bluuebunny/crossref_metadata_2025_split huggingface dataset:
On D. J. Lewis's Equation x3+117y3 = 5
Authors: Finkelstein R. , London H. 
Published: December 2010

In a recent publication [2], D. J. Lewis stated that the Diophantine equation x3+117y3 = 5 has at most 18 integer solutions, but the exact number is unknown. In this paper we shall solve this problem by proving the followingTheorem. The equationx3+117y3 = 5 has no integer solutions.
Some Remarks Concerning Contraction Mappings
Authors: Reich Simeon 
Published: December 2010

The following result is proved in [1, p. 6].Theorem 1. Let X be a complete metric space, and let T and Tn(n = 1, 2,…)be contraction mappings of X into itself with the same Lipschitz constant k<1, and with fixed points u and un respectively. Suppose that limn → ∞ Tn(x) = T(x) for every x ∊ X. Then limn → ∞ un = u.
On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property
Authors: Haruki Hiroshi 
Published: December 2010

We consider the following functional equation1where ƒ = ƒ(x, y) is a real-valued function of two real variables x, y on the whole xy-plane and t is a real variable.With regard to the geometric meaning of (1), the equation is called the “square” functional equation.
Integer-Valued Continuous Functions II
Authors: Subramanian H. 
Published: December 2010

We follow [6] and [7] for all terminologies. The purpose of this note is to proveTheorem 1. Let X and Y be any two integer-compact spaces. The following are equivalent:(1)X is homeomorphic to Y.(2)C(X, Z) and C(Y, Z) are isomorphic as rings.(3)C(X, Z) and C(F, Z) are isomorphic as lattices.(4)C(X, Z) and C(Y, Z) are isomorphic as p.o. groups.(5)C(X, Z) and C(Y, Z) are isomorphic as multiplicative semigroups.
On Linear Functional Equations with Nonpolynomial C∞ Solutions
Authors: Światak Halina 
Published: December 2010

It is known (cf. M. A. McKiernan [6]) that the only measurably bounded solutions ƒ of the equations1where x ∊ Rn, t ∊ R, αi(i= 1, …, m) span the space , and Σi ∊ 1 μi ≠0 for any I ⊂ {1, …, m}, are polynomials. The degree of these polynomials and the dimension of the solution space can be estimated by numbers depending on m and n. (For estimates and other details concerning equations (1) see see [1], [2], [3], [4], [5], [6].)
On Convergence of Iterations for Fixed Points of Repulsive Type
Authors: Koneru Rao S. , Lalli B. S. 
Published: December 2010

This paper deals with the convergence of iterations of the equation1.1with u0 ∊ Rn, both as a root and a point of repulsion. Here u and ϕ are real n-vectors and ϕ is continuously differentiate with respect to u. By taking u0 as an initial approximation to u0 in a neighbourhood of u0 we define the sequence of iterates {uk+1} by1.1For the sake of convenience we shall, sometimes, call the equation (1.1) an iteration.
Characterizations of p-Spaces
Authors: Pareek C. M. 
Published: December 2010

The concept of p-space is quite recent. It was introduced by Arhangel'skii [2]. The definition of p-space given in [2] involves compactification of the space. In view of the interesting properties of p-spaces obtained in [2], Alexadroff [1] suggested a problem of finding a direct intrinsic definition (without appeal to compactification). The main aim of this note is to answer the above problem.I am grateful to Dr. S. K. Kaul for his comments.
Oscillation on Finite or Infinite Intervals of Second Order Linear Differential Equations(1)
Authors: Willett D. 
Published: December 2010

Recently, Ronveaux [11] has shown how to use a combination of a Riccati transformation and a homographie transformation to estimate both from below and above the distance between a zero and the succeeding or preceding extremum (zero of y' ) of solutions of1.1In this paper, we show how such transformations can be used to derive an equation from which the distance between successive zeros of a solution y of (1.1) can be estimated directly.
A Family of Combinatorial Identities
Authors: Andrews G. E. , Subbarao M. V. , Vidyasagar M. 
Published: December 2010

In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,1.1and obtained the following infinite family of identities:For A= 1,2, 3,…, let1.2where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then1.3As Eden noted, Fh(b;x) is the generating function of ph(m, n) which denotes the number of partitions of n into m parts, in which the largest part appears exactly h times and all other parts are distinct:
On a Problem of Groübaum
Authors: Erdös P. 
Published: December 2010

Pn will denote a set of n points in the plane. A well known theorem of Gallai- Sylvester (see e.g. [4]) states that if the points of Pn do not all lie on a line then they always determine an ordinary line, i.e. a line which goes through precisely two of the points of Pn.Using this theorem I proved that if the points do not all lie on a line, they determine at least n lines. I conjectured that if n>n0 and no n—1 points of Pn are on a line, they determine at least 2n-4 lines. This conjecture was proved by Kelly and Moser [3], who, in fact, proved the following more general result: Let Pn be such that at most n—k of its points are collinear.
On the Product of the Primes
Authors: Hanson Denis 
Published: December 2010

In recent years several attempts have been made to obtain estimates for the product of the primes less than or equal to a given integer n. Denote by the above-mentioned product and define as usualAnalysis of binomial and multinomial coefficients has led to results such as A(n)<4n, due to Erdôs and Kalmar (see [2]). A note by Moser [3] gave an inductive proof of A(n)<(3.37)n, and Selfridge (unpublished) proved A(n)<(3.05)n More accurate results are known, in particular those in a paper of Rosser and Schoenfeld [4] in which they prove Θ(n)< 1.01624n; however their methods are considerably deeper and involve the theory of a complex variable as well as heavy computations. Using only elementary methods we will prove the following theorem, which improves the results of [2] and [3] considerably.
Some Theorems on Strong Nörlund Summability
Authors: Cass Frank P. 
Published: December 2010

Throughout this paper H, H1 etc. will denote positive constants which will not necessarily be the same at different occurrences.
If is a series, we shall use the notation For a real, define1Let {pn} be a sequence with p0>0 and pn≥0 for n > 0. Define2The following identities are immediate:34where5
Riemannian Structures Subordinate to Certain Almost Tangent Structures
Authors: Closs M. P. 
Published: December 2010

Almost tangent structures have been studied by Eliopoulos [1] and certain Riemannian structures subordinate to almost tangent structures have been studied by Closs [2]. In this paper we investigate those subordinate Riemannian structures for which the underlying almost tangent structure is without torsion and those for which the fundamental form is closed.Similar studies have been carried out with respect to Riemannian structures subordinate to almost complex structures by Lichnerowicz [4] and with respect to Riemannian structures subordinate to almost product structures by Legrand [5].
Zeros of Linear Combinations of Polynomials
Authors: Rahman Q. I. 
Published: December 2010

The following theorem is due to J. L. Walsh (see [2, Theorem 17, 2a]):Theorem. If all the zeros of f1(z)=zn+a1zn-1+ … + an lie in or on the circle C1 with centre c1 and radius r1 and if all the zeros of f2(z)=zn+b1zn-1+ … + bn lie in or on the circle C2 with centre c2 and radius r2, then each zero of the polynomiallies in at least one of the circles Γk with centre γk and radius ρk, whereand where the ωk (k= 1, 2,…, n) are the nth roots of λ.
On the Multiplicative Inverse Eigenvalue Problem
Authors: De Oliveira G. N. 
Published: December 2010

By "multiplicative inverse eigenvalue problem" (m.i.e.p., for short) we mean the following. Let A be an n×n matrix and let s1,…, sn be n given numbers. Under what conditions does there exist an n×n diagonal matrix V such that VA has eigenvalues s1,…,sn?In the "additive inverse eigenvalue problem" (a.i.e.p., for short) we seek the diagonal matrix V so that A + V has eigenvalues s1,…, sn?.In the present paper we extend to the m.i.e.p. the ideas used in [7] for the a.i.e.p.By per X we denote the permanent of the square matrix X.
Group Partition, Factorization and the Vector Covering Problem
Authors: Herzog M. , Schönheim J. 
Published: December 2010

The covering problem. Let Si(i = 1, 2,…,n) be given sets containing mi elements respectively and let1be their cartesian product. The elements of S(n) will be called vectors. The vector (x1 x2,…, xn) covers (y1 y2,…, yn) if xi =yi for at least n—1 values of i. A subset M of S(n) is said to be a covering (perfect covering) of S(n) if each member of S(n) is covered by at least (exactly) one member of M. A covering M is said to be linear if the sets Si are groups Gi and M is a subgroup of G(n) = S(n) Denote by σ(n; m1 m2,…, mn) the value of min |M| when M runs through all coverings of S(n) and by σ(n; m1 m2,…, mn) the value of min |M| when the sets Si are given groups Gi and M runs through all linear coverings of G(n).
On the Monotone Nature of Boundary Value Functions for nth-Order Differential Equations
Authors: Peterson A. C. 
Published: December 2010

We are concerned with the nth (n≥3) order linear differential equation1where the coefficients are continuous on (∞, ∞). Our main result is to give conditions under which the two-point boundary value function rij(t) (see Definition 2) are strictly increasing continuously differentiable functions of t. Levin [1] states without proof a similar theorem concerning just the monotone nature of the rij(t) but assumes that the coefficients in (1) satisfy the standard differentiability conditions when one works with the formal adjoint of (1). Bogar [2] looks at the same problem for an nth-order quasi-differential equation where he makes no assumption concerning the differentiability of the coefficients in the quasi differential equation that he considers. Bogar gives conditions under which the rij(t) are strictly increasing and continuous. The different approach of the author to this problem also enables the author to establish the continuous differentiability of the rij(t) and to express the derivatives in terms of the principal solutions Uj(x, t), j=0, 1,…,n-1 (see Definition 4).
Consistency in the Reconstruction of Patterns from Sample Data
Authors: Moore Marc 
Published: December 2010

Let A be a k-dimensional Euclidean region having unit volume. An m-colors pattern is a partition PA of A into m sets Ai, i—1,…, m with positive volume. PA is called a random pattern if in addition the partition of A is a realization of a random process with the following stationarity and isotropy properties:(i) for all points s ∊ A, P(s ∊ Ai) =pi9, i = 1,..., m(ii) for all pair of points s, s'∊ A with distance |s—s|=d between them, P(s' ∊ Ai | s ∊ Aj)Pij(d) i,j= 1,..., m.
On the ith Latent Root of a Complex Matrix(1)
Authors: Al-Ani Sabri 
Published: December 2010

Goodman [1] has pointed out the applications of the distributional results of the complex multivariate normal statistical analysis. Khatri [4], has suggested the maximum latent root statistic for testing the reality of a covariance matrix. The joint distribution of the latent roots under certain null hypotheses can be written as, [2], [3],1whereand
On Sturm's Separation Theorem
Authors: Beesack Paul R. 
Published: December 2010

The purpose of this note is to obtain an extension of the classical Sturm separation theorem for the second order, linear selfadjoint differential equation1to the case of a noncompact interval. The classical theorem (cf. [3, p. 209], [4, p. 224]) assumes that r and s are continuous with r positive on a compact interval I, and concludes that between each pair of zeros (on I) of one (nontrivial) solution of (1) there lies precisely one zero of any other linearly independent solution of (1). If I is not compact, a function y which is a solution of (1) on /may often be extended (continuously) to an endpoint, say a, of I.
Local Malcev Conditions
Authors: Pixley Alden F. 
Published: December 2010

AbstractLet p and q be polynomial symbols of a type of algebras having operations ∨, ∧, and; (interpreted as the join, meet, and product of congruence relations). If is an algebra, L(), the local variety of , is the class of all algebras such that for each finite subset G of there is a finite subset F of such that every identity of F is also an identity of G.THEOREM. There is an algorithm which, for each inequalityp≤q,and pair of integers n, k≥2, determines a set Un, k of (Malcev) equations with the property:For each algebra, p≤q is true in the congruence lattice offor each∊L() if and only if for each finite subset F ofand integer n≥2 there is a k=k(n, F) such that Un, kare identities of F.This generalizes a corresponding result for varieties due to Wille (Kongruenzklassengeometrien, Lect. Notes in Math. Springer- Verlag, Berlin-Heidelberg, New York, 1970) and at the same time provides a more direct proof.
On Fixed Point Theorems for Mappings in a Separated Locally Convex Space
Authors: Lee Cheng-Ming 
Published: December 2010

The Banach contraction principle has been generalized by Tan [6] to the mappings in separated locally convex spaces. We show that the result of Sehgal [5] and also of Holmes [3] can be generalized in the same way.Throughout this note, we let X be a separated locally convex space, U a base for the closed absolutely convex neighborhoods of the origin O in X, K a nonempty subset of X, and Ta mapping from K to K.
Oscillation Criteria for Second Order Nonlinear Delay Equations
Authors: Erbe Lynn 
Published: December 2010

It is the purpose of this paper to establish oscillation criteria for second order nonlinear differential equations with retarded argument. Specifically, we consider the equation1.1where f ∊ C[0, + ∞) x R2, g ∊ C[0, + ∞), and1.2We shall restrict attention to solutions of (1.1) which exist on some ray [T, + ∞). A solution of (1.1) is called oscillatory if it has no largest zero.
Hypersurfaces Fixed by Equiaffinities
Authors: Fisher J. C. 
Published: December 2010

In this note we state and prove the followingAny equiaffinity acting on the points of an n-dimensional vector space (n ≥2) leaves invariant the members of a one parameter family of hypersurfaces defined by polynomials p(xl…,xn)=c of degree m ≤n.The theorem, restricted to the real plane, appears to have been discovered almost simultaneously by Coxeter [4] and Komissaruk [5]. The former paper presents an elegant geometric argument, showing that the result follows from the converse of Pascal's theorem. The present approach is more closely related to that of [5], in which the transformations are reduced to a canonical form.
Note Sur un Probleme de Maeda
Authors: Constantin Julien 
Published: December 2010

Maeda ([1, p. 29, Problème 1]) pose la question suivante: Est-ce qu'un treillis ⏊-symétrique et relativement semi-orthocomplémenté est nécessairement M-symétrique? Nous donnons une réponse affirmative à cette question.Soit L un treillis, et a,b,y ∊ L. Si (a,b)M et y≤b, alors (y V a,b)M.
Kiss-Precise Sequential Rotatable Designs
Authors: Herzberg Agnes M. , Garner C. W. L. , Springer B. G. F. 
Published: December 2010

SummaryA sequential procedure for the exploration of response surfaces is proposed. The procedure, which is for experiments with two factors, uses the kiss-precise configuration, i.e., the design points are on circles in mutual contact at each stage. Only three points need be added at each stage and the design points form a first-order rotatable design. A second-degree surface may be fitted when a near stationary region is reached.
On a Relation Between a Theorem of Hartman and a Theorem of Sherman
Authors: Peterson A. C. 
Published: December 2010

We are concerned with the nth-order linear differential equation1where the coefficients are assumed to be continuous. Hartman [1] proved that (see Definition 2) the first conjugate point η1(t) of t satisfies2Hartman actually proved a more general result which has very important applications in nonlinear differential equations.
On the Reducibility of Appell's Function F4
Authors: Srivastava H. M. 
Published: December 2010

Put1For the Appell function F4 defined by [3, p. 224]2Saxena [5, p. 216] proved a reduction formula in the form3whereIt may be of interest to point out that formula (3) is not correct. Indeed we first establish the following general result.
Hermite Conjugate Functions and Rearrangement Invariant Spaces
Authors: Andersen Kenneth F. 
Published: December 2010

The Hermite conjugate Poisson integral of a given f ∊ L1(μ), dμ(y)= exp(—y2) dy, was defined by Muckenhoupt [5, p. 247] aswhereIf the Hermite conjugate function operator T is defined by (Tf) a.e., then one of the main results of [5] is that T is of weak-type (1, 1) and strongtype (p,p) for all p>l.
On a Class of Positive Linear Operators
Authors: Swetits J. , Wood B. 
Published: December 2010

In a recent paper [3] Meir and Sharma introduced a generalization of the Sα- method of summability. The elements of their matrix, (ank), are defined by(1)where is a sequence of complex numbers. if 0 < αj < l for each j = 0, 1, 2,… then ank≥0 for each n = 0, 1, 2,… and k = 0,1,2,…
On M-Symmetric Lattices
Authors: Padmanabhan R. 
Published: December 2010

Every ⊥-symmetric relatively semi-orthocomplemented lattice is M-symmetric. This answers the Problem 1 in [2] in the affirmative and provides a new proof to a result on ⊥-symmetric lattices proved in [2] (Corollary below). The notation and terminology are as in [2].Let 〈L; ⋀, V〉 be a lattice. Two elements a and b of L are said to form a modular pair, in symbols aMb, ifThe relation aM✶b is defined dually.
Partially Closed Braids
Authors: Thomas R. S. D. 
Published: December 2010

The purpose of this paper is to define partially closed braids (§3) and to prove that every partially closed braid has a canonical form easily obtainable (§5). These objects are of interest because they can be used to represent knots tied in a string.Braids have an obvious intuitive meaning to which we shall refer. Braids are also elements of the braid groups of E. Artin [1], defined for each integer n greater than one by the presentation
A Remark on the Units of Finite Order in The Group Ring of a Finite Group
Authors: Losey Gerald 
Published: December 2010

Let G be a group, ZG its integral group ring and U(ZG) the group of units of ZG. The elements ±g∈U(ZG), g∈G, are called the trivial units of ZG. In this note we will proveLet G be a finite group. If ZG contains a non-trivial unit of finite order then it contains infinitely many non-trivial units of finite order.In [1] S. D. Berman has shown that if G is finite then every unit of finite order in ZG is trivial if and only if G is abelian or G is the direct product of a quaternion group of order 8 and an elementary abelian 2-group.
Example of an Injective Module which is Not Nice
Authors: Michler Gerhard O. 
Published: December 2010

In [1] Lambek calls the injective R-module I nice if every torsionfree factor module of the ring of quotients Q of R with respect to lis divisible. If lis nice then g is a dense subring of the bicommutator BicRI of I with respect to the finite topology (see [1, Proposition 2]). We now give an example of an injective R-module over an Artinian ring R which is not nice. Since R is Artinian, Q=BicRI, by Proposition B of [1].Before we give the example, we state the following, which depends on [2] for terminology.
The Range Sequence of an Operator
Authors: Vasilescu F.-H. 
Published: December 2010

Let T be a linear operator on a Banach space X and consider the sequence of rangeswhere the inclusions are not necessarily proper. The linear subspaces Xn=TnX (n>0) are, in general, not closed but they have some remarkable properties [1], [2]. Let X0=X and denote by |x|0 (x∈X0) the norm of X0.
Tauberian Theorems for Borel-Type Methods of Summability
Authors: Borwein D. , Smet E. 
Published: December 2010

Suppose throughout that s, an (n=0,1, 2,…) are arbitrary complex numbers, that α>0 and β is real and that N is a non-negative integer such that αN+β≧l. Letwhere z=x+iy is a complex variable and the power zr is assumed to have its principal value.
On the Inequality
Authors: Fischer Pal 
Published: December 2010

In this article, we are concerned with the following inequality(1)where 0<pi<1, 0<q<1, (i=l, 2,…,n), n is a fixed positive integer, n≥2 and f(p)≠0 for <p<l.This inequality was first considered by A. Renyi, who gave the general differentiate solution of (1) for n≥3, [1]. With the help of this inequality one can characterize Renyi’s entropy [2].We shall state later the Renyi’s result, which will be a special case of the Theorem 3.
A Note on Lie Isomorphisms
Authors: Martindale Wallace S. 
Published: December 2010

Main Theorem. The purpose of this note is to remove the assumption of characteristic different from 3 from a recent result of ours ([1], Theorem 11) so as to obtainLet S be a prime ring with 1, of characteristic different from 2 and containing two non-zero idempotents e1 and e2 whose sum is 1.
The Range of Invariant Means on Locally Compact Abelian Groups
Authors: Snell Roy C. 
Published: December 2010

AbstractIt has been shown by E. Granirer that for certain infinite amenable discrete groups G there exists a nested family of left almost convergent subsets of G on which every left invariant mean on m(G) attains as its range the entire [0,1] interval. This paper examines the range of left invariant means on L∞(G) for infinite locally compact abelian groups G and demonstrates the existence in every such group of a nested family of left almost convergent Borel subsets on which every left invariant mean on L∞ (G) attains as its range the interval [0,1],
Best Possible Nets in a Normed Linear Space1
Authors: Keener L. L. 
Published: December 2010

In this note we examine the question of the existence of a best possible N-net for a bounded set in a normed linear space. A sufficient condition for existence is given which leads to easy proofs of some of the standard results. The pertinent reference here is the paper by Garkavi [1].Let E be a normed linear space and let M be a bounded set in E. Any system of N points in E will be called an N-net. For a given M and the net SN = {y1, y2,…, yN} defineand
On GLn(B) Where B is a Boolean Ring
Authors: Gonshor H. 
Published: December 2010

The aim of this paper is to generalize the main results of [1] to GLn(B) by means of proofs which are more conceptual and less computational. In addition, by means of the Stone space we will obtain results which are new even for the case n = 2. Finally we shall make some remarks of a categorical nature.The author is especially interested in the subject because of the overlap here of many areas of mathematics. Concepts from topology, model theory, and category theory are all relevant.
A Characterization of Exponential Functions with Non-Linear Exponents
Authors: Światak Halina 
Published: December 2010

It is well known (see e.g. [1]) that the Cauchy functional equationcharacterizes the function f:x→exx.It was mentioned in [2D that the functions f:x→A exp(αx2m), g:x→exx/A can be characterized by the equation(1)but the proof was done only for m=l which was considerably simple.
A Note on Radical Extensions of Rings
Authors: Chacron M. , Lawrence J. , Madison D. 
Published: December 2010

All rings are associative. A ring T is said to be radical over a subring R if for every t ∈ T, there exists a natural number n(t) such that tn(t) ∈ R.In [1] Faith showed that if T is radical over R and T is primitive, then R is primitive. We might then ask if the same is true if prime is substituted for primitive.