bluuebunny/crossref_metadata_2025 huggingface dataset:
Simplicite des Groupes Unitaires Definis par un Facteur Simple
Authors: Giordano Thierry , Harpe Pierre De La
Published: December 2010

Let B be a σ-finite von Neumann factor of type II1 or III and let σ be an involutory *-antiautomorphism of B. We consider U(B) the unitary group of B and its subgroup G = {g ∈U(B) | σ(g) = g*}, which are unitary classical groups. In this paper, we prove that G has a unique non trivial normal subgroup, which is its centre {±1}.
Centralizing Mappings of Prime Rings
Authors: Mayne Joseph H.
Published: December 2010

Let R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R. If L is a nontrivial automorphism or derivation of R such thatuL(u)—L(u)u is in the center of R for every u in U, then the ring R is commutative.
On Uchimura’s Connection between Partitions and the Number of Divisors
Authors: Bressoud D. M. , Subbarao M. V.
Published: December 2010

A combinatorial proof is given for Uchimura’s identity

As a corollary to this proof we derive a formula for the sum of the nth powers of the divisors of m in terms of partitions of m.
An Elementary Probabilistic Computation of the Poisson Kernel for the n = 2 and 3 Euclidean Ball
Authors: Vauthier Jacques
Published: December 2010

Direct and elementary derivation of the classical Poisson kernel for the ball in n = 2 or n = 3 dimensions starting with the usual expression involving the brownian motion bω, the stopping time T on the boundary, and Ex the conditional expectation on paths starting at x.
Isometric Images of C* Algebras
Authors: O’Donovan Donal P. , Davidson Kenneth R.
Published: December 2010

It is shown that if the isometric image of a linear subspace of Hilbert space operators is irreducible in a strong sense, then the isometry is either a multiplicative or anti-multiplicative map, possibly followed by multiplication by a unitary.
Diviseurs Dans Les Anneaux De Series Formelles En Une Infinite D’Indeterminees
Authors: Ballet B.
Published: December 2010

Resume

Etant donné un anneau commutatif unitaire A et un ensemble d’indices infini I; on peut obtenir, par passage à la limite projective, essentiellement trois anneaux A1, A2, A3 de séries formelles en des indéterminées indexées par I et à coefficients dans A. On étudie alors les implications A factoriel ⇒ A1, A2, A3 factoriels et A de Krull ⇒ A1, A2, A3 de Krull. On donne à cet effet des conditions pour qu’une limite projective d’anneaux factoriels soit factorielle.
Free Subgroups of Units in Group Rings
Authors: Gonçalves Jairo Zacarias
Published: December 2010

In this paper we give necessary and sufficient conditions under which the group of units of a group ring of a finite group G over a field K does not contain a free subgroup of rank 2.

Some extensions of this results to infinite nilpotent and FC groups are also considered.
Topological Completeness of Order Intervals in Riesz Spaces
Authors: Dodds P. G.
Published: December 2010

It is shown that if L is a Dedekind complete Riesz space equipped with a locally solid topology T defined by strongly (A, 0) Riesz pseudonorms, then order intervals of L are T-complete. This is an extension of a well known theorem of Nakano. The second part of the paper gives a necessary and sufficient condition for topological completeness of order intervals in a Dedekind σ-complete Riesz space which has a weak order unit and which is equipped with a locally solid σ-Fatou topology.
Divisorial Prime Ideals in Prüfer Domains
Authors: Fontana Marco , Huckaba James A. , Papick Ira J.
Published: December 2010

Given a Prüfer domain R and a prime ideal P in R, we study some conditions which force P to be a divisorial ideal of R. This paper extends some recent work of Huckaba and Papick.
Mean Growth of Harmonic Functions of Beurling Type
Authors: Collier Manning G. , Kelingos John A.
Published: December 2010

A harmonic function on the unit disc is of Beurling type ω if its Fourier (or Taylor) coefficients grow no faster than exp ω(|n|) as |n|→∞, where ω is a given increasing, concave function with ω(x)/x ↓ 0 as x → ∞. These harmonic functions are characterized by the growth rate of their L1-norms on circles of radius r as r → 1. The classical Schwartz result follows as a corollary by taking ω(x) = log(1+x). The Gevrey case is also included in the general result if one uses ω(x) = xα, 0 < α < 1.
A Decomposition Theorem for Certain Bipolynomial Hopf Algebras
Authors: Baker Andrew
Published: December 2010

In this note we generalise a result of D. Husemoller to certain bipolynomial Hopf algebras and are able to give Hopf algebra decompositions for these. As an easy consequence of our approach we give a simplified derivation of recent results of P. Hoffman on polynomial generators for these algebras; we also give explicit systems of “Borel generators” for a related family of quotient Hopf algebras considered by Hoffman.
On Homotopy Domination
Authors: Kwasik Sławomir
Published: December 2010

A short proof of the following result of Bernstein and Ganea is given:

“Let X be a topological space which is homotopy dominated by a closed connected n-dimensional manifold M. If Hn(X; Z2) ≠ 0 then X has the homotopy type of M”.

It is also shown that the manifold in this theorem can be replaced by a Poincaré complex.
On the Commutativity of a Ring with Identity
Authors: Tong Jingcheng
Published: December 2010

Let R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R:

(I)

xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0;

(II)

xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0;

(III)

xmyn = ynxm and m! n! x≠0 except x = 0;

(IV)

(xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite positive integer. Then R is commutative.
Short Proof of an Internal Characterization of Complete Regularity
Authors: Brandenburg Harald , Mysior Adam
Published: December 2010

A short proof is given of an internal characterization of completely regular spaces due to J. Kerstan.
Inequalities for Entire Functions of Exponential Type
Authors: Frappier Clément
Published: December 2010

Bernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis then

Genchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, then

Using a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.
Tensor Products and Singularly Continuous Spectrum
Authors: White Denis A. W.
Published: December 2010

An example of a bounded self adjoint operator A is constructed so that A⊗I + α(I⊗A) is purely singularly continuous but A⊗1 + β(I⊗A) is purely absolutely continuous, for some real α and β. In fact α - β can be chosen arbitrarily small.
A Finite Index Property of Certain Solvable Groups
Authors: Rhemtulla A. H. , Smith H.
Published: December 2010

A group G is said to have the FINITE INDEX property (G is an FI-group) if, whenever H≤G, xp ∈ H for some x in G and p > 0, then |〈H, x〉: H| is finite. Following a brief discussion of some locally nilpotent groups with this property, it is shown that torsion-free solvable groups of finite rank which have the isolator property are FI-groups. It is deduced from this that a finitely generated torsion-free solvable group has an FI-subgroup of finite index if and only if it has finite rank.
Finite Unions of Quasi-Independent Sets
Authors: Grow David , Whicher William C.
Published: December 2010

The analogue of Horn's theorem characterizing finite unions of linearly independent sets in a vector space is shown to fail in the group of integers.
On The Existence of Restricted K-Limits
Authors: Cegrell Urban
Published: December 2010

The purpose of this paper is to generalize the Lindelöf-Čirka theorem.
Another Class of Cyclicly Extensible and Reducible Properties
Authors: Lehman B.
Published: December 2010

A space S has property P-1 if S is nonempty. For n > — 1, S has property Pn if it is locally connected, has property Pn-1 and if whenever it is written as a union, S = A ∪ B where each of A and B is closed and has property Pn-1, then A ∩ B also has property Pn-1. The purpose of this paper is to establish that for locally compact spaces, each of the properties Pn is both cyclicly extensible and reducible.
On the Branch Points in the Branched Coverings of Links
Authors: Kinoshita Shintchi
Published: December 2010

Let l be a polygonal link in a 3-sphere S3 and a branched covering of l, which depends on the choice of a monodromy map ϕ. Let be the link in over l. In this paper we determine the exact position of in for some cases. For instance, if l is a torus link ((n + 1)p, n) and ϕ is an appropriate monodromy map of the fundamental group of S3 - l into the symmetric group of degree n + 1, then is an S3 and l is a torus link (np,n2). The 3-fold irregular branched covering of a doubled knot k is an S3, if it exists. The position of the link over k is shown in a figure. The link over knot 61 is obtained by K. A. Perko and the author, independently, and shown without proof in a paper by R. H. Fox [Can. J. Math. 22 (1970), 193-201]. The result mentioned in the above includes this case.
Approximation Theorems for Manis Valuations
Authors: Arapović Miroslav
Published: December 2010

Throughout this paper rings are understood to be commutative with unity. In this paper we prove the general approximation theorem for valuations whose infinite ideals have large Jacobson radicals. We give an example in which it is shown that approximation theorems for Manis valuations do not hold in the general case. Also we prove that every valuation pair (Rv, Pv) of a total quotient ring T(R) whose infinite ideal has large Jacobson radical is a Prüfer valuation pair.
Sur le Lemme de Schwarz
Authors: Yamashita Shinji
Published: December 2010

Nous allons proposer un lemme de type de Schwarz pour fonctions holomorphes dans |z| < 1 en termes de leurs moyennes
Germs Associated to Regular Unipotent Classes in p-adic SL(n)
Authors: Repka Joe
Published: December 2010

For an elliptic torus in SL(n), explicit formulae are given for the germs which are associated to the regular unipotent conjugacy classes. Using them, a formula is found for the germ associated to the "subregular" class, the class whose Jordan canonical form contains a 1 x 1 and an (n - 1) x (n - 1) block.
Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions
Authors: Odoni R. W. K.
Published: December 2010

We consider Dirichlet series R(s), constructed by taking scalar products of Hecke L-series with ray-class characters. Using a theorem of G. W. Mackey on tensor products of representations of finite groups we show that R(s) has a meromorphic continuation into Re(s) > 1/2 (obtained by more sophisticated methods in [l]-[5]); we then obtain estimates for the growth of R(s) on vertical lines. Via the Mellin transformation we deduce asymptotics for various weighted moment sums involving ideals of given ray-class and norm, in one or several fields simultaneously.
The Construction of Automorphic Forms From the Derivatives of a Given Form II
Authors: Rankin R. A.
Published: December 2010

Explicit constructions of polynomials of preassigned degree and weight in the derivatives of a given automorphic form are described and studied, supplementing the results of an earlier paper. It turns out that the problem is essentially one concerning symmetric functions rather than automorphic forms.
The Simplicial Helix and the Equation tan nθ = n tan θ
Authors: Coxeter H. S. M.
Published: December 2010

Buckminster Fuller has coined the name tetrahelix for a column of regular tetrahedra, each sharing two faces with neighbours, one 'below' and one 'above' [A. H. Boerdijk, Philips Research Reports 7 (1952), p. 309]. Such a column could well be employed in architecture, because it is both strong and attractive. The (n — 1)-dimensional analogue is based on a skew polygon such that every n consecutive vertices belong to a regular simplex. The generalized twist which shifts this polygon one step along itself is found to have the characteristic equation

(λ - 1)2{(n - 1)λn-2 + 2(n - 2)λn-3 + 3(n - 3)λn-4 + . . . + (n - 2)2λ + (n - 1)} = 0,

which can be derived from tan nθ = n tan θ by setting λ = exp (2θi).
A Multiple Exponential Sum to Modulus p2
Authors: Heath-Brown D. R.
Published: December 2010

For suitable polynomials f(x) ∊ ℤ[x] in n variables, of total degree d, it is shown that

This is, formally, a precise analogue of a theorem of Deligne [1] on exponential sums (mod p). However the proof uses no more than elementary algebraic geometry.
The Estimation of Complete Exponential Sums
Authors: Loxton J. H. , Vaughan R. C.
Published: December 2010

This paper proves a conjecture of Loxton and Smith about the size of the exponential sum S(f;q) formed by summing exp (2πif(x)/q) over x mod q, where f is a polynomial of degree n with integer coefficients. It is shown that |S(f;q)| ≤ Cfdn(q)qe/(e+1), where e is the maximum of the orders of the complex zeros of f'. An estimate is also obtained for Cf in terms of n, e and the different of f, and a number of examples are given to show that the estimate is best possible.
Une Remarque Sur les Deformations d'un Germe D'Hypersurfaces a Type Topologique Constant
Authors: Pnevmatikos Spyros N.
Published: December 2010

Resumé

Soit f un germe de fonction holomorphe centré à l'origine de ℂn à singularité isolée et F une déformation centrée de f de base ℂp. On se propose d'établir que lorsque la déformation Xt, = (0) de l'hypersurface X0 = f-l(0) est à type topologique constant alors la factorisation de F à travers la déformation miniverselle centrée de f concernant les espaces de paramètres correspondants est unique. Il en résulte en particulier immédiatement le théorème classique de détermination finie pour les fonctions ainsi que pour leurs déformations.
Perron Integrability Versus Lebesgue Integrability
Authors: Schurle Arlo W.
Published: December 2010

The paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.
A Note on Net Replacement in Transposed Spreads
Authors: Johnson N. L.
Published: December 2010

Let P be a translation plane containing a net N which is replaceable by . Let P' denote the transposed plane. We note that N' is replaceable by ()'. This result shows how to relate the various constructions of the two translation planes of order 16 that admit PSL(2, 7).
On the Number of Binomial Coefficients Which are Divisible by their Row Number: II
Authors: Robbins Neville
Published: December 2010

If n is a natural number, let A(n) denote the number of integers, k, such that 0 < k < n and n divides . Let ϕ(n) denote Euler's totient function. Necessary and sufficient conditions are given so that A(n) = ϕ(n) when n is square-free.
Certain Values of Completeness and Saturatedness of a Uniform Ideal Rule out Certain Sizes of The Underlying Index Set
Authors: Franek Frantisek
Published: December 2010

Using the method of non-well-founded generic ultra-powers, we shall prove a generalization of a theorem of Taylor that certain values of completeness and saturatedness of a uniform ideal rule out certain sizes of the underlying index set.
The Definability of the Commutator Subgroup in a Variety Generated by a Finite Group
Authors: Lawrence John
Published: December 2010

In a variety generated by a finite non-Abelian group, the commutator subgroup is not definable by a first-order formula.
An Almost Krull Domain with Divisorial Height One Primes
Authors: Arnold J. T. , Matsuda Ryuki
Published: December 2010

E. Pirtle has conjectured that if D is an almost Krull domain in which the height one prime ideals are divisorial then D is a Krull domain. An example is given to show that this is not the case. Further, let U = and let denote the set of prime ideals of D which are minimal over some ideal (a):(b), where a, b ∈ D. If Dp is a valuation ring for each let then Huckaba and Papick have asked whether D[x]U must be a Prufer domain. The given example shows that it need not be.
Finite Extensions of Valued Fields
Authors: Warner Seth
Published: December 2010

A corollary of the main result is that if L is a finite-dimensional Galois extension of a field K and if w is a valuation of L extending a valuation v of K, then K is closed in L if and only if all valuations of L extending v are dependent. A further consequence is a generalization of Ostrowski's criterion for a real-valued valuation to be henselian.
One-Sided L1-Approximation
Authors: Pinkus A. , Totik V.
Published: December 2010

Let Un be an n-dimensional subspace of C[0, 1]. We prove that if n ≥ 2, and Un contains a function which is strictly positive on (0, 1), then there exists an f ∈ C[0, 1] which has more than one best one-sided L '-approximation from Un. We also characterize those Un with the property that each f ∈ C[0, 1] has a unique best one-sided L1(w)-approximation from Un with respect to every strictly positive continuous weight function w.
Asymptotic Approximation of an Integral Involving the Normal Distribution*
Authors: McClure J. P. , Wong R.
Published: December 2010

An asymptotic approximation is obtained, as k → ∞, for the integral

where Φ is the cumulative distribution function for a standard normal random variable, and L is a positive constant. The problem is motivated by a question in statistics, and an outline of'the application is given. Similar methods may be used to approximate other integrals involving the normal distribution.
A Categorical Characterization of the Four Colour Theorem
Authors: Fawcett Barry
Published: December 2010

The surjectivity of epimorphisms in the category of planar graphs and edge-preserving maps follows from and is implied by the Four Colour Theorem. The argument that establishes the equivalence is not combinatorially complex.
A Characterization of Projective Metric Spaces
Authors: Frank Rolfdieter
Published: December 2010

A projective metric space is a pappian projective space together with a quadric and a certain equivalence relation on the pairs of those points which do not belong to the quadric. This equivalence relation is defined by means of the corresponding quadratic form and satisfies a condition which is a projective version of Miquel's theorem. We characterize the projective metric spaces of dimension at least two over fields of order at least 13.
Cup Products in Sheaf Cohomology
Authors: Jardine J. F.
Published: December 2010

Let k be an algebraically closed field, and let l be a prime number not equal to char(k). Let X be a locally fibrant simplicial sheaf on the big étale site for k, and let Y be a k scheme which is cohomologically proper. Then there is a Künneth-type isomorphism

which is induced by an external cup-product pairing. Reductive algebraic groups G over k are cohomologically proper, by a result of Friedlander and Parshall. The resulting Hopf algebra structure on may be used together with the Lang isomorphism to give a new proof of the theorem of Friedlander-Mislin which avoids characteristic 0 theory. A vanishing criterion is established for the Friedlander-Quillen conjecture.
Pre-Tits Systems
Authors: Moran Siegfried
Published: December 2010

A Tits system gives rise to the corresponding pre-Tits system which is the free product of the standard parabolic subgroups of rank 1 amalgamating B. Some properties of this system are investigated.
Dickson Polynomials Over Finite Fields and Complete Mappings
Authors: Mullen Gary L. , Niederreiter Harald
Published: December 2010

Dickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.
On Vector-Valued Lipschitz Function Spaces
Authors: Galindo Pablo
Published: December 2010

This paper is devoted to obtaining sequence space representations of spaces of vector-valued Ck-functions defined on an open subset, Ω, of ℝn, whose kth derivatives satisfy a Lipschitz condition on compact subsets of Ω.
Rectangularity Versus Piecewise Rectangularity of Product Spaces
Authors: Tsuda Kôichi
Published: December 2010

We shall discuss relations between rectangularity and piecewise rectangularity of product spaces. In particular, we show that for each positive integer n there exists an n-dimensional, collectionwise normal, non-piecewise rectangular product X × Y which satisfies the inequality dim (X × Y) ≤ dim X + dim Y.
Continuous Images of Compact Semilattices
Authors: Bell Murray , Pelant Jan
Published: December 2010

Hyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.
Hypersurfaces Framées et L'Élément β1, de Toda
Authors: Baker A. , Ray N. , Schwartz L.
Published: December 2010

L'objet de cet article est de construire un modèle pour l'élément β1, de Toda (premier élément non nul de la composante p - primaire de l'homotopie stable des sphères qui n'est pas dans l'image du J-homomorphisme, p ≠ 2). Le modèle construit possède en outre la propriété de se plonger, comme variété différentiable, en codimension 1.

La construction, basée sur la J-théorie et la chirurgie, exhibe en outre des complexes cellulaires satisfaisant à certaines conditions de plongement, répondant partiellement à un problème posé par le 2e et le 3e auteur.
On Darboux and Mean Value Properties
Authors: Bullen P. S. , Sarkhel D. N.
Published: December 2010

In this paper we extend and greatly generalize, with some new information, the well known results that an approximately continuous function is Darboux, and that a finite approximate derivative has the mean value property and is Darboux. Our theorems on Darboux and mean value properties of derivatives include also those of selective derivatives and I-approximate derivatives.
On Incomplete Character Sums to a Prime-Power Modulus
Authors: Chalk J. H. H.
Published: December 2010

Let x denote a primitive character to a prime-power modulus k = pα. The expected estimate

for the incomplete character sum has been established for r = 1 and 2 by D. A. Burgess and recently, he settled the case r = 3 for all primes p < 3, (cf. [2] for the proof and for references). Here, a short proof of the main inequality (Theorem 2) which leads to this result is presented; the argument being based upon my characterization in [3] of the solution-set of a related congruence.
Un Théorème de Transfert Pour la Propriété des Boules
Authors: Deville Robert
Published: December 2010

We show that, if X and Y are Banach spaces such that X has the Mazur's intersection property and such that there exists T, an operator from Y into X so that T* and T** are injective, then there exists on Y an equivalent norm which has the Mazur's intersection property.

We deduce from this result and from a result of M. Talagrand that there exists on the long James space J(η) an equivalent norm which has the Mazur's intersection property.
Local Complements to the Hausdorff-Young Theorem for Amalgams
Authors: Torres de Squire Maria L.
Published: December 2010

Let G be a locally compact abelian group. An amalgam space (Lp ℓq)(G) (1 ≦ p,q ≦ ∞) is a Banach space of functions which belong locally to LP(G) and globally to ℓq. In this paper we present noninclusion results related to the Hausdorff-Young theorem for amalgams.
Non-Isomorphic Equivalent Azumaya Algebras
Authors: Childs Lindsay N.
Published: December 2010

We explicitly describe an infinite collection of pairs of Azumaya algebras over the ring of integers of real quadratic number fields K which are maximal orders in the usual quaternion algebra over K, hence Brauer equivalent, but are not isomorphic. The result follows from an identification of the groups of norm one units, using the classification of Coxeter.
Oppenheim's Inequality for the Second Immanant
Authors: Merris Russell
Published: December 2010

Denote by d2 the immanant afforded by Sn and the character corresponding to the partition (2, 1n-2). If n ≥ 4, the following analog of Oppenheim's inequality is proved:

for all n-by-n positive semidefinite hermitian A and B.
On The Number of Groups of Squarefree Order
Authors: Ram Murty M. , Srinivasan S.
Published: December 2010

Let G(n) denote the number of non-isomorphic groups of order n. We prove that for squarefree integers n, there is a constant A such that

where denotes the Euler function. This upper bound is essentially best possible, apart from the constant A.
Anneaux de Bezout, Hermite et Kaplansky "Universels"
Authors: Carbonne Philippe
Published: December 2010

Les anneaux de Kaplansky sont aussi connus sous le nom d'anneaux à diviseurs élémentaires.

On construit pour un cardinal donné un anneau de Bezout (resp. Hermite, resp. Kaplansky) tel que tout anneau de même cardinal de la même classe soit un quotient de l'anneau construit.

Comme application on montre que l'on a ainsi des contreexemples nouveaux à deux problèmes classiques. On réduit aussi un troisième problème, posé par Kaplansky, sans arriver à le résoudre.
Groupe de Brauer d'une Courbe de Tate
Authors: Touibi C.
Published: December 2010

Soient k un corps de séries formelles à corps résiduel fini et X une courbe elliptique définie sur k dont l'invariant modulaire j n'est pas un entier de k. On détermine le groupe de Brauer Br(X) de X, ainsi que le groupe Br(X(q) ) où X(q) est la courbe de Tate définie sur k et associée à un élément q de k* et on établit une dualité entre Br(X) et Pic(X). On examine ensuite le cas où le corps résiduel est quasi-fini.
Some New Product Theorems in Summability
Authors: Parameswaran Mangalam R.
Published: December 2010

Let A, B denote sequence-to-sequence matrix methods of summability and A · B the “dot” or iteration product defined by (A · B)x = A(Bx) for all sequences x for which this exists. Some inclusion relations are given involving the methods A, B, A · B, B · A and the method defined by the matrix product AB. We take A, B to be of certain types whose products have not been studied extensively before, e.g. H* · Ck or Ck · H* where H* is quasi-Hausdorff (and hence upper triangular) and Ck is a Cesàro matrix (which is lower triangular). The investigations show also a link between the “Product Property” A ⊂ A · B and the translativity properties of A and B.
Integrally Closed Torsionless Rings
Authors: Rush David E.
Published: December 2010

A characterization of torsionless rings is given which shows that the integral closure of a torsionless ring need not be Prüfer.
Isomorphisms and Automorphisms of Witt Rings
Authors: Leep David , Marshall Murray
Published: December 2010

For a field F, char(F) ≠ 2, let WF denote the Witt ring of quadratic forms of F and let denote the multiplicative group of 1-dimensional forms It follows from a construction of D. K. Harrison that if E, F are fields (both of characteristic ≠ 2) and ρ.WE → WF is a ring isomorphism, then there exists a ring isomorphism which “preserves dimension” in the sense that In this paper, the relationship between ρ and is clarified.
Comments on a Paper of R. A. Brualdi
Authors: Bongiovanni G. , Bovet D. P. , Cerioli A.
Published: December 2010

R. A. Brualdi [1] presents a construction yielding matrices whose Birkhoff representation consists of the maximum number of permutation matrices and having 0(2n2) line sum. In this note a counterexample to such a construction is given. Furthermore, a new construction is presented, yielding matrices with lower line sums.
A Remark on Maps Between Classifying Spaces of Compact Lie Groups
Authors: Wojtkowiak Zdzisław
Published: December 2010

We show that two maps between classifying spaces of compact, connected Lie groups are homotopic after inverting the order of the Weyl group of the source if and only if they induce the same maps on rational cohomology. We shall also give some results on maps from classifying spaces of finite groups to classifying spaces of compact Lie groups. Among other things we construct a map from B(Z/2 + Z/2 4- Z/3) into BSO(3) which is not induced by a homomorphism.
Semiderivations and Commutativity in Prime Rings
Authors: Bell H. E. , Martindale W. S.
Published: December 2010

A semiderivation of a ring R is an additive mapping f:R → R together with a function g:R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x) ) = g(f(x)) for all x, y ∊ R. Motivating examples are derivations and mappings of the form x → x — g(x), g a ring endomorphism. A semiderivation f of R is centralizing on an ideal U if [f(u), u] is central for all u ∊ U. For R prime of char. ≠2, U a nonzero ideal of R, and 0 ≠ f a semiderivation of R we prove: (1) if f is centralizing on U then either R is commutative or f is essentially one of the motivating examples, (2) if [f(U), f(U) ] is central then R is commutative.
Asymptotic Properties of Semilinear Equations
Authors: Edelson Allan L.
Published: December 2010

We study the asymptotic properties of positive solutions to the semilinear equation — Δu = f(x, u). Existence and asymptotic estimates are obtained for solutions in exterior domains, as well as entire solutions, for n ≧ 2. The study uses integral operator equations in Rn, and convergence theorems for solutions of Poisson's equation in bounded domains. A consequence of the method is that more precise estimates can be obtained for the growth of solutions at infinity, than have been obtained by other methods. As a special case the results are applied to the generalized Emden-Fowler equation — Δu = p(x)uγ, for γ > 0
U-Sets in Compact, 0-Dimensional, Metric Groups
Authors: Grubb D. J.
Published: December 2010

This paper studies a pointwise definition of sets of uniqueness on compact, 0-dimensional, metric groups. It is shown that this definition is equivalent for closed sets to one based on supports of pseudo functions. An analog of Rajchman's theorem is given leading to examples of sets of uniqueness.
On Condensed Noetherian Domains Whose Integral Closures are Discrete Valuation Rings
Authors: Gottlieb Christian
Published: December 2010

A condensed domain is an integral domain such that IJ = {xy : x ∊ I, y ∊ J } holds for each pair I, J of ideals. We prove that, under suitable conditions, a subring of a discrete valuation ring is condensed if and only if it contains an element of value 2. We also define the concept strongly condensed.
On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
Authors: Connor Jeff
Published: December 2010

The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that Astatistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.
A New Proof of the d-Connectedness of d-Polytopes
Authors: Brøndsted A. , Maxwell G.
Published: December 2010

Balinski has shown that the graph of a d-polytope is d-connected. In this note we give a new proof of Balinski's theorem.
On invariant radicals
Authors: Sands A. D.
Published: December 2010

It is shown that the concepts of normal radical as introduced by Jaegermann [2] and of invariant radical as introduced by Anderson, Divinsky and Sulinski [1] are equivalent.
Absolute Retracts and Amalgamation in Certain Congruence Distributive Varieties
Authors: Jipsen Peter , Rose Henry
Published: December 2010

It is shown that if V is a congruence distributive variety whose members have one element subalgebras, then the class of absolute retracts of V is closed under direct products. If V is residually small, then a characterisation of the amalgamation class of V is given.
Differential Completions and Differentially Simple Algebras
Authors: Seibt Peter
Published: December 2010

Differentially simple local noetherian Q -algebras are shown to be always (a certain type of) subrings of formal power series rings. The result is established as an illustration of a general theory of differential filtrations and differential completions.
Approximation of Lp-Contractions by Isometries
Authors: Akcoglu M. A. , Boivin D.
Published: December 2010

We construct a positive linear contraction T of all LP(X, μ)- spaces, 1 ≦ p ≦ ∞, μ(X) = 1 such that T1 = 1, T* 1 = 1 and also Tf > 0 a.e. for all f ≧ 0 a.e., f ≢ 0 but for which there is an f ∊ L∞ such that (Tnf — ∫ fdμ) does not converge in L1-norm. We also show that if T is a contraction of a Hilbert space H, there exists an isometry Q and a contraction R such that ∥Tnx - QnRx∥ —> 0 as n —» ∞ for all x in H
A Note on M-Ideals of Compact operators
Authors: Cho Chong-Man
Published: December 2010

Suppose X and Y are closed subspaces of (ΣXn)p and (ΣYn)q (1 < p ≦ q < ∞, dim Xn < ∞, dimYn < ∞), respectively. If K(X, Y), the space of the compact linear operators from X to Y, is dense in L(X, Y), the space of the bounded linear operators from X to Y, in the strong operator topology, then K(X, Y) is an M-ideal in L(X, Y).
Généralisation d'un Lemme de Kummer
Authors: Hoechsmann Klaus
Published: December 2010

If A is a finite abelian group and ZAits integral group ring, consider unitsu∊ ZAwhich have coefficient sum = 1 and are fixed under the involution a —> a-1, a ∊A. For an odd regular primepand ap-groupA, it is shown thatu≡ 1 mod p if only ifu = π(v)v-p, where v is the same kind of unit, and π is the ring endomorphism given bya —> ap, a∊A.
On Coefficients of Artin L Functions as Dirichlet Series
Authors: Funakura Takeo
Published: December 2010

The paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.
Limit Cycles Close to Infinity of Certain Non-Linear Differential Equations
Authors: Guíñez Víctor , Sáez Eduardo , Szántó Iván
Published: December 2010

Through successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.
Ring Derivations on Function Algebras
Authors: Nandakumar N. R.
Published: December 2010

In this paper we show that a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set.
Ends of spaces related by a covering map
Authors: peschke Georg
Published: December 2010

Consider a covering p : X → B of connected topological spaces. If
B is a compact polyhedron, a classical result of H. Hopf [4] says that the end space
E(X) of X is an invariant of the group G of covering transformations. Thus it becomes
meaningful to define the end space of the finitely generated group G as E(G) := E(X).
Image Area and the Weighted Subspaces of Hardy Spaces
Authors: Kwon E. G.
Published: December 2010

Let Hp,ϕ be the subspace of Hardy space Hp consisting of those f ∊ Hp(Bn) satisfying where ϕ is a positive decreasing differentiable function on [0, 1) with ϕ(1—) = 0. Concerning image area growth, criteria for f to be of Hp,ϕ are considered extending known results for Hp.
The Splitting of the Hochschild-Serre Spectral Sequence for a Product of Groups
Authors: Jannsen Uwe
Published: December 2010

We show that the Hochschild-Serre spectral sequence for a product G x H of abstract or profinite groups splits for G-modules, and that this splitting is not functorial.
On the Non-Isomorphism of and
Authors: Mingo James A.
Published: December 2010

We show that for a discrete ICC group G, which is not inner amenable and is such that has a weakly outer automorphism, is not isomorphic to .
The Integrability of Riemann Summable Trigonometric Series
Authors: Bullen P. S. , Mukhopadhyay S. N.
Published: December 2010

It is shown that if a trigonometric series is (R, 3), respectively (R, 4), summable then its (R, 3) sum, respectively (R, 4) sum, is James P3—, respectively P4—, integrable and that such series are Fourier series with respect to these integrals.
A Decomposition Theorem for Positive Superharmonic Functions
Authors: Eriksson-Bique Sirkka-Liisa
Published: December 2010

Let X be a harmonic space in the sense of C. Constantinescu and A. Cornea. We show that, for any subset E of X, a positive superharmonic function u on X has a representation u = p + h, where p is the greatest specific minorant of u satisfying . This result is a generalization of a theorem of M. Brelot. We also state some characterizations of extremal superharmonic functions.
Indecomposable Positive Quadratic Forms
Authors: Krüskemper Martin
Published: December 2010

Let F be a formally real field. A quadratic form q is called positive if sgnp ≧ 0 for all orderings P of F. A positive q is called decomposable if there exist positive forms q1, q2 such that q = q1⊥q2. Otherwise it is called indecomposable. In a first part we ask for which F there exist indecomposable three dimensional forms over F. We show that such forms exist iff F does not satisfy the property (A) defined in (J. K. Arason, A. Pfister: Zur Théorie der quadratischen Formen über formal reellen Körpern, Math Z. 153, 289-296 (1977)). We use an indecomposable three dimensional form defined by Arason and Pfister to construct indecomposable forms of arbitrary dimension. Then we examine the question for which fields F every positive form over F represents a nonzero sum of squares.
Fuglede's Commutativity Theorem and ∩ R(T - λ)
Authors: Whitley Robert
Published: December 2010

Fuglede's commutativity theorem for normal operators is an easy consequence of the result that: For T normal, denoting the range of T - λ by R(T - λ), ∩ {R(T - λ) : all λ} = {0}:
Unstable Neutral Fuctional Differential Equations
Authors: Feldstein Alan , Jackiewicz Zdzislaw
Published: December 2010

Let y be the solution of the equation

where A, B, C, λ and η aie complex numbers and It is shown that y has exponential order equal to one if A ≠ 0 and if y is not a polynomial; otherwise, y has exponential order equal to zero. In the latter case, y and all of its derivatives are unbounded on any ray.
The Relationship Between Distance Formulae and Compact Perturbations for Reflexive Algebras
Authors: Davidson Kenneth R.
Published: December 2010

For completely distributive CSL algebras, hyper-reflexivity is equivalent to a description of the compact perturbation of the algebra analogous to the Fall-Arveson-Muhly Theorem for nest algebras.
A Characterization of the Minkowski Norms
Authors: Anderson C. L.
Published: December 2010

If n > 2 and M(m1,..., xn) is a symmetric norm of the form m(x1, m(x2, m{...)...), where m is a symmetric norm on ℝ2, then m(x, y) = (|x|p + |y|p)1/p for some p ≥ 1 or else m(x, y) = max{|x|,|y|}.
A Characterization of the Quadratic Irrationals
Authors: Brown Tom C.
Published: December 2010

Let α be a positive irrational real number, and let fα (n) = [(n + l)α] — [nα] — [α],n > 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain 'substitution property' if and only if α is the root of a quadratic equation over the rationals.
On Elementary Abelian Cartesian Groups
Authors: Evans Anthony B.
Published: December 2010

J. Hayden [2] proved that, if a finite abelian group is a Cartesian group satisfying a certain "homogeneity condition", then it must be an elementary abelian group. His proof required the character theory of finite abelian groups. In this note we present a shorter, elementary proof of his result.
Two Consequences of Brunel's Theorem
Authors: Olsen James H.
Published: December 2010

In this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.
Komlos Limits and Fatou's Lemma in Several Dimensions
Authors: Page Frank H.
Published: December 2010

Using Komlos' Theorem, a sequence decomposition result due to Gaposhkin, and two results due to Artstein, we prove a result concerning the properties of Komlos limits. We then show that a stronger version of Fatou's Lemma in several dimensions can be deduced from Artstein's version of the Lemma. The version of Fatou's Lemma proved here subsumes the most recent version of the Lemma in several dimensions given by Balder.
Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
Authors: Shieh Narn-Rueih
Published: December 2010

Let X be a real stochastic process. We localize S. M. Berman's formulation on the local nondeterminism of X to a fixed level. With this localized idea, we prove that, for large classes of Gaussian and Markov X, at each x the level set X(t, w) = x has infinite Hausdorff ϕ - measure (ϕ is certain measure function) for w in a set of positive probability.
K-Uniform Rotundity of Sequence Orlicz Spaces
Authors: Tingfu Wang , Shutao Chen
Published: December 2010

This paper presents a criterion of KUR for sequence Orlicź spaces with Luxemburg's norm. The result also indicates that for any integer k ≥ 1, there exists a k + 1-uniformly rotund Banach space not being k-uniformly rotund.
On Unit Solutions of the Equation xyz = x + y + z in Not Totally Real Cubic Fields
Authors: Zhang Liang-Cheng , Gordon Jonathan
Published: December 2010

It is shown that the equation xyz = x+y+z has unit solutions in only four not totally real cubic fields: two fields which are real and two fields which are imaginary. These fields are then listed.
On the Kuiper-Kuo Theorem
Authors: Chu Chuan I.
Published: December 2010

In this note we shall give a simple and more direct proof of the Kuiper- Kuo Theorem. Also, we shall simplify Kuiper's proof of the Morse Lemma.
Approximation Holomorphe Globale Sur L'union de Deux Sous-Espaces Totalement Réels Maximaux de Cn
Authors: Frih El Mostapha
Published: December 2010

Let E and F be real subspaces of Cn which contain no non trivial complex subspace of Cn and intersecting only at the origin. We prove in a special case that every continuous function on E ∪ F can be asymptotically approximated on E ∪ F by an entire function.
Global Holomorphic Approximation on the Product of Curves in Cn
Authors: Frih El Mostapha , Gauthier Paul M.
Published: December 2010

We prove that every continuous function on the product of certain curves can be asymptotically approximated by entire functions.
A New Approach to Operator Spaces
Authors: Effros Edward G. , Ruan Zhong-Jin
Published: December 2010

The authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.
A Note on Minimal Usco Maps
Authors: Verona Andrei , Verona Maria Elena
Published: December 2010

We prove that the composition of a minimal usco map, defined on a Baire space, with a lower semicontinuous function is single valued and usco at each point of a dense G$ subset of its domain. This extends earlier results of Kenderov and Fitzpatrick. As a first consequence, we prove that a Banach space, with the property that there exists a strictly convex, weak* lower semicontinuous function on its dual, is a weak Asplund space. As a second consequence, we present a short proof of the fact that a Banach space with separable dual is an Asplund space.
On an Estimate of the Partial Sums of Vilenkin-Fourier
Authors: Young Wo-Sang
Published: December 2010

We show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].
Some Remarks on Rotors in Link Theory
Authors: Jin Gyo Taek , Rolfsen Dale
Published: December 2010

We present examples showing that certain results on the invariance of link polynomials under generalized mutation are the best possible. They show, moreover, that this generalized mutation cannot be effected by a sequence of ordinary mutations. One of the examples also shows that the reduced Jones polynomial can be a more sensitive invariant than the Jones polynomial itself.
Independence for Sets of Topological Spheres
Authors: Pakula Lewis , Schwartzman Sol
Published: December 2010

Consider a collection of topological spheres in Euclidean space whose intersections are essentially topological spheres. We find a bound for the number of components of the complement of their union and discuss conditions for the bound to be achieved. This is used to give a necessary condition for independence of these sets. A related conjecture of Griinbaum on compact convex sets is discussed.
Closure of Leaves in Transversely Affine Foliations
Authors: Wolak Robert A.
Published: December 2010

We present first examples of complete transversely affine foliations on compact manifolds with leaves whose closures are not submanifolds. Moreover, we prove that under some additional assumptions the closures of leaves form a singular foliation.
A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings
Authors: Xu Hong-Kun
Published: December 2010

As a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.
A Maximum Principle for Subharmonic and Plurisubharmonic Functions
Authors: Huaihui Chen , Gauthier P. M.
Published: December 2010

We give a simple description of boundary sets which may be ignored in calculating the maximum of subharmonic or plurisubharmonic functions.
Compact Multipolar Sets
Authors: Gowrisankaran Kohur , Jesuraj Ramasamy
Published: December 2010

It is proved that a compact subset of a finite product of Brelot harmonic spaces is multipolar if it is a locally multipolar set.
A Divisor Problem for Values of Polynomials
Authors: Mercier Armel , Nowak Werner Georg
Published: December 2010

In this article we investigate the average order of the arithmetical function

where p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.