bluuebunny/crossref_metadata_2025_split huggingface dataset:
On certain pairs of automorphisms of rings
Authors: Brešar Matej 
Published: April 2009

AbstractIn this paper we prove algebraic generalizations of some results of C. J. K. Batty and A. B. Thaheem, concerned with the identity α + α−1 = β + β−1 where α and β are automorphisms of a C*-algebra. The main result asserts that if automorphisms α, β of a semiprime ring R satisfy α + α-1 = β + β−1 then there exist invariant ideals U1, U2 and U3 of R such that Ui ∩ Uj = 0, i ≠ j, U1 ⊕ U2 ⊕ U3 is an essential ideal, α = β on U1, α = β−1 on U2, and α2 = β2 = α−2 on U3. Furthermore, if the annihilator of any ideal in R is a direct summand (in particular, if R is a von Neumann algebra), then U1 ⊕ U2 ⊕ U3 = R.
Biduals of weighted banach spaces of analytic functions
Authors: Bierstedt K. D. , Summers W. H. 
Published: April 2009

AbstractFor a positive continuous weight function ν on an open subset G of CN, let Hv(G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when Hν(G) is naturally isometrically isomorphic to Hν0(G)**, and show in particular that this is the case whenever the closed unit ball in Hν0(G) in compact-open dense in the closed unit ball of Hν(G).
On certain subrings of prime rings with derivations
Authors: Brešar M. , Vukman J. 
Published: April 2009

AbstractLet D be a nonzero derivation of a noncommutative prime ring R, and let U be the subring of R generated by all [D(x), x], x ∞ R. A classical theorem of Posner asserts that U is not contained in the center of R. Under the additional assumption that the characteristic of R is not 2, we prove a more general result stating that U contains a nonzero left ideal of R as well as a nonzero right ideal of R.
Regulating hulls of almost completely decomposable groups
Authors: Mader A. , Vinsonhaler C. 
Published: April 2009

AbstractThis note investigates torsion-free abelian groups G of finite rank which embed, as subgroups of finite index, in a finite direct sum C of subgroups of the additive group of rational numbers. Specifically, we examine the relationship between G and C when the index of G in C is minimal. Some properties of Warfield duality are developed and used (in the case that G is locally free) to relate our results to earlier ones by Burkhardt and Lady.
Congruences on free monoids and submonoids of polycyclic monoids
Authors: Meakin John , Sapir Mark 
Published: April 2009

AbstractWe establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.
The number of exceptional approximations in Roth's theorem
Authors: Schmidt Wolfgang M. 
Published: April 2009

AbstractRoth's Theorem says that given ρ < 2 and an algebraic number α, all but finitely many rational numbers x/y satisfy |α - (x/y)|< |y|-ρ. We give upper bounds for the number of these exceptional rationals when 3 ≤ ρ ≤ d, where d is the degree of α. Our result suplements bounds given by Bombieri and Van der Poorten when 2 > ρ ≤ 3; naturally the bounds become smaller as ρ increases.
Groups with all subgroups normal-by-finite
Authors: Buckley J. T. , Lennox John C. , Neumann B. H. , Smith Howard , Wiegold James 
Published: April 2009

AbstractA groupGhas all of its subgroups normal-by-finite ifH/ coreG(H) is finite for all subgroupsHofG. These groups can be quite complicated in general, as is seen from the so-called Tarski groups. However, the locally finite groups of this type are shown to be abelian-by-finite; and they are then boundedly core-finite, that is to say, there is a bound depending onGonly for the indices |H: coreG(H)|.
Growth of linear semigroups
Authors: Okniński Jan 
Published: April 2009

AbstractWe show that the growth function of a finitely generated linear semigroup S ⊆ Mn(K) is controlled by its behaviour on finitely many cancellative subsemigroups of S. If the growth of S is polynomially bounded, then every cancellative subsemigroup T of S has a group of fractions G ⊆ Mn (K) which is nilpotent-by-finite and of finite rank. We prove that the latter condition, strengthened by the hypothesis that every such G has a finite unipotent radical, is sufficient for S to have a polynomial growth. Moreover, the degree of growth of S is then bounded by a polynomial f(n, r) in n and the maximal degree r of growth of finitely generated cancellative T ⊆ S.
Hall's ray in inhomogeneous diophantine approximation
Authors: Cusick T. W. , Moran W. , Pollington A. D. 
Published: April 2009

AbstractThe aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.
Banach space operators with a boundedH∞ functional calculus
Authors: Cowling Michael , Doust Ian , Micintosh Alan , Yagi Atsushi 
Published: April 2009

AbstractIn this paper, we give a general definition forf(T)whenTis a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent bounds, and whenfis holomorphic on a larger sector.We also examine how certain properties of this functional calculus, such as the existence of a boundedH∈functional calculus, bounds on the imaginary powers, and square function estimates are related. In particular we show that, ifTis acting in a reflexiveLpspace, thenThas a boundedH∈ functional calculus if and only if bothTand its dual satisfy square function estimates. Examples are given to show that some of the theorems that hold for operators in a Hilbert space do not extend to the general Banach space setting.
Commutative rings with comparable regular elements
Authors: Zanardo Paolo 
Published: April 2009

AbstractLet ℜbe the class of commutative ringsRwith comparable regular elements, that is, given two non zero-divisors inR, one divides the other. Applying the notion ofV-valuation due to Harrison and Vitulli, we define the classV-val ofV-valuated rings, which is contained in ℜand contains the class of Manis valuation rings. We prove that these inclusions of classes are both proper. We investigate Prüfer rings inside ℜ, showing that there exist Prüfer rings which lie in ℜbut not inV-val; we prove that a ringRis a Prüfer valuation ring if and only if it is Prüfer andV-valuated, if and only if its lattice of regular ideals is a chain. Finally, we introduce and investigate the idealI∞of a ringR∈ ℜ, which corresponds to the counterimage of ∞, wheneverRisV-valuated.
Spectral synthesis and applications to C0-groups
Authors: Zarrabi M. 
Published: April 2009

AbstractLet k ≥ 0 be an integer, T = (T(t))t ∈R a C0-group of bounded operators and A the infinitesimal generator of T. We prove that if, and , and if the spectrum of A is equal to {λ}, then A is bounded and (A – λ)k+1 = 0. Examples are given to show that these conditions are, essentially, the best possible.
A non-coprime Hall-Higman reduction theorem
Authors: Wang Yan-Ming 
Published: April 2009

AbstractIn a well-known paper, Hall and Higman proved the reduction theorem on a coprime order operator group acting on a finite group. This theorem plays an important role in local analysis of finite group theory. In this paper, we generalize the Hall-Higman reduction theorem by dropping the restrictive hypothesis (|G|, |H|) = 1 and determine the detailed structure of G completely.
Approximation and extension of continuous functions
Authors: Hernández-Muñoz Salvador 
Published: April 2009

AbstractIn this paper we study the approximation of vector valued continuous functions defined on a topological space and we apply this study to different problems. Thus we give a new proof of Machado's Theorem. Also we get a short proof of a Theorem of Katětov and we prove a generalization of Tietze's Extension Theorem for vector-valued continuous functions, thereby solving a question left open by Blair.
Partial regularity and everywhere continuity for a model problem from non-linear elasticity
Authors: Fusco Nicola , Hutchinson John E. 
Published: April 2009

AbstractWe prove a new energy or Caccioppoli type estimate for minimisers of the model functional ∫Ω|Du|2 + (det Du)2, where Ω ⊂ 2 and u: Ω → 2. We apply this to establish C∞ regularity for minimisers except on a closed set of measure zero. We also prove a maximum principle and use this to establish everywhere continuity of minimisers.
Modules with finite spanning dimension
Authors: Satyanarayana Bhavanari 
Published: April 2009

AbstractIt is well known that if M is a module with finite spanning dimension, then one can talk of Sd(K), the spanning dimension of K only when K is a supplement submodule in M. In this paper we extend this concept to general submodules and obtained some important results. We characterize the set of all supplement submodules of the module R/(x) over R where R is a Euclidean domain and x ∈ R. Moreover, it is proved that the number of distinct supplements in R/(x) is 2k and Sd(R/(x)) = k where k is the number of distinct nonassociate prime factors of x.
Subelliptic operators on Lie groups: regularity
Authors: Elst A. F. M. Ter , Robinson Derek W. 
Published: April 2009

AbstractLet (ℋ,G, U) be a continuous representation of the Lie groupGby bounded operatorsg↦U(g)on the Banach space ℋ and let (ℋ,g, dU) denote the representation of the Lie algebragobtained by differentiation. Ifa1,…, ad′is a Lie algebra basis ofgandAi= dU(ai)then we examine elliptic regularity properties of the subelliptic operatorswhere (cij) is a real-valued strictly positive-definite matrix andc0, c1,…, cd′∈ C. We first introduce a family of Lipschitz subspaces ℋγ, γ > 0, of ℋ which interpolate between theCn-subspaces of the representation and for which the parameter γ is a continuous measure of differentiability. Secondly, we give a variety of characterizations of the spaces in terms of the semigroup generated by the closureofHand the group representation. Thirdly, for sufficiently large values of Rec0the fractional powers of the closure ofHare defined, and we prove that D()γ⊆γ′, for γ′ < 2γ/rwhereris the rank of the basis. Further we establish that 2γ/ris the optimal regularity value and it is attained for unitary representations or for the representations obtained by restrictingUto ℋγ. Many other regularity properties are obtained.
Generalized theorem of Hartman-Grobman on measure chains
Authors: Hilger Stefan 
Published: April 2009

AbstractWe will prove the Theorem of Hartman-Grobman in a very general form. It states the topological equivalence of the flow of a nonlinear non-autonomous differential or difference equation with critical component to the flow of a partially linearized equation. The critical spectrum has not necessearily to be contained in the imaginary axis or the unit circle respectively. Further on we will employ the socalled calculus on measure chains within dynamical systems theory. Within this calculus the usual one dimensional time scales can be replaced by measure chains which are essentially closed subsets of R. The paper can be understood without knowledge of this calculus.So our main theorem will be valid even for equations defined on very strange time scales such as sequences of closed intervals. This is especially interesting for applications within the theory of differential-difference equations or within numerical analysis of qualitative phenomena of dynamical systems.
Discrete C*-coactions and C*-algebraic bundles
Authors: Quigg John C. 
Published: April 2009

AbstractDiscrete C*-coactions are shown to be equivalent to discrete C* -algebraic bundles. Simplicity, primeness, liminality, postliminality, and nuclearity are related to the fixed point algebra and the cocrossed product. Ergodic, and more generally homogeneous, C*-coactions are characterized.
Locally graded groups with all subgroups normal-by-finite
Authors: Smith Howard , Wiegold James 
Published: April 2009

AbstractIn a paper published in this journal [1], J. T. Buckely, J. C. Lennox, B. H. Neumann and the authors considered the class of CF-groups, that G such that |H: CoreG (H)| is finite for all subgroups H. It is shown that locally finite CF-groups are abelian-by-finite and BCF, that is, there is an integer n such that |H: CoreG(H)| ≤ n for all subgroups H. The present paper studies these properties in the class of locally graded groups, the main result being that locally graded BCF-groups are abelian-by-finite. Whether locally graded CF-groups are BFC remains an open question. In this direction, the following problems is posed. Does there exist a finitely generated infinite periodic residually finite group in which all subgroups are finite or of finite index? Such groups are locally graded and CF but not BCF.
On irregularities of distribution III
Authors: Chen W. W. L. 
Published: April 2009

AbstractWe study the Lw-norm (2 ≤ W < ∞) of the discrepancy of a sequence of points in the unit cube relative to similar copies of a given convex polygon. In particular, we prove the rather surprising result that the estimates obtained have the same order of magnitude as the analogous question when the sequence of points is replaced by a set of points.
Coefficients of an analytic function subordination class determined by rotations
Authors: Kim Seok Chan 
Published: April 2009

AbstractLet A denote the set of all functions analytic in U = {z: |;z| < 1} equipped with the topology of unifrom convergence on compact subsets of U. For F ∈ A define Let s(F) and s(F) denote the closed convex hull of s(F) and the set of extreme points of , respectively. Let R denote the class of all F ∈ A such that = {Fx}: |x| = 1} where Fx = F(xz).We prove that |An| ≤ |AMN| for all positive integers M and N, and for . We also prove that if , then F is a univelaent halfplane mapping.
On the eigenvalues of Redheffer's matrix, II
Authors: Vaughan R. C. 
Published: April 2009

AbstractThe Redheffer matrix An = (aij)n×n defined by aij = 1 when i|j or j = 1 and aij = 0 otherwise has many interesting number theoretic properties. In this paper we give fairly precise estimates for its eigenvalues in punctured discs of small radius centred at 1.
Some examples related to Kato's conjecture
Authors: Hughes Rhonda J. , Chernoff Paul R. 
Published: April 2009

AbstractWe show that the Kato conjecture is true for m-accretive operators with highly singular coefficients. For operators of the form A = *F, where formally corresponds to d/dx + zδ on L2 (R), we prove that Dom (A1/2) = Dom() = e-zHH1(R) where H is the Heavysied function. By adapting recent methods of Auscher and Tchamitchian, we characterize Dom (A) in terms of an unconditional wavelet basis for L2(R).
The behaviour of the fourth type of Lauricella's hypergeometric series in n variables near the boundaries of its convergence region
Authors: Saigo Megumi , Srivastava H. M. 
Published: April 2009

AbstractFor Lauricella's hypergeometric function F(n)D of n variables, we prove two formulas exhibiting its behaviour near the boundaries of the n-dimensional region of convergence of the multiple series defining it. Each of these results can be applied to deduce the corresponding properties of several simpler hypergeometric functions of one, two, and more variables.
Insertion of a measurable function
Authors: Kotzé Wesley , Kubiak Tomasz 
Published: April 2009

AbstractSome theorems on the existence of continuous real-valued functions on a topological space (for example, insertion, extension, and separation theorems) can be proved without involving uncountable unions of open sets. In particular, it is shown that well-known characterizations of normality (for example the Katětov-Tong insertion theorem, the Tietze extension theorem, Urysohn's lemma) are characterizations of normal σ-rings. Likewise, similar theorems about extremally disconnected spaces are true for σ-rings of a certain type. This σ-ring approach leads to general results on the existence of functions of class α.
The difference of consecutive eigenvalues
Authors: Ku Hsu-Tung , Ku Mei-Chin 
Published: April 2009

AbstractLet M be a smooth bounded domain in Rn with smooth boundary, n ≥ 2, and . We prove an inequality involving the first k + 1 eigenvalues of the eigenvalue problem: where am−1 ≥ 0 are constants and at−1 = 1. We also obtain a uniform estimate of the upper bound of the ratios of consecutive eigenvalues.
Convergence of the backfitting algorithm for additive models
Authors: Ansley Craig F. , Kohn Robert 
Published: April 2009

AbstractThe backfitting algorithm is an iterative procedure for fitting additive models in which, at each step, one component is estimated keeping the other components fixed, the algorithm proceeding component by component and iterating until convergence. Convergence of the algorithm has been studied by Buja, Hastie, and Tibshirani (1989). We give a simple, but more general, geometric proof of the convergence of the backfitting algorithm when the additive components are estimated by penalized least squares. Our treatment covers spline smoothers and structural time series models, and we give a full discussion of the degenerate case. Our proof is based on Halperin's (1962) generalization of von Neumann's alternating projection theorem.
Approximations of positive operators and continuity of the spectral radius III
Authors: Aràndiga F. , Caselles V. 
Published: April 2009

AbstractWe prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.
On recursive solutions of a unit fraction equation
Authors: Brenton Lawrence , Bruner Robert R. 
Published: April 2009

AbstractWe consider the Egyptian fraction equation and discuss techniques for generating solutions. By examining a quadratic recurrence relation modulo a family of primes we have found some 500 new infinite sequences of solutions. We also initiate an investigation of the randomness of the distribution of solutions, and show that there are infinitely many solutions not generated by the aforementioned technique.
On convex and starlike functions in a sector
Authors: Nunokawa M. , Thomas D. K. 
Published: April 2009

AbstractLet f be analytic in D = {z: |z| < 1} with f(0) = f′(0)−1=0. For γ > 0, the largest α (γ) and β(γ) are found such that . The results solve the inclusion problem for convex and starlike functions defined in a sector.
Minimal annuli in R3 bounded by non-compact complete convex curves in parallel planes
Authors: Fang Yi 
Published: April 2009

AbstractIn this paper we consider the Plateau problem for surfaces of annular type bounded by a pair of convex, non-compact curves in parallel planes. We prove that for certain symmetric boundaries there are solutions to the non-compact Plateau problems (Theorem B). Except for boundaries consisting of a pair of parallel straight lines, these are the first known examples.
Extrapolation of the functional calculus of generalized Dirac operators and related embedding and Littlewood-Paley-type theorems. I
Authors: Ajiev Sergey S. 
Published: April 2009

AbstractSeveral rather general sufficient conditions for the extrapolation of the calculus of generalized Dirac operators from L2 to Lp are established. As consequences, we obtain some embedding theorems, quadratic estimates and Littlewood–Paley theorems in terms of this calculus in Lebesgue spaces. Some further generalizations, utilised in Part II devoted to applications, which include the Kato square root model, are discussed. We use resolvent approach and show the irrelevance of the semigroup one. Auxiliary results include a high order counterpart of the Hilbert identity, the derivation of new forms of ‘off-diagonal’ estimates, and the study of the structure of the model in Lebesgue spaces and its interpolation properties. In particular, some coercivity conditions for forms in Banach spaces are used as a substitution of the ellipticity ones. Attention is devoted to the relations between the properties of perturbed and unperturbed generalized Dirac operators. We do not use any stability results.
The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring
Authors: Yu Yaoming , Wang Guorong 
Published: April 2009

AbstractIn this paper we establish the definition of the generalized inverse A(2)T, Swhich is a {2} inverse of a matrixAwith prescribed imageTand kernelsover an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverseand some explicit expressions forof a matrix A over an associative ring, which reduce to the group inverse or {1} inverses. In addition, we show that for an arbitrary matrixAover an associative ring, the Drazin inverse Ad, the group inverse Agand the Moore-Penrose inverse. if they exist, are all the generalized inverse A(2)T, S.
Markoff type inequalities for curved majorants
Authors: Varma A. K. , Mills T. M. , Smith Simon J. 
Published: April 2009

AbstractLet pn(x) be a real algebraic polynomial of degree n, and consider the Lp norms on I = [−1, 1]. A classical result of A. A. Markoff states that if ‖pn‖. ∞ ≤ 1, then ‖P′n‖∞ ≤ n2. A generalization of Markoff's problem, first suggested by P. Turán, is to find upper bounds for ‖pn(J)‖p if ∣pn(x)∣≤ ψ(x)x ∈ I. Here ψ(x) is a given function, a curved majorant. In this paper we study extremal properties of ‖p′n‖2 and ‖p″n‖2 if pn(x) has the parabolic majorant ∣p(x)∣≤ 1 − x2, x ∈ I. We also consider the problem, motivated by a well-known result of S. Bernstein, of maximising ‖(1 − x2)
The least number of coincidence points on surfaces
Authors: Jezierski Jerzy 
Published: April 2009

AbstractBo Ju Jiang introduced an invariant lying in the braid group which is the best lower bound of the number of fixed points in a homotopy class of a given pair of self maps of a surface. Here we modify this construction to get a lower bound of the number of coincidence points of a pair of maps between two closed surfaces.
Level crossings of a random trigonometric polynomial with dependent coefficients
Authors: Farahmand K. 
Published: April 2009

AbstractThis paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g1 cos x + g2 cos 2x+ … + gn cos nx where gj (j = 1, 2, …, n) are dependent normally distributed random variables with mean zero and variance one. The two cases of ρjr, the correlation coeffiecient between the j-th and r-th coefficients, being either (i) constant, or (ii) ρ∣j−r∣ρ, j ≠ r, 0 < ρ < 1, are considered. It is shown that the previous result for ρjr = 0 still remains valid for both cases.
Some remarks on modularity of the congruence lattice of regular ω-semigroups
Authors: Bonzini C. , Cherubini A. 
Published: April 2009

AbstractIn this paper conditions of M-symmetry, strong, semimodularity and θ-modularity for the congruence lattice L (S) of a regular ω-semigroup S are studied. They are proved to be equivalent to modularity. Moreover it is proved that the kernel relation is a congruence on L(S) if and only if L(S) is modular, generalizing an analogous result stated by Petrich for bisimple ω-semigroups.
Concentration-cancellation and Hardy spaces
Authors: Vecchi Italo 
Published: April 2009

AbstractLet υ∈ be a sequence of DiPema-Majda approximate solutions to the 2-d incompressible Euler equations. We prove that if the vorticity sequence is weakly compact in the Hardy space H1 (R2) then a subsequence of υ∈ converges strongly in the energy norm to a solution of the Euler equations.