bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multipliers from spaces of test functions to amalgams
Authors: De Squire Maria Torres 
Published: April 2009

AbstractIn this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.
Geometric and arithmetic postulation of the exponential function
Authors: Pila J. 
Published: April 2009

AbstractThis paper presents new proofs of some classical transcendence theorems. We use real variable methods, and hence obtain only the real variable versions of the theorems we consider: the Hermite-Lindemann theorem, the Gelfond-Schneider theorem, and the Six Exponentials theorem. We do not appeal to the Siegel lemma to build auxiliary functions. Instead, the proof employs certain natural determinants formed by evaluating n functions at n points (alternants), and two mean value theorems for alternants. The first, due to Pólya, gives sufficient conditions for an alternant to be non-vanishing. The second, due to H. A. Schwarz, provides an upper bound.
Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives
Authors: Yong Jiongmin , Pan Liping 
Published: April 2009

AbstractA class of functional differential equations in some Hilbert space are studied. The results are applicable to many quasi-linear parabolic paratial differential equations with (possibly) countably many discrete delays and finitely many distributed delays in the highest order spatial derivatives. For the linear case, an evolution operator on the underline space H is introduced, via which a variation of constant formula for the solution of the equation in the underline space H is derived. Some spectral properties of the generator of the solution semigroup defined on some appropriate space are discussed as well.
Rosenthal sets and the Radon-Nikodym property
Authors: Dowling Patrick N. 
Published: April 2009

AbstractLet X be a complex Banach space, G a compact abelian metrizable group and Λ a subset of Ĝ, the dual group of G. If X has the Radon-Nikodym property and is separable then has the Radon-Nikodym property. One consequence of this is that CΛ(G, X) has the Radon-Nikodym property whenever X has the Radon-Nikodym property and the Schur property and Λ is a Rosenthal set. A partial stability property for products of Rosenthal sets is also obtained.
Gevrey spaces and their intersections
Authors: Ter Elst A. F. M. 
Published: April 2009

AbstractFor unbounded operators A1, …, Ad, Gevrey spaces Sλ1, …, λd (A1, …, Ad) of order (λ1, …, λd) are introduced, where the orders λ1, …, λd need not be equal. These extend the notion of Gevrey space defined by Goodman and Wallach where λ1 = … = λd. Several mild conditions on the operators A1, … Ad and the orders λ1, …, λd are presented such that the equality is valid. Examples are included.
The locally convex topology on the space of meromorphic functions
Authors: Grosse-Erdmann Karl-Goswin 
Published: April 2009

AbstractWe give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.
On diameters of orbits of compact groups in unitary representations
Authors: Deutsch Annabel , Valette Alain 
Published: April 2009

AbstractFor a compact group G, we compute the Kazhdan constants κ(G, G) obtained by taking G itself as a generating subset. We get κ(G, G) = if G is finite of order n, and κ(G, G) = if G is infinite.
Categorical compactness for rings
Authors: Fay Temple H. , Joubert Stephan V. 
Published: April 2009

AbstractIn this paper we study categorical compactness with respect to a class of objects F being motiveated by examples arising from modules, abelian groups, and various classes of non-abelian groups. This theory is then applied to the category of not necessarily associative rings. In particular, we study the example arising from the class of all torsion-free rings. This work extends some recent results of B. J. Gardner for associative rings and radical classes.
On the uniform Kadec-Klee property with respect to convergence in measure
Authors: Sukochev F. A. 
Published: April 2009

AbstractLet E(0, ∞) be a separable symmetric function space, let M be a semifinite von Neumann algebra with normal faithful semifinite trace μ, and let E(M, μ) be the symmetric operator space associated with E(0, ∞). If E(0, ∞) has the uniform Kadec-Klee property with respect to convergence in measure then E(M, μ) also has this property. In particular, if LΦ(0, ∞) (ϕ(0, ∞)) is a separable Orlicz (Lorentz) space then LΦ(M, μ) (Λϕ (M, μ)) has the uniform Kadec-Klee property with respect to convergence in measure on sets of finite measure if and only if the norm of E(0, ∞) satisfies G. Birkhoff's condition of uniform monotonicity.
Commutators in pseudo-orthogonal groups
Authors: Arlinghaus F. A. , Vaserstein L. N. , You Hong 
Published: April 2009

AbstractWe study commutators in pseudo-orthogonal groups O2nR (including unitary, symplectic, and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO2nR. We estimate the number of commutators, c(O2nR) and c(GO2nR), needed to represent every element in the commutator subgroup. We show that c(O2nR) ≤ 4 if R satisfies the ∧-stable condition and either n ≥ 3 or n = 2 and 1 is the sum of two units in R, and that c(GO2nR) ≤ 3 when the involution is trivial and ∧ = R∈. We also show that c(O2nR) ≤ 3 and c(GO2nR) ≤ 2 for the ordinary orthogonal group O2nR over a commutative ring R of absolute stable rank 1 where either n ≥ 3 or n = 2 and 1 is the sum of two units in R.
A generalization of Evans' Theorem: embedding partial tricycle systems
Authors: Lindner C. C. , Rodger C. A. 
Published: April 2009

AbstractIn 1960, Trevor Evans gave a best possible embedding of a partial latin square of order n in a latin square of order t, for any t ≥ 2n. A latin square of order n is equivalent to a 3-cycle system of Kn, n, n, the complete tripartite graph. Here we consider a small embedding of partial 3k-cycle systems of Kn, n, n of a certain type which generalizes Evans' Theorem, and discuss how this relates to the embedding of patterned holes, another recent generalization of Evans' Theorem.
The uniform Kadec-Klee property for the Lorentz spaces Lw,1
Authors: Dilworth S. J. , Hsu Yu-Ping 
Published: April 2009

AbstractIn this paper we show that the Lorentz space Lw, 1(0, ∞) has the weak-star uniform Kadec-Klee property if and only if inft>0 (w(αt)/w(t)) > 1 and supt>0(φ(αt) / φ(t))< 1 for all α ∈ (0, 1), where φ(t) = ∫t0 w(s) ds.
Discrete coactions on C*-algebras
Authors: Ng Chi-Keung 
Published: April 2009

AbstractWe will consider coactions of discrete groups on C*-algebras and imitate some of the results about compact group actions on C*-algebras. In particular, the crossed product of a reduced coaction ∈ of a discrete amenable group G on A is liminal (respectively, postliminal) if and only if the fixed point algebra of ∈ is. Moreover, we will also consider ergodic coactions on C*-algebras.
Injective endomorphisms of 𝒢x-normal semigroups: finite defects
Authors: Levi Inessa 
Published: April 2009

AbstractA semigroup of transformations of an infinite set X is called 𝒢x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of 𝒢x-normal semigroups of total one-to-one transformations f such that the range of f has a finite non-empty complement in X.
Flat functors and free exact categories
Authors: Hu Hongde 
Published: April 2009

AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.
On products of almost strong liftings
Authors: Macheras N. D. , Strauss W. 
Published: April 2009

AbstractDealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.
Endomorphisms of type II1-factors and Cuntz algebras
Authors: Enomoto Masatoshi , Watatani Yasuo 
Published: April 2009

AbstractAny unital *-endomorphism of a type II1-factor is implemented by isometries of a Cuntz algebra outside the factor. If the Jones index of the range of the *-endomorphism is an integer and the algebras act on the standard space, the Jones index must agree with the number of the generators of the Cuntz algebra. We also study (outer) conjugacy of *-endomorphisms using Cuntz algebras.
On the L1-convergence of Fourier transforms
Authors: Giang Dᾰng Vũ , Móricz Ferenc 
Published: April 2009

AbstractWe study cosine and sine Fourier transforms defined by F(t):= (2/π) and (t):= (2/π), where f is L1-integrable over[0, ∞]. We also assume than F are locally absolutely continuous over [0, ∞). In particular, this is the case if both f(x) and xf(x) are (L1-integrable over [0, ∞). Motivated by the inversion formulas, we consider the partial integras Sν (f, x):= and ν(f, x):= , the modified partial integrals uν (f, x):= sν(f, x) - F(ν)(sin νx)/x and ũν(f, x):= ν(f, x) + (ν) (cos νx)/x, where ν > 0. We give necessary and sufficient conditions for(L1 [0, ∞)-convergence of uν (f) and ũν (f) as well as for the L1 [0, X]-convergence of sν (f) and ν(f) to f as ν← ∞, where 0 < X < ∞ is fixed. On the other hand, in certain cases we conclude that sν(f) and ν(f) cannot belong to (L1 [0,∞). Conequently, it makes no sense to speak of their (L1 [0, ∞)-convergence as ν ← ∞.As an intermediate tool, we use the Cesàro means of Fourier transforms. Then we prove Tauberian type results and apply Sidon type inequalities in order to obtain Tauberian conditions of Hardy-Karamata kind.We extend these results to the complex Fourier transform defined by G(t):= , where g is L1- integrable over (−∞, ∞).
Weighted composition operators on Orlicz-Sobolev spaces
Authors: Arora Subhash C. , Datt Gopal , Verma Satish 
Published: April 2009

AbstractFor an open subset Ω of the Euclidean space Rn, a measurable non-singular transformation T: Ω → Ω and a real-valued measurable function u on Rn, we study the weighted composition operator uCτ: f ↦ u · (f º T) on the Orlicz-Sobolev space W1·Ψ (Ω) consxsisting of those functions of the Orlicz space LΨ (Ω) whose distributional derivatives of the first order belong to LΨ (Ω). We also discuss a sufficient condition under which uCτ is compact.
On finite generation and presentability of Schützenberger products
Authors: Gallagher Peter , Ruškucs Nik 
Published: April 2009

AbstractThe finite generation and presentation of Schützenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schützenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite.
Permutable functions concerning differential equations
Authors: Hua X. , Vaillancourt R. , Wang X. L. 
Published: April 2009

AbstractLet f and g be two permutable transcendental entire functions. Assume that f is a solution of a linear differential equation with polynomial coefficients. We prove that, under some restrictions on the coefficients and the growth of f and g, there exist two non-constant rational functions R1 and R2 such that R1 (f) = R(g). As a corollary, we show that f and g have the same Julia set: J(f) = J(g). As an application, we study a function f which is a combination of exponential functions with polynomial coefficients. This research addresses an open question due to Baker.
Characterization of left Artinian algebras through pseudo path algebras
Authors: Li Fang 
Published: April 2009

AbstractIn this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field k when the quotient algebra can be lifted by a radical. Our particular interest is when the dimension of the quotient algebra determined by the nth Hochschild cohomology is less than 2 (for example, when k is finite or char k = 0). Using generalized path algebras, a generalization of Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebra is introduced as a new generalization of path algebras, whose quotient by ken is a generalized path algebra (see Fact 2.6).The main result is that(i) for a left Artinian k–algebra A and r = r(A) the radical of A. if the quotient algebra A/r can be lifted then A ≅ PSEk (Δ, , ρ) with Js ⊂ (ρ) ⊂ J for some s (Theorem 3.2);(ii) If A is a finite dimensional k–algebra with 2-nilpotent radical and the quotient by radical can be lifted, then A ≅ k(Δ, , ρ) with 2 ⊂ (ρ) ⊂ 2 + ∩ ker (Theorem 4.2),where Δ is the quiver of A and ρ is a set of relations.For all the cases we discuss in this paper, we prove the uniqueness of such quivers Δ and the generalized path algebras/pseudo path algebras satisfying the isomorphisms when the ideals generated by the relations are admissible (see Theorem 3.5 and 4.4).
The limiting distribution of a recursive resampling procedure
Authors: Zukang Zheng , Lipeng Wu 
Published: April 2009

AbstractA recursive resampling method is discussed in this paper. Let X1, X2,…, Xn, be i.i.d. random variables with distribution function F and construct the empirical distribution function Fn. A new sample Xn+1 is drawn from Fn and the new empirical distribution function 1 in the wide sense, is computed from X1, X2,…, Xn, Xn+1. Then Xn+2 is drawn from 1 and 2 is obtained. In this way, Xn+m and m are found. It will be proved that m converges to a random variable almost surely as m goes to infinity and the limiting distribution is a compound beta distribution. In comparison with the usual non-recursive bootstrap, the main advantage of this procedure is a reduction in unconditional variance.
Hyperbolic linear invariance and hyperbolic k-convexity
Authors: Ma Wancang , Minda David 
Published: April 2009

AbstractPommerenke initiated the study of linearly invariant families of locally schlicht holomorphic functions defined on the unit disk The concept of linear invariance has proved fruitful in geometric function theory. One aspect of Pommerenke's work is the extension of certain results from classical univalent function theory to linearly invariant functions. We propose a definition of a related concept that we call hyperbolic linear invariance for locally schlicht holomorphic functions that map the unit disk into itself. We obtain results for hyperbolic linearly invariant functions which generalize parts of the theory of bounded univalent functions. There are many similarities between linearly invariant functions and hyperbolic linearly invariant functions, but some new phenomena also arise in the study of hyperbolic linearly invariant functions.
On commutator laws in groups, 3
Authors: Macdonald I. D. , Neumann B. H. 
Published: April 2009

AbstractIn this final contribution to the investigation of commutator laws in groups, we answer some of the questions left open in the previous two papers. The principal result is the independence of the Jacobi-Witt-Hall type laws from the so-called standard set of laws. The main results of the earlier papers are summarised. An interlude corrects some of the numerous printing errors in the second of our papers.
On different types of cleavability of topological spaces
Authors: Arhangel'skii A. V. , Cammaroto F. 
Published: April 2009

AbstractThe notion of pointwise cleavability is introduced. We clarify those results concerning cleavability which can be or can not be generalized to the case of pointwise cleavability.The importance of compactness in this theory is shown. Among other things we prove that t, ts, πx, the property to be Fréchet-Urysohn, radiality, biradiality, bisequentiality and so on are preserved by pointwise cleavability on the class of compact Hausdorff spaces.
Characterization of lipschitz spaces on compact Lie groups
Authors: Fan Dashan , Xu Zengfu 
Published: April 2009

AbstractLipschitz spaces are important function spaces with relations to Hp spaces and Campanato spaces, the other two important function spaces in harmonic analysis. In this paper we give some characterizations for Lipschitz spaces on compact Lie groups, which are analogues of results in Euclidean spaces.
Complex extreme measurable selections
Authors: Mupasiri Douglas 
Published: April 2009

AbstractWe give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.
Duality in fractional minimax programming
Authors: Chandra S. , Kumar Viveka 
Published: April 2009

AbstractCertain omissions in the recently introduced dual for fractional minimax programming problem ‘minimize max y ∈ Y f(x, y) / h(x, y), subject to g(x) ≤ 0’, are indicated and two modified duals for this problem are presented. Various fractional programming and generalized fractional programming duals are shown to be special cases of this study.
The class L(log L)α and some lacunary sets
Authors: Gupta Sanjiv Kumar , Madan Shobha , Tewari U. B. 
Published: April 2009

AbstractA well-known result of Zygmund states that if f ∈ L (log+L) ½ on the circle group T and E is a Hadamard set of integers, then . In this paper we investigate similar results for the classes on an arbitrary infinite compact abelian group G and Sidon subsets E of the dual Γ. These results are obtained as special cases of more general results concerning a new class of lacunary sets Sαβ, 0 < α ≤ β, where a subset E of Γ is an Sα β set if . We also prove partial results on the distinctness of the Sαβ sets in the index β.
Right inverses of vector fields
Authors: Virsik George 
Published: April 2009

AbstractD. Przeworska-Rolewicz developed an algebra-based theory around linear, not necessarily continuous, operators D: X → X which admit a right inverse, the elementary example being D = d/dt or, more generally, where ai are constants. We give conditions for the right invertibility of D in the case where ai are functions, or more generally, where D is the Lie or convariant derivative associated with a vector field on a (Banach) manifold M.
Extensions of regular orthogroups by groups
Authors: Szendrei Mária B. 
Published: April 2009

AbstractA common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an orthogroup K by a group, can be embedded into a semidirect product of an orthogroup K′ by a group, where K′ belongs to the variety of orthogroups generated by K. The proof is based on a criterion of embeddability into a semidirect product of an orthodox semigroup by a group and uses bilocality of orthogroup bivarieties.
The continuous Diophantine approximation mapping of Szekeres
Authors: Lagarias Jeffrey C. , Pollington Andrew D. 
Published: April 2009

AbstractSzekeres defined a continuous analogue of the additive ordinary continued fraction expansion, which iterates a map T on a domain which can be identified with the unit square [0, 1]2. Associated to it are continuous analogues of the Lagrange and Markoff spectrum. Our main result is that these are identical with the usual Lagrange and Markoff spectra, respectively; thus providing an alternative characterization of them.Szekeres also described a multi-dimensional analogue of T, which iterates a map Td on a higherdimensional domain; he proposed using it to bound d-dimensional Diophantine approximation constants. We formulate several open problems concerning the Diophantine approximation properties of the map Td.
A problem on growth sequences of groups
Authors: Erfanian A. 
Published: April 2009

AbstractThe aim of this paper is to consider Problem 1 posed by Stewart and Wiegold in [6]. The main result is that if G is a finitely generated perfect group having non-trivial finite images, then there exists a finite image B of G such that the growth sequence of B is eventuallly faster than that of every finite image of G. Moreover we investigate the growth sequences of simple groups of the same order.
An application of Lyapunov's direct method to the study of oscillations of a delay differential equation of even order
Authors: Terry Raymond D. 
Published: April 2009

AbstractThe direct method of Lyapunov is utilized to obtain a variety of criteria for the nonexistence of certain types of positive solutions of a delay differential equation of even order. Previous results of Terry (Pacific J. Math. 52 (1974), 269–282) are seen to be corollaries of the more general results of this paper.
On generalizations of C*-embedding for wallman rings
Authors: Bentley H. L. , Taylor B. J. 
Published: April 2009

AbstractBiles (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on X in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z(A). Here we introduce two different generalizations of the concept of “a C*-embedded subset” and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).
The Stone-Weierstrass theorem for wallman rings
Authors: Bentley H. L. , Taylor B. J. 
Published: April 2009

AbstractBiles has called a subring A of the ring C(X) a Wallman ring on X whenever Z(A), the zero sets of function belonging to A, forms a normal base on X in the sense of Frink (1964). In the following, we are concerned with the uniform topology of C(X). We formulate and prove some generalizations of the Stone–Weierstrass theorem in this setting.