bluuebunny/crossref_metadata_2025 huggingface dataset:
Pointwise estimates of the size of characters of compact Lie groups
Authors: Hare Kathryn E. , Wilson David C. , Yee Wai Ling
Published: April 2009

Pointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained with which allow us to study the singularity of central measures. For example, we find the minimal integer k such that any continuous orbital measure convolved with itself k times belongs to L2. We also prove that if k = rank G then μ 2k ∈ L1 for all central, continuous measures μ. This improves upon the known classical result which required the exponent to be dimension of the group G.
Theta series liftings from orthogonal groups to semi-simple groups
Authors: Lee Min Ho
Published: April 2009

We study a correspondence between automorphic forms on an orthogonal group and automorpbic forms on a semi-simple Lie group associated to an equivariant holomorphic map of a symmetric domain into a Siegel upper half space. We construct an automorphic form on the symmetric domain thatg corresponds to an automorphic form on an orthogonal group using theta series, and prove that such a correspondence is compatible with the appropriate Hecks operator actions on the corresponding automorphic forms. As an example, we describe the case of spin groups.
Stability and constant boundary-value problems of harmonic maps with potential
Authors: Chen Qun
Published: April 2009

Let M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.
Transformation formula of higher order integrals
Authors: Qian Tao , Zhong Tongde
Published: April 2009

By using integration by parts and Stokes' formula the authors give a new definition of the Hadamard principal value of higher order singular integrals on the complex hypersphere in Cn. Then the transformation formula for the higher order singular integrals is deduced.
Automatic continuity and second order cohomology
Authors: Runde Volker
Published: April 2009

Many Banach algebrasAhave the property that, although there are discontinuous homomorphisms fromAinto other Banach algebras, every homomorphism fromAinto another Banach algebra is automatically continuous on a dense subspace—preferably, a subalgebra—ofA. Examples of such algebras areC*-algebras and the group algebrasL1(G), whereGis a locally compact, abelian group. In this paper, we prove analogous results for, whereEis a Banach space, and. An important rôle is played by the second Hochschild cohomology group ofand, respectively, with coefficients in the one-dimensional annihilator module. It vanishes in the first case and has linear dimension one in the second one.
8-dimensional Einstein-Thorpe manifolds
Authors: Kim Jaeman
Published: April 2009

We prove that a compact orientable Einstein-Thorpe manifold of dimension 8 that satisfies 6X = |P2| must be flat.
Finitely generated residually torsion-free nilpotent groups. I
Authors: Baumslag Gilbert
Published: April 2009

The object of this paper is to study the sequence of torsion-free ranks of the quotients by the terms of the lower central series of a finitely generated group. This gives rise to the introduction into the study of finitely generated, residually torison-free nilpotent groups of notions relating to the Gelfand-Kirillov dimension. These notions are explored here. The main result concerning the sequences alluded to is the proof that there are continuously many such sequences.
Some questions aboutp-groups
Authors: Mann Avinoam
Published: April 2009

We present some questions that we feel are important and interesting for the theory of finitep-groups, and survey known results regarding these questions.

Mike, the other year you asked me how I saw the future of p-group theory. All I can offer in answer are more questions.
Algorithmic Questions in rings of rational matriecs
Authors: Sims Charles C.
Published: April 2009

This paper discusses several algorithmic problems related to rings of rational matrices. It provides solutions to these problems in the commutative case and points out some of the difficulties to be overcome in the general case. A connection with attempts to construct Gröbner bases for ideals in free rings is also illustrated.
Endoprimal abelian groups
Authors: Kaarli Kalle , Márki László
Published: April 2009

A group A is said to be endoprimal if its term functions are precisely the functions which permute with all endomorphisms of A. In this paper we describe endoprimal groups in the following three classes of abelian groups: torsion groups, torsionfree groups of rank at most 2, direct sums of a torsion group and a torsionfree group of rank 1.
Non-wandering points and the depth of a graph map
Authors: Ye Xiangdong
Published: April 2009

Lef: G → G be a continuous map of a graph and let d(A) denote the derived set (or limit points) of A ⊂ G. We prove that d(Ω(f)) ⊂ λ (f) and the depth of f is at most three. We also prove that if f is piecewise monotone or has zero topological entropy, then the depth of f is at most two. Furthermore, we obtain some results on the topological structure of Ω(f).
Tameness and geodesic cores of subgroups
Authors: Gitik Rita
Published: April 2009

Let N be a finitely generated normal subgroup of a finitely generated group G. We show that if the trivial subgroup is tame in the factor group G/N, then N is that in G. We also give a short new proof of the fact that quasiconvex subgroups of negatively curved groups are tame. The proof utilizes the concept of the geodesic core of the subgroup and is related to the Dehn algorithm.
Equivalence of certain categories of modules for quantized affine lie algebras
Authors: Futorny Vyacheslav M. , Melville Duncan J.
Published: April 2009

We show that a quantum Verma-type module for a quantum group associated to an affine Kac-Moody algebra is characterized by its subspace of finite-dimensional weight spaces. In order to do this we prove an explicit equivalence of categories between a certain category containing the quantum Verma modules and a category of modules for a subalgebra of the quantum group for which the finite part of the Verma module is itself a module.
Integration maps and local equicontinuity of spectral measures
Authors: Okada S. , Ricker W. J.
Published: April 2009

One of the useful features of spectral measures which happen to be equicontinuous is that their associated integration maps are bicontinuous isomorphisms of the corresponding L1-space onto their ranges. It is shown here that equicontinuity is not necessary for this to be the case; a somewhat weaker property suffices. This is of some interest in practice since there are many natural examples of spectral measures which fail to be equiconontinuous.
Nonsmooth critical point theory and nonlinear elliptic equations at resonance
Authors: Kourogenis Nikolaos C. , Papageorgiou Nikolaos S.
Published: April 2009

In this paper we complete two tasks. First we extend the nonsmooth critical point theory of Chang to the case where the energy functional satisfies only the weaker nonsmooth Cerami condition and we also relax the boundary conditions. Then we study semilinear and quasilinear equations (involving the p-Laplacian). Using a variational approach we establish the existence of one and of multiple solutions. In simple existence theorems, we allow the right hand side to be discontinuous. In that case in order to have an existence theory, we pass to a multivalued approximation of the original problem by, roughly speaking, filling in the gaps at the discontinuity points.
On profinite groups in which commutators are Engel
Authors: Shumyatsky Pavel
Published: April 2009

We show that if G is a finitely generated profinite group such that [x1, x2, …, xk] is Engel for any x1, x2, …, xk ∈ G, then γ(G) is locally nilpotent, and if [x1, x2, …, xk] has finite order for any x1, x2, …, xk ∈ G then, under some additional assumptions, γk(G) is locally finite.
Bases for cyclotomic units over function fields
Authors: Bae S. , Jung H.
Published: April 2009

We find a basis for the universal punctured even distribution and then a basis for the cyclotomic units over function fields.
Path properties of the primitives of a Brownian motion
Authors: Lin Zhengyan
Published: April 2009

Let {W(t),t≥ 0} be a standard Brownian motion. For a positive integerm, define a Gaussian processWatanabe and Lachal gave some asymptotic properties of the processXm(·),m≥ 1. In this paper, we study the bounds of its moduli of continuity and large increments by establishing large deviation results.
Remarks concerning finitely generated semigroups having regular sets of unique normal forms
Authors: Cutting Andrew , Solomon Andrew
Published: April 2009

Properties such as automaticity, growth and decidability are investigated for the class of finitely generated semigroups which have regular sets of unique normal forms. Knowledge obtained is then applied to the task of demonstrating that a class of semigroups derived from free inverse semigroups under certain closure operations is not automatic.
The torsion of the group of homeomorphisms of powers of the long line
Authors: Deo Satya , Gauld David
Published: April 2009

By blending techniques from set theory and algebraic topology we investigate the order of any homeomorphism of the nth power of the long ray or long line L having finite order, finding all possible orders when n = 1, 2, 3 or 4 in the first case and when n = 1 or 2 in the second. We also show that all finite powers of L are acyclic with respect to Alexander-Spanier cohomology.
Diameter-preserving linear bijections of function spaces
Authors: Rao T. S. S. R. K. , Roy A. K.
Published: April 2009

In this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.
Minimum sized fibres in distributive lattices
Authors: Duffus Dwight , Sands Bill
Published: April 2009

A subset F of an ordered set X is a fibre of X if F intersects every maximal antichain of X. We find a lower bound on the function ƒ (D), the minimum fibre size in the distributive lattice D, in terms of the size of D. In particular, we prove that there is a constant c such that In the process we show that minimum fibre size is a monotone property for a certain class of distributive lattices. This fact depends upon being able to split every maximal antichain of this class of distributive lattices into two parts so that the lattice is the union of the upset of one part and the downset of the other.
A generalisation of the Morse inequalities
Authors: Bhupal Mohan
Published: April 2009

In this paper we construct a family of variational families for a Legendrian embedding, into the 1-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embdeddings, by discretising the action functional. We compute the second variation of a generating funciton obtained as above at a nondegenerate critical point and prove a formula relating the signature of the second variation to the Maslov index as the mesh goes to zero. We use this to prove a generlisation of the Morse inequalities thus refining a theorem of Chekanov.
Unique Hahn-Banach theorems for spaces of homogeneous polynomials
Authors: Aron R. , Boyd C. , Choi Y. S.
Published: April 2009

We investigate certain norm and continuity conditions that provide us with ‘uniqe Hahn-Banch Theorems’ from (nc0) to (nℓ∞) and from N(nE) to N(nE″). We show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on complex c0 to ℓ∈ but there is no unique norm-preserving extension from (3c0) to (3ℓ∈).
Fractional parts of Linear polynomials and an application to hypergeometric functions
Authors: Dvornicich Roberto , Zannier Umberto
Published: April 2009

Using a result on arithmetic progressions, we describe a method for finding the rational h–tuples ρ = (ρl,…,ρh) such that all the multiples mρ (for m coprime to a denominator of ρ) lie in a linear variety modulo Z. We give an application to hypergeometric functions.
On Banach-Mazur compacta
Authors: Ageev Sergei M. , Repovŝ Duŝan
Published: April 2009

We study Banach-Mazur compacta Q(n), that is, the sets of all isometry classes of n-dimensional Banach spaces topologized by the Banach-Mazur metric. Our main result is that Q(2) is homeomorphic to the compactification of a Hilbert cube manifold by a point, for we prove that Qg(2) = Q(2) / {Eucl.} is a Hilbert cube manifold. As a corollary it follows that Q(2) is not homogeneous.
Estimation and filtering of fractional generalised random fields
Authors: Angulo J. M. , Ruiz-Medina M. D. , Anh V. V.
Published: April 2009

This paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of random fields for which the least-squares linear estimation problem is solved in a weak-sense are also investigated in terms of the covariance spectrum of the information random field.
Norm inequalities relating one-sided singular integrals and the one-sided maximal function
Authors: Riveros M. S. , de la Torre A.
Published: April 2009

In this paper we prove that if a weight w satisfies the condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal function, for 1 < p < q < ∞.
Locally graded groups with a nilpotency condition on infinite subsets
Authors: Delizia Costantino , Rhemtulla Akbar , Smith Howard
Published: April 2009

A group G is locally graded if every finitely generated nontrivial subgroup of G has a nontrivial finite image. Let N (2, k)* denote the class of groups in which every infinite subset contains a pair of elements that generate a nilpotent subgroup of class at most k. We show that if G is a finitely generated locally graded N (2, k)*-group, then there is a positive integer c depending only on k such that G/Zc (G) is finite.
Composition operators on Qp spaces
Authors: Lou Zengjian
Published: April 2009

A holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.
The perturbation theory for the Drazin inverse and its applications II
Authors: Rakočevič Vladimir , Wei Yimin
Published: April 2009

We study the perturbation of the generalized Drazin inverse for the elements of Banach algebras and bounded linear operators on Banach space. This work, among other things, extends the results obtained by the second author and Guorong Wang on the Drazin inverse for matrices.
Essentially commutative C*-algebras with essential spectrum homeomorphic to S2n−1
Authors: Guo Kunyu
Published: April 2009

This paper gives a complete classification of essentially commutative C*-algebras whose essential spectrum is homeomorphic to S2n−1 by their characteristic numbers. Let 1, 2 be such two C*-algebras; then they are C*-isomorphic if and only if they have the same n-th characteristic number. Furthermore, let γn() = m then is C*-isomorphic to C*(Mzl, …, Mzn) if m = 0, is C*-isomorphic C*(Tz1, …, Tzn−1, Tznm) if m ≠ 0. Some examples are given to show applications of the classfication theorem. We finally remark that the proof of the theorem depends on a construction of a complete system of representatives of Ext(S2n−1).
Dual characterizations of relative continuity of convex functions
Authors: Benoist J. , Daniilidis A.
Published: April 2009

Various properties of continuity for the class of lower semicontinuous convex functions are considered and dual characterizations are established. In particular, it is shown that the restriction of a lower semicontinuous convex function to its domain (respectively, domain of subdifferentiability) is continuous if and only if its subdifferential is strongly cyclically monotone (respectively, σ-cyclically monotone).
Extrema of random algebraic polynomials with non-identically distributed normal coefficients
Authors: Farahmand K. , Grigorash A.
Published: April 2009

An asymptotic estimate is derived for the expected number of extrema of a polynomial whose independent normal coefficients possess non-equal non-zero mean values. A result is presented that generalizes in terms of normal processes the analytical device used for construction of similar asymptotic estimates for random polynomials with normal coefficients.
Locally full HNN extensions of inverse semigroups
Authors: Yamamura Akihiro
Published: April 2009

We investigate a locally full HNN extension of an inverse semigroup. A normal form theorem is obtained and applied to the word problem. We construct a tree and show that a maximal subgroup of a locally full HNN extension acts on the tree without inversion. Bass-Serre theory is employed to obtain a group presentation of the maximal subgroup as a fundamental group of a certain graph of groups associated with the D-structure of the original semigroup.
Scale functions and tree ends
Authors: Kepert A. , Willis G.
Published: April 2009

A 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

For 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

We 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

The 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.
Lacunarity on nonabelian groups and summing operators
Authors: Dodds P. G.
Published: April 2009

In this note we investigate lacunarity or ‘thin’ subsets in the dual object of a compact group via different classes of summing operators between Banach spaces. In particular, we give characterisations of Sidon and ∧ (p) sets, 2 < p < ∞
Nilpotency indices of the radicals of finite p-solvable group algebras, I
Authors: Ninomiya Yasushi
Published: April 2009

Let 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

LetGbe 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

Acoverfor 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.
Cyclic permutable subgroups of finite groups
Authors: Cossey John , Stonehewer Stewart E.
Published: April 2009

The authors describe the structure of the normal closure of a cyclic permutable subgroup of odd order in a finite group.
Young modules for symmetric groups
Authors: Erdmann Karin
Published: April 2009

Let 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

A 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.
Counting irreducible Goppa codes
Authors: Fitzpatrick Patrick , Ryan John A.
Published: April 2009

We consider ineducible Goppa codes of length qm over Fq defined by polynomials of degree r, where q = pt and p, m, r are distinct primes. The number of such codes, inequivalent under coordinate permutations and field automorphisms, is determined.
On the tensor product of polynomials over a ring
Authors: Glasby S. P.
Published: April 2009

Given 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

The 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

We 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

In 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

A 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

For 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

In 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

Let 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.
Even and odd entire functions
Authors: Beardon A. F.
Published: April 2009

We examine what can be said about a polynomial p and an entire function f given that p o f is an even, or an odd, function.
Parametrizing simple closed geodesy on Γ3\ℋ
Authors: Schmidt Thomas A. , Sheingorn Mark
Published: April 2009

We 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

We 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

Pseudo-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.
On normal families of meromorphic functions
Authors: Xu Yan , Fang Mingliang
Published: April 2009

In this paper we obtain some normality criteria of families of meromorphic functions, which improve and generalize the related results of Gu and Bergweiler, respectively. Some examples are given to show the sharpness of our results.
Paschke's conjecture for the endpoint anisotropic series representations of the free group
Authors: Kuhn M. Gabriella , Steger Tim
Published: April 2009

Let 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

One 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

We 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

If 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

Let 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

Let 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

Let 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

For 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

The 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

It 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

The 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

Let 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

In 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

We 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.
Calderón-type reproducing formulae on Lipschitz curves and surfaces
Authors: Qian Tao
Published: April 2009

Calderón type reproducing formulae with applications have been studied on one- and higher-dimensional Lipschitz graphs. In this note we study higher order Calderón reproducing formulae on star-shaped and non-star-shaped closed Lipschitz curves and surfaces.
Convexity of generalized numerical range associated with a compact Lie group
Authors: Tam Tin-Yau
Published: April 2009

Westwick's convexity theorem on the numerical range is generalized in the context of compact connected Lie groups.
On the Gauss maps of singular projective varieties
Authors: Ballico E.
Published: April 2009

Here 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.
Elements of rings with equal spectral idempotents
Authors: Koliha J. J. , Patricio Pedro
Published: April 2009

In this paper we define and study a generalized Drazin inverse xD for ring elements x, and give a characterization of elements a, b for which aaD = bbD. We apply our results to the study of EP elements in a ring with involution.
Computation of nonsquare constants of Orlicz spaces
Authors: Yan Y. Q.
Published: April 2009

In 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
On finiteJ-groups
Authors: Ballester-Bolinches A. , Esteban-Romero R.
Published: April 2009

Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.
Optimality criteria in set-valued optimization
Authors: Lalitha C. S. , Dutta J. , Govil Misha G.
Published: April 2009

The 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.
An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators
Authors: Amor Ali Ben
Published: April 2009

Given two m-tuples of commuting spectral operators on a Hilbert space, T = (T1,…, Tm) and S = (S1,…, Sm), an extended version of Henrici perturbation theorem is obtained for the joint approximate spectrum of S under perturbation by T. We also derive an extended version of Bauer-Fike theorem for such tuples of operators. The method used involves Clifford algebra techniques introduced by McIntosh and Pryde.
The Lp-Lp mapping properties of convolution operators with the affine arclength measure on space curves
Authors: Choi Youngwoo
Published: April 2009

The Lp-improving properties of convolution operators with measures supported on space curves have been studied by various authors. If the underlying curve is non-degenerate, the convolution with the (Euclidean) arclength measure is a bounded operator from L3/2()3 into L2(3). Drury suggested that in case the underlying curve has degeneracies the appropriate measure to consider should be the affine arclength measure and the obtained a similar result for homogeneous curves t→(t, t2, tk), t >0 for k ≥ 4. This was further generalized by Pan to curves t → (t, tk, tt), t > 0 for l < k < l, k+l ≥ 5. In this article, we will extend Pan's result to (smooth) compact curves of finite type whose tangents never vanish. In addition, we give an example of a flat curve with the same mapping properties.
Nilpotent groups are not dualizable
Authors: Quackenbush R. , Szabó C. S.
Published: April 2009

It is shown that no finite group containing a non-abelian nilpotent subgroup is dualizable. This is in contrast to the known result that every finite abelian group is dualizable (as part of the Pontryagin duality for all abelian groups) and to the result of the authors in a companion article that every finite group with cyclic Sylow subgroups is dualizable.
Hypergroups associated to harmonic NA groups
Authors: Blasio Bianca Di
Published: April 2009

A harmonic NA group is a suitable solvable extension of a two-step nilpotent Lie group N of Heisenberg type by R+, which acts on N by anisotropic dilations. A hypergroup is a locally compact space for which the space of Borel measures has a convolution structure preserving the probability measures and satisfying suitable conditions. We describe a class of hypergroups associated to NA groups.
Lattice points on circles
Authors: Cilleruelo Javier
Published: April 2009

We prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.
Ricci curvature of submanifolds in Sasakian space forms
Authors: Mihai Ion
Published: April 2009

Recently, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Afterwards, we dealt with similar problems for submanifolds in complex space forms.

In the present paper, we obtain sharp inequalities between the Ricci curvature and the squared mean curvature for submanifolds in Sasakian space forms. Also, estimates of the scalar curvature and the k-Ricci curvature respectively, in terms of the squared mean curvature, are proved.