bluuebunny/crossref_metadata_2025_split huggingface dataset:
An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators
Authors: Amor Ali Ben 
Published: April 2009

AbstractGiven 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

AbstractThe 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

AbstractIt 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

AbstractA 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.
Ricci curvature of submanifolds in Sasakian space forms
Authors: Mihai Ion 
Published: April 2009

AbstractRecently, 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.
The Bernstein-von Mises theorem and spectral asymptotics of Bayes estimators for parabolic SPDEs
Authors: Bishwal J. P. N. 
Published: April 2009

AbstractThe Bernstein-von Mises theorem, concerning the convergence of suitably normalized and centred posterior density to normal density, is proved for a certain class of linearly parametrized parabolic stochastic partial differential equations (SPDEs) as the number of Fourier coefficients in the expansion of the solution increases to infinity. As a consequence, the Bayes estimators of the drift parameter, for smooth loss functions and priors, are shown to be strongly consistent, asymptotically normal and locally asymptotically minimax (in the Hajek-Le Cam sense), and asymptotically equivalent to the maximum likelihood estimator as the number of Fourier coefficients become large. Unlike in the classical finite dimensional SDEs, here the total observation time and the intensity of noise remain fixed.
A generalisation of Lorentz-equivalence in a substratum theory
Authors: Prokhovnik S. J. 
Published: April 2009

AbstractIt has been shown that the assumption of a specified cosmological substratum leads to the Lorentz-equivalencc of observers whose uniform motion in the substratum lies along a common straight line. The result is generalised for any pair of unaccelerated observers thus confirming that only the relative velocity of such observers is relevant in relating their observations of an event.
String vibrating at finite amplitude
Authors: Stuart I. M. 
Published: April 2009

SummaryEquations of motion of a vibrating string are established in terms of the transverse and longitudinal displacements. These equations contain the terms of lowest order which are neglected in the classical treatment with vanishing amplitude. These extra terms lead to the natural modes being dependent on amplitude. By a simple procedure a solution of these equations is obtained which separates, as in the classical theory. The familiar circular functions are replaced by a Mathiew Function of position and a Jacobi elliptic function of time. Agreement with a previous study is shown.
On the transient behaviour of a Poisson branching process
Authors: Seneta E. 
Published: April 2009

SummaryIn general, information concerning the distribution of the time to absorption,T, of a simple branching (Galton-Watson) process for which extinction in finite mean time is certain, is difficult to obtain. The process of greatest biological interest is that for which the offspring distribution is Poisson, having p.g.f.F(s) =em(s-1),m< 1.
Effect of Cosserats' couple-stresses on the stress distribution in a semi-infinite medium with varying modulus of elasticity
Authors: Paria Gunadhar 
Published: April 2009

SummaryThe theory of Cosserats' couple-stresses is briefly described in a cartesian system of coordinates, and is applied to the problem of stress distribution in a semi-infinite medium which possesses a non-homogeneous elastic property of an exponential type. Effects of couple-stresses on the stress concentration factors are determined both in homogeneous and non-homogeneous materials.
On Rotor calculus, I
Authors: Buchdahl H. A. 
Published: April 2009

SummaryIt is known that to every proper homogeneous Lorentz transformation there corresponds a unique proper complex rotation in a three-dimensional complex linear vector space, the elements of which are here called “rotors”. Equivalently one has a one-one correspondence between rotors and self- dual bi-vectors in space-time (w-space). Rotor calculus fully exploits this correspondence, just as spinor calculus exploits the correspondence between real world vectors and hermitian spinors; and its formal starting point is the definition of certain covariant connecting quantities τAkl which transform as vectors under transformations in rotor space (r-space) and as tensors of valence 2 under transformations in w-space.
On Rotor calculus, II
Authors: Buchdahl H. A. 
Published: April 2009

SummaryIn the development of the rotor calculus presented in a previous paper space-time was taken to be flat. This work is now extended to the case of curved space-times, which, in the first instance, is taken to be Riemannian. (The calculus bears at times a strong formal resemblance to the spinor analysis of Infeld and van der Waerden, but it is in fact developed quite independently of this.) Owing to the fact that all general relations had earlier already been written in a generally covariant form they may be taken over unchanged into the present context. In particular,now serves as a defining relation for the connecting quantities τAkl. A linear rotor connection is introduced, and the covariant derivative of a rotor defined. The covariant constancy of the τAkl establishes the relation between the linear connections in w-space and in r-space. A rotor curvature tensor is considered alongside a number of other curvature objects. Next, conformal transformations are dealt with, of which duality rotations may be considered as a special case. This leads naturally to a gauge-covariant generalization of the whole calculus. A so-called rotor-derivative is defined, and some general relations involving such derivatives investigated. The relation of the rotor curvature tensor to the spin-curvature tensor is touched upon, after which the introduction of “geodesic frames” is considered. After this general theory some points concerning the Maxwell field are dealt with, which is followed by some work concerning basic quadratic and cubic invariants. Finally, a certain basic symmetric rotor is re-considered in the context of the classification of Weyl tensors, and the idea of a canonical representation suggested.
Another Law for the 3-Metabelian Groups
Authors: Macdonald I. D. 
Published: April 2009

Journal of the Australian Mathematical Society 4 (1964), 452–453The second paragraph should be deleted. The alleged commutator identity (3) is false and is certainly not due to Philip Hall. The correct form isas Dr. N. D. Gupta of Canberra has pointed out to me. According to Professor B. H. Neumann, this identity appeared in his (Professor Neumann's) thesis.Nevertheless the theorem is valid and the proof given is correct.
Extreme coverings ofn-space by spheres
Authors: Barnes E. S. , Dickson T. J. 
Published: April 2009

It is well known that the problem of determining the most economical covering ofn-dimensional Eucidean space, by equal spheres whose centres form a lattice, may be formulated in terms of positive definite quadratic forms, as follows: Letbe positive definite, andFor real α, set(the minimum being taken over integralx),
Damping loss in a cascade of fluttering phased aerofoils
Authors: Thornton B. S. 
Published: April 2009

SummaryA study is made of the aerodynamic damping in a cascade of oscillating aerofoils in subsonic compressible flow with the system mode described by a constant interblade phasing predicted by Lane (9). The integral downwash equation is obtained as an extension of Possio's equation for an isolated aerofoil. Procedures for a practical solution of the equation have allowed the aerodynamic reactions and damping derivatives to be evaluated with a digital computer after minimisation of the critical flutter velocity with respect to interbiade phase angle. The effect of aerodynamic lag in separation conditions as a function of reduced frequency and chordwise location is compared with results without separation.
Toeplitz Determinants and Szegö's Formula
Authors: Hartwig R. E. 
Published: April 2009

AbstractIn this paper the Toeplitz determinant of order s ≧ 1 generated by the rational function , with , and , is evaluated exactly for all values of s ≧ m, as , where in with and , thus proving Szegö's formula for the function fm, n(z).By forming the rational approximation of the generating function the formula is then extended to enabling the evaluation of the limit of Toeplitz determinants generated by certain classes of complex valued functions.
Optimal quadrature formulae and minimal monosplines in Lq
Authors: Kautsky J. 
Published: April 2009

SummaryThe quadrature formula of order m using values of derivatives up to the m — 1st order with the best possible bound in is derived. Using certain properties of the polynomials minimal in Lq norm, it is proved that the optimal formula not use the derivatives of m — 1st order if m is even.
The automata theory of semigroup embeddings
Authors: Arbib Michael 
Published: April 2009

AbstractThe theorem of Trevor Evans [1] that every countable semigroup can be embedded in a two-generator semigroup becomes obvious in automata theory as the statement that every countable automaton can be embedded in one with binary inputs. Standard techniques of automata theory [1], [3] yield a proof of the Evans Theorem using wreath products, as in Neumann [4].
Cubic identity graphs and planar graphs derived from trees
Authors: Balaban A. T. , Davies Roy O. , Harary Frank , Hill Anthony , Westwick Roy 
Published: April 2009

AbstractThe smallest (nontrivial) identity graph is known to have six points and the smallest identity tree seven. It is now shown that the smallest cubic identity graphs have 12 points and that exactly two of them are planar, namely those constructed by Frucht in his proof that every finite group is isomorphic to the automorphism group of some cubic graph. Both of these graphs can be obtained from plane trees by joining consecutive endpoints; it is shown that when applied to identity trees this construction leads to identity graphs except in certain specified cases. In appendices all connected cubic graphs with 10 points or fewer, and all cubic nonseparable planar graphs with 12 points, are displayed.
The serial correlation coefficients of waiting times in a stationary single server queue
Authors: Daley D. J. 
Published: April 2009

SummaryIn a stationaryGI/G/1 queueing system in which the waiting time variance is finite, it can be shown that the serial correlation coefficients {ρn} of a (stationary) sequence of waiting times are non-negative and decrease monotonically to zero. By means of renewal theory we find a representation for Σ∞0ρnfrom which necessary and sufficient condition for its finiteness can be found. InM/G/1 rather more can be said: {ρn} is convex sequence, the asymptotic form of ρncan be given in a nearly saturated queue, and a simple explicit expression for Σ∞0ρnexists. For the stationaryM/M/1queue we find the ρn's explicitly, illustrate them numerically, and derive a representation which shows that {ρn} is completely monotonic.
Non-linear weak shock diffraction
Authors: De Mestre N. J. 
Published: April 2009

AbstractPerturbation expansions are sought for the flow variables associated with the diffraction of a plane weak shock wave around convex-angled corners in a polytropic, inviscid, thermally-nonconducting gas. Lighthill's method of strained co-ordinates [4] produces a uniformly valid expansion for most of the diffracted front, while the remainder of this front is treated by a modification of the shock-ray theory of Whitham [6]. The solutions from these approaches are patched just inside the ‘shadow’ region yielding a plausible description of the entire diffracted shock front.
A non-existence theorem for (v, k,λ)-graphs
Authors: Wallis W. D. 
Published: April 2009

A (ν, κ, λ)-graph is defined in [3] as a graph on ν points, each of valency κ, and such that for any two points P and Q there are exactly λ points which are joined to both. In other words, if Si is the set of points joined to Pi, thenSi has k elements for any iSiSj has λ elements if i≠jThe sets Si are the blocks of a (v, k, λ)-configuration, so a necessary condition on v, k, and λ that a graph should exist is that a (v, k, λ)- configuration should exist. Another necessary condition, reported by Bose (see [1]) and others, is that there should be an integer m satisfying have equal parity. We shall prove that these conditions are not sufficient.
Some Restricted Partition Functions: Congruences Modulo 5
Authors: Lahiri D. B. 
Published: April 2009

Ramanujan was the first mathematician to discover some of the arithmetical properties of p(n), the number of unrestricted partitions of n. His congruence,for example, is famous [2; 3]. Some progress has been made since then; it is known that the congruence,has an infinitude of solutions for any arbitrary value of r [4]. This is a somewhat weak relation, and one would have liked to obtain, if possible, stronger results of the type,for ‘almost all’ values of n, which in its turn is derivable from another stronger relation, viz.,also established by Ramanujan [2], where r(n) is Ramanujan's function defined by
On the laws of certain finite groups
Authors: Cossey John , MacDonald Sheila Oates , Street Anne Penfold 
Published: April 2009

In recent years a great deal of attention has been devoted to the study of finite simple groups, but one aspect which seems to have been little considered is that of the laws they satisfy. In a recent paper [3], the first two of the present authors gave a basis for laws ofPSL(2, 5). The techniques of [3] can be used to show that (modulo certain classification problems) a basis for the laws ofPSL(2, pn) can be made up from laws of the following types:(1) an exponent law,(2) laws which determine the Sylow subgroups,(3) laws which determine the normalisers of the Sylow subgroups,(4) in certain special cases, laws which determine subvarieties of smaller exponent, e.g. the subvariety of exponent 12 for thosePSL(2,pn) which containS4,(5) a law implying local finiteness.
Boundedness of sign-preserving charges, regularity, and the completeness of inner product spaces
Authors: Chetcuti Emmanuel , Dvurečenskij Anatolij 
Published: April 2009

AbstractWe introduce sign-preserving charges on the system of all orthogonally closed subspaces, F(S), of an inner product space S, and we show that it is always bounded on all the finite-dimensional subspaces whenever dim S = ∞. When S is finite-dimensional this is not true. This fact is used for a new completeness criterion showing that S is complete whenever F(S) admits at least one non-zero sign-preserving regular charge. In particular, every such charge is always completely additive.
Class number formulae in the form of a product of determinants in function fields
Authors: Ahn Jaehyun , Choi Soyoung , Jung Hwanyup 
Published: April 2009

AbstractIn this paper, we generalize the Kučera's group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.
Archimedean components of triangular norms
Authors: Klement Erich Peter , Mesiar Radko , Pap Endre 
Published: April 2009

AbstractThe Archimedean components of triangular norms (which turn the closed unit interval into anabelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.
Topologies on spaces of vector-valued meromorphic functions
Authors: Jordá Enrique 
Published: April 2009

AbstractThis paper presents two natural extensions of the topology of the space of scalar meromorphic functionsM(Ω) described by Grosse-Erdmann in 1995 to spaces of vector-valued meromorphic functionsM(ΩE). WhenEis locally complete and does not contain copies of ω we compare these topologies with the topology induced by the representationM (Ω, E) ≃ M(Ω)ε Erecently obtained by Bonet, Maestre and the author.
Elements of prime power order and their conjugacy classes in finite groups
Authors: Héthelyi László , Külshammer Burkhard 
Published: April 2009

AbstractWe show that, for any positive integer k, there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes of elements of prime power order. This generalizes a result of E. Landau from 1903. The proof of our generalization makes use of the classification of finite simple groups.
A generalization of the cofiniteness problem in local cohomology modules
Authors: Asadollahi J. , Khashyarmanesh K. , Salarian SH. 
Published: April 2009

AbstractLetRbe a commutative Noetherian ring with nonzero identity and letMbe a finitely generated R-module. In this paper, we prove that if an idealIofRis generated by a u.s.d-sequence onMthen the local cohomology module(M) isI-cofinite. Furthermore, for any system of ideals Φ of R, we study the cofiniteness problem in the context of general local cohomology modules.
Uniform asymptotic estimates of transition probabilities on combs
Authors: Bertacchi Daniela , Zucca Fabio 
Published: April 2009

AbstractWe investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular, we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting sub-Gaussian estimates involving the spectral and walk dimensions of the graph.
On calculation of the Witten invariants of 3-manifolds
Authors: Rafikov Eugene , Repovš Dušan , Spaggiari Fulvia 
Published: April 2009

AbstractIn this paper we present a short definition of the Witten invariants of 3-manifolds. We also give simple proofs of invariance of those obtained for r = 3 and r = 4. Our definition is extracted from the 1993 paper of Lickorish and the Prasolov-Sossinsky book, where it is dispersed over 20 pages. We show by several examples that it is indeed convenient for calculations.
On Ψ direct sums of Banach spaces and convexity
Authors: Kato Mikio , Saito Kichi-Suke , Tamura Takayuki 
Published: April 2009

AbstractLet X1, X2, …, XN be Banach spaces and ψ a continuous convex function with some appropriate conditions on a certain convex set in RN−1. Let (X1⊕X2⊕…⊕XN)Ψ be the direct sum of X1, X2, …, XN equipped with the norm associated with Ψ. We characterize the strict, uniform, and locally uniform convexity of (X1 ⊕ X2 ⊕ … ⊕ XN)Ψ; by means of the convex function Ψ. As an application these convexities are characterized for the ℓp, q-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p, q (1 < q ≤ p ≤ ∈, q < ∞), which includes the well-known facts for the ℓp-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p in the case p = q.
On convexity and weak closeness for the set of Φ-superharmonic functions
Authors: Lou Hongwei 
Published: April 2009

AbstractConvexity and weak closeness of the set of Φ-superharmonic functions in a bounded Lipschitz domain in Rn is considered. By using the fact of that Φ-superharmonic functions are just the solutions to an obstacle problem and establishing some special properties of the obstacle problem, it is shown that if Φ satisfies Δ2-condition, then the set is not convex unless Φ(r) = Cr2 or n = 1. Nevertheless, it is found that the set is still weakly closed in the corresponding Orlicz-Sobolev space.
Matrix-variate Kummer-Beta distribution
Authors: Nagar Daya K. , Gupta Arjun K. 
Published: April 2009

AbstractThis paper proposes matrix variate generalization of Kummer-Beta family of distributions which has been studied recently by Ng and Kotz. This distribution is an extension of Beta distribution. Its characteristic function has been derived and it is shown that the distribution is orthogonally invariant. Some results on distribution of random quadratic forms have also been derived.
Moment sequences and backward extensions of subnormal weighted shifts
Authors: Hoover Thomas , Jung Il Bong , Lambert Alan 
Published: April 2009

AbstractIn this note we examine the relationships between a subnormal shift, the measure its moment sequence generates, and those of a large family of weighted shifts associated with the original shift. We examine the effects on subnormality of adding a new weight or changing a weight. We also obtain formulas for evaluating point mass at the origin for the measure associated with the shift. In addition, we examine the relationship between the measure associated with a subnormal shift and those of a family of shifts substantially different from the original shift.
Metanilpotent varieties of groups
Authors: Bryant R. M. , Krasil'nikov A. N. 
Published: April 2009

AbstractFor each positive integer n let N2, n denote the variety of all groups which are nilpotent of class at most 2 and which have exponent dividing n. For positive integers m and n, let N2, mN2, n denote the variety of all groups which have a normal subgroup in N2, m with factor group in N2, n. It is shown that if G ∈N2, mN2, n, where m and n are coprime, then G has a finite basis for its identities.