riesz theory of a compact operator (see e.g. [1: XI. 3]). Several non-equivalent definitions for the spectrum of an operator on normed spaces have appeared in the literature. We shall discuss the relationship among these definitions and some of the difficulties that arise in applying these definitions to obtain a spectral theory.
Boundary value problems of singular elliptic partial differential equations
Authors: Lo Chi Yeung
Published: May 2009

In a recent paper [6], this author has extended the method of the kernel function [1] to the boundary value problems of the generalized axially symmetric potentials

This method can also be applied to a more general class of singular differential equations, namely

or, equivalently,

We shall derive in the sequel explicit formulas for the Dirichlet problems of (1.1) in the first quadrant of the x-y plane in terms of sufficiently smooth boundary data, and obtain an error-bound for their approximate solutions. We shall also indicate how the Neumann problem can be solved.
Compactness and ordinals
Authors: Knight C. J.
Published: May 2009

If p and q are cardinal numbers and E is a topological space, then the following property may or may not hold:

Every cover of Eby fewer than q open sets has a subcover by fewer than pof them. (1)

Clearly these properties, for various numbers p and q, are far from being independent; in this paper, we investigate some of the interrelationships between them.
On two-sided artinian quotient rings
Authors: Smith P. F.
Published: May 2009

Djabali [1] has proved that, if R is a right and left noetherian ring with an identity and if the proper prime ideals of R are maximal, then R has a right and left artinian two-sided quotient ring. Robson [5, Theorem 2.11] and Small [6, Theorem 2.13] have proved independently that, if Ris a commutative noetherian ring, then Rhas an artinian quotient ring if and only if the prime ideals of Rthat belong to the zero ideal are all minimal. We shall generalise these results by proving the

Theorem. Let R be a right and left noetherian ring with a regular element. Then R has a right and left artinian two-sided quotient ring if and only if each prime ideal of R consisting of zero–divisors is minimal.
Least squares approximations for dual trigonometric series
Authors: Kelman Robert B. , Koper Chester A.
Published: May 2009

A systematic and easily automated least squares procedure, not using integral equations or special functions, is presented for approximating the solutions of general dual trigonometric equations. This is desirable, since current analytic methods apply only to special equations, require the use of integral equation and special function theory, and do not lend themselves easily to numerical work; see, e.g. [1, 2, 6, 8, 9,10, 11, 12, 13, 14, 15, 16, 17].
On triple trigonometrical equations
Authors: Singh B. M.
Published: May 2009

An exact solution of triple trigonometrical equations is obtained by using the finiteHilbert transform. The solution of these equations is used to solve a two-dimensional electrostatic problem. The problem of determining the electrostatic potential due to two parallel coplanar strips of equal length, charged to equal and opposite potentials, each parallel to and equidistant from an earthed strip, is considered. Both the charged strips lie along the x-axis and they are equally spaced with respect to the y-axis. Finally the expression for the surface charge density (per unit depth) of the strip is derived
Semigroups of non-negative integral matrices
Authors: Cordes Craig M.
Published: May 2009

In [1], Pall proved an interesting result on a certain class of 2 × 2 integral matrices. He showed that the semigroup of 2 × 2 matrices of determinant 1 and non-negative entries contains exactly 2 primes , and every other non-unit is expressible uniquely as products of these primes. Before formally stating this result, we need some notation. Let Gn denote the semigroup of n × n matrices with determinant 1 and nonnegative integral entries, In the n × n identity matrix, the n × n matrix with a 1 as its (i, j) element and zeros elsewhere, and let . When the dimension is clear, we shall drop the superscripts.