bluuebunny/crossref_metadata_2025 huggingface dataset:
Onp-Large Subgroups ofp-Torsion Groups
Authors: Benabdallah K. , Yoshioka S.
Published: December 2010

Resumé

Les groupesp-torsion forment une classe de groupes abéliens mixtes dont les sous-groupes dep-base sont de torsion. Nous montrons ici que la généralisation naturelle à ces groupes de la notion de sous-groupe large développée pour les groupes primaires par R. S. Pierce, permet d'obtenir des résultats analogues. Ainsi nous caractérisons les sous-groupesp-larges d'un groupep-torsionGen fonction des suites non-décroissantes d'entiers non-négatifsu= (ui) qui satisfont à la condition d'écart pourG. On obtient: un sous-groupe A du groupep-torsionGestp-large si, et seulement si A est de la formeG(u) pour une suiteutelle que pour toutx ∈ G, la suite (h(pix)) est plus grande presque partout que la suiteu.

Nous déterminons aussi, les sous-groupesp-large de, le complétép-adique d'une somme directe de groupes cycliques non bornésB, ainsi que ceux des sous-groupesp-purs totalement invariants deengendrés par un élément.
Cubic and Higher Order Algorithms for π
Authors: Borwein J. M. , Borwein P. B.
Published: December 2010

We show that the theory of elliptic integral transformations may be employed to construct iterative approximations for π of order p (p any prime). Details are provided for two, three and seven. The cubic case proves amenable to surprisingly complete analysis.
Locally Uniformly Rotund Renorming and Injections Into c0(Γ)
Authors: Godefroy G. , Troyanski S. , Whitfield J. , Zizler V.
Published: December 2010

A norm |⋅| on a Banach space X is locally uniformly rotund (LUR) if lim |xn — x| = 0 for every xn, x ∈ X for which lim2|x|2 + 2 |xn|2-|xn+xn|2 = 0. It is shown that a Banach space X admits an equivalent LUR norm provided there is a bounded linear operator T of X into c0(Γ) such that T* c*0(Γ) is norm dense in X*. This is the case e.g. if X* is weakly compactly generated (WCG).
On a Result of Smith and Subbarao Concerning a Divisor Problem
Authors: Nowak Werner Georg
Published: December 2010

Let d(n;l,k) denote the number of divisors of the positive integer n which are congruent to I modulo k. The objective of the present paper is to prove that (for some exponent θ<⅓)

holds uniformly in l, k and x satisfying 1≤l≤k≤x. This improves a recent result due to R. A. Smith and M. V. Subbarao [3].
Two Inequalities for Planar Convex Sets
Authors: Tsintsifas George
Published: December 2010

B. Grünbaum, J. N. Lillington and lately R. J. Gardner, S. Kwapien and D. P. Laurie have considered inequalities defined by three concurrent straight lines in the interior of a planar compact convex set. In this note we prove two elegant conjectures by R. J. Gardner, S. Kwapien and D. P. Laurie.
Finite Intersections of Pid or Factorial Overrings
Authors: Anderson D. D. , Anderson David F.
Published: December 2010

In this paper we study when an integral domain is a finite intersection of PID or factorial overrings. We show that any Krull domain is the intersection of a PID and a field. We give several sufficient conditions for a Krull domain to be an intersection of two PID or factorial overrings.
Structure of Certain Periodic Rings
Authors: Abu-Khuzam Hazar , Yaqub Adil
Published: December 2010

Let R be a periodic ring, N the set of nilpotents, and D the set of right zero divisors of R. Suppose that (i) N is commutative, and (ii) every x in R can be uniquely written in the form x = e + a, where e2 = e and a ∊ N. Then N is an ideal in R and R/N is a Boolean ring. If (i) is satisfied but (ii) is now assumed to hold merely for those elements x ∊ D, and if 1 ∊ R, then N is still an ideal in R and R/N is a subdirect sum of fields. It is further shown that if (i) is satisfied but (ii) is replaced by: "every right zero divisor is either nilpotent or idempotent," and if 1 ∊ R, then N is still an ideal in R and R/N is either a Boolean ring or a field.
Connected Maps and Essentially Connected Spaces
Authors: Nishiura Eizo
Published: December 2010

The paper discusses some consequences of weak monotonicity for connected maps in relation to essential connectedness of a space. The first main result gives conditions under which the image by a connected map of an essentially connected space is essentially connected. The second is that, for a connected mapping of a connected, 1 .c. space to a WLOTS-wise and essentially connected space, w-monotonicity implies monotonicity. The remainder of the paper discusses continuity properties of connected, w-monotone mappings with WLOTS-wise and essentially connected range.
A Simple Proof of Integration by Parts for the Perron Integral
Authors: Bullen P. S.
Published: December 2010

This note presents a very simple proof for the integration by parts formula for the Perron integral.
Stiefel-Whitney Classes of a Symmetric Bilinear Form — A Formula of Serre
Authors: Snaith Victor
Published: December 2010

Let K be a field of characteristic different from two. Let L be a finite separable extension of K. If is the separable closure of K, we have a continuous homomorphism π : Ga(/K) → ∑n(n - [L : K]). We give a very short proof of Serre's formula which evaluates the Hasse-Witt invariant of a symmetric bilinear form, transferred from L, in terms of the topological Stiefel-Whitney classes of IT.
Nonexistence of Almost-Quaternion Substructures on the Complex Projective Space
Authors: Önder Turgut
Published: December 2010

It is shown that there are no almost-quaternion substructures on the complex projective space Pn(ℂ).
The Chowla-Selberg Method for Fourier Expansion of Higher Rank Eisenstein Series
Authors: Terras Audrey
Published: December 2010

The terms of maximal rank in Fourier expansions of Eisenstein series for GL(n, ℤ) are obtained by an analogue of a method of Chowla and Selberg. The coefficients involve matrix analogues of divisor functions as well as K-Bessel functions for GL(n). The discussion involves a few properties of Hecke operators.
Small Solutions of Congruences in a Large Number of Variables
Authors: Schmidt Wolfgang M.
Published: December 2010

It is shown that a system of congruences 1(x) ≡ . . . ≡

(x) = 0 (mod m)

where each i(x) = i,(x1, .. . ,x2,) is a form of degree at most k has a nontrivial solution x satisfying |xi|≦cm(½)+∊ (i=1,...,S)

with c = c(k,r,∊), provided that ∊ > 0 and that S > S1(k,r,∊).
Numbers Differing from Consecutive Squares by Squares
Authors: Barbeau E. J.
Published: December 2010

It is shown that there are infinitely many natural numbers which differ from the next four greater perfect squares by a perfect square. This follows from the determination of certain families of solutions to the diophantine equation 2(b2 + 1) = a2 + c2. However, it is essentially known that any natural number with this property cannot be 1 less than a perfect square. The question whether there exists a number differing from the next five greater squares by squares is open.
Convergence and Analytic Continuation for a Class of Regular C-Fractions
Authors: Masson D.
Published: December 2010

Regular C-fractions f(α) = 1 + a1α/1 + a2α/1 + . .. with an = an2 + bn + c + Vn, |Vn| sufficiently small are examined. In the case Vn = 0, exact expressions are obtained which reveal a two sheeted Riemann structure for f(α). If Vn ≠ 0 analytic properties are obtained by means of perturbation theory applied to the associated difference equation. A conjecture that f(α) is the ratio of two entire functions of for an even larger class of C-fractions is proved for the case .
Finiteness of Negative Spectra of Elliptic Operators
Authors: Murata Minoru
Published: December 2010

Finiteness criteria are established for the negative spectra of higher order elliptic operators on Rn. The results are obtained by establishing isomorphism theorems for elliptic operators and applying the abstract finiteness criterion of Konno-Kuroda.
M-Ideals in L(l1, E)
Authors: Fleming D. J. , Giarrusso D. M.
Published: December 2010

In this article it is shown that for any Banach space E,L (l1,E) always contains uncountably many distinct A/-ideals that are closed subspaces of K(l1,E) and which are not complemented in L (l1,E) . Using standard duality arguments one obtains the result that infinitely many distinct subspaces of K(E, c0) are M-ideals in L(E, c0). In particular, for the case E = c0, this shows that the uniqueness conditions enjoyed by K(lp), p > 1, is not valid for E = c0. The results are obtained by utilizing the identification of L (l1,E) with the vector-valued sequence space lx(E) and to exploit natural decompositions of lx(E)’ afforded by a class of Lprojections on lx(E)’ induced by certain E'-valued vector measures.
Mixed Norm Decay for the Klein-Gordon Equation with Initial Data in Lp
Authors: Marshall Bernard
Published: December 2010

This paper gives necessary conditions for mixed norm estimates from Lp to Lr (Lq) for solutions of the Klein-Gordon equation

These conditions are best possible if p = 2 or
Products and Cardinal Invariants of Minimal Topological Groups
Authors: Douglass L. Grant  , W. W. Comfort
Published: December 2010

It is a question of Arhangel'skiĭ [1] (Problem 2) whether the identity ψ(G) = X(G) holds for every minimal Hausdorff topological group G = 〈G,u〉). (Here, as usual, ψ(G), the pseudocharacter of G, is the least cardinal number K for which there is such that and and x(G), the character of G,is the least cardinality of a local base at e for (〈G,u〉.) That 〈G, u〉 is minimal means that, if v is a Hausdorff topological group topology for G and v ⊂ u, then v = u.

In this paper, we give some conditions on G sufficient to ensure a positive response to Arhangel'skiï's question, and we offer an example which responds negatively to a question on minimal groups posed some years ago (cf. [6] (p. 107) and [4] (p. 259)).
Functors on Finite Vector Spaces and Units in Abelian Group Rings
Authors: Hoechsmann Klaus
Published: December 2010

If A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the composite

where C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of
A Note on Permutations and Topological Entropy of Continuous Maps of the Interval
Authors: Byers Bill
Published: December 2010

Suppose f is a continuous endomorphism of an interval which has a periodic orbit, p0 < P1 < … < pn, that defines a permutation a by f(pi) = pσ(i). If σ is irreducible the topological entropy of f is bounded below by the logarithm of the spectral radius of an n x n matrix which is induced by σ.
A Problem on Relative Projectivity for Abelian Groups
Authors: Feigelstock S. , Raphael R.
Published: December 2010

The article studies the class of abelian groups G such that in every direct sum decomposition G = A ⊕ B, A is 5-projective. Such groups are called pds groups and they properly include the quasi-projective groups.

The pds torsion groups are fully determined.

The torsion-free case depends on a lemma that establishes freedom in the non-indecomposable case for several classes of groups. There is evidence suggesting freedom in the general reduced torsion-free case but this is not established and prompts a logical discussion. It is shown, for example, that pds torsion-free groups must be Whitehead if they are not indecomposable, but that there exists Whitehead groups that are not pds if there exist non-free Whitehead groups.

The mixed case is characterized and examples are given.
The K-Theory of the Cotangent Sphere Bundle of ℝPn
Authors: Snaith Victor
Published: December 2010

We calculate the topological K-theory of the cotangent sphere bundle of ℝPn and show the manner in which it is detected by the eta invariant.
Finite Regular Covers of Surfaces
Authors: Cusick Larry W.
Published: December 2010

Let Tk = T1#...#T1 T1 = Sl x Sl, Uk = ℝP2#... #ℝP2, and G is a finite group. We prove (1) Every free action of G on Ul + 2 lifts to a free action of G on the orientable two fold cover Tl+1 → Ul+1 and (2) The minimum k such that can act freely on Tk is ml((l - 2)/2) + 1 if m = 2 or l is even and ml((l - 1)/2) + 1 otherwise.
The Relation Between Stable Operations for Connective and Non-Connective p-Local Complex K-Theory
Authors: Johnson Keith
Published: December 2010

The question of which degree 0 stable cohomology operations for connective K-theory localized at a prime p arise from operations for non-connective K-theory is investigated. A necessary and sufficient condition is established, and an example of a connective operation not arising in this way is constructed.
The Long Annulus Theorem
Authors: Evans Benny
Published: December 2010

Given a properly embedded incompressible surface F in a Haken manifold M, there is an integer n depending only on M and F with the following property: If there is a singular annulus in M that meets F in more then n nontrivial loops that are not freely homotopic on F then M contains an essential torus or annulus, or M is a bundle with fiber F, or M is a doubled twisted I-bundle with doubling surface F.
A Practical Two-Dimensional Ergodic Theorem
Authors: Scarowsky Manny , Boyarsky Abraham
Published: December 2010

Let τ:[0, 1] → [0, 1] be defined by τ(x) = 2x on [0, 1/2,] and τ(JC) = 2(1 - x) on [5, 1], and let T:[0, 1] x [0, 1] → [0, 1] x [0, 1] be defined by T(x,y) = (τ(x), τ(y))- Let

where p is a prime > 2, and a and M are integers. Consider T restricted to θM x θN, 1 < M < N. Let X = ((2a)/(pM), (2b)/(pN)) ∈ θM x θN and let per(X) denote the length of the period of X.

Then,

where m is Lebesque measure on [0, 1], and C is independent of p, N, M, a and b. Thus, as p → or as N - M and M→ →,
Remarks on Entire Functions of Exponential Type
Authors: Frappier Clément
Published: December 2010

A classical result of Laguerre says that if P is a polynomial of degree n such that P(z) ≠ 0 for | z | < 1 then (ξ - z)P' (z) + nP(z) ≠ 0 for | z | < 1 and | ξ | < 1. Rahman and Schmeisser have obtained an extension of that result to entire functions of exponential type: if f is an entire function of exponential type τ, bounded on ℝ, such that hf(π/2) = 0 then (ξ- l)f'(z) + iτ(z) ≠ 0 for Im(z) > 0 and | ξ | < 1, whenever f(z) ≠ 0 if Im(z) > 0. We obtain a new proof of that result. We also obtain a generalization, to entire functions of exponential type, of a result of Szegö according to which the inequality | P(Rz) — P(z) | < Rn - 1, | z | ≤ 1, R ≥ 1, holds for all polynomials P, of degree ≤ n, such that | P(z) | ≤ 1 for | z | ≤ 1.
A Result on Derivations with Algebraic Values
Authors: Di Vincenzo Onofrio M.
Published: December 2010

Let R be a prime algebra over a field F and let d be a non-zero derivation in R such that for every x ∊ R, d(x) is algebraic over F of bounded degree. Then R is a primitive ring with a minimal right ideal eR, where e2 = e and eRe is a finite dimensional central division algebra.
Some Classes of Topological Spaces with Unique Quasi-Uniformity
Authors: Gregori V. , Ferrer J.
Published: December 2010

We follow P. Fletcher and W. F. Lindgren's work in the study of topological spaces with a unique quasi-uniformity by generalizing some of their results and constructing larger classes of uqu spaces which contain some of their examples as a particular case.
Hausdorff Distance and a Compactness Criterion for Continuous Functions
Authors: Beer Gerald
Published: December 2010

Let 〈X, dx〉 and 〈Y, dY〉 be metric spaces and let hp denote Hausdorff distance in X x Y induced by the metric p on X x Y given by p[(x1, y1), (x2, y2)] = max ﹛dx(x1, x2),dY(y1, y2)﹜- Using the fact that hp when restricted to the uniformly continuous functions from X to Y induces the topology of uniform convergence, we exhibit a natural compactness criterion for C(X, Y) when X is compact and Y is complete.
The Fractal Dimension of Sets Derived from Complex Bases
Authors: Gilbert William J.
Published: December 2010

For each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the positive root of λ3 - (2n - 1) λ2 - (n - 1) 2λ - (n2 + 1).
Fuzzy Set Theory and Topos Theory
Authors: Barr Michael
Published: December 2010

The relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.
An Amalgamation Theorem For Soluble Groups
Authors: Leinen Felix
Published: December 2010

A theorem of G. Higman about the embeddability of amalgams within the class of all finite ρ-groups is generalized to classes of soluble groups. We also give best possible bounds for the solubility lengths of the constructed completions. And, as an application, the super-soluble amalgamation bases in the class of all finite soluble π-groups are determined.
Sign Properties of Green's Functions For Two Classes of Boundary Value Problems
Authors: Eloe P. W.
Published: December 2010

Let G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.
Sharp Bounds on the Diameter of a Graph
Authors: Smyth W. F.
Published: December 2010

Let Dn.m, be the diameter of a connected undirected graph on n ≥2 vertices and n - 1 ≤ m ≤ s(n) edges, where s(n) = n(n — l)/2. Then Dn.s(n) = 1, and for ms(n) it is shown that

The bounds on Dn.m, are sharp.
A Hilbert Lattice With a Small Automorphism Group
Authors: Künzi Urs-Martin
Published: December 2010

We construct an orthomodular inner product space to answer the questions posed by R. P. Morash in his paper "Angle bisection and orthoautomorphisms in Hilbert lattices" [6]. For example we show that every automorphism of the Hilbert lattice belonging to our inner product space has the property, that no atom is orthogonal to its image.
A System of Operator Equations
Authors: Magajna Bojan
Published: December 2010

Let be a separable Hilbert space, the algebra of all bounded operators on and Ai, Bi, ∊ , i = 1,. . . , r. It is shown that if no nontrivial linear combination of the operators Ai, is compact, then there exist X, Y ∊ such that X Ai, Y = Bi, for all i. A related (but much milder) result is discussed in other algebras with the unique maximal ideal and an application to elementary operators is given.
How Intricate are (2s + 1)-Factorizations?
Authors: Hilton A. J. W.
Published: December 2010

The intricacy of the problem of (2s + 1 )-factorizating Kn is determined. Some generalizations are also given.
On the Semigroup of Probability Measures of a Locally Compact Semigroup II
Authors: Wong James C. S.
Published: December 2010

This is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.
Lie Derivations on Skew Elements in Prime Rings With Involution
Authors: Killam Eleanor
Published: December 2010

Let R be a prime ring with involution satisfying x/2 ∊ R whenever x ∊ R. Assume that R has two nontrivial symmetric idempotents e1, e2 whose sum is not 1, and that the subrings determined by e1, e2, 1 — (e1 + e2) are not orders in simple rings of dimension at most 4 over their centers. Then if L is a Lie derivation of the skew elements K into R there exists a subring A of R, A ⊆ , a derivation D :A → RC, the central closure of R, and a mapping T:R → C, satisfying L = D + T on K and = 0.
H-Simple H-Module Algebras
Authors: Cohen Miriam
Published: December 2010

Let A be an H-simple commutative H-module algebra, with AH = k and dimk H ≤ dimk A < ∞. We show that this implies that A # H is isomorphic to Mn(k), a central simple algebra. We apply this to characterize certain group graded algebras, algebras acted upon by a group as automorphisms, or by a nilpotent Lie algebra as derivations.
Derivatives and Length-Preserving Maps
Authors: Yamashita Shinji
Published: December 2010

Let a be a constant, |a| = 1. We shall prove meromorphic (M) and bounded-holomorphic (BH) versions of the following prototype: (P) Let f and g be holomorphic in a domain D. Then, |f'| = |g'| in D if and only if there exist constant a, b with f = ag + b in D. (M) Let f and g be meromorphic in D. Then, |f'|/(1 + |f|2) = |g'|/(1 + |g|2) in D if and only if there exist a, b with |b| ≦ ∞ such that f = a(g - b)/(\ + g). (BH) Let f and g be holomorphic and bounded, |f| < 1, |g| < 1, in D. Then, |f'|/ (1 - |f|2) = |g'|/(1 - |g|2) in D if and only if there exist a, b with |b| < 1, such that f = a(g - b)/(1 - g).
H-Semidirect Products
Authors: Peschke Georg
Published: December 2010

The concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.
The Action of the Dickson Invariants on Length n Steenrod Operations
Authors: Kulich James
Published: December 2010

The purpose of this paper is to give an explicit formula for the action of the n dimensional Dickson invariants on the admissible mod 2 Steenrod operations of length n.
On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial
Authors: Rahman Q. I. , Tariq Q. M.
Published: December 2010

Let P be a polynomial of degree n having all its zeros in the closed unit disk. Given that a is a zero (of P) of multiplicity k we seek to determine the radius ρ(n; k; a) of the smallest disk centred at a containing at least k zeros of the derivative P'. In the case k = 1 the answer has been conjectured to be 1 and is known to be true for n ≦ 5. We prove that ρ(n; k; a) ≦ 2k/(k + 1) for arbitrary k ∊ N and n ≦ k + 4.
Convolution with Odd Kernels Having a Tempered Singularity
Authors: Kerman R. A.
Published: December 2010

Suppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), by

Then, for a large class of b one has the rearrangement inequality

This inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.
On Quasisimilarity for Analytic Toeplitz Operators
Authors: Takahashi Katsutoshi
Published: December 2010

Let f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf.
Torsion-free Abelian Groups, Valuations and Twisted Group Rings
Authors: Bastos Gervasio G. , Viswanathan T. M.
Published: December 2010

Anderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.
On the Cardinality of Urysohn Spaces
Authors: Bella A. , Cammaroto F.
Published: December 2010

In this paper some cardinal inequalities for Urysohn spaces are established. In particular the following two theorems are proved:

(i)If where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;

(ii), where aL(X, X) is the smallest cardinal number m such that for every open cover of X there is a subfamily for which
Continuité des Caractères Dans les Algèbres de Fréchet à Bases
Authors: Akkar M. , El Azhari M. , Oudadess M.
Published: December 2010

In [1] and [2] T. Husain and J. Liang show the following results: RI. Every character on a Fréchet algebra with a Schauder basis (xi)i≧1 such that: (1) XiXj = XjXi = Xj if i ≦ j, (2) Pi(Xi) ≠ 0 and Pi(xi+1) = 0 (where (pi)i≧1 is a denumerable family of semi-norms defining the topology of the algebra) is continuous. R2. Every character on a Fréchet algebra with orthogonal and unconditional Schauder basis is continuous. The proofs of these last results are very long and introduce complex calculation without aid of spectral theory of locally ra-convex algebras. We give here short proofs of these results with aid of a characterization of elements of the spectrum in locally m-convex algebras with values of characters.
Sums of Multinomial Coefficients
Authors: Fixman Uri
Published: December 2010

Σ q!/(h1! . . . hn!) with h1 + . . . + hn = q, the first a hj’s odd and the rest even, is expressed in terms of values of Krawtchouk polynomials.
A Note on a Theorem on Lattices in Lie Groups
Authors: Wu T. S.
Published: December 2010

The aim of this note is to clarify some statements in the book: Discrete Subgroups of Lie groups: Springer, 1972.
Further Theorems of the Rogers-Ramanujan Type Theorems*
Authors: Subbarao M. V. , Agarwal A. K.
Published: December 2010

We give three new partition theorems of the classical Rogers-Ramanujan type which are very much in the style of MacMahon. These are a continuation of four theorems of the same kind given recently by the second author. One of these new theorems, very similar to one of the original Rogers-Ramanuj an - MacMahon type theorems is as follows: Let C(n) denote the number of partitions of n into parts congruent to ±2, ± 3, ±4, ± 5, ±6, ±7 (mod 20). Let D(n) denote the number of partitions of n of the form n = b1 + b2 + … + bt, where bt ≧ 2, bt ≧ bi + 1 and if 1 ≦ i ≦ [(t - 2)/2], bi - bi + 1 ≧ 2. Then C(n) = D(n).
On Steenrod Bundles and the van Kampen Theorem
Authors: Lundsgaard Hansen Vagn
Published: December 2010

We present a general method based on the van Kampen theorem for computing the fundamental group of the total space in certain Steenrod bundles. The method is applied to mapping spaces and Grassmann bundles.
Characterizations of Axiomatic Categories of Models Canonically Isomorphic to (Quasi-)Varieties
Authors: Hébert Michel
Published: December 2010

Letbe the category of all homomorphisms (i.e. functions preserving satisfaction of atomic formulas) between models of a set of sentencesTin a finitary first-order languageL.Functors between two such categories are said to becanonicalif they commute with the forgetful functors. The following properties are characterized syntactically and also in terms of closure offor some algebraic constructions (involving products, equalizers, factorizations and kernel pairs): There is a canonical isomorphism fromto a variety (resp. quasivariety) in a finitary expansion ofLwhich assigns to a model its (unique) expansion. This solves a problem of H. Volger.

In the case of a purely algebraic language, the properties are equivalent to:“is canonically isomorphic to a finitary variety (resp. quasivariety)” and, for the variety case, to “the forgetful functor ofis monadic (tripleable)”.
Quadratic forms and Linkage of Quaternion Algebras
Authors: Krishnamani Vatsala , Yucas Joseph
Published: December 2010

A field F satisfies n-linkage on a subset of Ḟ if whenever the quaternion algebras

are equal in Br(F) there exist z ∈ Ḟ with

for i = 1, 2, . . ., n. This linkage of quaternion algebras is examined and its relationship to the torsion freeness of I2(F) and to the strong approximation property is investigated.
Plans' Theorem for Links: an Application of tk Moves
Authors: Przytycki Józef H.
Published: December 2010

We use tk moves on links to prove that the first homology group with Z2-coefficients of an odd sheeted cyclic cover of S3 branched over a link is even dimensional.
Stability Theorems for Convex Domains of Constant Width
Authors: Groemer H.
Published: December 2010

It is known that among all plane convex domains of given constant width Reuleaux triangles have minimal and circular discs have maximal area. Some estimates are given concerning the following associated stability problem: If K is a convex domain of constant width w and if the area of K differs at most ∊ from the area of a Reuleaux triangle or a circular disc of width w, how close (in terms of the Hausdorff distance) is K to a Reuleaux triangle or a circular disc? Another result concerns the deviation of a convex domain M of diameter d from a convex domain of constant width if the perimeter of M is close to πd.
Isomorphisms of Prime Goldie Semi-Principal Left Ideal Rings, II
Authors: Wolfson Kenneth G.
Published: December 2010

A prime Goldie ring K, in which each finitely generated left ideal is principal is the endomorphism ring E(F, A) of a free module A, of finite rank, over an Ore domain F. We determine necessary and sufficient conditions to insure that whenever K ≅ E(F, A) ≅ E(G, B) (with A and B free and finitely generated over domains F and G) then (F, A) is semi-linearly isomorphic to (G, B). We also show, by example, that it is possible for K ≅ E(F, A ) ≅ E(G, B), with F and G, not isomorphic.
A Multilinear Young's Inequality
Authors: Oberlin Daniel M.
Published: December 2010

We prove an (n + l)-linear inequality which generalizes the classical bilinear inequality of Young concerning the LP norm of the convolution of two functions.
Primary Decomposition for Σ-Groups
Authors: Brunker Don , Higgs Denis
Published: December 2010

A Σ-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its p-components carries over to the case of Σ-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of Σ-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.
Decompositions of Localized Fibres and Cofibres
Authors: Oprea John
Published: December 2010

In this paper p-local versions of the Rational Fibre and Cofibre Decomposition Theorems are given. In particular, if there exists an element in the nth Gottlieb group of a space F such that its image under the Hurewicz map has infinite order, then Sn for almost all primes p. A dual result is proved for cofibrations.
Sufficient Conditions for the Oscillation of Delay and Neutral Delay Equations
Authors: Grove E. A. , Ladas G. , Schinas J.
Published: December 2010

We established sufficient conditions for the oscillation of all solutions of the delay differential equation

and of the neutral delay differential equation

where p, q, r and a are nonnegative constants and n is an odd natural number.
Efficient Presentations of the Groups PSL(2, 2p) and SL(2, 2p)
Authors: Robertson E. F. , Williams P. D.
Published: December 2010

Presentations which have a minima] number of defining relations are given for the groups SL(2, 2p) and PSL(2, 2p) where p is a prime greater than 3.
On the Residual Finiteness of Certain Polygonal Products
Authors: Allenby R. B. J. T. , Tang C. Y.
Published: December 2010

We give examples to show that unlike generalized free products of groups (g.f.p.) polygonal products of finitely generated (f.g.) nilpotent groups with cyclic amalgamations need not be residually finite (R) and polygonal products of finite p-groups with cyclic amalgamations need not be residually nilpotent. However, polygonal products f.g. abelian groups are R, and under certain conditions polygonal products of finite p-groups with cyclic amalgamations are R.
A Note on Blaschke Products with Zeroes in a Nontangential Region
Authors: Jevtić Miroljub
Published: December 2010

We show that if B is α Blaschke product with nontangential zero set {zk} and 0 < p < 1, 1/2 < αp < 1, then the condition sup0<r<1(l — r) Mp(r, D1+αB) < ∞ is equivalent to the condition {(1 - |zk|(1/p)-αKα} ∊ l∞.
Bireflectionality in Absolute Geometry
Authors: Ljubić Dragoslav
Published: December 2010

If G is any group then g ∊ G is called an involution if g ≠ 1 and g o g = 1. A group G is called bireflectional if every element in G is a product of two involutions. It is known that 2- dimensional, 3- dimensional, and some types of n-dimensional (n > 3) absolute geometries (in the sense of H. Kinder) are bireflectional. In this article the author proves the general result that every n-dimensional absolute geometry is bireflectional.
Cauchy Completion Categories
Authors: Kent D. C. , Richardson G. D.
Published: December 2010

A general procedure is introduced for identifying categories of Cauchy spaces which have completions which possess a certain convergence property P, and for constructing completion functors on such categories. These results are applied to obtain a characterization of Cauchy spaces which allow T3 completions, and to construct T3 completions for categories of Cauchy groups and Cauchy lattices.
A Stochastic Ergodic Theorem for General Additive Processes
Authors: Çömez Doḡan
Published: December 2010

In this article, we obtain the stochastic ergodic theorem for general additive processes. That is, we prove that there exists , such that whenever α > 0 and A is a measurable set with μ(A) < ∞, where and {U(ij)}} an arbitrary (two dimensional) semigroup of L1 -contractions. This result generalizes the stochastic ergodic theorem (SET) of U. Krengel and the SET of M. A. Akcoglu and L. Sucheston.
Sur une Propriete des Fonctions Propres de L'Operateur de Laplace-Beltrami
Authors: Chipot M. , Oliker V.
Published: December 2010

Si M est une variété riemannienne de dimension n, n ≧ 2, et de métrique g on s'intéresse au problème: trouver toutes les fonctions régulières F : M → IR qui sont valeurs propres ainsi que leur carré de l'opérateur de Laplace-Beltrami, Δ, associé à g.
A Remark on the Loewy-Series of Certain Hopf Algebras
Authors: Röhl Frank
Published: December 2010

An easy proof will be given to show that for finite dimensional Hopf-algebras with nilpotent augmentation ideal over the field of p elements, the upper and lower Loewy-series coincide. In particular, this holds for the restricted universal envelope of nilpotent Lie-p-algebras with
nilpotent p-map.
Grammar as Mathematics
Authors: Lambek J.
Published: December 2010

While there are a small number of reasonably deep theorems in mathematical linguistics, I wish to argue that grammar is mathematics at a very basic level, albeit "trivial" mathematics. Linguistic activities such as the production and recognition of sentences are quite analogous to the mathematical activities of proving theorems or making calculations, while learning a language involves something akin to the discovery or invention of postulates.
Conformally Flat Riemannian Manifolds as Hypersurfaces of the Light Cone
Authors: Asperti A. C. , Dajczer M.
Published: December 2010

Simply connected conformally flat Riemannian manifolds are characterized as hypersurfaces in the light cone of a standard flat Lorentzian space, transversal to its generators. Some applications of this fact are given.
Convolution Orthogonality and the Jacobi Polynominals
Authors: Allaway Wm. R.
Published: December 2010

Let α and β be any two real numbers and let be the Jacobi polynomial sequences. For any non-zero real number a, is an orthogonal polynomial sequence with respect to convolution if and only if either (i) b = 1, α = 0 and β + 1 is not equal to a negative integer or (ii) b = — 1, β = 0 and α + 1 is not equal to a negative integer.
On Takagi Fractal Surfaces
Authors: Dubuc Benoit
Published: December 2010

This paper presents a new type of fractal surfaces called the Takagi surfaces. These are obtained by summing up pyramids of increasing (doubling) frequencies scaled by a geometric ratio b. The fractal dimension (box dimension) of the graph of these functions is shown to be log 8b/log 2.
A Characterization of a Sparse Blaschke Product
Authors: Guillory Carroll
Published: December 2010

We give a characterization of a sparse Blaschke product b in terms of the separation of support sets of its zeros in M(H∞ + C) and the structure of the nonanalytic points. We use this characterization to give a sufficient condition on an interpolating Blaschke product q to have the following property: there exists a non trivial Gleason part P on which q is nonzero and less than one.
Differential Equation for Classical-Type Orthogonal Polynomials
Authors: Ronveaux A. , Marcellan F.
Published: December 2010

The second order differential equation of Littlejohn-Shore for Laguerre type orthogonal polynomials is generalized in two ways. First the positive Dirac mass can be situated at any point and secondly the weight can be any classical weight modified by an arbitrary number of Dirac distributions.
On B4-Sequences
Authors: Nash John C. M.
Published: December 2010

In [2], Erdös showed that the counting function A(n) of a B2-sequence satisfies Here it is shown that A(n) satisfies an analogous relationship for B4-sequences!
On Spaces of Compact Operators in Non-Archimedean Banach Spaces
Authors: Kiyosawa Takemitsu
Published: December 2010

Let K be a non-trivial complete non-Archimedean valued field and let E be an infinite-dimensional Banach space over K. Some of the main results are:

(1) K is spherically complete if and only if every weakly convergent sequence in l∞ is norm-convergent.

(2) If the valuation of K is dense, then C0 is complemented in E if and only if C(E,c0) is n o t complemented in L(E,c0), where L(E,c0) is the space of all continuous linear operators from E to c0 and C(E,c0) is the subspace of L(E, c0) consisting of all compact linear operators.
Sur les Sous-Groupes Purifiables des Groupes Abéliens Primaires
Authors: Benabdallah K. , Piché C.
Published: December 2010

The class of primary abelian groups whose subsocles are purifiable is not yet completely characterized and it contains the class of direct sums of cyclic groups and torsion complete groups. In sharp constrast with this, the class of groups whose p2-bounded subgroups are purifiable consist only of those groups which are the direct sum of a bounded and a divisible group. Various tools are developed and a short application to the pure envelopes of cyclic subgroups is given in the last section.
Some Special Conjugacy Closed Loops
Authors: Goodaire Edgar G. , Robinson D. A.
Published: December 2010

Some equationally defined classes of loops are identified and characterized among a class of loops which are isomorphic to all of their loop isotopes.
A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
Authors: Li Chengzhi , Rousseau Christiane , Wang Xian
Published: December 2010

We show that the Bogdanov-Takens system has at most one limit cycle. Similarly we show that the maximum number of limit cycles in the universal unfolding of the symmetric cusp of order 2 (resp. 3) is one (resp. 2). The proof uses the elementary technique of Liénard's equation, yielding a global result for all values of the parameters.
Sur les Fonctions Analytiques Multiformes dont les Valeurs Sont des Segments
Authors: Baribeau Une
Published: December 2010

Analytic multivalued functions are a powerful tool in spectral theory. In this paper we study analytic multivalued functions λ → K(λ) whose values are segments. Under the additional assumption that K is continuous, we prove that the endpoints of K vary locally holomorphically.
Can a Semi-Prime Ring be a Finite Union of Right Annihilators?
Authors: Lanski Charles
Published: December 2010

The interesting question of the title was posed by J. Bergen and this note answers it in the negative. The main result characterizes rings which can be a finite union of proper right annihilators, and shows that any such commutative ring must have a total annihilator.
Distribution of Weierstrass Points on Rational Cuspidal Curves
Authors: Little John B.
Published: December 2010

We study the set W(𝓛) of Weierstrass points of all positive tensor powers of an invertible sheaf 𝓛 on an irreducible rational curve X with g ≧ 2 ordinary cusps. Using an idea from B. Olsen's study of the analogous question on smooth curves, and an explicit formula for the "theta function" of a cuspidal rational curve, we show that W(𝓛) is never dense on X (in contrast to the case of smooth curves of genus g ≧ 2).
Product of Two Commutators as a Square in a Free Group
Authors: Comerford Jonell A. , Lee Y.
Published: December 2010

We show that, if [s,t][u, v] = x2 in a free group, x need not be a commutator. We arrive at our example by use of a result of D. Piollet which characterizes solutions of such equations using an algebraic interpretation of the mapping class group of the corresponding surface.
A Homotopical Conner-Raymond Theorem and a Question of Gottlieb
Authors: Oprea John
Published: December 2010

A homotopy theoretic version is given of the following result of Conner and Raymond: If the circle acts on a space so that the orbit map induces an injection in homology, then the space fibres over the circle with finite structure group. This homotopical analogue is related to recent results pertaining to the effect of the fundamental group's structure on the Euler characteristic. It is also used in the construction of a compact, simple 7-manifold with trivial Gottlieb group which, together with an infinite dimensional example of Ganea, answers a question of Gottlieb.
Proof of a Conjecture of Chowla and Zassenhaus on Permutation Polynomials
Authors: Cohen Stephen D.
Published: December 2010

The following conjecture of Chowla and Zassenhaus ( 1968) is proved. If f(x) is an integral polynomial of degree ≧ 2 and p is a sufficiently large prime for which f (considered modulo p) is a permutation polynomial of the finite prime field Fp, then for no integer c with 1 ≦ c < p is f(x) + cx a permutation polynomial of Fp.
On Products of Conditional Expectation Operators
Authors: Zaharopol Radu
Published: December 2010

Let (X, Σ, μ) be a probability space, let f1, f2, ..., Fk be k σ-subalgebras of Σ, and let p ∊ R be such that 1 < p < + ∞. Let Pi :LP(X, Σ, μ) → LP(X, Σ, μ) be the conditional expectation operator corresponding to fi for every i = 1,2,…, k, and set T = P1 . . . Pk. Our goal in the note is to give a new and simpler proof of the fact that for every f ∊ LP(X, Σ, μ), the sequence (Tnf)n∊N converges in the norm topology of LP(X, Σ, μ), and that its limit is the conditional expectation of f with respect to f1 ∩ f2 ∩ … ∩ Fk.
Sur la Non Compatibilité de l'Equivalence de Calkin Avec le Calcul Fonctionnel de Nagy-Foias
Authors: Esterle J. , Zarouf F.
Published: December 2010

Nous montrons qu'il existe deux contractions T1 et T2 de classe C0 telles que T1 — T2 soit compact et une fonction intérieure h telle que h(T1) — h(T2) soit non compact.
A Note on Relations Between the Zeta-Functions of Galois Coverings of Curves Over Finite Fields
Authors: Pacheco Amilcar
Published: December 2010

Let C be a complete irreducible nonsingular algebraic curve defined over a finite field k. Let G be a finite subgroup of the group of automorphisms Aut(C) of C. We prove that certain idempotent relations in the rational group ring Q[G] imply other relations between the zeta-functions of the quotient curves C/H, where H is a subgroup of G. In particular we generalize some results of Kani in the special case of curves over finite fields.
On a Relationship Between Adjoint Orbits and Conjugacy Classes of a Lie Group
Authors: Wildberger N. J.
Published: December 2010

Let G be a Lie group with adjoint orbits θi and corresponding conjugacy classes Ci = exp θi, i = 1, 2, 3. We show that if G is nilpotent or compact, there is a neighbourhood U of 0 in g such that if θi ∊ U then θ3 ⊂ θ1 + θ2 if and only if C3 ⊂ C1C2.
Oscillation Theorems for Delay Differential Equations via Laplace Transforms
Authors: Györi I. , Ladas G. , Pakula L.
Published: December 2010

Sufficient conditions for the oscillation of all solutions of the delay differention equation (1) below are obtained.
Hurwitz Groups and G2(q)
Authors: Malle Gunter
Published: December 2010

Finite factor groups of are called Hurwitz groups. Here we prove that apart from 2G2(3), G2(2), G2(3) and G2(4), all the groups 2G2(32n+1) and G2(q), q = pn, p € P, are Hurwitz groups. For the proof, (2, 3, 7) structure constants are calculated from the character tables [2], [7], and then with the lists of maximal subgroups [8], [5], the existence of generating triples is deduced.
A Comparison of Eigenvalues of Two Sturm-Liouville Problems
Authors: Yang Yisong
Published: December 2010

We compare, under some assumptions on mass density, the eigenvalues of the Sturm-Liouville problems satisfying homogeneous Dirichlet and Neumann boundary condition.
Vector Invariants of Symmetric Groups
Authors: Campbell H. E. A. , Hughes I. , Pollack R. D.
Published: December 2010

Let M be a free module of rank n over a commutative ring R with unit and let Σn denote the symmetric group acting on a fixed basis of M in the usual way. Let Mm denote the direct sum of m copies of M and let S be the symmetric ring of Mm over R. Then each element of Σn acts diagonally on Mm and consequently on S; denote by Xn the subgroup of Gl(Mm) so defined. The ring of invariants, SΣn, is called the ring of vector invariants by H. Weyl [ 3, Chapter II, p. 27] when R = Q. In this paper a set of generators valid over any ring R is given. This set of generators is somewhat larger than Weyl's. It is interesting to note that, over the integers, his algebra and SΣn have the same Hilbert-Poincaré series, are equal after tensoring with the rationals, and have the same fraction fields, although they
are not equal.
Pseudo-Integrality
Authors: Anderson David F. , Houston Evan G. , Zafrullah Muhammad
Published: December 2010

Let R be an integral domain. An element u of the quotient field of R is said to be pseudo-integral over R if uIv ⊆ Iv for some nonzero finitely generated ideal I of R. The set of all pseudo-integral elements forms an integrally closed (but not necessarily pseudo-integrally closed) overling R ofR. It is shown that , where X is a family of indeterminates; pseudo-integrality is analyzed in rings of the form D + M; and an example is given to show that pseudo-integrality does not behave well with respect to
localization.
On Superrecurrence
Authors: Dajani Karma
Published: December 2010

Let T be a non-singular, conservative, ergodic automorphism of a Lebesgue space. We study a kind of weighted cocycles called H-cocycles. We introduce the notions of H-superrecurrence and H-supertransience. We use skew products to give necessary and sufficient conditions for H-superrecurrence.
Generalized Fermat's Problem
Authors: Noda R. , Sakai T. , Morimoto M.
Published: December 2010

The following problem is studied. Generalized Fermat's problem: in an n-dimensional Hadamard manifold M, locate a point whose distances from the given k vertices of M have the smallest possible sum.
Stable Rank and the -Equation
Authors: Rupp Rudolf
Published: December 2010

Let G denote a plane domain bounded by finitely many closed, non-intersecting Jordan curves. We show the following refinement of the stable rank one property of : Suppose that for there exists δ > 0 such that . Then there exist such that

f + hg = exp (k).

Also we obtain a partial result for the algebra H∞(G).
The Parity Distribution of Traces in Imaginary Quadratic Fields
Authors: Dummit D. S.
Published: December 2010

Computations of the Iwasawa λ -invariant for imaginary quadratic fields showed a discrepancy in the proportion of even and odd traces of certain integers from these imaginary quadratic fields. This paper shows that such a discrepancy is in some sense to be expected and that the proportion of even and odd traces of principal generators of powers of prime ideals in imaginary quadratic fields is related to the 3-primary component of the class group.