bluuebunny/crossref_metadata_2025_split huggingface dataset:
III.—On the Moments and Regression Equations of the Fourfold Negative and Fourfold Negative Factorial Binomial Distributions
Authors: Wiid A. J. B. 
Published: July 2016

SynopsisThe bivariate distribution corresponding to the univariate negative binomial, and the corresponding distribution when sampling is without replacement, are investigated. Formulas are derived for the factorial moment generating functions and for the regression equations, which are linear.
IV.—The Differential Equations Associated with the Uniformization of Certain Algebraic Curves
Authors: Rankin R. A. 
Published: July 2016

SynopsisEvery algebraic equation can be uniformized by automorphic functions belonging to a certain group of bilinear transformations. In certain cases, such as for hyperelliptic equations, this group is a subgroup of the monodromic group of a differential equation of the formwhere R(z) is a rational function which, in general, contains unknown parameters as coefficients. A conjecture of E. T. Whittaker regarding the values of these parameters for the hyperelliptic case is proved for a wide variety of algebraic equations whose branch points possess certain symmetric properties, and is extended to equations of higher type. In several cases, the uniformizing functions belong to subgroups of the groups of the Riemann-Schwarz triangle functions.
VII.—Entropic Functions for Linear Algebras
Authors: Etherington I. M. H. 
Published: July 2016

SynopsisThe function ɸx = log x satisfies the functional equation ɸxy = λɸx + μɸy + ϰ, where in this case x, y are complex variables, λ = μ = i, and ϰ = 2πi, o or − 2πi according as σ < − π, − π < σ < π, π < σ, where σ = arg x + arg y. Generalizing this situation, let A be a linear algebra with basis e1, …, en over the real or complex field and let ɸx be a complexvalued function of the hypercomplex variable x = Σξiei, i.e. of the n real or complex variables ξi. Assume that the gradient ∂ɸx, i.e. the column vector of partial derivatives {∂ɸx/∂ξi}, exists at a general point of A. Then ɸx is called an entropic function if it satisfies a functional equation of the above-mentioned form and obeys certain other postulates, ϰ being a step function of the two hypercomplex variables. Values of the constants λ, μ (complex numbers, not both zero) for which a solution exists are entropic roots of A. They are usually discrete.
XVIII.—Energy Levels of B10: Evidence from the B10 γ-ray Spectrum.
Authors: Galloway R. B. , Sillitto R. M. 
Published: July 2016

SYNOPSISA study of the γ-rays produced during the bombardment of a thick Be9 target by 600 keV deuterons was made to investigate the possible existence of a level at 2·86 MeV in B10, about which contradictory reports have appeared in the literature.A spectrum of the γ-rays in coincidence with the 0·72 MeV B10 γ-ray (text-fig. 5) was obtained, and is interpreted as providing evidence for a level in B10 at 2·86 MeV. The relative intensities of the γ-rays in an ungated spectrum, and in spectra gated by the 0·72 and 1·02 MeV B10 γ-rays, were found, and a decay scheme consistent with the observations is deduced (text-fig. 6b). The relative intensities of the transitions in this decay scheme are consistent with the intensities of the neutron groups in a spectrum of the neutrons from this reaction. A spin value of 2 or 3 is suggested for the 2.86 MeV level.
XXII.—Some Nilpotent Algebras with Centres of Given Dimension
Authors: Wallace E. W. 
Published: July 2016

SYNOPSISAlgebras which are nilpotent and anti-commutative are studied. Canonical forms are found for all such algebras of dimension n whose centres have dimension n−r (r < 3), and characters are given which enable any two non-isomorphic algebras to be distinguished.A metrisable Lie algebra is a Lie algebra for which there is a non-singular, symmetric, adjoint-invariant bilinear form a(λ, μ), and such an algebra is reduced if its centre is contained in its derived algebra. The importance of the reduced algebras follows from the fact that every metrisable Lie algebra is the direct sum of a reduced metrisable Lie algebra and an abelian Lie algebra. Tsou (Thesis 1955) introduced metrisable Lie algebras, and obtained canonical forms for all real reduced metrisable Lie algebras whose derived algebras have dimension 3. We conclude this paper by providing an alternative derivation, two of the algebras being nilpotent.
XXIII.—Representations of a Number as the Sum of a Large Number of Squares
Authors: Rankin R. A 
Published: July 2016

SYNOPSISAn asymptotic formula is given for the number r(s, P; N) of representations of an integer N as the sum of s non-negative squares, where each square does not exceed P2. The numbers s, P and N are large and are subject to certain conditions, one of which is that N is approximately ⅓sP2.
VIII.—The Central Limit Theorem for a Convergent Non-homogeneous Finite Markov Chain
Authors: Mott J. L. 
Published: July 2016

SynopsisThe distribution of xn, the number of occurrences of a given one of k possible states of a non-homogeneous Markov chain {Pj} in n successive trials, is considered. It is shown that if Pn → P, a positive-regular stochastic matrix, as n → ∞ then the distribution about its mean of xn/n½ tends to normality, and that the variance tends to that of the corresponding distribution associated with the homogeneous chain {P}.
Food insecurity as a driver of obesity in humans: The insurance hypothesis
Authors: Nettle Daniel , Andrews Clare , Bateson Melissa 
Published: July 2016

AbstractIntegrative explanations of why obesity is more prevalent in some sectors of the human population than others are lacking. Here, we outline and evaluate one candidate explanation, the insurance hypothesis (IH). The IH is rooted in adaptive evolutionary thinking: The function of storing fat is to provide a buffer against shortfall in the food supply. Thus, individuals should store more fat when they receive cues that access to food is uncertain. Applied to humans, this implies that an important proximate driver of obesity should be food insecurity rather than food abundance per se. We integrate several distinct lines of theory and evidence that bear on this hypothesis. We present a theoretical model that shows it is optimal to store more fat when food access is uncertain, and we review the experimental literature from non-human animals showing that fat reserves increase when access to food is restricted. We provide a meta-analysis of 125 epidemiological studies of the association between perceived food insecurity and high body weight in humans. There is a robust positive association, but it is restricted to adult women in high-income countries. We explore why this could be in light of the IH and our theoretical model. We conclude that although the IH alone cannot explain the distribution of obesity in the human population, it may represent a very important component of a pluralistic explanation. We also discuss insights it may offer into the developmental origins of obesity, dieting-induced weight gain, and anorexia nervosa.
Elementary proofs of relations between Eisenstein series
Authors: Rankin R. A. 
Published: July 2016

SynopsisEisenstein series are entire modular forms Ek of even integral weight k≧ 4 with Fourier expansions given by (1.1). There are numerous identities, such as E8 = , relating these series. These are usually proved by arguments making use of the dimensions of vector spaces of modular forms, and not directly. The paper shows how such identities can be proved by elementary methods by studying chains of solutions of Diophantine equations of the form xξ+yη = n.
2.—Barriers bounded by Two Transition Points of Arbitrary Odd Order
Authors: Heading John 
Published: July 2016

SynopsisA generalisation is considered of the potential barrier problem beyond the familiar case in which the barrier is bounded by transition points of order one. Here, the two transition points involved are of arbitrary odd order. The approximate method employed, though formal in character, avoids certain pitfalls often made in the past whereby certain exponentially small terms within the barrier are confounded with inherent error terms. This confusion is avoided in the treatment given here by tracing uniformly approximate solutions round the transition points in the complex plane by means of the Stokes phenomenon, the method not requiring the dubious concept of a subdominant term existing in the presence of a dominant term on a Stokes line. At the same time, the solutions to which the reflection and transmission coefficients may be attached are carefully discussed, so that the appearance of a small exponential term may be seen to be genuine when taken in conjunction with inherent error terms. The resulting formula for the modulus of the reflection coefficient generalizes the more elementary formula.
12.—Spectral Theory of Rotating Chains
Authors: Stuart C. A. 
Published: July 2016

SynopsisTwo eigenvalue problems associated with steady rotations of a chain are considered. To compare the spectra of these two problems, let σK(n) denote the set of all angular velocities with which a chain of unit length with one end fixed and the other free can rotate in a vertical plane so as to have exactly n nodes on thevertical axis (including the fixed end). In a linearised theory σK(n) is a single point, i.e.In the full non-linear theory σK(n) is an infinite interval lying to the right of ⍵n. Indeed,This is established in [1].Next, let σM(β, n) denote the set of all angular velocities with which a chain, having ends fixed at unit distance apart on the vertical axis, can rotate in a vertical plane so as to have exactly n+l nodes on the vertical axis (including the ends) and so that the tension takes the value β at the lower end. This problem, in which the length of the chain is not prescribed is a model for a spinning process in which the ‘chain’ is continuously created in a rotating configuration. For β>0, we again have in the linearised theory that σM(β, n) is a singleton, i.e.In the full non-linear theory σM(β, n) lies to the left of λn(β). Although unable to determine exactly σM(β, n) for β>0, we havewhere ⍵n λn(β), and are all characterised as the nth zeros of known combinations of Bessel functions.
1.—On Square-integrable Solutions of Symmetric Systems of Differential Equations of Arbitrary Order.
Authors: Kogan V. I. , Rofe-Beketov F. S. 
Published: July 2016

SynopsisThe following results are obtained for symmetric differential expressions of arbitrary order r ≧ 1 with matrix coefficients on the half-line, with a non-negative (and possibly identically degenerate) weight matrix W(t), and with a spectral parameter λ: upper and lower bounds for the deficiency indices N(λ) are found; it is proved that N(λ) is independent of λ for Im λ< 0and for Im λ>0; under very general conditions it is proved that the maximum possible values of the deficiency indices in the half-planesIm λ≷0 can only be attained simultaneously; sufficient conditions for first-order expressions to be quasi-regular are derived; and it isshown that a symmetric system of any order reduces to a canonical, first-order system.Examples are constructed, and the case of the whole line is also touched on.
2.—On Weyl's Function m(λ).
Authors: Wray S. D. 
Published: July 2016

SynopsisA proof is given of a formula connecting Weyl's function m(λ) with a spectral integral, in the setting of the singular theory of the Sturm-Liouville differential equation. In addition, a relatively short treatment is given of the argument introducing the function. The theory applies to both the limitpoint and limit-circle cases.
4.—Perturbations of Non-linear Integral Operators
Authors: Stummel Friedrich 
Published: July 2016

SynopsisNon-linear integral operators are studied under perturbations of the integrals, the domains of integration, the kernels and the inhomogeneous terms. The main theorem establishes the local solubility of the perturbed integral equations, the biconvergence of their solutions and associated two-sided error estimates. This theorem is of interest even for the special class of linear Fredholm integral equations.
14.—Dynamic Programming applied to Some Non-linear Stochastic Control Systems
Authors: Fuller A. T. 
Published: July 2016

SynopsisOptimal switching curves are investigated for some second-order control systems with random disturbances, saturating control, and a mean-square-error performance index.It is first shown that the optimal switching curves are asymptotic at infinity to the optimal switching curves for corresponding deterministic systems.The systems are then discretised in time and state, and ordinary dynamic programming is applied to the resulting Markov chain models. The discretisation techniques are described in some detail.The same techniques are applied to a deterministic system for which the optimal switching curve is known, and it is found that the resulting discretisation errors are considerable.Thus it turns out that ordinary discrete dynamic programming gives only a rough approximation to the optimal switching curve. It seems desirable to tackle the equations of continuous dynamic programming by techniques more refined than crude discretisation. One such technique is suggested.
16.—On Uniqueness of Topological Degree for Set-valued Mappings
Authors: Webb J. R. L. , Everitt W. N. 
Published: July 2016

SynopsisIt is shown that three independent axioms uniquely determine the topological degree of set-valued maps of the form I – G, where G is a convex-valued, limit compact map. This extends earlier work of Amann and Weiss, Nussbaum, and others, in that, apart from dealing with set-valued maps, a larger class of maps is considered even in the single-valued case.
24.—The Solution of Initial-Boundary Value Problems for Pseudoparabolic Partial Differential Equations
Authors: Rundell William , Sneddon I. N. 
Published: July 2016

SynopsisA fundamental solution for equations of pseudoparabolic type is constructed by a method analogous to Hadamard's construction for elliptic equations. By the use of this fundamental solution we obtain a regularity theorem and integral representations for the solution to the more common initial boundary value problems that are associated with these equations.
Small solutions of a non-linear equation in Banach space for a degenerate case
Authors: Shearer M. 
Published: July 2016

SynopsisThe existence of zeroes of an operator in Banach space near a. known zero is examined, when the non-degeneracy condition of Magnus [1] is violated, and replaced by a condition which is called simple-degeneracy. Criteria are given which help determine the number and the structure of curves of zeroes of the operator, passing through the known zero.These conditions and results are interpreted in terms of bifurcation theory. By considering several different cases, it is shown that the failure of various conditions frequently employed in the Lyapunov–Schmidt method may be overcome using the idea of simple-degeneracy.
On the essential self-adjointness of powers of Schrödinger-type operators
Authors: Evans W. D. 
Published: July 2016

SynopsisLet T be the formally self-adjoint second-order elliptic differential expressionin ℝn, where the coefficients bj, ajk, q are real-valued and ajk ≈ akj. In this paper sufficient conditions for all positive integer powers Tm of T to be essentially self-adjoint on are obtained.
Application des méthodes de convexité et monotonie a l'étude de certaines équations quasi linéaires
Authors: Attouch H. , Damlamian A. 
Published: July 2016

SynopsisUsing Hilbert space methods, existence and uniqueness are proved for the solution of some strongly non-linear partial differential equations of elliptic and parabolic type.They are associated with quasi-linear operators of the form: -div(β(x, grad u)) + β0(x, u) where β (resp β0) is a maximal monotone subdifferential on ℝN(resp ℝ) depending smoothly on x in a bounded domain Ω of ℝNThese operators are shown to be the subdifierentials over Lp(Ω) of convex functional of the following type:where j is a normal convex integrand over Ω×ℝN+1 satisfying a coerciveness condition.This method avoids the theory of Sobolev-Orlicz spaces. An application is given also forthe gas-diffusion equation over ℝ+.
Related singular problems and the generalized Hilbert transform
Authors: Dettman John W. 
Published: July 2016

SynopsisAbstract versions of the Cauchy problem for the Euler-Poisson-Darboux equation and the Dirichlet problem for the equation of generalized axially symmetric potential theory are related by an integral transformation. In certain special cases, this leads to abstract versions of (1) the Poisson formula for the solution of G.A.S.P.T. in a half-space, (2) pseudo-analytic functions in a half-space, and (3) a generalized Hilbert transform related to the work of Heywood, Kober, and Okikiolu. Some properties of this generalized Hilbert transform are studied including an inversion theorem.
7.—Acoustic Diffraction by an Absorbing Semi-Infinite Plane in a Moving Fluid, II
Authors: Rawlins A. D. 
Published: July 2016

SYNOPSISThe diffraction of a line source by an absorbing semi-infinite plane in the presence of a subsonic fluid flow is examined. Expressions for the total far field for the leading edge (no wake present) and the trailing edge (wake present) situation are given.It is found that the presence of fluid flow attenuates the sound level in the shadow region of the absorbent screen. There is greater attenuation of the sound level in the trailing edge situation than there is for the leading edge situation.Sound level attenuation on the source side of the absorbent screen is found to depend more critically on the absorptive properties of the screen than on the fluid flow. The radiated sound intensity, in the half space in which the source is located, can be considerably reduced by a suitable choice of the absorption parameter.
The exceptional condition and unboundedness of solutions of hyperbolic systems of conservation type
Authors: Jeffrey A. 
Published: July 2016

SynopsisThis paper is concerned with quasilinear hyperbolic systems of conservation type and establishes two main results. The first is that when a general system is considered in one space dimension and time, then the exceptional nature of a characteristic field implies the coincidence of a shock with one of the characteristics of that field. The second result involves the demonstration by example that quasilinear hyperbolic systems of conservation type may possess solutions that become unbounded after only a finite time, even though they are exceptional.
Inverse semigroups generated by a pair of subgroups
Authors: McAlister D. B. 
Published: July 2016

SynopsisThe aim of this paper is to describe the free product of a pair G, H of groups in the category of inverse semigroups. Since any inverse semigroup generated by G and H is a homomorphic image of this semigroup, this paper can be regarded as asking how large a subcategory, of the category of inverse semigroups, is the category of groups? In this light, we show that every countable inverse semigroup is a homomorphic image of an inverse subsemigroup of the free product of two copies of the infinite cyclic group. A similar result can be obtained for arbitrary cardinalities. Hence, the category of inverse semigroups is generated, using algebraic constructions by the subcategory of groups.The main part of the paper is concerned with obtaining the structure of the free product G inv H, of two groups G, H in the category of inverse semigroups. It is shown in section 1 that G inv H is E-unitary; thus G inv H can be described in terms of its maximum group homomorphic image G gp H, the free product of G and H in the category of groups, and its semilattice of idempotents. The second section considers some properties of the semilattice of idempotents while the third applies these to obtain a representation of G inv H which is faithful except when one group is a non-trivial finite group and the other is trivial. This representation is used in section 4 to give a structure theorem for G inv H. In this section, too, the result described in the first paragraph is proved. The last section, section 5, consists of examples.
Some unsolved problems of unknown depth about operators on Hilbert space
Authors: Halmos P. R. 
Published: July 2016

SynopsisThe paper presents a list of unsolved problems about operators on Hilbert space, accompanied by just enough definitions and general discussion to set the problems in a reasonable context. The subjects are: quasitriangular matrices, the resemblances between normal and Toeplitz operators, dilation theory, the algebra of shifts, some special invariant subspaces, the category (in the sense of Baire) of the set of non-cyclicoperators, non-commutative(i.e. operator) approximation theory, infinitary operators, and the possibility of attacking invariance problems by compactness or convexity arguments.
Formation theory and groups of automorphisms of -groups
Authors: Tomkinson M. J. 
Published: July 2016

SynopsisFurther results from the theory of finite soluble groups are extended to the class of locally finite groups with a satisfactory Sylow structure. Let be a saturated U-formation and A a -group of automorphisms of the -group G. A is said to act -centrally on G if G has an A-composition series (Λσ/Vσ; σ ∈ ∑) such that A induces an f(p)-group of automorphisms in each p-factor Λσ/Vσ. We show that in this situation A is an -group, thus generalising the result of Schmid [8]. Associated results of Schmid and of Baer are also extended to the infinite case.
Hilbert boundary value problems—a distributional approach
Authors: Orton Marion 
Published: July 2016

SynopsisHilbert boundary value problems for a half-space are considered for analytic representations of Schwartz distributions: given data g ∈D'(ℛ) and a coefficient x we seek functions F(z) analytic for Jmz≠0 whose limits exist in D'(ℛ) and satisfy F+—XF– = g on an open subset U of the real line R. U is the complement of a finite set which contains the singular support and the zeros of X·X and its reciprocal satisfy certain growth conditions near the boundary points of U. Solutions F(z) are shown to exist, and their general form is determined by obtaining a suitable factorisation of x.
A note on the exterior problem for linear viscoelasticity
Authors: Beevers C. E. 
Published: July 2016

SynopsisSome continuous dependence theorems are presented for classical solutions of initial-boundary value problems in viscoelastic materials which occupy the exterior of a bounded domain in Euclidean three space. Two broad classes of anisotropic viscoelastic materials are considered. The theorems are proved by a combination of the Protter and the Graffi methods.
An elliptic boundary value problem for strongly non-linear equations in unbounded domains
Authors: Mustonen Vesa 
Published: July 2016

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.
An oscillation theorem for characteristic initial value problems in linear hyperbolic equations
Authors: Pagan Gordon 
Published: July 2016

SynopsisIt is established that under certain restrictions the solution u of the characteristic initial value problem uxy+g(x, y)u = 0, u(x, 0) = p(x) and u(0, y) = q(y), where p(x) > 0 and q(y) > 0, in [0, ∞) x [0, ∞) changes sign along a monotonic decreasing curve which is asymptotic to the axes.