bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the First Conjugate Point Function for Nonlinear Differential Equations
Authors: Peterson Allan C. , Sukup Dwight V. 
Published: December 2010

AbstractWe are concerned with the nth order differential equation y(n) = (x, y, y′, …,y(n-1)), where it is assumed throughout that f is continuous on [α,β) × Rn, α < β≤∞, and that solutions of initial value problems are unique and exist on [α, β). The definition of the first conjugate point function η1(t) for linear homogeneous equations is extended to this nonlinear case. Our main concern is what properties of this conjugacy function are valid in the nonlinear case.
A Banach Algebra Structure for Hp
Authors: Wigley Neil M. 
Published: December 2010

The Hardy space Hp=Hp(U), where 1≤p≤∞ and U is the unit disc |z|<1, is shown to be an algebra under the productMoreover for each p, 1≤p≤∞, there exists a constant Cp such that ‖f*g‖p,≤
Cp‖f‖p ‖g‖p.
On the Edelstein Contractive Mapping Theorem
Authors: Janos Ludvik 
Published: December 2010

AbstractLet X be a metrizable topological space and f:X→X a continuous selfmapping such that for every x ∈ X the sequence of iterates {fn(x)} converges. It is proved that under these conditions the following two statements are equivalent:1. There is a metrization of X relative to which f is contractive in the sense of Edelstein.2. For any nonempty f-invariant compact subset Y of X the intersection of all iterates fn(Y) is a one-point set. The relation between this type of contractivity and the Banach contraction principle is also discussed.
Pseudo-Noetherian Rings
Authors: McDowell Kenneth P. 
Published: December 2010

In the latter part of the 1950’s some interesting papers appeared (e.g. [2] and [10]) which examined the relationships occurring between the purely algebraic and homological aspects of the theory of finitely generated modules over Noetherian rings. Many of these relationships remain valid if one considers the much wider class of rings determined by the following definition.Definition. A commutative ring R is called pseudo-Noetherian if it satisfies the following two conditions.
An Inequality Satisfied by the Gamma Function
Authors: Selliah J. B. 
Published: December 2010

Gurland [1] by making use of the Cramer-Rao lower bound for the variance of an unbiased estimator obtained the following inequality1for real values of α and δ satisfying α+δ>0, α≠0, δ>0. He used the fact that (Γ(δ)Γ(δ+α))xα is an unbiased estimator of θα where θ is the parameter for the density function
Interpolation in Spaces of Entire Functions in ℂN
Authors: Gruman Lawrence 
Published: December 2010

Let {sm} be a discrete set of points in ℂN and λm any sequence of points in ℂ. We shall be interested in finding an entire function F(z) such that F(sm)=λm. This is of course easy if no restriction is placed on F, but we shall be interested in finding an F which in addition satisfies certain growth conditions.We shall denote the variable z=(z1,..., zN), zj=xj+iyj,
On Semiprime Ample Jordan Rings
Authors: Britten Daniel J. 
Published: December 2010

The purpose of this paper is to point out that the arguments of [2] with slight modification extend the main result of [2] to the case of H satisfying either ACC or DCC on quadratic ideals and they extend [6, Theorem 2] to R being semiprime. Thus we obtainTheorem 1. Let R be a semiprime associative ring with involution ✶ and J a closed ample quadratic Jordan subring of H(R) satisfying either ACC or DCC on quadratic ideals. Then R is Goldie. In this case, J has a Jordan ring of quotients J′ which is a closed ample quadratic Jordan subring of H(R′) where R′ is the associative ring of quotients of R.
Counterexamples to Two Problems on One-Relator Groups
Authors: Fischer J. 
Published: December 2010

In [2] G. Baumslag presents a list of twenty-three unsolved problems on one-relator groups. We give counterexamples to two of them.Problem 5 asks whether a maximal locally free subgroup of a one-relator group always has finite “rank” (G has “rank” k if each finitely generated subgroup of G is contained in a k-generator subgroup of G).
A Note on Banach Spaces Containing ℓ1
Authors: Lohman Robert H. 
Published: December 2010

AbstractIf Y is a subspace of a Banach space X, either Y contains an isomorphic copy of ℓ1 or each weak Cauchy sequence in X/Y has a subsequence that is the image under the quotient mapping of a weak Cauchy sequence in X. If X is weakly sequentially complete and Y is reflexive, X/Y is weakly sequentially complete. Related structural results are given.
Une Application de la Theorie de Ltnterpolation-(0,2)
Authors: Côté C. , Gervais R. 
Published: December 2010

Donné (n + 2) points dans l'intervalle [-1,1],1.1L. Fejér a montré ([3]) qu'il existe toujours un polynôme de degré inférieur ou égal à n + 1 tel que1.2et1.3
An Algorithm for the Permanent of Circulant Matrices
Authors: Cummings Larry J. , Wallis Jennifer Seberry 
Published: December 2010

The permanent of an n ✕ n matrix A = (aij) is the matrix function1where the summation is over all permutations in the symmetric group, Sn. An n ✕ n matrix A is a circulant if there are scalars a1 …, an such that2where P is the n ✕ n permutation matrix corresponding to the cycle (12 … n) in Sn.
Some Mappings Associated with the Permutation Groups
Authors: Davison J. L. 
Published: December 2010

Let Sn denote the permutation group on {1, 2, 3, …, n}. Let k ≥ 1 and n ≥ 1 be integers. For σ ∊ Sn we define ([1]) mk, n: Sn → Z byLet pn ∊ Sn be the reverse permutation: that is,
On Numbers Analogous to the Carmichael Numbers
Authors: Williams H. C. 
Published: December 2010

A base a pseudoprime is an integer n such that1A Carmichael number is a composite integer n such that (1) is true for all a such that (a, n ) = l. It was shown by Carmichael [1] that, if n is a Carmichael number, then n is the product of k(>2) distinct primes P1,P2,P3, … Pk, and Pi-1|n-1(i=1, 2, 3, …, k).
Dimension Theory Via Bisector Chains
Authors: Janos Ludvik 
Published: December 2010

AbstractFor two subsets Z and Y of a metric space (X, d) the set Z is said to be a bisector in Y iff Z ⊂ Y and there exist two distinct points y1, y2 ∊ Y such that Z = {z: d(z, y1) = d(z, y2) and z ∊ Y}. Considering chains of consecutive bisectors X ⊃ X1 ⊃ … ⊃ Xk we denote by b(X, d) the maximum of their length. The topological invariant b(X) is defined as the minimum of b(X, d) taken over the set of all metrizations of X. It is proved that if X is compact then dim(X) ≤ b(X) ≤ 2 dim(X) + 1, b(X) = 0 iff dim(X) = 0 and b(X) = n implies dim(X) = n for n = 1 and ∞. The sharp result b(En) = n for n = 1, 2, … is obtained for Euclidean space En.
Abelian Theorems for Hardy Transformations
Authors: Pathak R. S. , Pandey J. N. 
Published: December 2010

AbstractInitial and final value theorems for Hardy transformations and of a suitably chosen function f(x) under a certain set of conditions on v and p where1Jv(x) and Yv(x) being Bessel functions of the first and second kind, and2su, v(x) being Lommel's function, are proved.
Homomorphisms Between Lattices of Zero-Sets
Authors: Broverman S. 
Published: December 2010

AbstractFor a completely regular Hausdorff topological space X, let Z(X) denote the lattice of zero-sets of X. If T is a continuous map from X to Y, then there is a lattice homomorphism T” from Z(Y) to Z(X) induced by T which is defined by τ‘(A) = τ←(A). A characterization is given of those lattice homomorphisms from Z(Y) to Z(X) which are induced in the above way by a continuous function from X to Y.
Coexistence of some B.I.B. Designs
Authors: Majindar K. N. 
Published: December 2010

In this paper we have shown that the existence of some balanced incomplete block (b.i.b. for abbreviation) designs implies the existence of some others in some cases. We have here established the following theorems.Theorem 1. If there exists a symmetric b.i.b. design with parametersv, b, r, k, λ, (where v-b, r=k), then there exists a b.i.b. design with parameters,
On a Conjecture of Graham Concerning a Sequence of Integers
Authors: Chein E. Z. 
Published: December 2010

Let 0<a1<…<an be integers and (a, b) denotes the greatest common divisor of a, b. R. L. Graham [1] has conjectured thatfor some i and j. In a recent paper Weinstein [2] has improved Winterle's result [3] and has proven the following interesting theorem:If A is the sequence a1< … <an where ak = P, a prime for some k and , then.
Dimension Theory via Reduced Bisector Chains
Authors: Janos Ludvik 
Published: December 2010

AbstractLet (X, d) be a metric space and Y and Z subsets of X. We say that Z is a bisector in Y and write Y⊳Z iff Y⊃Z and there are two distinct points y1, y2 ∈ Y such that Z = ={z:d(z, y1) = d(z, y2) and z∈Y}. By a reduced bisector chain in (X, d) of length n we understand a chain X = such that dim Xn≤0 and dimXn-1>0). By r(X, d) we denote the maximum length of reduced bisector chains in (X, d). For a metrizable topological space X we introduce the topological invariant r(X) as the minimum of r(X, d) taken over the set of all metrizations d of X. We prove that the function r(X) coincides with the dimension of X on the class of compact metric spaces.
A Remark on Coherent Overrings
Authors: Papick Ira J. 
Published: December 2010

Throughout this note, let R be a (commutative integral) domain with quotient field K. A domain S satisfying R ⊆ S ⊆ K is called an overring of R, and by dimension of a ring we mean Krull dimension. Recall [1] that a commutative ring is said to be coherent if each finitely generated ideal is finitely presented.In [2], as a corollary of a more general theorem, Davis showed that if each overring of a domain R is Noetherian, then the dimension of R is at most 1. (This corollary is the converse of a version of the Krull-Akizuki Theorem [5, Theorem 93], and can also be proved directly by using the existence of valuation rings dominating finite chains of prime ideals [4, Corollary 16.6].) It is our purpose to prove that if R is Noetherian and each overring of R is coherent, then the dimension of £ is at most 1. We shall also indicate some related questions and examples.
Catching and Missing Finite Sets
Authors: Ellis Martin H. 
Published: December 2010

AbstractIfT is a 1-1 bimeasurable measure-preserving aperiodic transformation on a probability space X which is a Lebesgue space, then {A:A⊂X and for almost every pair of finite sets F and G there is an n∈N satisfying F⊂TnA and G ∩ TnA=ϕ} is dense in the σ-algebra of measurable sets.
On Levine′s Decomposition of Continuity
Authors: Rose David Alon 
Published: December 2010

AbstractA strong version of Levine′s decomposition of continuity leads to the result that a closed graph weakly continuous function into a rim-compact space is continuous. This result implies a closed graph theorem: every almost continuous closed graph function into a strongly locally compact space is continuous. An open problem of Shwu-Yeng T. Lin and Y.-F. Lin asks if every almost continuous closed graph function from a Baire space to a second countable space is necessarily continuous. This question is answered in the negative by an example.
An Elementary Proof of Johnson–Dulmage–Mendelsohn's Refinement of Birkhoff's Theorem on Doubly Stochastic Matrices
Authors: Nishi Akihiro 
Published: December 2010

SummaryA purely combinatorial and elementary proof of Johnson-Dulmage-Mendelsohn's theorem, which gives a quite sharp upper bound on the number of permutation matrices needed for representing a doubly stochastic matrix by their convex combination, is given.
A Note on [a, b]-Compact Spaces
Authors: Pareek C. M. , Hdeib H. Z. 
Published: December 2010

In this note we present an array of results which deals with the question "When is the product of two [a, b]-compact spaces an [a, b]-compact space".In section 1, we give some essential terminology. In section 2, we define some new classes of functions and then obtain some product theorems. In section 3, we give some applications of the product theorems obtained in section 2.
Permuting the Elements of a Finite Solvable Group
Authors: Cliff Gerald H. , Rhemtulla Akbar H. 
Published: December 2010

AbstractThe main result in this note is the followingTheorem: Let G be a finite solvable group. There exists a permutation σ of the set G such that {g • σ(g); g∈G} = G if and only if the Sylow 2-subgroup of G is non-cyclic or trivial
On Derivations in Prime Rings and a Question of Herstein
Authors: Kovacs Amos 
Published: December 2010

In [2], Herstein proves the following result:Theorem. Let R be a prime ring, d≠0 a derivation of R such that d(x) d(y) = d(y) d(x) for all x, y ∈ R. Then, if char r≠2, R is commutative, and if char R = 2, R is commutative or an order in a simple algebra which is 4-dimensional over its center.
Note on Best Approximation of |x|
Authors: Bennett Colin , Rudnick Karl , Vaaler Jeffrey D. 
Published: December 2010

In this note the best uniform approximation on [—1,1] to the function |x| by symmetric complex valued linear fractional transformations is determined. This is a special case of the more general problem studied in [1]. Namely, for any even, real valued function f(x) on [-1,1] satsifying 0 = f ( 0 ) ≤ f (x) ≤ f (1) = 1, determine the degree of symmetric approximationand the extremal transformations U whenever they exist.
Molchanov's Discrete Spectra Criterion for a Weighted Operator
Authors: Hinton Don B. 
Published: December 2010

We consider the second-order operator1where the coefficients are real continuous functions on an interval ℐ with w and p positive. The operator is assumed singular at only one endpoint which we take to be either 0 (finite singularity) or ∞ (infinite singularity). Let be the Hilbert space of all complex-valued, measurable functions f satisfying
Function Spaces Continuously Paired by Operators of Convolution-Type
Authors: Kerman R. A. 
Published: December 2010

AbstractCertain operators essentially defined by convolution are considered. Their possible domain and range spaces are determined; then conditions are given under which the construction of the optimal continuous partner may be carried out for a suitable domain or range. Special cases of operators of convolution-type are useful in studying the boundedness properties of conjugate function operators and, more generally, classes of operators satisfying restricted weak-type conditions.
On Inc-Extensions and Polynomials with Unit Content
Authors: Dobbs David E. 
Published: December 2010

AbstractIt is proved that if u is an element of a faithful algebra over a commutative ring R, then u satisfies a polynomial over R which has unit content if and only if the extension R ⊂ R[u] has the imcomparability property. Applications include new proofs of results of Gilmer-Hoffmann and Papick, as well as a characterization of the P-extensions introduced by Gilmer and Hoffmann.
On the Connectedness of Certain sets in Summability Theory
Authors: Parameswaran Mangalam R. 
Published: December 2010

AbstractThis note considers the question of the connectedness of the set of limit points of the A-transforms of a sequence, where A is a conservative Hausdorff, quasi-Hausdorff or Meyer-König- Ramanujan type of matrix. New proofs of some known results, as well as some new results are obtained.
Isomorphic Group Rings with Non-Isomorphic Coefficient Rings*
Authors: Grünenfelder L. , Parmenter M. M. 
Published: December 2010

The following question has been floating around for some time now and is also stated as Research Problem 26 in [4]:Let R, S be unital rings and let 〈x〉 be an infinite cyclic group. Does R〈x〉≃S〈x〉 imply R≃S?In this note, we present a collection of examples which answer the question in the negative. However, all of these examples consist of non-commutative rings, and the problem is still open in the case where R and S are assumed to be commutative.
A New Identity and Some Applications
Authors: Moser W. O. J. , Pollack Richard 
Published: December 2010

AbstractLet (n|k) denote the number of k-choices 1≤x1<x2<…<xk≤n satisfying xi-xi-1≥2, i = 2,…, k, n + x1-xk≥2; let (m, n | k) = Σi+j=k (m | i)(n | j). Several elementary proofs of the new identity (m, n|k) = (m + n | k) if 0≤k<m≤n. andif 0≤m≤n, m≤k, are given. Generalizations and applications are considered.
A Simple Proof of a Theorem on Reduced Rings
Authors: Klein Abraham A. 
Published: December 2010

We give a simple proof of a theorem by Andrunakievič and Rjabuhin which states that a reduced ring is a subdirect product of entire rings. Our proof makes no use of m-systems and is in some sense similar to the proof of the corresponding theorem in the commutative case due to Krull.A reduced ring is a ring without non-zero nilpotent elements. It is wellknown that if a reduced ring is commutative, then it is a subdirect product of integral domains [2]. This result has been generalized to arbitrary reduced rings [1]. The proof in the general case is somewhat complicated. We present a simple proposition which leads to a simple proof of the general case.
Topological Left Amenability of Semidirect Products
Authors: Junghenn H. D. 
Published: December 2010

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.
Ordinary Singularities of Algebraic Curves
Authors: Orecchia Ferruccio 
Published: December 2010

AbstractLet A be the local ring at a singular point p of an algebraic reduced curve. Let M (resp. Ml,..., Mh) be the maximal ideal of A (resp. of Ā). In this paper we want to classify ordinary singularities p with reduced tangent cone: Spec(G(A)). We prove that G(A) is reduced if and only if: p is an ordinary singularity, and the vector spaces span the vector space . If the points of the projectivized tangent cone Proj(G(A)) are in generic position then p is an ordinary singularity if and only if G(A) is reduced. We give an example which shows that the preceding equivalence is not true in general.
Existence of Solutions of an Ill-Posed Problem for the Vibrating String
Authors: Campbell L. L. 
Published: December 2010

AbstractThe Dirichlet problem is examined for the vibrating string equation on a rectangle with commensurable sides. As is well-known, a solution, if it exists, is not unique. A necessary and sufficient condition is obtained on the boundary values for existence of solutions. A simple formula for the solution is obtained.
Idempotent Ideals and Noetherian Polynomial Rings
Authors: Lanski Charles 
Published: December 2010

AbstractIf R is a commutative Noetherian ring and I is a nonzero ideal of R, it is known that R+I[x] is a Noetherian ring exactly when I is idempotent, and so, when R is a domain, I = R and R has identity. In this paper, the noncommutative analogues of these results, and the corresponding ones for power series rings, are proved. In the general case, the ideal I must satisfy the idempotent condition that TI = T for each right ideal T of R contained in I. It is also shown that when every ideal of R satisfies this condition, and when R satisfies the descending chain condition on right annihilators, R must be a finite direct sum of simple rings with identity.
On the Smoothness of Generic Rings for Stably Free Modules
Authors: Swift Robert W. 
Published: December 2010

AbstractWe show certain generic rings for stably free modules are smooth. Using the theory of smooth algebras we deduce that these rings are regular when the base ring is regular. Also this enables us to calculate the dimensions of these rings. Gabel used these generic rings to determine the freeness of certain stably free modules. Our results allow a strengthening of his results when restrictions are placed on the type of stably free module—for example orthogonal stably free modules.
Five Mutually Tangent Spheres and Various Associated Configurations
Authors: Rigby J. F. 
Published: December 2010

AbstractIf five spheres σ0, σ1, …, σ4 touch each other externally and have radii in geometrical progression, there is a dilative rotation mapping σ0, σ1, σ2, σ3, to σ1, σ2, σ3, σ4; the dilatation factor is shown to be negative. The ten points of contact of the spheres lie by fours on 15 circles, forming a (154106) configuration in inversive space. In the corresponding configuration in the inversive plane, the 15 circles meet again in 60 points, which lie by fours on 45 circles touching by threes at each of the 60 points, and forming a configuration isomorphic to that of 60 Pascal lines (associated with six points on a conic) meeting by fours at 45 points. The 45 circles arise from ten Money-Coutts configurations of nine anti-tangent cycles. Conjectures are made about other circles through the 60 points.
“Topologically Indexed Function Spaces and Adjoint Functors”
Authors: Niefield S. B. 
Published: December 2010

AbstractLet Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-point space, we describe a class of right adjoints Top → Top/T, and then show that every right adjoint Top → Top/T is isomorphic to one of this form. We conclude by giving necessary and sufficient conditions for a left adjoint Top/T → Top to be isomorphic to one of the form − XTY, where Y is a space over T, and xT denotes the fiber product with the product topology.
Cyclotomic Splitting Fields
Authors: Mollin R. A. 
Published: December 2010

AbstractLet D be a division algebra whose class [D] is in B(K), the Brauer group of an algebraic number field K. If [D⊗KL] is the trivial class in B(L), then we say that L is a splitting field for D or L splits D. The splitting fields in D of smallest dimension are the maximal subfields of D. Although there are infinitely many maximal subfields of D which are cyclic extensions of K; from the perspective of the Schur Subgroup S(K) of B(K) the natural splitting fields are the cyclotomic ones. In (Cyclotomic Splitting Fields, Proc. Amer. Math. Soc. 25 (1970), 630-633) there are errors which have led to the main result of this paper, namely to provide necessary and sufficient conditions for (D) in S(K) to have a maximal subfield which is a cyclic cyclotomic extension of K, a finite abelian extension of Q. A similar result is provided for quaternion division algebras in B(K).
Semi r-Free and r-Free Integers—A Unified Approach
Authors: Hardy G. E. , Subbarao M. V. 
Published: December 2010

AbstractWe obtain an asymptotic formula for the number of (k, r)-free integers that do not exceed x. By definition, a (k, r)-free integer is one in whose canonical representation no prime power is in the interval [r, k−1] where 1 < r < k are fixed integers. These include as special cases the r-free integers, the semi r-free integers and the k-full integers. We obtain an asymptotic formula for the number of representations of an integer as the sum of a prime and a (k, r)-free integer, and use the result to prove that every sufficiently large integer can be represented as the sum of a prime and m = abk where a and b are both square free, (a, b) = 1, b > 1 and k is any fixed integer, k ≥ 3.