bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Möbius Ladders
Authors: Guy Richard K. , Harary Frank 
Published: December 2010

Consider the graph Mn, where n = 2r ≥ 6, consisting of a polygon
of length n and all n/2 chords joining opposite pairs of vertices. This
graph has 2r vertices which we denote by 1, 2, 3,..., 2r, and the 3r
(undirected) edgesWe call Mn the n-ladder, defined thus far only for n even. The
three smallest n-ladders with n even are shown in Figure 1.
The Maximum Order of the Group of a Tournament
Authors: Dixon John D. 
Published: December 2010

To each tournament Tn with n nodes n there corresponds the
automorphism group G(Tn) consisting n of all dominance preserving
permutations of the set of nodes. In a recent paper [3], Myron Goldberg and
J. W. Moon consider the maximum order g(n) which the group of a tournament
with n nodes may have. Among other results they prove that12
On General Polynomials
Authors: Williams Kenneth S. 
Published: December 2010

Let d denote a fixed integer > 1 and let GF(q) denote the finite field of
q = pn elements. We consider q fixed ≥ A(d), where A(d) is a
(large) constant depending only on d. Let1where each aiεGF(q). Let nr(r = 2, 3, …, d) denote the
number of solutions in GF(q) offor which x1, x2, …, xr are all
different.
Lattice Paths in E3With Diagonal Steps
Authors: Stocks D.R. 
Published: December 2010

Moser and Zayachkowski [1] have discussed certain planar lattice paths from (0, 0) to (m, n). In this note we consider analogous paths in three dimensional space. For basic definitions see reference [2]. Throughout this note each of m, n and k is a positive integer and if S is a finite set, |S| will denote the number of elements of S.Each path under consideration here is such that each of its steps is of one of the following types:
On the Relation Between Boundedness and Oscillation of Differential Equations of Second Order
Authors: Kartsatos A. G. 
Published: December 2010

In this paper we are dealing with differential equations of the forms:Eiwhere the functions pi are positive.By a solution of an equation of the above forms, we mean a function x(t) ∈ C2 [c, + ∞) where c is a non-negative constant, which satisfies the corresponding equation on the whole interval [c, +∞). By an oscillatory solution of (Ei), we mean a solution with arbitrarily large zeros.
Footnote to a Formula of Gioia and Subbarao
Authors: Segal S. L. 
Published: December 2010

Recently Gioia and Subbarao [2] studied essentially the following problem: If g(n) is an arithmetic function, and , then what is the behaviour of H(a, n) defined for each fixed integer a ≥ 2 by1By using Vaidyanathaswamy′s formula [e.g., 1], they obtain an explicit formula for H(a, n) in case g(n) is positive and completely multiplicative (Formula 2.2 of [2]). However, Vaidyanathaswamy′s formula is unnecessary to the proof of this result, which indeed follows more simply without its use, by exploiting a simple idea used earlier by Subbarao [3] (referred to also in the course of [2]).
On Real Almost Hermitian Structures Subordinate to Almost Tangent Structures
Authors: Closs Mike P. 
Published: December 2010

Some of the most important G-structures of the first kind (1) are those defined by linear operators satisfying algebraic relations. Let J be a linear operator acting on the complexified space of a differentiable manifold V, and satisfying a relation of the formwhere λ is a complex constant and I is the identity operator. In the case λ ≠ 0 the manifold has an almost product structure (2) which in the case λ = i reduces to an almost complex structure (3). In the remaining case, λ = 0, the manifold has an almost tangent structure (4).
On Polynomials with Real Zeros
Authors: Ahmad Manzoor 
Published: December 2010

Letbe a polynomial of degree n with real and non-negative zeros x1 ≤ x2 ≤ … xn. The zeros xj. will be said to have extent 1 ifLet ξ1 ≤ ξ2 ≤ … ξn-1 be the zeros of the derived polynomial p'(x). The zeros ξ1, ξ2, …, ξn-1 are real and non-negative, and moreover their extent can be at most equal to the extent of the zeros x1, x2, …, xn. The two can indeed be equal. For if the extent of the zeros xj. is 1 and 1 is a multiple zero of p'(x) then ξn-1 = 1. However it is not quite clear how small ξn-1 = 1 can be if Xn = 1. The extent ξn-1 = 1. of the zeros of p'(x) is less than 1 only if 1 is not a multiple zero of p(x). So let us suppose that p(x) has a simple zero at x = 1. Consequently xn-1 is the largest zero of p(x)/(x-l) or equivalently the largest zero of p(x) in 0 < x < 1 and it follows by Rolle's theorem that p'(x) n as a zero in the interval (xn-1,1). Thus the extent ξn-1 of the zeros of p'(x) is greater than xn-1 and it remains to see how small it can be.
Gap Formulae for the Weierstrass Transforms
Authors: Ditzian Z. 
Published: December 2010

A gap formula for a transform(1)is an operator J on f(x)(2)Such operators are known for Laplace transform [1; p.91] and [4; pp. 296–299], Stieltjes transform [4; pp. 351–353], a class of convolution transforms [2] and others. Gap formulae for the Weierstrass transform(3)and the Weierstrass-Stieltjes transform(4)will be proved in the following two theorems.
On Exceptional Polynomials
Authors: Williams Kenneth S. 
Published: December 2010

Let f(x) be a polynomial of degree d ≥ 2 defined over the finite field kq with q = pn elements. LetIf f*(x, y) has no irreducible factor over kq which is absolutely irreducible, f is called an exceptional polynomial [1]. Davenport and Lewis have noted that when d is small compared with p, a permutation (substitution) polynomial is necessarily an exceptional polynomial. It is the purpose of this paper to prove the converse; that is, we will show the existence of a constant a(d), depending only on d, such that if f(x.) is an exceptional polynomial over kq, where p ≥ a(d), then f(x) is a permutation polynomial.
Constructing an Automorphism From an Anti-Automorphism
Authors: Ayoub Christine 
Published: December 2010

We consider the following problem: Let G be a group with distinct automorphisms β and σ and an anti-automorphism α such thatWhat can be said about G?If σ = α, σ is both an automorphism and an anti-automorphism so that G is abelian. Hence we assume that σ ≠ α. In this case, we show that G is non-abelian, but has an abelian subgroup of index 2. Conversely, for such a group G there always exist distinct automorphisms β and σ and an anti-automorphism α such that (1) holds.
Some Characterizations of the Ultraspherical Polynomials
Authors: Al-Salam N.A. , Al-Salam W. A. 
Published: December 2010

Let be the nth ultraspherical polynomial. Also let . The following generating relation is well known (3, p.98).It can also be written as1.1This suggests the consideration of the class of polynomial sets {Qn(x), n = 0, 1, 2,…}, Qn(x) is of exact degree n and1.2
More Problems Connected with Convexity
Authors: Melzak Z.A. 
Published: December 2010

This is a continuation of the author's article [3], and it contains further problems connected with the theory of convex sets in En. To the list of general references in [3] may be added the recent book [2] on convex polyhedra.1) Let A and B be two convex bodies in E2 and let a packing P = {B1, B2, …} be an infinite sequence of homothetic images of B sucn that:a)each Bn is a subset of A,b)no two of them share interior points,c)Area (A) = The existence of such packings is guaranteed by Vitali's Theorem. Let D(X) be the diameter of the set X and put .
A Note on the Diameter of a Graph
Authors: Bondy J. A. 
Published: December 2010

The distance d(x, y) between vertices x, y of a graph G is the length of the shortest path from x to y in G. The diameter δ(G) of G is the maximum distance between any pair of vertices in G. i.e. δ(G) = max max d(x, y). In this note we obtain an upper boundx ε G y ε Gfor δ(G) in terms of the numbers of vertices and edges in G. Using this bound it is then shown that for any complement-connected graph G with N verticeswhere is the complement of G.
A Note on Polar Topologies
Authors: Robertson J. M. , Wiser H. C. 
Published: December 2010

Let (E, E') be a dual pair and G be a collection of σ(E, E') bounded sets in E with the following properties:i)G contains all singletons.ii)If A, B are in G there is a C in G with A ∪B ⊆ C.iii)If A is in G then λ A ε G for any scaler λ.Then sets of the form the polar of Ai, form base of neighbourhoods in E' for the polar topology TG of G convergence.
A Note on the Jacobson And Brown-McCoy Radicals
Authors: Anderson T. , Heinicke A. 
Published: December 2010

Let J(R) and G(R) respectively denote the Jacobson and Brown-McCoy radicals of the ring R and recall that R = G(R) if and only if R can not be homomorphically mapped onto a simple ring with unity [1, p. 120].In general one knows that J(R) ⊆ G(R) [1, p. 118], while there do exist rings R for which J(R) ≠ G(R) (see [1, p. 120]).
Periodic Solutions by Picard's Approximations
Authors: Burton T.A. 
Published: December 2010

In [1] Demidovic considered a system of linear differential equationswith A(t) continuous, T-periodic, odd, and skew symmetric. He proved that all solutions of (1) are either T-periodic or 2T-periodic0 In [2] Epstein used Floquet theory to prove that all solutions of (1) are T-periodic without the skew symmetric hypothesis. Epstein's results were then generalized by Muldowney in [7] using Floquet theory. Much of the above work can also be interpreted as being part of the general framework of autosynartetic systems discussed by Lewis in [5] and [6]. According to private correspondence with Lewis it seems that he was aware of these results well before they were published. However, it appears that these theorems were neither stated nor suggested in the papers by Lewis.
Spaces A × B of Conilpotency ≤ 1
Authors: Hoo C.S. 
Published: December 2010

Let A and B be spaces having the homotopy type of countable CW-complexes. Then we prove the following theorems.Theorem 1. If conil(A × B) ≤ 1, then for each integer n ≥ 1, the inclusion j: ∑n A ∨ ∑n B → ∑nA × ∑n B is a homotopy equivalence.This result is obtained as a corollary of Theorem 2.
λ(n)-Parameter Families
Authors: Mathsen Ronald M. 
Published: December 2010

I is an interval of R, the set of real numbers, n is a positive integer and F ⊂ Cj (I) for j ≥ 0 large enough so that the following definitions are possible:(i) Let λ(n) = (λ1, λ2,…,λk) where k, λ1, λ2,…, λk, are positive integers and λ1 + λ2 +… +λk = n. Then λ(n) is an ordered partition of n. The set of all such partitions of n is denoted by P(n).
Polynomials with Irreducible Factors of Specified Degree
Authors: Williams Kenneth S. 
Published: December 2010

Let d be a positive integer and let p be a prime > d. Set q = pm, where m ≥ 1, and let I (q, d) denote the number of distinct primary irreducible polynomials of degree d over GF(q). It is a simple deduction from the well-known expression for I(q, d) that(1)where d* is the largest positive integer < d which divides d if d > 1, and d* is 0 if d = 1.
A Note on Quasi-Frobenius Rings and Ring Epimorphisms
Authors: Storrer H. H. 
Published: December 2010

In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.
Moment Sequences and the Bernstein Polynomials*
Authors: Eisenberg Sheldon M. 
Published: December 2010

The Bernstein polynomials(1.1)and the Bernstein power series(1.2)have been the subject of much research (e. g. [1; 2; 3; 6; 7; 8]). It is the purpose of this paper to demonstrate the relationship between these linear operators and certain classes of moment sequences defined below.
A Property of Groups with No Central Factors
Authors: Rhemtulla A. H. 
Published: December 2010

Let C1 denote the class of all groups with no non-trivial central factors. We prove the following theoremThere exist non-trivial locally solvable C1 groups; but there is no non-trivial locally k-step polynilpotent C1 group for any integer k.It is well known that a minimal normal subgroup of a locally solvable group is abelian. Thus no non-trivial locally solvable group can be pluperfect - the class of all perfect groups in which every subnormal subgroup is also perfect.
On Strong Upper Densities
Authors: Eames W. 
Published: December 2010

Let ψ be the outer measure generated by a gauge g and a sequential covering class C of closed sets of a metric space X, and let D be the resulting strong upper density function. That is, for each A ⊆ X and each x ∈ X:the infimum being taken over all countable subcollections {Iα} of C such that and, for all Iα in the subcollection, d(Iα) < ε where d(Iα) is the diameter of d(Iα).
Disconjugacy Conditions for the Third Order Linear Differential Equation
Authors: Erbe Lynn 
Published: December 2010

An nth order homogeneous linear differential equation is said to be disconjugate on the interval I of the real line in case no non-trivial solution of the equation has more than n - 1 zeros (counting multiplicity) on I. It is the purpose of this paper to establish several necessary and sufficient conditions for disconjugacy of the third order linear differential equation(1.1)where pi(t) is continuous on the compact interval [a, b], i = 0, 1, 2.
On a Result of A. M. Macbeath on Normal Subgroups of a Fuchsian Group
Authors: Jonsson W. 
Published: December 2010

A. M. Macbeath, in November 1965, communicated the following theorem to me which he proved with the aid of the Lefschetz fixed point formula.Theorem. If Γ is a Fuchsian group and N a torsion free normal subgroup, then the rank of N/[Γ, N] is twice the genus of the orbit space D/Γ where D denotes the hyperbolic plane which Γ acts.This theorem will follow from a consideration of the exact sequence*
Remarks on Quasigroups Obeying a Generalized Associative Law
Authors: Ford Gary G. 
Published: December 2010

T. Evans in [4] introduced a concept generalizing the associative law for groups. Certain very restricted cases of this generalization had occurred, somewhat as side results, in the considerations of A. K. Suškevič [7], D. C. Murdoch [5], [6], and R. H. Bruck [2] associated with quasigroups which obey theorems generalizing certain results in group theory.In this paper we consider quasigroups obeying an instance of Evans' generalization. We show two means of constructing such quasigroups, and we demonstrate these constructions with several examples. The principal result of this paper is a theorem which reveals a peculiar trait of quasigroups obeying an instance of the generalized associative law we are considering. Such a quasigroup obeys a law expressed with permutations in which the nontrivial permutations involved either are both automorphisms of the quasigroup or else both fail to distribute over any product from the quasigroup.
Lifting Ideals in Noncommutative Integral Extensions
Authors: Hoechsmann K. 
Published: December 2010

This note is intended as a commentary on a part of the paper [1] by Gulliksen, Ribenboim, and Viswanathan. It takes its inspiration from a colloquium talk by P. Ribenboim.Our aim is a partial generalization of the theorem of Cohen-Seidenberg (cf. [2], IX. 1, Propositions 9 and 10) to noncommutative algebras.Definition. Let A be a ring with 1 in the center of another ring B (with the same 1). B is said to be integral over A, if each element b ∊ B satisfies an integral equation
Inversion of a Class of Convolution Transforms of Generalized
Functions
Authors: Ditzian Z. 
Published: December 2010

The kernels of the transforms in the class that we shall treat satisfy1.1where Re ak = ak Re ck = ck, 0 ≤ ak/ck and Σa-2k (see also [1], [2], [3], [6], [7] and [8]).
On an Interpolation Theorem of Zygmund and
Koizumi
Authors: Heinig H. P. 
Published: December 2010

Let (X, , μ) and
(Y, ,
ν) be two σ-finite measure spaces. An operator
T, defined by h = Tf,
which maps functions on X into functions on
Y is called quasilinear if
T(f+g) is uniquely defined whenever
Tf and Tg are defined, and if1.1where is
independent of f and g. If the operator T is called
sublinear.
On the Modulii of Analytic Functions
Authors: Sherman Malcolm J. 
Published: December 2010

The problem to be considered in this note, in its most concrete form, is the determination of all quartets f1, f2, g1, g2 of functions analytic on some domain and satisfying*where p > 0. When p = 2 the question can be reformulated in terms of finding a necessary and sufficient condition for (two-dimensional) Hilbert space valued analytic functions to have equal pointwise norms, and the answer (Theorem 1) justifies this point of view. If p ≠ 2, the problem is solved by reducing to the case p = 2, and the reformulation in terms of the norm equality of lp valued analytic functions gives no clue to the answer.
On Rings of Fractions
Authors: Davison T. M. K. 
Published: December 2010

Let R be a commutative Noetherian ring with identity, and let M be a fixed ideal of R. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in R, and let j = js: R → S-1R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S-1R is a topological ring in ihe j(M)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂ p(S), whereHence S-1R is a topological ring for all S if and only if M ⊂ p*(R), where
On Certain Classes of Bounded Linear Operators
Authors: Lin C-S 
Published: December 2010

Let T—c be a Fredholm operator, where T is a bounded linear operator on a complex Banach space and c is a scalar, the set of all such scalars is called the Φ-set of T [2] and was studied by many authors. In this connection, the purpose of the present paper is to investigate some classes Φ(V) of all such operators for any subset V of the complex plane.Let X be a Banach space over the field C of complex numbers with dim Z = ∞, unless otherwise stated, B(X) the Banach algebra of all bounded linear operators and K(X) the closed two-sided ideal of all compact operators on X.
A Characterization and a Class of Distribution Functions for the Stieltjes-Wigert Polynomials
Authors: Chihara T. S. 
Published: December 2010

In his classic memoir on the moment problem that bears his name, Stieltjes [2] exhibited1as an example of an indeterminate (Stieltjes) moment sequence.Stieltjes also obtained the corresponding S-fraction and thus implicitly obtained the three-term recurrence formula satisfied by the corresponding orthogonal polynomials.
Another Note on Sperner's Lemma
Authors: Drake David A. 
Published: December 2010

Let Q be a finite partially ordered (by ≤) set with universal bounds O, I. The height function h of Q is defined by the rule: h(x) is the maximum length of a chain from O to x. Let h(I)=n. Suppose that for each k≥0, there exist positive integers a(k) and b(k) such that all elements of height k(i)are covered by a(k) elements of height k+1;(ii)cover b(k) elements of height k—1.Then we call Q a U-poset. Call a subset S of a partially ordered set an antichain if no two elements of S are comparable.
Convolution of Lp Functions on Non-Unimodular Groups
Authors: Milnes Paul 
Published: December 2010

In this note we prove the followingTheorem. If G is a nonunimodular locally compact group and 1<p<∞, then there is an open set, U, in G and there are functions, f simultaneously in every Lr(G), p≤r ≤∞, and g simultaneously in every Lq(G), 1 ≤q≤∞, such that the convolution, f * g(y), is not defined for any y in U.
Some Integral Equations with Rummer's Functions in the Kernels
Authors: Prabhakar Tilak Raj 
Published: December 2010

Since 1963 several authors ([13], [2], [6], [14], [10], [11], [12], [9]) have considered integral equations each one of which is contained as a special case in one of the two equations1.11.2for Re b > 0 and x ∊ [α, β].
On Approximately Continuous and Almost Continuous Functions
Authors: Chaika M. , Perlman S. 
Published: December 2010

The purpose of this note is to discuss the relationship between the concepts of approximate continuity and almost continuity of real functions of a real variable.Contrary to the papers of T. Husain [1], [2], [3], we shall show that there is little relationship between these concepts, that approximate continuity does not imply almost continuity without additional restrictions and we shall give one such restriction.
Totally Real Subfields of p-Adic Fields having the Symmetric Group as Galois Group
Authors: Kleiman Howard 
Published: December 2010

In this paper, an elementary proof is given of the following proposition:Theorem 1. If Qp is an arbitrary field of p-adic numbers, then it contains normal subfields Ln(2 ≤ n ≤ p) which have symmetric groups Sn as their respective Galois groups over Q, the field of rational numbers. Furthermore, each Ln may be chosen to be totally real.
On Some Functional Equations of Carleman
Authors: Costley Charles G. 
Published: December 2010

The celebrated Fredholm theory of linear integral equations holds if the kernel K(x, y) or one of its iterates K(n) is bounded. Hilbert utilizing his theory of quadratic form was able to extend the theory to the kernels K(x, y) satisfyingabwhere k is independent of u(x).These theories were extended considerably by T. Carleman who deleted condition (b) above.Equations involving this Carleman kernel have been found useful in connection with Hermitian forms, continued fractions, Schroedinger wave equations (see [1], [2]) and more recently in scattering theory in quantum physics, etc. [3]. See also [5] for a variety of applications and extensions.
A Flat Nonmetrizable Connexion
Authors: Helfenstein H. G. 
Published: December 2010

A linear connexion ∇ on a smooth manifold M with vanishing torsion and curvature is called flat. It is well known that such a connexion need not be the Levi-Civita connexion of a Riemannian (nor pseudo-Riemannian) structure (cf. [1]).The following example with M homeomorphic to a cylinder is particularly simple. Using polar coordinates the punctured plane M=R2\{0} is covered by a smooth atlas with two charts
Decomposition of the Multivariate Beta Distribution with Applications
Authors: Kabe D. G. , Gupta R. P. 
Published: December 2010

SummaryLet L be a positive definite symmetric matrix having a noncentral multivariate beta density of an arbitrary rank, see, e.g. Hayakawa ([2, p. 12, Equation 38]). Then an explicit procedure is given for decomposing the density of L in terms of densities of independent beta variates.
An Elementary Result on Exponential Measure Spaces
Authors: Shen C. Y. 
Published: December 2010

A simple but useful result in the measure theory for product spaces can be stated as follows:Theorem A. A necessary and sufficient condition that a measurable subset E of X×Y has measure zero is that almost every X-section (or almost every Y-section) has measure zero (see [1, §36]).We will show, in this short note, that a similar result also holds for the exponential of measure spaces. Before proceeding any further, we describe briefly here the exponential construction of a measure space.
The Bounds Based on the Functions of Observations for Maximum of Stable Law
Authors: Basu A. K. , Wasan M. T. 
Published: December 2010

Gnedenko and Kolmogorov [3, pp. 181-182] have shown that if Xn with law F(x) belong to the domain of normal attraction of a stable law of index 0<α<2, i.e. if partial sum Sn/an1/α converges in distribution to some stable law Vα, a>0 then there exist c1 and c2 such thatand
The Fixed Point Set of Real Multi-Valued Contraction Mappings
Authors: Finbow Arthur S. 
Published: December 2010

Let (X, d1) and (Y, d2) be metric spaces. A mapping f:X→Y is said to be a Lipschitz mapping if there exists a real number λ such thatfor each x,y∊X. We call λ a Lipschitz constant for f. If λ∊[0, 1), f is called a contraction mapping. Throughout this note CB(Y) denotes the set of closed and bounded subsets of Y equipped with the Hausdorff metric induced by d2.