bluuebunny/crossref_metadata_2025_split huggingface dataset:
An embedding theorem for groups
Authors: Chehata C. G. 
Published: May 2009

Let G by any given group. A homomorphic mapping μ of a subgroup A of G onto a second subgroup B of G, where A and B need not be distinct, is called a partial endomorphism of G. When μ is defined on the whole of G, that is when A = G, we call μ a total endomorphism of G; or simply an endomorphism of G.A partial (or total) endomorphism μ* of a supergroup G* of G is said to extend (or continue) μ if μ* is defined on a supergroup A* of A, that is, μ* is defined for at least the elements for which μ. is defined, and moreover μ* coincides with μ on A.
On the power of a prime dividing the order of the automorphism group of a finite group
Authors: Howarth J. C. 
Published: May 2009

The existence of a function g of hhaving the property that pr divides the order of the automorphism group of a finite group G whenever pg divides the order of G was first established by Ledermann and Neumann [4], who showed that the least such function g(h) satisfies the inequalityLater Green [2] improved this estimate toIn the Present paper this will be revised, for sufficiently large h, to
A further note on dual trigonometrical series
Authors: Tranter C. J. 
Published: May 2009

This note discusses the determination of the coefficients an in the dual trigonometrical serieswhere p = ± 1 and F(x), G(x) are prescribed functions of X. It is shown that this problem and the corresponding one in which the sines in equations (1) are replaced by cosines are easily reduced to a form in which the results I have recently given in this journal [1] may be applied.As with my previous paper on this subject, the analysis is purely formal and no attempt is made to give precise conditions for which the solution is valid.
Some triple integral equations
Authors: Tranter C. J. 
Published: May 2009

Potential problems in which different conditions hold over two different parts of the same boundary can often be conveniently reduced to the solution of a pair of dual integral equations. In some problems, however, the boundary condition is such that different conditions hold over three different parts of the boundary and, in such cases, the integral equations involved are frequently of the formwhere f(r), g(r) are specified functions of r, p = ± ½ and ø(u) is to be found. Such equations might well be called triple integral equations and, in this note, I point out certain special cases which I have found to be capable of solution in closed form.
Arithmetical Functions of a Greatest Common Divisor, III. Cesàro's Divisor Problem
Authors: Cohen Eckford 
Published: May 2009

Let σ1(n) denote the sum of the tth powers of the divisors of n, σ(n) = σ1(n). Also placewhere γ is Euler's constant, ζ(s) is the Riemann ζ-function and x ≧ 2. The function Δ(x) is the remainder term arising in the divisor problem for σ((m, n)). Cesàro proved originally [1], [6, p. 328] that Δ(x) = o(x2 log x). More recently in I [2, (3.14)] it was shown by elementary methods that . This estimate was later improved to in II [3, (3.7)]. In the present paper (§ 3) we obtain a much more substantial reduction in the order of Δ(x), by showing that Δ(x) can be expressed in terms of the remainder term in the classical Dirichlet divisor problem. On the basis of well known results for this problem, it follows easily that . The precise statement of the result for σ((m, n)) is contained in (3.2).
Two Notes on Matrices
Authors: Aitken A. C. 
Published: May 2009

1. The properties of the circulant determinant or the circulant matrix are familiar. The circulant matrix C of order 4 x 4, with elements in the complex field, will serve for illustration.The four matrix coefficients of c0, c1 c2, c3 form a reducible matrix representation of the cyclic group ℐ4, so that C is a group matrix for this. Let ω be a primitive 4th root of 1. Then Ω as below, its columns being normalized latent vectors of C,is unitary and symmetric, and reduces Cto diagonal form thus,where the μr, the latent roots of C, are given byAll of the above extends naturally to the n x n case.
On Riesz summability factors
Authors: Borwein D. , Shawyer B. L. R. 
Published: May 2009

1. Suppose throughout that a, k are positive numbers and that p is the integer such that k—l≦p<k. Suppose also that φ(w), ψ(w) are functions with absolutely continuous (p+1)th derivatives in every interval [a, W] and that φ(w) is positive and unboundedly increasing. Let λ ={λn} be an unboundedly increasing sequence with λ1 > 0.Given a series and a number m ≧0, we writeotherwise,and A(w) = AO(w).
Extension of partial endomorphisms of abelian groups
Authors: Chehata C. G. 
Published: May 2009

It is known [1] that for a partial endomorphism μ of a group G that maps the subgroup A ⊆ G onto B ⊆ G. G to be extendable to a total endomorphism μ* of a supergroup G* ⊆ G such that μ an isomorphism on G*(μ*)m for some positive integer m, it is necessary and sufficient that there exist in G a sequence of normal subgroupssuch that L1 ƞA is the kernel of μ andfor ι = 1, 2,…, m–1.The question then arises whether these conditions could be simplified when the group G is abelian. In this paper it is shown not only that the conditions are simplified when Gis abelian but also that the extension group G*⊇G can be chosen as an abelian group.
A generalization of Sonine's first finite integral
Authors: Tranter C. J. 
Published: May 2009

In this note I show thatwhere Jdenotes the Bessel function of the first kind of the orders and arguments indicated, n = 0, 1, 2, 3, … and the real parts of both μand v exceed — 1. This is a generalization of Sonine's first finite integral [1, p. 373] to which it reduces in the special case n = 0.
A note on the associated Legendre polynomials
Authors: Khandekar P. R. 
Published: May 2009

This paper is paper gives what appears to be a new Rodrigues’ formula for the Associated Legendre Polynomials defined by [5, p. 122]with the restriction that m is an even positive integer, which helps to evaluate some integrals. Putting m = 2k in (1.1) and replacing Pn(x) by the Gegenbauer Polynomial and using [3, p. 176]We obtainPutting a =v–½ in the relation [4, p. 283]We get
Notes on two lemmas concerning the Epstein zeta-function
Authors: Diananda P. H. 
Published: May 2009

1. We use Cassels's notation and define h (m, n), Q (m, n), Zh (s), Zh (1) – ZQ (1) and G (x, y) as in [1]. Rankin [5] proved that the Epstein zeta-function Zh (s) satisfies, for s ≧ 1·035, theTHEOREM. For s > 0, Zh (s) — ZQ (s) ≧ 0 with equality if and only ifh is equivalent to Q. Rankin then asked whether the theorem is true for all s > 1. Cassels [1] answered this question in the affirmative and proved further that the theorem is true for all s > 0.
Proximate order (R) of entire functions represented by Dirichlet series (IV)
Authors: Kamthan Pawan Kumar 
Published: May 2009

where be an entirefunction represented by a Dirichlet series whose order (R) and proximate order (R) are respectively ρ (0 < ρ < ∞) and ρ(σ). For proximate order (R) and its properties, see the paper of Balaguer [4, p. 28].
⋏-distributive Boolean matrices
Authors: Blyth T. S. 
Published: May 2009

In this paper we shall be concerned with the set Mn(B) of n x n matrices whose elements belong to a given Boolean algebra B(≤, ∪,∩,').It is well known that Mn(B) also forms a Boolean algebra with respect to the partial ordering ≼ defined byin which union (⋎), intersection (⋏) and complementation (*) are given by
Some integrability theorems
Authors: Chen Yung-Ming 
Published: May 2009

1. P. Heywood [3] proved the following theorems:Theorem A. If 0 ≦ λ < 2, if xy−1g(x) ε L(0, π), and iffor n = 1, 2, 3,…, then the seriesis convergent.Theorem B. If 0 ≦ λ < 1, if xy−1f(x)ε L(0, π), and iffor n = 1, 2, 3,…, then the seriesn−yanis convergent.
On integral equations involving Whittaker's function
Authors: Srivastava K. N. 
Published: May 2009

Recently some inversion integrals for integral equations involving Legendre, Chebyshev, Gegenbauer and Laguerre polynomials in the kernel have been obtained [1, 2, 3, 5, 6]. In this note, two inversion integrals for integral equations involving Whittaker's function in the kernel are obtained. We shall make use of the following known integral [4, p. 402]The results of this note are based on the following two integrals, which are derived from (1) by writing u – t = (v – t)x.for m + 1 > 2v > – 1;for m + 1 > 2v > – 1.
The Quadratic Law of Reciprocity and the Theory of Galois Fields
Authors: Zassenhaus Hans J. 
Published: May 2009

The theory of quadratic congruences modulo an integer is dominated by the Quadratic Law of Reciprocity (see § 1), which makes it possible to decide in a very short time whether a quadratic congruenceis solvable or not. The law was first proved by Gauss.* It took him over a year to obtain his first proof, which depends on a tedious lemma in elementary number theory. He subsequently obtained seven further proofs, and today more than fifty proofs are known, most of them based on the ideas of Gauss. The object of the present paper is to present a proof which is a modernised version of Gauss's seventh proof, applying the ideas of that proof to a finite set of objects, the elements of a finite or Galois field.
Some Integrals involving E-Functions
Authors: Macrobert T. M. 
Published: May 2009

This paper describes a simple method of evaluating integrals of a type some cases of which have been discussed by Dr. Ragab.The following formulae are required in the proofsIf p≧q + 1, z ≠ 0,If. p = q + 1, | z |>1 in this formula.
Audit and feedback: Effects on professional obstetrical practice and healthcare outcomes in a university hospital
Authors: COSTA MARIA L. , CECATTI JOSE G. , MILANEZ HELAINE M. , SOUZA JOAO P. , GÜLMEZOGLU METIN 
Published: May 2009

AbstractObjective. To assess the effects of audit and feedback on the practice of professionals in obstetrics. Design. Before–after intervention study. Setting. Obstetric unit of a university hospital in Brazil. Methods. Before the intervention the prevalence rates of six evidence‐based interventions were assessed. Seminars and workshops were administered, with the baseline results and also the main contents from systematic reviews on the topics studied, followed by detailed discussion of each topic, based on the Reproductive Health Library. After four months, the same practices were measured again and compared with the pre‐intervention period. Main outcome measures. Selective episiotomy; continuous electronic fetal monitoring (EFM) during labor of low‐risk pregnant women; antibiotic prophylaxis in cesarean section; active management of third stage of labor; routine induction of labor at 41 weeks for uncomplicated pregnancies; and continuous support for women during childbirth. Results. Both periods showed a similar number and mode of deliveries. There was a significant reduction in episiotomies (RR = 0.84; 0.73–0.97) and an increase in continuous support for women during childbirth by a companion (RR = 1.42; 1.24–1.63). Although there was not a significant change in the use of oxytocin during the third stage of labor, there was a shift to the internationally recommended dosage of 10 IU (p<0.0001). There was no significant change in the use of antibiotic prophylaxis for cesarean section, continuous EFM, or routine induction of labor at 41 weeks for uncomplicated pregnancies. Conclusion. Audit and feedback can be used as a tool to improve obstetrical practice, at least for some interventions and when the medical staff is open and receptive to change.
Introduction: Four Themes in Research on the Neurobiology of Memory
Authors: Eichenbaum Howard 
Published: May 2009

AbstractThis chapter introduces some of the philosophical and historical underpinnings of research on the biological bases of memory. It begins by presenting four central themes that have guided memory research for over a hundred years: connection, cognition, compartmentalization, and consolidation. Substantial preliminary evidence regarding each of these themes emerged during a “Golden Era” for neuroscience in the latter half of the 19th century and the beginning of the 20th century. A brief introduction to some of these accomplishments provides the background for a subsequent, more detailed summary of progress on each of the four central themes in the remainder of the book.
Locomotor and Exploratory Behavior
Authors: Golani Ilan , Benjamini Yoav , Dvorkin Anna , Lipkind Dina , Kafkafi Neri 
Published: May 2009

AbstractRat exploratory behavior includes motor, locomotor, motivational, and cognitive aspects; it consists of a stimulating combination of stochastic and lawful elements. As technology improves, it becomes increasingly more accessible for data acquisition and analysis. This chapter reviews studies relating to the animal's trajectory in the environment and relating to interlimb coordination. Each section starts from the stage of automated data acquisition and then proceeds through the isolation of patterns of movement to global regularities.
Sex
Authors: Jenkins William J. , Becker Jill B. 
Published: May 2009

AbstractThis chapter provides an overview of the reproductive systems and the neural systems that mediate sexual behavior, and discusses how to study sexual behavior in male and female rats. It shows that the male and female rat share many commonalities in terms of the anatomical substrates of sexual behavior. Another common feature in the sexual behavior of males and females is the role that the striatum and nucleus accumbens (NAcc) play in mediating sexual behavior and motivation.
Antipredator Defense
Authors: Blanchard D. Caroline , Blanchard Robert J. 
Published: May 2009

AbstractThis chapter discusses defensive behavior in rats. Topics covered include specific defensive behaviors (e.g., flight, hiding, freezing, alarm cries, defensive attack), stimuli that elicit defense, the role of “expediting” stimuli in controlling specific defenses, the role of threat intensity in controlling specific defenses, outcomes of defensive behaviors, and laboratory models of rat defensive behaviors.
Dead Reckoning
Authors: Wallace Douglas G. , Whishaw Ian Q. 
Published: May 2009

AbstractRats may use at least two navigational strategies that aid in the recovery of resources and protection from predation: allothetic and idiothetic. Allothetic navigation involves the use of external cues (visual, auditory, or olfactory cues). Idiothetic navigation involves the use of uses cues generated by self-movement (proprioceptive and vestibular cues, sensory flow, or efferent copies of movement commands). A prominent form of idiothetic navigation is dead reckoning, in which a rat locates its present position in relation to a starting position, to which it can return. This chapter presents behavioral techniques used to investigate dead reckoning and describes a theoretical framework for dead reckoning.
Case History and Initial Findings
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter provides a brief case history for AH and describes the preliminary results that led to a focus on her processing of visual location and orientation information. AH was an 18-year-old freshman at Johns Hopkins University when the study began in December 1991. When testing ended in May 1995, she was 21 years old and had just graduated from Johns Hopkins. Her neurological status, educational history, and impaired location and orientation processing are described. AH was strikingly impaired across a variety of direct-copy tasks with diverse stimulus materials. Despite the fact that the stimuli remained in view while she produced her copies, she made frequent and blatant errors even for very simple stimuli. AH's direct-copy errors systematically involved mislocation or misorientation of stimulus objects or their parts. Moreover, the location and orientation errors were not random but instead took the form of left-right or up-down reflections. These results clearly demonstrated that AH suffered from some form of impairment that affected her processing of location and orientation information.
Impaired Processing of Visual Location and Orientation Information
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter provides additional evidence demonstrating that AH has a selective deficit in visual location and orientation perception. Tests show that AH's impairment in processing visual location and orientation information is not limited to direct-copy tasks. She presented with severely impaired performance across a broad range of tasks that differed widely in the form of the stimuli, the nature of the responses, and other task requirements. As in the direct-copy tasks, her errors were extremely systematic, taking the form of left-right and/or up-down reflections.
Spelling and the Visual Deficit
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter discusses AH's spelling impairment, suggesting that AH's severely impaired spelling may be a nonobvious consequence of her perceptual deficit. Visual perception of location and orientation, although not required for performing a spelling task, is crucial for learning to spell: Experience with visually presented words plays a central role in acquisition of lexical-orthographic representations and sublexical sound-spelling correspondences. AH's deficit in visual location and orientation perception may therefore have disrupted her ability to acquire these forms of knowledge as a child and, hence, impaired her ability to spell as an adult.
A Paradox
Authors: McCloskey Michael 
Published: May 2009

AbstractThe results discussed in the preceding chapters lead to a paradox: On the one hand, data from a broad range of laboratory tasks implied that AH was severely impaired in perceiving the location and orientation of visual stimuli; yet, on the other hand, she was apparently leading a normal life, doing well in school and living independently with no special accommodations. This chapter attempts to resolve this paradox. In doing so, it develops three key points: First, AH is intact in extracting location and orientation information from certain forms of stimuli (e.g., moving visual stimuli), allowing her to succeed in many everyday tasks. Second, AH's performance in daily life is not, in fact, normal: Her self-reports and the results from laboratory tasks indicate that she encounters difficulty in a variety of circumstances. Third, compensatory processes help to reduce the impact of the deficit. These points, supported by AH's self-reports and data from several tasks, indicate that AH's performance in daily life can be reconciled with the laboratory evidence of a serious perceptual deficit.
How Does AH Succeed at Reading?
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter considers how AH is apparently able to read successfully in daily life and why she and others were unaware of her reading difficulties. It suggests that AH's reading processes rely heavily on knowledge of regularities at multiple levels in written language to constrain interpretation of the potentially inaccurate stimulus representations generated by her visual system. When the available constraints are strong, as in reading connected text, AH's reading processes may usually be able to “repair” the visual-system errors, resulting in good comprehension. However, when the constraints are weak, as with isolated words or sequences of unrelated words, recovery from visual errors may often not be possible. The use of knowledge-based constraints is not a conscious problem-solving process but rather proceeds without AH's awareness or control.
Related Cases
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter discusses other reported deficits in processing visual location and orientation information. It highlights a recently reported case, involving a patient named PR, that bears a striking resemblance to that of AH. Both AH and PR were impaired in location and orientation perception, both made systematic left-right reflection errors, and both showed the same dramatic effects of exposure duration, motion, flicker, and eccentricity. The commonalities between the two cases strongly suggest that the underlying deficits are very similar and provide a basis for increased confidence in conclusions about the normal visual system drawn from AH's (or PR's) performance.
Orientation Representations and Frames of Reference: The COR Hypothesis
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter presents the coordinate-system orientation representation (COR) hypothesis. It lays out the assumptions of the COR and then discusses the various forms of orientation errors that could arise in constructing or using the posited representations. The hypothesis provides something that has been lacking in cognitive research on orientation: a conceptual framework for thinking about how the orientation of objects might be represented. It also calls attention to nonobvious differences among forms of orientation error (e.g., tilt-direction errors, reflections across object axes, reflections across external axes) and suggests underlying causes for each error type. Most notably, the hypothesis provides specific interpretations for the various forms of mirror-reflection error.
Orientation Representations: Empirical Evidence
Authors: McCloskey Michael 
Published: May 2009

AbstractThis chapter interprets AH's orientation errors in light of the coordinate-system orientation representation (COR) hypothesis. It begins by discussing AH's performance on orientation perception tasks in light of the COR hypothesis, arguing that the hypothesis can account for her errors. It then describes three additional orientation studies that researchers have recently carried out, again arguing that the COR hypothesis can explain the results. The findings from all of the studies support the fundamental COR assumptions about representation of orientation.
Characteristics of Infectious Disease That Raise Distinctive Challenges for Bioethics
Authors: Battin Margaret P. , Francis Leslie P. , Jacobson Jay A. , Smith Charles B. 
Published: May 2009

AbstractThis chapter examines the characteristics of infectious disease that raise special medical and social ethical issues, and explores ways of integrating both current bioethics and classical public health ethics concerns. Many of the ethical issues raised by infectious disease are related to these diseases' powerful ability to engender fear in individuals and panic in populations. The chapter addresses the association of some infectious diseases with high morbidity and mortality rates, the sense that infectious diseases are caused by invasion or attack on humans by foreign microorganisms, the acute onset and rapid course of many infectious diseases, and, in particular, the communicability of infectious diseases. The individual fear and community panic associated with infectious diseases often leads to rapid, emotionally driven decision-making about public health policies needed to protect the community that may be in conflict with current bioethical principles regarding the care of individual patients. The discussion includes recent examples where dialogue between public health practitioners and bioethicists has helped resolve ethical issues that require us to consider the infected patient as both a victim with individual needs and rights, and as a potential vector of disease that is of concern to the community.