bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some irreducible free group representations in which a linear combination of the generators has an eigenvalue
Authors: Paschke William L. 
Published: April 2009

AbstractWe construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the eigenvalue is specified, we conjecture that there is only one such representation. The representation we have found is described explicitly (modulo inversion of a certain rational map on Euclidean space) in terms of a positive definite function, and also by means of a quasi-invariant probability measure on the combinatorial boundary of the group.
Supports and singular supports of pseudomeasures
Authors: Edwards R. E. 
Published: April 2009

SummaryLet G denote a Hausdorff locally compact Abelian group which is nondiscrete and second countable. The main results (Theorems (2.2) and (2.3)) assert that, for any closed subset E of G there exists a pseudomeasure s on G whose singular support is E; and that if no portion of E is a Helson set, then such an s may be chosen having its support equal to E. There follow (Corollaries (2.2.4) and (2.3.2)) sufficient conditions for the relations to hold for some pseudomeasure s, E and F being given closed subsets of G. These results are analogues and refinements of a theorem of Pollard [4] for the case G = R, which asserts the existence of a function in L∞(R) whose spectrum coincides with any preassigned closed subset of R.
The relativistic incompressible sphere
Authors: Buchdahl H. A. , Land W. J. 
Published: April 2009

SummaryThe Schwarzschild Interior Solution represents a static sphere the proper density of which has the same value throughout. Though it is sometimes referred to as an “incompressible” sphere it is physically unacceptable since (formally) the speed of sound within it is infinite. Perhaps the most natural analogue of the classical incompressible sphere is therefore a sphere such that the speed of sound is everywhere just equal to the speed of light. This paper investigates spheres of this kind in some detail.
On the Stability of Linear Canonical Systems with Periodic Coefficients
Authors: Coppel W. A. , Howe A. 
Published: April 2009

Journal of the Australian Mathematical Society 5 (1965), 169–195Theorem 9 (p. 183) should read: The indices of any closed curve inD have the formn+ = hp/s, n− = hq/sfor some integer h, where s (1 ≦ s ≦ n) is the largest number of identical blocks into which the signature σ can be partitioned. Moreover, for any integer h there exists a closed curve in d with these indices.
Certain topological semirings in R1
Authors: Pearson K. R. 
Published: April 2009

If we consider any particular topological semigroup S it may seem reasonable to ask for a characterization of all additions on S which make it a topological semiring. We are interested here in this problem when(i) S is an (I)-semigroup;(ii) S is [0, ∞) and the multiplication on S is such that 0 and 1 are Zero and identity respectively.
Some conformally separable metrics in flat space and their application to accelerated coordinate frameworks in special relativity
Authors: Taylor N. W. 
Published: April 2009

SummaryIf the metric of an n-dimensional space is taken in the form ds2 = u2dτ2+dσ2, where dτ2 and dσ2 are cartesian metrics of r and (n−r) dimensions, respectively, the various forms of u for flat space are quite simple. The study of accelerated motions in special relativity by various authors has led to four dimensional metrics of this form. Those in which u = ±1 at the space origin for all values of time are of particular interest. They are locally cartesian at the accelerated observer, and so the coordinates in the neighbourhood of the observer correspond directly to physical measurements. Hence, such metrics provide convenient means of describing physical conditions experienced by accelerated observers. If the τ-space contains the time direction and is of one or two dimensions, arbitrary rectilinear motions are allowed.
The iterated equation of generalized axially symmetric potential theory. V. Generalized weinstein correspondence principle
Authors: Burns J. C. 
Published: April 2009

Solutions of the iterated equation of generalized axially symmetric potential theory [1]where the operator Lk is defined bywill be denoted by except that when n = 1, fk will be written instead of . It is easily shown [2, 3] thatby which is meant that any function is a solution of (1).
A universal semigroup
Authors: Michael J. H. 
Published: April 2009

In [4] S. Ulam asks the following question.
‘Does there exist a universal compact semigroup; i.e., a semigroup U such that every compact topological semigroup is continuously isomorphic to a subsemigroup of it?’
The author has not been able to answer this question. However, in this paper, a proof is given for the following related result.Let Q denote the Hilbert cube of countably infinite dimension and C(Q) the Banach space of continuous real-valued functions on Q with the usual norm. Let U denote the semigroup consisting of all bounded linear operators T: C(Q)→ C(Q) with ∥T∥ ≦ 1 and let U be endowed with the strong topology. Then, for every compact metric semigroup S with the property:
(1.1) for all x, y ∈ S, with x ≠ y, there exists a z ∈ S, such that xz ≠ yz or zx ≠ zy;there exists a 1 − 1 mapping φ of S into U such that φ is both a semigroup isomorphism and a homeomorphism.U is metrizable, but is not compact; hence it does not provide an answer to the question of Ulam. The proof of the above statement leans heavily on a result of S. Kakutani [1].
Some results using general moment functions
Authors: Smith Walter L. 
Published: April 2009

SummaryLet {Xn} be a sequence fo independent and identically distributed random variables such that 0 <μ = εXn ≦ + ∞ and write Sn = X1+X2+ … +Xn. Letv ≧ 0 be an integer and let M(x) be a non-decreasing function of x ≧ 0 such that M(x)/x is non-increasing and M(0) > 0. Then if ε|X1νM(|X1|) < ∞ and μ < ∞ it follows that ε|Sn|νM(|Sn|) ~ (nμ)vM(nμ) as n → ∞. If μ = ∞ (ν = 0) then εM(|Sn|) = 0(n). A variety of results stem from this main theorem (Theorem 2), concerning a closure property of probability generating functions and a random walk result (Theorem 1) connected with queues.
On groups with special antiautomorphisms
Authors: Heineken Hermann 
Published: April 2009

This note is concerned with the following question: What is the structure of those groups which possess two antiautomorphisms different from identity such that every element of the group is fixed by (at least) one of them?C. Ayoub [1] stated this problem after having proved a statement equivalent to the following: The group G is a non-abelian extension of an abelian group by a group of order two, if, and only if, there is an automorphism α ≠ 1 and an antiautomorphism β ≠ 1 such that every element of G is fixed by a α by β. The Theorem at the end of the paper will show that the class of groups considered by C. Ayoub coincides with the class considered here.
Explicit formulae for two-bridge knot polynomials
Authors: Fukuhara Shinji 
Published: April 2009

AbstractA two-bridge knot (or link) can be characterized by the so-called Schubert normal formKp, qwherepandqare positive coprime integers. Associated toKp, qthere are the Conway polynomial ▽kp, q(z)and the normalized Alexander polynomial Δkp, q(t). However, it has been open problem how ▽kp, q(z) and Δkp, q(t) are expressed in terms ofpandq. In this note, we will give explicit formulae for the Conway polynomials and the normalized Alexander polynomials in the case of two-bridge knots and links. This is done using elementary number theoretical functions inpandq.
Iterative methods for computing generalized inverses related with optimization methods
Authors: Djordjević Dragan S. , Stanimirović Predrag S. 
Published: April 2009

AbstractWe develop several iterative methods for computing generalized inverses using both first and second order optimization methods in C*-algebras. Known steepest descent iterative methods are generalized in C*-algebras. We introduce second order methods based on the minimization of the norms ‖Ax − b‖2 and ‖x‖2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.
Infinitary lattice and Riesz properties of pseudoeffect algebras and po-groups
Authors: Dvurečenskij Anatolij , Vetterlein Thomas 
Published: April 2009

AbstractPseudoeffect (PE-) algebras generalize effect algebras by no longer being necessarily commutative. They are in certain cases representable as the unit interval of a unital po-group, for instance if they fulfil a certain Riesz property.Several infinitary lattice properties and the countable Riesz interpolation property are studied for PE-algebras on the one hand and for po-groups on the other hand. We establish the exact relationships between the various conditions that are taken into account, and in particular, we examine how properties of a PE-algebra are related to the analogous properties of a representing po-group.
Relatively free algebras with weak exchange properties
Authors: Fountain John , Gould Victoria 
Published: April 2009

AbstractWe consider algebras for which the operationPCof pure closure of subsets satisfies the exchange property. Subsets that are independent with respect to PC aredirectly independent. We investigate algebras in which PC satisfies the exchange property and which are relatively free on a directly independent generating subset. Examples of such algebras include independence algebras and dinitely generated free modules over principal ideal domains.
The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations
Authors: Chen Guowei , Wu Yongbin , Yang Xinan 
Published: April 2009

AbstractThe Hopf bifurcation and homoclinic bifurcation of the quintic Hamiltonian system is analyzed under quintic perturbations by using unfolding theory in this paper. We show that a quintic system can have at least 29 limit cycles.
Normal surfaces in non-compact 3-manifolds
Authors: Kang Ensil 
Published: April 2009

AbstractWe extend the normal surface Q-theory to non-compact 3-manifolds with respect to ideal triangulations. An ideal triangulation of a 3-manifold often has a small number of tetrahedra resulting in a system of Q-matching equations with a small number of variables. A unique feature of our approach is that a compact surface F with boundary properly embedded in a non-compact 3-manifold M with an ideal triangulation with torus cusps can be represented by a normal surface in M as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of F. The resulting surface , when normalized, will contain only a finite number of Q-disks and thus correspond to an admissible solution to the system of Q-matching equations. The correspondence is bijective.
Weyl quantization and a symbol calculus for abelian groups
Authors: Wildberger N. J. 
Published: April 2009

AbstractWe develop a notion of a *-product on a general abelian group, establish a Weyl calculus for operators on the group and connect these with the representation theory of an associated Heisenberg group. This can all be viewed as a generalization of the familiar theory for R. A symplectic group is introduced and a connection with the classical Cayley transform is established. Our main application is to finite groups, where consideration of the symbol calculus for the cyclic groups provides an interesting alternative to the usual matrix form for linear transformations. This leads to a new basis for sl(n) and a decomposition of this Lie algebra into a sum of C*artan subalgebras.
Asymptotic expansions of convolutions of regularly varying distributions
Authors: Barbe Philippe , McCormick William P. 
Published: April 2009

AbstractIn this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails.Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convolution from the parameters of the constituent distributions in the convolution. A Maple code is presented which does this task.
The spectral mapping property for p–multiplier operators on compact abelian groups
Authors: Ricker Werner J. 
Published: April 2009

AbstractLet G be a compact abelian group and 1< p < ∞. It is known that the spectrum σ (Tψ) of a Fourier p–multiplier operator Tψ acting in Lp(G), may fail to coincide with its natural spectrum ψ(Г) if p ≠ 2; here Γ is the dual group to G and the bar denotes closure in C. Criteria are presented, based on geometric, topological and/or algebraic properties of the compact set σ(Tψ), which are sufficient to ensure that the equality σ(Tψ) = ψ(Г)holds.
Finite p–nilpotent groups with some subgroups c–supplemented
Authors: Guo Xiuyun , Shum K. P. 
Published: April 2009

AbstractA subgroup H of a finite group G is said to be c–supplemented in G if there exists a subgroup K of G such that G = HK and H∩K is contained in coreG (H). In this paper some results for finite p–nilpotent groups are given based on some subgroups of Pc–supplemented in G, where p is a prime factor of the order of G and P is a Sylow p–subgroup of G. We also give some applications of these results.
The weak-type (1,1) of Fourier integral operators of order –(n–1)/2
Authors: Tao Terence 
Published: April 2009

AbstractLet T be a Fourier integral operator on Rn of order–(n–1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.
Approximation of *-nonexpansive random multivalued operators on Banach spaces
Authors: Beg Ismat , Khan A. R. , Hussain N. 
Published: April 2009

AbstractWe establish the existence and approximation of solutions to the operator inclusiony∈Tyfor deterministic and random cases for a nonexpansive and *-nonexpansive multivalued mappingTdefined on a closed bounded (not necessarily convex) subsetCof a Banach space. We also prover random fixed points and approximation results for*-nonexpansive random operators defined on an unbounded subjectCof a uniformly convex Banach space.
Correction to a paper by A. G. Pakes
Authors: Berg Christian 
Published: April 2009

AbsrtactStaring form a probability σ on the half-line moments of any order A. G. Pakes has defined probabilities σr, by length biasing order r and gr, by the stationary-excess operation of order r, r = 1, 2,…Examples are given to show that σ can bt determined in the Stieltjes sence while σ1 and g1 are indeterminate in the Stieltjes sence. This shows that a statement in a recent paper by Pakes does not hold.
A note on normality and shared values
Authors: Fang Mingliang , Zalcman Lawrence 
Published: April 2009

AbstractLet k be a positive integer and b a nonzero constant. Suppose that F is a family of meromorphic functions in a domain D. If each function f ∈ F has only zeros of multiplicity at least k + 2 and for any two functions f, g ∈ F, f and g share 0 in D and f(k) and g(k) share b in D, then F is normal in D. The case f ≠ 0, f(k) ≠ b is a celebrated result of Gu.
Strong and full dualisability: three-element unary algebras
Authors: Pitkethly J. G. 
Published: April 2009

AbstractWe characterise the strongly dualisable three-element unary algebras and show that every fully dualisable three-element unary algebra is strongly dualisable. It follows from the characterisation that, for dualisable three-element unary algebras, strong dualisability is equivalent to a weak form of injectivity.
Fitting classes and lattice formations II
Authors: Arroyo-Jordá M. , Pérez-Ramos M. D. 
Published: April 2009

AbstractGiven a lattice formation F of full characteristic, an F - Fitting class is a Fitting class with stronger closure properties involving F -subnormal subgroups. The main aim of this paper is to prove that the associated injectors possess a good behaviour with respect to F -subnormal subgroups.
Multiplicity results for some nonlinear elliptic problems
Authors: Chen Kuan-Ju 
Published: April 2009

AbstractIn this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.
Limit theorems for isotropic random walks on triangle buildings
Authors: Lindlbauer Marc , Voit Michael 
Published: April 2009

AbstractThe spherical functions of triangle buildings can be described in terms of certain two-dimensional orthogonal polynomials on Steiner's hypocycloid which are closely related to Hall-Littlewood polynomials. They lead to a one-parameter family of two-dimensional polynimial hypergroups. In this paper we investigate isotropic random walks on the vertex sets of triangle buildings in terms of their projections to these hypergroups. We present strong laws of large numbers, a central limit theorem, and a local limit theorem; all these results are well-known for homogeneous trees. Proofs are based on moment functions on hypergroups and on explicit expansions of the hypergroup characters in terms of certain two-dimensional Tchebychev polynimials.
Characteristic invatiant of tensor product actions and actions on crossed products
Authors: Miwa Yukako , Katayama Yoshikazu 
Published: April 2009

AbstractThe first purpose of this paper is to give a tensor product formula of the characteristic invariant and modular invariant for a tensor product action of a discrete group G on AFD factors. The second purpose is to describe a characteristic invariant and modular invariant of the extended action to a crossed product in terms of the original invariants.
Bounds for nilpotent-by-finite groups in certain varieties
Authors: Endimioni G. 
Published: April 2009

AbstractLet and denote respectively the variety of groups of exponent dividing e, the variety of nilpotent groups of class at most c, the class of nilpotent groups and the class of finite groups. It follows from a result due to Kargapolov and Čurkin and independently to Groves that in a variety not containing all metabelian groups, each polycyclic group G belongs to . We show that G is in fact in , where c is an integer depending only on the variety. On the other hand, it is not always possible to find an integer e (depending only on the variety) such that G belongs to but we characterize the varieties in which that is possible. In this case, there exists a function f such that, if G is d-generated, then G ∈ So, when e = 1, we obtain an extension of Zel'manov's result about the restricted Burnside problem (as one might expect, this result is used in our proof). Finally, we show that the class of locally nilpotent groups of a variety forms a variety if and only if for some integers c′, e′.
Sums of Cantor sets yielding an interval
Authors: Cabrelli Carlos A. , Hare Kathryn E. , Molter Ursula M. 
Published: April 2009

AbstractIn this paper we prove that if a Cantor set has ratios of dissection bounded away from zero, then there is a natural number N, such that its N-fold sum is an interval. Moreover, for each element z of this interval, we explicitly construct the N elements of C whose sum yields z. We also extend a result of Mendes and Oliveria showing that when s is irrational is an interval if and only if a /(1−2a) as/(1−2as) ≥ 1.
Valency enumeration of rooted plane trees
Authors: Mallows C. L. , Wachter K. W. 
Published: April 2009

AbstractWe obtain the enumerator by node-valencies of planted plane trees, whose square gives the enumerator of rooted plane trees. We also study the enumeration by number of nodes and black-node-valencies of bichromatic rooted plane trees, encountering a remarkably simple inversion formula. Finally, we remark that these bichromatic trees are in 1–1 correspondence with solutions to the weak lead ballot problem.
Constant curved minimal CR 3-spheres in CPn
Authors: Li Zhen-Qi , Huang An-Min 
Published: April 2009

AbstractIn this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space CPn are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be c = 1/(m2-1) for some integer m≥ 2, and the full dimension is n = 2m2-3. An explicit analytic expression for such an immersion is given.
Rees matrix semigroups and the regular semidirect product
Authors: Auinger K. , Szendrei M. B. 
Published: April 2009

AbstractA generalization of the Pastijn product is introduced so that, on the level of e-varieties and pseudoe-varieties, this product and the regular semidirect product by completely simple semigroups ‘almost always’ coincide. This is applied to give a model of the bifree objects in every e-variety formed as a regular semidirect product of a variety of inverse semigroups by a variety of completely simple semigroups that is not a group variety.
Volterra spaces revisited
Authors: Cao Jiling , Gauld David 
Published: April 2009

AbstractIn this paper, we investigate Volterra spaces and relevant topological properties. New characterizations of weakly Volterra spaces are provided. An analogy of the Banach category theorem in terms of Volterra properties is obtained. It is shown that every weakly Volterra homogeneous space is Volterra, and there are metrizable Baire spaces whose hyperspaces of nonempty compact subsets endowed with the Vietoris topology are not weakly Volterra.
Two weight norm inequalities for communtators of one-sided singular integrals and the one-sided discrete square function
Authors: Lorente M. , Riveros M. S. 
Published: April 2009

AbstractThe purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (-∞, 0)) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.
Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic
Authors: Liu Wende , Zhang Yongzheng 
Published: April 2009

AbstractLet ℋ(m;t) be the finite-dimensional odd Hamiltonian superalgebra over a field of prime characteristic. By determining ad-nilpotent elements in the even part, the natural filtration of ℋ (m;t) is proved to be invariant in the following sense: If ϕ: ℋ (m;t) → ℋ (m′t′) is an isomorphism then ϕ(ℋ(m;t)i) = ℋ (m′ t′) i for all i ≥ –1. Using the result, we complete the classification of odd Hamiltonian superalgebras. Finally, we determine the automorphism group of the restricted odd Hamiltonian superalgebra and give further properties.