bluuebunny/crossref_metadata_2025 huggingface dataset:
A Central Limit Theorem for Multiplicative Systems
Authors: Komlós J.
Published: December 2010

The central limit theorem was originally proved for independent random variables. The independence is a very strong notion and hard to check. There are various efforts to prove different theorems on independent variables (e.g. strong law of large numbers, central limit theorem, the law of iterated logarithm, convergence theorem of Kolmogorov) under weaker conditions, like mixing, martingale-difference, orthogonality. Among these concepts the weakest one is orthogonality, but this ensures only the validity of law of large numbers.
On an Inequality of Peano(1)
Authors: Muldowney James S.
Published: December 2010

Let f be a real valued function on an open subset of R2. It is assumed that f satisfies Carathéodory's conditions: f (t,x) is continuous in x for each t, Lebesgue measurable in t for each x and there is a locally integrable function m(t) such that |f(t, x)| ≤ m(t) uniformly in x. A proof will be given of the following theorem.
Pointwise Sequentially Closed Ideals in C*(X)
Authors: Wilson Richard G.
Published: December 2010

The purpose of this paper is to determine the conditions under which the maximal ideals of the ring C*(X)—the bounded real-valued continuous functions on a completely regular Hausdorff space X—are closed under pointwise convergence of sequences. Whereas the maximal ideals of C*(X) are closed under pointwise convergence of nets if and only if X is compact, it is shown that a necessary and sufficient condition for their pointwise sequential closure is that X be pseudocompact (i.e. that all real-valued continuous functions of X be bounded).
Hypersurfaces Fixed by Equiaffinities
Authors: Fisher J. C.
Published: December 2010

In this note we state and prove the following

Any 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.
On a Theorem of Sylvester and Schur
Authors: Hanson D.
Published: December 2010

In 1892, Sylvester [7] proved that in the set of integers n, n+l,…, n+k—1, n> k > 1, there is a number containing a prime divisor greater than k. This theorem was rediscovered, in 1929, by Schur [6]. More recent results include an elementary proof by Erdös [1] and a proof of the following theorem by Faulkner [2]: Let pk be the least prime ≥2k; if n≥pk then has a prime divisor ≥pk with the exceptions and In that paper the author uses some deep results of Rosser and Schoenfeld [5] on the distribution of primes.
Kiss-Precise Sequential Rotatable Designs
Authors: Herzberg Agnes M. , Garner C. W. L. , Springer B. G. F.
Published: December 2010

A 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.
The Fitting Length of a Finite Soluble Group and the Number of Conjugacy Classes of its Maximal Metanilpotent Subgroups
Authors: Makan A. R.
Published: December 2010

It is known that the Fitting length h(G) of a finite soluble group G is bounded in terms of the number v(G) of the conjugacy classes of its maximal nilpotent subgroups. For |G| odd, a bound on h(G) in terms of v(G) was discussed in Lausch and Makan [6]. In the case when the prime 2 divides |G|, a logarithmic bound on h(G) in terms of v(G) is obtained in [7]. The main purpose of this paper is to show that the Fitting length of a finite soluble group is also bounded in terms of the number of conjugacy classes of its maximal metanilpotent subgroups. In fact, our result is rather more general.
Separation of Functions
Authors: May L. E.
Published: December 2010

Eames [2], and Jeffery [5], consider separation of sets in a measure space and show that, if A is separated from B, then

where m*denotes outer measure.

In this paper we consider the class, , of nonnegative bounded real-valued functions of a real variable.
Nuclear Spaces of Generalized Test Functions
Authors: Millington H.
Published: December 2010

It is well known that a large proportion of the locally convex spaces encountered in distribution theory are nuclear (Grothendieck [4], Treves [10], Schaeffer [8].) In [1] Beurling introduced spaces of test functions more general than those previously used. In this paper we shall show that many of these spaces, and resulting spaces of distributions, are also nuclear spaces.
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 equation

1

where the coefficients are assumed to be continuous. Hartman [1] proved that (see Definition 2) the first conjugate point η1(t) of t satisfies

2

Hartman 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

Put

1

For the Appell function F4 defined by [3, p. 224]

2

Saxena [5, p. 216] proved a reduction formula in the form

3

where

It may be of interest to point out that formula (3) is not correct. Indeed we first establish the following general result.
On the Construction of Bibd With λ = 1
Authors: Scott Kenneth F. N.
Published: December 2010

In the past three decades the problem of generating (balanced incomplete block) designs by difference sets has received much attention. Bose [2] gave the two "fundamental theorems of the method of differences". Bose, Sprott [9], Lehmer [7], Chowla [4], Takeuchi [10] and others have given specific classes of difference sets.
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] as

where

If 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.
Amitsur Cohomology in Additive Functors
Authors: Dobbs David E.
Published: December 2010

Let L/k be a Galois extension of fields with group G and let A be the category of k-algebras isomorphic to finite products of finite field subextensions of L/k. It is known that, with appropriately defined covers, A is dual to the underlying category of a Grothendieck topology T [5, Ch. I, Theorem 4.2] and that (strict) cohomological dimension of G may be characterized via TCech cohomology with coefficients in either additive (product-preserving) functors or sheaves [5, Ch. I, Theorems 4.3 and 5.9].
A Construction of Subequalizers
Authors: Coppotelli Fred
Published: December 2010

Given a pair of functors F, G:A→B, Lambek defines [1] the subequalizing category, E of (F, G) as the category with objects, ordered pairs (A, b) with A ∈ |A| and b:FA→GA a morphism of B. The morphisms of E from (A, b) to (A′, b′) are ordered triples (b, a, b′) where a:A→A′ is a morphism of A and G(a)b = b′F(a).
On a Structure Defined by a Tensor Field F of Type (1, 1) Satisfying F2 = 0
Authors: Houh C. S.
Published: December 2010

Professor Eliopoulous studied almost tangent structure on manifolds M2n in [1], [2], [3]. An almost tangent structure F is a field of class C∞ of linear operations on M2n such that at each point x in M2n, Fx maps the complexified tangent space into itself and that Fx is of rank n everywhere and satisfies F2=0.
Overrings of Bezout Domains
Authors: Beauregard Raymond A.
Published: December 2010

In [2] Brungs shows that every ring T between a principal (right and left) ideal domain R and its quotient field is a quotient ring of R. In this note we obtain similar results without assuming the ascending chain conditions. For a (right and left) Bezout domain R we show that T is a quotient ring of R which is again a Bezout domain; furthermore Tis a valuation domain if and only if T is a local ring.
Uniqueness of the Coefficient Ring in Some Group Rings
Authors: Parmenter M. , Sehgal S.
Published: December 2010

Let 〈x〉 be an infinite cyclic group and Ri〈x〉 its group ring over a ring (with identity) Ri, for i = l and 2. Let J(Ri) be the Jacobson radical of Ri. In this note we study the question of whether or not R1〈x〉≃R2〈x〉 implies R1≃R2. We prove that this is so if Zi the centre of Ri is semi-perfect and J(Zi〈x〉) = J(Zi〈)x〉 for i = l and 2. In particular, when Zi is perfect the second condition is satisfied and the isomorphism of group rings Ri〈x〉 implies the isomorphism of Ri.
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,…
Equational Compactness of G-Sets
Authors: Banaschewski B.
Published: December 2010

This paper deals with the notion of equational compactness and related concepts in the special case of G-sets for an arbitrary group G. It provides characterizations of pure extensions, pure-essential extensions, and equational compactness in terms of the stability groups of a G-set, proves the general existence of equationally compact hulls, and gives an explicit description of these. Further, it establishes, among other results, that all G-sets are equationally compact iff all subgroups of the group G are finitely generated, that every equationally compact G-set is a retract of a topologically compact one, and that for free groups G with infinite basis there are homogeneous G-sets which are not equationally compact.
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, if

The 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
On A theorem of Niven
Authors: Dressler Robert E.
Published: December 2010

In [3], Niven proved that for any positive integer k, the density of the set of positive integers n for which (n, (φ(n))≤k is zero (where φ is the Euler to tient function). In this paper, we prove a related result—namely if k and j are any positive integers, then the density of the set of positive integers n for which (n,σj(n))≤k is zero (where σj(n) is the sum of the jth powers of the positive divisors of n). We will borrow from Niven’s technique, but we must make some crucial modifications.
Non-Convexity in Best Complex Chebyshev Approximation by Rational Functions
Authors: Dunham Charles B.
Published: December 2010

In real Chebyshev approximation by generalized rational functions, constraining denominators to be positive guarantees that the set of best coefficients is convex [1, 181]. We show by means of an example that denominators must be constrained to be of constant argument for such a convexity result to hold in complex Chebyshev approximation.
A Non-Reflexive Banach Space has Non-Smooth Third Conjugate Space
Authors: Giles J. R.
Published: December 2010

J. Dixmier has observed [3, p. 1070] that a non-reflexive Banach space has non-rotund fourth conjugate space. It is the aim of this paper to improve Dixmier’s result by showing that a non-reflexive Banach space already has non-smooth third conjugate space in that the images under natural embedding of the continuous linear functionals which do not attain their norm on the unit sphere are non-smooth points of the third conjugate space.
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 prove

Let 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 ranges

where 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. Let

where z=x+iy is a complex variable and the power zr is assumed to have its principal value.
The Oscillatory Behavior of a First Order Non-Linear Differential Equation with Delay
Authors: Burkowski Forbes J. , Ponzo Peter J.
Published: December 2010

Synopsis

This paper establishes the existence of an infinite set of zeros for the solution of a certain functional differential equation. The primary condition assuring this oscillatory behavior is expressed in terms of the magnitude of the delay.
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 obtain

Let 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.
On Regulating Sets and the Disparity of Planar Cubic Graphs
Authors: Fleischner Herbert
Published: December 2010

The goal of this paper is to relate plane cubic graphs which are not bipartite to plane bipartite cubic graphs which have properties (face-coloring with three colors, existence of two-factors whose cycles are boundaries of faces) characterizing this class of graphs.
Gaussian Processes with Markovian Covariances
Authors: Johnson Dudley Paul
Published: December 2010

We show that any Gaussian process can be derived in a simple manner from a Markov process if it has zero mean and covariance identical to the covariance of a real valued function of a temporally homogeneous Markov process.
On Pure-High Subgroups of Abelian Groups
Authors: Benabdallah K.
Published: December 2010

Fuchs, in [3], problem 14, proposes the study of pure-high subgroups of an abelian group. In this paper we show that in abelian torsion groups, pure-high subgroups are also high. A natural problem arises, that of characterizing the pure-absolute summands. We show that this concept is the same as absolute summands in torsion groups, but that it is more general in mixed abelian groups. There is a definite connection between the existence of pure TV-high subgroups and the splitting of mixed groups. The notation is that of [3].
When Flats are Torsion Free
Authors: Page S.
Published: December 2010

Given a complete Serre class τ this determines a torsion theory with T the class of torsion modules. It also determines the torsion free modules. For the classical torsion in the category of abelian groups the torsion free modules are flat and visa-versa. Which rings are characterized by this property? More precisely: Which rings admit a torsion theory for which the concepts of torsion free and flat are equivalent? We also dispose of the cases when R admits a toision theory for which torsion free is equivalent to injective and when projective is equivalent to torsion free.
A Note on Multiplier Operators and Dual B*-Algebras
Authors: Rowlands K.
Published: December 2010

Let A be a complex Banach algebra without order. Following Kellogg [4] and Ching and Wong [2], a mapping T of A into itself is called a right (left) multiplier on A if T(ab)=(Ta)b(T(ab)=a(Tb)) for all a, b in A. T is said to be a multiplier on A if it is both a right and left multiplier on A. Let M(A)(RM(A), LM(A)) be the set of all (right, left) multipliers on A.
The Range of Invariant Means on Locally Compact Abelian Groups
Authors: Snell Roy C.
Published: December 2010

It 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],
Integration of Non-Measurable Functions (II)
Authors: Zakon Elias
Published: December 2010

This is a supplement to a previous paper [4] in which integration was developed for arbitrary extended-real functions over arbitrary sets in an outer measure space S, ℳ*, m* where m*; also written m, is a regular outer measure on all subsets of an arbitrary set S≠ø, and ℳ* is thsetse family of all m*-measurable sets.
Non-Uniqueness of The Solution to a Generalized Dirichlet Problem
Authors: Koh E. L.
Published: December 2010

It is generally known [1] that the singular partial differential equation

may not have a unique solution because of the existence of nontrivial representations of zero.

1
On Lifting Idempotents
Authors: Koh Kwangil
Published: December 2010

Let N be an ideal of a ring A. We say that idempotents modulo N can be lifted provided that for every a of A such that a2-a ∈ N there exists an element e2=e ∈ A such that e-a ∈ N. The technique of lifting idempotents is considered to be a fundamental tool in the classical theory of nonsemiprimitive Artinian rings (refer [2; p. 72]).
On the Complete Regularity of Some Category Spaces
Authors: Eames W.
Published: December 2010

A category space is a measure space which is also a topological space, the measure and the topology being related by ‘a set is measurable iff it has the Baire property’ and ‘a set is null iff it is nowhere dense’ [4]. We considered some category spaces in [3]; now we show that if a null set is deleted from the space, then the topology can be taken to be completely regular. The essential part of the construction consists of obtaining a suitable refinement of the original sequential covering class and using the consequent strong upper density function to define the required topology. Then the complete regularity follows much as in [1].
A Spectral Theorem for Hermitian Operators of Meromorphic Type on Banach Spaces
Authors: Owusu-Ansah T.
Published: December 2010

It is well known that if T is a compact self-adjoint operator on a Hilbert space whose distinct non-zero eigenvalues {λn} are arranged so that |λn|≥|λn+1| for n = 1, 2…. and if En in the spectral projection corresponding to λn, then with convergence in the uniform operator topology. With the generalisation of self-adjoint operators on Hilbert spaces to Hermitian operators on Banach spaces by Vidav and Lumer, Bonsall gave a partial analogue of this result for Banach spaces when he proved the following theorem.
Wreath Products of Nonoverlapping Lattice Ordered Groups
Authors: Read John A.
Published: December 2010

One of the fundamental tools in the theory of totally ordered groups is Hahn’s Theorem (a detailed discussion may be found in Fuchs [3]), which asserts, roughly, that every abelian totally ordered group can be embedded in a lexicographically ordered (unrestricted) direct sum of copies of the ordered group of real numbers. Almost any general question regarding the structure of abelian totally ordered groups can be answered by reference to Hahn’s theorem. For the class of nonabelian totally ordered groups, a theorem which parallels Hahn’s Theorem is given in [5], and states that each totally ordered group can be o-embedded in an ordered wreath product of subgroups of the real numbers. In order to extend this theorem to include an “if and only if” statement, one must consider lattice ordered groups, as an ordered wreath product of subgroups of the real numbers is, in general, not totally-ordered, but lattice ordered.
On Some Numbers Related to the Bell Numbers
Authors: Tanny Stephen M.
Published: December 2010

The Bell numbersBncan be defined by Bn=whereS(n, k)is t n e Stirling number of the second kind. In this note we employ a technique developed by Rota (which formalizes the umbral calculus) to derive a veriety of facts concerning the related numbersand polynomials.
A Note on Torsion Free Groups Generated by Pairs of Matrices
Authors: Charnow A.
Published: December 2010

Let and let Gm be the group generated by A and the transpose of A. The problem of determining complex numbers m such that Gm is a free group had been studied by several authors [1, 2, 3]. In this note we characterize those rational values of m for which Gm is torsion free.
On extensions of the Riemann and Lebesgue Integrals by Nets
Authors: Bellamy O. S. , Ellis H. W.
Published: December 2010

In this note our principal interest is in using nets to give spaces of non-absolutely convergent integrals as extensions of the spaces of absolutely convergent Riemann and Lebesgue integrals. For this purpose we develop a general theory of extensions, by nets, of functions defined on the open intervals with closures in the complement of a fixed closed set, the nets being directed by inclusion for finite disjoint collections of such intervals. Two cases are considered leading to open extension (OE-) and conditional open extension (COE-) nets, the latter being subnets of the former. Necessary and sufficient conditions for the convergence of the OE- and COE-nets are given, those for the COE-nets being similar to conditions that arise in the definition of the restricted Denjoy integral. Properties of inner continuity, weak additivity and the existence of a continuous integral are defined and studied. These relate to the more specialized nets that are suitable for the extension of integrals.
Chebyshev Sets in C[0,1] Which are not Suns
Authors: Dunham Charles B.
Published: December 2010

Consider approximation of elements of C[0, 1] with respect to the sup-norm by a non-empty subset V of C[0, 1]. Of interest in recent years are subsets V called suns. As C[0, 1] is an MS-space [1, 5], the suns V of C[0, 1] are precisely those subsets V for which each local best approximation is a global best approximation.
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} define

and
Sublattices of Modular Lattices of Finite Length
Authors: Rival Ivan
Published: December 2010

It is well-known that the join-irreducible elements J(L) and the meet-irreducible elements M(L) of a lattice L of finite length play a central role in its arithmetic and, especially, in the case that L is distributive. In [3] it was shown that the quotient set Q(L) = {b/a | a ∊ J(L), b ∊ M(L), a ≤ b} plays a somewhat analogous role in the study of the sublattices of L. Indeed, in a lattice L of finite length, if S is a sublattice of L then S = L — ∪b/a∊A [a, b] for some A ⊆ Q(L). Furthermore, the converse actually characterizes finite distributive lattices [3].
Geodesic Correspondence in the Brans-Dicke Theory
Authors: Tupper B. O. J.
Published: December 2010

In a recent article [1] vacuum field solutions of the Brans-Dicke [2] field equations were found, the space-time metric in each solution being of the Friedmann type. Most of these solutions existed only for specific values of the parameter ω and, in particular, the two largest sets of solutions corresponded to the values and . Peters [3, 4] has shown that when all solutions of the Brans-Dicke vacuum equations are conformai to space-times with vanishing Ricci tensor. The purpose of this note is to investigate the possible geometric consequences of the value .
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 Central Limit Theorem with Conditioning on the Distant Past
Authors: McLeish D. L.
Published: December 2010

Serfling (1968) has considered a central limit theorem in which assumptions are made concerning the expectation of variables conditioned on their distant predecessors. Dvoretsky (1972, theorem 5.3) has continued this investigation. Serfling showed that both martingales and φ-mixing sequences satisfied his conditions, and Dvoretsky extended this to Strong mixing sequences of random variables.
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 equation

characterizes 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.
On a Problem of P. Turán
Authors: Vértesi P. O. H.
Published: December 2010

Let us consider the well-known Hermite-Fejér interpolating process on the interval [—1,1] i.e. let

(1.1)

(sometimes we omit the second indices),

(1.2)
On the Inversion of Right Invariant Elements
Authors: Beauregard Raymond A.
Published: December 2010

In this note we show that every (not necessarily commutative) integral domain R has a quotient ring which, although need not be a field, has the property that all of its right invariant elements are units. As an application this shows that every PRI (principal right ideal) domain can be embedded in a simple PRI domain which is, in general, not a field.
A Note on Some Prime Hausdorff Methods of Summability
Authors: Parameswaran M. R.
Published: December 2010

Given a matrix A = (ank) (n, k = 0, 1, 2, …), let (A) denote the set of all sequences x = {xk} such that {An(x)} ∊ c where An(x) = Σk=0∞ankxk (n≥0) and c denotes the set of all convergent sequences. It is well known (see e.g. Zeller [6] or Zeller and Beekmann [7], p. 48) that given an unbounded sequence x, there exists a regular (=permanent) matrix A with ank = 0 for k > n (and indeed with ann ≠ 0) such that (A) = c ⊕x, the linear space spanned by c and x. We call A an Einfolgenverfahren. (See [7].) In [4] Rhoades considered, inconclusively, the question whether there exists a Hausdorff matrix H such that (H)= c ⊕ x (for arbitrary unbounded sequence x).
Stability of Certain Dynamical Systems
Authors: Jeffries Clark
Published: December 2010

For n real variables {xi} of time t we consider the following equations:

(1)

Throughout {aij} and {fi} are assumed to be continuous. For any given initial conditions there is assumed to be at least one trajectory solution.
Uniqueness of Generalized Solutions of Abstract Differential Equations
Authors: Malik M. A.
Published: December 2010

Let Ω be an open subset of R and H be a complex Hilbert space; (,) represents scalar product in H.Let also A be a closed linear operator with domain DA dense in H and A* with domain D*A be its adjoint. Under graph scalar product DA and D*A are also Hilbert spaces.
Partial Orders on the 2-Cell
Authors: Tymchatyn E. D.
Published: December 2010

A partially ordered space is an ordered pair (X, ≤) where X is a compact metric space and ≤ is a partial ordering on X such that ≤ is a closed subset of the Cartesian product X×X. ≤ is said to be a closed partial order on X.
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.
Formula for the Nth Prime Number
Authors: Jones James P.
Published: December 2010

In this note we give a simple formula for the nth prime number. Let pn denote the nth prime number (p1=2, p2 = 3, etc.). We shall show that pn is given by the following formula.
On the Derivatives of the Γ-Function
Authors: Melzak Z. A.
Published: December 2010

The coefficients of the two series

(1)

are recursively given by Nielsen [1]: c0=g0=1 and

where s1 is the Euler constant γ and for n>1 sn = ζ(n).
Identite Entre L'ensemble Des Fonctions De Baire et L'Ensemble Des Fonctions Boreliennes
Authors: Fournier Gilles
Published: December 2010

Il est bien connu que l'ensemble des fonctions de Baire de ℝ dans ℝ est égal à l'ensemble des fonctions boréliennes de ℝ dans ℝ. Dans cet article, nous généraliserons ce théorème de deux façons: premièrement, en étudiant plutöt des fonctions de X à Y, deux espaces topoiogiques normaux; et deuxièmement, en utilisant les suites généralisées de cardinalité donnée.
Extension of Set Functions to Measures and Applications to Inverse Limit Measures
Authors: Mallory D.
Published: December 2010

In measure theory and probability it is often useful to be able to extend a set function g to a measure μ. One situation in which such an extension arises is that of obtaining limit measures for inverse (or projective) systems of measure spaces ([1], [5]).
On the First Conjugate Point Function for Nonlinear Differential Equations
Authors: Peterson Allan C. , Sukup Dwight V.
Published: December 2010

We 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.
Extension Function and Subcategories of Haus
Authors: Porter Jack R.
Published: December 2010

For each Hausdorff spaceX, letFXbe an Hausdorff extension ofX. The existence of the largest subcategory of HAUS on whichFs a functor and an epi-reflection is investigated.
Maximum Modulus Theorems and Schwarz Lemmata for Sequence Spaces
Authors: Shawyer B. L. R.
Published: December 2010

In this note, we prove analogues of the classical maximum modulus theorem and Schwarz lemma, for sequence spaces. We begin by stating these two results in a convenient way; that is for the unit disk and functions of bound one.
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 product

Moreover for each p, 1≤p≤∞, there exists a constant Cp such that ‖f*g‖p,≤
Cp‖f‖p ‖g‖p.
Regular Quotients of Metric Spaces
Authors: Warrack Brian
Published: December 2010

In this note we consider the class of topological spaces whose every Hausdorff quotient is regular (or equivalently, normal). Sufficient conditions in order that a space belongs to this class have appeared in papers by Morita [3], and more recently by MacDonald and Willard [2]. In both cases, the authors impose conditions implying paracompactness. We shall derive additional sufficient conditions here which show that paracompactness is not necessary in general.
On the Radon-Nikodym Derivative with a Chain Rule in a Von Neumann Algebra
Authors: Elliott George A.
Published: December 2010

The purpose of this paper is to show that by a reorganization of the proofs of the main results concerning Radon-Nikodym derivatives in a von Neumann algebra of Pedersen and Takesaki in [12] and of Connes in paragraphs 1.1 and 1.2 of [5], considerable technical simplification can be achieved. Roughly speaking, the analytic vector techniques developed by these authors for the study of weights on a von Neumann algebra can be replaced, to a large extent, by the tensor product methods introduced by Connes, which are essentially algebraic in nature. In the exposition which follows, analytic vectors are not used at all (see, however, 4.4).
On the Edelstein Contractive Mapping Theorem
Authors: Janos Ludvik
Published: December 2010

Let 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.
A Banach Space Whose Elements are Classes of Sets of Constant Width
Authors: Lewis J. E.
Published: December 2010

Let K be a compact subset of the real Euclidean space En. We say that K has constant width if the distance between each pair of distinct parallel hyperplanes which support K is constant. The collection of all compact convex subsets of En which have constant width is denoted .
A Class of Quasi-Nonexpansive Multi-Valued Maps
Authors: Shiau Chyi , Tan Kok-Keong , Wong Chi Song
Published: December 2010

Let (X, d) be a (nonempty) metric space. bc(X) will denote the family of all nonempty bounded closed subsets of X endowed with the Hausdorff metric D induced by d [2, pp. 205]. Let/be a map of X into bc(X). f is nonexpansive at a point x in X if for all y in X.
Strong Radical Classes and Idempotents
Authors: Stewart Patrick N.
Published: December 2010

All rings are associative but do not necessarily have identities. Definitions and basic results about radical classes can be found in [2]. A radical class is strong [3] if for every ring A, (A) contains all left and right -ideals of A.
Reciproque Du Theoreme Des Bases Sur Un Espace Vectoriel
Authors: Couture Raymond , Lavoie Mario
Published: December 2010

Sommaire

Nous donnons, dans ce qui suit, la preuve de la proposition suivante.
Dirac Delta Functions Via Nonstandard Analysis
Authors: Lightstone A. H. , Wong Kam
Published: December 2010

We recall that a Dirac delta function δ(x) in the real number system is the idealization of a function that vanishes outside a "short" interval and satisfies It is conceived as a function δ for which δ(0)=+ ∞, δ(t)=0 if t≠0, and This function should possess the "sifting property" for any continuous function f. Even though certain sequences of functions are used, via a limit operation, to approximate a Dirac delta function (for details, see [3] and [4]), no function in has these properties.
Derived Functors of Torsion
Authors: Hiller Howard Lyn
Published: December 2010

In this note we compute the derived functors of “torsion submodule” using a certain duality result for semi-exact functors on an abelian category of finite global dimension.
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 inequality

1

for 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,
The Uniform Continuity of Functions in Sobolev Spaces
Authors: Adams R. A.
Published: December 2010

Functions in , may have to be uniformly continuous on Ω even if Ω is not a Lipschitz domain.
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 obtain

Theorem 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.
Weak Parallelogram Laws for Banach Spaces
Authors: Bynum W. L.
Published: December 2010

It has been shown previously that the Lp(μ) spaces for 1 < p ≤ 2 satisfy a weak parallelogram law, and the same methods can be used to show that the Lp(μ) spaces for 2 ≤ p <∞ satisfy a related weak parallelogram law. This paper obtains several equivalent characterizations of Banach spaces which satisfy one of these two weak parallelogram laws. One such characterization involves the conditions on the moduli of convexity and smoothness analyzed by Lindenstrauss.
Products of Radon Measures: A Counter-Example
Authors: Fremlin D. H.
Published: December 2010

I show that if X is the hyperstonian space of Lebesgue measure on [0,1], then there are open sets in X×X which are not measurable for the simple product outer measure. This answers a question of M. C. Godfrey and M. Sion.
Representation of a Certain Class
of Polynomials
Authors: Leblanc Raymond
Published: December 2010

In this note, we discuss a representation of the class of polynomials with real coefficients having all zeros in a given disk of the complex plane C, in terms of convex combinations of certain extremal polynomials of this class. The result stated in the theorem is known [1] for polynomials having n real zeros in the interval [a.b.]. In the following z will be a complex number and D[(a + b)/2, (b-a)/2] the closed disk of the complex plane centered at the real point (a + b)/2 and having radius (b-a)/2.
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

If 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.
Some Arithmetic Properties of a Special Sequence of Integers
Authors: Carlitz L.
Published: December 2010

Leeming [3] has defined a sequence of polynomials {Q4n(x)} and a sequence of integers {Q4n} by means of

1.1

and

1.2

Thus

1.3

and equivalently

1.4
Weighted Maximal Inequalities for ℓr- Valued Functions
Authors: Heinig H. P.
Published: December 2010

C. Feffermann and E. M. Stein [2] have shown that the continuity property of the Hardy-Littlewood maximal functions between Lp-spaces, 1 < p < ∞, extends to ℓr-valued functions on ℝn. Specifically, if f = (f1, f2,…) is a sequence of functions defined on Rn, let for l<∞, |f(x)|r be given by
An Internal Solution to the Problem of Linearization of a Convexity Space
Authors: Szafron D. A. , Weston J. H.
Published: December 2010

Following Kay and Womble [2] an abstract convexity structure on a set X is a collection ξ of subsets of X which includes the empty set, X and is closed under arbitrary intersections. One of the natural problems that arises in convexity structures is to give necessary and sufficient conditions for the existance of a linear structure on X such that the collection of all convex sets in the resulting linear space is precisely ξ. An associated problem is to consider a set with a convexity structure and a topology and find necessary and sufficient conditions for the existance of a linear structure on X such that X becomes a linear topological space with again ξ the collection of convex sets.
On a Theorem of Lelong
Authors: Pham-Gia Thu
Published: December 2010

Let Γn = {z = (z1, z2,…, zn): and Re(zi)>0, ∀i}. For a multisequence Mj, = (j1, j2,…,jn) and 0 < M(j)≤∞, let , q(r) = sup|j||{r|j|Mj} and .
On Prime Goldie-Like Quadratic Jordan Matrix Algebras(1)
Authors: Britten Daniel J.
Published: December 2010

In [1] and [2], there was given a characterization for linear Jordan matrix algebras whose coordinatizing ring is *-prime Goldie or a Cayley-Dickson ring (C-D ring). If one considers the corresponding question in the more general setting of quadratic Jordan algebra as defined by McCrimmon in [11], then the result is similar. In this latter case the ample quadratic Jordan algebras, as studied by Montgomery in [12] and [13], are brought into play.
Accumulation Points of Continuous Realvalued Functions and Compactifications
Authors: Choo Eng Ung
Published: December 2010

All topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions on X. βX is the Stone-Cech compactification of X. A real number t is said to be an accumulation point of a function f ∊ C(X) if and only if f-1[[t-ε, t + ε]] is not compact for every ε > 0.
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],

1.1

L. Fejér a montré ([3]) qu'il existe toujours un polynôme de degré inférieur ou égal à n + 1 tel que

1.2

et

1.3
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 function

1

where 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 that

2

where 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 by

Let 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 that

1

A 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).
Combinatorial Property of a Special Polynomial Sequence
Authors: Carlitz L.
Published: December 2010

Leeming [4] has defined a sequence of polynomials {Q4n(x)} and a sequence of integers {Q4n} by means of

1

and

2

Thus

3

Leeming showed that the Q4n are all odd and that

4

It is proved in [3] that

5
On Some Integral Inequalities Related to Hardy's
Authors: Imoru Christopher Olutunde
Published: December 2010

We obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.