bluuebunny/crossref_metadata_2025_split huggingface dataset:
Near-rings of continuous functions on disconnected groups
Authors: Hofer Robert D. 
Published: April 2009

AbstractN(G) denotes the near-ring of all continuous selfmaps of the topological group G (under composition and the pointwise induced operation) and N0(G) is the subnear-ring of N(G) consisting of all functions having the identity element of G fixed. It is known that if G is discrete then (a) N0(G) is simple and (b) N(G) is simple if and only if G is not of order 2. We begin a study of the ideal structure of these near-rings when G is a disconnected group.
Some asymptotic methods in combinatorics
Authors: Plotkin J. M. , Rosenthal John 
Published: April 2009

AbstractLet 〈fn≧0 be nonnegative real numbers with generating function f(x) = Σfnxn. Assume f(x) has the following properties: it has a finite nonzero radius of convergence x0 with its only singularity on the circle of convergence at x = x0 and f(x0) converges to y0; y = f(x) satisfies an analytic identity F(x, y) = 0 near (x0, y0); Fy(l) (x0, y0)= 0, 0 ≦ i < k and Fy(k) (x0, y0) ≠ 0. There are constants γ, a positive rational, and c such that fn~cx0−n n−(1 +ggr;). Furthermore, we show (i) in all cases how to determine γ and c from f(x) and (ii) in certain cases how to determine them from F(x, y).
Relative stability, characteristic functions and stochastic compactness
Authors: Maller R. A. 
Published: April 2009

AbstractA recent result of Rogozin on the relative stability of a distribution function is extended, by giving equivalences for relative stability in terms of truncated moments of the distribution and in terms of the real and imaginary parts of the characteristic function. As an application, the known results on centering distributions in the domain of attraction of a stable law are extended to the case of stochastically compact distributions.
Verma modules over Virasoro-like algebras
Authors: Wang Xian-Dong , Zhao Kaiming 
Published: April 2009

AbstractLet K be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order ≺ on G, which is compatible with the addition, and for any ċ1, ċ2 ∈ K, we define G-graded highest weight modules M(ċ1, ċ2, ≺) over the Virasoro-like algebra , indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M (ċ1, ċ2, ≺) is completely determined and the structure of reducible module M (ċ1, ċ2, ≺)is also described.
Expansions of inverse semigroups
Authors: Lawson Mark V. , Margolis Stuart W. , Steinberg Benjamin 
Published: April 2009

AbstractWe construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we termF-morphisms. These play the same role in the theory of idempotent-pure homomorphisms thatF-inverse monoids play in the theory ofE-unitary inverse semigroups.
A lower bound for the degree of polynomials satisfied by matrices
Authors: Pearson K. R. 
Published: April 2009

AbstractR. Paré and W. Schelter (1978) have extended the Cayley-Hamilton theorem by showing that for each n<1 there is an integer k such that all n x n matrices over any (possibly noncommutative) ring satisfy a monic polynomial of degree k. We give a lower bound for this degree, namely π(n), which is defined as the shortest possible length of a sequence with entries from {1, 2, …, n}.
A class of regularities for rings
Authors: Roos C. 
Published: April 2009

AbstractIn this paper a general concept of regularity for rings is defined. It is shown that every regularity determines in a natural way a subradical and a radical for rings. A wide class of regularities is constructed: the class of polynomial regularities. All well-known regularities, such as the Perlis-Jacobson regularity, the von Neumann regularity and many others, belong to this class. Special attention is paid to regularities which are elementary in the sense that the so-called unic and nullic polynomial regularities can be thought of as intersections of the elementary ones.
Approximation by a sum of polynomials of different degrees involving primes
Authors: Liu Ming-Chit 
Published: April 2009

AbstractLet λj(1 ≦j≦ 4) be any nonzero real numbers which are not all of the same sign and not all in rational ratio and let pjbe polynomials of degree one or two with integer coefficients and positive leading coefficients. The author proves that if exactly two pjare of degree two then for any real n there are infinitely many solutions in primes pjof the inequality. where 0 <β < (√(21)–1)∖5760.
Retracts of partially ordered sets
Authors: Duffus Dwight , Rival Ivan 
Published: April 2009

AbstractLet P be a finite, connected partially ordered set containing no crowns and let Q be a subset of P. Then the following conditions are equivalent: (1) Q is a retract of P; (2) Q is the set of fixed points of an order-preserving mapping of P to P; (3) Q is obtained from P by dismantling by irreducibles.
Onf(n) modulo Ω(n) and ω(n) whenfis a polynomial
Authors: Luca Florian 
Published: April 2009

AbstractIn this paper we show that iff(X) ∈; Z [X ] is a nonzero polynomial, then ω(n)/f(n)holds only on a set ofnof asymptotic density zero, where for a positive integernthe number ω(n) counts the number of distinct prime factors ofn.
Ergodicity and stability of orbits of unbounded semigroup representations
Authors: Basit Bolis , Pryde A. J. 
Published: April 2009

AbstractWe develop a theory of ergodicity for unbounded functions ø: J → X, where J is a subsemigroup of a locally compact abelian group G and X is a Banach space. It is assumed that ø is continuous and dominated by a weight w defined on G. In particular, we establish total ergodicity for the orbits of an (unbounded) strongly continuous representation T: G → L(X) whose dual representation has no unitary point spectrum. Under additional conditions stability of the orbits follows. To study spectra of functions, we use Beurling algebras L1w(G) and obtain new characterizations of their maximal primary ideals, when w is non-quasianalytic, and of their minimal primary ideals, when w has polynomial growth. It follows that, relative to certain translation invariant function classes , the reduced Beurling spectrum of ø is empty if and only if ø ∈ . For the zero class, this is Wiener's tauberian theorem.
The size of characters of exceptional lie groups
Authors: Hare Kathryn E. , Yeats Karen 
Published: April 2009

AbstractPointwise bounds for characters of representations of the compact, connected, simple, exceptional Life groups are obtained. It is a classical result that if μ is a central, continuous measure on such a group, then μdimG is absolutely continuous. Our estimates on the size of characters allow us to prove that the exponent, dimension of G, can be replaced by approximately the rank of G. Similar results were obtained earlier for the classical, compact Lie groups.
The double cover relative to a convex domain and the relative isoperimetric inequality
Authors: Choe Jaigyoung 
Published: April 2009

AbstractWe prove that a domain Ω in the exterior of a convex domain C in a four-dimensional simply connected Riemannian manifold of nonpositive sectional curvature satisfies the relative isoperimetric inequality 64π2 Vol(Ω)3 < Vol(∂Ω ~ ∂C)4. Equality holds if and only if Ω is an Euclidean half ball and ∂Ω ~ ∂C is a hemisphere.
The Gelfand transform of homogeneous distributions on Heisenberg type groups
Authors: Astengo Francesca , Blasio Bianca Di 
Published: April 2009

AbstractA distribution on a Heisenberg type group of homogeneous dimension Q is a biradial kernel of type α if it coincides with a biradial function, homogeneous of degree α — Q, and smooth away from the identity. We prove that a distribution is a biradial kernel of type α, 0 < α < Q, if and only if its Gelfand transform, defined on the Heisenberg fan, extends to a smooth even function on the upper half plane, homogeneous of degree −α/2. A similar result holds for radial kernels on the Heisenberg group.
Filter games and pathological subgroups of a countable product of lines
Authors: Banakh Taras , Nickolas Peter , Sanchis Manuel 
Published: April 2009

AbstractTo each filter ℱ on ω, a certain linear subalgebra A(ℱ) of Rω, the countable product of lines, is assigned. This algebra is shown to have many interesting topological properties, depending on the properties of the filter ℱ. For example, if ℱ is a free ultrafilter, then A(ℱ) is a Baire subalgebra of ℱω for which the game OF introduced by Tkachenko is undetermined (this resolves a problem of Hernández, Robbie and Tkachenko); and if ℱ1 and ℱ2 are two free filters on ω that are not near coherent (such filters exist under Martin's Axiom), then A (ℱ1) and A(ℱ2) are two o-bounded and OF-undetermined subalgebras of ℱω whose product A(ℱ1) × A(ℱ2) is OF-determined and not o-bounded (this resolves a problem of Tkachenko). It is also shown that the statement that the product of two o-bounded subrings of ℱω is o-bounded is equivalent to the set-theoretic principle NCF (Near Coherence of Filters); this suggests that Tkachenko's question on the productivity of the class of o-bounded topological groups may be undecidable in ZFC.
Normal characterization by zero correlations
Authors: Seneta Eugene , Szekely Gabor J. 
Published: April 2009

AbstractSuppose Xi, i = 1,…,n are indepedent and identically distributed with E/X1/r < ∞, r = 1,2,…. If Cov (( − μ)r, S2) = 0 for r = 1, 2,…, where μ = EX1, S2 = , and , then we show X1 ~ N (μ, σ2), where σ2 = Var(X1). This covariance zero condition charaterizes the normal distribution. It is a moment analogue, by an elementary approach, of the classical characterization of the normal distribution by independence of and S2 using semi invariants. More generally, if Cov = 0 for r = 1,…, k, then E((X1 − μ)/σ)r+2 = EZr+2 for r = 1,… k, where Z ~ N(0, 1). Conversely Corr may be arbitrarily close to unity in absolute value, but for unimodal X1, Corr2( < 15/16, and this bound is the best possible.
C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems
Authors: Matsumoto Kengo 
Published: April 2009

AbstractA λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. InDoc. Math.7 (2002) 1–30, the author constructed aC*-algebraO£associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebraO£, under a certain condition on £ called (II). As a result, the class of theC*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.
The Weighted g-drazin inverse for operators
Authors: Dajić A. , Koliha J. J. 
Published: April 2009

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29(1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.
Homomorphisms of nonzero degree betweenPDn-groups
Authors: Hillman Jonathan A. 
Published: April 2009

AbstractWe give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply toPDn-groups which are virtually poly-Zor have a Kropholler decomposition into parts of generalized Seifert type, for alln.
On quasinilpotent Operators, II
Authors: Foiaş Ciprian , Jung Il Bong , Ko Eungil , Pearcy Carl 
Published: April 2009

AbstractIn this paper we continue to modify and expand a technique due to Enflo for producing nontrivial hyperinvariant subspaces for quasinilpotent operators, and thereby obtain such subspaces for some additional quasinilpotent operators on Hilbert space. We also obtain a structure theorem for a certain class of operators.
A dual differentiation space without an equivalent locally uniformly rotund norm
Authors: Kenderov Petar S. , Moors Warren B. 
Published: April 2009

AbstractA Banach space (X, ∥ · ∥) is said to be a dual differentiation space if every continuous convex function defined on a non-empty open convex subset A of X* that possesses weak* continuous subgradients at the points of a residual subset of A is Fréchet differentiable on a dense subset of A. In this paper we show that if we assume the continuum hypothesis then there exists a dual differentiation space that does not admit an equivalent locally uniformly rotund norm.
An LP version of Hardy's theorem for the Dunkl transform
Authors: Gallardo Léonard , Trimèche Khalifa 
Published: April 2009

AbstractIn this paper, we give a generalization of Hardy's theorems for the Dunkl transform ℱD on ℝd. More precisely for all a > 0, b > 0 and p, q ∈ [1, + ∞], we determine the measurable functions f on ℝd such that where are the Lebesgue spaces associated with the Dunkl transform.
Modular Lie representations of finite groups
Authors: Bryant R. M. 
Published: April 2009

AbstractLet K be a field of prime characteristic p and let G be a finite group with a Sylow p-subgroup of order p. For any finite-dimensional K G-module V and any positive integer n, let Ln (V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then Ln(V) can be considered as a K G-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of Ln(V) up to isomorphism.
The commutator subgroup and Schur multiplier of a pair of finite p-groups
Authors: Salemkar Ali Reza , Moghaddam Mohammad Reza R. , Saeedi Farshid 
Published: April 2009

AbstractLet (M, G) be a pair of groups, in which M is a normal subgroup of G such that G/M and M/Z(M, G) are of orders pm and pn. respectively. In 1998, Ellis proved that the commutator subgroup [M, G] has order at most pn(n + 2 m−1)/2.In the present paper by assuming /[M, G] = pn(n+2m−1)/2, we determine the pair (M, G). An upper bound is obtained for the Schur multiplier of the pair (M, G), which generalizes the work of Green (1956).
Finite Fourier series and ovals in PG(2, 2h)
Authors: Fisher J. Chris , Schmidt Bernhard 
Published: April 2009

AbstractWe propose the use of finite Fourier series as an alternative means of representing ovals in projective planes of even order. As an example to illustrate the method's potential, we show that the set {wj + w3j + w−3j: 0 ≤ j ≤ 2h} ⊂ GF (22h) forms an oval if w is a primitive (2h + 1)st root of unity in GF(22h) and GF(22h) is viewed as an affine plane over GF(2h). For the verification, we only need some elementary ‘trigonometric identities’ and a basic irreducibility lemma that is of independent interest. Finally, we show that our example is the Payne oval when h is odd, and the Adelaide oval when h is even.
Strict convexity of sets in analytic terms
Authors: Dalla Leoni , Hatziafratis Telemachos 
Published: April 2009

AbstractWe compare the geometric concept of strict convexity of open subsets of Rn with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2N-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.
On symmetric ideals of multilinear mappings between Banach spaces
Authors: Botelho Geraldo , Pellegrino Daniel M. 
Published: April 2009

AbstractIn this paper we provide examples and counterexamples of symmetric ideals of multilinear mappings between Banach spaces and prove that if I1, …, In are operator ideals, then the ideals of multilinear mappings L(I1, …, In) and /I1, …, In/ are symmetric if and only if I1 = … = In.
Continuous bijections on manifolds
Authors: Doyle P. H. , Hocking J. G. 
Published: April 2009

AbstractThe main results of the paper give necessary and sufficient conditions as well as sufficient conditions that continuous bijections of a manifold onto itself be homeomorphisms. Such conditions include the embedding of manifolds, preserving ends, preserving closed half-rays and restrictions on boundary components. A number of counterexamples are given to likely conjectures.
Finitely generated subgroups of amalgamated free products and HNN groups
Authors: Cohen Daniel E. 
Published: April 2009

AbstractThe theory of groups acting on trees due to Bass and Serre (1969) is applied to simplify some results of Burns (1972, 1973) giving conditions under which an amalgamated free product or HNN extension has the properties that any finitely generated subgroup containing an infinite subnormal subgroup must have finite index and that the intersection of two finitely generated subgroups is finitely generated.
Compatible tight Riesz orders on C(X)
Authors: Loci Elizabeth 
Published: April 2009

AbstractThe pointwise order makes the group C(X) of continuous real-valued functions on a topological space X a lattice-ordered group. We give a characterization of the compatible tight Riesz orders on C(X), and also of their maximal tangents, in terms of the zero-sets of X. The space of maximal tangents of a given compatible tight Riesz order T is studied, and consequently the concept of the T-radical of C(X) is introduced, the T-radical being the intersection of all the maximal tangents of T.
Conjugate purity and infinite groups
Authors: Balogun Bola O. 
Published: April 2009

AbstractIn Balogun (1974), we proved that a finite group in which every subgroup is conjugately pure is necessarily Abelian and we left open the infinite case. In this paper we settle this problem positively for soluble, locally soluble groups and certain classes of groups which include the FC-groups. In the last section of this paper we characterize groups which are conjugately pure in every containing group.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 E 99.
The automorphism group of the semigroup of finite complexes of a periodic abelian group
Authors: Byrd R. D. , Lloyd J. T. , Stepp J. W. 
Published: April 2009

AbstractIn this paper it is shown that ifGis a periodic Abelian group and ∣G∣ ≥ 6, then the only automorphisms of the semigroup of finite nonempty complexes ofGare induced by automorphisms ofG.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 M 15; secondary 20 K 30.
Order-bounded convergence structures on spaces of continuous functions
Authors: Schroder M. 
Published: April 2009

AbstractThis paper deals with solid topologies and convergence structures on the vector-lattice CX (the set of all continuous real-valued functions on a space X): the closed ideals and locally convex topologies associated with such structures are studied in particular. The work stems from E. Hewitt's paper on bounded linear functionals, touches on the classical theorems of L. Nachbin, T. Shirota and others (determining when the topology of compact convergence is barrelled or bornological), and extends some recent results on the duality between x and CX.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 35; secondary 54 A 20.
When is the iterate of a formal power series odd?
Authors: Reznick Bruce 
Published: April 2009

AbstractThe formal power series (fps) f(z) = Σ∞i=1ai zi is homozygous mod k if ai ≠ 0 implies i ≡ j mod k. This generalizes even and odd fps. If f is homozygous mod k then all iterates of f (fn = f ο fn−1) are also homozygous mod k, but the converse is false–there are many non-odd fps f for which f(f(z)) = z. It is shown that if f is not homozygous mod k but fn is homozygous, then fnr(z) = z for some r. If all coefficienrs ar real then, in fact, f(f(z)) = z.Subject classification (Amer. Math Soc. (MOS) 1970): 39 A 05.
Solutionally complete varieties
Authors: Hule Harald 
Published: April 2009

AbstractA veristy is called solutionally complete if any solvable system of algebraic equations over an algebra A in which has at most one solution in every extension of A in has the solution in A. A necessary and sufficient condition for solutional completeness is given which is a weaker form of the strong amalgamation property.Subject classification (Amer. Math. Soc. (MOS) 1970): 08 A 15.
On characters in the principal 2-block, II
Authors: Herzog Marcel , Praeger Cheryl E. 
Published: April 2009

AbstractLet k be a non-zero complex number and let u and v be elements of a finite group G. Suppose that at most one of u and v belongs to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(v)–X(u) = k for every complex nonprincipal irreducible character X in the principal 2-block of G, if and only if G/O(G) is isomorphic to one of the following groups: C2, PSL(2, 2n) or pΣL(2, 52a+1), where n≥2 and a ≥ 1.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20
Integral starlike trees
Authors: Watanabe Mamoru , Schwenk Allen J. 
Published: April 2009

AbstractIn this note we determine which of the trees homeomorphic to a star have a spectrum consisting entirely of integers. We also specify the integral double stars, and we consider the problem of trees with more complicated structure.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 05.
Compactifications of semitopological semigroups II
Authors: Milnes Paul 
Published: April 2009

AbstractCorrecting some “proofs” given in an earlier paper of the same title, we prove here, among other things, that, if S is a subgroup of a topological group that is complete in a left invariant metric or locally compact, then every weakly almost periodic function on S is (left and right) uniformly continuous. We also prove a theorem related to results of R. B. Burckel and of W. W. Comfort and K. A. Ross: a topological group is pseudocompact if and only if WAP(G) = C(G).
Regularly varying solutions of a linear functional equation
Authors: Kuczma Marek 
Published: April 2009

AbstractWe are concerned with the problem of the existence and uniqueness of regularly varying (in Karamata's sense) solutions ϕ of the linear functional equation in a right neighbourhood of x = 0. Under suitable conditions on the given functions f and h, the uniqueness of solutions depends essentially on whether the series Σh ∘ f1 converges or diverges; here fi denotes the i-th functional iterate of f. The existence of solutions may be proved under further assumptions.The case of the more general linear functional equation may be reduced to that of equation (*).
Some exact solutions of certain field equations in general relativity
Authors: Patel L. K. 
Published: April 2009

SummaryA general metric is considered. Some solutions correspoding to the field equations Rik λgik = −8πEik are obtained as particular cases. Details of these solutions are also discussed. An Einstein space corresponding to the field equations Rik = λ gik is also constructed as a particular case of the general metric.
An entire function which has wandering domains
Authors: Baker I. N. 
Published: April 2009

AbstractLet f(z) denote a rational or entire function of the complex variable z and fn(z), n = 1,2, …, the n−th iterate of f. Provided f is not rational of order 0 or 1, the set of those points where {fn(z)} forms a normal family is a proper subset of the plane and is invariant under the map z → f(z). A component G of is a wandering domain of f if fn(G)∩fn(G) = Ø for all k ≧ 1, n ≧ 1, k ≠ n. The paper contains the construction of a transcendental entire function which has wandering domains.