bluuebunny/crossref_metadata_2025 huggingface dataset:
A New Proof of the Snake Theorem
Authors: Keener Lee L.
Published: December 2010

The Snake Theorem (terminology of Krein), due to Karlin in its original form, has been periodically improved. The theorem shows under appropriate conditions the existence of a function p* from a Tchebycheff space T, with a graph that alternately "touches" the graphs of functions f and g where f < g and f ≤ p* ≤ g on a compact interval [a, b]. The number of "touchings" depends upon the dimension of T. In this paper the conditions assumed are not the weakest known (see Gopinath and Kurshan, J. of Approximation Theory 21 (1977), 151–173), but the apparently new proof offered is elementary and fairly short. f and g are not assumed continuous.
Some Inequalities Related to Planar Convex Sets
Authors: Gardner R. J. , Kwapien S. , Laurie D. P.
Published: December 2010

B. Grünbaum and J. N. Lillington have considered inequalities defined by three lines meeting in a compact convex subset of the plane. We prove a conjecture of Lillington and propose some conjectures of our own.
A Note on Asymptotic Normal Structure and Close-to-Normal Structure
Authors: Tan Kok-Keong
Published: December 2010

A closed convex subset X of a Banach space E is said to have (i) asymptotic normal structure if for each bounded closed convex subset C of X containing more than one point and for each sequence in C satisfying ‖xn − xn + 1‖ → 0 as n → ∞, there is a point x ∈ C such that ; (ii) close-to-normal structure if for each bounded closed convex subset C of X containing more than one point, there is a point x ∈ C such that ‖x − y‖ < diam‖ ‖(C) for all y ∈ C While asymptotic normal structure and close-to-normal structure are both implied by normal structure, they are not related. The example that a reflexive Banach space which has asymptotic normal structure but not close-to normal structure provides us a non-empty weakly compact convex set which does not have close-to-normal structure. This answers an open question posed by Wong in [9] and hence also provides us a Kannan map defined on a weakly compact convex set which does not have a fixed point.
Opérateurs à Itérés Uniformement Bornés
Authors: Nieto José I.
Published: December 2010

Dans un espace de Banach complexe (X, | |) on considère un opérateur linéaire borné A de spectre σ(A) et de rayon spectral r(A) = 1. On établit des conditions, en termes du spectre périphérique de A: σπ(A) = {λ ∊ σ(A): |λ| = 1}, qui garantissent l'existence d'une norme | |0, équivalente à | |, définie par un produit scalaire si | | l'est et telle que ‖A‖0 = Sup{|Ax|0: x|0 = 1} = 1. Si A est à itérés uniformément bornés (‖An‖ ≤ M pour n = 1, 2, …) une telle norme peut ne pas exister.
On the Number of Binomial Coefficients which are Divisible by their Row Number
Authors: Robbins Neville
Published: December 2010

If n is a natural number, let A(n) be the number of integers, k, such that 0 < k < n and n divides . Then ϕ(n) ≤ A(n) ≤ n - 1 - 2ω(n) + ɛ, where ?(n) denotes the number of distinct prime factors of n, and ɛ = 0 unless n is twice a prime, in which case ɛ = 1.
Almost Continuous Functions with Closed Graphs
Authors: Berner Andrew J.
Published: December 2010

A function f:X → Y is almost continuous if for every x ∊ X and for each open set V ⊂ Y containing f(x), Cl(f-l(V)) is a neighborhood of x. Various conditions are given that guarantee that an almost continuous function is continuous. The main theorem states that if f:X → Y is almost continuous with a closed graph (closed in X × Y) and X and Y are complete metric spaces, then f is continuous.
Strong and Quasistrong Disconjugacy
Authors: London David , Schwarz Binyamin
Published: December 2010

A complex linear homogeneous differential equation of the nth order is called strong disconjugate in a domain G if, for every n points z1,…, zn in G and for every set of positive integers, k1…, kl, k1 + … + kl = n, the only solution y(z) of the equation which satisfies

is the trivial one y(z) = 0. The equation y(n)(z) = 0 is strong disconjugate in the whole plane and for every other set of conditions of the form y(mk(zk) = 0, k = 1 , . . . , n, m1 ≤ m2... mn, there exist, in any given domain, points z1 , . . . , zn and nontrivial polynomials of degree smaller than n, which satisfy these conditions. An analogous results holds also for real disconjugate differential equations.
Rings with Automorphisms Leaving no Nontrivial Proper Ideals Invariant
Authors: Shamsuddin Ahmad
Published: December 2010

If an automorphism a on a ring R (with 1) leaves no non-trivial proper ideals of R invariant then we say that R is σ-simple. We construct examples of σ-simple rings and prove that finitely generated σ-simple algebras over fields are regular. A geometric interpretation of these concepts is also discussed.
A Characterization of the Topological Dimension
Authors: Rodé Gerd
Published: December 2010

This paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.
A Self-Dual Equational Basis for Boolean Algebras
Authors: Padmanabhan R.
Published: December 2010

The principle of duality for Boolean algebra states that if an identity ƒ = g is valid in every Boolean algebra and if we transform ƒ = g into a new identity by interchanging (i) the two lattice operations and (ii) the two lattice bound elements 0 and 1, then the resulting identity ƒ = g is also valid in every Boolean algebra. Also, the equational theory of Boolean algebras is finitely based. Believing in the cosmic order of mathematics, it is only natural to ask whether the equational theory of Boolean algebras can be generated by a finite irredundant set of identities which is already closed for the duality mapping. Here we provide one such equational basis.
An Oscillation Criterion for nth Order Non-Linear Differential Equations with Functional Arguments
Authors: Grace S. R. , Lalli B. S.
Published: December 2010

An oscillation criterion for an even order equation: x(n) + q(t)ƒ(x(t)), x[g(t)]) = 0 is provided. This criterion is an extension of a result established by Yeh for the second order equation ẍ + q(t)ƒ(x(t)), x[g(t)]) = 0.
Large Sets not Containing Images of a Given Sequence
Authors: Komjáth Péter
Published: December 2010

In the first part we construct a subsetHof positive measure in the unit interval and a zero-sequence {an} so thatHcontains no homothetic copy of {an}. In Theorem 2 we prove that if ε > 0 and a zero-sequence {an} are given then there exists a setAof measure less than ε so thatcovers the interval. An application of this result is Theorem 3: for any sequence {an} and ε > 0 there is a set H of measure 1 - ε such that for noNandcis {an+ c}n ≥ Ncontained byH.
On Lattice Analogues of Absolutely Summing Constants*
Authors: Szulga J.
Published: December 2010

Let E be a Banach lattice,

where x1, …, xn ∊ E. We study properties of constants

A characterization of AM-spaces is obtained which generalizes the result of Abramocič, Positselskiĭ, Yanovskii. Asymptotic estimates of φp for some classical finite dimensional lattices are given.
On the Rank of a p-Group of Class 2
Authors: Webb U. H. M.
Published: December 2010

Let d(G) denote the minimal number of generators of the finite p-group G, r(G) the maximum over all subgroups H of G of d(H) and ra(G) the maximum over all abelian subgroups H of G of d(H). If G is of class two it is clear that

By considering properties of the stability number of graphs we construct examples which show that any value of r(G) within these bounds can occur.
A Typical Nowhere Differentiable Function
Authors: Cater F. S.
Published: December 2010

We construct an explicit continuous functionFsuch that for each point x, every extended real number is a derived number ofFat x andFhas an infinite left and an infinite right derived number at x.
Embedding Theorems in Group C*-Algebras†
Authors: Lee Tan-Yu
Published: December 2010

Let G be a locally compact group and H an open subgroup of G. The embeddings of group C*-algebras associated with H into the group C*-algebras associated with G are studied. Three conditions for the embeddings given in terms of C*-norms of the group algebras, group representations and positive definite functions are shown to be equivalent. As corollary, we prove that the full C*-algebra of H can be embedded into the full C*-algebra of G in a natural way as well as the case for the reduced group C*-algebras. We also show that the embeddings hold for their duals and double duals.
A Note on Locally Expansive and Locally Accretive Operators
Authors: Torrejon Ricardo
Published: December 2010

Let X be a Banach space, D an open subset of X and Y a complete metric space. Assume that Y is metrically convex. For closed, locally m-expansive and mapping open subsets of D onto open subsets of Y, is is shown that y ∊ T(D) if and only if there exists x0 ∊ D such that d(Tx0, y) ≤ d(Tx, y) for all x ≤ ∂D.
Krasnosel'skii Theorems for Non-Separating Compact Sets
Authors: Stavrakas N.
Published: December 2010

Let S ⊂ Rd, d ≥ 2, be compact and let E denote the set (d — 2) — extreme points of S. M. Breen has shown that if E is countable and S ≠ E, then S is planar. A new proof of this result is given as well as a Krasnosl'skii theorem for (d - 2) extreme points which combines and generalizes previous results.
Derivations in Prime Rings
Authors: Bergen Jeffrey
Published: December 2010

Let R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
A Multivariable form of the Fundamental Theorem of Algebra
Authors: Salzberg Pablo M.
Published: December 2010

Let H(x) be a homogeneous polynomial in n indeterminates over an algebraically closed field K. A necesssary and sufficient condition is given for H(x) to admit a factorization of the form

a, b∈ Kn, and “∘” is the usual inner product. This condition involves the linear derivatives of H(x).
Oriented Matroids and Geometric Sorting
Authors: Cordovil Raul
Published: December 2010

Recently Goodman and Pollack [3] have proved a theorem which can be applied to encode in a compact form the order properties of an arbitrary configuration of points in ℝd. In this note we generalise this theorem to oriented matroids.
Certain Characteristics of the Curvature Tensor of an Affinely Connected Manifold
Authors: Sharma Ramesh
Published: December 2010

We show how flatness and symmetry of an affinely connected manifold relate themselves to the symmetry of the curvature tensor and its covariant derivative in certain slots. Then we reduce Bianchi first identity to the same form as when the connexion is symmetric; even when the connexion is non-symmetric by considering other conditions.
The Shrinking Property
Authors: Rudin Mary Ellen
Published: December 2010

A space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa| a ∈ A} withfor each a ∈ A.lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property.
The Equation Xk + Yk = Zk In Commuting Rational Matrices
Authors: Rush David E.
Published: December 2010

Solutions of Xk + Yk = Zk in invertible pairwise commuting rational 2 × 2 matrices are determined for k = 3, 4, 6, 9, from the analogous results of A. Aigner for algebraic number fields.
Extra Countably Compact Spaces
Authors: Saks Victor
Published: December 2010

A completely regular HausdorfT space is extra countably compact if every infinite subset of βX has an accumulation point in X. It is a theorem of Comfort and Waiveris that if X either an F-space or realcompact (topologically complete), then there is a set {Pξ:ξ<2C} of extra countably compact (countably compact) subspaces of αX such that Pξ ∩ Pξ = X, for ξ<ξ'<2C. Comfort and Waiveris conjecture that in all three cases, the spaces may be chosen pairwise non-homeomorphic. We prove this conjecture, using D- limits and weak P-points. We also give a partial solution to another question asked by Comfort and Waiveris.
Majorations Explicites Pour le Nombre de Diviseurs de N
Authors: Nicolas J. L. , Robin G.
Published: December 2010

Let

It is proved that the function f reaches its maximum for n = 6 983 776 800, and that maxn≥2f(n) = 1.5379. The proof deals with superior highly composite numbers introduced by Ramanujan.
The Height of Two-Dimensional Cohomology Classes of Complex Flag Manifolds
Authors: Broughton S. Allen , Hoffman Michael , Homer William
Published: December 2010

For a parabolic subgroup H of the general linear group G = Gl(n, C), we characterize the Kähler classes of G/H and give a formula for the height of any two-dimensional cohomology class. As an application, we classify the automorphisms of the cohomology ring of G/H when this ring is generated by two-dimensional classes.
Regular and Mercerian Generalized Lototsky Method
Authors: Miller J. F. , Skerry H. B.
Published: December 2010

Necessary conditions and sufficient conditions are obtained for the generalized Lototsky summability matrix method (F, dn) to be regular and Mercerian. In particular, a set of conditions equivalent to being regular and Mercerian is given for real {dn} and for complex {dn} eventually in any closed half-plane containing the origin.
On Evaluation Subgroups of Generalized Homotopy Groups
Authors: Lim K. L.
Published: December 2010

G(A, X) consists of all homotopy classes of cyclic maps from a space A to another space X. If A is an H-cogroup, then G(A, X) is a group. G(A, X) preserves products in the second variable and is a contravariant functor of A from the full subcategory of H-cogroups and maps into the category of abelian groups and homomorphisms. If X is an H-cogroup, then G(X, X) is a ring.
Nearly Open, According to a Subset, Linear Maps Which are Open
Authors: Pomerol J. Ch.
Published: December 2010

For a linear map we introduce two notions of being open according to a subset. With these two definitions, we characterize the linear, nearly open mappings which are open. Thus we generalize a famous theorem of V. Pták.
A Second Order Superlinear Oscillation Criterion
Authors: Philos Ch. G.
Published: December 2010

A new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x″(t)+ a(t)f[x(t)]=0, where a ∈ C([t0∞,)), f∈C(R) with yf(y)>0 for y≠0 and and f is continously differentiable on R-{0} with f'(y)≥0 for all y≠O. In the special case of the differential equation (γ > 1) this criterion leads to an oscillation result due to Wong [9].
The Fixed Subring of Some Groups of Ring Automorphisms
Authors: Dowlen Mary
Published: December 2010

Let Zm denote the ring of integers modulo an integer m > 1 and let G(Zm) be the group under composition of all Zm-automorphisms of Zm[X]. In this paper we determine Zm[X]G(zm) the subring of Zm[X] left fixed by elements of G(Zm).
A Note on Bernoulli-Goss Polynomials
Authors: Ireland K. , Small D.
Published: December 2010

In an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l ≤ n ≤ p2-2 we derive a closed form for the nth Bernoulli polynomial. Using this result a computer search for regular quadratic polynomials of the form x2-a was made. For primes less than or equal to 269 regular quadratics exist for p= 3, 5, 7, 13, 31.
On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
Authors: Steinlein H.
Published: December 2010

Let p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S(m-1)(p-1)-1. Let f:S→S be a map without fixed points and with fp = idS. We show that there exists an h: S→ℝm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U1,…, U4m of S with Uinf(Ui) = Ø for i = 1,…, 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.
On the Associated Lie Ring and the Adjoint Group of a Radical Ring
Authors: Laue Hartmut
Published: December 2010

We investigate connections between the associated Lie ring and the adjoint group of a radical ring, studying their upper central chains. Part of a conjecture of S. A. Jennings is proved, and one of our results improves a theorem of his.
Gelfand-Kirillov Dimension is Exact for Noetherian PI Algebras
Authors: Lenagan T. H.
Published: December 2010

If O → A → C → B → O is a short exact sequence of finitely generated modules over a Noetherian Pi-algebra then we show that GK(C) = max{GK(A), GK(B)}.
Logical Aspects of Combinatorial Duality
Authors: McKee T. A.
Published: December 2010

D. R. Woodall has introduced closely-related notions of Menger and König duals which can be applied to a broad range of combinatorial contexts. The present paper considers these two notions for finite ground sets in terms of syntactic duality principles. Specific graph-theoretic interpretations are cited.
How Good is Hadamard’s Inequality for Determinants?
Authors: Dixon John D.
Published: December 2010

Let A be a real n × n matrix and define the Hadamard ratio h(A) to be the absolute value of det A divided by the product of the Euclidean norms of the columns of A. It is shown that if A is a random variable whose distribution satisfies some simple symmetry properties then the random variable log h(A) has mean and variance . In particular, for each ε > 0, the probability that h(A) lies in the range tends to 1 as n tends to ∞.
The Absolute Galois Group of a Rational Function Field in Characteristic Zero is a Semi-Direct Product
Authors: Van Den Dries Lou , Ribenboim Paulo
Published: December 2010

Let K be a field of characteristic 0 and t an indeterminate. It is shown that the absolute Galois group of K(t) is the semi-direct product of a free profinite group with the absolute Galois group of K.
Asymptotic Error Expansions for Spline Interpolation
Authors: Dikshit H. P. , Sharma A. , Tzimbalario J.
Published: December 2010

During the last decade or so there has been a revival of interest in the analysis of error-bounds f(s)-S(s) for different classes of functions and their interpolatory splines of odd degree on a finite interval with variations on end conditions. Our object is to present a unified treatment of the asymptotic error expansion both for even and for odd degree interpolatory splines.
A Remark on Bases in Hardy Spaces
Authors: Sjögren Peter
Published: December 2010

The Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in Hp(ℝn) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the Hp quasi-norm is equivalent to a certain expression containing the coefficients of the function with respect to this basis. We prove this equivalence for all p > n/(n + m +1).
A Note About Linear Systems on Curves
Authors: Tannenbaum Allen
Published: December 2010

Inverting the Castelnuovo bound in two ways, we show that for given integers p ≥ 0, d > 1, n > 1, we can find a smooth irreducible curve of genus p which contains a linear system of degree d and of maximal dimension relative to the given data p and d, and a smooth irreducible curve of genus p which contains a linear system of dimension n and of minimal degree relative to the data p and n.
Transitive Vector Spaces of Bounded Operators
Authors: Grabiner Sandy
Published: December 2010

The linear subspace S of B(X, Y), the space of bounded operators from the Banach space X to the Banach space Y, is said to be transitive if Sx is dense in Y for all x ≠ 0. We give a number of conditions, involving operators intertwined by S, which imply that S is not transitive, and conditions which, when X = Y, imply that the commutant of S is also not transitive.
Generalized Cesàro Matrices
Authors: Rhaly H. C.
Published: December 2010

For α ∈ [0, 1] the operator is the operator formally defined on the Hardy space H2 by

If α = 1, then the usual identification of H2 with l2 takes A1 onto the discrete Cesàro operator. Here we see that {Aα: α ∈ [0, 1]} is not arcwise connected, that Re Aα ≥ 0, that Aα is a Hilbert-Schmidt operator if α ∈[0, 1), and that Aα is neither normaloid nor spectraloid if α ∈(0, 1).
A Compactification for Convergence Ordered Spaces
Authors: Kent D. C. , Richardson G. D.
Published: December 2010

Compactifications are constructed for convergence ordered spaces and topological ordered spaces with extension properties that resemble those of the Stone-Čech compactification.
Approximation Par des Fonctions Lipschitziennes et Critere de Convergence Etroite D'une Suite de Probabilites
Authors: Rihaoui I.
Published: December 2010

In this paper, we prove that a real valued bounded function, defined on a metric space and uniformly continuous is the uniform limit of a sequence of Lipschitzian bounded functions.

As a consequence, a new criterion for the weak convergence of probabilities is given.
Cycles and Harmonic Forms on Locally Symmetric Spaces
Authors: Millson John J.
Published: December 2010

Two constructions of cohomology classes for congruence subgroups of unit groups of quadratic forms over totally real number fields are given and shown to coincide. One is geometric, using cycles, and the other is analytic, using the oscillator (Weil) representation. Considerable background material on this representation is given.
Residual Canonical Correlations
Authors: Kshirsagar Anant M. , Gupta R. P.
Published: December 2010

Residual canonical correlations are defined and are derived in terms of canonical correlations. Some measures of residual association are also defined, in terms of the residual canonical correlations and some possible applications are suggested.
More on Convergence of Continuous Functions and Topological Convergence of Sets
Authors: Beer Gerald
Published: December 2010

Let C(X, Y) denote the set of continuous functions from a metric space X to a metric space Y. Viewing elements of C(X, Y) as closed subsets of X × Y, we say {fn} converges topologically to f if Li fn = Lsfn = f. If X is connected, then topological convergence in C(X,R) does not imply pointwise convergence, but if X is locally connected and Y is locally compact, then topological convergence in C(X, Y) is equivalent to uniform convergence on compact subsets of X. Pathological aspects of topological convergence for seemingly nice spaces are also presented, along with a positive Baire category result.
Extended Centroids of Skew Polynomial Rings
Authors: Rosen Jerry D. , Rosen Mary Peles
Published: December 2010

Let R be a prime ring with σ ∊ Aut (R). We determine the extended centroid of the skew polynomial ring R[x, σ] when (i) 〈σ〉 is X-outer of finite order, (ii) 〈σ〉 is X-outer and infinite, (iii) σm is X-inner and no smaller power of σ fixes the extended centroid of R.
Integrally Closed Condensed Domains are Bézout
Authors: Anderson David F. , Arnold Jimmy T. , Dobbs David E.
Published: December 2010

It is proved that an integral domainRis a Bézout domain if (and only if)Ris integrally closed andI J= {ij|i∊I, j ∊J} for all idealsIandJofR; that is, if (and only if) R is an integrally closed condensed domain. The article then introduces a weakening of the "condensed" concept which, in the context of thek+Mconstruction, is equivalent to a certain field-theoretic condition. Finally, the field extensions satisfying this condition are classified.
On Quasisimilarity for Toeplitz Operators
Authors: Seddighi K.
Published: December 2010

In this article we give a sufficient condition for quasisimilar analytic Toeplitz operators to be unitarily equivalent. We also use a result of Deddens and Wong to give a sufficient condition for an operator intertwining two analytic Toeplitz operators to intertwine their inner parts too. Analytic Toeplitz operators with univalent symbols satisfying a suitable normalization that are quasisimilar are shown to have equal symbols.
Boundary and Angular Layer Behavior in Singularly Perturbed Semilinear Systems
Authors: Chang K. W. , Liu G. X.
Published: December 2010

Some authors have employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ∊ → 0+, of the solutions of scalar boundary value problems

∊y" = h(t,y), a < t < b,

y(a,∊) = A, y(b,∊) = B.

In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u = u(t) of the reduced equation 0 = h(t,u).

Two types of asymptotic behavior are studied, depending on whether the reduced solution u(t) has or does not have a continuous first derivative in (a,b), leading to the phenomena of boundary and angular layers.
Connection Properties in Nearness Spaces
Authors: Baboolal D. , Bentley H. L. , Ori R. G.
Published: December 2010

We prove that a topological space X has a locally connected regular T1, extension if and only if X is the underlying topological space of a nearness space Y which is concrete, regular and uniformly locally uniformly connected.
The Abelian Case of Solitar's Conjecture on Infinite Nielsen Transformations
Authors: Macedonska-Nosalska Olga
Published: December 2010

The paper proves that the group of infinite bounded Nielsen transformations is generated by elementary simultaneous Nielsen transformations modulo the subgroup of those transformations which are equivalent to the identical transformation while acting in a free abelian group. This can be formulated somewhat differently: the group of bounded automorphisms of a free abelian group of countably infinite rank is generated by the elementary simultaneous automorphisms. This proves D. Solitar's conjecture for the abelian case.
Upper Triangular Invariants
Authors: Campbell H. E. A.
Published: December 2010

We modify the construction of the mod 2 Dyer-Lashof (co)-algebra to obtain a (co)-algebra W which is (also) unstable over the Steenrod algebra A*. W has canonical sub-coalgebras W[k] such that the hom-dual W[k:]* is isomorphic as an A-algebra to the ring of upper triangular invariants in ℤ/2ℤ [x1, . . . , xk].
Range Inclusion for Multilinear Mappings: Applications
Authors: Fong C. K.
Published: December 2010

The result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).
The Value Distribution of Reducible Cubics
Authors: Elliott P. D. T. A.
Published: December 2010

The representation of integers by the products and quotients of the values of x(x2 + a) at integer points is considered.
A Functional Equation for Degree two Local Factors
Authors: Gérardin Paul , Winnie Li Wen-Ch'ing
Published: December 2010

We show that the Fourier transforms of the admissible irreducible representations of the group GL2 over a nonarchimedian local field F are characterized by a functional equation (MF). We also prove that the functions satisfying (MF) and having at most one pole are exactly the Fourier transforms of the irreducible representations of the quaternion group H over F. The Jacquet-Langlands correspondence between irreducible representations of H and discrete series of GL2 then follows immediately from our criteria.
On a Congruence Related to Character Sums
Authors: Chalk J. H. H.
Published: December 2010

If χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the type

f(x)g'(x) - f'(x)g(x) ≡ 0(pα),

where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.
A Cardinal Structure Theorem for an Ultrapower
Authors: Apter Arthur W.
Published: December 2010

In this note, we construct a model with a normal measure U over a measurable cardinal κ so that the cardinal structures of V and Vκ/U are the same ≤2κ. We then show that it is possible to construct a model where this is not true.
A Reflexive LUR Banach Space that Lacks Normal Structure
Authors: Smith Mark A. , Turett Barry
Published: December 2010

An example of the type described in the title is given.
Cauchy Integral of Calderón on the Graphs of Functions with BMO Derivatives
Authors: Yabuta Kôzô
Published: December 2010

We first note that each graph (x,A(x)) of a function A(x) with BMO derivative is a chord-arc curve. Using this, Muckenhoupt's Ap theory, and the theory of Calderón-Zygmund operators, we shall derive weighted norm inequalities for the Cauchy integral on such graphs from a recent theorem of G. David on the L2-boundedness of Cauchy integral on almost-lipschitzian curves.
Non-Averaging Sets, Dimension and Porosity
Authors: Foran James
Published: December 2010

A subset of the line is called non-averaging if, whenever two points belong to the set, their average does not. This paper provides an example of a closed set which is small in the sense that it is non-averaging and has porosity 1 at each of its points and yet large in the sense that its Hausdorff dimension is 1.
An Endpoint Estimate for Certain k-Plane Transforms
Authors: Drury S. W.
Published: December 2010

In this paper we extend a result of Oberlin and Stein on
Radon Transforms to /c-plane transforms for Specifically let

where the supremum is taken over all affine k-planes ∏ parallel to the vector k-plane π. We show that F is in Ln of the Grassmann manifold Gn,k whenever f is in the Lorentz space L(n/k, 1) of ℝn. The proof relies very heavily on the ideas of M. Christ.
On the Cardinality of Subrings of a Commutative Ring
Authors: Gilmer Robert , Heinzer William
Published: December 2010

If R is an uncountable commutative ring, it is shown that there exists a proper subring of R having the same cardinality as R. It is also shown that if |R| = ω is an uncountable regular cardinal, and if R1 is a subring of R containing an identity of R and such that |R1| < ω, then there exists a proper R1-subalgebra S of R such that |S| = |R|.
Mathematical Problems in Transonic Flow
Authors: Morawetz Cathleen Synge
Published: December 2010

We present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial airlines. The problem is simplified and the important role of modifying the equations with physics terms is examined.
Algebraic Elements and Sets of Uniqueness in the Group of Integers of a p-Series Field
Authors: Aubertin Bruce
Published: December 2010

Let G be the group of integers of a p-series field. A class {E(θ)} of perfect null subsets of G is introduced and classified into M-sets and U-sets according to the arithmetical nature of the field element θ. This is analogous to the well-known classification, involving Pisot numbers, of certain Cantor sets on the circle.
An Inverse Mapping Theorem in Frechet Spaces
Authors: Gautrin Henri-François , Imam Khaldoun , Klemola Tapio , Terrier Jean-Marc
Published: December 2010

Within the framework of a-differentiability, introduced by H. R. Fischer in locally convex spaces, sufficient conditions for an inverse mapping theorem between Fréchet spaces are established.
Fixed Points of Holomorphic Mappings in the Cartesian Product of n Unit Hilbert Balls
Authors: Kuczumow T. , Stachura A.
Published: December 2010

Every continuous mapping T = (T1,. . ., Tn): holomorphic in Bn has a fixed point.
H(ϕ) Spaces
Authors: W. Deeb  , M. Marzuq
Published: December 2010

Let ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfy

and the space H+ (ψ) is the space of a f ∊ H(ψ) for which

where almost everywhere.

In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).
Counterexamples to Smoothing Convex Functions
Authors: Smith Patrick Adrian Neale
Published: December 2010

Greene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).
An Elementary Proof of a Theorem on Unilateral Derivatives
Authors: Cater F. S.
Published: December 2010

We give an elementary proof of the theorem of Saks that states that most functions in C[0, 1] have infinite unilateral derivatives at a continuum many points.
On Indecomposable Projective Modules
Authors: O'Neill John D.
Published: December 2010

If P is an indecomposable projective R-module generated by a countable set X, then, for some countable subring S of R, P contains an indecomposable projective S-module generated by X. The subring S may be chosen to inherit many standard ring-theoretic properties from R.
Injective Approximations
Authors: Varadarajan K.
Published: December 2010

Let C be a cochain complex satisfying the condition that inj.dim. Hq(C) < ∞. Then we prove that C admits an injective approximation.
Reciprocal Algebraic Integers Whose Mahler Measures are Non-Reciprocal
Authors: Boyd David W.
Published: December 2010

The Mahler measure M (α) of an algebraic integer α is the product of the moduli of the conjugates of α which lie outside the unit circle. A number α is reciprocal if α- 1 is a conjugate of α. We give two constructions of reciprocal a for which M (α) is non-reciprocal producing examples of any degree n of the form 2h with h odd and h ≥ 3, or else of the form with s ≥ 2. We give explicit examples of degrees 10, 14 and 20.
Centralizing Mappings of Semiprime Rings
Authors: Bell H. E. , Martindale W. S.
Published: December 2010

Let R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.
On The Lavrentiev Phenomenon
Authors: Loewen Philip D.
Published: December 2010

A new look at Manià's classical example of the Lavrentiev Phenomenon leads to several pertinent observations.
The Eta Invariant and Non-Singular Bilinear Products on Rn
Authors: Gilkey Peter B.
Published: December 2010

Milnor showed that non-singular bilinear products on Rn exist only if n = 1, 2, 4, 8 using topological methods. In this note, we give a proof of this result by purely analytical methods.
Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk
Authors: Schulte E. , Wills J. M.
Published: December 2010

The paper describes polyhedral realizations for Felix Klein's map {3, 7}8 of genus 3, for Gordan's map {4, 5}6 of genus 4, and for two maps of genus 5, the Klein-Fricke map of type {3, 8} and Sherk's map of type {4, 6}. The polyhedra have self-intersections but high symmetry and thus are close analogues to the Kepler-Poinsot-polyhedra.
On Modulus of Noncompact Convexity and Its Properties
Authors: Banaś Józef
Published: December 2010

In this paper we prove some properties of the so-called modulus of noncompact convexity. This notion was recently introduced by K. Goebel and T. Sȩkowski [6] and it appears to be an interesting and useful generalization of the classical Clarkson modulus of convexity. We extend the results obtained in [6] showing that the modulus of noncompact convexity is continuous and has some extra properties in reflexive Banach spaces. The properties applicable in the fixed point theory are also stated.
Lower Bounds For Induced Forests in Cubic Graphs
Authors: Bondy J. A. , Hopkins Glenn , Staton William
Published: December 2010

If G is a connected cubic graph with ρ vertices, ρ > 4, then G has a vertex-induced forest containing at least (5ρ - 2)/8 vertices. In case G is triangle-free, the lower bound is improved to (2ρ — l)/3. Examples are given to show that no such lower bound is possible for vertex-induced trees.
On the Number of Maximal Elements in a Partially Ordered Set
Authors: Ginsburg John
Published: December 2010

Let P be a partially ordered set. For an element x ∊ P, a subset C of P is called a cutset for x in P if every element of C is noncomparable to x and every maximal chain in P meets {x} ∪ C. The following result is established: if every element of P has a cutset having n or fewer elements, then P has at most 2n maximal elements. It follows that, if some element of P covers k elements of P then there is an element x ∊ P such that every cutset for x in P has at least log2k elements.
First Order Theory of Complete Stonean Algebras (Boolean-Valued Real and Complex Numbers)
Authors: Jech Thomas
Published: December 2010

We axiomatize the theory of real and complex numbers in Boolean-valued models of set theory, and prove that every Horn sentence true in the complex numbers is true in any complete Stonean algebra, and provable from its axioms.
Bound Sets in Partial Orders and the Fixed Point Property
Authors: Höft Hartmut
Published: December 2010

In this paper we introduce several properties closely related to the fixed point property of a partially ordered set P: the comparability property, the fixed point property for cones, and the fixed point extension property. We apply these properties to the sets of common bounds of the minimal (maximal) elements of the partially ordered set P in order to derive fixed point theorems for P.
On the Kobayashi Pseudometric Reduction of Homogeneous Spaces
Authors: Gilligan Bruce
Published: December 2010

Given any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.
Nonoccurence of Stability Switching in Systems with Discrete Delays
Authors: Freedman H. I. , Gopalsamy K.
Published: December 2010

A two dimensional system of differential equations with a finite number of discrete delays is considered. Conditions are derived for there to be no stability switching for arbitrary such delays.
Spaces of Continuous Vector Functions as Duals
Authors: Cambern Michael , Peter Greim
Published: December 2010

A well known result due to Dixmier and Grothendieck for spaces of continuous scalar-valued functions C(X), X compact Hausdorff, is that C(X) is a Banach dual if, and only if, Xis hyperstonean. Moreover, for hyperstonean X, the predual of C(X) is strongly unique. Here we obtain a formulation of this result for spaces of continuous vector-valued functions. It is shown that if E is a Hilbert space and C(X, (E, σ *) ) denotes the space of continuous functions on X to E when E is provided with its weak * ( = weak) topology, then C(X, (E, σ *) ) is a Banach dual if, and only if, X is hyperstonean. Moreover, for hyperstonean X, the predual of C(X, (E, σ *) ) is strongly unique.
On Shift Operators
Authors: Holub J. R.
Published: December 2010

A definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.
The Enumeration of Maps on the Torus and the Projective Plane
Authors: Bender E. A. , Canfield E. R. , Robinson R. W.
Published: December 2010

The enumeration of rooted maps (embedded graphs), by number of edges, on the torus and projective plane, is studied. Explicit expressions for the generating functions are obtained. From these are derived asymptotic expressions and recurrence relations. Numerical tables for the numbers with up to 20 edges are presented.
Symmetric Green's Function for a Class of CIV Boundary Value Problems
Authors: Kreith Kurt
Published: December 2010

Generalized boundary value problems are considered for hyperbolic equations of the form utt — uss + λp(s, t)u = 0. By constructing symmetric Green's functions appropriate to such problems the existence of eigenvalues is established.
A Remark on Complex Convexity*
Authors: Leranoz Camino
Published: December 2010

We present a quasi-normed space which is locally H∞-convex but is not locally PL-convex in the sense of Davis, Garling and Tomczak-Jaegermann.
Kummer's and Iwasawa's Version of Leopoldt's Conjecture
Authors: Sands Jonathan W.
Published: December 2010

We present a refinement of Iwasawa's approach to Leopoldt's conjecture on the non-vanishing of the p-adic regulator of an algebraic number field K. As an application, the conjecture for K implies the conjecture for a solvable extension L of degree g over K if g is relatively prime to p — 1 and p does not divide g, the discriminant of K, and the quotient of class numbers where is a primitive pth root of unity. This can be viewed as generalizing a theorem of Kummer on cyclotomic units.
On the Constant in the Pólya-Vinogradov Inequality
Authors: Hildebrand Adolf
Published: December 2010

The Pólya-Vinogradov inequality states that for any non-principal character x modulo q and any N ≧ 1,

where c is an absolute constant. We show that (*) holds with c = 2/(3π2) + o(1) in the case x is primitive and x (— 1) =1 with c = 1/(3π) + o(l) in the case x is primitive and x(— 1) = — 1- This improves by a factor 2/3 the previously best-known values for these constants.
The Proximal Subgradient Formula in Banach Space
Authors: Loewen Philip D.
Published: December 2010

The proximal subgradient formula is a refinement due to Rockafellar of Clarke's fundamental proximal normal formula. It expresses Clarke's generalized gradient of a lower semicontinuous function in terms of analytically simpler proximal subgradients. We use the infinite-dimensional proximal normal formula recently given by Borwein and Strojwas to derive a new version of the proximal subgradient formula in a reflexive Banach space X with Frechet differentiable and locally uniformly convex norm. Our result improves on the one given by Borwein and Strojwas by referring only to the given norm on X.
Eventual Disconjugacy and Right Disfocality of Linear Difference Equations
Authors: Eloe P. W.
Published: December 2010

Let a ≧ 0, Ia = ﹛a, a + 1, …﹜ and consider the nth order linear difference m ∈ Ia, α0(m) = 1 on Ia. Summability conditions are placed on the coefficients αj(m), 1 ≦ j ≦ n, such that the equation Pu(m) = 0 is eventually disconjugate. Conditions for eventual right disfocality are also given.
Groups Formed by Redefining Multiplication
Authors: Chandler K. A.
Published: December 2010

Let G be a group with elements 1,…, n such that the group operation agrees with ordinary multiplication whenever the ordinary product of two elements lies in G. We show that if n is odd, then G is abelian.
Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems
Authors: Rahman Mizan
Published: December 2010

A seven-parameter extension of Askey and Wilson's four parameter q-beta integral is written in a symmetric form as the sum of multiples of two very-well-poised balanced basic hypergeometric 10Φ9 series. Two special cases are considered in which the evaluation of the integral gives single terms by the q-Dixon formula in one case and by a special case of the Verma-Jain formula in the other. An orthogonal polynomial system is obtained in the first case and a system of biorthogonal rational function is obtained in the second. It is also shown that the biorthogonal system represents a generalization of Rogers’ q-ultraspherical polynomials.
Approximation of a Function and its Derivatives by Entire Functions of Several Variables
Authors: Mostapha Frih El , Gauthier Paul M.
Published: December 2010

The paper gives a good approximation of a Ck function on Rn and its derivatives by the restriction of an entire function on Cn and its derivatives respectively.
Uniqueness of Preduals for Spaces of Continuous Vector Functions
Authors: Cambern Michael , Greim Peter
Published: December 2010

A. Grothendieck has shown that if the space C(X) is a Banach dual then X is hyperstonean; moreover, the predual of C(X) is strongly unique. In this article we give a vector analogue of Grothendieck's result. We show that if E* is a reflexive Banach space and C(X, (E*, σ*)) denotes the space of continuous functions on X to E* when E* is provided with its weak* (= weak) topology then the full content of Grothendieck's theorem for C(X) can be established for C(X,(E*,σ*)). This improves a result previously obtained for the case in which E* is Hilbert space.
A New Space With no Locally Uniformly Rotund Renorming
Authors: Haydon Richard , Zizler Vaclav
Published: December 2010

We construct a Banach space X which has no equivalent (wLUR) norm but which has no subspace isomorphic to l∞.
Algebraic Deformations and Bicohomology
Authors: Fox Thomas F.
Published: December 2010

Recently we have introduced an enriched cohomology theory for categories that are tripleable (algebraic) over a category of modules. The cohomology admits a circle product, related to the obstruction problem for algebraic deformations, making the total complex a graded ring. We here offer similar constructions in two other situations - coalgebraic and bialgebraic categories. Examples include categories of bialgebras, sheaves of modules, and sheaves of algebras over a sheaf of rings.
Embedding Uncountably Many Mutually Exclusive Continua into Euclidean Space
Authors: Baker B. J. , Laidacker Michael
Published: December 2010

Uncountable collections of continua of dimension m embeddable in En are investigated, where the difference between m and n is not restricted to one. Collections of isometric copies of continua equivalent to Menger universal continua and collections of continua analogous to G. S. Young's Tn-sets are the main considerations.
Zp-Towers in Demuškin Groups
Authors: Simons Lloyd D.
Published: December 2010

In this note, we develop the notion of a Zp-tower in a Demuskin group, and apply the results of Koch and Wingberg on the uniqueness of so-called Demuškin formations to give a classification of such towers in the case p ≠ 2.
Simple Divisible Modules Over Integral Domains
Authors: Facchini Alberto
Published: December 2010

An R-module is a simple divisible module if it is a nonzero divisible module that has no proper non-zero divisible submodules. We study simple divisible modules and their endomorphism rings, give some examples and determine all simple divisible modules over some classes of rings.
Embedding of Accessible Regular Categories
Authors: Barr Michael
Published: December 2010

The purpose of this note is to prove that a regular accessible category has a full regular embedding into a set-valued functor category.