bluuebunny/crossref_metadata_2025_split huggingface dataset:
Scale functions and tree ends
Authors: Kepert A. , Willis G. 
Published: April 2009

AbstractA class of totally disconnected groups consisting of partial direct products on an index set is examined. For such a group, the scale function is found, and for automorphisms arising from permutations of the index set, the tidy subgroups are characterised. When applied to the case where the index set is a finitely-generated free group and the permutation is translation by an element x of the group, the scale depends on the cyclically reduced form of x and the tidy subgroup on the element which conjugates x to its cyclically reduced form.
Goldie dimensions of quotient modules
Authors: Dauns John 
Published: April 2009

AbstractFor an infinite cardinal ℵ an associative ring R is quotient ℵ<-dimensional if the generalized Goldie dimension of all right quotient modules of RR are strictly less than ℵ. This latter quotient property of RR is characterized in terms of certain essential submodules of cyclic modules being generated by less than ℵ elements, and also in terms of weak injectivity and tightness properties of certain subdirect products of injective modules. The above is the higher cardinal analogue of the known theory in the finite ℵ = ℵ0 case.
Gérard-Sibuya's versus Majima's concept of asymptotic expansion in several variables
Authors: Hernández J. A. , Sanz J. 
Published: April 2009

AbstractWe give an example of a holomorphic function, admitting Gérard-Sibuya asymptotic expansion on a polysector of Cn, and such that none of its derivatives admits such an expansion. This motivates the study of the relationship between the concepts of asymptotic expansion in several variables respectively given by Gérard-Sibuya and Majima. For a functionf, Majima's notion is proved to be equivalent, on the one hand, to the existence of Gérard-Sibuya asymptotic expansion forfand its derivatives, and on the other hand, to the boundedness of the derivatives offon bounded proper subpolysectors ofS.
Towers, ladders and the B. B. Newman Spelling Theorem
Authors: Hruska G. Christopher , Wise Daniel T. 
Published: April 2009

AbstractThe Spelling Theorem of B. B. Newman states that for a one-relator group (a1, … |Wn), any nontrivial word which represents the identity must contain a (cyclic) subword ofW±nlonger thanWn−1. We provide a new proof of the Spelling Theorem using towers of 2-complexes. We also give a geometric classification of reduced disc diagrams in one-relator groups with torsion. Either the disc diagram has three 2-cells which lie almost entuirly along the bounday, or the disc diagram looks like a ladder. We use this ladder theorem to prove that a large class of one-relator groups with torsion are locally quasiconvex.
Nilpotency indices of the radicals of finite p-solvable group algebras, I
Authors: Ninomiya Yasushi 
Published: April 2009

AbstractLet k be a field of characteristic p > 0, G a finite p-solvable group and pm the highest power of p dividing the order of G. We denote by t(G) the nilpotency index of the (Jacobson) radical of the group algebra k[G]. The groups G with t(G) ≥ pm−1 are already classified. The aim of this paper is to classify the p-solvable groups G with pm−2 < t(G) < pm−1 for p odd.
Lie powers of free modules for certain groups of prime power order
Authors: Bryant R. M. , Michos I. C. 
Published: April 2009

AbstractLetGbe a finite group of orderpk, wherepis a prime andk≥ 1, such thatGis either cyclic, quaternion or generalised quaternion. LetVbe a finite-dimensional freeKG-module whereKis a field of characteristicp. The Lie powersLn(V) are naturallyKG-modules and the main result identifies these modules up to isomorphism. There are only two isomorphism types of indecomposables occurring as direct summands of these modules, namely the regularKG-module and the indecomposable of dimensionpk–pk−1induced from the indecomposableK H-module of dimensionp− 1, whereHis the unique subgroup ofGof orderp. Formulae are given for the multiplicities of these indecomposables inLn(V). This extends and utilises work of the first author and R. Stöhr concerned with the case whereGhas orderp.
A note on minimal coverings of groups by subgroups
Authors: Bryce R. A. , Serena L. 
Published: April 2009

AbstractAcoverfor a group is a finite set of subgroups whose union is the whole group. A cover isminimalif its cardinality is minimal. Minimal covers of finite soluble groups are categorised; in particular all but at most one of their members are maximal subgroups. A characterisation is given of groups with minimal covers consisting of abelian subgroups.
Young modules for symmetric groups
Authors: Erdmann Karin 
Published: April 2009

AbstractLet K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as Mλ, play a central role not only for symmetric groups but also for general linear groups, via Schur algebras. The indecomposable direct summands of these Mλ were parametrized by James; they are now known as Young modules; and Klyachko and Grabmeier developed a ‘Green correspondence’ for Young modules. The original parametrization used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.
Bounds on finite quasiprimitive permutation groups
Authors: Praeger Cheryl E. , Shalev Aner 
Published: April 2009

AbstractA permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitive, but the converse is not true. In this paper we start a project whose goal is to check which of the classical results on finite primitive permutation groups also holds for quasiprimitive ones (possibly with some modifications). The main topics addressed here are bounds on order, minimum degree and base size, as well as groups containing special p-elements. We also pose some problems for further research.
On the tensor product of polynomials over a ring
Authors: Glasby S. P. 
Published: April 2009

AbstractGiven polynomialsaandbover an integral domainR, their tensor product (denoteda ⊗ b) is a polynomial overRof degree deg(a) deg(b) whose roots comprise all products αβ, where α is a root of a, and β is a root ofb. This paper considers basic properties of ⊗ including how to factora ⊗ binto irreducibles factors, and the direct sum decomposition of the ⊗-product of fields.
Torsion-free groups isomorphic to all of their non-nilpotent subgroups
Authors: Longobardi Patrizia , Maj Mercede , Smith Howard , Wiegold James 
Published: April 2009

AbstractThe main result is that every torsion-free locally nilpotent group that is isomorphic to each of its nonnilpotent subgroups is nilpotent, that is, a torsion-free locally nilpotent group G that is not nilpotent has a non-nilpotent subgroup H that is not isomorphic to G.
Nilpotent injectors and conjugacy classes in solvable groups
Authors: Robinson Geoffrey R. 
Published: April 2009

AbstractWe provide an upper bound for the order of a nilpotent injector of a finite solvable group with Fitting subgroup of ordern. We also show that the same bound is an upper bound for the number of conjugacy classes, provided that thek(G V)-conjecture holds for solvableGall primes dividingn.
Fregean subtractive varieties with definable congruence
Authors: Agliano Paolo 
Published: April 2009

AbstractIn this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.
Osserman pseudo-Riemannian manifolds of signature (2,2)
Authors: Blažić Novica , Bokan Neda , Rakić Zoran 
Published: April 2009

AbstractA pseudo-Riemannian manifold is said to be timelike (spacelike) Osserman if the Jordan form of the Jacobi operator Kx is independent of the particular unit timelike (spacelike) tangent vector X. The first main result is that timelike (spacelike) Osserman manifold (M, g) of signature (2, 2) with the diagonalizable Jacobi operator is either locally rank-one symmetric or flat. In the nondiagonalizable case the characteristic polynomial of Kx has to have a triple zero, which is the other main result. An important step in the proof is based on Walker's study of pseudo-Riemannian manifolds admitting parallel totally isotropic distributions. Also some interesting additional geometric properties of Osserman type manifolds are established. For the nondiagonalizable Jacobi operators some of the examples show a nature of the Osserman condition for Riemannian manifolds different from that of pseudo-Riemannian manifolds.
Three bimodules for Mansfield's imprimitivity theorem
Authors: Kaliszewski S. , Quigg John 
Published: April 2009

AbstractFor a maximal coaction δ of a discrete group G on a C*-algebra A and a normal subgroup N of G, there are at least three natural A × G ×δ| N - A ×δ|1 G/N imprimitivity bimodules: Mansfield's bimodule ; the bimodule assembled by Ng from Green's imprimitivity bimodule and Katayama duality; and the bimodule assembled from and the crossed-product Mansfield bimodule . We show that all three of these are isomorphic, so that the corresponding inducing maps on representations are identical. This can be interpreted as saying that Mansfield and Green induction are inverses of one another ‘modulo Katayama duality’. These results pass to twisted coactions; dual results starting with an action are also given.
Congruence quasi-orderability in subtractive varieties
Authors: Agliano Paolo 
Published: April 2009

AbstractIn this paper we investigate subtractive varieties of algebras that are congruence quasi-orderable. Though this concept has its origin in abstract algebraic logic, it seems to be worth investigating in a purely algebraic fashion. Besides clarifying the algebraic meaning of this notion, we obtain several structure theorems about such varieties. Also several examples are provided to illustrate the theory.
A characterization of weighted Bergman-Orlicz spaces on the unit ball in Cn
Authors: Matsugu Yasuo , Miyazawa Jun 
Published: April 2009

AbstractLet B denote the unit ball in Cn, and ν the normalized Lebesgue measure on B. For α > −1, define Here cα is a positive constant such that να(B) = 1. Let H(B) denote the space of all holomorphic functions in B. For a twice differentiable, nondecreasing, nonnegative strongly convex function ϕ on the real line R, define the Bergman-Orlicz space Aϕ(να) by In this paper we prove that a function f ∈ H(B) is in Aϕ(να) if and only if where is the radial derivative of f.
Parametrizing simple closed geodesy on Γ3\ℋ
Authors: Schmidt Thomas A. , Sheingorn Mark 
Published: April 2009

AbstractWe exhibit a canonical geometric pairing of the simple closed curves of the degree three cover of the modular surface, Γ3\ℋ, with the proper single self-intersecting geodesics of Crisp and Moran. This leads to a pairing of fundamental domains for Γ3with Markoff triples.The routes of the simple closed geodesics are directly related to the above. We give two parametrizations of these. Combining with work of Cohn, we achieve a listing of all simple closed geodesics of length within any bounded interval. Our method is direct, avoiding the determination of geodesic lengths below the chosen lower bound.
Two weighted ineqalities for maximal functions related to Cesàro convergence
Authors: Bernardis A. L. , Martín-Reyes F. J. 
Published: April 2009

AbstractWe characterize the pairs of weights (u, v) for which the maximal operator is of weak and restricted weak type (p, p) with respect to u(x)dx and v(x)dx. As a consequence we obtain analogous results for We apply the results to the study of the Cesàro-α convergence of singular integrals.
Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras
Authors: Dvurečenskij Anatolij 
Published: April 2009

AbstractPseudo-effect algebras are partial algebras (E; +, 0, 1) with a partially defined addition + which is not necessary commutative and with two complements, left and right ones. We define central elements of a pseudo-effect algebra and the centre, which in the case of MV-algebras coincides with the set of Boolean elements and in the case of effect algebras with the Riesz decomposition property central elements are only characteristic elements. If E satisfies general comparability, then E is a pseudo MV-algebra. Finally, we apply central elements to obtain a variation of the Cantor-Bernstein theorem for pseudo-effect algebras.
Paschke's conjecture for the endpoint anisotropic series representations of the free group
Authors: Kuhn M. Gabriella , Steger Tim 
Published: April 2009

AbstractLet Γ be a free noncommutative group with free generating set A+. Let μ ∈ ℓ1(Γ) be real, symmetric, nonnegative and suppose that supp. Let λ be an endpoint of the spectrum of μ considered as a convolver on ℓ2(Γ). Then λ − μ is in the left kernel of exactly one pure state of the reduced in particular, Paschke's conjecture holds for λ − μ.
Theta functions on Hermitian symmetric domains and fock representations
Authors: Lee Min Ho 
Published: April 2009

AbstractOne way of realizing representations of the Heisenberg group is by using Fock representations, whose representation spaces are Hilbert spaces of functions on complex vector space with inner products associated to points on a Siegel upper half space. We generalize such Fock representations using inner products associated to points on a Hermitian symmetric domain that is mapped into a Seigel upper half space by an equivariant holomorphic map. The representations of the Heisenberg group are then given by an automorphy factor associated to a Kuga fiber variety. We introduce theta functions associated to an equivariant holomorphic map and study connections between such generalized theta functions and Fock representations described above. Furthermore, we discuss Jacobi forms on Hermitian symmetric domains in connection with twisted torus bundles over symmetric spaces.
Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration
Authors: Wu Zhen 
Published: April 2009

AbstractWe first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.
Group Laws Implying Virtual Nilpotence
Authors: Burns R. G. , Medvedev Yuri 
Published: April 2009

AbstractIf ω ≡ 1 is a group law implying virtual nilpotence in every finitely generated metabelian group satisfying it, then it implies virtual nilpotence for the finitely generated groups of a large class of groups including all residually or locally soluble-or-finite groups. In fact the groups of satisfying such a law are all nilpotent-by-finite exponent where the nilpotency class and exponent in question are both bounded above in terms of the length of ω alone. This yields a dichotomy for words. Finally, if the law ω ≡ 1 satisfies a certain additional condition—obtaining in particular for any monoidal or Engel law—then the conclusion extends to the much larger class consisting of all ‘locally graded’ groups.
Embeddings of ℓp into Non-commutative Spaces
Authors: Randrianantoanina Narcisse 
Published: April 2009

AbstractLet ℳ be a semi-finite von Neumann algebra equipped with a faithful normal trace τ. We prove a Kadec-Pelczyński type dichotomy principle for subspaces of symmetric space of measurable operators of Rademacher type 2. We study subspace structures of non-commutative Lorentz spaces Lp, q, (ℳ, τ), extending some results of Carothers and Dilworth to the non-commutative settings. In particular, we show that, under natural conditions on indices, ℓp cannot be embedded into Lp, q (ℳ, τ). As applications, we prove that for 0 < p < ∞ with p ≠ 2, ℓp cannot be strongly embedded into Lp(ℳ, τ). This provides a non-commutative extension of a result of Kalton for 0 < p < 1 and a result of Rosenthal for 1 ≦ p < 2 on Lp [0, 1].
Two Results About H∞ Functional Calculus on Analytic umd Banach Spaces
Authors: Le Merdy Christian 
Published: April 2009

AbstractLet X be a Banach space with the analytic UMD property, and let A and B be two commuting sectorial operators on X which admit bounded H∞ functional calculi with respect to angles θ1 and θ2 satisfying θ1 + θ2 > π. It was proved by Kalton and Weis that in this case, A + B is closed. The first result of this paper is that under the same conditions, A + B actually admits a bounded H∞ functional calculus. Our second result is that given a Banach space X and a number 1 ≦ p < ∞, the derivation operator on the vector valued Hardy space Hp (R; X) admits a bounded H∞ functional calculus if and only if X has the analytic UMD property. This is an ‘analytic’ version of the well-known characterization of UMD by the boundedness of the H∞ functional calculus of the derivation operator on vector valued Lp-spaces Lp (R; X) for 1 < p < ∞ (Dore-Venni, Hieber-Prüss, Prüss).
On The Asymptotic Values of Length Functions In Krull And Finitely Generated commutative Monoids
Authors: Chapman S. T. , Rosales J. C. 
Published: April 2009

AbstractLet M be a commutative cancellative atomic monoid. We consider the behaviour of the asymptotic length functions and on M. If M is finitely generated and reduced, then we present an algorithm for the computation of both and where x is a nonidentity element of M. We also explore the values that the functions and can attain when M is a Krull monoid with torsion divisor class group, and extend a well-known result of Zaks and Skula by showing how these values can be used to characterize when M is half-factorial.
Engel Series Expansions of Laurent Series and Hausdorff Dimensions
Authors: Wu Jun 
Published: April 2009

AbstractFor any positive integer q≧2, let Fq be a finite field with q elements, Fq ((z-1)) be the field of all formal Laurent series in an inderminate z, I denote the valuation ideal z-1Fq [[z-1]] in the ring of formal power series Fq ((z-1)) normalized by P(l) = 1. For any x ∈ I, let the series be the Engel expansin of Laurent series of x. Grabner and Knopfmacher have shown that the P-measure of the set A(α) = {x ∞ I: limn→∞ deg an(x)/n = ά} is l when α = q/(q -l), where deg an(x) is the degree of polynomial an(x). In this paper, we prove that for any α ≧ l, A(α) has Hausdorff dimension l. Among other thing we also show that for any integer m, the following set B(m) = {x ∈ l: deg an+1(x) - deg an(x) = m for any n ≧ l} has Hausdorff dimension 1.
Multiplicities of Higher Lie Characters
Authors: Schocker Manfred 
Published: April 2009

AbstractThe higher Lie characters of the symmetric groupSnarise from the Poincaré-Birkhoff-Witt basis of the free associative algebra. They are indexed by the partitions ofnand sum up to the regular character ofSn. A combinatorial description of the multiplicities of their irreducible components is given. As a special case the Kraśkiewicz-Weyman result on the multiplicities of the classical Lie character is obtained.
Higher Dimensional Cohomology of Weighted Sequence Algebras
Authors: Pourabbas A. 
Published: April 2009

AbstractIt is well known thatc0(Z) is amenable and so its global dimension is zero. In this paper we will investigate the cyclic and Hochschild cohomology of Banach algebrac0(Z, ω-1) and its unitisation with coefficients in its dual space, where ω is a weight on Z which satisfies inf {ω(i)} = 0.Moreover we show that the weak homological bi-dimension ofc0(Z, ω-1) is infinity.
Lacunas in the Support of the Weyl Calculus for Two Hermitian Matrices
Authors: Jefferies Brian , Straub Bernd 
Published: April 2009

AbstractThe connection between Clifford analysis and the Weyl functional calculus for ad-tuple of bounded selfadjoint operators is used to prove a geometric condition due to J. Bazer and D. H. Y. Yen for a point to be in the support of the Weyl functional calculus for a pair of hermitian matrices. Examples are exhibited in which the support has gaps.
Interpolation problem for l1 and a uniform algebra
Authors: Nakazi Takahiko 
Published: April 2009

AbstractLet A be a uniform algebra and M(A) the maximal ideal space of A. A sequence {an} in M(A) is called l1-interpolating if for every sequence (αn) in l1 there exists a function f in A such that f (an) = αn for all n. In this paper, an l1-interpolating sequence is studied for an arbitrary uniform algebra. For some special uniform algebras, an l1-interpolating sequence is equivalent to a familiar l-interpolating sequence. However, in general these two interpolating sequences may be different from each other.
A problem on rough parametric Marcinkiewicz functions
Authors: Ding Yong , Lu Shanzhen , Yabuta Kôzô 
Published: April 2009

AbstractIn this note the authors give theL2(n) boundedness of a class of parametric Marcinkiewicz integralwith kernel function Ω inLlog+L(Sn−1) and radial functionh(|x|) ∈ l ∞ l(Lq)(+) for 1 < q ≦.As its corollary, theLp(n)(2 < p < ∞) boundedness of andandwith Ω inLlog+L (Sn-1) and h(|x|) ∈ l∞(Lq)(+) are also obtained. Hereandare parametric Marcinkiewicz functions corresponding to the Littlewood-Paleyg*λ-function and the Lusin area functionS, respectively.
Radicals and polynomial rings
Authors: Beidar K. I. , Puczyłowski E. R. , Wiegandt R. 
Published: April 2009

AbstractWe prove that polynomial rings in one indeterminate over nil rings are antiregular radical and uniformly strongly prime radical. These give some approximations of Köthe's problem. We also study the uniformly strongly prime and superprime radicals of polynomial rings in non-commuting indeterminates. Moreover, we show that the semi-uniformly strongly prime radical coincides with the uniformly strongly prime radical and that the class of semi-superprime rings is closed under taking finite subdirect sums.
On the Gauss maps of singular projective varieties
Authors: Ballico E. 
Published: April 2009

AbstractHere we study the dimension δ(m, X) of the general fibers of the m-Gaussian map of a singular n-dimensional variety X ⊂ Pn. We show that for all integers a, b, c, d with n ≦ a < b ≦ c < d ≦ N − 1 and a + d = b + c we have δ (a, X) + δ(d, X) > δ(b, X) + δ(c, X). If δ(X, N − 1) is very large we give some classification results which extend to the singular case some results of Ein.
Computation of nonsquare constants of Orlicz spaces
Authors: Yan Y. Q. 
Published: April 2009

AbstractIn this paper, we present the computation of exact value of nonsquare constants for some types of Orlicz sequence and function spaces. Main results: Let φ(u) be an N-function, φ(t) be the right derivative of φ(u), then we have (i) if φ (t) is concave, then (ii) if φ (t)is convex, then
Optimality criteria in set-valued optimization
Authors: Lalitha C. S. , Dutta J. , Govil Misha G. 
Published: April 2009

AbstractThe main aim of this paper is to obtain optimality conditions for a constrained set-valued optimization problem. The concept of Clarke epiderivative is introduced and is used to derive necessary optimality conditions. In order to establish sufficient optimality criteria we introduce a new class of set-valued maps which extends the class of convex set-valued maps and is different from the class of invex set-valued maps.