bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Functional Stable Limit Theorems
Authors: Beuerman D. R. 
Published: December 2010

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.
A Generalization of a Fixed Point Theorem of Reich
Authors: Hardy G. E. , Rogers T. D. 
Published: December 2010

The following theorem is the principal result of this paper.Let (M, d) be a metric space and T a self-mapping of M satisfying the condition for x,y ∊ M1where a, b, c, e,f are nonnegative and we set α=a+b+c+e+f.
The Cardinalities of A+A and A-A
Authors: Stein Sherman K. 
Published: December 2010

H. T. Croft's Research Problems, 1967, contains the following problem due to J. H. Conway. "Let A = {a1, a2,…, aN} be a finite set of integers, and defineandProve that A—A always has more members than A+A, unless A is symmetric about 0."Marica in [1] showed that the conjecture is false for the set A = {1, 2, 3, 5, 8, 9, 13, 15, 16}. In this case A+A has 30 elements and A—A has 29 elements.
The Kloosterman Sum Revisited
Authors: Williams Kenneth S. 
Published: December 2010

Let p be an odd prime, n an integer not divisible by p and α a positive integer. For any integer h with (h,pα)=l, is defined as any solution of the congruence (mod,pα). The Kloosterman sum Ap α(n) (see for example [4]) is defined by(1.1)where the dash (') indicates that the letter of summation runs only through a reduced residue system with respect to the modulus.
Epimorphisms of Modules which must be Isomorphisms
Authors: Djoković D. Ž. 
Published: December 2010

Let R be an associative ring (not necessarily with identity).R is a left П-ring if it has the following property: Let M be a finitely generated left R-module, N a submodule of M and ϕ:N→M an epimorphism. Then ϕ is an isomorphism.
Rings with A Finitely Generated Total Quotient Ring
Authors: Adams John Conway 
Published: December 2010

Let R be a commutative ring with non-zero identity and let K be the total quotient ring of R. We call R a G-ring if K is finitely generated as a ring over R. This generalizes Kaplansky′s definition of G-domain [5].Let Z(R) be the set of zero divisors in R. Following [7] elements of R—Z(R) and ideals of R containing at least one such element are called regular. Artin-Tate's characterization of Noetherian G-domains [1, Theorem 4] carries over with a slight adjustment to characterize a Noetherian G-ring as being semi-local in which every regular prime ideal has rank one.
An Inequality for Positive Semidefinite Hermitian Matrices(1)
Authors: Merris Russell 
Published: December 2010

Let A and B be positive semidefinite Hermitian n-square matrices. If A—B is positive semidefinite, write A≥B. Haynsworth [1] has proved that if A≥B then det(A+B)≥det A+n det B.Let G be a subgroup of the symmetric group, Sn, and let λ be a character on G. Letwhere A = (aij) and Er is the rth elementary symmetric function.
On Injective Near-Ring Modules
Authors: Seth V. , Tewari K. 
Published: December 2010

Let N be a left near ring and let M be a right N-module. We recall [1] that M is called injective iff every diagram can be embedded into a commutative diagram where A and B are right N-modules with exact.The purpose of this note is to show that if N is a d.g. near-ring with identity, then M is injective iff for every right ideal u of N and every N-homomorphism f:u→N, there exists an element m in M such that f(a)=ma for all a in u.
Right-Ordered Polycyclic Groups
Authors: Mura Roberta Botto 
Published: December 2010

One of the features that make right-ordered groups harder to investigate than ordered groups is that their system of convex subgroups may fail to have the following property:(*) if C and C’ are convex subgroups of G and C’ covers C, then C is normal in C’ and C’/C is order-isomorphic to a subgroup of the naturally ordered additive group of real numbers.
The Matrix EquationsA = XYZAndB = ZYXand Related Ones
Authors: Brenner J. L. , Lim M. J. S. 
Published: December 2010

In [15], O. Taussky-Todd posed the problem of title, namely to findX, Y, ZwhenA, Bare given. Clearly ifX, Y, Zexist thenA, Bare either both invertible or both noninvertible.In section 1, the problem is reviewed in caseA, Bare both invertible. The problem is seen to be fundamentally one of group theory rather than matrix theory. Application of results of Shoda, Thompson, Ree to the general group-theoretical results allows specialization to certain matrix groups.In Section 2, examples and counterexamples are given in caseA, Bare noninvertible. A general necessary condition for solvability (involving ranks) is obtained. This condition may or may not be sufficient. For dimA=2, 3 the problem is settled: there is always a solution in the noninvertible case.
Carathéodory’s Theorem with Linear Constraints
Authors: Cook W. D. 
Published: December 2010

Carathéodory has shown that if x1, x2,…, xm, (m finite) are points of Rn and if somethen ∃μ∈Ω with at most n+1 nonzero components and for which (See [5]). The authors of [2] have extended this result to include the case where m= +∞. In theorems 1 and 2 below we establish somewhat similar results for the case in which Ω is further restricted by a finite system of linear inequalities (or equalities).
Numerical Range and Convex Sets*
Authors: Pollack Fredric M. 
Published: December 2010

The numerical range W(T) of a bounded linear operator T on a Hilbert space H is defined byW(T) is always a convex subset of the plane [1] and clearly W(T) is bounded since it is contained in the ball of radius ‖T‖ about the origin. Which non-empty convex bounded subsets of the plane are the numerical range of an operator? The theorem we prove below shows that every non-empty convex bounded subset of the plane is W(T) for some T.
An Elementary Proof of the Frobenius Factorization Theorem for Differential Equations
Authors: Kennedy E. W. 
Published: December 2010

Consider the 1st order linear system1 when An(t) is real valued and continuous on I, ai, i+1(t) ≠ 0, aij(t) ≡ 0 for j ≥ i + 2, t ∊ I and i = 1, …, n — l. In what follows, components cj of a vector c will be identifiable by the superscript. The purpose of this note is to give a simple induction proof of the following theorem of Frobenius [1].
Quasi-Differentiable Norms
Authors: Whitfield J. H. M. 
Published: December 2010

Let E be a real Banach space with norm ρ. Let S={x ∊ E: ρ(x) = 1}. A norm on E is admissible if it generates the same topology as ρ.The normρ is Gateaux differ-entiable if for each x ∊ S and u ∊ Eexists.
Lyapunov Inequalities and Bounds on Solutions of Certain Second Order Equations*
Authors: Eliason Stanley B. 
Published: December 2010

In this paper we consider the equation(1.1) (r(t)y′(t))′+p(t)f(y(t)) = 0under the conditions((H0): the real valued functions r, r′ and p are continuous on a non-trivial interval J of reals, and r(t)>0 for t∈J;and(H1):f:R→R is continuously differentiable and odd with f'(y)>0 for all real y. We also consider the equation(1.2) y″(t)+m(t)y′(t)+n(t)f(y(t)) = 0under the conditions (H1) and(H2): the real valued functions m and n are continuous on a non-trivial interval J of reals.
Integral Domains which have Finite Character Locally
Authors: Pacholke Kenneth 
Published: December 2010

AbstractIn recent papers Brewer and Mott have studied integral domains which have finite character globally. This paper concentrates on domains which have finite character locally. Examples include global finite character domains plus Prufer, almost Dedekind, and almost Krull domains. General properties are given, including a valuation-theoretic characterization. The effect of requiring essential and/or rank one valuations is also studied.
Fixed Point Theorems for Point-to-Set Mappings
Authors: Wong Chi Song 
Published: December 2010

AbstractLet (X, d) be a metric space. Let Xc be the family of all non-empty closed subsets of X endowed with the Hausdorff metric D induced by d. Let f be a non-expansive mapping of X into Xc (D(f(x), f(y))≤d(x, y) for all x, y in X). Some fixed point theorems are obtained by imposing certain conditions on f and X.
Group Partitions and Mixed Perfect Codes
Authors: Lindström Bernt 
Published: December 2010

AbstractLet G be a finite abelian group of the order pr and type (p, …, p), where p is a prime. A necessary and sufficient condition is determined for the existence of subgroups G1, G2, ⋯, Gn, one of the order pa and the rest of the order pb, such that G = G1 ∪ G2 ∪ ⋯ ∪ Gn and Gi, ∩ Gj,= {θ} when i ≠ j.
Some Admissible Estimators in Extreme Value Densities
Authors: Singh R. 
Published: December 2010

Let X be a random variable having the extreme value density of the form(1)where r is assumed to be a positive Lebesgue measurable function of x and the function q is defined byfor all θ in Ω = (0, ∞). It is further assumed that q(θ) approaches zero as θ → ∞.In this note we are concerned with estimating parametric functions g(θ) of the form [1/q(θ)]α, α any real number. The loss function is assumed to be squared error and the estimators are assumed to be functions of a single observation X.
L1-Sequential Convergence on Stone Spaces and Stone's Theorem on Unitary Semigroups
Authors: Cooper J. B. 
Published: December 2010

The following theorem is a well-known tool in the study of measurable functions:Theorem. Let (M; μ) be a finite measure space and let (xn) be a sequence of functions in L1(M; μ) so that xn→0 in the norm of L1(M; μ). Then there is a sub-sequence so that xnk →0 pointwise almost everywhere on M.
Interpolation by Linear Sums of Harmonic Measures
Authors: Ortel Marvin 
Published: December 2010

Let α be an open arc on the unit circleand for z=reiθ, 0 ≤ r < 1, let(1)The function ω(z; α) is called the harmonic measure of the arc α with respect to the unit disc, (Nevanlinna 2); it is harmonic and bounded in the unit disc and possesses (Fatou) boundary values 1 and 0 at interior points of α and the complementary arc β respectively.
Sequences by Number of w-Rises
Authors: Abramson Morton 
Published: December 2010

An m-permutation of n, repetitions allowed, is an m-sequence(1)A w-rise is a pair (ei, ei+1) such that ei+1-ei≥w>0. In this note we find an expression for Tk, w(n, m), the number of m-sequences having precisely k w-rises. The case w = 1 is given in [1] [2]. Also, when w = 1 we give the number when each of the integers 1, 2, …, r must appear at least once.
EP Operators and Generalized Inverses
Authors: Campbell Stephen L. , Meyer Carl D. 
Published: December 2010

AbstractThe relationship between properties of the generalized inverse of A, A†, and of the adjoint of A, A*, are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EPr. A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.
Contraction Property of the Operator of Integration
Authors: Janos Ludvik 
Published: December 2010

AbstractIt is shown that the operator of integration Fy(x) = ∫x0y(t) dt defined on the space C(—∞, ∞) of all continuous real valued functions on (—∞, ∞) is a contraction relative to a certain family of seminorms generating the topology of uniform convergence on compacta. However, as a contrast to this it is proved that F is not contractive with respect to any metric on C(—∞, ∞) inducing the above topology on C(—∞, ∞).
A Remark on Talenti's Semigroup
Authors: Seidman Thomas I. 
Published: December 2010

For α>0 the Riemann-Liouville Integral J(α) is given for suitable functions g by1For a variety of function spaces (e.g., C[0, 1] or Lp(0, 1) with p≥1) this defines a C0 semigroup which has been extensively studied (cf., e.g., [3]).
A Metrization Theorem for 2-Manifolds
Authors: Vincent Paul A. 
Published: December 2010

There are few known metrization theorems for manifolds (locally Euclidean, connected, Hausdorff space). It is well known that for manifolds metrizability, second countability, Lindelöf's condition, σ-compactness and paracompactness are equivalent. Although these conditions imply separability, the latter does not imply any of the former (see Example 2.2), as is often believed. A common source of metrization for a covering manifold is that lifted from the base manifold [8; p. 181].For 2-manifolds, the presence of a complex analytic structure gives us a metrization theorem; it has been shown [1] that such manifolds are topologically characterized as those which are orientable and second countable.
On Rings with Many Endomorphisms
Authors: Neggers Joseph 
Published: December 2010

AbstractAll rings have an identity, all homomorphisms map identities to identities, all homomorphisms on algebras over fields are algebra homomorphisms. A ring R is a quotient-embeddable ring (a QE-ring) if for any proper ideal a of R there is an endomorphism of R whose kernel is the ideal a. A QE-ring U is a receptor of R if for any proper ideal a of R there is a homomorphism from R to U whose kernel is the ideal a.Theorem. A ring R has a receptor if and only if it is a K-algebra over some field K contained in the center of R. If R is a commutative K-algebra of this type, then it has a commutative receptor.
A Generalization of the Cyclotomic Polynomial
Authors: Rao K. Nageswara 
Published: December 2010

AbstractIn this paper, the cyclotomic polynomial is generalized and several of its properties based on the Môbius inversion are derived. It is deduced that a polynomial whose roots are the roots of a cyclotomic polynomial multiplied by those of another cyclotomic polynomial is the product of cyclotomic polynomials. Character sums and finite Fourier series are employed for the latter result.
Approximation by Generalised Polynomials with Integral Coefficients
Authors: Tzimbalario J. 
Published: December 2010

Let C[0,1] be the space of all continuous real valued functions defined in [0,1] with the supremum norm1The subspace of C[0,1] consisting of all functions f(x) for which f(0) and f(l) are integers will be denoted by C0[0,1], Let be a sequence of real numbers satisfying:2
Probabilistic Proofs of the Little Riesz Theorem
Authors: Al-Hussaini A. N. 
Published: December 2010

The following theorem is a widely used corollary of the Thorn-Riesz convexity theorem ([1], pp. 526).Theorem. Let (Ω, a, μ) be a positive measure space, and letbe a linear operator with ‖T‖1≤1, ‖T‖∞≤1. Then ‖T‖p≤1, 1≤p≤∞
Multiplicities in the Tensor Product of Finite-Dimensional Representations of Discrete Groups
Authors: Djoković Dragomir Ž. 
Published: December 2010

Let G be a group and ρ and σ two irreducible unitary representations of G in complex Hilbert spaces and assume that dimp ρ= n < ∞. D. Poguntke [2] proved that is a sum of at most n2 irreducible subrepresentations. The case when dim a is also finite he attributed to R. Howe.We shall prove analogous results for arbitrary finite-dimensional representations, not necessarily unitary. Thus let F be an algebraically closed field of characteristic 0. We shall use the language of modules and we postulate that allour modules are finite-dimensional as F-vector spaces. The field F itself will be considered as a trivial G-module.
Thin Lens Spaces
Authors: Hoffman P. , Zabrodsky A. 
Published: December 2010

In Theorem 1 below we study the existence of spaces whose cohomology rings are isomorphic (as ungraded rings) to those of lens spaces. The case p = 2 is very simple and instructive, so let us consider it first.Suppose X is a space such that where dim x = 2d (for example X = RP4 with d = 1).
Regular Partitions of Regular Graphs
Authors: Kleinschmidt Peter 
Published: December 2010

In the study of the combinatorial structure of edge-graphs of convex polytopes one may ask whether a given graph possesses a partition consisting of certain kinds of subgraphs.In this paper we describe some special partitions of 3-valent and 4-valent graphs. These partitions can serve as examples for a type of partially ordered structures, called polystromas, which have recently been considered by Griinbaum [3].
Fixed Points can Characterise Curves
Authors: Schirmer Helga 
Published: December 2010

AbstractThe concept of a firm fixed point of a selfmap of a metric space is introduced. Loosely speaking a fixed point is firm if it cannot be moved to a point nearby with the help of a map which is arbitrarily close to the given map. It is shown that a continuum always admits a selfmap with a firm fixed point if the continuum contains a triod and if the vertex of the triod has a neighbourhood which is a dendrite. This condition holds in particular for local dendrites. Hence a local dendrite is an arc or a simple closed curve if and only if it does not admit a selfmap which has a firm fixed point.
On the Convergence Vector Space ℒ,(E, F) and its Dual Space
Authors: Beattie Ronald 
Published: December 2010

Let E be a locally convex tvs, F a normed space and the space of continuous linear mappings from E into F In this paper, we investigate the continuous convergence structure (c-structure) on. denotes the resulting convergence vector space (cvs).The c-structure is by definition the coarsest cvs structure on making evaluation a continuous mapping.
On Earle's mod n Relative Teichmüller Spaces
Authors: Zarrow Robert 
Published: December 2010

In this paper we answer an open question of C. J. Earle ([2] §3.3 remarks (a) and (b)) in several cases. We first give some definitions and state some results which are given in greater detail in [2].We let X be a smooth surface of genus g ≥ 2 and let M (X) be the space of smooth complex structures with the C∞topology. If μ∈M(X) let Xμdenote the Riemann surface determined by μ.
The Chinese Remainder Theorem and the Invariant Basis Property
Authors: Anderson David F. 
Published: December 2010

AbstracrtThe Chinese Remainder Theorem states that if I and J are comaximal ideals of a ring R, then A/(I∩J)A is isomorphic to A/IA×A/JA for any left R-module A. In this paper we study the converse; when does A/(I∩J)A and A/IA×A/JA isomorphic imply that I and J are comaximal?
On the Power Map and Ring Commutativity
Authors: Bell Howard E. 
Published: December 2010

Let R denote an associative ring with 1, letnbe a positive integer, and letk= 1, 2, or 3. The ringRwill be called an (n, k)-ring if it satisfies the identitiesfor all integers m with n ≤ m ≤ n + k - 1. It was shown years ago by Herstein (See [2], [9], and [10]) that forn >1, any(n,l)-ring must have nil commutator idealC(R).Later Luh [12] proved that primary (rc, 3)-rings must in fact be commutative, and Ligh and Richoux [11] recently showed that all (n, 3)-rings are commutative.
Nonoscillatory Solutions of x(m) = (-1)mQ(t)x
Authors: Cheng Sui-Sun 
Published: December 2010

AbstractA continuous real vector function is said to be nonoscillatory on an interval if at least one of its components is of constant positive or negative sign there. In this note, various existence criteria for nonoscillatory solutions of the system x(m) = (-l)mQ(t)x are established. In some cases, additional monotonicity properties for these solutions are also given.
On a Class of Polynomials Associated with the Stars of a Graph and its Application to Node-Disjoint Decompositions of Complete Graphs and Complete Bipartite Graphs into Stars
Authors: Farrell E. J. 
Published: December 2010

AbstractA star is a connected graph in which every node but possibly one has valency 1. Let G be a graph and C a spanning subgraph of G in which every component is a star. With each component α of C let us associate a weight wα. Let Пα wα be the weight associated with the entire subgraph G the star polynomial of G is ΣПα wα where the summation is taken over all spanning subgraphs of G consisting of stars. In this paper an algorithm for finding star polynomials of graphs is given. The star polynomials of various classes of graphs are then found, and some results about node-disjoint decomposition of complete graphs and complete bipartite graphs are deduced.
A Second Note on Ingham's Summation Method
Authors: Segal S. L. 
Published: December 2010

A series ∑ an is said to be summable (I) to the limit A if(*)Clearly the limit is the same whether x→∞ through all real values or only positive integer values, and the expression whose limit is being taken can also be expressed in the two equivalent formswhere [x] is the greatest integer ≤x.
Semilinear Second Order Elliptic Oscillation
Authors: Swanson C. A. 
Published: December 2010

These pages summarize recent progress on the oscillation problem for semilinear elliptic partial differential equations of the form(1)in unbounded domains Ω in n-dimensional Euclidean space Rn. Our attention is restricted to the second order symmetric equation (1), and completeness is not attempted; the emphasis is on results obtained in the last five years.
Sur le Dérivé du Cuboïde Eulérien
Authors: Lagrange Jean 
Published: December 2010

L'objet de cette note est de montrer que le dérivé d'un cuboïde eulérien n'est jamais parfait.(1) Appelons cuboïde entier un cuboïde dont les arêtes et les diagonales des faces sont des entiers; appelons cuboïde parfait un cuboïde entier dont la diagonale intérieure est un entier.
Permutations Related to Secant, Tangent and Eulerian Numbers
Authors: Abramson Morton 
Published: December 2010

It is well known that1whereAndenotes the number of "up-down" or alternating permutations2of 1, 2, …,n. The numbersA2nandA2n+1are known as the secant and tangent numbers respectively andA2n= (—l)"E2n, whereEnis the Euler number.
Bounds on Positive Integral Solutions of Linear Diophantine Equations II
Authors: Borosh I. , Treybig L. B. 
Published: December 2010

AbstractLet A be an m × n matrix of rank r and B an m × 1 matrix, both with integer entries. Let M2 be the maximum of the absolute values of the r × r minors of the augmented matrix (A | B). Suppose that the system A x = B has a non-trivial solution in non-negative integers. We prove (1) If r = n - 1 then the system A x = B has a non-negative non-trivial solution with entries bounded by M2. (2) If A has a r x n submatrix such that none of its r x r minors is 0 and x ≥ 0 is a solution of Ax=B in integers such that is minimal, then .
Modules Behaving Like Torsion Abelian Groups
Authors: Zubair Khan M. 
Published: December 2010

Recently H. Marubayashi [1,2] and S. Singh [10,11,12] generalized some results of torsion abelian groups for modules over some restricted rings, like bounded Dedekind prime rings, bounded hereditary Noetherian prime rings. Singh [12] introduced the concept of h-purity for a module MR satisfying the following conditions:(I) Every finitely generated submodule of every homomorphic image of M is a direct sum of uniserial modules.
On the Inequality
Authors: Kardos Peter 
Published: December 2010

In this paper, we are concerned with the functional inequality1where 0 < Pi < l, 0 < qi < l, fi(p)≠0, for 0 < P < 1, (i = 1, 2,..., n) and n is a fixed positive integer, n ≥ 2.Inequality (1) was studied by Rényi and Fischer, (see [1], [3]) in the special case2and this provided a characterization of Rényi's entropy.
Minimally Generated Modules
Authors: Rant W. H. 
Published: December 2010

AbstractA non-zero module M having a minimal generator set contains a maximal submodule. If M is Artinian and all submodules of M have minimal generator sets then M is Noetherian; it follows that every left Artinian module of a left perfect ring is Noetherian. Every right Noetherian module of a left perfect ring is Artinian. It follows that a module over a left and right perfect ring (in particular, commutative) is Artinian if and only if it is Noetherian. We prove that a local ring is left perfect if and only if each left module has a minimal generator set.