bluuebunny/crossref_metadata_2025 huggingface dataset:
Evaluating Perioperative Nursing in Finland: An Initial Validation of Perioperative Nursing Data Set Outcomes
Authors: Lamberg Eija , Salanterä Sanna , Junttila Kristiina
Published: July 2013

The current Finnish version of AORN's Perioperative Nursing Data Set consists of nursing diagnoses and interventions but not outcomes. During the early Finnish validation phase, researchers determined that almost half of the outcomes listed in the AORN version were impossible to measure in Finland. We conducted this study to determine the applicability of the nursing outcomes identified in the Perioperative Nursing Data Set, 2nd ed Rev, and to test the use of the outcomes by exploring the relevance of the outcome indicators for eight selected outcomes. We collected the data by using two surveys with structured questionnaires that were provided to an expert panel of nurses and physicians. Panel members found that most of the outcomes were acceptable for use in Finnish perioperative care; however, further validation of the outcome indicators is needed to develop tools to support nurses in their attempts to reach desirable nursing‐sensitive outcomes for patients.
PepBind: A Comprehensive Database and Computational Tool for Analysis of Protein–Peptide Interactions
Authors: Das Arindam Atanu , Sharma Om Prakash , Kumar Muthuvel Suresh , Krishna Ramadas , Mathur Premendu P.
Published: July 2013

Protein–peptide interactions, where one partner is a globular protein (domain) and the other is a flexible linear peptide, are key components of cellular processes predominantly in signaling and regulatory networks, hence are prime targets for drug design. To derive the details of the protein–peptide interaction mechanism is often a cumbersome task, though it can be made easier with the availability of specific databases and tools. The Peptide Binding Protein Database (PepBind) is a curated and searchable repository of the structures, sequences and experimental observations of 3100 protein–peptide complexes. The web interface contains a computational tool, protein inter-chain interaction (PICI), for computing several types of weak or strong interactions at the protein–peptide interaction interface and visualizing the identified interactions between residues in Jmol viewer. This initial database release focuses on providing protein–peptide interface information along with structure and sequence information for protein–peptide complexes deposited in the Protein Data Bank (PDB). Structures in PepBind are classified based on their cellular activity. More than 40% of the structures in the database are found to be involved in different regulatory pathways and nearly 20% in the immune system. These data indicate the importance of protein–peptide complexes in the regulation of cellular processes. PepBind is freely accessible at http://pepbind.bicpu.edu.in/.
A Computational Workflow to Identify Allele-Specific Expression and Epigenetic Modification in Maize
Authors: Wei Xiaoxing , Wang Xiangfeng
Published: July 2013

Allele-specific expression refers to the preferential expression of one of the two alleles in a diploid genome, which has been thought largely attributable to the associated cis-element variation and allele-specific epigenetic modification patterns. Allele-specific expression may contribute to the heterosis (or hybrid vigor) effect in hybrid plants that are produced from crosses of closely-related species, subspecies and/or inbred lines. In this study, using Illumina high-throughput sequencing of maize transcriptomics, chromatic H3K27me3 histone modification and DNA methylation data, we developed a new computational framework to identify allele-specifically expressed genes by simultaneously tracking allele-specific gene expression patterns and the epigenetic modification landscape in the seedling tissues of hybrid maize. This approach relies on detecting nucleotide polymorphisms and any genomic structural variation between two parental genomes in order to distinguish paternally or maternally derived sequencing reads. This computational pipeline also incorporates a modified Chi-square test to statistically identify allele-specific gene expression and epigenetic modification based on the Poisson distribution.
The impact of sourcing enterprise system use and work process interdependence on sourcing professionals’ job outcomes
Authors: Rai Arun , Hornyak Rob
Published: July 2013

We examine sourcing professionals’ work context to conceptualize how they use sourcing enterprise systems (SESs) and to understand when SES use results in positive/negative job outcomes. We differentiate between SES use for supplier selection and supplier governance, identify sourcing professionals’ work process interdependence as a moderator for the impacts of SES use on job satisfaction, and suggest job satisfaction mediates the impacts of SES use on job performance. We conducted a field study of sourcing professionals’ SES use at one of the largest consumer product companies in the United States, which has implemented an SES to innovate its sourcing professionals’ work processes. Based on our analysis of the survey and qualitative data we collected, we found the impacts of both types of SES use (1) to be negative on job satisfaction when work process interdependence was high, (2) to be positive on job satisfaction when work process interdependence was low, and (3) to be mediated by job satisfaction for job performance. We discuss the implications of our findings for the literature at the intersection of information systems and operations management as well as for the information technology enabled innovation of sourcing processes and, more generally, complex business processes.
The relationship between information technology capability, inventory efficiency, and shareholder wealth: A firm‐level empirical analysis
Authors: Mishra Saurabh , Modi Sachin B. , Animesh Animesh
Published: July 2013

Inventories represent an important strategic resource for firms, with implications for shareholder wealth. As such, firms expend considerable effort in managing their inventories efficiently. Among other factors, information technology (IT) capability can play an important role in enabling inventory efficiency and financial performance. However, insight into the chain‐of‐effects linking IT capability, inventory efficiency, and stock market returns and risk remains limited. In this paper, we provide a conceptual model outlining the relationships between these constructs. Next, we evaluate the model using secondary information on firms from multiple industries across the 10‐year time period of 2000–2009. Our analysis confirms that firms’ IT capability plays a significant role in enhancing their inventory efficiency, which, in turn, is observed to increase stock market returns. Our results also reveal that firms’ IT capability directly reduces their stock market risk and enhances their stock market returns. Taken together, these findings, along with the conceptual model that we advance, have important research and managerial implications.
Survey examining the views of Adult Psychiatry Consultants and Senior Registrars regarding ADHD
Authors: Beirne M. , McNamara N. , O'Keeffe G. , McNicholas F.
Published: July 2013

Objectives

Attention deficit hyperactivity disorder (ADHD) persists into adulthood in ∼2/3 of patients, yet services for adults are lacking in Ireland. This may involve negative attitudes and beliefs as to the validity of ADHD or lack of knowledge and training in its treatment. The objectives of this study are to explore the views of Adult Psychiatrists regarding ADHD knowledge and the treatment options available and pursued in Ireland.

Methods

A questionnaire was constructed based on the stated aims of the study, and was either posted, emailed or handed to 400 Consultants and Senior Registrars throughout the Republic of Ireland between February and December 2011. A total of 92 questionnaires were returned (23%); one was excluded from analysis due to insufficient information entered by the respondent.

Results

Seventy-five per cent of respondents correctly estimated the prevalence rates of adult ADHD to be under 3%, but stated it is currently under-diagnosed (77%). Seventy-four per cent indicated that Adult ADHD should be a diagnostic category in the Diagnostic and Statistical Manual, 5th Edition (DSM V). Sixty-six per cent of respondents were willing to accept referrals of childhood ADHD for ongoing care and a similar number for new ADHD assessments (61%). Less than half (42%) surveyed had actually diagnosed ADHD and of these, only 33% felt confident in managing ADHD in their patients.

Conclusions

Although there is a general willingness to offer services for new and existing ADHD cases and a recognition that Adult ADHD is valid and under-diagnosed, the low confidence levels when treating ADHD and the perception of under-diagnosis suggests a role for further training and links between child and adult services.
Impact of human pressure and forest fragmentation on the Endangered Barbary macaque Macaca sylvanus in the Middle Atlas of Morocco
Authors: Ménard Nelly , Rantier Yann , Foulquier Adrien , Qarro Mohamed , Chillasse Lahcen , Vallet Dominique , Pierre Jean-Sébastien , Butet Alain
Published: July 2013

Overexploitation of forests by humans can lead to highly fragmented populations of forest-dependent species that have poor dispersal abilities. We tested the influence of habitat quality, landscape structure and human pressure on densities of the Barbary macaque Macaca sylvanus in the largest wild population, in the Middle Atlas of Morocco. We surveyed 14 forest fragments of 5–142 km2 that are separated from each other by an inhospitable matrix. We estimated the habitat quality of these forest patches by analysing the vegetation structure and the intensity of human pressure. We studied the distribution of forest patches and estimated macaque densities by combining line-transect sampling and complete group counts. We estimated mean density of individuals to be 9 km−2 (range 0.2–23 km−2). Differentiation of forest patches by a principal component analysis did not show any significant relationship between vegetation type and macaque density. A linear regression model showed that human pressure had a negative impact on density and that density responded positively to patch size. Patch shape, connectivity and altitude did not explain variation in population density. The size of this population is estimated to be c. 5,000 individuals. The survival of several small subpopulations is seriously threatened. As the Middle Atlas is the stronghold of this Endangered species, we recommend modifying forestry practices, reducing overgrazing by livestock within forests, and halting clear-cutting of holm oaks.
Phenology, abundance and consumers of figs (Ficus spp.) in a tropical cloud forest: evaluation of a potential keystone resource
Authors: Kattan Gustavo H. , Valenzuela Leonor A.
Published: July 2013

Fig trees (Ficus spp) produce fruit year-round and figs are consumed by a large proportion of frugivores throughout the tropics. Figs are potential keystone resources that sustain frugivore communities during periods of scarcity, but studies have produced contradictory results. Over 1 y we monitored the phenology of 206 trees of five Ficus species in a Colombian cloud forest, to test whether figs produced fruit during periods of low overall fruit availability. We also measured fig tree densities in 18 0.5-ha plots and made 190 h of observations at 24 trees of three species to determine whether figs were abundant and consumed by a large proportion of the local frugivores. The five species produced fruit year-round but fig availability varied monthly by orders of magnitude. Fig trees reached comparatively high densities of 1–5 trees ha−1 and were consumed by 36 bird species (60% of the local frugivore assemblage) and three mammal species. However, there was no season of fruit scarcity and figs represented on average 1.5% of the monthly fruit biomass. Figs in this Andean forest are part of a broad array of fruiting species and at least during our study did not seem to constitute a keystone resource.
Why Are Returns to Education Higher for Women than for Men in Urban China?
Authors: Hannum Emily , Zhang Yuping , Wang Meiyan
Published: July 2013

It is well established that returns on education are higher for women than for men in urban China. We argue that this finding, while accurate, is misleading owing to its individualist perspective. The income to which most working-age women and men have access includes not only their own income, but also spouse income. Furthermore, decisions about participation and investment in the labour force, both consequential for income trajectories, are likely to be made with partner income and potential income in mind. To our knowledge, no research in China has explored the returns to education enjoyed via spouse income, or the implications of pooling couple income, for illuminating the returns to schooling difference for women and men. In this article, using data from the China Urban Labour Survey (2001), we argue that the returns for women, conventionally defined, are higher than for men because many women trade their own income for spouse income, and this is particularly true among less educated women. We demonstrate, first, that women who are more educated are less likely to get married, while the reverse is true for men. Second, we show that among couples there is evidence of a trade-off in investments in careers. Moreover, among couples, the less educated the woman and the more educated the man, the less likely the couple is to depend heavily on her income. Finally, we show that among couples there is a compensating reverse pattern of returns differences by sex when income is conceptualized as spouse income. Thus, in terms of total couple income, there are no returns differences by sex.
Varicella zoster virus in American Samoa: seroprevalence and predictive value of varicella disease history in elementary and college students
Authors: MAHAMUD A. , LEUNG J. , MASUNU-FALEAFAGA Y. , TESHALE E. , WILLIAMS R. , DULSKI T. , THIEME M. , GARCIA P. , SCHMID D. S. , BIALEK S. R.
Published: July 2013

The epidemiology of varicella is believed to differ between temperate and tropical countries. We conducted a varicella seroprevalence study in elementary and college students in the US territory of American Samoa before introduction of a routine varicella vaccination programme. Sera from 515 elementary and 208 college students were tested for the presence of varicella-zoster virus (VZV) IgG antibodies. VZV seroprevalence increased with age from 76·0% in the 4–6 years group to 97·7% in those aged ⩾23 years. Reported history of varicella disease for elementary students was significantly associated with VZV seropositivity. The positive and negative predictive values of varicella disease history were 93·4% and 36·4%, respectively, in elementary students and 97·6% and 3·0%, respectively, in college students. VZV seroprevalence in this Pacific island appears to be similar to that in temperate countries and suggests endemic VZV circulation.
Video Self-instruction for Police Officers in Cardiopulmonary Resuscitation and Automated External Defibrillators
Authors: Aldeen Amer Z. , Hartman Nicholas D. , Segura Adriana , Phull Amit , Shaw Diane M. , Chiampas George T. , Courtney D. Mark
Published: July 2013

Introduction

Police officers often serve as first responders during out-of-hospital cardiac arrests (OHCA). Current knowledge and attitudes about resuscitation techniques among police officers are unknown.

Hypothesis/problem

This study evaluated knowledge and attitudes about cardiopulmonary resuscitation (CPR) and automated external defibrillators (AEDs) among urban police officers and quantified the effect of video self-instruction (VSI) on these outcomes.

Methods

Urban police officers were enrolled in this online, prospective, educational study conducted over one month. Demographics, prior CPR-AED experience, and baseline attitudes were queried. Subjects were randomized into two groups. Each group received a slightly different multiple-choice test of knowledge and crossed to the alternate test after the intervention, a 10-minute VSI on CPR and AEDs. Knowledge and attitudes were assessed immediately before and after the intervention. The primary attitude outcome was entering “very likely” (5-point Likert) to do chest compressions (CC) and use an AED on a stranger. The primary knowledge outcomes were identification of the correct rate of CC, depth of CC, and action in an OHCA scenario.

Results

A total of 1616 subjects responded with complete data (63.6% of all electronic entries). Randomization produced 819 participants in group 1, and 797 in group 2. Groups 1 and 2 did not differ significantly in any background variable. After the intervention, subjects “very likely” to do CC on a stranger increased by 17.2% (95% CI, 12.5%-21.8%) in group 1 and 21.2% (95% CI, 16.4%-25.9%) in group 2. Subjects “very likely” to use an AED on a stranger increased by 20.0% (95% CI, 15.3%-24.7%) in group 1 and 25.0% (95% CI, 20.2%-29.6%) in group 2. Knowledge of correct CC rate increased by 59.0% (95% CI, 55.0%-62.8%) in group 1 and 64.8% (95% CI, 60.8%-68.3%) in group 2. Knowledge of correct CC depth increased by 44.8% (95% CI, 40.5%-48.8%) in group 1 and 54.4% (95% CI, 50.3%-58.3%) in group 2. Knowledge of correct action in an OHCA scenario increased by 27.4% (95% CI, 23.4%-31.4%) in group 1 and 27.2% (95% CI, 23.3%-31.1%) in group 2.

Conclusion

Video self-instruction can significantly improve attitudes toward and knowledge of CPR and AEDs among police officers. Future studies can assess the impact of VSI on actual rates of CPR and AED use during real out-of-hospital cardiac arrests.

AldeenAZ, HartmanND, SequraA, PhullA, ShawDM, ChiampasGT, CourtneyDM. Video self-instruction for police officers in cardiopulmonary resuscitation and automated external defibrillators. Prehosp Disaster Med. 2013;28(5):1-6.
Similarity computation using semantic networks created from web-harvested data
Authors: IOSIF ELIAS , POTAMIANOS ALEXANDROS
Published: July 2013

We investigate language-agnostic algorithms for the construction of unsupervised distributional semantic models using web-harvested corpora. Specifically, a corpus is created from web document snippets, and the relevant semantic similarity statistics are encoded in a semantic network. We propose the notion of semantic neighborhoods that are defined using co-occurrence or context similarity features. Three neighborhood-based similarity metrics are proposed, motivated by the hypotheses of attributional and maximum sense similarity. The proposed metrics are evaluated against human similarity ratings achieving state-of-the-art results.
Parallel language activation during word processing in bilinguals: Evidence from word production in sentence context
Authors: STARREVELD PETER A. , DE GROOT ANNETTE M. B. , ROSSMARK BART M. M. , VAN HELL JANET G.
Published: July 2013

In two picture-naming experiments we examined whether bilinguals co-activate the non-target language during word production in the target language. The pictures were presented out-of-context (Experiment 1) or in visually presented sentence contexts (Experiment 2). In both experiments different participant groups performed the task in Dutch, their native language (L1), or in English, their second language (L2). The pictures’ names were Dutch–English cognates or non-cognates, the cognate effect serving as the marker of activation of the non-target language. In Experiment 2 we also examined the effect of sentence constraint. In both experiments a cognate effect occurred, but it was modulated by language and sentence constraint: The effect was larger in L2 than in L1, larger with low-constraint sentences than with high-constraint sentences, and disappeared in the high-constraint L1 condition. These results extend earlier bilingual word-recognition and out-of-context production studies, suggesting that also during word production in context, co-activation of the non-target language occurs.
A BIOLOGICAL PROCESS SUBJECT TO NONCOMPETITIVE SUBSTRATE INHIBITION IN A GENERALIZED FLOW REACTOR
Authors: NELSON M. I. , NICHOLLS T. , HAMZAH N.
Published: July 2013

We analyse the steady-state operation of a continuous flow bioreactor in which the biochemical reaction is governed by noncompetitive substrate inhibition (Andrews kinetics). A generalized reactor model is used in which the well-stirred bioreactor and the idealized membrane bioreactor are special cases. As generic properties of systems subject to substrate inhibition have been obtained by other authors, we discuss reaction engineering features specific to Andrews kinetics.
Dynamics as a School Subject
Authors: Anderson W.
Published: July 2013

The inclusion of Dynamics in a school curriculum is a topic that affords always much scope for discussion among interested teachers, and widely opposed opinions are held. I venture to state my own opinion, and to suggest a somewhat fuller treatment in dealing with one or two sections of the subject than is usual in the text-book.
Two Illustrations of Newton's Third Law
Authors: M'Bride J. A.
Published: July 2013

I. Statical.—The first body A, say a wooden block, is suspended by a rubber cord (R) and a spring balance (S) from a fixed support. A copy of the scale is taken on paper, inverted and gummed on so that the zero is opposite the index when the block A hangs freely.
Multiplication and Division of Vulgar Fractions
Authors: Philip G.
Published: July 2013

The difficulty in teaching Multiplication and Division of Fractions consists solely in the fact that the ideas formerly associated with these operations when whole numbers were concerned no longer fit the case when we come to deal with fractions, e.g., 9 × 7 can be intelligibly interpreted as meaning the number of articles in 9 bundles, each containing 7 articles. In this respect, multiplication is simply contracted addition. When we come to a case like , we cannot frame a question on the lines of the former. But if we present the problem in a concrete form we are more likely to be successful in teaching young pupils the method of multiplying and dividing vulgar fractions.
Geometrical Illustrations of Algebraic Identities
Authors: Comrie Peter
Published: July 2013

All these identities may be proved after one method as follows:—

Draw two straight lines at right angles and mark off parts a and b as indicated in the figures. At the points of section draw perpendiculars to the lines. All the figures thus formed are rectangles, and therefore have their opposite sides equal. The proofs should then be obvious.
The Fallacy of the Figure in Geometry
Authors: Dougall John
Published: July 2013

(1) Let EA, EB be tangents to a circle with centre O. To prove EA = EB, the following is often served up:—

By subtraction from the equal angles EAO, EBO
Decimalisation of shillings and pence
Authors: Holm A.
Published: July 2013

For some questions in arithmetic it is convenient to be able to decimalise shillings and pence mentally to any required number of decimal places.
Position-Ratio
Authors: Turner John
Published: July 2013

The position-ratio of any point N on the line SX is defined as the ratio .
The Reciprocal Polar of a Circle
Authors: Philip G.
Published: July 2013

The reciprocal polar figure of a circle s, with regard to another circle c, is a conic, one of whose foci is the centre of the reciprocating circle. The polar reciprocal of a with regard to c is obtained by taking the polars of points on s with regard to c, and then constructing the envelope of these lines.
Note on Geometric Series
Authors: Bell R. J. T.
Published: July 2013

The formula for the sum of n terms of the geometric series

where T1 is the first term and Tn+1 the term immediately succeeding the last to be summed This form is useful for finding the sum of a closed geometric series without first finding the number of terms. Thus

since the terms of the series which succeed 32 and a19 are respectively 64 and a21.
The Tangents of 15° and of 22½°
Authors: Ramsay Peter
Published: July 2013

I. Let ABO be a triangle in which = 30°, B = 60°, C = 90°.

Produce AC to D so that AD = AB. Join BD.
The Numerically Greatest Term of a Binomial Expansion
Authors: Sommerville D. M. Y.
Published: July 2013

The problem of the greatest term of a binomial expansion is a favourite one in elementary text-books, and its solution is often difficult to a beginner. The difficulty, at least in the case where the index is negative or fractional, seems to be caused by the fact that a “formula” is provided which gives a value for r, such that the (r + 1)th term is the greatest. Moreover, this formula is not always the same. Sometimes it is sometimes ; and unless the student has a very good memory he is sure sometimes to make mistakes. Elementary mathematics ought not to be a memory exercise. It is a platitude to say that the educational value of the teaching of mathematics lies in its training of the powers of reasoning. This element is eliminated when processes of reasoning are reduced to a rule of thumb. As well might one use “Molesworth” as a text-book of the principles of mechanics.
Note on Fermat's Theorem
Authors: Lindsay W. A.
Published: July 2013

The Theorem that an – a is exactly divisible by n, if n be a prime number, may be established as follows from the Binomial Theorem.
Fermat's Theorem deduced from the theory of circulating Radix Fractions:
Authors: Donaldson J. A.
Published: July 2013

is an integer, if x is an integer, and n + 1 is a prime integer which is not a factor of x.

This is not a neat proof of Fermat's theorem, but, as far as I know, it is a new proof, and it may have some little interest, as it seems very possible that the theorem may have been suggested to Fermat in this way. Fermat published the theorem without any demonstration and without indicating what had suggested it, and any proofs, that I have seen, give no indication why one should look for such a theorem, and would very possibly never have been given if the theorem had not been already known.
Logarithms and the Reciprocals of Numbers
Authors: M‘Leod C.
Published: July 2013

—The writer when introducing his pupils to the use of Logarithmic Tables is accustomed to give them exercise with the number 1·00023. This number, he tells them, without explaining how he obtains it, is such that 1·00023 × 1·00023 × … 10,000 times would give a, number which read to the 3rd decimal place is equal to 10. He makes this the basis of practical exercises in approximations, and builds on it lessons in Indices, and in the use of Logarithmic Tables, with particular explanation of the Mean Difference Columns.
The Arithmetic Mean of a number of real positive numbers is not less than their Geometric Mean.—
Authors: Milne William P.
Published: July 2013

The subjoined proof is not given in the current text books, but is handed on by oral tradition.

The usual proof requires in general the assumption of an infinite series of operations (with the consequent limit theorems involved), as all the n given numbers tend to equality. Let us take an arithmetical example, and let us tabulate the sequences involved in the way suggested in my paper on “The Teaching of Limits and Convergence to Scholarship Candidates” in the May (1911) issue of the Mathematical Gazette.
Additional “Note on Right-Angled Triangles.”—
Authors: Martin Artemas
Published: July 2013

On pp. 95 and 96 of No. 8 (October 1911) of Mathematical Notes is given a numerical method of finding rational right-angled triangles.

It has been known for centuries that

are the sides of a rational right-angled triangle whatever be the values of p and q; for
Introductory Lessons in Solid Geometry
Authors: Ramsay Peter
Published: July 2013

The difficulty which every student beginning the study of solid geometry finds in interpreting diagrams representing solid figures may be largely met, and an interest in the subject may be aroused at the outset, by a few lessons in drawing the simplest regular solids and in the study of the drawings made, before the formal propositions of Euclid, Book XI. are attacked.
Geometrical Construction for Refracted Ray
Authors: Miller William
Published: July 2013

The following variation seems an improvement on the usual method of tracing a refracted ray. In the usual method when an incident ray OP is given, any radius OP is taken and a circle described. PA is drawn perpendicular to the surface AB. OA is then sub-divided into the number of units expressed in the numerator of the fraction μ, and OB is measured backwards, the number of units expressed by the denominator. BQ is then drawn perpendicular to AB to meet the circle in Q. OQ is the refracted ray.
An Interesting Example in Curve Tracing
Authors: Bell R. J. T.
Published: July 2013

It is proposed to trace the curves represented by the equation

for the values of a (i) a = 2, (ii) a = 1.
Cauchy's Condensation Test.—
Authors: Vickers Robert
Published: July 2013

Theorem.—If the terms of the series Σf(n) never increase as n increases, and if f(n) = 0 then Σf(n) converges or diverges with
To show that the equation
Authors: Jones H. Spencer
Published: July 2013

has three real roots.—Let x1 be any one root. Then ξ, η, ζ can be chosen uniquely to satisfy simultaneously the three equations

If x1 is complex, so also will be ξ, η, ζ. Let their conjugate complexes be , so that

; etc.
On the necessary and sufficient condition for the degeneracy of a quadratic function of a number of variables
Authors: Dougall John
Published: July 2013

The following method for three variables can be extended at once to the general case.
Geometrical summation of the series
Authors: Stokes G. D. C.
Published: July 2013

a, (a + d)r, (a + 2d)r2,…

The following method of summing the mixed series is an extension of the well-known method for the G.P. given by Dr Dougall in the April issue of the Notes for 1909.
Deduction of Propositions on Tangents from Propositions on Secants.–
Authors: Pinkerton P.
Published: July 2013

In Vol. XXII., p. 64, of the Proceedings of the Society, Professor Gibson called attention to difficulties in the treatment of tangents by the method of limits. The aim of the following remarks is to show how young students may become accustomed to regard a tangent as the limit of a secant, and at the same time to furnish a type of exercise which might encourage initiative and research in the early study of Geometry.
Elementary proof of the formula for αn + βn in terms of α+ β and αβ.
Authors: Dougall John
Published: July 2013

The proof given by Chrystal uses infinite series, but by a simple modification it may be put in an elementary form.
Arithmetical Solution of the Ages Problem
Authors: Dougall John
Published: July 2013

The following solution of an old problem may be new to some readers.

“The ages of A and B are as 3 to 1, and in 15 years they will be as 2 to 1. Find their ages.”
Integration by Parts. A Failing Case
Authors: Milne J. R.
Published: July 2013

Integrate tanx; by parts as follows:—

i.e. 0= — 1, which is absurd.

It might be conjectured at first sight that the above result is due to a disregarded constant of integration, but this is not so, because we can imagine all the integrals taken between the same limits, in which case there is no constant. The true explanation is to be found by considering the proof of the theorem of integration by parts.
Vectors as applied to Problems in Velocity
Authors: Boxer Stanley V.
Published: July 2013

A velocity is a vector quantity, for it possesses magnitude and direction. It is, of course, necessary to make clear in every case what given point (moving or not) is considered as fixed for the time being, to which the vclocity of the moving point (so-called, though it may only be relatively moving) is referred.
A Direct Reading Hygrometer
Authors: Jamieson Walter
Published: July 2013

The instrument is an ordinary dry and wet bulb hygrometer adapted to give a direct

reading of the percentage humidity. I, I are pointers set at the dry and wet bulb readings by means of pieces sliding on the rods A, B and joined together by a link C, which actuates by a slot the scale F (movable in the vertical) on which the percentage humidity is read at the pointer D.
Geometrical Illustrations of a Formula in the Differential Calculus
Authors: Davis R. F.
Published: July 2013

In this note the formula

is illustrated for a few curves.
Geometrical Proof of a Trigonometrical Identity
Authors: Bell R. J. T.
Published: July 2013

The following method of proof of the identity,

where A, B, C are the angles of a triangle, was proposed in an examination paper, and it has been suggested to me that it might be of interest to teachers. It is rather easier than that given on p. 344 of “New Trigonometry for Schools” by Lock and Child.
Proof of some Triangle Formulae
Authors: Burgess A. G.
Published: July 2013

Let I be the incentre of ΔABC, and let the excentre opposite A be I1 Draw perpendiculars IF and I1F1 to AB. IBI1 = 90°.
On the Determination of Centres of Curvature
Authors: Bryan G. H.
Published: July 2013

In Mathematical Notes for May 1915, Dr J. M'Whan gives a note on the determination of centres of curvature, stating that “the only assumption involved is, therefore, as stated, that of the definition of the centre of curvature as the limiting position of the intersection of these normals.”
On the Solutions of the Differential Equation
Authors: Steggall J. E. A.
Published: July 2013

The following is a direct proof that any n + 1 particular integrals of the differential equation

where

and P1, P2 … Pn are functions of t alone, are connected by a linear relation.
On the Solutions of
Authors: Bell R. J. T.
Published: July 2013

The following note gives a proof of the theorem that if x, y, z are any three values of u which satisfy the differential equation where l, m, n are constants. If the dots denote differentiation with respect to t, we have
On the Direction-Cosines of the Axes of the Conicoid f(xyz) ≡ ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy = 1
Authors: Bell R. J. T.
Published: July 2013

Some time ago I received from Dr Muirhead the following theorem:—“If lr, mr, nr (r=1, 2, … 3) are the direction-cosines of the axes of the conicoid
A Method of obtaining Examples on the Multiplication of Determinants
Authors: MacRobert Thomas M.
Published: July 2013

In the ordinary text-books on Algebra there is a lack of suitable examples on Multiplication of Determinants. Most of the examples that are given are particular cases of the theorem

where A1 A2, …, B1, …, are the co-factors of a1, a2, …, b1 …, in D.
Geometrical Proof of tan A + tan B + tan C = tan A tan B tan C
Authors: Kesson Colin
Published: July 2013

Let ABC be the Δ, AD ⊥ to BC produced to meet circumcircle in K, BL a diameter of circumcircle, LM ⊥ to AK. Let BK, KG, CL and LA be joined.
The Diametric Section Axis of Two Circles
Authors: Finlayson William
Published: July 2013

Mr Burgess' pretty solution of the problem “to draw a circle cutting three circles diametrically” suggests a question as to the use of sign in treating of co-axial circles.
Geometrical proof that tan x tan y + tan y tan z + tan z tan x= 1 when x + y + z = 90°
Authors: Crawford G. E.
Published: July 2013

H being the orthocentre of a triangle ABC, we may call the angles HAC, HBA, HCB = x, y, z respectively, for their sum is 90°.

Now tan x tan z =

∴ tan x tan z + tan z tan y + tan x tan y = 1.
An Infinite Product of Euler
Authors: Aitken A. C.
Published: July 2013

In a letter to Stirling, dated July 27, 1738, Euler mentions having happened on the infinite product, “satis notatu dignam,” the numerators being the odd primes in their natural order, the denominators the multiples of 4 nearest to those primes. He says he can prove that the limit of this product is His proof was probably as follows:
An Elementary Proof of Girard's Theorem
Authors: Aitken A. C.
Published: July 2013

Girard enunciated in 1625 the following celebrated theorem, which is associated with the name of Fermat:

Every prime of the form 4m + 1 is the sum of two squares in one way only, and no prime of the form 4m - 1 is a factor of the sum of two squares that are not both multiples of that prime.
Coordinates, Conics and Conjugate Points
Authors: Dougall John
Published: July 2013

A fundamental result in the theory of conics is the following:

Two opposite vertices of a complete quadrilateral are conjugate points for any conic which passes through the four remaining vertices.
A Limit Proof of the Theorem Euc. III, 35
Authors: Stokes G. D. C.
Published: July 2013

Let AB be any chord passing through the fixed point P. Draw the diameter AOC, join CP and let it meet the circumference at D Then in triangle ACP, AC2 = AP2 + CP2 together with either 2AP. PB or 2 CP. PD according as CP is projected on AP or AP on CP. Hence AP.PB = CP.PD. Now draw the diameter DOE, join EP and let it meet the circumference at F. Then the theorem is true for chords CD. EF.
Series summable as Arithmetical Progressions
Authors: Ayyangar A. A. Krishnaswami
Published: July 2013

We may group the terms of the A. P. a, a + d, a + 2d, …… as follows: the first p terms, the next p + t terms, the next p + 2t terms, and so on. The sum of the terms comprising the nth group is

which is a rational integral function of n of the third degree.
Kepler's Law of Refraction
Authors: Houstoun R. A.
Published: July 2013

The correct law of refraction, sin i = μ. sin r, is usually assumed to have been first discovered by Snell in 1621, although he did not express it in this form. The astronomer Kepler laboured hard to discover it, but in vain, and Whewell in the History of the Inductive, Sciences says that it is strange that he should have failed, when the law is so simple. There is, however, a good reason for his want of success.
A physical solution of the Apollonian problem
Authors: Dougall John
Published: July 2013

This celebrated problem—to describe a circle to touch three given circles—admits of a simple experimental solution which might be found interesting by a mathematical class.

The surface on which the circles lie may be either a plane or a sphere, but the latter case is the more convenient to deal with, and will be the one taken.
A Note on Conjugate Permutations
Authors: Aitken A. C.
Published: July 2013

§ 1. Two permutations of the natural order (123 … n) are said to be conjugate when each number and the number of the place in the one permutation are interchanged in the case of the other permutation.
A Footnote to Euclid, Book III
Authors: Muirhead R. F.
Published: July 2013

The following two propositions are converses of Euclid III., 11 and 12.

Prop. 1. If the circumferences of two circles whose centres are A and B have a common point C lying in the straight line AB, then the circles touch each other externally at C.
On the Treatment in School Texts of the Sphere, Cone and Pyramid
Authors: Lawson G.
Published: July 2013

An important note in the Proc. Edin. Math. Soc. of May 1904 pointed out that the then prevalent School method of tangents made it difficult for the pupil to gain sound knowledge in his later studies. The same criticism may, I submit, be directed against the treatment, now prevalent in school texts, of (1) surface of sphere, (2) volume of sphere, and (3) volume of cone and pyramid.
The Remainder Theorem
Authors: Hyslop James
Published: July 2013

No theorem of elementary algebra has given rise to more discussion than the Remainder Theorem:

If a polynomial f(x) be divided by (x — a), the remainder is f(a).

It is hoped that this note may be the means of settling questions connected with it once for all, and may aid in bringing about correct methods in teaching.
Linear Transformations and Geometry
Authors: Hyslop James
Published: July 2013

The following note suggests certain connections between the theory of linear transformations and quadratic forms on the one hand, and the geometry of second degree surfaces on the other. It is hoped that the note may prove useful to those who may have to teach either theory to students who already possess an elementary knowledge of the other. The general ideas may be such as may well have occurred to anyone familiar with both theories, but the examples given may be new to readers.
A Proof of the Theorem of Pythagoras
Authors: MacRobert T. M.
Published: July 2013

The triangle ABC has a right angle at B. On AC, on the same side as B, describe a square ADEC. Draw DF perpendicular to AB or AB produced.

The triangles ABC and DFA are congruent, having sides CA and AD equal, and the corresponding angles equal. Hence DF is equal to AB.
Equimomental Tetrads of a Rigid Body
Authors: Sommerville D. M. Y.
Published: July 2013

A lamina of mass m can be replaced by an equimomental system of three equal particles m placed at the vertices of a maximum inscribed triangle of a momental ellipse for the centre of mass. Similarly any rigid body can be replaced by an equimomental system of four equal particles (cf. Routh, Elementary Rigid Dynamics, 7th ed. (1905), Art. 44 and Note, p. 423).
The Number of Lines that may lie upon a Surface of given Order
Authors: Richmond H. W.
Published: July 2013

The greatest number of straight lines that can lie upon a surface of order n (not being a ruled surface) is unknown, except if n is three. Salmon and Clebsch have shown that the points of contact of lines which have a four-point contact with the surface lie upon a locus of order n (11n – 24), the intersection of the surface of order n with another of order 11n – 24. Since a straight line lying wholly on the former surface must form a part of this locus, the number n (11n – 24) is an upper limit to the number of lines; if n is three, this gives 27, the correct number. But for values of n > 3, it is improbable that this limit1 can be reached.
The “Pellian Equation” and Some Series for π
Authors: Aitken A. C.
Published: July 2013

§ 1. The craze for extensive π-calculation which was so strange a feature of the last century was probably brought to an end not so much by the famous 707 decimals of W. Shanks in 1873 as by the demonstrations of Hermite and Lindemann, about the same time, regarding the transcendental nature of both e and π. Sporadic minor outbreaks of the disease still occur, of course, —Ramanujan in his earlier days was not entirely immune—and the series of the present note may seem symptomatic. It is hoped, however, that they will not be devoid of interest from the point of view of elementary trigonometry.
The Latus Rectum of the Parabola: (ax + by)2 + 2gx + 2fy + c = 0
Authors: Bell Robert J. T.
Published: July 2013

If a circle has double contact with a parabola, the points of contact being P and P′, its centre, G, is the point of intersection of the axis with the normals at P and P′, and the perpendicular from G to PP′ is the subnormal GN, which is half the latus rectum.
The Polar Equation of the Tangent and Normal to a Conic
Authors: Bell Robert J. T.
Published: July 2013

The property of a conic: “if the projections of K, any point on a tangent, on the directrix and the focal radius of the point of contact be I and U respectively, SU = e. KI,” is known as Adams's Property. The statement of the above property in terms of the polar coordinates of K is the equation of the tangent. Hence, if the eccentric angle of the point of contact is a

or = cos (θ — α) + e cos θ is the equation of the tangent.
Note on a Property of the Cycloid
Authors: Bell Robert J. T.
Published: July 2013

The area of the triangle whose sides are a variable tangent to the cycloid, the tangent at the cusp and the tangent at the vertex is maximum when the point of contact of the variable tangent is the point of intersection of the cycloid and the generating circle at the cusp.
Note on Polynomial Interpolation
Authors: Aitken A. C.
Published: July 2013

The formulae of interpolation of Lagrange and Newton are easily retained in the memory if one considers a simple way in which each can be derived, for polynomials.
A Note on Mathematical Expectation
Authors: Aitken A. C.
Published: July 2013

If there are n coins in a bag, of any individual values but of total value P, and if m are drawn at random, without replacement, it may be proved that the mathematical expectation, or probable value, of the draw is mP/n. It must be well known, though I cannot find any reference in the texts, that the same result holds if the coins are replaced after each drawing, or indeed if replacements after certain specified drawings, but not after others, are permitted.
The Works of Sir John Leslie (1766–1832)
Authors: Horsburgh E. M.
Published: July 2013

The Edinburgh Mathematical Society, at the opening of the session on 4th November, 1932, paid tribute to the fame of Professor Sir John Leslie by a Centenary celebration. An account of this will be found in the Edinburgh University Journal for the current year. In view of the recent amazing advances in Science, both pure and applied, it is of interest to observe where mathematics and physics stood at the beginning of this brief interval of exactly one century.
A Note on Stirling's Theorem
Authors: Wilton J. R.
Published: July 2013

Let Γ(1 + x) = √(2πx)xxe–x φ(x);

This result is Stirling's theorem. A simple proof is given in § 1.87 of Titchmarsh's Theory of Functions (Oxford Univ. Press, 1932).

Rather more than Stirling's theorem can be proved by a method which assumes nothing but the definition of the Γ-function, and Γ (½) = √π, from which it follows that
A Formula in the Theory of Correlation
Authors: Hope A. E.
Published: July 2013

The formula in question gives the correlation between two variables for a number n1 and nz of individuals when the ordinary parameters, including correlations, are available for the separate groups of n1 and n2 individuals; and it is extended to more than two groups. It is possible, even probable, that the formula is known, but the writer has not found any direct references to it; in any case its practical value is such that there can be no harm in drawing attention to it.
A Problem in Combinations
Authors: Aitken A. C.
Published: July 2013

1. If there are n individuals A1, A2,.…, An, in how many ways can they be put into groups? For example, if there are three individuals A, B, C, they may be grouped as

that is, in 5 ways, the respective subgroups, 1, 3, 1 in number, corresponding to the partitions 1 + 1 + 1, 1 + 2, 3 of the integer 3. Hence P (3), say, is 5.
A Series Identity
Authors: Miller J. C. P.
Published: July 2013

In connection with some work on the theory of probable errors, the following series identity arose:—

where a is a positive integer.

As the main interest of this identity appears to lie in itself and in the method of proof, and not in its connection with the theory of probable errors, it seems worth while to record it separately.
A Relation between two Ordinary Linear Differential Equations of the Second Order
Authors: Taylor D. G.
Published: July 2013

1. Between the solutions of the equations

a relation can be established, provided the functional symbols f, ø are inverse to one another. For example, let f (x) = sin x, then ø(ξ)= arcsin ξ, and the two equations are

The process consists in obtaining from (1) the second order equation satisfied by yx = dy/dx, making a change of independent variable in (2), and comparing the resulting equations.
A Generalisation of a Theorem of Wolstenholme
Authors: Gupta Hansraj
Published: July 2013

§ 1. Chowla has generalised Wolstenholme's Theorem as follows:

where p denotes as usual a prime, and < is used for “less than and prime to.”
Note on the Summation of Finite Algebraic Series
Authors: Macdonald J. A.
Published: July 2013

In order that an algebraic series of a finite number of terms may be summed in simple form, there must exist a difference equation satisfied by the terms. But, owing to the fact that no general method of finding this equation is given in textbooks, the beginner does not acquire confidence in summation until his experience is wide enough to include all of the usual types of such series; and even then he may come to the conclusion that the finding of the difference equation is no more than a lucky chance. It is therefore proposed in the following notes to show that the ordinary types of summable terminating series can be reduced to one, and to find a single general expression for the sum. It will also be shown that the criterion of summability is the “convergency ratio.”