bluuebunny/crossref_metadata_2025 huggingface dataset:
Rational solutions of linear differential equations
Authors: Bezivin J.-P. , Robba P.
Published: April 2009

LetLbe a linear differential operator with rational coefficients such that 0 is not an irregular singularity ofLand that for sufficiently manyp's the equationLv= 0 has no zero solution modp. We show that ifuis a formal power series whose coefficients are p-adic integers for almost allpand ifLuis rational, thenutoo is rational.
The asymmetric product of three inhomogeneous linear forms
Authors: Grover V. K.
Published: April 2009

Let Λ be a lattice in R3 of determinant 1. Define the homogeneous minium of Λ as mn (Λ) = inf |u1, u2, u3| extended over all points (u1, u2, u3) of Λ other than the origin. It is shown that for any given (c1, c2, c3) in R3 there exists a point (u1, u2, u3) of Λ for which provided that ρσ > 1/64 if mn (Λ) = 0, and ρσ ≥1/16.81 if mn (A) > 0.
Fractional powers of generators of equicontinuous semigroups and fractional derivatives
Authors: Lanford Oscar E. , Robinson Derek W.
Published: April 2009

We analyze fractional powersHα, α > 0, of the generatorsHof uniformly bounded locally equicontinuous semigroupsS. TheHαare defined as the αth derivative δαof the Dirac measure δ evaluated onS. We demonstrate that theHαare closed operators with the natural properties of fractional powers, for example,HαHβ=Hα+βfor α, β > 0, and (Hα)β=Hαβfor 1 > α > 0 and β > 0. We establish thatHα can be evaluated by the Balakrishnan-Lions-Peetre algorithmwheremis an integer larger than α,Cα, mis a suitable constant, and the limit exists in the appropriate topology if, and only if,x ∈ D(Hα). Finally we prove thatH∈is the fractional derivation ofSin the sensewhere the limit again exists if, and only if,x∈ D(Hα).
Archimedes integrals and conuclear spaces
Authors: Jefferies B. , Okada S.
Published: April 2009

The lack of completeness with respect to the semivariation norm, of the space of Banach space valued functions, Pettis integrable with respect to a measure μ, often impedes the direct extension of results involving integral representations, true in the finite-dimensional setting, to the general vector space setting. It is shown here that the space of functions with values in a space Y, μ-Archimedes integrable in a Banach space X embedded in Y, is complete with respect to convergence in semivariation, provided the embedding from X into Y is completely summing. The result is applied to the case when Y is a conuclear space, in particular, when X is a function space continuously included in a space of distributions.
On the arithmetic properties of the values of G-functions
Authors: Väänänen K. , Guangshan Xu
Published: April 2009

In a recent paper Chudnovsky considered the arithmetic properties of certain values of classical Siegel G-function solutions of a system of linear homogeneous differential equations without any restrictive conditions. The present paper generalizes some results of Chudnovsky in both the archimedian and the p-adic case.
A construction for Fitting formations II
Authors: Cossey John
Published: April 2009

A construction for Fitting formations given by the author and C. L. Kanes is generalised. The original examples were based on the use of Fitting families of modules over algebraically closed fields. An example of Haberl and Heineken in 1984 suggested that the methods should work with modules over arbitrary fields. We show that this is indeed the case, provided we restrictthe class of groups considered.
Boolean near-rings and weak commutativity
Authors: Hansen D. J. , Luh Jiang
Published: April 2009

It is shown that every boolean right near-ring R is weakly commutative, that is, that xyz = xzy for each x, y, z ∈ R. In addition, an elementary proof is given of a theorem due to S. Ligh which states that a d.g. boolean near-ring is a boolean ring. Finally, a characterization theorem is given for a boolean near-ring to be isomorphic to a particular collection of functions which form a boolean near-ring with respect to the customary operations of addition and composition of mappings.
Generalized differentiability for a class of nondifferentiable operators with applications to nonsmooth optimization
Authors: Reiland Thomas W.
Published: April 2009

A theory of generalized gradients is presented for a class of Lipschitz vector-valued mappings from a Banach space to a locally convex order complete vector lattice. Necessary optimality conditions are obtained for nonconvex programming problems on Banach spaces with vector- valued operator constraints and/or an arbitrary set constraint. Sufficient optimality conditions are also obtained under mild convexity assumptions.
The existence of a class of Kirkman squares of index 2
Authors: Lamken E. R. , Vanstone S. A.
Published: April 2009

A Kirkman square with index λ, latinicity μ, block size k and ν points, KSk(v; μ, λ), is a t × t array (t = λ(ν−1)/μ(k − 1)) defined on a ν-set V such that (1) each point of V is contained in precisely μ cells of each row and column, (2) each cell of the array is either empty or contains a k-subset of V, and (3) the collection of blocks obtained from the nonempty cells of the array is a (ν, k, λ)-BIBD. For μ = 1, the existence of a KSk(ν; μ, λ) is equivalent to the existence of a doubly resolvable (ν, k, λ)-BIBD. In this case the only complete results are for k = 2. The case k = 3, λ = 1 appears to be quite difficult although some existence results are available. For k = 3, λ = 2 the problem seems to be more tractable. In this paper we prove the existence of a KS3(ν; 1, 2) for all ν ≡ 3 (mod 12).
Graphs whose full automorphism group is a symmetric group
Authors: Liebeck Martin W.
Published: April 2009

We address the problem of describing all graphs Γ such that Aut Γ is a symmetric group, subject to certain restrictions on the sizes of the orbits of Aut Γ on vertices. As a corollary of our general results, we obtain a classification of all graphs Γ on v vertices with Aut Γ ≅ Sn, where ν < min{5n, ½n(n – 1)}.
Some limit theorems for continuous-state branching processes
Authors: Pakes Anthony G
Published: April 2009

The most general continuous time and state branching (C.B.) process (Xt) can be constructed as a certain random time transformation of a spectrally positive Levy process. When the generating process is compound Poisson with a superimposed negative linear drift and the C.B. process is not supercritical, then there is a random timeTsuch thatXt+T= e-ctXTwherec> 0 is the drift parameter. ThusTis the last epoch of random variation.
On a class of finite groups
Authors: Wamsley J. W.
Published: April 2009

Let G be a finite P-group. Denote dim H1 (G, Zp) by d(G) and dimH2(G, Zp) by r(G), then d(G) is the minimal number of generators of G and G has a presentation where F is free on x1, …, xd(G) and R is the normal closure in F of R1, …, Rm. We have always that m ≧ r(G) = d(R/[F, R]) and we say that G belongs to a class, Gp, of the finite pgroups if m = r(G). It is well known (see for example Johnson and Wamsley (1970)) that if G and H are finite p-groups then r(G x H) = r(G) + r(H) + d(G)d(H) and hence G, H∈Gp implies Gx H∈Gp, also it is shown in Wamsley (1972) that if G is any finite pgroup then there exists an H∈Gp such that G x H belongs to Gp. Let G1 = G and Gk = Gk-1 x G then we show in this note that if G is any finite p-group, there exists an integer n(G), such that Gk∈Gp for alal k ≧ n(G).
An example for homotopy commutativity of h-spaces
Authors: Williams F. D.
Published: April 2009

In this note we give an example of a homotopy commutative H-space X that is not dominated by any homotopy associative, homotopy commutative H-space. In particular, X is not dominated by Ω2S2X.
Characterization of finite amenable transformation semigroups: corrigendum
Authors: Wilde C. O.
Published: April 2009

Theorem 6 of Wilde (1971) is in error. Følner's condition is necessary, but not sufficient, for amenability of a τ-semigroup. For clearly sufficiency would imply that every finite τ-semigroup is amenable, and the simple example on p. 503 of Wilde (1971) shows that this is not so. We refer the reader to Namioka (1964) for a lucid explanation of the fundamental ideas involved.
Maps into Dynkin diagrams arising from regular monoids
Authors: Augustine M. K. , Putcha Mohan S.
Published: April 2009

It has been shown by one of the authors that the system of idempotents of monoids on a group G of Lie type with Dynkin diagram Γ can be classified by the following data: a partially ordered set U with maximum element 1 and a map λ: U → 2Γ with λ(1) = Γ and with the property that for all J1, J2, J3 ∈ U with J1 > J2 > J3, any connected component of λ(J2) is contained in either λ(J1) or λ(J3). In this paper we show that λ comes from a regular monoid if and only if the following conditions are satisfied: (1) U is a ∧-semilattice; (2) If J1, J2 ∈ U, then λ(J1)∧ λ(J2) λ(J1 ∧ J2); (3) If θ ∈ Γ, J ∈ U, then max{J1 ∈ U|J1 > J, θ ∈ λ (J1)} exists; (4) If J1, J2 ∈ U with J1 > J2 and if X is a two element discrete subset of λ(J1) ∪ λ(J2), then X λ(J) for some J ∈ UJ with J1 > J > J2.
On conjugacy p-separability of free centre-by-metabelian groups
Authors: Gupta C. K. , Gupta N. D. , Levin F.
Published: April 2009

A group G is said to be conjugacy p-separable if two non-conjugate elements of G remain non-conjugate in some finite p-group endomorphic image of G. We show that the non-cyclic free centre-by-metabelian groups are not conjugacy p-separable for any prime p. On the other hand, we show that every free centre-by-metabelian group has the solvable conjugacy problem
On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes
Authors: Ecker Klaus
Published: April 2009

We prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.
Topologically rigid non-Haken 3-manifolds
Authors: Hass J. , Menasco W.
Published: April 2009

A closed irreducible 3-manifold M is topologically rigid if any homotopy equivalent irreducible 3-manifold is homeomorphic to M. A construction is given which produces infinitely many non-Haken topologically rigid 3-manifolds
Roots of unity and the character variety of a knot complement
Authors: Cooper D. , Long D. D.
Published: April 2009

Using elementary methods we give a new proof of a result concerning the special form of the character of the bounded peripheral element which arises at an end of a curve component of the character variety of a knot complement.
On a Converse to the Tscgebotarev density theorem
Authors: Van Der Ploeg C. E.
Published: April 2009

Using an elementary counting procedure on biquadratic polynomials over Zp it is shown that the probability distribution of odd, unramified rational primes according to decomposition type in a fixed dihedral numberfield is identical to the probility of separable quartic polynomials (mod p) whose roots generate numberfields with normal closure having Galois group isomorphic to D4, as p → ∞. This verifies a conjecture about a converse to the Tschebotarev density theorem. Further evidence in support of this conjecture is provided in quadratic and coubic numberfields.
Some inequalities that arise in measure theory
Authors: Brown Gavin
Published: April 2009

The Lebesgue measure, λ (E + F), of the algebraic sum of two Borel sets, E, F of the classical “middle-thirds’ Cantor set on the circle can be estimated by evaluating the Cantor meaure, μ of the summands. For example log λ (E + F) exceeds a fixed scalar multiple of log μ (E)+ log μ (F). Several numerical inequalities which are required to prove this and related results look tantalizingly simple and basic. Here we isolate them from the measure theory and present a common format and proof.
Regularity of mean-values
Authors: Meaney Christopher
Published: April 2009

LetXbe either thed-dimensional sphere or a compact, simply connected, simple, connected Lie group. We define a mean-value operator analogous to the spherical mean-value operator acting on integrable functions on Euclidean space. The value of this operator will be written as ℳf(x, a), wherex∈Xandavaries over a torusAin the group of isometries ofX. For each of these cases there is an intervalpO<p≦ 2, where thep0depends on the geometry ofX, such that iffis inLp(X) then there is a set full measure inXand ifxlies in this set, the function a ↦ℳf(x, a) has some Hölder continuity on compact subsets of the regular elements ofA.
The isometries of Hp(K)
Authors: Lin Pei-Kee
Published: April 2009

Let 1 ≤ p < ∞, p ≠ 2 and let K be any complex Hilbert space. We prove that every isometry T of Hp(K) onto itself is of the form , where U ia a unitary operator on K and φ is a conformal map of the unit disc onto itself.
Full C*-Crossed product duality
Authors: Quigg John C.
Published: April 2009

Takai duality for full C*-crossed products holds for twisted actions in the sense of Green and fails for coactions.
The characterization problem for endomorphism rings
Authors: García J. L.
Published: April 2009

We consider the problem of characterizing by abstract properties the rings which are isomorphic to the endomorphism ring End (RF) of some free module F over a ring R in a given class R of rings. We solve this problem when R is any class of rings (by employing topological notions) and when R is the class of all the left Kasch rings (in terms of algebraic properties only).
On weighted inductive limits of spaces of Fréchet-valued continuous functions
Authors: Galbis Antonio
Published: April 2009

In this article we continue the study of weighted inductive limits of spaces of Fréchet-valued continuous functions, concentrating on the problem of projective descriptions and the barrelledness of the corresponding “projective hull”. Our study is related to the work of Vogt on the study of pairs (E, F) of Fréchet spaces such that every continuous linear mapping from E into F is bounded and on the study of the functor Ext1 (E, F) for pairs (E, F) of Fréchet spaces.
A subspace theorem for ordinary linear differential equations
Authors: Miller Alice Ann
Published: April 2009

The study of the S-unit equation for algebraic numbers rests very heavily on Schmidt's Subspace Theorem. Here we prove an effective subspace theorem for the differential function field case, which should be valuable in the proof of results concerning the S-unit equation for function fields. Theorem 1 states that either has a given upper bound where are linearly independent linear forms in the polynomials with coefficients that are formal power series solutions about x = 0 of non-zero differential equations and where Orda denotes the order of vanishing about a regular (finite) point of functions ƒk, i: (k = 1, n; i = 1, n) or lies inside one of a finite number of proper subspaces of (K(x))n. The proof of the theorem is based on the wroskian methods and graded sub-rings of Picard-Vessiot extensions developed by D. V. Chudnovsky and G. V. Chudnovsky in their function field analogues of the Roth and Schmidt theorems. A brief discussion concerning the possibility of a subspace theorem for a product of valuations including the infinite one is also included.
On certain methods of solving a class of integral equations of Fredholm type
Authors: Srivastava H. M. , Raina R. K.
Published: April 2009

The authors begin by presenting a brief survey of the various useful methods of solving certain integral equations of Fredholm type. In particular, they apply the reduction techniques with a view to inverting a class of generalized hypergeometric integral transforms. This is observed to lead to an interesting generalization of the work of E. R. Love [9]. The Mellin transform technique for solving a general Fredholm type integral equation with the familiarH-function in the kernel is also considered.
Integral formulas with weight factors
Authors: Hatziafratis Telemachos
Published: April 2009

A Bochner-Martinelli-Koppelman type integral formula with weight factors is derived on complete intersection submanifolds of domains of Cn.
On positive solutions of some semilinear elliptic equations
Authors: Wang Shin-Hwa , Kazarinoff Nicholas D.
Published: April 2009

The existence of positive solutions of some semilinear elliptic equations of the form −Δu = λf(u) is studied. The major results are a nonexistence theorem which gives a λ* = λ*(f,Ω) > 0 below which no positive solutions exist and a lower bound theorem for umax for Ω a ball. As a corollary of the nonexistence theorem that describes the dependence of the number of solutions on λ, two other nonexistence theorems, and an existence theorem are also proved.
Factorization of probability measures on symmetric hypergroups
Authors: Voit Michael
Published: April 2009

Generalizing known results for special examples, we derive a Khintchine type decomposition of probability measures on symmetric hypergroups. This result is based on a triangular central limit theorem and a discussion of conditions ensuring that the set of all factors of a probability measure is weakly compact. By our main result, a probability measure satisfying certain restrictions can be written as a product of indecomposable factors and a factor in I0(K), the set of all measures having decomposable factors only. Some contributions to the classification of I0(K) are given for general symmetric hypergroups and applied to several families of examples like finite symmetric hypergroups and hypergroup joins. Furthermore, all results are discussed in detail for a class of discrete symmetric hypergroups which are generated by infinitely many joins, for a class of countable compact hypergroups, for Sturm-Liouville hypergroups on [0, ∞[ and, finally, for polynomial hypergroups.
Optimal approximation by continued fractions
Authors: Bosma Wieb , Kraaikamp Cor
Published: April 2009

Among all possible semiregular continued fraction expansions of an irrational number the one with the best approximation properties, in a well-defined and natural sense, is determined. Some properties of this so called optimal continued fraction expansion are described.
On the construction of convergent iterative sequences of polynomials
Authors: Weiyuan Qiu
Published: April 2009

We answer two conjectures suggested by Zalman Rubinstein. We prove his Conjecture 1, that is, we construct convergent iterative sequences for with an arbitrary initial point, where with m ≥ 2. We also show by several counterexamples that Rubinstein's Conjecture 2 is generally false.
Prime rings for which the set of nonzero ideals is a special class
Authors: Gardner B. J.
Published: April 2009

We show that the rings described in the title are precisely the indecomposable injectives for the category whose objects are the associative rings and whose morphisms are the ring homomorphisms with accessible images. These rings are more or less completely known. Those of cardinality greater than that of the continuum are subdirectly irreducible but there are some nontrivial principal ideal domains in the class.
A decomposition of integer vectors. IV
Authors: Schinzel A.
Published: April 2009

Given m linearly independent vectors n1,…, nm ∈ zk and an integer l ∈ [m, k] one proves the existence of / linearly independent vectors P1,…, P1 ∈ Zk or q1 ∈ Zk of small size (suitably measured) such that the ni's are linear combinations of pj's with rational coefficients or of qj's with integer coefficients.
Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms
Authors: Baird Paul , Wood John C.
Published: April 2009

A complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.
An extremal problem in hypergraph theory (II)
Authors: Abbott H. L. , Hanson D. , Liu A. C.
Published: April 2009

Let t, m > 2 and p > 2 be positive integers and denote by N(t, m, p) the largest integer for which there exists a t-uniform hypergraph with N (not necessarily distinct) edges and having no independent set of edges of size m and no vertex of degree exceeding p. In this paper we complete the determination of N(t, m, 3) and obtain some new bounds on N(t, 2, p).
On special radicals, supernilpotent radicals and weakly homomorphically closed classes
Authors: Rjabuhin Ju. M. , Wiegandt R.
Published: April 2009

It is proved that a regular essentially closed and weakly homomorphically closed proper subclass of rings consists of semiprime rings. A regular class M defines a supernilpotent upper radical if and only if M consists of semiprime rings and the essential cover Mk of M is contained in the semisimple class S U M. A regular essentially closed class M containing all semisimple prime rings, defines a special upper radical if and only if M satisfies condition (S): every M-ring is a subdirect sum of prime M-rings. Thus we obtained a characterization of semisimple classes of special radicals; a subclas S of rings is the semisimple class of a special radical if and only if S is regular, subdirectly closed, essentially closed, and satisfies condition (S). The results are valid for alternative rings too.
On generalizations of projectivity for modules over Dedekind domains
Authors: Hausen Jutta
Published: April 2009

A module M over a ring R is κ-projective, κ a cardinal, if M is projective relative to all exact sequence of R-modules 0 → A → B → C → 0 such that C has a generating set of cardinality less than κ. A structure theorem for κ-projective modules over Dedekind domains is proven, and the κ-projectivity of M is related to properties of ExtR (M, ⊕ R). Using results of S. Chase, S. Shelah and P. Eklof, the existence of non-projective и1-projective modules is shown to undecidable, while both the Continuum Hypothesis and its denial (Plus Martin's Axiom) imply the existence of a reduced И0-projective Z-module which is not free.
The Hadamard conjecture and circuits of length four in a complete bipartite graph
Authors: Little Charles H. C. , Thuente David J.
Published: April 2009

We show that the problem of settling the existence of an n × n Hadamard matrix, where n is divisible by 4, is equivalent to that of finding the cardinality of a smallest set T of 4-circuits in the complete bipartite graph K n, n, such that T contains at least one circuit of each copy of K2,3 in Kn, n.
On strong lifting compactness, with applications to topological vector spaces
Authors: Babiker A. G. A. G. , Heller G. , Strauss W.
Published: April 2009

The notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.
Absolutes of almost realcompactifications
Authors: Tikoo Mohan L.
Published: April 2009

Given Hausdorff spacesXandYand a perfect irreducible and θ-continuous mapffromXontoY, technique that carries open (ultra) filters onXto open (ultra) filters onYback and forth in a natural way is introduced. It is proved that iffis a perfect irreducible and θ-continuous map fromXontoY, thenXis almost realcompact if and only ifYis almost realcompact. Several commutativity relations between the ‘absolutes of almost realcompactifications’ and the ‘almost realcompactifications of absólutes’ of a spaceXare discussed.
Almost Krull rings
Authors: Jespers E. , Wauters P.
Published: April 2009

The notion of an almost Krull domain is extended to rings satisfying a polynomial identity. Some general structural results are obtained. We also prove that skew polynomial rings R [ X, σ] remain almost Krull if R is an almost Krull ring. Finally, we study when semigroup ring R[S] are almost Krull rings, in the case when the group of quotients of S has the ascending chain condition on cyclic subgroups. An example is included to show that the general (semi-) group ring case is much more difficult to deal with.
Regularity of spherical means and localization of spherical harmonic expansions
Authors: Colzani Leonardo
Published: April 2009

Let G/K be a compact symmetric space, and let G = KAK be a Cartan decomposition of G. For f in L1(G) we define the spherical means f(g, t) = ∫k∫k ∫(gktk′) dk dk′, g ∈ G, t ∈ A. We prove that if f is in Lp(G), 1 ≤ p ≤ 2, then for almost every g ∈ G the functions t → f(g, t) belong to certain Soblev spaces on A. From these regularity results for the spherical means we deduce, if G/K is a compact rank one symmetric space, a theorem on the almost everywhere localization of spherical harmonic expansions of functions in L2 (G/K).
Numerical ranges in locally M-convex algebras. I
Authors: Chryssakis Thanassis
Published: April 2009

The bidual of a unital infrabarrelled l.m.c. C* algebra E, equipped with the bidual topology and the regualr Arens product, is always an l.m.c. C*-algebra. On the other hand, a unital l.m.c. *-algebra E has the C*-property if and only if every self-adjoint element x of E is strongly hermitian (x has real numerical range), or the sets of normalized states and normalized continuous positive linear forms of E coincide. Finally, every unital cpmplete l.m.c. C* algebra satisfying, locally, the property ‘the extreme points are dense in that set of continuous positive linear forms” (antiliminal algebra) has the complexes as its only normal elements.
Inscribed centers, reflexivity, and some applications
Authors: Astaneh A. A.
Published: April 2009

We first define an inscribed center of a bounded convex body in a normed linear space as the center of a largest open ball contained in it (when such a ball exists). We then show that completeness is a necessary condition for a normed linear space to admit inscribed centers. We show that every weakly compact convex body in a Banach space has at least one inscribed center, and that admitting inscribed centers is a necessary and sufficient condition for reflexivity. We finally apply the concept of inscribed center to prove a type of fixed point theorem and also deduce a proposition concerning so-called Klee caverns in Hilbert spaces.
Representations of minimally almost periodic groups
Authors: Valette Alain
Published: April 2009

For any groupG, we introduce the subsetS(G) of elementsgwhich are conjugate tofor some positive integerk. We show that, for any bounded representation π ofGanyginS(G), either π(g) = 1 or the spectrum of π(g) is the full unit circle in C. As a corollary,S(G) is in the kernel of any homomorphism fromGto the unitary group of a post-liminalC*-algebra with finite composition series.

Next, for a topological groupG, we consider the subset of elements approximately conjugate to 1, and we prove that it is contained in the kernel of any uniformly continuous bounded representation ofG, and of any strongly continuous unitary representation in a finite von Neumann algebra.

We apply these results to prove triviality for a number of representations of isotropic simple algebraic groups defined over various fields.
L1-convergence of Fourier series
Authors: Chen Chang-Pao
Published: April 2009

For an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.
The structure of exponential Weyl algebras
Authors: Robinson P. L.
Published: April 2009

abstract

We present structural properties of the complex associative algebra generated by the canonical commutation relations in exponential form. In particular, we show it to be a central simple algebra that lacks zero divisors and is not Noetherian on either side; in addition, we determine explicitly its units and its automorphisms.
Inhomogeneous minima of a class of ternary quadratic forms
Authors: Raka Madhu
Published: April 2009

Let denote the kth successive inhomogeneous minima for positive values of real indefinite ternary quadratic forms of type (2, 1). Here it is proved that for the class of zero forms, All the critical forms have also been obtained. is already known. For non-zero forms it is proved that .
Coincidence and common fixed points of hybrid contractions
Authors: Khan M. S. , Cho Y. J. , Park W. T. , Mumtaz T.
Published: April 2009

In this paper, we show the existence of solutions of functional equations fix ∈ Sx ∪ Tx and x = fix ∈ Sx ∪ Tx under certain nonlinear hybrid contraction and asymptotic regularity conditions, generalize and improve a recent result due to Kaneko concerning common fixed points of multivalued mappings weakly commuting with a single-valued mapping and satisfying a generalized contraction type. Some related results are also obtained.
Rigidity of Decomposition laws and number fields
Authors: Klingen Norbert
Published: April 2009

We speak of rigidity, if partial information about the prime decomposition in an extension of number fields K¦k determines the decomposition law completely (and hence the zeta function ζK), or even fixes the field K itself. Several concepts of rigidity, depending on the degree of information we start from, are introduced and studied. The strongest concept (absolute rigidity) was only known to hold for the ground field and all quadratic extensions. Here a complete list of all Galois quartic extensions which are absolutely rigid is given. For the weaker concept of rigidity, all rigid situations among the fields of degree up to 8 are determined.
Generalised partial transformation semigroups
Authors: Sullivan R. P.
Published: April 2009

It is well-known that for any set X, px, the semigroup of all partial transformations on X, can be embedded in Jx∪a for some a ∉ X (see for example Clifford and Preston (1967) and Ljapin (1963)). Recently Magill (1967) has considered a special case of what we call ‘generalised partial transformation semigroups’. We show here that any such semigroup can always be embedded in a full transformation smigroup in which the operation is not in general equal to the usual composition of mappinas. We then examine conditions under which such a semigroup, (J x, θ), is isomorphic to the semigroup, under composition, of all transformations on the same set X.
A dual approach to embedding the complement of two lines in a finite projective plane
Authors: Batten Lynn Margaret
Published: April 2009

Let S be a finite linear space on v ≥ n2 –n points and b = n2+n+1–m lines, m ≧ 0, n ≧ 1, such that at most m points are not on n + 1 lines. If m ≧ 1, except if m = 1 and a unique point on n lines is on no line with two points, then S embeds uniquely in a projective plane of order n or is one exceptional case if n =4. If m ≦ 1 and if v ≧ n2 – 2√n + 3, + 6, the same conclusion holds, except possibly for the uniqueness.

1991 Mathematics subject classification (Amer. Math. Soc.) 05 B 05, 51 E 10.
Unions of well-ordered sets
Authors: Howard Paul
Published: April 2009

In Zermelo-Fraenkel set theory weakened to permit the existence of atoms and without the axiom of choice we investigate the deductive strength of five statements which make assertions about the cardinality of the union of a well-ordered collection of sets. All five of the statements considered are consequences of the axiom of choice.
Congruence networks for completely simple semigroups
Authors: Petrich Mario
Published: April 2009

The operators K, k, T and t are defined on the lattice of congruences on a Rees matrix semigroup S as follows. For ρ ∈ (S), ρK and ρk (ρT and ρt) are the greatest and the least congruences with the same kernel (trace) as ρ, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence ρ ∈ (S) and the lattice generated by it. The latter is then represented by generators and relations.
A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold
Authors: Carreras Francisco J. , Giménez Fernando , Miquel Vicente
Published: April 2009

We give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.
Groups whose proper quotients are hypercentral
Authors: Kurdachenko L. A. , Subbotin I. Y.
Published: April 2009

Groups, all proper factor-groups of which are hypercentral of finite torsion-free rank, are studied in this article.
Lattice-ordered power series fields
Authors: Redfield R. H.
Published: April 2009

A lattice-ordered power series algebra of a totally ordered field over a rooted abelian group may be constructed in a way that is arbitrary only in requiring that a factor set be chosen in the field and an extended total order be chosen on the group modulo its torsion subgroup. The resulting algebra is a field if and only if the subalgebra of elements with torsion support form a field. It follows that if the torsion subgroup may be independently embedded in the algebraic closure of the totally ordered field, or if the resulting algebra has no zero-divisors, then the algebra is a field. The set of supporting subsets for the power series may be characterized abstractly in such a way that previous representation theorems of lattice-ordered fields into power series algebras may be applied to produce representations into power series fields.
The lattice of ideals of MR(R2)Ra commutative pir
Authors: Maxson C. J. , Van Wyk L.
Published: April 2009

In this paper we characterize the ideals of the centralizer near-ring N = MR(R2), where R is a commutative principle ideal ring. The characterization is used to determine the radicals Jυ(N) and the quotient structures N/ Jv(N), v = 0, 1, 2.
On the spectrum of C1 as an operator on bv0
Authors: Okutoyi J. I.
Published: April 2009

In 1985 John Reade determined the spectrum of C1 regarded as an operator on the space c0 of all null sequences normed by ║x║ = supn≧0|xn|. It is the purpose of this paper to determine the spectrum of C1 regarded as an operator on the space bv0 of all sequences x such that xk → 0 as k → ∞ and .
Convolutions of distrbutions with exponential and subexponential tails: Corrigendum
Authors: Cline Daren B. H.
Published: April 2009

The proof of Lemma 2.3(ii) as originally given is incomplete since we cannot recursively apply (2.1) with a fixed to. This is corrected below. In addition, we are able to extend the result so the conclusion is that H ∈ ℒα.
Preorders on canonical families of modules of finite length
Authors: Fixman Uri , Okoh Frank
Published: April 2009

Let R be an artinian ring. A family, ℳ, of isomorphism types of R-modules of finite length is said to be canonical if every R-module of finite length is a direct sum of modules whose isomorphism types are in ℳ. In this paper we show that ℳ is canonical if the following conditions are simultaneously satisfied: (a) ℳ contains the isomorphism type of every simple R-module; (b) ℳ has a preorder with the property that every nonempty subfamily of ℳ with a common bound on the lengths of its members has a smallest type; (c) if M is a nonsplit extension of a module of isomorphism type II1 by a module of isomorphism type II2, with II1, II2 in ℳ, then M contains a submodule whose type II3 is in ℳ and II1 does not precede II3. We use this result to give another proof of Kronecker's theorem on canonical pairs of matrices under equivalence. If R is a tame hereditary finite-dimensional algebra we show that there is a preorder on the family of isomorphism types of indecomposable R-modules of finite length that satisfies Conditions (b) and (c).
Ideals and other generalizations of congruence classes
Authors: Agliano Paolo , Ursini Aldo
Published: April 2009

In the general context of ideals in universal algebras, we study varietal properties connected with ideals that are equivalent both to Ma'cev conditions and congruence properties such as 0-regularity, 0-permutability, etc.
The second dual of C0 (S, A)
Authors: Choy Stephen T. L. , Wong James C. S.
Published: April 2009

The second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.
Twisted crossed products by coactions
Authors: Phillips John , Raeburn Iain
Published: April 2009

We consider coactions of a locally compact group G on a C*-algebra A, and the associated crossed product C*-algebra A× G. Given a normal subgroup N of G, we seek to decompose A× G as an iterated crossed product (A× G/ N) × N, and introduce notions of twisted coaction and twisted crossed product which make this possible. We then prove a duality theorem for these twisted crossed products, and discuss how our results might be used, especially when N is abelian.
Harmonic analysis for groups acting on triangle buildings
Authors: Cartwright Donald I. , MŁotkowski Wojciech
Published: April 2009

Let Δ be a thick building of type Ã2, and letbe its set of vertices. We study a commutative algebraof ‘averaging’ operators acting on the space of complex valued functions on. This algebra may be identified with a space of ‘biradial functions’ on, or with a convolution algebra of bi-K-invariant functions onG, ifGis a sufficiently large group of ‘type-rotating’ automorphisms of Δ, andKis the subgroup ofGfixing a given vertex. We describe the multiplicative functionals onand the corresponding spherical functions. We consider theC*-algebra induced byonl2, find its spectrum Σ, prove positive definiteness of a kernelkzfor eachz∈ Σ, find explicity the spherical Plancherel formula for any groupGof type rotating automorphisms, and discuss the irreducibility of the unitary representations appearing therein. For the class of buildings ΔJarising from the groups ΓJintroduced in [2], this involves proving that the weak closure ofis maximal abelian in the von Neumann algebra generated by the left regular representation of ΓJ.
Linear operators in l2 with a universality property
Authors: Edelstein Michael , Holmes Raymond D.
Published: April 2009

A collection P of bounded linear operators in l2 is constructed in such a manner that given any separable metric space X, and any countable collection F of continuous self-maps of X, there is a homeomorphism h of X onto a subset of l2 such that for each f ∈ F there is P ∈ P with hf = Ph.

While similar results were obtained by Baayen and Dc Groot, our construction makes it possible to impose additional conditions on h (depending on F). For example, if all the members of F are uniformly continuous then h too can be made uniformly continuous.
Some examples concerning normal and uniform normal structure in Banach spaces
Authors: Smith Mark A. , Turett Barry
Published: April 2009

Examples are given that show the following: (1) normal structure need not be inherited by quotient spaces; (2) uniform normal structure is not a self-dual property; and (3) no degree of k–uniform rotundity need be present in a space with uniform normal structure.
Amenability and ideals in A(G)
Authors: Forrest Brian
Published: April 2009

Closed ideals in A(G) with bounded approximate identities are characterized for amenable [SIN]-groups and arbitrary discrete groups. This extends a result of Liu, van Rooij and Wang for abelian groups.
Oscillation theorems for second order superlinear differential equations with damping
Authors: Grace S. R. , Lalli B. S.
Published: April 2009

Some oscillation criteria for solutions of a general second order ordinary superlinear differential equation with alternating coefficients are given. The results generalize and complement some existing results in the literature.
Coherent Monoids
Authors: Gould Victoria
Published: April 2009

This paper is concerned with a new notion of coherency for monoids. A monoid S is right coherent if the first order theory of right S-sets is coherent; this is equivalent to the property that every finitely generated S-subset of every finitely presented right S-set is finitely presented. If every finitely generated right ideal of S is finitely presented we say that S is weakly right coherent. As for the corresponding situation for modules over a ring, we show that our notion of coherency is related to products of flat left S-sets, although there are some marked differences in behaviour from the case for rings. Further, we relate our work to ultraproducts of flat left S-sets and so to the question of axiomatisability of certain classes of left S-sets.

We show that a monoid S is weakly right coherent if and only if the right annihilator congruence of every element is finitely generated and the intersection of any two finitely generated right ideals is finitely generated. A similar result describes right coherent monoids. We use these descriptions to recognise several classes of (weakly) right coherent monoids. In particular we show that any free monoid is weakly right (and left) coherent and any free commutative monoid is right (and left) coherent.
Total chromatic number of graphs of high degree, II
Authors: Yap H. P. , Chew K. H.
Published: April 2009

We prove Theorem 1: suppose G is a simple graph of order n having Δ(G) = n − k where k ≥ 5 and n ≥ max (13, 3k −3). If G contains an independent set of k − 3 vertices, then the TCC (Total Colouring Conjecture) is true. Applying Theorem 1, we also prove that the TCC is true for any simple graph G of order n having Δ(G) = n −5. The latter result together with some earlier results confirm that the TCC is true for all simple graphs whose maximum degree is at most four and for all simple graphs of order n having maximum degree at least n − 5.
The Toeplitz operator proof of noncommutative Bott periodicity
Authors: Phillips N. Christopher
Published: April 2009

We adapt the Toeplitz operator proof of Bott periodicity to give a short direct proof of Bott periodicity for the representable K-theory of σ-C*-algebras. We further show how the use of this proof and the right definitions simplifies the derivation of the basic properties of representable K-theory.
On pairwise paracompactness
Authors: Ganster M. , Reilly I. L.
Published: April 2009

This paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.
Embeddings of quaternion space in S4
Authors: Katanaga Atsuko , Saeki Osamu
Published: April 2009

Consider a (real) projective plane which is topologically locally flatly embedded in S4. It is known that it always admits a 2-disk bundle neighborhood, whose boundary is homeomorphic to the quaternion space Q, the total space of the nonorientable S1-bundle over RP2 with Euler number ± 2, with fundamental group isomorphic to the quaternion group of order eight. Conversely let f: Q → S4 be an arbitrary locally flat topological embedding. Then we show that the closure of each connected component of S4 − f(Q) is always homeomorphic to the exterior of a topologically locally flatly embedded projective plane in S4. We also show that, for a large class of embedded projective planes in S4, a pair of exteriors of such embedded projective planes is always realized as the closures of the connected components of S4 − f(Q) for some locally flat topological embedding f: Q → S4.
Non-expansive derived horseshoes
Authors: Sakai Kazuhiro
Published: April 2009

For a two parameter family of C3 diffeomorphisms having a homoclinic orbit of tangency derived from a horseshoe, the relationship between the measure of the parameter values at which the diffeomorphism (restricted to a certain compact invariant set containing the horseshoe) is not expansive and the Hausdorff dimension of the horseshoe associated to the homoclinic orbit of tangency is investigated. This is a simple application of the Newhouse-Palis-Takens-Yoccoz theory.
Time-isolated Singularities of Temperatures
Authors: Watson Neil A.
Published: April 2009

We study singularities of solutions of the heat equation, that are not necessarily isolated but occur only in a single characteristic hyperplane. We prove a decomposition theorem for certain solutions on D+ = D ∩ (Rn × ]0. ∞[), for a suitable open set D, with singularities at compact subset K of Rn × {0}, in terms of Gauss-Weierstrass integrals. We use this to prove a representation theorem for certain solutions on D+, with singularities at K, as the sums of potentials and Dirichlet solutions. We also give conditions under which K is removable for solutions on D∖K.
Extensions of G-posets and Quillen's complex
Authors: Segev Yoav , Webb Peter
Published: April 2009

We develop techniques to compute the homology of Quillen's complex of elementary abelian p-subgroups of a finite group in the case where the group has a normal subgroup of order divisible by p. The main result is a long exact sequence relating the homologies of these complexes for the whole group, the normal subgroup, and certain centralizer subgroups. The proof takes place at the level of partially-ordered sets. Notions of suspension and wedge product are considered in this context, which are analogous to the corresponding notions for topological spaces. We conclude with a formula for the generalized Steinberg module of a group with a normal subgroup, and give some examples.
Numerical Range of the Derivation of an Induced Operator
Authors: Holmes Randall R. , Li Chi-Kwong , Tam Tin-Yau
Published: April 2009

Let V be an n–dimensional inner product space over , let H be a subgroup of the symmetric group on {l,…, m}, and let x: H → be an irreducible character. Denote by (H) the symmetry class of tensors over V associated with H and x. Let K (T) ∈ End((H)) be the operator induced by T ∈ End(V), and let DK(T) be the derivation operator of T. The decomposable numerical range W*(DK(T)) of DK(T) is a subset of the classical numerical range W(DK(T)) of DK(T). It is shown that there is a closed star-shaped subset of complex numbers such that

⊆ W*(DK(T)) ⊆ W(DK(T)) = con

where conv denotes the convex hull of . In many cases, the set is convex, and thus the set inclusions are actually equalities. Some consequences of the results and related topics are discussed.
Extremal characterizations of reflexive spaces
Authors: Wang Xianfu
Published: April 2009

Assume that a Banach space has a Fréchet differentiable and locally uniformly convex norm. We show that the reflexive property of the Banach space is not only sufficient, but also a necessary condition for the fulfillment of the proximal extremal principle in nonsmooth analysis.