bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some results on the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments
Authors: Philos Ch. G. , Sficas Y. G. , Staikos V. A. 
Published: April 2009

AbstractThis paper deals with some asymptotic properties of nonoscillatory solutions of a class of n-th order (n < 1) differential equations with deviationg arguments involving the so called n-th order r-derivative of the unknown function x defined bywhere ri (i = 0,1…n) are positive continous functions on [t0, ∞). The fundamental purpose of this paper is to find for any integer m, 0 < m < n – 1, a necessary and sufficient condition (depending on m) in order that three exists at least one (nonoscillatory) solution x so that the exists in R – {0} The results obtained extend some recent ones due to Philos (1978a) and they prove, in a general setting, the validity of a conjecture made by Kusano and Onose (1975).
Identifiability of mixtures
Authors: Tallis G. M. , Chesson P. 
Published: April 2009

AbstractLet F(x, θ) be a family of distribution functions indexed by θ ∈ Ω. If G(θ) is a distribution function on Ω H(x) = ƒohm; F(x, θ) dG(θ) is a mixture with respect to G. If there is a unique G yielding H, the mixtures is said to be identifiable.This paper summarises some known results related to identifiability of special types of mixtures and then discusses the general problem of identifiability in terms of mappings. Some new results follow for mappings with special features.
A note on an ill-posed problem for the heat equation
Authors: Talenti Giorgio , Vessella Sergio 
Published: April 2009

AbstractIn this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation ut – uxx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x = x1,…, x = xn, are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0.
Duality theorems and an optimality condition for non-differentiable convex programming
Authors: Kanniappan P. , Sastry Sundaram M. A. 
Published: April 2009

AbstractNecessary and sufficient optimality conditions of Kuhn-Tucker type for a convex programming problem with subdifferentiable operator constraints have been obtained. A duality theorem of Wolfe's type has been derived. Assuming that the objective function is strictly convex, a converse duality theorem is obtained. The results are then applied to a programming problem in which the objective function is the sum of a positively homogeneous, lower-semi-continuous, convex function and a continuous convex function.
Matroids whose ground sets are domains of functions
Authors: Oxley James , Prendergast Kevin , Row Don 
Published: April 2009

AbstractFrom an integer-valued function f we obtain, in a natural way, a matroid Mf on the domain of f. We show that the class of matroids so obtained is closed under restriction, contraction, duality, truncation and elongation, but not under direct sum. We give an excluded-minor characterization of and show that consists precisely of those transversal matroids with a presentation in which the sets in the presentation are nested. Finally, we show that on an n-set there are exactly 2n members of .
Congruences on regular and completely regular semigroups
Authors: Trotter P. G. 
Published: April 2009

AbstractCongruences on regular semigroups have been characterized in terms of normal equivalences on sets of idempotents and kernels of congruences. A revised characterization is presented here with considerably simplified expressions for the least and greatest congruences associated with normal equivalences and with a new description of kernels. The results are then applied to characterize congruences on completely regular semigroups.
Criteria for extreme forms
Authors: Barnes E. S. 
Published: April 2009

A positive quadratic form, of determinantand minimum M for integral, is said to be extreme if the ratiois a (local) maximum for small variations in the coefficients.Minkowski [3] has given a criterion for extreme forms in terms of a fundamental region (polyhedral cone) in the coefficient space. This criterion, however, involves a complete knowledge of the edges of the region and is therefore of only theoretical value.
On distributions whose moments are majorated by the moments of a known distribution
Authors: Laha R. G. , Lukacs Eugene 
Published: April 2009

SummaryLet F(x) be a distribution function and denote by its characteristic function and by its moment of order k H. Milicer-Grużewska [2]has derived the following theorem: Suppose that F(x) has moments of all orders and that they satisfy the relations. where while C is a positive constant. Then f(t) is an entire function of order not exceeding two. The proof given by H. Milicer-Gruzewska is rather complicated, moreover the restriction (1.2) seems to be artificial and motivated only by the particular method of proof. We note that condition (1.1) means that the moments of F (x) are majorated by the moments of a normal distribution and we use this remark to generalize the problem.
The survival of a mutant gene under selection
Authors: Moran P. A. P. 
Published: April 2009

AbstractThe problem of the survival of a single mutant in a haploid genetic population when there exists selection is considered for a type of population model in which the generations ar overlapping. The results are compared with the previous work of Fisherand others for other models. The need is stressed for a solution of the same problem in a diploid population with general phenotypic selection coefficients.
The joint distribution of occupation totals for a simple random walk
Authors: Barnett V. D. 
Published: April 2009

SummaryA great deal of attention has been given in the literature to the various properties of the simple binomial random walk. Explicit expressions are available for first passage times, absorption probabilities, average duration of the walk up to absorption and other quantities of interest. One aspect of the behaviour of this work which has, however, attracted little attention is the form of the distribution of occupation totals. This paper is devoted to the derivation of an explict expression for the joint probility generating function of the occupation totals up to absorption, for the binomial random walk in the presence of two absorbing points. The appropriate marginal form of this p.g.f. yields the distribution of the occupation total, and expected occupation total, at any particular lattice point. The limiting forms of these results provide explicit expressions for the corresponding quatities in the case of a binomial random walk having a single absorbing point and, where relevent, in the case of the unrestricted binomial random walk.
A simple proof of Watson's partition congruences for powers of 7
Authors: Garvan F. G. 
Published: April 2009

AbstractRamanujan conjectured that ifnis of a specific form thenp(n), the number of unrestricted partitions ofn, is divisible by a high power of 7. A modified version of Ramanujan's conjecture was proved by G. N. Watson.In this paper we establish appropriate generating formulae, from which Watson's results follow easily.Our proofs are more straightforward than those of Watson. They are elementary, depending only on classical identities of Euler and Jacobi. Watson's proofs rely on the modular equation of seventh order. We also need the modular equation but we derive it using the elementary techniques of O. Kolberg.
(PVB) functions and integration
Authors: Sarkhel D. N. , Kar A. B. 
Published: April 2009

AbstractWe introduce the notion of functions of bounded proximal variation and the notion of orderly connected topology on the real line. Using these notions, we define in a novel way an integral of Perron type, including virtually all the known integrals of Perron and Denjoy types and admitting mean value theorems and integration by parts and the analog of Marcinkiewicz theorem for the ordinary Perron integral.
Epimorphisms preserving perfect radicals
Authors: Berrick A. J. 
Published: April 2009

AbstractThis is an investigation of whether a group epimorphism maps the maximal perfect subgroup of its domain onto that of its image. It is shown how the question arises naturally from considerations of algebraic K-theory and Quillen's plus-construction. Some sufficient conditions are obtained; these relate to the upper central series, or alternatively the derived series, of the domain. By means of topological/homological techniques, the results are then sharpened to provide, in certain circumstances, conditions which are necessary as well as sufficient.
A generalized Fourier transformation for L1(G)-Modules
Authors: Liu Teng-Sun , Rooij Arnoud C. M. Van , Wang Ju-Kwei 
Published: April 2009

AbstractLet G be a compact abelian group with dual Ĝ and let K be a Banach L1 (G)-module. We introduce the notion of character convolution transformation of K which reduces to ordinary Fourier or Fourier-Stieltjes transformation when K is one of the spaces Lp(G), M(G). We show that the question of what maps Ĝ → K extend to multipliers of K is a question of asking for descriptions of the character convolution transforms. In this setting some results of Helson-Edward and Schoenberg-Eberlein find generalizations, as do some classical results, including the inversion formula and the Parseval relation. We then apply these results to transformation groups, obtaining a variant of a theorem of Bochner and an extension of a theorem of Ryan.
A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results
Authors: Hoek John Van Der , Barnes C. J. , Knight J. H. 
Published: April 2009

AbstractA field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.
On the theory of a cascade of stalled aerofoils
Authors: Woods L. C. 
Published: April 2009

SummaryA mathematical theory of the separating flow past a cascade of aerofoils is developed. The flow is assumed to be inviscid, incompressible and twodimensional. The wakes are represented by regions of stationary fluid, which could, in the general case, maintain a pressure gradient, although much of the theory is developed for the case of constant wake pressure.
Unsteady flow through a cascade of aerofoils
Authors: Low A. H. , Woods L. C. 
Published: April 2009

SummaryThis paper extends some earlier work by Woods [8] on the transient forces caused by unsteady transverse motions of a rigid cascade of aerofoils to the case when the inlet velocity is varying in magnitude. The flow is incompressible and two-dimensional. Expressions for the growth of lift and moment on a member of the cascade with increasing inlet velocity are evaluated and shown to be generalizations of Wagner's classical results for an isolated aerofoil.
Quadratic forms in Poisson and multi-nomial variables
Authors: Whittle P. 
Published: April 2009

SummaryLetrepresent the deviations from expectation of a set of multinomial or independent Poisson variables, and Η be a positive definite matrix. A lower bound is obtained forPrin terms ofPr, Whereis a vector of normal variables with the same mean and covariance matrix as Δ.
A characterization of semi-prime ideals in near-rings
Authors: Groenewald N. J. 
Published: April 2009

AbstractIt is well-known that in any near-ring, any intersection of prime ideals is a semi-prime ideal. The aim of this note is to prove that any ideal is a prime ideal if and only if it is equal to its prime radical. As a consequence of this we have any semi-prime ideal I in a near-ring N is the intersection of minimal prime ideals of I in N and that I is the intersection of all prime ideals containing I.
Powers of chordal graphs
Authors: Balakrishnan R. , Paulraja P. 
Published: April 2009

AbstractAn undirected simple graph G is called chordal if every circle of G of length greater than 3 has a chord. For a chordal graph G, we prove the following: (i) If m is an odd positive integer, Gm is chordal. (ii) If m is an even positive integer and if Gm is not chordal, then none of the edges of any chordless cycle of Gm is an edge of Gr, r < m.
Linearity and weak convergence on the boundary of numerical range
Authors: Das K. C. , Craven B. D. 
Published: April 2009

AbstractStampfli and Embry have shown that a point of the numerical range of an operator is extreme if and only if a set of vectors corresponding to it is linear. This is generalized here to show that a point of the closure of the numerical range is extreme if and only if a corresponding set of sequences forms a linear space. A more geometric alternative proof is given for a theorem of Das and Garske concerning weak convergence to zero at the unattained extreme points of the closure of the numerical range.The result is shown to hold also for lone extreme points of the numerical range which lie on line segments on its boundary. Further, a bound is obtained on the norm of the weak limit of the weakly convergent sequences corresponding to points on a line segment on the boundary of numerical range.
A few more balanced Room squares
Authors: Stinson D. R. , Vanstone S. A. 
Published: April 2009

AbstractThe existence problem for balanced Room squares is, in general, unsolved. Recently, B. A. Anderson gave a construction for a class of these designs with side 2n − 1, where n is odd and n ≥ 3. For n even, the existence has not yet been settled. In this paper, we use the affine geometry of dimension 2 k and order 2, and a hill-climbing algorithm, to construct a number of new balanced Room squares directly. Recursive techniques based on finite geometries then give new squares of side 22k − 1 for infinitely many values of k.
A generalization of Tong's theorem and properties of pairwise perfectly normal spaces
Authors: López-Pellicer Manuel , Gutiérrez Angel 
Published: April 2009

AbstractIn this paper we give some properties of the pairwise perfectly normal spaces defined by Lane. In particular we prove that a space (X, P, Q) is pairwise perfectly normal if and only if every P(Q)–closed set is the zero of a P(Q)–l.s.c. and Q(P)–u.s.c. function. Also we characterize the pairwise perfect normality in terms of sequences of semicontinuous functions by means of a result which contains the known Tong's characterization of perfectly normal topological spaces, whose proof we modify by using the technique of binary relations.
The range of an o-weakly compact mapping
Authors: Dodds P. G. 
Published: April 2009

AbstractIt is shown that a weakly compact convex set in a locally convex space is a zonoform if and only if it is the order continuous image of an order interval in a Dedekind complete Riesz space. While this result implies the Kluv´nek characterization of the range of a vector measure, the techniques of the present paper are purely order theoretic.
A note on generalised wreath product groups
Authors: Praeger Cheryl E. , Rowley C. A. , Speed T. P. 
Published: April 2009

AbstractGeneralised wreath products of permutation groups were discussed in a paper by Bailey and us. This note determines the orbits of the action of a generalised wreath product group on m–tuples (m ≥ 2) of elements of the product of the base sets on the assumption that the action on each component is m–transitive. Certain related results are also provided.
Scales of functions
Authors: Erdös P. , Rogers C. A. , Taylor S. J. 
Published: April 2009

We consider real-valued functions ƒ(x) which are defined for all sufficiently large real numbers x. In discussing the behaviour of such functions as x → + ∞, it is useful to compare ƒ with the functions of some “comparison scale”. The early work in this field was due to Du Bois-Reymond (see, for example, (2), (3)). This was elaborated by Hardy, (6), who was mainly concerned with what he calls the “logarithmico-exponential” scale of functions. This “scale of Hardy” may be defined as the smallest class ℋ of functions ƒ with the following properties:(i) if ƒ ∈ ℋ, ƒ, is defined and continuous for all sufficiently large values of x;(ii) (a) the function ƒ(x) ≡ α, where α is any real constant, is in ℋ;(b) the function ƒ(x) ≡ x is in ℋ;(iii) if ƒ and g are in ℋ and g is non-zero for all sufficiently large values of x, thenare also in ℋ.
Expectation values of operators in the quasi chemical equilibrium theory
Authors: Blatt John M. 
Published: April 2009

AbstractExpectation values of one-particle and two-particle operators are evaluated in the quasi-chemical equilibrium (pair correlation) approximation to statistical mechanics. Certain reductions, corresponding to the “quenching” of interactions by the Pauli exclusion principle, are carried out quite generally. More specific reductions, which lead to immediately useful expressions, are possible on the assumption of extreme Bose-Einstein condensation of the correlated pairs.
Cocycles and representations of groups of CAR type
Authors: Carey A. L. , Moran William 
Published: April 2009

AbstractRepresentations of non-type I groups G which may be expressed as an increasing union of type I normal subgroups are considered. Groups with this structure are natural generalisations of the CAR algebra (viewed as a twisted group C*-algebra) and are also group theoretic analogues of AF algebras. This paper gives a systematic account of their representation theory based on a canonical construction of one-cocycles for the G-action on the dual of a normal subgroup. Some examples are considered showing how to construct inquivalent irreducible representations (non-cohomologous cocycles) and also factor representations by a method which generalises the well-known construction of non-isomorphic factors for the CAR algebra.
Cumulants and partition lattices II: generalised k-statistics
Authors: Speed T. P. 
Published: April 2009

AbstractThe role played by the Möbius function of the lattice of all partitions of a set in the theory of k-statistics and their generalisations is pointer out and the main results conscerning these statistics are drived. The definitions and formulae for the expansion of products of generalished k-statistics are presented from this viewpoint and applied to arrays of random variables whos moments satisfy stitable symmentry constraints. Applications of the theory are given including the calculation of (joint) cumulants of k-statistics, the minimum variace estimation of (generalised) moments and the asymptotic behaviour of generalised k-statistics viewed as (reversed) martingales.
Special series of unitary representations of groups acting on homogeneous trees
Authors: Mantero Anna Maria , Zappa Anna 
Published: April 2009

AbstractLet G be a group acting faithfully on a homogeneous tree of order p + 1, p > 1. Let be the space of functions on the Poission boundary ω, of zero mean on ω. When p is a prime. G is a discrete subgroup of PGL2(Qp) of finite covolume. The representations of the special series of PGL2(Qp), Which are irreducible and unitary in an appropriate completion of , are shown to be reducible when restricted to G. It is proved that these representations of G are algebraically reducible on and topologically irreducible on endowed with the week topology.
Orbit entropy in noninvertible mappings
Authors: Burkart Uhland 
Published: April 2009

AbstractBassed on the intrinsic structure of a selfmapping T: S → S of an arbitrary set S, called the orbit-structure of T, a new entropy is defined. The idea is to use the number of preimages of an element x under the iterates of T to characterize the complexity of the transformation T and their orbit graphs. The fundamental properties of the orbit entropy related to iteration, iterative roots and iteration semigroups are studied. For continuous (differentiable) functions of Rn to Rn, the chaos of Li and Yorke is characterized by means of this entropy, mainly using the method of Straffingraphs.
Eigenfunctions of plane elastostatics III the Wedge
Authors: Buchwald V. T. 
Published: April 2009

SummaryThe boundary value problem of the infinite wedge in plane elastostatics is reduced to the solution of a differential-difference equation. The complementary function of this equation is determined in the form of a Fourier integral, which, on expansion by residue theory, gives the complete eigenfunction expansion for the wedge. The properties of the eigenfunctions are discussed in some detail, and orthogonality property is derived.
Neo-Lorentzian relativity
Authors: Prokhovnik S. J. 
Published: April 2009

AbstractOur present view of the universe suggest that the set of mutually receding galaxies may provide a natural substratum for the propagation of light. It is shown that this assumption leads to a consistent derivation and interpretation of special relativity, along the lines evvisaged by Lorentz but requiring also the employment of Einstein's measurement definitions. The time-dilatation and Fitzgerald contraction effects emerge as intelligible consequences of this approach, and their interaction with an associated anisotropy effect produces the relativity of simultaneity, the reciprocity phenomenon and the results described by Einstein's principles; the approach provides a definitive resolution of the “clock paradox” within the framework of Special Relativity.
The practical use of variation principles in non-linear mechanics
Authors: Blatt J. M. , Lyness J. N. 
Published: April 2009

AbstractContrary to the general impression that variation principles are of purely theoretical interest, we show by means of examples that they can lead to considerable practical advantages in the solution of non-linear vibration problems. In this paper, we develop a variation principle for the period of a free oscillation, as a function of the average value of the Lagrangian over one period. Even extremely simple-minded approximations to the true motion lead to excellent values for the period. The stability of such free oscillations against small disturbances of the initial conditions is treated in a previous paper.
The endomorphism ring of a locally free module
Authors: Franzsen W. N. , Schultz P. 
Published: April 2009

AbstractWe identify a large class of rings over which locally free modules are determined by their endomorphism rings. We characterize these endomorphism rings and consider under what circumstances the conditions on the locally free modules can be relaxed, for example by requiring that only one of the rings need be in the special class, or by replacing ‘free' by “projective”.
On maxi-quasiprojective modules
Authors: Harada Manabu 
Published: April 2009

AbstractWe have defined a mini-injective module and given some structures of self mini-injective rings and certain relationships between such rings and QF-rings in [8] and [9].In this short note we shall study the modules dual to mini-injective modules, which we call maxi-quasiprojective modules. We shall give a characterization and some structures, in terms of the above modules, of those rings whose every injective modules has the lifting property of direct decompositions modulo the Jacobian radical (see [5], [6] and [7]). Furthermore, we shall show that the above rings are closely related to QF-rings (see [8] and [9]).
A problem in two-dimensional integration
Authors: Henstock Ralph 
Published: April 2009

AbstractIf two functions of a real variable are integrable over two intervals, say oft, τ, respectively, then the product of the two functions should be integrable over the rectangular product of the two intervals oftand τ. For the Lebesgue integral, definable using non-negative functions alone, the proof is easy. For non-absolute integrals such as the Perron, Çesàro-Perron, and Marcinkiewicz-Zygmund integrals we have difficulties since the functions cannot be assumed non-negative. But the present paper gives a proof.