bluuebunny/crossref_metadata_2025 huggingface dataset:
Radius of convexity of partial sums of a certain power series
Authors: Singh Ram
Published: April 2009

Let , be regular in the unit disc . G. Szegö [5] and Y. Miki [3] proved that if f(z), given by (1), is univalent (starlike with respect to the origin; convex; close-to-convex in E) then any one of the partial sums , is also univalent (starlike with respect to the origin; convex; close-to-convex) in |z| < ¼and that the constant ¼ cannot be replaced by a larger one.
Torsion and protorsion modules over free ideal rings
Authors: Cohn P. M.
Published: April 2009

Free ideal rings (or firs, cf. [2, 3] and § 2 below) form a noncommutative analogue of principal ideal domains, to which they reduce in the commutative case, and in [3] a category TR of right R-modules was defined, over any fir R, which forms an analogue of finitely generated torsion modules. The category TR was shown to be abelian, and all its objects have finite composition length; more over, the corresponding category RT of left R-modules is dual to TR.
TTF-classes over perfect rings
Authors: Alin J. S. , Armendariz E. P.
Published: April 2009

For a ring R with unit, let RM denote the category of unitary left R-modules. Following S.E. Dickson [3], a(non-empty) class of R-modules is a torsion class in rM if is closed under factors, extensions, and direct sums. If, in addition, is closed under submodules, then is said to be hereditary.
On the residual finiteness of permutational products of groups
Authors: Allenby R. B. J. T.
Published: April 2009

In a recent paper Gregorac [1] has posed the following question: if P is a permutational product of the amalgam = A ∪ B|H and if P is residually finite are all the permutational products of residually finite?
Explicit formulae for two-bridge knot polynomials
Authors: Fukuhara Shinji
Published: April 2009

A 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.
On cardinality of sumsets
Authors: Garaev M. Z. , Kueh Ka-Lam
Published: April 2009

In this article we study some special problems of the additive number theory connected with an estimate of cardinality of a sum of two sets, which can be convex as well as non-convex sequences.
Iterative methods for computing generalized inverses related with optimization methods
Authors: Djordjević Dragan S. , Stanimirović Predrag S.
Published: April 2009

We 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

Pseudoeffect (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

We 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.
Smale's mean value conjecture for odd polynomials
Authors: Ng T. W.
Published: April 2009

In this paper, we shall show that the constant in Smale's mean value theorem can be reduced to two for a large class of polynomials which includes the odd polynomials with nonzero linear term.
On the Steinberg Character of a Finite Simple Group of Lie Type
Authors: Srinivasan Bhama
Published: April 2009

Let K be an algebraically closed field of characteristic ρ >0. If G is a connected, simple connected, semisimple linear algebraic group defined over K and σ an endomorphism of G onto G such that the subgroup Gσ of fixed points of σ is finite, Steinberg ([6] [7]) has shown that there is a complex irreducible character χ of Gσ with the following properties. χ vanishes at all elements of Gσ which are not semi- simple, and, if x ∈ G is semisimple, χ(x) = ±n(x) where n(x)is the order of a Sylow p-subgroup of (ZG(x))σ (ZG(x) is the centraliser of x in G). If G is simple he has, in [6], identified the possible groups Gσ they are the Chevalley groups and their twisted analogues over finite fields, that is, the ‘simply connected’ versions of finite simple groups of Lie type. In this paper we show, under certain restrictions on the type of the simple algebraic group G an on the characteristic of K, that χ can be expressed as a linear combination with integral coefficients of characters induced from linear characters of certain naturally defined subgroups of Gσ. This expression for χ gives an explanation for the occurence of n(x) in the formula for χ (x), and also gives an interpretation for the ± 1 occuring in the formula in terms of invariants of the reductive algebraic group ZG(x).
Lattices of Subsemivarieties of Certain Varieties
Authors: Shafaat Ahmad
Published: April 2009

For all positive integers m, n, m ≤ n, let m,n denote the variety of algebras with m n-ary operations ω1, …, ωm and n m-ary operations φ1, …, φn satisfying the system of identities The varieties m,n are considered by Swierczkowski [1] and by Akataeb and Smirnov [2]. Jonsson and Tarski [3] consider m,n in the case m = 1, n = 2. In [2] it is shown that the lattice Lm,n of subvarieties of m,n, is uncountable except when m = 1 in which case Lm,n has a very simple description. In particular, for n > 1 the lattice L1,n is the two element chain which means that 1,n has no proper subvarieties.
Varieties of Metabelian p-Groups of Class b, p+1
Authors: Brisley Warren
Published: April 2009

A large number of results are available on the lattice of subvarieties of the variety of metabelian groups. When considering metabelian p-groups (for odd p), the immediate division is between groups of nilpotency class less than p, and those of class at least p. The first case was dealt with in some detail in [1], and this paper extends the results to the next interesting cases, classes p and p + 1. The main results are stated in Theorems 2 and 4, which give the basis laws for certain varieties, and 3 and 5, which assert the existence of specific generating groups for these varieties, and hence their non-trivial existence. The notation, and the essential parts of the logic, are as in [1]; for the purposes of this paper, the following modification of Lemma 1.1 of [1], and also the ring-of-integer operations used in its proof, are together dubbed the ‘Stirling manipulation’:
A Note on Commutative l-Groups
Authors: Speed T. P. , Strzelecki E.
Published: April 2009

Let G be a commutative lattice ordered group. Theorem 1 gives necessary and sufficient conditions under which a⊥ with a∈G is a maximal l-ideal. A wide family of, l-groups G having the property that the orthogonal complement of each atom is a maximal l-ideal is described. Conditionally σ-complete and hence conditionally complete vector lattices belong to the family.It follows immediately that if a is an atom in a conditionally complete vector lattice then a⊥ is a maximal vector lattice ideal. This theorem has been proved in [7] by Yamamuro. Theorem 2 generalizes another result contained in [7]. Namely we prove that if M is a closed maximal l-ideal of an archimedean l-group G then there exists an atom a ∈ G such that M = a⊥.
Characterization of Some Fully Ordered Rings
Authors: Satyanarayana M.
Published: April 2009

In a fully ordered (f.o.) ring with identity, the set of all bounded elements as defined below might be an Archimedian subring. Most of the examples of f.o. rings constructed in literature having the bounded set as Archimedian subring are polynomial rings. For example I[x], R[x] etc., where I is the ring of integers and R is the field of rationals, with lexicographic ordering. Now we ask whether a f.o. ring with identity, with the set of bounded elements as Archimedian subring can be a polynomial ring over an Archimedian subring. This is answered affirmatively in Theorem 1. It is proved in Theorem 3 that f.o. rings with identity and with every positive element a large element, belong to the above class. The problem then arises as to when the set of all bounded elements, called a weak Archimedian sub- ring in [2], becomes an Archimedian subring. This problem is completely solved in Theorem 2. The concept of weak Archimedian rings is found to be useful by the author in characterizing some f.o. rings as algebraic algebras in [3].
Commutation Properties of Operator Polynomials
Authors: Caradus S. R.
Published: April 2009

Suppose A and B are continuous linear operators mapping a complex Banach space X into itself. For any polynomial pC, it is obvious that when A commutes with B, then p(A) commutes with B. To see that the reverse implication is false, let A be nilpotent of order n. Then An commutes with all B but A cannot do so. Sufficient conditions for the implication: p(A) commutes with B implies A commutes with B: were given by Embry [2] for the case p(λ) = λn and Finkelstein and Lebow [3] in the general case. The latter authors proved in fact that if f is a function holomorphic on σ(A) and if f is univalent with non-vanishing derivative on σ(A), then A can be expressed as a function of f(A).
A Finiteness Condition for Locally Compact Abelian Groups
Authors: Grove L. C. , Lardy L. J.
Published: April 2009

A map f: A→B in category is called monic if fg = fh implies that g = h for all maps g, h: C → A; it is called epic if gf = hf implies that g = h for all maps g, h: B → C. An object A ∈ is called an S-object if every monic map f: A → A is also epic; it is called a Q-object if every epic map f: A → A is also monic. If A is both an S-object and a Q-object then A is called an SQ-object. In the category of sets the SQ-sets are the finite sets. In the category of vector spaces over a field F the SQ-spaces are precisely the finite dimensional spaces. In the light of these simple examples, it seems reasonable to view the SQ-objects of a category as being of ‘finite type’. We shall be chiefly concerned with investigating the SQ-objects in certain subcategories of the category of locally compact abelian groups.
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

The 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.
Categorical constructions in C*-algebra theory
Authors: Khoshkam M. , Tavakoli J.
Published: April 2009

The notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.
Normal surfaces in non-compact 3-manifolds
Authors: Kang Ensil
Published: April 2009

We 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

We 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

In 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

Let 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

A 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

Let 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

We 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

Absrtact

Staring 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

Let 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

We 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

Given 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.
The Dixmier-Douady class of groupoid crossed products
Authors: Muhly Paul S. , Williams Dana P.
Published: April 2009

We give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.
Multiplicity results for some nonlinear elliptic problems
Authors: Chen Kuan-Ju
Published: April 2009

In 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

The 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

The 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

Let 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

In 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.
Definitions of integral elements and quotient rings over non-commutative rings with identity
Authors: Atterton T. W.
Published: April 2009

Let B be an associative ring with identity, A a subring of B containing the identity of B. If B is commutative then it is customary to define an element b of B to be integral over A if it satisties an equation of the form for some a1, a2, …, an A. This definition does not generalize readily to the case when B is non-commutative. Van der Waerden ([11], p. 75) defines b ∈ B to be integral over A if all powers of b belong to a finite A-module. This definition is quite satisfactory when A satisfies the ascending chain condition for left ideals, but in the general case this type of integrity is not necessarily transitive, even when B is commutative. Krull [6] calls an element b ∈ B which satisfies the above condition almost integral over A (but he only considers the commutative case). The subset Ā of B consisting of all almost integral elements over A is called the complete integral closure of A in B. If Ā = A, A is said to be completely integrally closed in B. More recently (in [3]), Gilmer and Heinzer (see also Bourbaki, [1]) have discussed these properties in the commutative case and have shown that the complete integral closure of A in B need not be completely integrally closed in B. If B is not commutative, the set A of elements of B almost integral over A, may not even form a ring. In [5] p. 122, Jacobson uses a definition equivalent to Van der Waerden's for the non-commutative case but the definition applies only for a very restricted class of rings.
On a type of K-contact Riemannian manifold
Authors: Chaki M. C. , Ghosh D.
Published: April 2009

Let M be an n-dimensional (n = 2m + 1, m ≦ 1) real differentiable manifold. if on M there exist a tensor field , a contravariant vector field ξi and a convariant vector field ηi such that then M is said to have an almost contact structure with the structure tensors (φ,ξ, η) [1], [2]. Further, if a positive definite Riemannian metric g satisfies the conditions then g is called an associated Riemannian metric to the almost contact structure and M is then said to have an almost contact metric structure. On the other hand, M is said to have a contact structure [2], [4] if there exists a 1-form η over M such that η ∧ (dη)m ≠ 0 everywhere over M where dη means the exterior derivation of η and the symbol ∧ means the exterior multiplication. In this case M is said to be a contact manifold with contact form η. It is known [2, Th. 3,1] that if η = ηidxi is a 1-form defining a contact structure, then there exists a positive definite Riemannian metric in gij such that and define an almost contact metric structure with and ηi where the symbol ∂i standing for ∂/∂xi.
On the existence of an exact solution of the Navier-Stokes equation pertaining to certain vortex motion
Authors: Tam K. Kuen
Published: April 2009

In 1942, Burgers [1] observed that in cylindrical polar coordinates, the steady Navier-Stokes equation governing viscous incompressible fluid motion can be reduced to a set of ordinary differential equations if the velocity components vr, vo and vz are assumed to have a special form.
Valency enumeration of rooted plane trees
Authors: Mallows C. L. , Wachter K. W.
Published: April 2009

We 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

In 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.
Negative definite and Schoenberg functions on commutative hypergroups
Authors: Bloom Walter R. , Ressel Paul
Published: April 2009

In this paper we investigate when negative definite functions on commutative hypergroups satisfy the Schoenberg criterion.
Rees matrix semigroups and the regular semidirect product
Authors: Auinger K. , Szendrei M. B.
Published: April 2009

A 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

In 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

The 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

Let 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.
Some Fourier division problems
Authors: Edwards R. E.
Published: April 2009

Let T denote the circle group, C the set of continuous complex-valued functions on T, and A the set of f ∈ C having absolutely convergent Fourier series:

I standing for the set of integers.
An inner orthogonality of Hadamard matrices
Authors: Bush K. A.
Published: April 2009

We say a matrix H of order 4t is Hadamard if each entry is 1 or — 1, and the inner product of any two rows is zero. We shall consider only Hadamard matrices in normal form with the first row consisting solely of 1 while any two of the remaining rows have the property that hik = hjk = 1, hik = –hjk = 1, —hik = hjk = 1, and –hik = –hjk = 1 each occur t times. We can induce a further normalization by choosing the second row of H to have the first 2t entries 1 and the last 2t entries — 1, and this will be the standard form we consider. We now call the submatrix obtained by deleting the first two rows of H and the first It columns. H therefore is of dimension 4t — 2 x 2t. We prove the following theorem:
Weak compactness in normed linear spaces
Authors: Tacon D. G.
Published: April 2009

The notion of weak compactness plays an important role in normed linear space theory. However in many instances norm completeness of the space is an important assumption for obtaining relevant theorems. This note generalises the concept of weak compactness for subsets of normed linear spaces and obtains generalisations of known theorems including that of Eberlein [2]. We use the methods and techniques of “non-standard analysis” in the proofs; several useful non-standard results for normed linear spaces are given.
A class of two generator two relation finite groups
Authors: Wamsley J. W.
Published: April 2009

A group which is minimally generated by n generators and defined by n relations is said to have zero deficiency. The class of finite groups known to have zero deficiency is small, consisting of cyclic groups, certain metacyclic groups [4] and classes of groups given in [1], [2] and [3].
On the lattice of congruences on a band
Authors: Baird G. R.
Published: April 2009

Lattices of congruences have been studied by many authors. Hall [4] has shown that the lattice of congruences on a semilattice satisfy a certain chain condition which is a natural extension to arbitrary lattices of the Jordan-Dedekind chain condition for finite lattices.
Central Sidon and central ∧p sets
Authors: Parker Willard A.
Published: April 2009

Central Sidon sets and central ∧p sets are defined and equivalent characterizations are given. It is shown that a central Sidon set with an upper bound on the degrees of its elements is a ∧p set (1 < p < ∞ ). The bound on the degrees is shown to be necessary by an example.
The Dedekind property for semirings
Authors: Dulin Bill J. , Mosher James R.
Published: April 2009

In this article the concept of Dedekind semidomain is defined, and it is shown that certain structures of this kind are Noetherian, have integral closure, and have the property that their primek-ideals are maximal. The second section provides the appropriate transportation theorems, while the third gives the main result concerning Dedekind semidomains. Examples are given throughout the paper to show that the hypothesies of certain theorems in the paper cannot be greatly weakened.
Rings related to completely 0-simple semigroups
Authors: McAlister D. B.
Published: April 2009

A.H. Clifford ([2], [3]) has shown that all finite dimensional irreducible representations of a completely 0-simple semigroup can be obtained as extensions of those of its maximal subgroups. Lallement and Petrich, [7], have given an alternative method for constructing the irreducible representations of a finite 0-simple semigroup from its Schutzenberger representation ([13]). Using the form which they obtain for the irreducible representations of a finite 0-simple semigroup S = M0(G; m, n; P), Lallement and Petrich show that where M is the Munn algebra isomorphic to the (contracted) algebra Φ(S) of S over Φ.
Congruences on Orthodox Semigroups
Authors: Meakin John
Published: April 2009

A semigroup S is called regular if a ∈ aSa for every element a in S. The elementary properties of regular semigroups may be found in A. H. Clifford and G. B. Preston [1]. A semigroup S is called orthodox if S is regular and if the idempotents of S form a subsemigroup of S.
A Graphical Exposition of the Ising Problem
Authors: Harary Frank
Published: April 2009

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.
A light-weight version of Waring's problem
Authors: Wooley Trevor D.
Published: April 2009

An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.
On decomposition of sub-linearised-polynomials
Authors: Coulter Robert S. , Havas George , Henderson Marie
Published: April 2009

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.
Invariants in abstract mapping pairs
Authors: Ronglu Li , Junming Wang
Published: April 2009

In a topological vector space, duality invariant is a very important property, some famous theorems, such as the Mackey-Arens theorem, the Mackey theorem, the Mazur theorem and the Orlicz-Pettis theorem, all show some duality invariants.

In this paper we would like to show an important improvement of the invariant results, which are related to sequential evaluation convergence of function series. Especially, a very general invariant result is established for an abstract mapping pair (Φ, B(Φ, X)) consisting of a nonempty set Φ and B(Φ, X) = {f ∈ XΦ: f (Φ) is bounded}, where X is a locally convex space.
One-sided ideals and approximate identities in operator algebras
Authors: Blecher David P.
Published: April 2009

A left ideal on anyC*-algebra is an example of an operator algebra with a right contractive approximate indentiy (r.c.a.i.). Indeed, left ideal inC*-algebras may be charcterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. shoulod be studied in terms of a certain let ideal of aC*-algebra. We study left ideals from the perspective of ‘Hamana theory’ and using the multiplier algebras of an operator space studied elsewhere by the author. More generally, we develop some general theory for operator algebras which have a 1-sided identity or approzimate indentity, including a Banach-Stone theorem for these algebras, and an analysis of the ‘multiplier operator algebra’.
Polynomial approximations on a polydisc
Authors: Chui Charles K.
Published: April 2009

Throughout this paper, we will use the terminologies and notations as in [4]. Thus, UN denotes the open unit polydisc in the space CN of N complex variables, TN the distinguished boundary of UN and .
Finite soluble groups with certain splitting properties
Authors: Bryce R. A. , Cossey John
Published: April 2009

Abstract. In a recent paper, Bechtell obtained detailed structure theorems for finite supersoluble groups with the property that every minimal supplement for a non-Frattini normal subgroup is a complement. We consider finite soluble groups with this property. The situation is rather different to the supersoluble case, and the information we obtain is not as complete, though for such groups with non-trivial Frattini subgroup, some of the results are analogous.
A class of extreme lattice-coverings ofn–space by spheres
Authors: Barnes E. S. , Trenerry D. W.
Published: April 2009

All extreme lattice-coverings ofn–space by spheres are known forn≦ 4; see for example [3]. Only one class of extreme covering is known for largen, namely that corresponding to the quadratic formthis was first shown to be extreme for alln≧ 2 by Bleicher [2].
Types over c(k) spaces
Authors: Pomper Markus
Published: April 2009

Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K, with the sup norm. Types over C(K) (in the sense of Krivine and Maurey) are represented here by pairs (l, u) of bounded real-valued functions on K, where l is lower semicontinuous and u is upper semicontinuous, l ≤ u and l(x) = u(x) for every isolated point x of K. For each pair the corresponding type is defined by the equation τ(g) = max{║l + g║∞, ║u + g║∞} for all g ∈ C(K), where ║·║∞ is the sup norm on bounded functions. The correspondence between types and pairs (l, u) is bijective.
Geodesic flow of visibility manifolds
Authors: Kim Hyun Jung
Published: April 2009

We prove that the conservativity of the geodesic flow is equivalent to the ergodicity of the geodesic flow with respect to the Bowen-Margulis measure on visibility manifolds.
On a differentiability condition for reflexivity of a Banach space
Authors: Giles J. R.
Published: April 2009

In studying the geometry of normed linear space it is useful to draw attention to the following mapping.
A Remark on p-Valent Functions
Authors: Jenkins James A. , Oikawa Kôtaro
Published: April 2009

In the theory of multivalent functions there are several different levels of postulates for p-valency. Perhaps the most well-known is the class of mean p-valent functions in the sense of Spencer [8] (we shall refer to them as areally mean p-valent functions), whose basic properties are found, e.g., in Hayman [4]. Recently Eke [1, 2] extended to these functions a number of results which had been known for circumferentially mean p-valent functions.
Closed categories generated by commutative monads
Authors: Kock Anders
Published: April 2009

The notion of commutative monad was defined by the author in [4]. The content of the present paper may briefly be stated: The category of algebras for a commutative monad can in a canonical way be made into a closed category, the two adjoint functors connecting the category of algebras with the base category are in a canonical way closed functors, and the front- and end-adjunctions are closed transformations. (The terms ‘Closed Category’ etc. are from the paper [2] by Eilenberg and Kelly). In particular, the monad itself is a ‘closed monad’; this fact was also proved in [4].
Some approximate results in renewal and dam theories
Authors: Phatarfod R. M.
Published: April 2009

It is well known that Wald's Fundamental Identity (F.I.) in sequential analysis can be used to derive approximate (and, sometimes exact) results in most situations wherein we have essentially a random walk phenomenon. Bartlett [2] used it for the gambler's ruin problem and also for a simple renewal problem. Phatarfod [18] used it for a problem in dam theory. It is the purpose of this paper to show how a generalization of the Fundamental Identity to Markovian variables, (Phatarfod [19]) can be used to derive approximate results in some problems in dam and renewal theories where the random variables involved have Markovian dependence. The reason for considering both the theories together is that the models usually proposed for both the theories — input distribution for dam theory, and lifedistribution for renewal theory — are similar, and only a slight modification (to account for the ‘release rules’ in dam theory, plus the fact that we have two barriers) is necessary to derive results in dam theory from those of renewal theory.
The H-function transform II
Authors: Gupta K. C. , Mittal P. K.
Published: April 2009

In this paper first we prove the uniqueness theorem for an integral transform whose kernel is H-function. Later on we establish a new and interesting theorem concerning this transform and a generalized Laplace transform whose kernel is Meijer's G-function.
On the lattice of congruences on a semilattice
Authors: Hall T. E.
Published: April 2009

Lattices of congruences are studied in section II.6 of Cohn [2]. Papers [5] and [6] by Munn deal with lattices of congruences on semigroups and conditions under which these lattices are modular. In [4] Lallement shows that the lattice of congruences on a completely 0-simple semigroup is semimodular, giving an alternative proof of the result, due to Preston [7], that the lattice of congruences on a completely 0-simple semigroup satisfies a certain chain condition which is a natural extension to arbitrary lattices of the Jordan-Dedekind chain condition for finite lattices.
Quadrics associated with a simplex in n-space
Authors: Konnully Augustine O.
Published: April 2009

It is well known that the projections of a pair of points from the vertices of a triangle onto the opposite sides lie on a conic and that when the points are the centroid and orthocentre of the triangle, this conic is a circle. Analogously the projections of the centroid and orthocentre of a simplex from its vertices onto the opposite (n—1)-dimensional faces, if the simplex is orthocentric, lie on a hypersphere [2, 5]. Further the projections of two points onto the edges of a general simplex from the opposite faces lie on quadric [1]; and when the points are the centroid and orthocentre respectively and the simplex is orthocentric, this quadric is a hypersphere [2]. The results as regards projections onto (n—l)-dimensional and 1-dimensional faces being thus known, it remains to see what results hold in the case of intermediary faces. And in this note we prove that a similar result holds for projections onto intermediary faces as well.
High Reynolds number flow between two inflnite rotating disks
Authors: Rasmussen H.
Published: April 2009

In 1921 von Karman [1] showed that the Navier-Stokes equations for steady viscous axisymmetric flow can be reduced to a set of ordinary differential equations if it is assumed that the axial velocity component is independent of the radial distance from the axis of symmetry. He used these similarity equations to obtain a solution for the flow near an infinite rotating disk. Later Batchelor [2] and Stewartson [3] applied these equations to the problem of steady flow between two infinite disks rotating in parallel planes a finite distance apart.
Conjugacy in singular Artin monoids
Authors: Corran Ruth
Published: April 2009

We define a notion of conjugacy in singular Artin moniods, and solve the corresponding conjugacy problem for finite types. We sgiw that this definition is appropriate to describe type (1) singular Markov moves on singular braids. Parabolic submonoids of singular Artin monoids are defined and, in finite type, are shown to be singular Artin monoids. Solutions to conjugacy-type problems of parabolic submonoids are described. Geometric objects defined by Fenn, Rolfsen and Zhu, called (j, k)-bands, are algebraically characterised, and a procedure is given which determines when a word represents a (j, k)-band.
On properties of group closures of one-to-one transformations
Authors: Levi Inessa
Published: April 2009

For a permutation group H on an infinite set X and a transformation f of X, let 〈f: H〉 = 〈{hfh-1:h є; H}〉 be a group closure of f. We find necessary and sufficient conditions for distinct normal subgroups of the symmetric group on X and a one-to-one transformation f of X to generate distinct group closures of f. Amongst these group closures we characterize those that are left simple, left cancellative, idempotent-free semigroups, whose congruence lattice forms a chain and whose congruences are preserved under automorphisms.
The k(GV)-problem revisited
Authors: Keller Thomas Michael
Published: April 2009

Suppose that the finite group G acts faithfully and irreducibly on the finite G-module V of characteristic p not dividing |G|. The well-known k(GV)-problem states that in this situation, if k(G V) is the number of conjugacy classes of the semidirect product GV, then k(GV) ≤ |V|. For p—solvable groups, this is equivalent to Brauer's famous k(B)-problem. In 1996, Robinson and Thompson proved the k(GV) problem for large p. This ultimately led to a complete proof of the k(GV)-problem. In this paper, we present a new proof of the k(G V)-problem for large p.
Fixed points and iteration homotopies
Authors: Papp Francis J.
Published: April 2009

Suppose that Ф is a topological space equipped with a Hausdorff topology and that T is a continuous function mapping Ф into Ф. We discuss the existence and uniqueness of fixed points of T and the convergence of the Picard sequence of iterates, from the viewpoint of the existence of a homotopy with special properties.
A cauchy criterion and a convergence theorem for Riemann-complete integral
Authors: Pu H. W.
Published: April 2009

In 1957 Kurzweil [1] proved some theorems concerning a generalized type of differential equations by defining a Riemann-type integral, but he did not study its properties beyond the needs of that research. This was done by R. Henstock [2, 3], who named it a Riemann-complete integral. He showed that the Riemann-complete integral includes the Lebesgue integral and that the Levi monotone convergence theorem holds. The purpose of the present paper is to give a necessary and sufficient condition for a function to be Riemann-complete integrable and to establish a termwise integration theorem for a uniformly convergent sequence of Riemann-complete integrable functions.
Permutational products of lattice ordered groups
Authors: Reilly N. R.
Published: April 2009

Let H be a group, let {G1: i ∈ I} be a set of groups and, for each i, let θi be a a monomorphism: H → G1, with Hθ1 = H1. We call such a system of groups and monomorphisms an amalgam and denote it by [G1; H; θi; Hi]. By an embedding of the amalgam into a group G is meant a set of monomorphisms ϕi: G1 → G such that θiϕi= θjϕjfor all i, j and G1ϕi = Hθϕk, for all i, j, k.