bluuebunny/crossref_metadata_2025_split huggingface dataset:
Digit patterns and transcendental numbers
Authors: Morton Patrick , Mourant W. J. 
Published: April 2009

AbstractWe use a theorem of Loxton and van der Poorten to prove the transcendence of certain real numbers defined by digit patterns. Among the results we prove are the following. If k is an integer at least 2, P is any nonzero pattern of digits base k, and counts the number of occurrences (mod r) of p in the base k representation of n, then is transcendental except when k = 3, P = 1 and r = 2. When (r, k − 1) = 1 the linear span of the numbers has infinite dimension over Q, where P ranges over all patterns base k without leading zeros.
Goldie M-groups
Authors: Chowdhury K. C. 
Published: April 2009

AbstractIf (G+) is a group and M is a nonempty set of endomorphisms of G operating on the left then G is said to be M-Goldie when (i) G has no infinite independent family of nonzero M-subgroups, and (ii) annihilators in M of subsets of G satisfy the a.c.c. (under set inclusion). Here we prove some results, analogous to those of a Noetherian module in some special cases, even when the set M of operators has no other algebraic structure than the existence of a zero element or in some cases M is at most a finite dimensional commutative near-ring. Precisely speaking, we prove that the collection of associated operating sets of G is finite and there exists a primary decomposition of 0 of such a Goldie M-group, and then if M is a finite dimensional commutative near-ring with unity, for any x belonging to each associated operating set of G, a power of it belongs to the annthilator of G.
On Grasia's criterion for uniform convergence of Fourier series
Authors: Oehring Charles 
Published: April 2009

AbstractGarsia's discovery that functions in the periodic Besov space λ(p-1,p, 1), with 1 <p< ∞, have uniformly convergent Fourier series prompted him, and others, to seek a proof based on one of the standard convergence tests. on one of the standard convergence tests. We show that Lebesgue's test is adequate, whereas Garsia's criterion is independent of other classical critiera (for example, that of Dini-Lipschitz). The method of proof also produces a sharp estimate for the rate of uniform convergence for functions in λ(p-1,p, 1). Further, it leads to a very simple proof of the embedding theorem for these spaces, which extends (though less simply) to λ(α,p, q)
Diophantine approximation by continued fractions
Authors: Tong Jingcheng 
Published: April 2009

AbstractLet ξ be an irrational number with simple continued fraction expansion be its ith convergent. Let Mi = [ai+1,…, a1]+ [0; ai+2, ai+3,…]. In this paper we prove that Mn−1 < r and Mn R imply which generalizes a previous result of the author.
Groups of odd order in which every subnormal subgroup has defect at most two
Authors: Cossey John 
Published: April 2009

AbstractIn 1980, McCaughan and Stonehewer showed that a finite soluble group in which every subnormal subgroup has defect at most two has derived length at most nine and Fitting length at most five, and gave an example of derived length five and Fitting length four. In 1984 Casolo showed that derived length five and Fitting length four are best possible bounds.In this paper we show that for groups of odd order the bounds can be improved. A group of odd order with every subnormal subgroup of defect at most two has derived and Fitting length at most three, and these bounds are best possible.
Radical Theory for Granded Rings
Authors: Fang Honghin , Stewart Patrick 
Published: April 2009

AbstractIn this paper we propose a general setting in which to study the radical theory of group graded rings. If is a radical class of associative rings we consider two associated radical classes of graded rings which are denoted by G and ref. We show that if is special (respectively, normal), then both G and ref are graded special (respectively, graded normal). Also, we discuss a graded version of the ADS theorem and the termination of the Kurosh lower graded radical construction.
Conjugate polynomials over quadratic algebras
Authors: Stokes Timothy 
Published: April 2009

AbstractThis paper gives variants of results from classical algebraic geometry and commutative algebra for quadratic algebras with conjugation. Quadratic algebras are essentially two-dimensional algebras with identity over commutative rings with identity, on which a natural operation of conjugation may be defined. We define the ring of conjugate polynomials over a quadratic algebra, and define c-varieties. In certain cases a close correspondence between standard varieties and c-varieties is demonstrated, and we establish a correspondence between conjugate and standard polynomials, which leads to variants of the Hilbert Nullstellensatz if the commutativering is an algebraically closed field. These results may be applied to automated Euclidean geometry theorem proving.
The continuity of derivations from group algebras: factorizable and connected groups
Authors: Willis George 
Published: April 2009

AbstractA group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.
Type radicals and quasi-decompositions of torsion-free abelian groups
Authors: Mutzbauer Oteo 
Published: April 2009

AbstractA composition sequence for a torsion-free abelian group A is an increasing sequenceof pure subgroups with rank 1 quotients and union A. Properties of A can be described by the sequence of types of these quotients. For example, if A is uniform, that is all the types in some sequence are equal, then A is complete decomposable if it is homogeneous. If A has finite rank and all permutations ofone of its type sequences can be realized, then A is quasi-isomorphic to a direct sum of uniform groups.
Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable
Authors: Hillman J. A. , Linnell P. A. 
Published: April 2009

AbstractIf G is an elementary amenable group of finite Hirsch length h, then the quotient of G by its maximal locally finite normal subgroup has a maximal solvable normal subgroup, of derived length and index bounded in terms of h.
Oscillations of higher order neutral differential equations
Authors: Bilchev S. J. , Grammatikopoulos M. K. , Stavroulakis I. P. 
Published: April 2009

AbstractConsider the nth-order neutral differential equation where n ≥ 1, δ = ±1, I, K are initial segments of natural numbers, pi, τi, σk ∈ R and qk ≥ 0 for i ∈ I and k ∈ K. Then a necessary and sufficient condition for the oscillation of all solutions of (E) is that its characteristic equation has no real roots. The method of proof has the advantage that it results in easily verifiable sufficient conditions (in terms of the coefficients and the arguments only) for the oscillation of all solutionso of Equation (E).
Large transcendence degree
Authors: Tubbs Robert 
Published: April 2009

AbstractIn this paper we study the transcendence degree of fields generated over Q by the numbers associated with values of one-parameter subgroups of commutative algebraic groups. We show that in many instances these fields have a large transcendence degree when measured in terms of the available data.Our method deals with points which are “well distributed” (in a sense which is made precise) among certain algebraic subgroups of the algebraic group under consideration. We verify that these results apply in many classical situations.
Amenability and weak amenability of tensor algebras and algebras of nuclear operators
Authors: Grønbaek Niels 
Published: April 2009

AbstractLet E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, Nf (E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim KF ≦ 1, and the trace on E⊗F is injective on KF. Here KF is the kernel of the canonical map E⊗^F →NF(E). On the route we find the corresponding statements for the associated tensor algebra, E⊗^F.
Embedding finite semigroup amalgams
Authors: Okniński Jan , Putcha Mohan S. 
Published: April 2009

AbstractLet S, T1,… Tk be finite semigroups and Ψ: S → Ti, be embeddings. When C[S] is semisimple, we find necessary and sufficient conditions for the semigroup amalgam (T1,…, Tk; S) to be embeddable in a finite semigroup. As a consequence we show that if S is a finite semigroup with C[S] semisimple, then S is an amalgamation base for the class of finite semigroups if and only if the principal ideals of S are linearly ordered. Our proof uses both the theory of representations by transformations and the theory of matrix representations as developed by Clifford, Munn and Ponizovskii
Zero square near-rings
Authors: Jones Patricia 
Published: April 2009

AbstractThe purpose of this paper is to provide examples and explore properties of a wide variety of zero square (left) near rings. Among the main results are complete classifications of (i) finite Abelian groups which are the additive group of a zero square near-ring and (ii) finite non-Abelian groups which support 3-nilpotent distributive zero square near-rings.
Integration with respect to vector valued Radon polymeasures
Authors: Jefferies Brian , Ricker Werner J. 
Published: April 2009

AbstractProblems dealing with certain functional calculi for systems of non-commuting operators, and ordered calculi for systems of certain types of pseudo-differential operators, can sometimes be treated via the methods of integration with respect to polymeasures. The polymeasures arising in this fashion (called Radon polymeasures) often have additional structure not available in the general theory. This allows for a more extensive class of “integrable” functions than just the product functions allowed in the abstract theory. The purpose here is to further develop special aspects of integration with respect to Radon polymeasures with a particular emphasis on identifying large classes of “integrable” functions.
Maximum principles for parabolic equations
Authors: Porru Giovanni , Serra Salvatore 
Published: April 2009

AbstractLet u(x, t) be a smooth function in the domain Q = Ω × (0, L), Ω in n, let Du be the spatial gradient of u(x, t) and let ∇u = (Du, u1). If u(x, t) satisfies the parabolic equation F(u, Du, D2u) = ut, we define w(x, t) by g(w) = │∇u│−1G(∇u) (g is positive and decreasing, G is concave and homogeneous of degree one) and we prove that w(x, t) attains its maximum value on the parabolic boundary of Q. If u(x, t) satisfies the equation Δu + 2h(q2) uiujuij = ut(q2 = │Du│2, 1 + 2q2h(q2) > 0) we prove that qf (u) takes its maximum value on the parabolic boundary of Q provided f satisfies a suitable condition. If u(x, t) satisfies the parabolic equation aij (Du)uij − b(x, t, u, Du) = ut (b is concave with respect to (x, t, u)) we define C(x, y, t, τ) = u(z, θ) − αu(x, t) − βu(y, τ) (0 < α, 0 < β, α + β = 1, z αx +y, θ = αt + βτ) and we prove that if C(x, y, t, r) ≤0 when x, y, z ∈ Ω2 and one of t, τ = 0, and when t, τ ∈ (0, L], and one of x, y, z, ∈ ∂Ω, then it is C(x, y, t, τ) ≤0 everywhere.
Vertex-transitive graphs which are not Cayley graphs, I
Authors: McKay Brendan D. , Praeger Cheryl E. 
Published: April 2009

AbstractThe Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph which is not a Cayley graph. We consider the problem of determining the orders of such graphs. In this, the first of a series of papers, we present a sequence of constructions which solve the problem for many orders. In particular, such graphs exist for all orders divisible by a fourth power, and all even orders which are divisible by a square.
On the Fourier transform of a compact semisimple Lie group
Authors: Wildberger N. J. 
Published: April 2009

AbstractWe develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case ofSU(2) is treated in some detail, where some interesting connections with classical spherical trigonometry are obtained.
Invariant subspaces in the bidisc and commutators
Authors: Nakazi Takahiko 
Published: April 2009

AbstractLet M be an invariant subspace of L2 (T2) on the bidisc. V1 and V2 denote the multiplication operators on M by coordinate functions z and ω, respectively. In this paper we study the relation between M and the commutator of V1 and , For example, M is studied when the commutator is self-adjoint or of finite rank.
On the Lebesgue function of weighted Lagrange interpolation. II
Authors: Vértesi P. 
Published: April 2009

AbstractThe aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on ℝ and weights on [−1, 1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains.
The Plancherel formula for the horocycle spaces and generalizations, II
Authors: Lipsman Ronald L. 
Published: April 2009

AbstractThe Plancherel formula for various semisimple homogeneous spaces with non-reductive stability group is derived within the framework of the Bonnet Plancherel formula for the direct integral decomposition of a quasi-regular representation. These formulas represent a continuation of the author's program to establish a new paradigm for concrete Plancherel analysis on homogeneous spaces wherein the distinction between finite and infinite multiplicity is de-emphasized. One interesting feature of the paper is the computation of the Bonnet nuclear operators corresponding to certain exponential representations (roughly those induced from infinite-dimensional representations of a subgroup). Another feature is a natural realization of the direct integral decomposition over a canonical set of concrete irreducible representations, rather than over the unitary dual.
The growth of certain amalgamated free products and HNN-extensions
Authors: Edjvet M. , Johnson D. L. 
Published: April 2009

AbstractHere we mean growth in the sense of Milnor and Gromov. After a brief survey of known results, we compute the growth series of the groups, with respect to generators {x, y}. This is done using minimal normal forms obtained by informal use of judiciously chosen rewrite rules. In both of these examples the growth series is a rational function, and we suspect that this is not the case for the Baumslag-Solitar group.
Quasi θ-spaces and pairwise θ-perfect irreducible mappings
Authors: Kandil A. , Kerre E. E. , El-Shafei M. E. , Nouh A. A. 
Published: April 2009

AbstractIn this paper we extend the notion of perfect, θ-continuous, irreducible and θ-perfect mappings to bitopological spaces. The main result is the following: the (small) image of an (i, j)-canonical open sets is an (i, j)-canonical open set under a pairwise θ-closed irreducible surjective mapping. Also we extend the notion of θ-proximity spaces to quasi θ-proximity spaces and point out the interrelation between it and separated quasi-proximity spaces by means of a pairwise θ-perfect irreducible mappings.
Bifurcation and stability of positive solutions of a two-point boundary value problem
Authors: Wang Shin-Hwa , Kazarinoff Nicholas D. 
Published: April 2009

AbstractWe consider the existence of multiple positive solutions of a nonlinear two-point boundary value problem by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the number of positive solutions and find their Conley indices and thus determine their stabilities.
Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable
Authors: Wang Shin-Hwa , Kazarinoff Nicholas D. 
Published: April 2009

AbstractWe study the bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the exact number of steady-state solutions which are totally ordered in an order interval. We are then able to find their Conley indices and thus determine their stabilities.
Isomorphisms of hypergroups
Authors: Bloom Walter R. , Walter Martin E. 
Published: April 2009

AbstractLet K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.
Euclidean linear invariance and uniform local convexity
Authors: Ma Wancang , Minda David 
Published: April 2009

AbstractLet S(p) be the family of holomorphic functions f defined on the unit disk D, normalized by f(0) = f1(0) – 1 = 0 and univalent in every hyperbolic disk of radius p. Let C(p) be the subfamily consisting of those functions which are convex univalent in every hyperbolic disk of radius p. For p = ∞ these become the classical families S and C of normalized univalent and convex functions, respectively. These families are linearly invariant in the sense of Pommerenke; a natural problem is to calculate the order of these linearly invariant families. More precisely, we give a geometrie proof that C(p) is the universal linearly invariant family of all normalized locally schlicht functions of order at most coth(2p). This gives a purely geometric interpretation for the order of a linearly invariant family. In a related matter, we characterize those locally schlicht functions which map each hyperbolically k-convex subset of D onto a euclidean convex set. Finally, we give upper and lower bounds on the order of the linearly invariant family S(p) and prove that this class is not equal to the universal linearly invariant family of any order.
The associated order of a preorder
Authors: Miller John Boris 
Published: April 2009

AbstractAny preorder P on a set X has an associated preorder P′, P″, P‴, … The proerties of this sequence are studied. When X is finite the sequence is eventually periodic with period P = 1 or p = 1, the eventual constant preorder is full p = 2 the possible forms which the eventual alternating order can take are examined: first, the possible combinations of components are enumerated; second, the notion of ramification at a caste is used to show that X may in a heuristic sense be of unbounded complexity. If X is orderdense the periodicity starts at P′.
Subdirect products of E–inversive semigroups
Authors: Mitsch H. 
Published: April 2009

AbstractA semigroup S is called E-inversive if for every a ∈ S ther is an x ∈ S such that (ax)2 = ax. A construction of all E-inversive subdirect products of two E-inversive semigroups is given using the concept of subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an E-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least group congruence on an arbitrary E-inversive semigroup is given. The special case of full subdirect products of a semilattice and a group (that is, containing all indempotents of the direct product) is investigated and, following an idea of Petrich, a construction of all these semigroups is provided. Finally, all periodic semigroups which are subdirect products of a semilattice or a band with a group are characterized.
A new approach to the distribution of the duration of the busy period for a G/G/l queueing system
Authors: Stadje Wolfgang 
Published: April 2009

AbstractFor a G/G/l queueing system let Xt be the number of customers present at time t and Yt(Zt) be the time elapsed since the last arrival of a customer (the last completion of a service) at time t. Let τl be the time until the number of customers in the sustem is reduced from j to j – l, given that X0 = j ≧ l, Y0 = y, Z0 = z. For the joint distribution of τl and Yτl and the Laplace transforms of the τl intergral equations are derived. Under slight conditions these integral equations have unique solutions which can be determined by standard methods. Our results offer a method for calculating the busy period distribution which is completely different from the usual fluctuatuion theoretic approach.
Minimal varieties and quasivarieties
Authors: Bergman Clifford , McKenzie Ralph 
Published: April 2009

AbstractWe prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.
Collineation groups preserving an oval in a projective place of odd order
Authors: Biliotti Mauro , Korchmaros Gabor 
Published: April 2009

AbstractIn this paper we investigate the structure of a collineation group G of a finite projective plane Π of odd order, assuming that G leaves invariant an oval Ω of Π. We show that if G is nonabelian simple, then G ≅ PSL(2, q) for q odd. Several results about the structre and the action of G are also obtained under the assumptions that n ≡ 1 (4) and G is transitive on the points of Ω.
M-Cohyponormal powers of composition operators
Authors: Khurana Satish K. , Ram Babu 
Published: April 2009

AbstractLet T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.
Self-complementary graph decompositions
Authors: Rodger C. A. 
Published: April 2009

AbstractA complementary decomposition of λKn into a graph G is an edge-disjoint decomposition of λKn into copies of G such that if each copy H of G is replaced by its complement in V(H) then the result is an edge-disjoint decomposition of λKn into copies of GC it is a self- complementary decomposition if G = Gc. The spectrum for the last self-complementary graph on at most 7 vertices is found.
Uniform distribution and lattice point counting
Authors: Everest G. R. 
Published: April 2009

AbstractA well-known theorem of Hardy and Littlewood gives a three-term asymptotic formula, counting the lattice points inside an expanding, right triangle. In this paper a generalisation of their theorem is presented. Also an analytic method is developed which enables one to interpret the coefficients in the formula. These methods are combined to give a generalisation of a “heightcounting” formula of Györy and Pethö which itself was a generalisation of a theorem of Lang.
Multiplication Operators and Dynamical Systems
Authors: Singh R. K. , Manhas Jasbir Singh 
Published: April 2009

AbstractLet X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X, T) induced by operator-valued mappings and then obtain a (linear) dynamical system on this weighted function space.