bluuebunny/crossref_metadata_2025_split huggingface dataset:
On decomposition of sub-linearised-polynomials
Authors: Coulter Robert S. , Havas George , Henderson Marie 
Published: April 2009

AbstractWe 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

AbstractIn 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

AbstractA 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’.
Finite soluble groups with certain splitting properties
Authors: Bryce R. A. , Cossey John 
Published: April 2009

AbstractAbstract. 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.
Types over c(k) spaces
Authors: Pomper Markus 
Published: April 2009

AbstractLet 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.
Conjugacy in singular Artin monoids
Authors: Corran Ruth 
Published: April 2009

AbstractWe 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

AbstractFor 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

AbstractSuppose 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.
Loomis-Sikorski theorem for monotone σ-complete effect algebras
Authors: Dvurečenskij Anatolij 
Published: April 2009

AbstractWe show that monotone σ -complete effect algebras under some conditions are σ - homomorphic images of effect-tribes (as monotone σ -complete effect algebras), which are nonempty systems of fuzzy sets closed under complements, sums of fuzzy sets less than 1, and containing all pointwise limits of nondecreasing fuzzy sets. Because effect-tribes are generalizations of Boolean σ -algebras of subsets, we present a generlization of the Loomis-Sikorski theorem for such effect algebras. We show that we can choose an effect-tribe to be a system of affin fuzzy sets. In addition, we present a new version of the Loomis-Sikorski theorem for σ-complete MV-algebras.
Pseudo-elliptic integrals, units, and torsion
Authors: Pappalardi Francesco , Van Der Poorten Alfred J. 
Published: April 2009

AbstractWe remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomialD(x)whose square root generates a quadratic function field with non-trivial unit. We detail the genus I case.
Two index laws for fractional integrals and derivatives
Authors: Love E. R. 
Published: April 2009

SummaryThe first index law, or addition theorem, is well known. The second is much less well known; but both have been found to be of importance in recent studies of hypergeometric integral equations. The first law has usually been considered only in the simple case of orders of integration which have positive real part, or in the context of generalized functions. Arising out of the need to manipulate expressions involving several fractional integrals and derivatives, our aim here is to establish both laws for all combinations of complex orders of integration and differentiation, and for nearly all functions for which the fractional derivatives involved exist as locally integrable functions.
On fundamental operations in groups
Authors: Fajtlowicz S. 
Published: April 2009

By anoperationin equationally definable class of group we mean here the element of a free group in this class generated by set {x, y}.An operation ω(x, y) is calledfundamentalin a class of groupsKif for every groupGωKthe operationxy−1can be expressed in terms of ω.Higman and Neumann raised in [1] the problem: Is there any binary operation other thanxy-1,x-1y,yx-1,y-1xfundamental in the class of all groups?*
N-compact spaces as limits of inverse systems of discrete spaces
Authors: Chew Kim-Peu 
Published: April 2009

AbstractLetNdenote the discrete space of all natural numbers. A spaceXisN-compact if it is homeomorphic with some closed subspace of a product of copies ofN. In this paper,N-compact spaces are characterized as homeomorphs of inverse limit space of inverse systems of copies of subsets ofN. Also, it is shown that a spaceXisN-compact if and only if the space(X) of all non-empty compact subsets ofXwith the finite topology isN-compact.
A note on the characterization of CM-fields
Authors: Blanksby P. E. , Loxton J. H. 
Published: April 2009

AbstractThis note deals with some properties of algebraic number fields generated by numbers having all their conjugates on a circle. In particular, it is shown that an algebraic number field is a CM-field if and only if it is generated over the rationals by an element (not equal to ±1) whose conjugate all lie on the unit circle.Subject classification(Amer. Math. Soc.(MOS)1970): 12 A 15, 12 A 40, 14 K 22.
Algebraic independence properties of the Fredholm series
Authors: Loxton J. H. , van der Poorten A. J. 
Published: April 2009

AbstractWe consider algebraic independence properties of series such as We show that the functions fr(z) are algebraically independent over the rational functions Further, if αrs (r = 2, 3, 4, hellip; s = 1, 2, 3, hellip) are algebraic numbers with 0 < |αrs|, we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr(αrs) over the rationals.
On localizing orderable modules
Authors: Fox Colin D. 
Published: April 2009

AbstractIf A is a T-orderable R-module and S is a multiplicative subsemigroup of R, each s∈S acting as a monomorphism of A, then it is possible sometimes A in a T-orderable R-module on which each s∈S as an automorphism. We show that such an embedding does not always exist and, by generalizing a theorem of Kokorin and Kopytov, provide a partial answer to the question “when is such an embedding possible?”Subject classification (Amer. Math. Soc. (MOS) 1970): 06 A 70, 16 A 08, 16 A 64.
A uniqueness set for all Hp(Bn) with p>0
Authors: Chee P. S. 
Published: April 2009

AbstractFor n≥2, a hypersurface in the open unit ball Bn in is constructed which satisfies the generalized Blaschke condition and is a uniqueness set for all Hp(Bn) with p>0. If n≥3, the hypersurface can be chosen to have finite area.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 32 A 10.
Normal partitions of idempotents of regular semigroups
Authors: Trotter P. G. 
Published: April 2009

AbstractA characterization is provided here for any normal partition of the set of idempotents of a regular semigroup S. As a by-product of the method used, a new characterization of the greatest congruence on S corresponding to a given normal partition of its idempotents is obtained.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 M 10.
Integrability of Fourier transforms under an ergodic hypothesis
Authors: Brown Gavin 
Published: April 2009

AbstractThe object is to unify and complement some recent theorems of Hewitt and Ritter on the integrability of Fourier transforms, but the underlying theme is the ancient one that Plancherel's theorem is the “only” integrability constraint on Fourier transforms. The distinguishing feature of the results is that we restrict attention to positive measures (or functions) which satisfy an ergodic condition and whose transforms are positive. (In fact we employ sums of discrete random variables, a technique which seems to have been largely ignored in context.) The general setting is that of locally compact abelian groups but we are chiefly interested in the line or the circle, and it appears that the theorems are new for these classical groups.
Characterization of pseudocompactness by the topology of uniform convergence on function spaces
Authors: McCoy R. A. 
Published: April 2009

AbstractIt is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.
On the Lie-Kolchin-Mal'cev theorem
Authors: Wehrfritz B. A. F. 
Published: April 2009

AbstractWe discuss generalizations of the Lie-Kolchin-Mal'cev theorem. For example we show that if G is a soluble linear group of degree n, then G contains a triangularizable subgroup T whose index in G is bounded by function of n only and such that T is normalized by every automorphism of G normalizing G0, the Zariski connected component of G containing the identity. We also prove that in certain situations at least the index of G0 in G can be bounded in terms of the degree and the ground field.
Positive points in polar lattices
Authors: Hossain F. , Worley R. T. 
Published: April 2009

AbstractThe authors investigate max min μF(x) F(y)for two standard distance functions F in R2, where μ denotes the area of {x ∈ R2; F(x)≤ 1}, the maximum is over all (geometric) lattices Λ in R2 and the minimum is over all positive points x ∈ Λ and y ∈ Λ* (the polar lattice of Λ). An application is given to a problem on fractional parts.
Varieties that make one Cross
Authors: MacDonald Sheila Oates , Vaughan-Lee M. R. 
Published: April 2009

AbstractAn example is constructed of a locally finite variety of non-associative algebras which satisfies the maximal condition on subvarieties but not the minimal condition. Based on this, counterexamples to various conjectures concerning varieties generated by finite algebras are constructed. The possibility of finding a locally finite variety of algebras which satisfies the minimal condition on subvarieties but not the maximal is also investigated.
The characters and structure of a class of modular representation algebras of cyclic p-groups
Authors: Renaud J. C. 
Published: April 2009

AbstractLet p,m be the modular representation algebra of the cyclic group of order pm over the prime field Zp. The characters of p, m are derived. For p = 2, this provides an alternative proof of a result due to Carlson (1975), tha 2,m is a local ring. It is shown that for p>2, p, m is a direct sum of 2m local rings. Their dimensions and primitive idempotents are derived.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20, 12 C 05, 12 C 30, 33 A 65.
Completion of lattices of semi-continuous functions
Authors: August John , Byrne Charles 
Published: April 2009

AbstractIf U and V are toplogies on an abstract set x, then the triple (X, U, V) is a bitopologica space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued functions on certain bitopological spaces. The distributivity of certain lattices is investigated, and the theorem of Funayama on distributive normal completions is generalized.
Necessary and sufficient conditions for the existence of a generalized Stieltjes integral
Authors: Russell A. M. 
Published: April 2009

AbstractIn Russell (1973) a Riemann-type necessary and sufficient condition was given for the existence of (defined also in Russell (1975)) when f was bounded and g was k-convex in [a′, b′]. In this paper we present necessary and sufficient conditions for the existence of a particular Stieltjes-type integral without imposing a convexity condition upon g. These conditions are used to obtain an additivity result for the integral over adjoining intervals without any additional restrictions being imposed upon the functions involved.
Optimality conditions for a cone-convex programming problem
Authors: Massam Hélène M. 
Published: April 2009

AbstractOptimality conditions without constraint qualifications are given for the convex programming problem: Maximize f(x) such that g(x) ∈ B, where f maps X into R and is concave, g maps X into Rm and is B-concave, X is a locally convex topological vector space and B is a closed convex cone containing no line. In the case when B is the nonnegative orthant, the results reduce to some of those obtained recently by Ben-Israel, Ben-Tal and Zlobec.
A lambda calculus with naive substitution
Authors: Staples John 
Published: April 2009

AbstractAn alternative approach is proposed to the basic definitions of the lassical lambda calculus. A proof is sketched of the equivalence of the approach with the classical case. The new formulation simplifies some aspects of the syntactic theory of the lambda calculus. In particular it provides a justification for omitting in syntactic theory discussion of changes of bound variable.
Direct decompositions of groups with finitely generated commutator quotient group
Authors: Hirshon Ronald 
Published: April 2009

AbstractLet G/G' be finitely generated and let G = B1 x A1 = B2 x A2 = … = Bi x Ai = … with each Bi isomorphic to a fixed group B which obeys the maximal condition for normal subgroups. Then the Ai represent only finitely many isomorphism classes. We give an example with B infinite cyclic, G/G' free abelian of infinite (countable) rank and such that G is decomposed as above with no two Ai isomorphic.
Measurability of cross section measure of a product Borel set
Authors: Johnson Roy A. 
Published: April 2009

AbstractSuppose μ and ν are Borel measures on locally compact spaces X and Y, respectively. A product measure λ can be defined on the Borel sets of X x Y by the formula λ(M) = ∫ν(Mx) dμ, provided that vertical cross section measure ν(Mx) is a measurable function in x. Conditions are summarized for ν(Mx) to be measurable as a function in x, and examples are given in which the function ν(Mx) is not measurable. It is shown that a dense, countably compact set fails to be a Borel set if it contains no nonempty zero set.
Radical properties defined locally by polynomial identities II
Authors: Gardner B. J. 
Published: April 2009

AbstractA radical class R of rings (not necessarily associtative) is called an n-radical class if it has the property that a ring is in R if and only if every subring generated by ≤n elements is in R. A transfer theorem is proved, relating n-radical classes in two universal varieties which share the same ≤n-generator rings. Partially through the use of this result, we obtain information about extension closed subvarieties of various universal varieties of power-associative rings.
Some problems in partitio numerorum
Authors: Erdös P. , Loxton J. H. 
Published: April 2009

AbstractWe consider some unconventional partition problems in which the parts of the partition are restricted by divisibility conditions, for example, partitions n = a1+…+ak into positive integers a1, …, ak such that a1 ∣ a2 ∣ … ∣ ak. Some rather weak estimates for the various partition functions are obtained.
Permutation characters of finite groups of Lie type
Authors: Surowski David B. 
Published: April 2009

AbstractLet g be a connected reductive linear algebraic group, and let G = gσ be the finite subgroup of fixed points, where σ is the generalized Frobenius endomorphism of g. Let x be a regular semisimple element of G and let w be a corresponding element of the Weyl group W. In this paper we give a formula for the number of right cosets of a parabolic subgroup of G left fixed by x, in terms of the corresponding action of w in W. In case G is untwisted, it turns out thta x fixes exactly as many cosets as does W in the corresponding permutation representation.
The 𝒥-classes of an inverse semigroup
Authors: Ash C. J. 
Published: April 2009

AbstractIt is shown, using the author's construction for ‘labelled semilattices’, that every partially ordered set, in which every two elements have a common lower bound, is isomorphic to the partiallyordered set of 𝒥-classes of some completely semi-simple inverse semigroup.1980 Mathematics subject classification (Amer. Math. Soc): primary 20 M 10, secondary 04 A 05, 08 A 05.
Resolvable (r, λ)-designs and the Fisher inequality
Authors: Vanstone S. A. 
Published: April 2009

AbstractIt is well known that in any (v, b, r, k, λ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.
Balanced binary arrays iii: the hexagonal grid
Authors: Oates-Williams Sheila , Street Anne Penfold 
Published: April 2009

AbstractWe consider the following problem arising in agricultural statistics. Suppose that a large number of plants are set out on a regular grid, which may be triangular, square or hexagonal, and that among these plants, half are to be given one and half the other of two possible treatments. For the sake of statistical balance, we require also that, if one plant in every k plants has i of its immediate neighbours receiving the same treatment as itself, then k is constant over all possible values of i. For square and triangular grids, there exist balanced arrays of finite period in each direction, but for the hexagonal grid, we show that no such balanced array can exist. Several related questions are discussed.
Group algebras with an Engel group of units
Authors: Bovdi A. 
Published: April 2009

AbstractLet F be a field of characteristic p and G a group containing at least one element of order p. It is proved that the group of units of the group algebra FG is a bounded Engel group if and only if FG is a bounded Engel algebra, and that this is the case if and only if G is nilpotent and has a normal subgroup H such that both the factor group G/H and the commutator subgroup H′ are finite p–groups.
Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type
Authors: Deng Dongguo , Yang Dachun 
Published: April 2009

AbstractLet (X, ρ, μ)d, θbe a space of homogeneous type withd< 0 and θ ∈ (0, 1],bbe a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0∈ (0, 1) be some constant depending ond, ∈ ands. The authors introduce the Besov spacebBspq(X) with a0> p ≧ ∞, and the Triebel-Lizorkin spacebFspq(X) with a0>p> ∞ and a0> q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov spaceb−1Bs(X) and the Triebel-Lizorkin spaceb−1Fspq(X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems,T btheorems, and the lifting property by introducing some new Riesz operators of these spaces.
Using cyclotomy to construct orthogonal designs
Authors: Cooper Joan , Wallis Jennifer Seberry 
Published: April 2009

An orthogonal design of order n and type (s1, s2) on the commuting variables x1, x2 is a matrix of order n with entries from {0, ± x1, ± x2} whose row vectors are formally orthogonal.This note uses cyclotomy to construct orthogonal designs and finds several infinite families of new designs.