bluuebunny/crossref_metadata_2025 huggingface dataset:
On Almost Continuous Mappings and Baire Spaces
Authors: Lin Shwu-Yeng T. , Lin You-Feng
Published: December 2010

It is proved, in particular, that a topological space X is a Baire space if and only if every real valued function f: X →R is almost continuous on a dense subset of X. In fact, in the above characterization of a Baire space, the range space R of real numbers may be generalized to any second countable, Hausdorfï space that contains infinitely many points.
An Interpolatory Rational Approximation
Authors: Meir A.
Published: December 2010

The classical Hermite-Fejér interpolation process is a positive linear mapping from C[-1, 1] into the space of polynomials of degree ≤2n-1. If Tn(x) denotes the Tchebisheff polynomial of degree n and xk = xnk(k = 1,2, …, n) its roots, then for any given f∈ C[-1, 1] the Hermite-Fejér image Hnf of f is defined by

1.1
On Square Pseudo-Lucas Numbers
Authors: Eswarathasan A.
Published: December 2010

J. H. E. Cohn (1) has shown that

are the only square Fibonacci numbers in the set of Fibonacci numbers defined by

If n is a positive integer, we shall call the numbers defined by

(1)

pseudo-Lucas numbers.
A Characterization of Soft Hypergraphs
Authors: Slater Peter J.
Published: December 2010

A hypergraph is a subtree of a tree (SOFT) hypergraph if there exists a tree T such that X=V(T) and for each there is a subtree Ti of T such that Ei = V(Ti). It is shown that H is a SOFT hypergraph if and only if has the Helly property and , the intersection graph of is chordal. Results of Berge and Gavril have previously shown these to be necessary conditions.
Note on Attaching Dold Fibrations
Authors: Heath Philip R. , Kamps Klaus Heiner
Published: December 2010

In this note, we patch up the proof of a Theorem due to Handel on the characterization of homotopy epimorphisms ([6], 2.2) and generalize a Theorem due to Ibisch on attaching disk-bundles to Dold fibrations ([7], Satz 1).

We work throughout in the category TopB of spaces over B for some fixed topological space B.
A Note on the Length of Trivectors
Authors: MacDougall J. A.
Published: December 2010

This note concerns elements (called trivectors) of the third Grassmann product of a complex vector space U. Usually there are many ways to write a given trivector as the sum of simple or decomposable trivectors, and it is an interesting problem to find those representations which contain the smallest possible number of decomposables. This number we shall call the length of the trivector. Let N(n) denote the length of the longest trivector in ∧3U where U has dimension n. In this note we give upper bounds for N(n) when n ≤ 8.
On Approximately Finite-Dimensional Von Neuman Algebras, II
Authors: Elliott George A.
Published: December 2010

An intrinsic characterization is given of those von Neumann algebras which are injective objects in the category of C*-algebras with completely positive maps. For countably generated von Neumann algebras several such characterizations have been given, so it is in fact enough to observe that an injective von Neumann algebra is generated by an upward directed collection of injective countably generated sub von Neumann algebras. The present work also shows that three of the intrinsic characterizations known in the countably generated case hold in general.
Linear Functional-Differential Equations in a Banach Algebra*
Authors: Fitzpatrick W. J. , Grimm L. J.
Published: December 2010

The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].

In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting. The method, based on functional analysis, had been used extensively by L. Cesari [1] in similar forms for boundary value problems, and by J. K. Hale, S. Bancroft, and D. Sweet [2]. We also obtain as corollaries several results for ordinary differential equations in Banach algebras which were proved in a different way by Hille.
Idempotents in The Groupoid of all SP Classes of Lattices
Authors: Day Alan
Published: December 2010

In [5], Mal'cev generalized the group theoretical results of H. Neumann (see [6] Chapter 2) to produce the notion of the product, of two subclasses of a given variety of algebras, Following the group theorectic example, members of were called extensions of algebras in by algebras in
An Inequality for Complete Symmetric Functions
Authors: Ilori Samuel A.
Published: December 2010

Consider the identity

where aj, …, am are positive real numbers. Then for r = 1, 2, 3, … Tr =Tr(a1, …, am) is called the rth complete symmetric function in a1, …, am (T0=l).
Modules Over Bounded Hereditary Noetherian Prime Rings
Authors: Khan M. Zubair
Published: December 2010

Singh introduced two conditions on a module MR in [7]. The author introduced the concept of h-neat submodule of such module in [3] and generalized some of the well known results of neat subgroups. A theorem of Erdelyi was also shown to be true for such modules in [4]. The main purpose of this paper is to generalize a well known result of K. M. Benabdallah and J. M. Irwin and M. Rafiq [2, Theorem 10].
On the Zeros of Power Series with Logarithmic Coefficients
Authors: Stadtmüller U.
Published: December 2010

Equivalence problems in Riesz-summability lead to the problem of finding the zeros of special power series in the unit circle, i.e.
A Note on Isomorphisms of Multiplier Algebras
Authors: Wong Pak-Ken
Published: December 2010

LetA1,A2be commutative semi-simple Banach algebras andM(A1),M(A2) their multiplier algebras. Birtel in [2] has proved that every isomorphism ofA1ontoA2induces an isomorphism ofM(A1) ontoM(A2). In this note, we extend this result to the noncommutative case. We also show that ifAis a dualA*-algebra which is a dense two-sided ideal of aB*-algebraB, thenM(A) is isomorphic toM(B). Thus the converse of the previous result cannot hold. All algebras under consideration are over the complex field.
Identité Pour
Authors: Mercier Armel
Published: December 2010

Dans cet article, nous établirons un théorème sur la représentation de certaines séries de Dirichlet (ceci généralise un résultat de [3]). Avec ce nouveau résultat nous donnerons seulement quelques applications qui évidemment pourraient être augmentées de beaucoup. Par exemple, nous donnerons une expression asymptotique pour

1
On Surfaces of Order Three
Authors: Bisztriczky Tibor
Published: December 2010

A surface of order threeFin the real projective three-spaceP3is met by every line, not inF, in at most three points.

In the present paper, we determine the existence and examine the distribution of elliptic, parabolic and hyperbolic points; that is, the differentiable points ofFwhich do not lie on any line contained inF.
On Localization at an Ideal
Authors: Beachy John A.
Published: December 2010

Conditions are given under which the ring of quotients defined by an ideal is semisimple Artinian modulo its Jacobson radical.
Infrasequential Topological Algebras
Authors: Husain T.
Published: December 2010

The notion of sequential topological algebra was introduced by this author and Ng [3], Among a number of results concerning these algebras, we showed that each multiplicative linear functional on a sequentially complete, sequential, locally convex algebra is bounded ([3], Theorem 1). From this it follows that every multiplicative linear functional on a sequential F-algebra (complete metrizable) is continuous ([3], Corollary 2).
Branching Measures of Information on Strings
Authors: Ebanks Bruce R.
Published: December 2010

In classical information theory, the amount of information provided by an experiment is measured by a function of the probability distribution of the outcomes of the experiment. In this paper, information measures are functions of sequences of elements of a monoid (S, ∘) with identity e. It is assumed that the measures {μn: Sn → ℝ} of information are branching.
On Basis Constants and Duality in Banach Spaces
Authors: Dor Leonard E.
Published: December 2010

Every Banach space with a non-shrinking (unconditional) basis (Xi) can be renormed so that the biorthogonal sequence has a much smaller (unconditional) basis constant than (xi). On the other hand, if the unconditional constant of is C < 2 then the unconditional constant of (xi) is at most C/(2—C). This estimate is sharp.
On Quotient Loops of Normal Subloops
Authors: Santhakumari C.
Published: December 2010

The following result is due to Wielandt [1, Lemma 2.9]: Let A, B, K be N-submodules of some N-module, where N is a zero symmetric near-ring. Then the N-module, Γ: = (A + K) ∩ (B + K) | (A ∩ B) + K is commutative. Using this result Wielandt obtained density theorem for 2-primitive near-rings with identity. Betsch [1] used Wielandt's result to obtain the density theorem for O-primitive near-rings. The purpose of this paper is to extend this result for loops.
Upper Semi-Continuity of Subdifferential Mappings
Authors: Gregory David A.
Published: December 2010

Characterizations of the upper semi-continuity of the subdifferential mapping of a continuous convex function are given.
Une Double Généralisation du Théorème de Fejér-Lebesgue
Authors: Lessard Sabin
Published: December 2010

Sommaire

Nous nous emploierons dans cet article à démontrer la convergence presque partout pour les moyennes de projections orthogonales croissantes sur L2, qui sont ou bien u.a.c. ou bien positives, ce qui nous donnera une double généralisation du théorème classique de Fejér-Lebesgue pour les séries de Fourier. Enfin nous terminerons en énonçant un résultat général qui englobe tous ceux connus jusqu'à maintenant avec la condition u.a.c. (cf. R. Duncan, Can. Math. Bull. 20 (1977) 277-284).
Splicing n-Convex Functions using Splines
Authors: Cross G. E.
Published: December 2010

It is proved that a regular piecewise n-convex function differs from an n-convex function only by a polynomial spline of degree n - 1. The argument is given in terms of Peano and de la Vallée Poussin derivatives.
The Individual Ergodic Theorem for Contractions with Fixed Points
Authors: Olsen James H.
Published: December 2010

Let (X, I, μ) be a σ-finite measure space and let T take Lp to Lp, p fixed, 1<p<∞,‖t‖p≤1. We shall say that the individual ergodic theorem holds for T if for any uniform sequence K1, k2,… (for the definition, see [2]) and for any f∊LP(X), the limit

exists and is finite almost everywhere.
Adjonction ou Suppression D'objectifs en Programmation à Objectifs Linéaires Multiples
Authors: Bragard L. , Vangeldère J.
Published: December 2010

La portée et les buts de cet article sont signalés au début des différents paragraphes et dans les remarques qui suivent le théorème 3, le lemme 5 et le théorème 21. Limitons-nous à mentionner ici que le sujet traité est à la fois en relation avec la théorie des systèmes d'inéquations linéaires (théorie des polyèdres coniques), avec le concept de point Λ-extrême, avec les diverses notions d'efficacité par rapport à un système d'objectifs linéaires et avec la programmation à objectifs linéaires multiples.
Multifunctions and Inverse Cluster Sets
Authors: Joseph James E.
Published: December 2010

In this paper the notion of inverse cluster set, which was recently introduced and studied for functions by T. R. Hamlett and P. E. Long (Proc. Amer. Math. Soc, 53 (1975), 470-476), is extended to and investigated for multifunctions. We generalize the notion of inverse cluster set, extend to multifunctions and generalize some known results for inverse cluster sets of functions and offer some new results. In the latter sections, compactness generalizations are characterized in terms of inverse cluster sets and some results on connected and conectivity functions are extended to multifunctions.
On the Continued Fractions of Conjugate Quadratic Irrationalities
Authors: Herzog Fritz
Published: December 2010

Let

1

be the simple continued fraction (SCF) of an irrational number x. The partial quotients ai which we shall sometimes refer to as the "terms" of the SCF are integers and, for i ≥ 2, they are positive. If x is a quadratic irrationality then, by Lagrange's Theorem, the right side of (1) becomes periodic from some point on.
A Construction of Approximately Finite-Dimensional Non-ITPFI Factors
Authors: Connes Alain , Woods E. J.
Published: December 2010

A von Neumann algebra is said to be approximately finite-dimensional if it is of the form

where Mn⊆Mn+1 for each n and each Mn is a finite-dimensional matrix algebra. A factor is said to be ITPFI if it is of the form
A Characterisation of Locally Compact Amenable Subsemigroups
Authors: Wong James C. S.
Published: December 2010

In this paper, we prove that if S is a locally compact semigroup and T a locally compact Borel measurable subsemigroup of S, then T has a topological left invariant mean if and only if there is a topological left T-invariant mean M on S such that M(xT) = 1, where xT is the characteristic functional of T in S.
Coincidence of Nodes for Generalized Convex Functions
Authors: Mathsen R. M.
Published: December 2010

In a recent paper [1] I. B. Lazarevic announced an extension of results of L. Tornheim [2; Theorems 2 & 3] concerning points of contact between two distinct members of an n-parameter family and between a member of an n-parameter family and a corresponding convex function. In the proofs of these extensions [1; Theorems 3.1 & 3.2] use is made of Tornheim′s Convergence Theorem [2; Theorem 5]; however this theorem is not correctly applied in [1] since it requires distinct limiting nodes, and that hypothesis necessarily fails in the approach used in [1], In this note proofs of results more general than those in [1] are given independent of convergence theorems.
Least Positive Residues and the Quadratic Character of Two
Authors: Rosen Kenneth H.
Published: December 2010

Let be the least positive residue modulo 2tk of (2j- l)h. Define ut to be the number of with l≤j≤2t-2k such that . At the Special Session in Combinatorial Number Theory at the 1977 Summer AMS Meeting Szekeres [2] asked for a simple proof that if (h, 2k)=1, then

Here a simple proof will be given for the following equivalent result.
Spherical Harmonics on the Heisenberg Group
Authors: Greiner Peter C.
Published: December 2010

H1. Equip ℝ3 with the group law

(1.1)

where (z, t) stands for (x, y, t). This is a nilpotent Lie group, usually referred to as the first Heisenberg group, H1. In general Hk denotes ℝ2k+1 equipped with a similar group law, namely
A Note on the Universe of a Category of Fractions
Authors: Nanda Sribatsa
Published: December 2010

Let be a small -category where is a fixed Grothendieck universe, i.e., the objects of form a set which is a subset of and, for every pair of objects X, Y of the set is an element of . If S is a set of morphisms of , then, in general, the category of fractions [S- 1] would belong to a higher universe ([4], p. 256).
Orthogonal Completions of Reduced Rings with Respect to Abian Order
Authors: Rai R. K.
Published: December 2010

In this paper, it is proved that a reduced ring R has an orthogonal completion if and only if for every idempotent e e R, eR has an orthogonal completion. Every orthogonal subset X of R has a supremum in Q max(R), the maximal two sided ring of quotients of R, and the orthogonal completion of a reduced ring R, if it exists, is isomorphic to a unique subring of Q max(R). Hence the orthogonal completion of a reduced ring R, if it exists, is unique upto isomorphism. A reduced ring R has an orthogonal completion if and only if the collection of those elements of Q max(R) which are supremums of orthogonal subsets of R form a subring of Q max(R). Furthermore, every projectable ring R has an orthogonal completion , which is a Baer ring. It is also proved that for projectable rings R, where is the idempotent filter of those dense right ideals of R which contain a maximal orthogonal subset of idempotents of R.
Some Spaces are not the Domain of a Closed Linear Operator in a Banach Space
Authors: Dierolf Peter , Dierolf Susanne
Published: December 2010

Let be a linear partial differential operator with C∞- coefficients. The study of P(∂) as an operator in L2(ℝn) usually starts with the investigation of the minimal operator P0 which is the closure of P(∂) acting on . In the case of constant coefficients it is known that the domain D(P0) of P0 at least contains the space (cf. Schechter [4, p. 58, Lemma 1.2]).
Sur Une Equation Differentielle Fonctionnelle Analytique*
Authors: Bélair Jacques
Published: December 2010

Nous considérons dans cette note une classe d′équations différentielles fonctionnelles linéaires dont les coefficients sont analytiques; des résultats sur l′ordre des solutions et leur comportement asymptotique seront obtenus.

Il s'agit d'une généralisation à des équations du deuxiéme ordre d'une propriété d'équations d'ordre un [2]: la démonstration du théoréme principal demeure valable dans ce dernier cas.
On Finitely Generated Simple Complemented Lattices
Authors: Poguntke Werner
Published: December 2010

Let L be a lattice, and let P and Q be partially ordered sets. We say that L is generated by P if there is an isotone mapping from P into L with its image generating L. P contains Q if there is a subset Q’ of P which, with the partial ordering inherited from P, gives an isomorphic copy of Q. For an integer n > 0, the lattice of partitions of an n-element set will be denoted by II(n); it is well-known that II(rc) is simple and complemented (cf. P. Crawley-R. P. Dilworth [1; p. 96]).
On L2-Betti Numbers for Abelian Groups
Authors: Donnelly Harold
Published: December 2010

Let M be a differentiable manifold which admits the free action of a group Γ with compact quotient M’ = M/Γ. Suppose that the Γ action lifts to a Hermitian vector bundle E→M. If Γ leaves invariant a measure μ on M, then denote by L2(E) the completion of with respect to the inner product .
On the Homological Dimension of Valuated Vector Spaces
Authors: White Errin Erb
Published: December 2010

Following L. Fuchs [1], we define a valuated vector space to be a vector spaceVwith a valuation fromVto a totally ordered setΓin which every nonempty subset has a supremum. It is assumed thatΓhas a maximum element. A standard model for Γ is a closed initial segment of ordinals with the symbol ∞ adjoined.
On Edge-Colorability of Cartesian Products of Graphs*
Authors: Mahamoodian E. S.
Published: December 2010

In an article P. E. Himelwright and J. E. Williamson [3] proved a theorem on 1-factorability of Cartesian product of two graphs. With a very short proof we prove a more general theorem which immediately implies their theorem as a corollary. We will follow the notations and definitions of [1], [2] and [3].
On the Relation between the Logarithmic and Borel-Type Summability Methods
Authors: Borwein D. , Watson B.
Published: December 2010

Suppose throughout that {sn} is a sequence of real numbers, λ > - 1, a > 0, and β is real. Let N be any non-negative integer such that αN + β > l.

We are concerned primarily with the logarithmic summability method L and the Borel-type method (B, α, β). Some known results involve the Abel-type summability method Aγ.
On Certain Sequence Spaces
Authors: Kizmaz H.
Published: December 2010

In this paper define the spaces l∞(Δ), c(Δ), and c0(Δ), where for instance l∞(Δ) = {x=(xk):supk |xk -xk + l|< ∞}, and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l∞(Δ) or c(Δ) into l∞ or c, and investigate related questions.
A Probabilistic Approach to the Convolution Transform
Authors: Rivest Louis-Paul
Published: December 2010

The inversion and the characterization of the convolution transform is derived via the concept of unimodality introduced by Khintchine (1938). This method yields simple and intuitively appealing proofs.
Sur une Famille de Groupes Abéliens Super-Décomposables
Authors: Benabdallah K. , Birtz A.
Published: December 2010

Un groupe abélien est dit super-décomposable si il ne possède pas de facteur direct indécomposable non nul. Les groupes super-décomposables doivent être nécessairement sans-torsion et un premier exemple en fut donné par A. L. S. Corner [1]. Un exemple différent apparait dans P. A. Krylov [4]. De plus P. Jambor et J. Bečvar, ont développé, dans [3] une généralisation de la notion de sous-groupe de base dans laquelle apparait de façon naturelle des groupes super-décomposables. Dans cette note, nous donnons d'abord un critère pour qu'un groupe soit super-décomposable et nous construisons ensuite une famille de groupes qui satisfont à ce critère, donnant ainsi de nouveaux exemples de groupe super-décomposable.
Independent Sets of Axioms In Lκα
Authors: Caicedo Xavier
Published: December 2010

A set of sentences T is called independent if for every . It is countably independent if every countable subset is independent. In flnitary first order logic, Lωω, the two notions coincide because of compactness. This is not the case for infinitary logic.
Essential Extensions of T1-Spaces
Authors: Hoffmann Rudolf-E.
Published: December 2010

In the categoryof T1-spaces and continuous maps, every spaceXhas a unique maximal essential extension.Xhas an injective hull iff card X≤1.
Construction of Satisfaction Classes for Nonstandard Models
Authors: Kotlarski H. , Krajewski S. , H. Lachlan A.
Published: December 2010

Given a resplendent model for Peano arithmetic there exists a full satisfaction class over , i.e. an assignment of truth-values, to all closed formulas in the sense of with parameters from , which satisfies the usual semantic rules. The construction is based on the consistency of an appropriate system of -logic which is proved by an analysis of standard approximations of nonstandard formulas.
Full Satisfaction Classes and Recursive Saturation
Authors: Lachlan A. H.
Published: December 2010

It is shown that a nonstandard model of Peano arithmetic which has a full satisfaction class is necessarily recursively saturated.
Coefficient Inequalities for Lp-Valued Analytic Functions
Authors: Harris Lawrence A.
Published: December 2010

A Hausdorff-Young theorem is given for Lp-valued analytic functions on the open unit disc and estimates on such functions and their derivatives are deduced.
Some Further Extensions of Hardy's Inequality
Authors: Chan Ling-Yau
Published: December 2010

Let p > l, r≠1, and let f(x) be a non-negative function defined in [0, ∞). The following inequality is due to G. H. Hardy [5, Ch. IX]:

1.1

where according as r>1 or r < l.
On Integrals and Summable Trigonometric Series
Authors: Lee Cheng-Ming
Published: December 2010

In considering a problem on certain summable (C, k) trigonometric series, R. D. James [13] used a symmetric pk+2- integral defined earlier to recapture the coefficients of the series from the sum function. James' formulas for the coefficients are more complicated than the usual Euler-Fourier form since the pk + 2 - integral is of order k + 2. It is shown that a generalized integral of order one for each non-negative integer k can be suitably defined to reduce James' formulas to the usual form.
The Integers as Differences of a Sequence
Authors: Pollington Andrew , Vanden Eynden Charles
Published: December 2010

It is shown that there exists a sequence of integers a1 < a2 <... such that each positive integer is a difference of elements of the sequence in exactly one way, and such that ak does not exceed a constant times k3. In fact we construct such a sequence with each ak in [C(k -1)3, Ck3), where C is an absolute constant.
Polyedres Equilibres
Authors: Bantegnie Robert , Coxeter H. S. M.
Published: December 2010

Dans une note au C. R. Math. Rep. Ac. Se. Canada [1] qui peut servir de préliminaire, j’ai annoncé qu'on ne pouvait trouver de polyèdres convexes équilibrés non strictement équilibrés qui, à une isomorphic près, ne soient pas dans la liste de Johnson [4]. Nous donnons ici la preuve.

Rappelons qu'on dit qu'un polyèdre convexe fermé borné est strictement équilibré resp. équilibré quand le cycle resp. le pseudocycle de chaque sommet est le même. Les polyèdres strictement équilibrés sont α) les polyèdres uniformes β) le polyè'dre de Miller appelé pseudo-rhombicuboctaèdre dans [9], petit rhombicuboctaèdre tordu dans [6], gyrobicupola carré allongé dans [4] et attribué à tort à Ashkinuze dans [7].
Oscillation Criteria for a Class of Perturbed Schrödinger Equations
Authors: Kusano Takaŝi , Naito Manabu
Published: December 2010

We are concerned with the oscillatory behavior of the second order elliptic equation

1

where Δ is the Laplace operator inn-dimensional Euclidean spaceRn,Eis an exterior domain inRn, andc:E × R → Randf:E → Rare continuous functions.

A functionv : E − Ris called oscillatory inEifv(x) has arbitrarily large zeros, that is, the set {x∈E:v(x) = 0} is unbounded. For brevity, we say that equation (1) is oscillatory inEif every solutionu∈C2(E) of (1) is oscillatory inE.
Integral Comparison Theorems for Scalar Riccati Equations and Applications
Authors: Erbe Lynn
Published: December 2010

Comparison theorems are developed for the pair of first order Riccati equations (1) and (2) . The comparisons are of an integral type and involve an auxiliary function μ. Applications are given to disconjugacy theory for self-adjoint equations of the second and fourth order.
Functions in All Hp Spaces, p < ∞
Authors: Campbell Douglas M.
Published: December 2010

Let Ĥ denote the class of functions analytic in |z| < 1 which are in every Hp class, 0 < p < ∞. The class Ĥ strictly contains H∞ and consists of those functions that are ‘almost in H∞’ in the sense of integration. L. Hansen and W. Hayman have given simple geometric conditions for a function to belong to Ĥ. The purpose of this note is to show that Hansen and Hayman's conditions are far from necessary. Using techniques from normal functions, gap series, characterizations of BMOA, subordination, Bloch functions, and VMOA, six completely different examples of functions in Ĥ are given which ‘fill the plane’.
A Group Theoretic Approach to the Equations of Plasma Physics
Authors: Marsden Jerrold E.
Published: December 2010

This paper concerns the interaction between group theory and classical mechanics in general and with the application of this theory to plasma physics in particular.

Mechanics has had a profound role in the historical development of mathematics. Leading original thinkers in pure mathematics such as Newton, Euler, Lagrange, Jacobi, Laplace, Cauchy, Gauss, Riemann, Poincaré, Hilbert, Birkhofï, Smale and Arnold were also great original thinkers in various facets of mechanics. The interaction between mechanics and pure mathematics remains one of the most active and flourishing areas of current research. It is this flavor which I hope to convey in this lecture.
Solvable Groups of Unipotent Elements in a Ring
Authors: Klein Abraham A.
Published: December 2010

Let R be a ring with 1 whose nil subrings are nilpotent modulo the sum of nilpotent ideals. It is proved that if G is a locally solvable group of unipotent elements in R, then the subring generated by {g −1 g ∈ G} is nil. This result implies a result of Sizer showing that a solvable group of unipotent matrices over a skew field can be simultaneously triangularized.
Notes on the Birkhoff Algorithm for Doubly Stochastic Matrices
Authors: Brualdi Richard A.
Published: December 2010

The purpose of this note is to tie together some results concerning doubly stochastic matrices and their representations as convex combinations of permutation matrices.
On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.
Authors: Leonard Philip A. , Williams Kenneth S.
Published: December 2010

Let h(m) denote the class number of the quadratic field Q(√m). In this paper necessary and sufficient conditions for h (m) to be divisible by 16 are determined when m = −p, where p is a prime congruent to 1 modulo 8, and when m = −2p, where p is a prime congruent to ±1 modulo 8.
Discrete Sets and Discrete Maps
Authors: Warren Richard H.
Published: December 2010

A subset of a topological space is called discrete iff every point in the space has a neighborhood which meets the set in at most one point. Discrete sets are useful for decomposing the images of certain maps and for generalizing closed maps. All discrete sets are closed iff the space is T1. As a result of characterizing discrete and countably discrete maps, theorems due to Vaĭnšteĭn and Engelking are extended to these maps.
The Extended Center of Coproducts
Authors: Martindale Wallace S.
Published: December 2010

The sole purpose of this paper is to prove that if R1 and R2 are algebras with 1 over a common field F, with each (Ri:F) > 1 and at least one (Ri:F) > 2, then the extended center of the coproduct R1∐R2 is equal to F.
A Counterexample in the Perturbation Theory of C*-Algebras
Authors: Johnson B. E.
Published: December 2010

The strongest positive results in the stability theory of C*-algebras assert that if are sufficiently close C*-subalgebras of (H) of certain kinds, then there is a unitary operator U on H near I, such that . We give examples of C*-algebras , both isomorphic to the algebra of continuous functions from [0, 1] to the algebra of compact operators on Hilbert space, which can be as close as we like, yet for which there is no isomorphism α: → with . Thus the results mentioned do not extend to these C*-algebras.
On Fractional Integrals Equivalent to a Constant
Authors: Roberts K. L.
Published: December 2010

The paper is concerned with the Liouville-Riemann and Weyl fractional integrals. Necessary and sufficient conditions are obtained for a function to have a fractional integral which is equivalent to a constant.
K0 D’Un Anneau Dont Les Localises Centraux Sont Simples Artiniens
Authors: Burgess W. D. , Goursaud J.-M.
Published: December 2010

The purpose of the note is to calculate the group K0(A) where A is a ring all of whose Pierce stalks are simple artinian. This generalizes known results for A self injective of type In. For A regular, with injective hull, Â, of type In, a characterization is given for when A → Â it induces an isomorphism K0(A) → K0(Â).
Free Summands of Stably Free Modules
Authors: Swift Robert W.
Published: December 2010

In this note we show that the generic orthogonal stably free modules of type (2, 7) and (3, 8) have one free summand. This completes the work of other authors on free summands of orthogonal stably free modules.
Abel Transformations Into I1
Authors: Fridy J. A.
Published: December 2010

Let t be a sequence in (0,1) that converges to 0, and define the Abel matrix At by ank = tn(1-tn)k. The matrix At determines a sequence-to-sequence variant of the classical Abel summability method. The purpose of this paper is to study these transformations as l-l summability methods: e.g., At maps l1 into l1 if and only if t is in l1. The Abel matrices are shown to be stronger l-l methods than the Euler-Knopp means and the Nӧrlund means. Indeed, if t is in l1 and Σ xk has bounded partial sums, then Atx is in l1. Also, the Abel matrix is shown to be translative in an l-l sense, and an l-l Tauberian theorem is proved for At.
Retracts and Injectives
Authors: Feigelstock Shalom , Klein Aaron
Published: December 2010

Embedding theorems are employed to show that many important categories do not possess non-trivial retracts or injectives. E.g., the categories of monoids, groups, rings, rings with unity, polynomial identity rings, nilpotent groups, solvable groups, and several varieties of groups.
Bounded Solutions of a Functional Inequality
Authors: Albert Michael , Baker John A.
Published: December 2010

It is known that if f is a real valued function on a rational vector space V, δ > 0,

1

and if f is unbounded then f(x + y) = f(x)f(y) for all x, y ∊ V. In response to a problem of E. Lukacs, in this paper we study the bounded solutions of (1). For example, it is shown that if f is a bounded solution of (1) then - δ ≤ f(x) ≤ (1 + (1 + 4δ)1/2)/2 for all x ∊ V and these bounds are optimal.
The Local Class Group of a Krull Domain
Authors: Bouvier A.
Published: December 2010

The local class group of a Krull domain A is the quotient group G(A) = CI(A)/Pic(A). A Krull domain A is locally factorial if and only if G(A) = 0. In this paper, we characterize the Krull domains for which G(A) is a torsion group. We evaluate the local class group of several examples and finally, we explain why every abelian group is the local class group of a Krull domain.
On Uniform Semigroup-Valued Additive Set Functions
Authors: Fox Geoffrey , Morales Pedro
Published: December 2010

The main results of this paper are the following: (1) An extension theorem for a uniform semigroup-valued measure on a ring to the generated σ-ring. This result unifies the classieal Hahn-Carathéodory theorem, the extension theorem of Sion and a more recent result of Weber.

(2) A theorem stating that every monocompact additive uniform semigroup-valued set function on a semiring is σ-additive. This result generalizes several earlier theorems of Alexandroff, Dinculeanu-Kluvanek, Glicksberg, Huneycutt, Mallory, Marczewski, Millington and Topsøe.
A Topological Characterization of Gleason Parts of Real Function Algebras
Authors: Kulkarni S. H. , Limaye B. V.
Published: December 2010

It is well-known that a topological space is a Gleason part of some complex function algebra if and only if it is completely regular and σ-compact. In the present paper, a Gleason part of a real function algebra is characterized as a completely regular σ-compact topological space which admits an involutoric homeomorphism.
A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
Authors: Polak T. , Sims Brailey
Published: December 2010

A Banach space is fully 2-rotund if (xn) converges whenever ‖xn + xm‖ converges as m, n → ∞ and locally uniformly rotund if xn → x whenever ‖xn‖ and ‖(xn + x)/2‖ → ‖x‖.

We show that I2 with the equivalent norm

is fully 2-rotund but not locally uniformly rotund, thus answering in the negative a question first raised by Fan and Glicksberg in 1958.
On the Quadratic Residues (Modp) in the Interval (0,p/4)
Authors: Williams Kenneth S.
Published: December 2010

A short proof is given of a result of Burde giving the parity of the number of quadratic residues (modp) in the interval (0,p/4), wherep≡ 1(mod 4) is prime.
On k-Cycled Refinements of Certain Graphs
Authors: Hartman Jehuda , Katchalski Meir
Published: December 2010

A graph is k -cycled if all its cycles are integral multiples of an integer k ≥ 2. We determine the structure of refinements of Kn and Kn, m which are k-cycled.
A Regular Summability Method which Sums the Geometric Series to its Proper Value in the Whole Complex Plane
Authors: Tomm Ludwig
Published: December 2010

In this paper an explicit regular sequence-to-sequence summability method is presented which sums the geometric series to the value 1/(1-z) in all of ℂ\{1} and to infinity at the point 1. The method also provides compact convergence in ℂ \ [ 1, ∞) and therefore improves well-known results by Le Roy, Lindelöf and Mittag-Leffler.
Hülder Conditions and the Topology of Simply Connected Domains*
Authors: Aharonov Dov
Published: December 2010

Let ƒ be regular univalent and normalized in the unit disc U (i.e. ƒ ∊ S) and continuous on U ∈ T, where T denotes the boundary of U.

Recently Essén proved [5] a conjecture of Piranian [7] stating that if the derivative of ƒ ∊ S is bounded in U and ƒ(z1) = ƒ(z2) = … = ƒ(zn) for Zj ∊ T, 1 ≤ j ≤ n, then n ≤ 2. In fact, Essén proved a more general result, using a deep result on harmonic functions. The aim of the following article is to replace Essén's proof by a completely different proof which is based only on Goluzin's inequalities and is much more elementary.
Sur Les Sous-Groupes Normaux De SL2 Sur Un Anneau Local
Authors: Lacroix N. H. J. , Levesque C.
Published: December 2010

Resume

Soit GLn (υ) le groupe des matrices inversibles n × n sur υ et soit SLn (υ) le groupe des matrices n × n de déterminant 1 sur υ. Lorsque υ est un anneau local avec idéal maximal p, W. Klingenberg (Amer. J. Math. 1961) a classifié les sous-groupes normaux de GLn(υ) et de SLn(υ) au moyen de certains groupes de congruences déterminés par les idéaux de o, sauf lorsque n = 2 et 2 ∊ p ou υ/p = 𝔽3. Ces cas furent étudiés par N. H. J. Lacroix (Can. J. Math. 1969) qui trouva (lorsque υ/p≠𝔽2) la même classification pour les sous-groupes normaux de GL2(υ) ; sa méthode donne simultanément la même classification également pour les sous-groupes normaux de SL2(υ) si l'anneau o satisfait à une forte condition appelée Propriété T.

Au cours de cette note, nous précisons que les sous-groupes normaux de SL2(υ) obéissent à la classification de Klingenberg si et seulement si υ a la Propriété T. Par la suite nous montrons qu'en l'absence de cette condition, l'on n'a pas de vraie classification basée sur les transvections. Divers résultats sur les sous-groupes normaux illustrent ce qu'on peut attendre d'une entreprise visant à décrire les sous-groupes normaux de SL2(υ) en l'absence de la Propriété T.
q -Analogs of Some Biorthogonal Functions
Authors: Al-Salam W. A. , Verma A.
Published: December 2010

In this note we obtain a q-analog of a pair of biorthogonal sets of rational functions which have been obtained recently by M. Rahman in connection with the addition theorem for the Hahn polynomials.
Semigroup Compactifications of Direct and Semidirect Products
Authors: Milnes Paul
Published: December 2010

A classical result of I. Glicksberg and K. de Leeuw asserts that the almost periodic compactification of a direct product S × T of abelian semigroups with identity is (canonically isomorphic to) the direct product of the almost periodic compactiflcations of S and T. Some efforts have been made to generalize this result and recently H. D. Junghenn and B. T. Lerner have proved a theorem giving necessary and sufficient conditions for an F-compactification of a semidirect product S⊗σT to be a semidirect product of compactiflcations of S and T. A different such theorem is presented here along with a number of corollaries and examples which illustrate its scope and limitations. Some behaviour that can occur for semidirect products, but not for direct products, is exposed
FPF Rings and Some Conjectures of C. Faith
Authors: Page S. S.
Published: December 2010

A left FPF ring is a ring R such that every finitely generated faithful left R -module generates the category of left R-modules. It is shown that such rings split into R = A⊕B, where A is a two sided ideal, and A contains the left singular ideal of R as an essential submodule. If R is FPF on both sides B is two sided too, and R is the product of A and B. An example shows this is the best possible and that right FPF does not imply left FPF.
On the Principle of Dependent Choices and Some Forms of Zorn's Lemma
Authors: Wolk Elliot S.
Published: December 2010

The main result of this paper is to prove that a generalization of the Principle of Dependent Choices, introduced by A. Levy [2; see also 1, Chapter 8], is equivalent to a form of Zorn's Lemma.
Inclusion Theorems for the Absolute Summability of Divergent Integrals
Authors: Diamond Harvey , Kuttner Brian , Raphael Louise A.
Published: December 2010

Some inclusion theorems are obtained relating the absolute summability of divergent integrals of the form under three summability methods: Abelian A(x), Abelian A(lnx) and Stieltjes S(x).
Curvature of Level Curves of Harmonic Functions
Authors: Ortel Marvin , Schneider Walter
Published: December 2010

If H is an arbitrary harmonic function defined on an open set Ω⊂ℂ, then the curvature of the level curves of H can be strictly maximal or strictly minimal at a point of Ω. However, if Ω is a doubly connected domain bounded by analytic convex Jordan curves, and if H is harmonic measure of Ω with respect to the outer boundary of Ω, then the minimal curvature of the level curves of H is attained on the boundary of Ω.
Nearnesses and T0-Extensions of Topological Spaces
Authors: Dean Alice M.
Published: December 2010

In [3], Reed establishes a bijection between the (equivalence classes of) principal T1-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the T0 case by obtaining a one-to-one correspondence between the principal T0-extensions of a space X and the collections of sets (called “t-grill sets”) which generate a certain class of nearnesses which we call “t-bunch generated” nearnesses. This correspondence specializes to principal T0-compactifications. Finally, we show that there is a bijection between these t-grill sets and the filter systems of Thron [5], and that the corresponding extensions are equivalent.
Metrizability Conditions for Completely Distributive Lattices
Authors: Gierz G. , Lawson J. D. , Stralka A. R.
Published: December 2010

A lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.
Lie Ideals in Associative Algebras
Authors: Murphy G. J.
Published: December 2010

It is shown that in a certain extensive class of algebras one can associate with each Lie ideal a corresponding associative ideal which facilitates the study of Lie ideals, especially for simple algebras. We apply this construction to obtain new, simpler proofs of some known results of Herstein [10] and others on the Lie structure of associative rings.
Characterizations of *-Multiplication Domains
Authors: Houston Evan G. , Malik Saroj B. , Mott Joe L.
Published: December 2010

Let * be a finite-type star-operation on an integral domain D. If D is integrally closed, then D is a *-multiplication domain (the *-finite *-ideals form a group) if and only if each upper to 0 in D[x] contains an element f with c(f)* = D. A finite-type star operation on D[x] naturally induces a finite-type star operation on D, and, if each *-prime ideal P of D[x] satisfies P ∩ D = 0 or P = (P ∩ D)D[x], then D[x] is a *-multiplication domain if and only if D is.
On Fundamental Approximative Absolute Neighborhood Retracts
Authors: Sanjurjo J. M. R.
Published: December 2010

In this paper we define and study a class of compacta under the name of Fundamental Approximative Absolute Neighborhood Retracts. This class includes Borsuk’s Fundamental Absolute Neighborhood Retracts and Approximative Absolute Neighborhood Retracts in the sense of M. H. Clapp as proper subclasses. We also introduce the notion of q-strong movability and prove that Fundamental Approximative Absolute Neighborhood Retracts coincide with q-strongly movable compacta.
Von Neumann Operators in
Authors: Seddighi Karim
Published: December 2010

For a connected open subset Ω of the plane and n a positive integer, let be the space introduced by Cowen and Douglas in their paper, “Complex geometry and operator theory”. Our main concern is the case n = 1, in which case we show the existence of a functional calculus for von Neumann operators in for which a spectral mapping theorem holds. In particular we prove that if the spectrum of , is a spectral set for T, and if , then σ(f(T)) = f(Ω)- for every bounded analytic function f on the interior of L, where L is compact, σ(T) ⊂ L, the interior of L is simply connected and L is minimal with respect to these properties. This functional calculus turns out to be nice in the sense that the general study of von Neumann operators in is reduced to the special situation where Ω is an open connected subset of the unit disc with .
A Note on Partition-Inducing Automorphism Groups
Authors: Pettet Martin R.
Published: December 2010

We consider a finite group G with a group A acting on it in such a way as to induce a partition of G# (a situation which arises in the study of centralizer near-rings). With the additional hypothesis that (|Aω|, |G|) = 1, it is shown that either A is semiregular on G# or G is an irreducible module for A.
Semicritical Rings and the Quotient Problem
Authors: Kosler Karl A.
Published: December 2010

The purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.
Factorized Groups with max, min and min-p
Authors: Amberg Bernhard
Published: December 2010

Let be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.
A Measure for Polynomials in Several Variables
Authors: Myerson Gerald
Published: December 2010

We define a notion of measure for polynomials in several variables, basing our construction on the geometry of the zero-set of the polynomial. For polynomials in one variable, this measure reduces to the usual one. We begin the development of the theory of this measure along lines parallel to the theory of Mahler’s measure, indicating the differences and similarities between the two.

Let P be a polynomial in one variable with complex coefficients, P(z) = a0Π(z - αj). The measure of P, denoted M(P), is defined by

1

As is well-known, an application of Jensen’s formula yields

2
On an Oval with the Four Point Pascalian Property
Authors: Fernandes Olga
Published: December 2010

In this paper it is proved that a finite translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, or a finite dual translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, can be coordinatized by a commutative semifield.
Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
Authors: Gonçalves Jairo Z.
Published: December 2010

Let KG be the group ring of the group G over the field K and U(KG) its unit group. When G is finite we derive conditions which imply that every noncentral subnormal subgroup of U(KG) contains a free group of rank two. We also show that residual nilpotence of U(KG) coincides with nilpotence, this being no longer true if G is infinite.

We can answer partially the following question: when is G sub-normal in U(KG)?
Commutative Systems of Covariance and a Generalization of Mackey's Imprimitivity Theorem
Authors: Ali S. Twareque
Published: December 2010

Two results are obtained in this paper. The first is a generalization of the imprimitivity theorem of Mackey, when the associated projection-valued measure is replaced by a commutative positive operator valued measure. The second is a necessary and sufficient condition for such a system of covariance to possess an overcomplete, covariant family of coherent states.