bluuebunny/crossref_metadata_2025 huggingface dataset:
Dimension Theory Via Bisector Chains
Authors: Janos Ludvik
Published: December 2010

For 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

Initial 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 where

1

Jv(x) and Yv(x) being Bessel functions of the first and second kind, and

2

su, v(x) being Lommel's function, are proved.
Orthogonally Complete Rings
Authors: Raphael R. , Stephenson W.
Published: December 2010

In this note we continue the study of Abian's order for reduced rings initiated in papers such as [1], [5], [3], [4]. A simple proof is given of Abian's result that taking suprema commutes with ring multiplication. The properties of orthogonally complete rings and of rings satisfying chain conditions with respect to Abian's order are investigated.
Certain Summation Formulae for Basic Hypergeometric Series
Authors: Verma Arun
Published: December 2010

In 1927, Jackson [5] obtained a transformation connecting a

where N is any integer, with a

viz.,

1

where | q | > l and |qγ-α-βN| > l.
Applications of Decomposition Theorems to Trivializing h-Cobordisms
Authors: Lawson Terry
Published: December 2010

A geometric proof is presented that, under certain restrictions, the product of an h-cobordism with a closed manifold of Euler characteristic zero is a product cobordism. The results utilize open book decompositions and round handle decompositions of manifolds.
Trivectors in a Space of Seven Dimensions
Authors: Westwick R.
Published: December 2010

In their paper [1], Buseman and Glassco state that N(C, 7, 3) = 5 has been claimed but questioned. Schouten in [2] provides a classification of the orbits of ∧3V under the action of the group of automorphisms of ∧3V induced by automorphisms of V when dim V = 7.
Dependence of Best Rational Chebyshev Approximations on the Domain
Authors: Dunham Charles B.
Published: December 2010

Sufficient conditions are given for the error norm and coefficients of best rational Chebyshev approximation on a domain to depend continuously on the domain. Examples of discontinuity are given.
Functions of Exponential Type are Differences of Functions of Bounded Index
Authors: Shah Shantilal N.
Published: December 2010

The notion of entire function of Bounded Index is by now well established. It may be stated as follows.

An entire function f(z) is said to be of Bounded Index if for some fixed s

for all n and all z. (See [1], [2].)
On the Commutativity of Semi-Simple Associative Algebras
Authors: Stitzinger Ernest L.
Published: December 2010

Recall that an automorphism ϕ of an algebra A is called regular if, for all x∊A, ϕ(x) = x implies x = 0. For various types of algebras it is known that the existence of a regular automorphism implies that the algebra is radical. Here, for associative algebras, we relax the restrictions on the fixed points so that all automorphisms of commutative algebras immediately satisfy the hypothesis on the fixed points.
Thinnest Packing of Cubes with a Given Number of Neighbours
Authors: Tóth L. Fejes , Sauer N.
Published: December 2010

As a contribution to various investigations [1-11] about packing of convex bodies with certain conditions imposed on the number of neighbours of each body, V. Chvátal [12] recently proved the following theorem: If in a packing of translates of a square each square has at least six neighbours then the density of the packing is at least 11/15.
On the Derived Cuboid of an Eulerian Triple
Authors: Chein E. Z.
Published: December 2010

One of the interesting mathematical problems is whether the system of four Diophantine equations

1

2

has a solution in x, y, z, I, m, n, w. To this day the problem has not been shown to be impossible, nor has it been solved.
Local Central Λ(p) Dual Objects
Authors: Parker Willard A.
Published: December 2010

The dual object T of a compact group is called a local central A(p) set if there is a constant K such that ‖X‖P < K ‖X‖1 for all irreducible characters X of G. For each γ∊Γ, Dr is an irreducible representation of G of dimension dγ. Several authors [1, 2, 3, 4] have observed that Γ is a local central Λ(p) set for p∞, and some of them [2, 3] conjectured the converse. Cecchini [1] showed that Γ is not a local central Λ(4) set if G is a compact Lie group.
Homomorphisms Between Lattices of Zero-Sets
Authors: Broverman S.
Published: December 2010

For 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,
An Elementary Proof of a Fixed Point Theorem of J. Lewittes and D. L. McQuillan
Authors: Wayman Arthur K.
Published: December 2010

In (3), J. Lewittes establishes a connection between the number of fixed points of an automorphism of a compact Riemann surface and Weierstrass points on the surface; Lewittes′ techniques are analytic in nature. In (4), D. L. McQuillan proved the result by purely algebraic methods and extended it to arbitrary algebraic function fields in one variable over algebraically closed ground fields, but with restriction to tamely ramified places. In this paper we will give a different proof of the theorem and show that it is an elementary consequence of the Riemann-Hurwitz relative genus formula. Moreover, we can remove the tame ramification restriction.
The Spectral Radius of a Non-Negative Matrix
Authors: Berman A.
Published: December 2010

A max min formula for the spectral radius of a non-negative matrix is derived from a characterization of non-singular M-matrices in terms of diagonal stability.
Variations on a Theme of Kronecker
Authors: Boyd David W.
Published: December 2010

In 1857, Kronecker [10] showed that if θ1,…, θn are the roots of the polynomial P(z)= zn|cn-1+ … + cn, where c1, …, cn are integers with cn≠0, and if |θ1| ≤ 1, …, |θ1| ≤1, then θ1, …, θn are roots of unity. The proof is short and ingenious: Consider the polynomials Pm(z) whose roots are The condition on the size of the roots and the fact that the ci are integers implies that there can only be a finite number of different Pm. Thus two distinct powers of each root must coincide and this means that each root is a root of unity.
An Abstract Version of a Result of Fong and Sucheston
Authors: Kopp P. E.
Published: December 2010

Nagel [3] has given a purely functional-analytic proof of Akcoglu and Sucheston's operator version [1] of the Blum-Hanson theorem. The purpose of this note is to show that the same techniques may be applied to obtain a proof, in the context of (AL)-spaces, of a more general result due to Fong and Sucheston [2]. By Kakutani's representation theorem, any (AL)-space can of course be represented as an L-1-space. Thus the present result is simply a reformulation of that of Fong and Sucheston.
A Reflexive Banach Space that is Lur and Not 2R
Authors: Smith Mark A.
Published: December 2010

An example of the type described in the title is given.
The Hausdorff Moment Problem
Authors: Borwein David
Published: December 2010

Suppose throughout that

and that {μn}(n≥ 0) is a sequence of real numbers. The (generalized) Hausdorff moment problem is to determine necessary and sufficient conditions for there to be a function x in some specified class satisfying

.
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 that

for 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

Let (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.
Automorphisms of Full II1 Factors, II
Authors: Phillips John
Published: December 2010

The purpose of this note is to continue the author's study of the automorphisms of certain factors of type II1 Namely, those factors arising from the left regular representation of a free nonabelian group. Our main result shows that the outer conjugacy classes of automorphisms of such a factor are not countably separated. This had previously been shown only when the number of free generators was assumed to be infinite.
Paracompactness for Ordered Sums
Authors: Fleischer Isidore
Published: December 2010

Let us say that an order embedding of an uncountable regular cardinal in a linearly ordered set is continuous if it preserves the suprema (for all smaller limit ordinals). This makes the embedding a homeomorphism for the two order topologies; and if the image has no supremum, it is a closed subspace. Since uncountable regular cardinals fail to be paracompact, a linearly ordered set can be paracompact only if it admits no such embedding or anti-embedding. Conversely, Gillman and Henriksen have shown that this suffices (Trans. A.M.S. 77 (1954) pp. 352 ff).
A Note on Derivations
Authors: Herstein I. N.
Published: December 2010

In this note we prove two results about derivations. The first result holds in any ring, whereas the second one is valid in prime rings. From the nature of the results one would expect them to be known, but we have not been able to locate them in the literature.
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.
Note on an Asymptotic Formula for a Class of Digraphs
Authors: Sridharan M. R.
Published: December 2010

Self-complementary digraphs, and oriented type of these were counted by Read [4] and Sridharan [5] respectively. In [3] Palmer obtained an asymptotic formula for the number of self-complementary digraphs following a method of Oberschelp [2]. An asymptotic formula for the number of self-complementary oriented graphs is given here. We refer to [1] for definitions and details not mentioned here.
Catching and Missing Finite Sets
Authors: Ellis Martin H.
Published: December 2010

IfT 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

A 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.
On the Conjugacy Classes in an Integral Group Ring
Authors: Williamson Alan
Published: December 2010

Let G be a periodic group and ZG its integral group ring. The elements ±g(g∈G) are called the trivial units of ZG. In [1], S. D. Berman has shown that if G is finite, then every unit of finite order is trivial if and only if G is abelian or the direct product of a quaternion group of order 8 and an elementary abelin 2-group. By comparison, Losey in [7] has shown that if ZG contains one non-trivial unit of finite order, then it contains infinitely many.
On Pseudo-Lucas Numbers of the form 2s2
Authors: Eswarathasan A.
Published: December 2010

I [1] have shown that

are the only square pseudo-Lucas numbers in the set of pseudo-Lucas numbers defined by

1

In this paper, it is shown that none of the pseudo-Lucas numbers are of the form 2S2, where S is an integer.
An Elementary Proof of Johnson–Dulmage–Mendelsohn's Refinement of Birkhoff's Theorem on Doubly Stochastic Matrices
Authors: Nishi Akihiro
Published: December 2010

A 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.
Multiplication Modules
Authors: Singh Surjeet , Mehdi Fazal
Published: December 2010

All rings R considered here are commutative with identity and all the modules are unital right modules. As defined by Mehdi [6] a module MR is said to be a multiplication module if for every pair of submodules K and N of M, K ⊂ N implies K=NA for some ideal A of R. This concept generalizes the well known concept of a multiplication ring.
A Counterexample in Finite Fixed Point Theory
Authors: Enos H. C.
Published: December 2010

This note answers a question raised by Lee Mohler in 1970, by exhibiting a finite topological space X which is the union of closed subspaces Y, Z, such that Y, Z, and Y ⋂ Z, but not X, have the fixed point property. The example is a triangulation △ of S3, the points of X being the simplices of Δ and the closed sets the subcomplexes of △.
A Central Limit Theorem for General Stochastic Processes
Authors: Johnson Dudley Paul
Published: December 2010

We show that under mild conditions the Central Limit Theorem holds for general stochastic processes.
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.
On a Functional Equation
Authors: Al-Salam Nadhla A. , Al-Salam Waleed A.
Published: December 2010

Let P stand for a polynomial set (p.s.), i.e., a sequence {P0(x), P1(x), P2(x),...} such that for each n P0(x) is a polynomial in x of exact degree n and P0(x)≠0. We refer to Pn(x) as the nth component of P.
Hitting Time Distributions When Σ xk/dk Has a Smooth Density
Authors: Johnson Dudley Paul
Published: December 2010

In this paper we construct the hitting time distributions for stochastic processes Xk, taking on values amongst the integers 0, 1, …, d -1 for which has a smooth polynomial density with respect to the Lebesgue measure on [0,1].
Permuting the Elements of a Finite Solvable Group
Authors: Cliff Gerald H. , Rhemtulla Akbar H.
Published: December 2010

The main result in this note is the following

Theorem: 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 approximation

and 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 operator

1

where 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
A Necessary and Sufficient Condition for the Equivalence of the Topologies of Uniform and Compact Convergence
Authors: Clapp Michael H. , Shiflett Ray C.
Published: December 2010

Let (X, p) and (Y, d) be metric spaces with at least two points. It is usual for introductory courses in topology to study the set Yx of all functions mapping X to Y with the pointwise, compact-open, uniform convergence, and uniform convergence on compacta topologies. Some care is taken to show sufficient conditions for these topologies to be equivalent [1, 2]. However, the question of necessary conditions are dismissed with examples showing that the topologies are not in general equivalent.
On Regular-Closed and Minimal Regular Spaces
Authors: Joseph James E.
Published: December 2010

This paper contains several characterizations of regular-closed and minimal regular topological spaces along with some related properties.
Function Spaces Continuously Paired by Operators of Convolution-Type
Authors: Kerman R. A.
Published: December 2010

Certain 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.
A Note on Degree Sequences of Graphs
Authors: Brualdi Richard A.
Published: December 2010

Sufficient conditions for a sequence of numbers to be the degree sequence of a graph are derived from the Erdos-Gallai theorem on degree sequences of graphs.
On Inc-Extensions and Polynomials with Unit Content
Authors: Dobbs David E.
Published: December 2010

It 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.
Right Cyclically Ordered Groups(1)
Authors: Oltikar B. C.
Published: December 2010

This paper presents a study of right cyclically ordered groups (RCO-groups) and their relation to right ordered groups (RO-groups). Cyclically ordered groups (CO-groups) and their connection with ordered groups (O-groups) have been studied by Rieger in [7] and by Swierczkowski in [8]. While some of the properties of RCO-groups are analogous to the corresponding ones for COgroups, there are interesting exceptions.
A Note on Strongly Closed 2-Subgroups
Authors: Fong Paul , Harris Morton E.
Published: December 2010

Let T be a Sylow 2-subgroup of the finite group G and let 1<S≤T with S strongly closed in T with respect to G. Let Γ=〈CG(s), NG(Ω1(S))| s∊I(S)〉. Suppose that Γ≤H<G for some subgroup H of G. Then H∩〈SG〉 is strongly embedded in 〈SG〉 and S=T∩〈SG〉 or S=Ω1(T∩〈SG〉). Also if m(S) = 1, then S=T∩〈SG〉.
On the Connectedness of Certain sets in Summability Theory
Authors: Parameswaran Mangalam R.
Published: December 2010

This 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

Let (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. and

if 0≤m≤n, m≤k, are given. Generalizations and applications are considered.
On the Number of Zeros Over a Finite Field of Certain Symmetric Polynomials
Authors: Ceccherini P. V. , Hirschfeld J. W. P.
Published: December 2010

A variety of applications depend on the number of solutions of polynomial equations over finite fields. Here the usual situation is reversed and we show how to use geometrical methods to estimate the number of solutions of a non-homogeneous symmetric equation in three variables.
A Note on Doubles of 4-Manifolds
Authors: Weintraub Steven H.
Published: December 2010

If M is a simply-connected 4-manifold with boundary, let D(M) denote its double MU∂M(-M). If M is closed, let D(M) denote M#-M. In either case, D(M) is a simply-connected 4-manifold of index zero, and so by a theorem of Wall [8], M#k(S2xS2) must be standard for k sufficiently large, where by standard we mean diffeomorphic to the connected sum of copies of S2 x S2 and S2×S2, the non-trivial S2 bundle over S2 (which is itself diffeomorphic to ℂP2#-ℂP2 [7]). In this paper we give abound on k, in the case where M has no 3-handles.
On Property B of Families of Sets
Authors: Abbott H. L. , Liu A. C.
Published: December 2010

A family of sets is said to have property B if there exists a set S such that S∩F≠ ϕ and SF for all F . S is called a B-set for . Let n≥2 and N≥2n-1. Let V = { 1, 2,≠, N} and let = {G:G⊂ V, |G| = rc}. Erdös [3] defined mN(n) to be the size of a smallest subfamily of which does not have property B and proved the following results:
Units of the Group Ring
Authors: Groenewald N. J.
Published: December 2010

If R is a ring such that x, y ∈ R and xy = 0 imply yx = 0 and G≠ 1, an ordered group, then we show that ∑ αgg is a unit in RG if and only if there exists ∑ βhh in RG such that ∑ αgβg-1 = 1 and αgβh is nilpotent whenever gh≠l. We also show that if R is a ring with no nilpotent elements ≠ 0 and no idempotents ≠ 0, 1 then RG has only trivial units. Some applications are also given.
Noetherian Rings in Which Every Ideal is a Product of Primary Ideals
Authors: Anderson D. D.
Published: December 2010

The classical rings of number theory, Dedekind domains, are characterized by the property that every ideal is a product of prime ideals. More generally, a commutative ring R with identity has the property that every ideal is a product of prime ideals if and only if R is a finite direct sum of Dedekind domains and special principal ideal rings. These rings, called general Z.P.I. rings, are also characterized by the property that every (prime) ideal is finitely generated and locally principal.
Periodic and Nil Polynomials in Rings
Authors: Felzenszwalb Bernardo , Giambruno Antonino
Published: December 2010

Let R be an associative ring and f(x1,…, xd) a polynomial in noncommuting variables. We say that f is periodic or nil in R if for all r1,…, rd ∈ R we have that f(r1,…, rd) is periodic, respectively nilpotent (recall that a ∈ R is periodic if for some integer ).
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.
A Non-Normal Function Whose Derivative is of Hardy Class Hp, 0<p<1
Authors: Yamashita Shinji
Published: December 2010

Let Hp(0<p≤∞) be the Hardy class of functions holomorphic in D={|z|<1}, and let f be a function holomorphic in D. It follows from the well known theorem [1, Theorem 3.11, p. 42] that if (I) , then (II) f can be extended continuously to the closed disk {|z|≤1}, and consequently, (III) f is normal in D in the sense of O. Lehto and K. I. Virtanen [2]. Since there is a considerable gap between (II) and (III), one would suspect that the condition (I) might be much stronger than necessary to obtain the conclusion (III). However, it is curious that the implication (I)⇒(III) is sharp as the following theorem shows.
Non-singular Periodic Flows on T3 and Periodic Homeomorphisms of T2
Authors: Hartzman C. S.
Published: December 2010

A homeomorphism f of a space M is pointwise periodic if for each m ∈ M there exists an integer k such that fk(m) =m, where fk is the kth iterate of f. Montgomery proves [5] that if M is a connected topological manifold, then f is periodic; i.e., there exists an integer n such that fn = id. Noting this, Weaver [7] proves that if M is an orientable 2-manifold of class C1, U⊆M open and C ⊆ U a compact connected set and if g : U → M of class C1 is such that (i) g(C) = C and (ii) whenever the derivative of g at points x∈C has rank 2 it is orientation preserving, then f = g|c : C → C periodic implies that all but a finite number of points of C have as least period the period of f.
A Transformation Formula for a Class of Arithmetic Sums
Authors: Subbarao M. V. , Harris V. C.
Published: December 2010

Arithmetic sums of the form

where f is an arithmetic function and [ ] is the greatest integer function frequently occur in various situations in the theory of numbers and have much of interest in their own right. Two instances appear in the well-known results.
Topological Left Amenability of Semidirect Products
Authors: Junghenn H. D.
Published: December 2010

Let 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.
In Search of a Pappian Lattice Identity
Authors: Day Alan
Published: December 2010

In [8] and subsequent papers, Jônsson (et al) developed a lattice identity which reflects precisely Desargues Law in projective geometry in that a projective geometry satisfies Desargues Law if and only if the geometry, qua lattice, satisfies this identity. This identity, appropriately called the Arguesian law, has become exceedingly important in recent investigations in the variety of modular lattices (see for example [2], [3], [9], and [12]). In this note, we supply two possible lattice identities for the Pappus' Law of projective geometry.
The Stieltjes Moment Problem
Authors: Klambauer G.
Published: December 2010

We shall apply the spectral theorem for self adjoint operators in Hilbert space to study an operator version of the Stieltjes moment problem [1]. In the course of the work we shall make use of the Friedrichs extension theorem which states that any non-negative symmetric operator in Hilbert space has a non-negative self adjoint extension.
Tauberian Conditions for the Equivalence of Weighted Mean and Power Series Methods of Summability
Authors: Borwein David
Published: December 2010

Suppose throughout that {pn} is a sequence of non-negative numbers with p0>0, that

and that {sn} is a sequence of real numbers.
A Class of Spaces in Which Compact Sets are Finite
Authors: Sharma P. L.
Published: December 2010

It is shown that in a dense-in-itself Hausdorff space if every set having a dense interior is open, then every compact set is finite.
Ordinary Singularities of Algebraic Curves
Authors: Orecchia Ferruccio
Published: December 2010

Let 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

The 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

If 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

We 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

If 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

Let 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.
A Presentation for a Group of Integer Matrices
Authors: Smythe N.
Published: December 2010

Let Λn be the kernel of the map from GL(n, ) to GL(n, 2) induced by the quotient map ℤ → ℤ2. We give a presentation for Λn.
Cyclotomic Splitting Fields
Authors: Mollin R. A.
Published: December 2010

Let 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).
On the Number of Partitions of { 1, …, n} into Two Sets of Equal Cardinalities and Equal Sums
Authors: Prodinger Helmut
Published: December 2010

Let A(n) be the number of partitions of { 1 , … , n} into two sets A, B of cardinality n/2 such that . Then there is the asymptotic result
Semi r-Free and r-Free Integers—A Unified Approach
Authors: Hardy G. E. , Subbarao M. V.
Published: December 2010

We 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.
On Delay Differential Inequalities of Higher Order
Authors: Ladas G. , Stavroulakis I. P.
Published: December 2010

Consider the nth order (n ≥ 1) delay differential inequalities and and the delay differential equation , where q(t) ≥ 0 is a continuous function and p, τ are positive constants. Under the condition pτe ≥ 1 we prove that when n is odd (1) has no eventually positive solutions, (2) has no eventually negative solutions, and (3) has only oscillatory solutions and when n is even (1) has no eventually negative bounded solutions, (2) has no eventually positive bounded solutions, and every bounded solution of (3) is oscillatory. The condition pτe > 1 is sharp. The above results, which generalize previous results by Ladas and by Ladas and Stavroulakis for first order delay differential inequalities, are caused by the retarded argument and do not hold when τ = 0.
Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications
Authors: Temam R.
Published: December 2010

In the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.

This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.
Local Freeness of Profinite Groups
Authors: Pletch Andrew
Published: December 2010

In this paper we discuss the relationship between local properties such as freeness and projectivity of a group and the freeness or projectivity of its pro-C-completion. We show that for certain classes, C, of finite groups (e.g. p-groups, nilpotent groups, super-solvable groups) the pro-C-completion of a locally free pro-C-group is a free pro-C-group. We also show that under certain circumstances the converse is also true but we leave open the question, for example, of whether a locally free pro-p-group is free.
Note on a Stability Theorem
Authors: Székelyhidi László
Published: December 2010

In this note the stability theorem of Albert and Baker concerning the n-th difference equation is proved by using invariant means.
Rings with a Special Kind of Automorphism
Authors: Bergen Jeffrey , Herstein I. N.
Published: December 2010

In this paper we examine the nature of rings R with unit having an automorphism ϕ ≠ 1 such that x — ϕ(x) is 0 or invertible for every x ∊ R. We show that the only examples of such rings are R = D, R = D2, and R = D ⊕ D, where D is a division ring. Furthermore, for the case D2, we describe the division rings that are possible.
On Ergodic Extensions of Stationary Measures with Minimal Support
Authors: Krebs William B. , Robertson James B.
Published: December 2010

Let T be an ergodic measure preserving transformation with the following property: there exists a positive integer n and a finite partition α such that the number of atom of is one more than that of , and the probability of at least one of the atoms is irrational. Then there exists a unique (up to conjugacy) transformation S such that there is a partition β with S restricted to isomorphic to T restricted to and the number of atoms in is one more than the number of atoms in for all m ≥ n. Moreover this transformation has discrete spectrum with at most two generators. If there are two generators, one of them must be a root of unity.
A Structure Theorem in Finite Topology
Authors: Ginsburg John
Published: December 2010

Simple structure theorems or representation theorems make their appearance at a very elementary level in subjects such as algebra, but one infrequently encounters such theorems in elementary topology. In this note we offer one such theorem, for finite topological spaces, which involves only the most elementary concepts: discrete space, indiscrete space, product space and homeomorphism. Our theorem describes the structure of those finite spaces which are homogeneous.
The Poincaré Map in Mixed Exterior Algebra
Authors: Vanstone J. R.
Published: December 2010

The Poincaré map of mixed exterior algebra generalizes the Hodge star operator and it plays a central rôle in the proofs of many classical identities of linear algebra. The principal purpose of this paper is to derive a new formula for it. This formula is useful in circumstances when the definition is too implicit. Several applications are discussed.
Covering Problem for Idempotent Latin Squares
Authors: Heinrich Katherine
Published: December 2010

Let A = (aij) be an idempotent latin square of order n, n ≥ 3, in which aii = i, 1 ≤ i ≤ nc. A set S ⊆ N = {1, 2, …, n} is a cover of A if (N × N)\{(i, i):i ∉ S} = {(i, j): i ∊ S, j ∊ N} ∪ {(j, i): i ∊ S, j ∊ N} ∪ {(i, j): aij ∊ S}. A cover S is minimum for A if |S| < |T| for every cover T of A and we write c(A) = |S|. We denote by c(n) the maximum value of c(A) over all idempotent latin squares A of order n and in this paper show that (7n/10)-3.8 ≤ c (n) < n - n1/3 + 1 for all n ≥ 15. The problem of determining c(n) was first raised by J. Schönheim.
Coincidence Sets of Coincidence Producing Maps
Authors: Schirmer Helga
Published: December 2010

A theorem by H. Robbins shows that every closed and non-empty subset of the unit ball Bn in Euclidean n-space is the fixed point set of a self map of Bn. This result is extended to coincidence producing maps of Bn, where a map ƒ:X → Y is coincidence producing (or universal) if it has a coincidence with every map g:X → Y. The main result implies that if ƒ:Bn, Sn - 1 → Bn, Sn - 1 is coincidence producing and A⊂Bn closed and nonempty, then there exist a map ƒ': Bn, Sn - 1 → Bn, Sn - 1 and a map g: Bn → Bn such that ƒ' | Sn - 1 is homotopic to ƒ | Sn-1 and A is the coincidence set of ƒ' and g.
Extremal Positive Solutions of Semilinear Schrödinger Equations
Authors: Swanson C. A.
Published: December 2010

Necessary and sufficient conditions are proved for the existence of maximal and minimal positive solutions of the semilinear differential equation Δu = -ƒ(x, u) in exterior domains of Euclidean n-space. The hypotheses are that ƒ(x, u) is nonnegative and Hölder continuous in both variables, and bounded above and below by ugi(| x |, u), i = 1, 2, respectively, where each gi(r, u) is monotone in u for each r > 0.
Optimal Stopping Under General Dependence Conditions
Authors: Longnecker M.
Published: December 2010

Let {Xn} be a sequence of random variables, not necessarily independent or identically distributed, put and Mn =max0≤k≤n|Sk|. Effective bounds on in terms of assumed bounds on , are used to identify conditions under which an extended-valued stopping time τ exists. That is these inequalities are used to guarantee the existence of the stopping time τ such that E(ST/aτ) = supt ∈ T∞ E(|Sτ|/at), where T∞ denotes the class of randomized extended-valued stopping times based on S1, S2, … and {an} is a sequence of constants. Specific applications to stochastic processes of the time series type are considered.
An Algebraic Characterization of Remainders of Compactifications
Authors: Hatzenbuhler James , Mattson Don A. , Sizer Walter S.
Published: December 2010

Let X be a locally compact, completely regular Hausdorff space. In this paper it is shown that all compact metric spaces are remainders of X if and only if the quotient ring C*(X)/C∞(X) contains a subring having no primitive idempotents.
Asymptotic Results for Class Number Divisibility in Cyclotomic Fields
Authors: Gerth Frank
Published: December 2010

Let n ≥3 and m≥3 be integers. Let Kn be the cyclotomic field obtained by adjoining a primitive nth root of unity to the field of rational numbers. Let denote the maximal real subfield of Kn. Let hn (resp., ) denote the class number of Kn (resp., ). For fixed m we show that m divides hn and hn for asymptotically almost all n. Also for those Kn and with a given number of ramified primes, we obtain lower bounds for certain types of densities for m dividing hn and .
A Multiple Sequence Ergodic Theorem
Authors: Olsen James H.
Published: December 2010

Let be a σ-finite measure space, {T1, …, Tk} a set of linear operators of , some p, 1≤p≤∞.If

exists a.e. for all f ∊ Lp, we say that the multiple sequence ergodic theorem holds for {T1, …, Tk}. If f≥0 implies Tf≥0, we say that T is positive. If there exists an operator S such that |Tf(x)|≥S |f|(x) a.e., we say that T is dominated by S. In this paper we prove that if T1, …, Tk are dominated by positive contractions of , p fixed, 1<p<∞, then the multiple sequence ergodic theorem holds for {T1, …, Tk}.
Absolute Summability Factors in a Sequence
Authors: Baron S.
Published: December 2010

Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method Cα

Another theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and B=(bnk) satisfying , where (ξnk) = (ank)-1.
Primary Groups Whose Basic Subgroup Decompositions can be Lifted
Authors: Benabdallah K. , Laroche A.
Published: December 2010

A primary group G is said to be a l.i.b. group if every idempotent endomorphism of every basic subgroup of G can be extended to an endomorphism of G. We establish the following characterization: A primary group is a l.i.b. group if and only if it is the direct sum of a torsion complete group and a divisible group. The technique used consists of a close analysis of certain subgroups of Prufer-like primary groups.
Split Graphs with Specified Dilworth Numbers
Authors: Nara Chiê , Sato Iwao
Published: December 2010

Let G be a split graph with the independent part IG and the complete part KG. Suppose that the Dilworth number of (IG, ≼) with respect to the vicinal preorder ≼ is two and that of (KG, ≼) is an integer k. We show that G has a specified graph Hk, defined in this paper, as an induced subgraph.
(HM)-Spaces and Measurable Cardinals
Authors: Aguirre José A. Facenda
Published: December 2010

A locally convex space E is called an (HM)-space if E has invariant nonstandard hulls. In this paper we prove that if E is an (HM)-space, then E is a T(μ)-space, where μ is the first measurable cardinal. This is equivalent to say that in an (HM)-space, with dim(E)≧μ, does not exist a continuous norm. With this result, we prove that there exists an inductive semi-reflexive space E such that the bounded sets in E are finite-dimensional but E is not an (HM)-space. Thus, we answer negatively to an open problem raised up by Bellenot. In this paper, we do not use nonstandard analysis.
Free Actions By Elementary Abelian 2-Groups on Stiefel Manifolds
Authors: Cusick Larry W.
Published: December 2010

Let Vn, k denote the Stiefel manifold of k-frames in ℝn. There is a free action on Vn, k by the group . We show that if acts freely on and

then l≤k