bluuebunny/crossref_metadata_2025 huggingface dataset:
Annihilator equivalence of torsion-free abelian groups
Authors: Schultz P. , Vinsonhaler C. , Wickless W. J.
Published: April 2009

We define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent ifevery pure subgroup of one has a non-zero image in the other, and each has a non-zero image in every torsion-free factor of the other.

We study the closure properties of the equivalence classes, and the structural properties of the class of all equivalence classes. Finally we identify a class of groups which satisfy Krull-Schmidt and Jordan-Hölder properties with respect to the equivalence.
An improvement of a transcendence measure of Galochkin and Mahler's S-numbers
Authors: Amou Masaaki
Published: April 2009

We give a transcendence measure of special values of functions satisfying certain functional equations. This improves an earlier result of Galochkin, and gives a better upper bound of the type for such a number as an S-number in the classification of transcendental numbers by Mahler.
Ribbon knot families via stallings' twists
Authors: Hitt L. Richard , Silver Daniel S.
Published: April 2009

We investigate the effect on the Jones polynomial of a ribbon knot when two of its bands are twisted together. We use our results to prove that each of the three S-equivalence classes of genus 2 fibered doubly slice knots in S3 can be represented by infinitely many distinct prime fibered doubly slice ribbon knots.
Best Simultaneous approximation of quasi-continuous functions by monotone functions
Authors: Sahab Salem M. A.
Published: April 2009

Let Q denote the Banach space (under the sup norm) of quasi-continuous functions on the unit interval [0, 1]. Let ℳ denote the closed convex cone comprised of monotone nondecreasing functions on [0, 1]. For f and g in Q and 1 < p < ∞, let hp denote the best Lp-simultaneous approximant of f and g by elements of ℳ. It is shown that hp converges uniformly as p → ∞ to a best L∞-simultaneous approximant of f and g by elements of ℳ. However, this convergence is not true in general for any pair of bounded Lebesgue measurable functions. If f and g are continuous, then each hp is continuous; so is limp→∞ hp = h∞.
Rates of strong convergence for U-statistics in finite populations
Authors: Kokic P. N. , Weber N. C.
Published: April 2009

Let UNn be a U-statistic based on a simple random sample of size n selected without replacement from a finite population of size N. Rates of convergence results in the strong law are obtained for UNn, which are similar to those known for classical U-statistics based on samples of independent and identically distributed (iid) random variables.
Reflexive open mappings on generalized graphs
Authors: Miklos Stanislaw
Published: April 2009

In this paper we show that a locally connected and locally compact metric image of a generalized graph under a reflexive open mapping is a generalized graph; further, we characterize all acyclic generalized graphs X with the property that any locally one-to-one reflexive open mapping of X into a Hausdorff space is globally one-to-one. Several problems are posed and some examples are given.
Continuous-trace algebras from the bundle theoretic point of view
Authors: Rosenberg Jonathan
Published: April 2009

Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their K-theory. We also present a classification of real continuous-trace algebras from the same point of view.
Graphs associated with triangulations of lattice polygons
Authors: DeTemple Duane , Robertson Jack M.
Published: April 2009

Two graphs, the edge crossing graph E and the triangle graph T are associated with a simple lattice polygon. The maximal independent sets of vertices of E and T are derived including a formula for the size of the fundamental triangles. Properties of E and T are derived including a formula for the size of the maximal independent sets in E and T. It is shown that T is a factor graph of edge-disjoint 4-cycles, which gives corresponding geometric information, and is a partition graph as recently defined by the authors and F. Harary.
Approximate dual and approximate vector variational inequality for multiobjective optimization
Authors: Chen G.–Y. , Craven B. D.
Published: April 2009

An approximate dual is proposed for a multiobjective optimization problem. The approximate dual has a finite feasible set, and is constructed without using a perturbation. An approximate weak duality theorem and an approximate strong duality theorem are obtained, and also an approximate variational inequality condition for efficient multiobjective solutions.
On the zeroes of profiles
Authors: Wallis W. D.
Published: April 2009

The k-profile of an Hadamard matrix of order n is a function defined on the integers 0, 1,…,n. If k is even, k-profile of an Hadamard matrix of order n (k even) has non-zero terms only in every eighth position. If k is divisible by 4, the non-zero positions are those congruent to n (modulo 8).
Function classes related to Ruscheweyh derivatives
Authors: Ahuja O. P. , Silverman H.
Published: April 2009

We investigate a family consisting of functions whose convolution with is starlike of order α 0 ≤ α < 1. We determine extreme points, inclusion relations, and show how this family acts under various linear operators.
Walsh-Fourier series with coefficients of generalized bounded variation
Authors: Móricz F.
Published: April 2009

We extend in different ways the class of null sequences of real numbers that are of bounded variation and study the Walsh-Fourier series of integrable functions on the interval [(0, 1) with such coefficients. We prove almost everywhere convergence as well as convergence in the pseu dometric of Lr(0, 1) for 0 < r < 1.
On the product of distances to a point set on a sphere
Authors: Wagner Gerold
Published: April 2009

Let S be the surface of the unit sphere in three-dimensional euclidean space, and let WN=(x1x2, xN)be an N-tuple of points on S. We consider the product of mutual distances and, for the variable point x on S, the product of distance from x to the points of ωN. We obtain essentially best possible bounds for maxωN p(ΩN) and for minωN maxx∈sp(x, ωN).
Bounds for the solutions of some diophantine equations in terms of discriminants
Authors: Brindza B. , Evertse J. H. , Györy K.
Published: April 2009

Several effective upper bounds are known for the solutions of Thue equations, Thue-Mahler equations and superelliptic equations. One of the basic parameters occurring in these bounds is the height of the polynomial involved in the equation. In the present paper it is shown that better (and, in certain important particular cases, best possible) upper bounds can be obtained in terms of the height, if one takes into consideration also the discriminant of the polynomial.
Star-center points of univalent functions
Authors: Artémiadis Nicolas K.
Published: April 2009

Let be the class of normalized univalent functions in the unit disk. For f ∈ let Sf be the set of all star center points of f. Let 0 = where is the interior of Sf. The influence that the size of the set has on the Taylor coefficients of a function f ∈ 0 is examined, and estimates of these coefficients depending only on , as well as other results, are obtained.
Additive relations in fields
Authors: Van Der Poorten A. J. , Schlickewei H. P.
Published: April 2009

This paper is the first part of a long delayed revision of the manuscript ‘The growth conditions recurrence sequences’ (circulated in 1982) in which the authors outlined a proof of the now well known theorem on the finiteness of the number of solutions of S-unit equations. The argument lifting the result from number fields to arbitrary fields of characteristic zero has original features.
Functorial properties of algebraic closure and Skolemization
Authors: Ash C. J. , Nerode A.
Published: April 2009

It is shown that no functor F exists from the category of sets with injections, to the category of algebraically closed fields of given characteristic, with monomorphisms, having the properties that for all sets A. F(A) is an algebraically closed field having transcendence base A and for all injections f. F(f) extends f. There does exist such a functor from the category of linearly-ordered sets with order monomorphisms.

An application to model-theory using the same methods is given showing that while the theory of algebraically closed fields is ω-stable, its Skolemization is not stable in any power.
Commuting rings of simple A(k)-modules
Authors: Farkas Daniel R. , Snider Robert L.
Published: April 2009

For the Weyl algebra A(k) and each finite dimensional division ring D over k, there exists a simple A(k)-module whose commuting ring is D.

It has been known for some time that if A(k) denotes the Weyl algebra over a field k of characteristic zero, the commuting ring of a simple A(k)-module is a division algebra finite dimensional over k (see the introduction of [1]). Which division algebras actually appear? Quebbemann [1] showed that if D is a finite dimensional division algebra whose center is k, then it occurs as a commuting ring. We complete this circle of ideas by showing that any D appears: a division algebra over k appears as the commuting ring of a simple A(k)-module if and only if it is finite dimensional over k.
Convergence in kth variation and RSk integrals
Authors: Das U. , Das A. G.
Published: April 2009

In recent papers, Russell introduced the notions of functions of bounded kth variation (BVk functions) and the RSk integral. Das and Lahiri enriched Russell's works along with a convergence formula of RSk integrals depending on the convergence of integrands. In this paper a convergence theorem analogous to Arzela's dominated convergence theorem has been presented. An investigation to the convergence in kth variation has been made leading to some convergence theorems of RSk integrals depending on the convergence of integrators.
The diameter of an immersed Riemannian manifold with bounded mean curvature
Authors: Koufogiorgos Th. , Baikoussis Ch.
Published: April 2009

Let M be an n-dimensional complete Riemannian manifold with Ricci curvature bounded from below. Let be an N-dimensional (N < n) complete, simply connected Riemannian manifold with nonpositive sectional curvature. We shall prove in this note that if there exists an isometric immersion φ of M into with the property that the immersed manifold is contained in a ball of radius R and that the mean curvature vector H of the immersion has bounded norm ∥H∥ > H0, (H0 > 0) then R > H−10.
On the ranks of some (0, 1)-matrices with constant row sums
Authors: Odlyzko A. M.
Published: April 2009

Let g(n, m) denote the maximal number of distinct rows in any (0, 1 )-matrix with n columns, rank < n, – 1, and all row sums equal to m. This paper determines g(n, m) in all cases:

In addition, it is shown that if V is a k-dimensional vector subspace of any vector space, then V contains at most 2k vectors all of whose coordinates are 0 or 1.
Chaotic difference equations in Rn
Authors: Kloeden P. E.
Published: April 2009

Sufficient conditons are given for the chaotic behaviour of difference equations defined in terms of continuous mappings in Rn. These conditions are applicable to both difference equations with snap-back repellors and with saddle points. They are applied here to the twisted-horseshoe difference equation of Guckenheimer, Oster and Ipaktchi.
Another class of graceful trees
Authors: Koh K. M. , Rogers D. G. , Tan T.
Published: April 2009

We discuss the problem of constructing large graceful trees from smaller ones and provide a partial answer in the case of the product tree Sm {g} by way of a sample of sufficient conditions on g. Interlaced trees play an important role as building blocks in our constructions, although the resulting valuations are not always interlaced.
The least α for which E(α) is inadmissible
Authors: Hoole M. R. R.
Published: April 2009

This paper attempts to classify the least ordinal α0 for which E(α0) (the E closure of α0 ∪ {α0}) is inadmissible. Among the result proved are (i)Lα0 = ZFC-; (ii)α0 is very large in comparison with the least ordinal satifying (i); (iii) (α0, α] marks precisely an ω-Gap, where α¯ = E(α0) ∩ ON; (iv) the Kr-sequence of α0 has length ω.
Extremal problems for a class of functions of positive real part and applications
Authors: Anh V. V. , Tuan P. D.
Published: April 2009

In this paper we determine the lower bound on |z| = r < 1 for the functional Re{αp(z) + β zp′(z)/p(z)}, α ≧0, β ≧ 0, over the class Pk (A, B). By means of this result, sharp bounds for |F(z)|, |F',(z)| in the family and the radius of convexity for are obtained. Furthermore, we establish the radius of starlikness of order β, 0 ≦ β < 1, for the functions F(z) = λf(Z) + (1-λ) zf′ (Z), |z| < 1, where ∞ < λ <1, and .
Bilinear forms and 2-dimensional cohomology
Authors: Moskowitz Martin
Published: April 2009

This paper calculates the central Borel 2 cocycles for certain 2-step nilpotent Lie groups G with values in the injectives A of the category of 2nd countable locally compact abelian groups. The G's include, among others, all groups locally isomorphic to a Heisenberg group. The A's are direct sums of vector groups and (possibly infinite dimensional) tori, and in particular include R, T, and Cx. The main results are as follows.

(4.1) Every symmetric central 2 cocycle is trivial.

(4.2) Every central 2 cocycle is cohomologous with a skew symmetric bimultiplicative one (which is necessarily jointly continuous by [7]).

(4.3) The corresponding cohomology group H2cent (G, A) is calculated as the skew symmetric jointly continuous bimultiplicative maps modulo Homcont ([G, G]–, A).

These results generalize the case when G is a connected abelian Lie group and A = T, due to Kleppner [3]. Using standard facts of the cohomology of groups they can be interpreted as classifying all continuous central extensions (1) → A → E → G → (1) of the group G by the abelian group A. Finally some counterexamples are given to extending these results.
Smallest regular graphs without near 1-factors
Authors: Chartrand Gary , Ruiz Sergio , Wall Curtiss E.
Published: April 2009

A near 1-factor of a graph of order 2n ≧ 4 is a subgraph isomorphic to (n − 2) K2 ∪ P3 ∪ K1. Wallis determined, for each r ≥ 3, the order of a smallest r-regular graph of even order without a 1-factor; while for each r ≧ 3, Chartrand, Goldsmith and Schuster determined the order of a smallest r-regular, (r − 2)-edge-connected graph of even order without a 1-factor. These results are extended to graphs without near 1-factors. It is known that every connected, cubic graph with less than six bridges has a near 1-factor. The order of a smallest connected, cubic graph with exactly six bridges and no near 1-factor is determined.
A function is Perron integrable if it has locally small Riemann sums
Authors: Schurle Arlo W.
Published: April 2009

We say that a function has locally small Riemann sums on an interval if for each pointxin the interval, and for each positive number ε, all sufficiently fine partitions of intervals lying in neighborhood ofxbut not containingxhave Riemann sums of absolute value less than ε. The main result is then as the title states. We use the generalized Riemann approach to Perron integration, assuming that functions are measurable only to insure that conditions involving the positive and negative parts of the functions are satisfied.
2-groups with every automorphism central
Authors: Glasby S. P.
Published: April 2009

An infinite family of 2-groups is produced. These groups have no direct factors and have a non-abelian automorphism group in which all automorphisms are central.
A new bitopological paracompactness
Authors: Raghavan T. G. , Reilly I. L.
Published: April 2009

In this paper we define generalization of paracompactness for bitopological spaces. (X, τ1, τ2) is Δ-pairwise paracompact if and only if every τi open cover admits a τ1 ∨ τ2 open refinement which is τ1 ∨ τ2 locally finite. Every quasimetric space (X, τp, τq) is Δ-pairwise paracompact. An analogue of Michael's characterization of regular paracompact spaces is proved for Δ-pairwise paracompact spaces.
Digraphs with eulerian chains
Authors: Skilton D. K.
Published: April 2009

An eulerian chain in a directed graph is a continuous directed route which traces every arc of the digraph exactly once. Such a route may be finite or infinite, and may have 0, 1 or 2 end vertices. For each kind of eulerian chain, there is a characterization of those diagraphs possessing such a route. In this survey paper we strealine these characterizations, and then synthesize them into a single description of all digraphs having some eulerian chain. Similar work has been done for eulerian chains in undirected graphs, so we are able to compare corresponding results for graphs and digraphs.
Twenty-step algorithm for determining the asymptotic number of trees of various species: corrigenda
Authors: Harary Frank , Robinson Robert W. , Schwenk Allen J.
Published: April 2009

John W. Moon has discovered several computational errors in our article above (J. Austral. Math. Soc. (Series A) 20 (1975), 483–503). The five constants reported for identity trees below Table 1 at the bottom of page 502 are all wrong. The correct values are
On a problem of Niederreiter and Robinson about finite fields
Authors: Wan Daqing
Published: April 2009

In this article, we prove that for a finite field Fq with even q > 3, any complete mapping polynmial of Fq has reduced degree at most q − 3. This is a solution to a problem of Niederreiter and Robinson about finite fields.;
On the number of p-blocks of a p-soluble group
Authors: Cossey John
Published: April 2009

A technique is described for calculating the number of block ideals of FG, where F is a algebraically closed field of characteristic p, and where G is a p-soluble finite group. Among its consequences are the following: if U is a G-invariant irreducible FOp′(G)-module, then there is a unique block ideal of FG whose restriction to Op′(G) has all its composition factors isomorphic to U; and if G has p′-length 1, the number of block ideals of FG is the number of G-conjugacy classes of Op′(G)
Products of locally finite groups with min-p
Authors: Amberg Bernhard , Moghaddam Mohammad Reza R.
Published: April 2009

The paper is devoted to showing that if the factorized group G = AB is almost solvable, if A and B are π-subgroups with min-p for some prime p in π and also if the hypercenter factor group A/H(A) or B/H(B) has min p for the prime p. then G is a π-group with min-p for the prime p.
A class of finite groups having nilpotent injectors
Authors: Iranzo M. J. , Monasor F. Pérez
Published: April 2009

The purpose of this paper is to construct a class of groups which properly contains the class of N-constrained groups, and which is such that all groups in this class have N-injectors.
Growth of solutions of weakly coupled parabolic systems and Laplace's equation
Authors: Watson N. A.
Published: April 2009

Let ui(x, t) be the ith component of a nonnegative solution of a weakly coupled system of second-order, linear, parabolic partial differential equations, for x ∈ Rn and 0 < t < T. We obtain lower estimates, near t = 0, for the Lebesgue measure of the set of x for which exceeds 1. Related results for Poisson integrals on a half-space are also described, some applications are given, and interesting comparisons emerge.
Critical associated metrics on contact manifolds. II
Authors: Blair D. E. , Ledger A. J.
Published: April 2009

The study of the integral of the scalar curvature, ∫MRdVg, as a function on the set of all Riemannian metrics of the same total volume on a compact manifold is now classical, and the critical points are the Einstein metrics. On a compact contact manifold we consider this and ∫M (R − R* − 4n2) dv, with R* the *-scalar curvature, as functions on the set of metrics associated to the contact structure. For these integrals the critical point conditions then become certain commutativity conditions on the Ricci operator and the fundamental collineation of the contact metric structure. In particular, Sasakian metrics, when they exist, are maxima for the second function.
Construction methods for Bhaskar Rao and related designs
Authors: Gibbons Peter B. , Mathon Rudolf
Published: April 2009

Mathématical and computational techniques are described for constructing and enumerating generalized Bhaskar Rao designs(GBRD's). In particular, these methods are applied toGBRD(k + 1, k, 1(k − 1); G)'sfor 1 ≥ 1. Properties of the enumerated designs, such as automorphism groups, resolutions and contracted designs are tabulated. Also described are applications to group divisible designs, multi-dimensional Howell cubes, generalized Room squares, equidistant permutation arrays, and doubly resolvable two-fold triple systems.
Subnormal subgroups and formation projectors
Authors: Förster Peter
Published: April 2009

We discuss intersections of subnormal subgroups and formation projectors in finite (not necessarily soluble) groups.
Compact generation in partially ordered sets
Authors: Erné Marcel
Published: April 2009

Several “classical” results on algebraic complete lattices extend to algebraic posets and, more generally, to so called compactly generated posets; but, of course, there may arise difficulties in the absence of certain joins or meets. For example, the property of weak atomicity turns out to be valid in all Dedekind complete compactly generated posets, but not in arbitrary algebraic posets. The compactly generated posets are, up to isomorphism, the inductive centralized systems, where a system of sets is called centralized if it contains all point closures. A similar representation theorem holds for algebraic posets; it is known that every algebraic poset is isomorphic to the system i(Q) of all directed lower sets in some poset Q; we show that only those posets P which satisfy the ascending chain condition are isomorphic to their own “up-completion” i(P). We also touch upon a few structural aspects such as the formation of direct sums, products and substructures. The note concludes with several applications of a generalized version of the Birkhoff Frink decomposition theorem for algebraic lattices.
Quasi-additive solutions of nonlinear differential equations
Authors: Jones A. S.
Published: April 2009

Some nonlinear second order ordinary differential equations have solutions which can be represented as sums of solutions of related equations. This paper classifies the equations for which this is possible and derives the corresponding forms.
Limit theorems for triangular arrays under a relaxed asymptotic negligibility condition
Authors: Jirina Miloslav
Published: April 2009

Let {Xnk} be a triangular array of independent random variables satisfying the so-called tail-negligibility condition, i.e. such that Prob{|Xnk| > a} → 0 as both k, n → ∞. It is also assumed that for each fixed k, Xnk converges in distribution as n → ∞. Theorems on the asymptotic behavior of the row sums of the array, analogous to those of the classical theory under the uniform negligibility condition, are presented.
On the existence of rings R with R isomorphic to RFM(R)
Authors: Abrams Gene D.
Published: April 2009

We construct a class of associative rings with the property that, for each ring R in the class, R≅End .
Abundant Rees matrix semigroups
Authors: Lawson M. V.
Published: April 2009

The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic counterparts of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP-rings are abundant. In this paper we investigate the properties of Rees matrix semigroups over abundant semigroups. Some of our results generalise McAlister's work on regular Rees matrix semigroups.
A natural representation of partitions as terms of a universal algebra
Authors: Lakser Harry
Published: April 2009

We consider a variety of algebras with two binary commutative and associative operations. For each integer n ≥ 0, we represent the partitions on an n-element set as n-ary terms in the variety. We determine necessary and sufficient conditions on the variety ensuring that, for each n, these representing terms be all the essentially n-ary terms and moreover that distinct partitions yield distinct terms.
Three additive congruences to a large prime modulus
Authors: Atkinson O. D. , Brüdern J. , Cook R. J.
Published: April 2009

Let k ≥ 3 and n > 6k be positive integers. The equations, with integer coefficients, have nontrivial p-adic solutions for all p > Ck8, where C is some positive constant. Further, for values k≥ K we can take C = 1 + O(K-½).
Saddle point theorem and nonlinear scalar Neumann boundary value problems
Authors: Nkashama M. N.
Published: April 2009

We are concerned with existence results for nonlinear scalar Neumann boundary value problems u″ + g(x, u) = 0, u′(0) = u′(π) = 0 where g(x, u) satisfies Carathéodory conditions and is (possibly) unbounded. On the one hand we only assume that the function (sgn u)g(x, u) is bounded either from above or from below in some function space, and we impose conditions which relate the asymptotic behavior of the function (for¦u¦large) with the first two eigenvalues of the corresponding linear problem (here G(x, u) = is the potential generated by g). On the other hand we consider cases where the function (sgn u)g(x, u) is unbounded. The potential G(x, u) is not necessarily required to satisfy a convexity condition. Our method of proof is variational, we make use of the Saddle Point Theorem.
Integral representation theorems in partially ordered vector spaces
Authors: Pavlakos Panaiotis K.
Published: April 2009

Defining a Radon-type integration process we extend the Alexandroff, Fichtengolts-KantorovichHildebrandt and Riesz integral representation theorems in partially ordered vector spaces.

We also identify some classes of operators with other classes of operator-valued set functions, the correspondence between operator and operator-valued set function being given by integration.

All these established results can be immediately applied inC* -algebras (especially inW* -algebras andAW* -algebras of type I), in Jordan algebras, in partially ordered involutory (O*-)algebras, in semifields, in quantum probability theory, as well as in the operator Feynman-Kac formula.
Digit patterns and transcendental numbers
Authors: Morton Patrick , Mourant W. J.
Published: April 2009

We use a theorem of Loxton and van der Poorten to prove the transcendence of certain real numbers defined by digit patterns. Among the results we prove are the following. If k is an integer at least 2, P is any nonzero pattern of digits base k, and counts the number of occurrences (mod r) of p in the base k representation of n, then is transcendental except when k = 3, P = 1 and r = 2. When (r, k − 1) = 1 the linear span of the numbers has infinite dimension over Q, where P ranges over all patterns base k without leading zeros.
Goldie M-groups
Authors: Chowdhury K. C.
Published: April 2009

If (G+) is a group and M is a nonempty set of endomorphisms of G operating on the left then G is said to be M-Goldie when (i) G has no infinite independent family of nonzero M-subgroups, and (ii) annihilators in M of subsets of G satisfy the a.c.c. (under set inclusion). Here we prove some results, analogous to those of a Noetherian module in some special cases, even when the set M of operators has no other algebraic structure than the existence of a zero element or in some cases M is at most a finite dimensional commutative near-ring. Precisely speaking, we prove that the collection of associated operating sets of G is finite and there exists a primary decomposition of 0 of such a Goldie M-group, and then if M is a finite dimensional commutative near-ring with unity, for any x belonging to each associated operating set of G, a power of it belongs to the annthilator of G.
Duality for distributive bisemilattices
Authors: Gierz Gerhard , Romanowska Anna
Published: April 2009

We establish a duality between distributive bisemilattices and certain compact left normal bands. The main technique in the proof utilizes the idea of Plonka sums.
Is the Union-closed sets conjecture the best possible?
Authors: Renaud J. C.
Published: April 2009

A slightly strengthened version of the union-closed sets conjecture is proposed. It is shown that this version holds for a minimum set size of one or two and an examination of a boundary function shows that it holds for collections containing up to 19 sets. Some related conjectures are outlined.
Pointwise estimates for an interpolation process of S. N. Bernstein
Authors: Varma A. K. , Yu Xiang Ming
Published: April 2009

The main object of this paper is to provide the solution of an open problem raised by Professor Ron DeVore concerning constructing interpolating process Hn [f, x] satisfying the inequality (1.11). Results on simultaneous approximation are also obtained.
Characterizations of s-closed Hausdorff spaces
Authors: Noiri Takashi
Published: April 2009

A topological space X is said to be S-closed if every cover of X by regular closed sets of X has a finite subcover. In this note some characterizations of S-closed Hausdorff spaces are obtained.
On Grasia's criterion for uniform convergence of Fourier series
Authors: Oehring Charles
Published: April 2009

Garsia's discovery that functions in the periodic Besov space λ(p-1,p, 1), with 1 <p< ∞, have uniformly convergent Fourier series prompted him, and others, to seek a proof based on one of the standard convergence tests. on one of the standard convergence tests. We show that Lebesgue's test is adequate, whereas Garsia's criterion is independent of other classical critiera (for example, that of Dini-Lipschitz). The method of proof also produces a sharp estimate for the rate of uniform convergence for functions in λ(p-1,p, 1). Further, it leads to a very simple proof of the embedding theorem for these spaces, which extends (though less simply) to λ(α,p, q)
Diophantine approximation by continued fractions
Authors: Tong Jingcheng
Published: April 2009

Let ξ be an irrational number with simple continued fraction expansion be its ith convergent. Let Mi = [ai+1,…, a1]+ [0; ai+2, ai+3,…]. In this paper we prove that Mn−1 < r and Mn R imply which generalizes a previous result of the author.
Groups of odd order in which every subnormal subgroup has defect at most two
Authors: Cossey John
Published: April 2009

In 1980, McCaughan and Stonehewer showed that a finite soluble group in which every subnormal subgroup has defect at most two has derived length at most nine and Fitting length at most five, and gave an example of derived length five and Fitting length four. In 1984 Casolo showed that derived length five and Fitting length four are best possible bounds.

In this paper we show that for groups of odd order the bounds can be improved. A group of odd order with every subnormal subgroup of defect at most two has derived and Fitting length at most three, and these bounds are best possible.
Radical Theory for Granded Rings
Authors: Fang Honghin , Stewart Patrick
Published: April 2009

In this paper we propose a general setting in which to study the radical theory of group graded rings. If is a radical class of associative rings we consider two associated radical classes of graded rings which are denoted by G and ref. We show that if is special (respectively, normal), then both G and ref are graded special (respectively, graded normal). Also, we discuss a graded version of the ADS theorem and the termination of the Kurosh lower graded radical construction.
Conjugate polynomials over quadratic algebras
Authors: Stokes Timothy
Published: April 2009

This paper gives variants of results from classical algebraic geometry and commutative algebra for quadratic algebras with conjugation. Quadratic algebras are essentially two-dimensional algebras with identity over commutative rings with identity, on which a natural operation of conjugation may be defined. We define the ring of conjugate polynomials over a quadratic algebra, and define c-varieties. In certain cases a close correspondence between standard varieties and c-varieties is demonstrated, and we establish a correspondence between conjugate and standard polynomials, which leads to variants of the Hilbert Nullstellensatz if the commutativering is an algebraically closed field. These results may be applied to automated Euclidean geometry theorem proving.
The continuity of derivations from group algebras: factorizable and connected groups
Authors: Willis George
Published: April 2009

A group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.
Type radicals and quasi-decompositions of torsion-free abelian groups
Authors: Mutzbauer Oteo
Published: April 2009

A composition sequence for a torsion-free abelian group A is an increasing sequenceof pure subgroups with rank 1 quotients and union A. Properties of A can be described by the sequence of types of these quotients. For example, if A is uniform, that is all the types in some sequence are equal, then A is complete decomposable if it is homogeneous. If A has finite rank and all permutations ofone of its type sequences can be realized, then A is quasi-isomorphic to a direct sum of uniform groups.
Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable
Authors: Hillman J. A. , Linnell P. A.
Published: April 2009

If G is an elementary amenable group of finite Hirsch length h, then the quotient of G by its maximal locally finite normal subgroup has a maximal solvable normal subgroup, of derived length and index bounded in terms of h.
The spectra of weighted mean operators on bν0
Authors: Rhoades B. E.
Published: April 2009

In a series of papers, the author has previously investigated the spectra and fine spectra for weighted mean matrices, considered as bounded operators over various sequence spaces. This paper examines the spectra of weighted mean matrices as operators over bνv0, the space of null sequences of bounded variation.
Oscillations of higher order neutral differential equations
Authors: Bilchev S. J. , Grammatikopoulos M. K. , Stavroulakis I. P.
Published: April 2009

Consider the nth-order neutral differential equation where n ≥ 1, δ = ±1, I, K are initial segments of natural numbers, pi, τi, σk ∈ R and qk ≥ 0 for i ∈ I and k ∈ K. Then a necessary and sufficient condition for the oscillation of all solutions of (E) is that its characteristic equation has no real roots. The method of proof has the advantage that it results in easily verifiable sufficient conditions (in terms of the coefficients and the arguments only) for the oscillation of all solutionso of Equation (E).
One-relator groups that are residually of prime power order
Authors: Gildenhuys D.
Published: April 2009

If C is a class of groups, we denote by RC the class of groups which are residually in C i.e. G ∈ RC if and only if 1 ≠ g ∈ G implies that there exists a normal subgroup N of G such that g ∈ N and G/N ∈ C. A group G is residually a finite p-group if it belongs RFp, where Fp denotes the class of finite p-groups. One also says that the groups in RFp are residually of order equal to a power of the prime p. Given a group G with one defining relator r, one might ask for conditions on the “form” of the relator that would guarantee that G have certain residual properties. In this context, Baumslag (1971) has proved that if all the exponents of the generators appearing in r are positive, then G is residually solvable. In the same paper he also concerned himself with the residual nilpotence of one-relator groups, and found that the situation there was much more complicated. If one goes one step further and asks for conditions that will ensure that for a given prime p the one-relator group be residually a finite p-group, then very little seems to be known. Of course, if one takes r to be one of the generators: then G is freely generated by the remaining generators, and hence is in RFp for all primes p (Mahec (1949), Lazard (1965), 3.1.4). Our main purpose in this paper is to develop methods of generating examples of one-relator groups that are residually of order equal to a given prime p.
Some results concerning a transformation semigroup
Authors: Symons J. S. V.
Published: April 2009

The full transformation semigroup F(X) is extremely important. As far back as 1952, Malcev (1952) showed that its automorphism group consisted of mappings of the form g-1 · g, g ∈ G(X). The present work is devoted to a generalization of this result.
Minimal arcs in metric spaces
Authors: Hildebrand S. K. , Milnes Harold Willis
Published: April 2009

In this paper we discuss the existence of an are of minimal length joining two arbitrary, yet fixed points in a complete metric space, where the metric is restricted only by the properties (A) and (B) given below. It is shown that under these conditions an arc of least length joining any two fixed points exists, and is unique. In addition, its length is shown to be equal to the metrie distance between the points.
Ordering finite groups by involvement
Authors: Atkinson M. D.
Published: April 2009

In the study of locally finite varieties of groups it has often been illuminating to consider when a group A is a factor (i.e. quotient of a subgroup) of a group B. We write A ⋨ B to express this and say that A is involved in B. It follows from elementary isomorphism theorems that the relation ⋨ is a partial order on any set of finite groups. The conjecture that we consider in this paper (and to which we only give the beginning of an answer) is the following:
Filters and overrings
Authors: Brungs H. H.
Published: April 2009

Let R be an integral domain. It is well known (see Lambek (1971), Stenström (1971)), that idempotent filters of right ideals, torsion radicals and trosio theories are in one-to-one correspondence, but that different idempotent filters F of right ideals may lead to the same rings of quotiens Rf. We have always R ⊃ Rf ⊂Qmax(R). Given this situation one can ask a number of questions. For example: Describe all different idempotent filters for a given ring. Determine all different rings of quotients. When do different filters lead to the same ring of quotients? When are all rings between R and Qmax(R) of the form RF. When is every RF of the form RS−1, where S is an Ore system?
Nonlinear symmetric bending of circular elastic plates
Authors: Garfoot B. P.
Published: April 2009

In recent years, there has been considerable interest in the refining of thin plate theories. In this paper, the method of matching asymptotic expansions is used to obtain one such refinement which is believed to be an improvement on several previous results. Previous authors(Habip (1967), Widera (1969)) attempted such refinemnts within the framework of a partially nonlinear theory of elasticity whereas in the present work all terms neglected by these authors have been retained.
Star center points of starlike functions
Authors: Raymon Louis , Tepper David E.
Published: April 2009

Let be regular and unvivalent in the unit disk D and map D onto a region R. A point w0∈ R is called a star-center point of f(z), or of R, if tf(z)+(1−t)w0∈ R for z∈D and 0≦ t≦ 1. In this paper we consider only functions of the form (1) where w = 0 is a star-center point, i.e., those functions that are starlike with respect to the origin.
Large transcendence degree
Authors: Tubbs Robert
Published: April 2009

In this paper we study the transcendence degree of fields generated over Q by the numbers associated with values of one-parameter subgroups of commutative algebraic groups. We show that in many instances these fields have a large transcendence degree when measured in terms of the available data.

Our method deals with points which are “well distributed” (in a sense which is made precise) among certain algebraic subgroups of the algebraic group under consideration. We verify that these results apply in many classical situations.
On the quadratic reciprocity law
Authors: Rousseau G.
Published: April 2009

A version of Gauss's fifth proof of the quadratic reciprocity law is given which uses only the simplest group-theoretic considerations (dispensing even with Gauss's Lemma) and makes manifest that the reciprocity law is a simple consequence of the Chinese Remainder Theorem.
An existence theorem for abstract stable sets
Authors: Chang Chih , Chang Gerard J.
Published: April 2009

We provide an existence theorem for stable sets which is equivalent to Zorn's lemma and study the connections between the unique stable set for majorization and the stable sets for the dominance relation.
Quartic normal extensions of the rational field
Authors: Jian-er Tang
Published: April 2009

There are two types of quartic normal extensions of the rational field, depending on the Galois group of the generating equation. All such extensions are described here in a uniquely parametrized form.
Amenability and weak amenability of tensor algebras and algebras of nuclear operators
Authors: Grønbaek Niels
Published: April 2009

Let E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, Nf (E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim KF ≦ 1, and the trace on E⊗F is injective on KF. Here KF is the kernel of the canonical map E⊗^F →NF(E). On the route we find the corresponding statements for the associated tensor algebra, E⊗^F.
Embedding finite semigroup amalgams
Authors: Okniński Jan , Putcha Mohan S.
Published: April 2009

Let S, T1,… Tk be finite semigroups and Ψ: S → Ti, be embeddings. When C[S] is semisimple, we find necessary and sufficient conditions for the semigroup amalgam (T1,…, Tk; S) to be embeddable in a finite semigroup. As a consequence we show that if S is a finite semigroup with C[S] semisimple, then S is an amalgamation base for the class of finite semigroups if and only if the principal ideals of S are linearly ordered. Our proof uses both the theory of representations by transformations and the theory of matrix representations as developed by Clifford, Munn and Ponizovskii
Zero square near-rings
Authors: Jones Patricia
Published: April 2009

The purpose of this paper is to provide examples and explore properties of a wide variety of zero square (left) near rings. Among the main results are complete classifications of (i) finite Abelian groups which are the additive group of a zero square near-ring and (ii) finite non-Abelian groups which support 3-nilpotent distributive zero square near-rings.
Integration with respect to vector valued Radon polymeasures
Authors: Jefferies Brian , Ricker Werner J.
Published: April 2009

Problems dealing with certain functional calculi for systems of non-commuting operators, and ordered calculi for systems of certain types of pseudo-differential operators, can sometimes be treated via the methods of integration with respect to polymeasures. The polymeasures arising in this fashion (called Radon polymeasures) often have additional structure not available in the general theory. This allows for a more extensive class of “integrable” functions than just the product functions allowed in the abstract theory. The purpose here is to further develop special aspects of integration with respect to Radon polymeasures with a particular emphasis on identifying large classes of “integrable” functions.
Maximum principles for parabolic equations
Authors: Porru Giovanni , Serra Salvatore
Published: April 2009

Let u(x, t) be a smooth function in the domain Q = Ω × (0, L), Ω in n, let Du be the spatial gradient of u(x, t) and let ∇u = (Du, u1). If u(x, t) satisfies the parabolic equation F(u, Du, D2u) = ut, we define w(x, t) by g(w) = │∇u│−1G(∇u) (g is positive and decreasing, G is concave and homogeneous of degree one) and we prove that w(x, t) attains its maximum value on the parabolic boundary of Q. If u(x, t) satisfies the equation Δu + 2h(q2) uiujuij = ut(q2 = │Du│2, 1 + 2q2h(q2) > 0) we prove that qf (u) takes its maximum value on the parabolic boundary of Q provided f satisfies a suitable condition. If u(x, t) satisfies the parabolic equation aij (Du)uij − b(x, t, u, Du) = ut (b is concave with respect to (x, t, u)) we define C(x, y, t, τ) = u(z, θ) − αu(x, t) − βu(y, τ) (0 < α, 0 < β, α + β = 1, z αx +y, θ = αt + βτ) and we prove that if C(x, y, t, r) ≤0 when x, y, z ∈ Ω2 and one of t, τ = 0, and when t, τ ∈ (0, L], and one of x, y, z, ∈ ∂Ω, then it is C(x, y, t, τ) ≤0 everywhere.
Vertex-transitive graphs which are not Cayley graphs, I
Authors: McKay Brendan D. , Praeger Cheryl E.
Published: April 2009

The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph which is not a Cayley graph. We consider the problem of determining the orders of such graphs. In this, the first of a series of papers, we present a sequence of constructions which solve the problem for many orders. In particular, such graphs exist for all orders divisible by a fourth power, and all even orders which are divisible by a square.
On the Fourier transform of a compact semisimple Lie group
Authors: Wildberger N. J.
Published: April 2009

We develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case ofSU(2) is treated in some detail, where some interesting connections with classical spherical trigonometry are obtained.
Invariant subspaces in the bidisc and commutators
Authors: Nakazi Takahiko
Published: April 2009

Let M be an invariant subspace of L2 (T2) on the bidisc. V1 and V2 denote the multiplication operators on M by coordinate functions z and ω, respectively. In this paper we study the relation between M and the commutator of V1 and , For example, M is studied when the commutator is self-adjoint or of finite rank.
Some Finiteness Conditions in Latticesusing Nonstandard Proof Methods
Authors: Insall Matt
Published: April 2009

In [1], the notion of a local join (meet) endomorphism of a lattice was defied. This notion, though interesting in the context of infinitary lattice operations, is redundant in the finitary setting, so its removal from all hypotheses does not affect the results presented therein. The author regrets this oversight and wishes to thank those readers who are patient enough to read over this error.
On the Lebesgue function of weighted Lagrange interpolation. II
Authors: Vértesi P.
Published: April 2009

The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on ℝ and weights on [−1, 1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains.
Lagrangian conditions for a nonsmooth vector-valued minimax
Authors: Craven B. D. , Luu D. V.
Published: April 2009

Lagrangian necessary and sufficient conditions for a nonsmooth vector-valued minimax in terms of Clarke's generalized Jacobians are established under suitable invexity hypotheses.