bluuebunny/crossref_metadata_2025_split huggingface dataset:
An Infinite Construction in Ring Theory
Authors: Whelan E. A. 
Published: May 2009

1. Point (3) of the main theorem of our paper [3, Theorem 1.1] is incorrect: this note corrects the main and consequential errors, and shows that (after minor adjustments) almost all the other results of [3], including the remaining seven points of Theorem 1.1, remain correct.2. The theme of [3] was a family of functors G,(–), defined on the category of rings
with unity for each cardinal t. For t = 0, 1, the results of [3] are unchanged, but, for 2≤t<∞, major, and, for t infinite, less major, corrections are necessary; we therefore assume 2≤t. Terminology and notation are standard or as in [3], and I would like to thank A. W. Chatters and an anonymous referee for comments which prompted this correction.
On approximating Lebesgue integrals by Riemann sums
Authors: Révész Szilárd GY. , Ruzsa Imre Z. 
Published: May 2009

Iffis a real function, periodic with period 1, we defineIn the whole paper we write ∫ for,mEfor the Lebesgue measure ofE∩ [0,1], whereE⊂ ℝ is any measurable set of period 1, and we also useXEfor the characteristic function of the setE. Consistent with this, the meaning of ℒpis ℒp[0, 1]. For all realxwe haveiffis Riemann-integrable on [0, 1]. However,∫fexists for allf∈ ℒ1and one would wish to extend the validity of (2). As easy examples show, (cf. [3], [7]), (2) does not hold forf∈ ℒpin general ifp< 2. Moreover, Rudin [4] showed that (2) may fail for allxeven for the characteristic function of an open set, and so, to get a reasonable extension, it is natural to weaken (2) towhereS⊂ ℕ is some “good” increasing subsequence of ℕ. Naturally, for different function classes ℱ ⊂ ℒ1we get different meanings of being good. That is, we introduce the class of ℱ-good sequences as
On a periodic neutral logistic equation
Authors: Gopalsamy K. , He Xue-Zhong , Wen Lizhi 
Published: May 2009

The oscillatory and asymptotic behaviour of the positive solutions of the autonomous neutral delay logistic equationwith r, c, T, K ∈ (0, ∞) has been recently investigated in [2]. More recently the dynamics of the periodic delay logistic equationin which r, K are periodic functions of period τ and m is a positive integer is considered in [6]. The purpose of the following analysis is to obtain sufficient conditions for the existence and linear asymptotic stability of a positive periodic solution of a periodic neutral delay logistic equationin which Ṅ denotes and r, K, c are positive continuous periodic functions of period τ at and m is a positive integer. For the origin and biological relevance of (1.3) we refer to [2].
The zeros of a certain family of trinomials
Authors: Dilcher Karl , Nulton James D. , Stolarsky Kenneth B. 
Published: May 2009

Many of the classical inequalities of analysis can be written in the form P(x) ≥ 0 for x ∈ I or P(x) > 0 for x ∈ I′, where P(x) is a polynomial and I′ ⊂ I are certain intervals on the real line. This gives rise to the question of where the zeros of P(x) are located. For example, if f is a polynomial with real zeros, then an inequality of Laguerre [8, p. 171 f.] asserts thatfor all x. A detailed study of the zeros of this particular P(x) has been made [5].
On the Gauss map of ruled surfaces
Authors: Baikoussis Christos , Blair David E. 
Published: May 2009

Let M2 be a (connected) surface in Euclidean 3-space E3, and let G:M2→S2(1) ⊂ E3 be its Gauss map. Then, according to a theorem of E. A. Ruh and J. Vilms [3], M2 is a surface of constant mean curvature if and only if, as a map from M2 to S2(1), G is harmonic, or equivalently, if and only ifwhere δ is the Laplace operator on M2 corresponding to the induced metric on M2 from E3 and where G is seen as a map from M2to E3. A special case of (1.1) is given byi.e., the case where the Gauss map G:M2→E3 is an eigenfunction of the Laplacian δ on M2.
The modularity of the lattice of varieties of completely regular semigroups and related representations
Authors: Petrich Mario , Reilly Norman R. 
Published: May 2009

A semigroup endowed with a unary operation satisfying the identitiesis a completely regular semigroup. In several recent papers devoted to the study of the lattice of subvarieties of the variety of completely regular semigroups, various results have been obtained which decompose special intervals in into either direct products or subdirect products. Petrich [14], Hall and Jones [6] and Rasin [20] have shown that certain intervals of the form , where is the trivial variety and are subdirect products of and Pastijn and Trotter [13] show that certain intervals of the form are direct products of the intervals and The main objective of this paper is to develop an appropriate lattice theoretic framework for these representations.
Generalized fractions and Hughes' gradetheoretic analogue of the Cousin complex
Authors: Sharp R. Y. , Yassi M. 
Published: May 2009

Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [19, Section 2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n ∈ N0 (we use N0 to denote the set of non-negative integers),Cohen–Macaulay rings can be characterized in terms of the Cousin complex: A is a Cohen–Macaulay ring if and only if C(A) is exact [19, (4.7)]. Also, the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring (see [19,(5.4)]).
Inverse semigroups with certain types of partial automorphism monoids
Authors: Goberstein Simon M. 
Published: May 2009

AbstractFor an inverse semigroupS, the set of all isomorphisms betweeninverse subsemigroups ofSis an inverse monoid under composition which is denoted by(S) and called the partial automorphism monoid ofS. Kirkwood [7] and Libih [8] determined which groups have Clifford partial automorphism monoids. Here we investigate the structure of inverse semigroups whose partial automorphism monoids belong to certain other important classes of inverse semigroups. First of all, we describe (modulo so called “exceptional” groups) all inverse semigroupsSsuch that(S) is completely semisimple. Secondly, for an inverse semigroupS, we find a convenient description of the greatest idempotent-separating congruence on(S), using a well-known general expression for this congruence due to Howie, and describe all those inverse semigroups whose partial automorphism monoids are fundamental.
Duals of Banach spaces of entire functions
Authors: Anderson J. M. , Duncan J. 
Published: May 2009

Let w be a strictly positive function on ℂ and let , respectively denote the Banach spaces of those entire functions φ(z) with ∣φ(z)∣= O(w(z)) and ∣φ(z)∣ = o(w(z)). In this generality, these spaces may contain only constants, but for many functions w(z) these will be interesting Banach spaces with norm.We study two specific problems.
Union results for thin sets
Authors: Hare Kathryn E. 
Published: May 2009

Let G be a compact abelian group and let Γ be its (discrete) dual group. Denote by M(G) the space of complex regular Borel measures on G.Let E be a subset of Γ. Then:(i) E is called a Rajchman set if, for all μ ∈M(G) implies (ii) E is called a set of continuity if given ε > 0 there exists δ > 0 such that if and(iii) E is called a parallelepiped of dimension N if |E| = 2N and there are two-element sets . (The multiplication indicated here is the group operation.)
Homological stability for On,n over semi-local rings
Authors: Betley Stanislaw 
Published: May 2009

Let R be a commutative, semi-local ring. Let On,n be the group of linear automorphisms of R2n which preserve the bilinear form . The main result of this paper is the following theorem.Theorem A. The natural inclusion of Onn into On,n into On+1,n+1induces an isomorphism on the ith homology group if only n is large enough with respect to i.
Semi-normal operators on uniformly smooth Banach spaces
Authors: Chō Muneo 
Published: May 2009

In this paper we shall examine the relationship between the numerical ranges and the spectra for semi-normal operators on uniformly smooth spaces.Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. A linear functional F on B(X) is called state if ∥F∥ = F(I) = 1. When x ε X with ∥x∥ = 1, we denoteD(x) = {f ε X*:∥f∥ = f(x) = l}.
The range of a continuous linear functional over a class of functions defined by subordination
Authors: Fournier Richard 
Published: May 2009

Let Δ = {z ∈ ℂ ⃒ ⃓z⃓ <1) and H(Δ) the set of analytic functions on Δ. We recall the definition of subordination between two functions, say ƒ and g, analytic on Δ: this means that f(0)= g(0) and there is a function ρ ∈ H (Δ) such that ρ(0) = 0, ⃒ ρ(z)⃒<1 if z ∈ Δ, and f(z) ≡ g(ρ(z)). Subordination between f and g will be denoted byf<g. The Hadamard product (or convolution) of two functions and in H(Δ)is the function f * g ∈ H(Δ)definedas f * g (z)= .
A note on the characterisation of eigencurves for certain two parameter eigenvalue problems in ordinary differential equations
Authors: Browne Patrick J. , Sleeman B. D. 
Published: May 2009

We are interested in two parameter eigenvalue problems of the formsubject to Dirichlet boundary conditionsThe weight function 5 and the potential q will both be assumed to lie in L2[0,1]. The problem (1.1), (1.2) generates eigencurvesin the sense that for any fixed λ, ν(λ) is the nth eigenvalue ν, (according to oscillation indexing) of (1.1), (1.2). These curves are in fact analytic functions of λ and have been the object of considerable study in recent years. The survey paper [1] provides background in this area and itemises properties of eigencurves.
Positive solutions of integrodifferential and difference equations with unbounded delay
Authors: Kiventidis Thomas 
Published: May 2009

AbstractWe establish a necessary and sufficient condition for the existence of a positive solution of the integrodifferential equationwhere nis an increasing real-valued function on the interval [0, α); that is, if and only if the characteristic equationadmits a positive root.Consider the difference equation , where is a sequence of non-negative numbers. We prove this has positive solution if and only if the characteristic equation admits a root in (0, 1). For general results on integrodifferential equations we refer to the book by Burton [1] and the survey article by Corduneanu and Lakshmikantham [2]. Existence of a positive solution and oscillations in integrodifferential equations or in systems of integrodifferential equations recently have been investigated by Ladas, Philos and Sficas [5], Györi and Ladas [4], Philos and Sficas [12], Philos [9], [10], [11].Recently, there has been some interest in the existence or the non-existence of positive solutions or the oscillation behavior of some difference equations. See Ladas, Philos and Sficas [6], [7].The purpose of this paper is to investigate the positive solutions of integrodifferential equations (Section 1) and difference equations (Section 2) with unbounded delay. We obtain also some results for integrodifferential and difference inequalities.
Double MSn-algebras and double Kn.m-algebras
Authors: Sequeira M. 
Published: May 2009

AbstractThe variety O2 of all algebras (L; ∧, ∨, f, g, 0, 1) of type (2, 2, 1, 1, 0, 0) such that (L; ∧, ∨, f, 0, 1) and (L; ∧, ∨, g, 0, 1) are Ockham algebras is introduced, and, for n, m εℕ, its subvarieties DMSn, of double MSn-algebras, and DKn,m, of double Kn,m-algebras, are considered. It is shown that DKn,m has equationally definable principal congruences: a description of principal congruences on double Kn,m-algebras is given and simplified for double MSn-algebras. A topological duality for O2-algebras is developed and used to determine the subdirectly irreducible algebras in DKn,m and in DMSn. Finally, MSn-algebras which are reduct of a (unique) double MSn-algebra are characterized.
Some remarks on pramarts and mils
Authors: Wang Zhen-Peng , Xue Xing-Hong 
Published: May 2009

Let F be a Banach space, (ω, ℱ, P) a fixed probability space, D a directed set filtering to the right with the order ≤, and (ℱt, D) a stochastic basis of ℱ, i.e. (ℱt, D) is an increasing family of sub-σ-algebras of ℱ:ℱs ⊂ for any s,t ε D and s≤t. Throughout this paper, (Xt) is an F-valued, (ℱt)-adapted sequence, i.e. Xt, is ℱt-measurable, t ε D. We also assume that Xt, ∈ L1, i.e. ∫ ∥Xt∥ <∞. We use I(H) to denote the indicator function of an event H. Let ∞ be a such element: t <∞, t ∈ D, = D ∪ ∞, and ℱ∞ = σ. A stopping time is a map τ:Ω→ such that (τ<t) ∈ ℱt, t ∈ D. A stopping time τ is called simple (countable) if it takes finitely (countably) many values in D(). Let T and Tc be the sets of simple and countable stopping times respectively and Tf = {τ ∈ Tc: τ<∞ a.s.}. Clearly, (T, <) and (Tf, <) are directed sets filtering to the right. For τ ∈ Tc, letand= {(Xt): there is σ∈ Tf such that ∫(ι<∞) ∥Xι∥ < ∞, σ ≤ τ ∈ Tc},= {(Xt):(Xι, ι ∈ T) converges stochastically (i.e. in probability) in the norm topology},ℰ = {(Xt):(Xι, ι ∈ T) converges essentially in the norm topology}.
Some characterizations of the hereditary pretorsion class of semigroup automata
Authors: Lam Clement S. 
Published: May 2009

AbstractLet S be a semigroup. A class of S-automata is called a hereditary pretorsion class (HPC) if it is closed under quotients, subautomata, coproducts (disjoint unions) and finite products. In this paper we present two characterizations of HPC. Specifically, we show that there is a bijective correspondence between the HPCs of S-automata, the right linear topologies on S′ and the idempotent preradicals r on the category of S-automata such that the set of automata {M|r(M) = M} is closed under subautomata and finite products.
Some results on stable p-harmonic maps
Authors: Cheung Leung-Fu , Leung Pui-Fai 
Published: May 2009

For each p ∈ [2, ∞)a p-harmonic map f:Mm→Nn is a critical point of the p-energy functionalwhere Mm is a compact and Nn a complete Riemannian manifold of dimensions m and n respectively. In a recent paper [3], Takeuchi has proved that for a certain class of simply-connected δ-pinched Nn and certain type of hypersurface Nn in ℝn+1, the only stable p-harmonic maps for any compact Mm are the constant maps. Our purpose in this note is to establish the following theorem which complements Takeuchi's results.
On the vanishing viscosity in the Cauchy problem for the equations of a nonhomogeneous incompressible fluid
Authors: Itoh Shigeharu 
Published: May 2009

Let us consider the Cauchy problemin QT= ℝ3 × [0, T], where f(x, t), ρ0(x) and v0(x) are given, while the density ρ(x, t), the velocity vector v(x, t)= (υ1(x, t), υ2(x, t), υ3(x, t)) and the pressure p(x, t) are unknowns. The viscosity coefficient μ is assumed to be nonnegative. In these equations, the pressure p is automatically determined (up to a function of t) by ρ and v, namely, by solving the equationThus we mention (ρ, v) when we talk about the solution of (1.1:μ).
The kernel and trace operators for ideal extensions of regular semigroups
Authors: Petrich Mario 
Published: May 2009

AbstractLet V be a regular semigroup and an ideal extension of a semigroup S by a semigroup Q Congruences on V can be represented by triples of the form (σ, P, τ), here called admissible, where a is a congruence on S, P is an ideal of Q and τ is a O-restricted congruence on Q/P satisfying certain conditions. We characterize the trace relation T on V in terms of admissible triples. When the extension V of S is strict, for a congruence v on V given in terms of an admissible triple, we characterize vK, vK, vT and vT again in terms of admissible triples.
Primes of the form [pc] and related questions
Authors: Harman Glyn , Rivat Joël 
Published: May 2009

Much interest has been shown in determining the range of values of c for which the sequence [n]c contains infinitely many primes. The result is an elementary deduction from the prime number theorem, of course, of 0<c≤l. In 1953, Piatetski–Shapiro [9] showed thatfor 1<c<12/11, where xc(X) stands for the number of primes in the set {[nc]n≤x}.
Equality of essential spectra of quasisimilar operators with property (δ)
Authors: Miller T. L. , Miller V. G. 
Published: May 2009

AbstractA Banach space operator has property (δ) if and only if it is the quotient of a decomposable operator, equivalently, if and only if its adjoint has Bishop's property (β). Within this class of operators, it is shown that quasisimilarity preserves essential spectra.
On linear recurrence sequences with polynomial coefficients
Authors: van der Poorten A. J. , Shparlinski I. E. 
Published: May 2009

We consider sequences (Ah)defined over the field ℚ of rational numbers and satisfying a linear homogeneous recurrence relationwith polynomial coefficients sj;. We shall assume without loss of generality, as we may, that the sj, are defined over ℤ and the initial values A0A]…, An−1 are integer numbers. Also, without loss of generality we may assume that S0 and Sn have no non-negative integer zero. Indeed, any other case can be reduced to this one by making a shift h → h – l – 1 where l is an upper bound for zeros of the corresponding polynomials (and which can be effectively estimated in terms of their heights)
Mixed Hilbert modular forms and families of abelian varieties
Authors: Lee Min Ho 
Published: May 2009

In [18] Shioda proved that the space of holomorphic 2-forms on a certain type of elliptic surface is canonically isomorphic to the space of modular forms of weight three for the associated Fuchsian group. Later, Hunt and Meyer [6] made an observation that the holomorphic 2-forms on a more general elliptic surface should in fact be identified with mixed automorphic forms associated to an automorphy factor of the formfor z in the Poincaré upper half plane ℋ, g = and χ(g) = , where g is an element of the fundamental group Γ⊂PSL(2, R) of the base space of the elliptic fibration, χ-Γ→SL(2, R) the monodromy representation, and w: ℋ→ℋ the lifting of the period map of the elliptic surface.
An estimate on the eigenvalues in bifurcation for gradient mappings
Authors: Chiappinelli Raffaele 
Published: May 2009

Let H be a real Hilbert space and let A: H→H be a nonlinear operator such that A(0) = 0. We consider the eigenvalue problemRecall that λ0 ε ℝ is said to be a bifurcation point for (1.1) if every neighbourhood of (λ0, 0) in ℝ × H contains solutions of (1.1).
On the complexity of computing the 2-Selmer group of an elliptic curve
Authors: Siksek S. , Smart N. P. 
Published: May 2009

AbstractIn this paper we give an algorithm for computing the 2-Selmer group of an elliptic curvewhich has complexityO(LD(0·5),c1)), whereDis the absolute discriminant of the curve. Our algorithm is unconditional but the complexity estimate assumes the GRH and a standard conjecture on the distribution of smooth reduced ideals. This improves on the corresponding algorithm of Birch and Swinnerton-Dyer, which has complexity ofO(√D).
On 2-class field towers for quadratic number fields with 2-class group of type (2,2)
Authors: Gerth Frank 
Published: May 2009

LetKbe a quadratic number field with 2-class group of type (2,2). Thus ifSkis the Sylow 2-subgroup of the ideal class group ofK, thenSk= ℤ/2ℤ × ℤ/2ℤ LetK ⊂ K1⊂ K2⊂ K3⊂…the 2-class field tower ofK. ThusK1is the maximal abelian unramified extension ofKof degree a power of 2;K2is the maximal abelian unramified extension ofKof degree a power of 2; etc. By class field theory the Galois group Ga1 (K1/K) ≅Sk≅ ℤ/2ℤ × ℤ/2ℤ, and in this case it is known that Ga(K2/Kl) is a cyclic group (cf. [3] and [10]). Then by class field theory the class number ofK2is odd, and henceK2=K3=K4= …. We say that the 2-class field tower ofKterminates atK1if the class number ofK1is odd (and henceK1=K2=K3= … ); otherwise we say that the 2-class field tower ofKterminates atK2. Our goal in this paper is to determine how likely it is for the 2-class field tower ofKto terminate atK1and how likely it is for the 2-class field tower ofKto terminate atK2. We shall consider separately the imaginary quadratic fields and the real quadratic fields.
Gauss sums for U(2n, q2)
Authors: Kim Dae San 
Published: May 2009

AbstractFor a lifted nontrivial additive character λ' and a multiplicative character λ of the finite field with q2 elements, the “Gauss” sums Σ λ'(trg) over g ∈SU(2n, q2) and Σ λ (detg)λ'(trg) over g ∈ U(2n, q2) are considered. We show that the first sum is a polynomial in q with coefficients involving averages of “bihyperkloosterman sums” and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums. As a consequence, we can determine certain “generalized Kloosterman sums over nonsingular Hermitian matrices”, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.
On Peiffer central series
Authors: Ellis Graham 
Published: May 2009

Let G be a group. A precrossed G-module is a group homomorphism ∂: M → G together with a group action (g, m) ↦gm of G on M, such that ∂(gm) = g(∂m)g−1. The Peiffer commutator < m, m′ > of two elements m, m′ ∊ M is denned as< m, m′ >= mm′ m−1(∂mm′)−1If all Peiffer commutators are trivial, the precrossed G-module is said to be a crossed G-module. The subgroup < M, M > generated by all Peiffer commutators is called the Peiffer subgroup of M; it is the second term of a lower Peiffer central series (see below). The following table indicates how these concepts reduce to more standard concepts when restrictions are placed on ∂ and G.
On joint essential spectra of doubly commuting n-tuples of p-hyponormal operators
Authors: Jeon In Ho 
Published: May 2009

AbstractLet A be an operator on a Hillbert space with polar decomposition A = |A|, let Â = |A|½U|A|½ and let Â = V|Â| be the polar decomposition of Â. Write Ã for the operatorÃ = |Â|½V|Â|½. If = (A1,…,AN) is a doubly commuting n-tuple of p-hyponormal operators on a Hillbert space with equal defect and nullity, then = (Ã1,…,Ãn) is a doubly commuting n-tuple of hyponormal operators. In this paper we show thatwhere σ* denotes σTe (Taylor essential spectrum), σTw (Taylor-Weyl spectrum) and σTb (Taylor-Browder spectrum), respectively.
A metrical result on the discrepancy of (nα)
Authors: Schoissengeier J. 
Published: May 2009

In the following let Ω be the set of irrational numbers in the interval [0,1] and let λ be Lebesgue measure restricted to Ω. For any real number x, let {x} = x - [x] be the fractional part of x. Let N be anatural number and let α e Ω. Thenis known as the discrepancy of the sequence (nα)n>1 modulo 1; here c[x, y) denotes the characteristic function of the interval [x, y).
Excitation of electrostatic ion-cyclotron-like modes by the electron density ripple in dusty magnetoplasmas
Authors: SHUKLA P. K. 
Published: May 2009

AbstractIt is shown that electrostatic ion-cyclotron (EIC)-like modes can be excited by the pre-existing electron density ripple across the external magnetic field in a dusty magnetoplasma. For this purpose, we use the ion continuity and momentum equations, together with the Boltzmann-distributed electrons, and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that the EIC-like modes in dusty magnetoplasmas can be driven due to the free energy in the electron density ripple.