bluuebunny/crossref_metadata_2025 huggingface dataset:
The persistence of universal formulae in free algebras
Authors: Gaglione Anthony M. , Spellman Dennis
Published: April 2009

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements:

(1) Fr(V) discriminates V. (1*) The Fs(V) satisfy the same universal sentences for all s≥r. Moreover, we have introduced the concept of strong discrimination in such a way that for a fixed finite cardinal r the following two statements are equivalent:

(2) Fr(V) strongly discriminates V. (2*) The Fs(V) satisfy the same universal formulas for all s ≥ r whenever elements of Fr(V) are substituted for the unquantified variables. On the surface (2) and (2*) appear to be stronger conditions than (1) and (1*). However, we have shown that for particular varieties (of groups) (2) and (2*) are no stronger than (1) and (1*).
Optimal results in local bifurcation theory
Authors: Esquinas J. , López-Gómez J.
Published: April 2009

Let us consider the abstract equation

(0.1) L (ɛ) u + F (ɛ,u) = 0,

where F (ɛ,u) = 0 (|u|2) for ɛ near zero. In this paper we define a multiplicity depending only on L (ɛ) allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (ɛ,u) such that the only solution to (0.1) near the origin are the trivial ones”.
Non-symmetric translation invariant Dirichlet forms on hypergroups
Authors: Bloom Walter R. , Heyer Herbert
Published: April 2009

In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The examples of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.
Asymptotic distribution of the number and size of parts in unequal partitions
Authors: Szekeres G.
Published: April 2009

An asymptotic formula is derived for the number of partitions of a large positive integernintorunequal positive integer parts and maximal summandk. The number of parts has a normal distribution about its maximum, the largest summand an extreme-value distribution. For unrestricted partitions the two distributions coincide and both are extreme-valued. The problem of joint distribution of unrestricted partitions withrparts and largest summandkremains unsolved.
On the ordered set of reflective subcategories
Authors: Kelly G. M.
Published: April 2009

Given a category A, we consider the (often large) set Ref A of its reflective (full, replete) subcategories, ordered by inclusion. It is known that, even when A is complete and cocomplete, wellpowered and cowellpowered, the intersection of two reflective subcategories need not be reflective. Supposing that A admits (i) small limits and (ii) arbitrary (even large) intersections of strong subobjects, we prove that an infimum ∧iCi in Ref A must necessarily be the intersection ∩iCi. Accordingly Ref A is not in general, even for good A, a complete lattice. We show, however, under the same conditions on A, that Ref A does admit small suprema ∨iCi, given by the closure in A of the union ∪iCi under the limits of type (i) and (ii) above.
Some aspects of relative injectivity
Authors: Feigelstock S. , Raphael R.
Published: April 2009

If H and M are right R-modules, H is M-injective if every R-homonorphism N → H, N a right R-submodule of M, can be extended to an R-homonorphism from M to H.

H is strongly M-injective if H is injective for inclusions whose cokernels are isomorphic to factor modules of M.

For the case of abelian groups H and M, one settles the questions “when is H M-injective” and “when is H strongly M-injective”. The latter can be characterized in terms of the vanishing of Ext. Results for general module categories are also given.
Minimality and stability of minimal hypersurfaces in IRn
Authors: Lin Fang Hua
Published: April 2009

In this paper we show that the hypercone over S2 × S4 is strictly area-minimizing in ℝ8. We also show the existence of smooth embedded stable hypersurfaces in ℝ8 which are not area-minimizing.
Operators on locally convex spaces of vector-valued continuous functions
Authors: López A. García
Published: April 2009

LetEandFbe locally convex spaces and letKbe a compact Hausdorff space.C(K,E) is the space of allE-valued continuous functions defined onK, endowed with the uniform topology.

Starting from the well-known fact that every linear continuous operatorTfromC(K,E) toFcan be represented by an integral with respect to an operator-valued measure, we study, in this paper, some relationships between these operators and the properties of their representing measures. We give special treatment to the unconditionally converging operators.

As a consequence we characterise the spacesEfor which an operatorTdefined onC(K,E) is unconditionally converging if and only if (Tfn) tends to zero for every bounded and converging pointwise to zero sequence (fn) inC(K,E).
Forced oscillations of solutions of parabolic equations
Authors: Yoshida Norio
Published: April 2009

Parabolic equations with forcing terms are studied and sufficient conditions are given that all solutions of boundary value problems are oscillatory in a cylindrical domain.
On cyclic group actions of even order on the three dimensional torus
Authors: Natsheh M.A.
Published: April 2009

In this paper, we prove that if h is a generator of a Z2n, action on S1 × S1 × S1, and Fix(hn) consists of two disjoint tori, one torus, four simple closed curves, or two simple closed curves, then h is equivalent to the obvious actions.
Monochromatic triangles in three colours
Authors: Sane S.S. , Wallis W.D.
Published: April 2009

Suppose the edges of the complete graph on 17 vertices are coloured in three colours. It is shown that at least five monochromatic triangles must aris.
Tolerances and Commutators on lattices
Authors: Schweigert Dietmar
Published: April 2009

The commutator has the following order theoretic properties: [α, β] ≦ α ∧ β, [α, β] = [β α],[α1∨ α2,β] = [α1, β] ∨ [α2, β] for congruences α, β ∈ ConAof an algebraAin a congruence modular variety generalising the original concept in group theory. A tolerance of a latticeLis a reflexive and symmetric sublattice ofL2. We show that to every commutator [ , ] of ConAcorresponds a ∧-subsemilattice of the lattice of tolerances of ConA. It can be shown thatAin a congruence modular variety is nilpotent if |conA| > 2 and ConAis simple.
V-Modules with krull dimension
Authors: Yousif Mohamed F.
Published: April 2009

Boyle and Goodearl proved that if R is a left V-ring then R has left Krull dimension if and only if R is left Neotherian. In this paper we extend this result to arbitrary V-modules.
The cardinality of the set of left invariant means on topological semigroups
Authors: Dzinotyiweyi Heneri A.M.
Published: April 2009

For a very large class of topological semigroups, we establish lower and upper bounds for the cardinality of the set of left invariant means on the space of left uniformly continuous functions. In certain cases we show that such a cardinality is exactly , where b is the smallest cardinality of the covering of the underlying topological semigroup by compact sets.
Modular group acting on real quadratic fields
Authors: Mushtaq Q.
Published: April 2009

Coset diagrams for the orbit of the modular group G = 〈x, y: x2 = y3 = 1〉 acting on real quadratic fields give some interesting information. By using these coset diagrams, we show that for a fixed value of n, a non-square positive integer, there are only a finite number of real quadratic irrational numbers of the form , where θ and its algebraic conjugate have different signs, and that part of the coset diagram containing such numbers forms a single circuit (closed path) and it is the only circuit in the orbit of θ.
Jordan derivations on prime rings
Authors: Brešar M. , Vukman J.
Published: April 2009

The purpose of this paper is to present a brief proof of the well known result of Herstein which states that any Jordan derivation on a prime ring with characteristic not two is a derivation.
On safety and rivals in power-structures
Authors: Miller John Boris
Published: April 2009

It is shown that every minimal power-structure other than the singleton power-structure has at least two contenders; that is, any contender has at least one rival. The safe core of a power-structure is empty if and only if the power-structure is minimal.
Barrelled spaces and dense vector subspaces
Authors: Robertson W.J. , Saxon S.A. , Robertson A.P.
Published: April 2009

This note presents a structure theorem for locally convex barrelled spaces. It is shown that, corresponding to any Hamel basis, there is a natural splitting of a barrelled space into a topological sum of two vector subspaces, one with its strongest locally convex topology. This yields a simple proof that a barrelled space has a dense infinite-codimensional vector subspace, provided that it does not have its strongest locally convex topology. Some further results and examples discuss the size of the codimension of a dense vector subspace.
An inversion theorem for set-valued maps
Authors: Aze D.
Published: April 2009

The aim of this paper is to give an inversion theorem for set-valued maps involving both some known results for functions and set-valued maps. To do this we introduce a notion of strict differentiability for set-valued maps and we use a Newton like method assuming the derivative to be surjective. Moreover we prove the pseudo-Lipschitz regularity of the inverse.
On the structure of a real crossed group algebra
Authors: Buzási K.
Published: April 2009

The main result of this paper is that there exist non-principal left ideals in a certain twisted group algebraAof the infinite dihedral group ≤a, b|b−1ab=a−1,b2= 1 ≥ over the field R of real numbers: namely in theAdefined byb−lab = a−1, b2= −1, and λa=aλ, λb=bλ for all real λ.

The motivation comes from the study (in a series of papers by Berman and the author) of finitely generated torsion-free RG-modules for groupsGwhich have an infinite cyclic subgroup of finite index. In a sense, this amounts to studying modules over (full matrix algebras over) a finite set of R-algebras [namely, for the groups in question, these algebras take on the role played by R, C and H (the real quaternions) in the theory of real representations of finite groups]. For all but two algebras in that finite set, satisfying results have been obtained by exploiting the fact that each of them is either a ring with zero divisors or a principal left ideal ring. The other two are known to have no zero divisors. One of them is the presentA. The point of the main result is that new ideas will be needed for understandingA-modules.

A number of subsidiary results are concerned with convenient generating sets for left ideals inA.
Weak compactness in spaces of vector valued measures
Authors: Wiid F.G.J.
Published: April 2009

We characterise relative weak compactness in σBM(∑, X), the space of sigma-additive, X-valued measures of bounded variation, where X is a Banach space.
Rings isomorphic to their unbounded left ideals
Authors: Feigelstock Shalom
Published: April 2009

A complete description is given of rings isomorphic to their unbounded left (right) ideals. The same problem for 2-sided ideals remains open.
Finite coverings by 2-engel groups
Authors: Kappe Luise-Charlotte
Published: April 2009

Bear's characterisation of central-by-finite groups as groups possessing a finite covering by abelian subgroups if the starting point for this invertigation. We characterise groups with a finite covering by 2-Engel subgroups as groups for which the subgroup of right 2-Engel elements has finite index; and the groups having a finite covering by normal 2-Engel subgroups are exactly the 3-Engel groups among those having a finite covering by 2-Engel subgroups. The second centre of a group having a finite covering by class two subgroups does not necessarily have finite index. However, a group has a finite covering by subgroups in a variety containing all cyclic groups if the margin of thes variety in the group has finite index.
Recurrence in Lipschitz stable flows
Authors: Lee Keon-Hee
Published: April 2009

The purpose of this paper is to get some necessary conditions for a Poisson stable flow to be recurrent and to analyse the bilateral versions of positive and negative Lipschitz stability. Moreover, a characterisation of recurrent orbits is obtained in a certain flow.
A topological zero-one law for open continuous maps
Authors: Barone E. , Bhaskara Rao K.P.S.
Published: April 2009

We obtain a topological zero-one law for sets with the Baire property which are invariant under a semigroup of open continuous maps acting on a topological space.
On commutativity of associative rings
Authors: Ashraf Mohd. , Quadri Murtaza A.
Published: April 2009

In this paper we prove that if R is a ring with unity satisfying [xy − xn, ym = 0, for all x, y ∈ R and fixed integers m ≥ 1, n ≥ 1, then R is commutative.
Control point insertion for B-spline curves
Authors: Gonska Heinz H. , Röth Andreas
Published: April 2009

Inserting new knots into B-spline curves is a well-known technique in CAGD to gain extra flexibility for design purposes. However, from a user's point of view, the insertion of knots is somewhat unsatisfactory since the newly generated control points sometimes show up in unexpected locations. The aim of this note is to show that these problems can be circumvented by inserting the control vertices directly, thus also providing a more natural user interface.
Binomial permutations of finite fields
Authors: Chou Wun-Seng
Published: April 2009

We discuss permutation properties of a specific kind of binomials over finite fields. As a result, we complete Cavior's classification of binomial octic permutation polynomials over Fq with q odd.
A topological characterisation of finite dimensionality ofC* -algebras
Authors: Tang Wai-Shing
Published: April 2009

AC*-algebraAis finite-dimensional if and only if the coneis closed inM2⊗A.
Characterisation of functional properties by nets
Authors: Borges Carlos R.
Published: April 2009

We characterise continuous closed (perfect, open) functions in terms of nets. This enables us to improve some significant results, with much simpler proofs.
Reflections and symmetries in compact symmetric spaces
Authors: Chen Bang-Yen , Vanhecke Lieven
Published: April 2009

Point symmetries and reflections are two important transformations on a Riemannian manifold. In this article we study the interactions between point symmetries and reflections in a compact symmetric space when the reflections are global isometries.
On the monotone simultaneous approximation on [0, 1]
Authors: Sahab Salem M.A.
Published: April 2009

Let Ω denote the closed interval [0, 1] and let bA denote the set of all bounded, approximately continuous functions on Ω. Let Q denote the Banach space (sup norm) of quasi-continuous functions on Ω. Let M denote the closed convex cone in Q comprised of non-decreasing functions. Let hp, 1 < p < ∞, denote the best Lp-simultaneaous approximation to the bounded measurable functions f and g by elements of M. It is shown that if f and g are elements of Q, then hp converges unifornily to a best L1-simultaneous approximation of f and g. We also show that if f and g are in bA, then hp is continuous.
Meromorphic Lipschitz functions
Authors: Yamashita Shinji
Published: April 2009

Let f be a function meromorphic in D = {|z| < 1} and let X be the chordal distance on the Riemann sphere. Then f satisfies the Lipschitz condition

in D if and only if |f′(z)|/(1 + |f(z)|2) = O((1 – |z|)α−1) and |z| → 1.
The dirichlet problem for degenerate elliptic 2-dimensional monge-ampère equation: corrigendum
Authors: Amano Kazuo
Published: April 2009

The author would like to make several minor amendments to [1].
Hypertypes of torsion-free abelian groups of finite rank
Authors: Goeters H.P. , Vinsonhaler C. , Wickless W.
Published: April 2009

Let G be a torsion-free abelian group of finite rank n and let F be a full free subgroup of G. Then G/F is isomorphic to T1 ⊕ … ⊕ Tn, where T1 ⊆ T2 ⊆ … ⊆ Tn ⊆ ℚ/ℤ. It is well known that type T1 = inner type G and type Tn = outer type G. In this note we give two characterisations of type Ti for 1 < i < n.
James quasi reflexive space has the fixed point property
Authors: Khamsi M.A.
Published: April 2009

We prove that the classical sequence James space has the fixed point property. This gives an example of Banach space with a non-unconditional basis where the Maurey-Lin's method applies.
A-bilinear forms and generalised A-quadratic forms on unitary left A-modules
Authors: Lin C.-S.
Published: April 2009

In this paper we shall define a generalised A-quadratic form and prove that in some way this form and an A-bilinear form are equivalent to each other. Our result characterises that of Vukman in the sense that we use any n vectors for a fixed n ≥ 2, instead of any two vectors. Consequently, a new generalisation of an inner product space among vector spaces is obtained. This also leads to a new relationship between a 2-inner product space and a 2-normed space.
A distance function property implying differentiability
Authors: Giles J.R.
Published: April 2009

In a real normed linear spaceX, properties of a non-empty closed setKare closely related to those of the distance functiondwhich it generates. IfXhas a uniformly Gâteaux (uniformly Fréchet) differentiable norm, thendis Gâteaux (Fréchet) differentiable atx∈X/Kif there exists ansuch that

and is Géteaux (Fréchet) differentiable onX/Kif there exists a setP+(K) dense inX/Kwhere such a limit is approached uniformly for allx∈P+(K). WhenXis complete this last property implies thatKis convex.
The invariants of projective linear group actions
Authors: Chu Huah , Kang Ming-Chang , Tan Eng-Tjioe
Published: April 2009

Let Fq be the field with q elements and let G = PGLn(Fq) or PSLn(Fq) act on Fq(x1,…,xn−1), the rational function field of n − 1 variables. Then Fq(x1,…,xn−1)G is purely transcendental over Fq. In fact, a set of n − 1 generators of Fq(x1,…xn−1)G, over Fq is exhibited. The case n = 2 is treated by direct computation.
Starlike functions with a fixed coefficient
Authors: Anh V.V.
Published: April 2009

This paper establishes several conditions on the parametersA, B, bfor the exact radius of convexity of the class

where

k=1,2,3,…, −1 ≤B≤A≤ 1, 0 ≤b≤ 1.
On the semigroup of an ordinary multiple point
Authors: Kulkarni Devadatta M.
Published: April 2009

In this paper we define the semigroup of an ordinary multiple point of an analytic plane curve f. This semigroup on tuples of integers is completely characterised in terms of the order of f, that is the number of distinct tangent directions to f at that point.
Function spaces and the Mosco topology
Authors: Beer Gerald , Tamaki Robert
Published: April 2009

Let X and Y be Banach spaces and let C(X, Y) be the functions from X to Y continuous with respect to the weak topology on X and the strong topology on Y. By the Mosco topology τM on C(X, Y) we mean the supremum of the Fell topologies determined by the weak and strong topologies on X × Y, where functions are identified with their graphs. The function space is Hausdorff if and only if both X and Y are reflexive. Moreover, τM coincides with the stronger compact-open topology on C(X, Y) provided X is reflexive and Y is finite dimensional. We also show convergence in either sense is properly weaker than continuous convergence, even for continuous linear functionals, whenever X is infinite dimensional. For real-valued weakly continuous functions, τM is the supremum of the Mosco epitopology and the Mosco hypotopology if and only if X is reflexive.
Cauchy representation of distributions and applications to probability
Authors: Chaudhry M. Aslam
Published: April 2009

The Cauchy representation is not valid for every Schwartz distribution f ∈ (D(R))′ because (t – x)−l ∉ D(R). Since for all z ∈ {z: Im z ≠ 0} the kernel (t – z)−l belongs to (R) (1 > p > ∞), the Cauchy representation of the distributions in ((R))′ seems possible.

In this paper, we prove this fact. It is also proved that every probability density defines a generalised function on the space (R)(1 < p < ∞), of test functions. Applications of these results in probability theory are discussed.
A fixed point theorem in H-space and related results
Authors: Tarafdar E.
Published: April 2009

The equivalence of a fixed point theorem and the Fan-Knaster-Kuratowski-Mazurkiewicz theorem in H-space has been established. The fixed point theorem is then applied to obtain a theorem on sets with H-convex sections, and also results on minimax inequalities.
Single laws for two subvarieties of squags
Authors: Donovan Diane
Published: April 2009

We give single laws for two subvarieties of Steiner quasigroups (squags); the subvariety of squags whose underlying triple systems are the affine spaces over GF[3], and the subvariety of squags whose underlying triple systems are the affine triple systems.
Geometric coverings of groups and their directions
Authors: Brandl Rolf
Published: April 2009

Let a group G be covered by finitely many disjoint cosets of subgroups Gi. We study conditions which imply that the subgroups Gi are conjugate in G.
On the isometry of surfaces preserving the lines of curvature
Authors: Yang Wenmao
Published: April 2009

In this paper we study the isometric deformations of surfaces in E3, which preserve the lines of curvature. We call a surface M and LC-surface if it admits a non-trivial deformation of this type. We distinguish three types of LC-surfaces, and obtain some new results about these three types of surfaces.
Translation invariant linear functionals on segal algebras
Authors: Takahashi Yuji
Published: April 2009

Let S(G) be a Segal algebra on an infinite compact Abelian group G. We study the existence of many discontinuous translation invariant linear functionals on S(G). It is shown that if G/CG contains no finitely generated dense subgroups, then the dimension of the linear space of all translation invariant linear functionals on S(G) is greater than or equal to 2C and there exist 2C discontinuous translation invariant linear functionals on S(G), where c and CG denote the cardinal number of the continuum and the connected component of the identity in G, respectively.
Orbital decompositions of representations of non-simply connected nilpotent groups
Authors: Lipsman Ronald L.
Published: April 2009

An orbital integral formula is proven for the direct integral decomposition of an induced representation of a connected nilpotent Lie group. Previous work required simple connectivity. An explicit description of the spectral measure and spectral multiplicity function is derived in terms of orbital parameters. It is also proven that connected (but not necessarily simply connected) exponential solvable symmetric spaces are multiplicity free. Finally, the qualitative properties of the spectral multiplicity function are examined via several illuminating examples.
A class of null sets associated with convex functions on Banach spaces
Authors: Rainwater John
Published: April 2009

A generalisation of the notion of “sets of measure zero” for arbitrary Banach spaces is defined so that continuous convex functions are automatically Gateaux differentiable “almost everywhere”. It is then shown that this class of sets satisfies all the properties tht one expects of sets of measure zero. Moreover (in a certain large class of Banach spaces, at least) nonempty open sets are not of “measure zero”.
Average distance constants for polygons in spaces with non-positive curvature
Authors: Kulshestha Devendra K. , Sag Tom W. , Yang Lu
Published: April 2009

In this paper we show that the average distance constant of a general polygon which is a subset of an M-space with non-positive curvature can be expressed as the extreme value of either of two nonlinear programs and discuss the practical application of one of these nonlinear programs for the determination of the average distance constant for a polygon in general, and in particular for a planar triangle.
A distance for similarity classes of submanifolds of a Euclidean space
Authors: Frosini Patrizio
Published: April 2009

A distance is defined on the quotient of the set of submanifolds of a Euclidean space, with respect to similarity. It is then related to a previously defined function which captures the metric behaviour of paths.
On products of Sobolev-Orlicz spaces
Authors: Appell J. , Hardy G.
Published: April 2009

We give conditions under which pointwise multiplication is a continuous bounded operation on kth order Sobolev-Orlicz spaces. This result is used to derive a sufficient condition under which the superposition operator is a continuous bounded operator on these spaces.
Some properties of the Hausdorff distance in metric spaces
Authors: Banaś Józef , Martinón Antonio
Published: April 2009

Some properties of the Hausdorff distance in complete metric spaces are discussed. Results obtained in this paper explain ideas used in the theory of measures of noncompactness.
Variational and numerical methods for symmetric matrix pencils
Authors: Lancaster Peter , Ye Qiang
Published: April 2009

A review is presented of some recent advances in variational and numerical methods for symmetric matrix pencils λA – B in which A is nonsingular, A and B are hermitian, but neither is definite. The topics covered include minimax and maximin characterisations of eigenvalues, perturbation by semidefinite matrices and interlacing properties of real eigenvalues, Rayleigh quotient algorithms and their convergence properties, Rayleigh-Ritz methods employing Krylov subspaces, and a generalised Lanczos algorithm.
Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
Authors: Schu J.
Published: April 2009

Let T be an asymptotically nonexpansive self-mapping of a closed bounded and convex subset of a uniformly convex Banach space which satisfies Opial's condition. It is shown that, under certain assumptions, the sequence given by xn+1 = αnTn(xn) + (1 - αn)xn converges weakly to some fixed point of T. In arbitrary uniformly convex Banach spaces similar results are obtained concerning the strong convergence of (xn) to a fixed point of T, provided T possesses a compact iterate or satisfies a Frum-Ketkov condition of the fourth kind.
Lefschetz numbers and unitary groups
Authors: Lai K.F.
Published: April 2009

We give a formula for the Euler-Poincare characteristic of the fixed point set of the Cartan involution on the set of integral equivalence classes of integral unimodular hermitian forms, in terms of a product of special values of Riemann zeta functions and Dirichlet L-functions. This is done via reduction by Galois cohomology to a volume computation using the Tamagawa measure on the unitary groups.
A note on universally zero-divisor rings
Authors: Visweswaran S.
Published: April 2009

In this note we consider commutative rings with identity over which every unitary module is a zero-divisor module. We call such rings Universally Zero-divisor (UZD) rings. We show (1) a Noetherian ring R is a UZD if and only if R is semilocal and the Krull dimension of R is at most one, (2) a Prüfer domain R is a UZD if and only if R has only a finite number of maximal ideals, and (3) if a ring R has Noetherian spectrum and descending chain condition on prime ideals then R is a UZD if and only if Spec (R) is a finite set. The question of ascent and descent of the property of a ring being a UZD with respect to integral extension of rings has also been answered.
Automorphisms of directed triple systems
Authors: Colbourn Charles J.
Published: April 2009

The obvious necessary conditions for a triple system of index two having a given automorphism group to underly a directed triple system having the same group are shown to be sufficient. An efficient algorithm for directing the triple system in a way that preserves its group is given. Applications to the existence of directed triple systems with various automorphisms are outlined.
A property of subgroups of free groups
Authors: Rosenberger Gerhard
Published: April 2009

Let F be a free group on a1,…, ap (p ≥ 1), and X a finitely generated subgroup in F. Suppose either that X contains some non-trivial power of , or that p is even and X contains some nontrivial power of [a1, a2]…[ap−1, ap]. We discuss some properties of X which we can derive from this assumption.
On weak spectral synthesis
Authors: Parthasarathy K. , Varma Sujatha
Published: April 2009

Weak spectral synthesis fails in the group algebra and the generalised group algebra of any non compact locally compact abelian group and also in the Fourier algebra of any infinite compact Lie group.
Some inequalities on quasi-subordinate functions
Authors: Ren Fuyao , Owa Shigeyoshi , Fukui Seiichi
Published: April 2009

The object of the present paper is to derive some interesting coefficient estimates for quasi-subordinate functions. Furthermore, a conjecture for quasi-subordinate functions is shown.
On the generators of S-unit groups in algebraic number fields
Authors: Brindza B.
Published: April 2009

Given a finitely generated multiplicative subgroup Us in a number field, we employ a simple argument from the geometry of numbers and an inequality on multiplicative dependence in number fields to obtain a minimal set of generators consisting of elements of relatively small height.
J-nonexpansive mappings in uniform spaces and applications
Authors: Angelov Vasil G.
Published: April 2009

The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.
Signal spaces—an axiomatic approach to space-time
Authors: Szekeres Peter
Published: April 2009

An axiomatic approach to relativity theory is proposed which is based entirely on a single reflexive relation called signalling. This generalises and simplifies earlier schemes of Kronheimer and Penrose and of Carter which are based on causality relations. Many of the features of space-times, such as photon paths and topology, have their counterparts in general signal spaces.
Volume inequalities using sections of convex sets
Authors: Scott Paul R.
Published: April 2009

We give a general result for the lower bound of the volume of a compact convex set K in Ed in terms of the volumes of orthogonal sections of K.
Separable measures and the Dunford-Pettis property
Authors: Aguayo José , Sánchez José
Published: April 2009

Let X be a complete regular space. We denote by Cb(X) the Banach space of all real-valued bounded continuous functions on X endowed with the supremumnorm.

In this paper we give a characterisation of weakly compact operators defined from Cb(X) into a Banach space E which are β∞-continuous, where β∞ is a locally convex topology on Cb(X) introduced by Wheeler. We also prove that (Cb(X), β∞) has the strict Dunford-Pettis property and, if X is a σ-compact space, (Cb(X), β∞), has the Dunford-Pettis property.
Generalised Helly and Radon numbers
Authors: Kolodziejczyk Krzysztof
Published: April 2009

At the Second Oklahoma Conference on Convexity and Related Combinatorial Geometry (1980) G.Sierksma posed several problems dealing with the generalised Helly and Radon numbers of a convexity space. The aim of this note is to give answers to and comment on some of Sierksma's questions.
On the construction problem for single-exit Markov chains
Authors: Pollett P.K.
Published: April 2009

I shall consider the following problem: given a stable, conservative, single-exit q-matrix, Q, over an irreducible state-space S and a μ-subinvariant measure, m, for Q, determine all Q-processes for which m is a μ-invariant measure. I shall provide necessary and sufficient conditions for the existence and uniqueness of such a process.
A note on shortly connected inverse semigroups
Authors: Goberstein S.M.
Published: April 2009

Shortly connected and shortly linked inverse semigroups arise in the study of inverse semigroups determined by the lattices of inverse subsemigroups and by the partial automorphism semigroups. It has been shown that every shortly linked inverse semigroup is shortly connected, but the question of whether the converse is true has not been addressed. Here we construct two examples of combinatorial shortly connected inverse semigroups which are not shortly linked. One of them is completely semisimple while the other is not.
Bounds on the fitting length of finite soluble groups with supersoluble Sylow normalisers
Authors: Bryce R.A. , Fedri V. , Serena L.
Published: April 2009

We prove that, in a finite soluble group, all of whose Sylow normalisers are super-soluble, the Fitting length is at most 2m+ 2, wherepmis the highest power of the smallest primepdividing |G/Gs| hereGsis the supersoluble residual ofG. The bound 2m+ 2 is best possible. However under certain structural constraints onG/GS, typical of the small examples one makes by way of experimentation, the bound is sharply reduced. More precisely letpbe the smallest, andrthe largest, prime dividing the order of a groupGin the class under consideration. If a Sylowp–subgroup ofG/GSacts faithfully on everyr-chief factor ofG/GS, thenGhas Fitting length at most 3.
The patterns of the isonemal two-colour two-way two-fold fabrics
Authors: Hoskins J.A. , Thomas R.S.D.
Published: April 2009

This paper connects the literature on weaving with that on coloured tilings of the plane. It sets the many published designs of woven cloth in the context of (2, 2, 2)-fabrics, that is, those in which strands of two colours run in two perpendicular directions to cover the plane doubly almost everywhere. At the same time, it connects with the interesting topological question of when a weave hangs together. The main result is that isonemal (2, 2, 2)-fabrics can be made from isonemal un-coloured fabrics either by colouring them in the conventional way (black warp, white weft), or by colouring warp and weft in thin or thick stripes to give the visual appearance of conventionally coloured isonemal pre-fabrics that fall apart, and in no other way. Such visual appearance can always be realised by the striping of an isonemal fabric, but not uniquely. A figure showing the fifty isonemal (2, 2, 2)-fabrics of exact orders up to sixteen coloured by striping is included.
Commutativity of rings satisfying certain polynomial identities
Authors: Abu-Khuzam Hazar , Bell Howard , Yaqub Adil
Published: April 2009

It is shown that an n-torsion-free ring R with identity such that, for all x, y in R, xnyn = ynyn and (xy)n+1 − xn+1yn+1 is central, must be commutative. It is also shown that a periodic n–torsion-free ring (not necessarily with identity) for which (xy)n − (yx)n is always in the centre is commutative provided that the nilpotents of R form a commutative set. Further, examples are given which show that all the hypotheses of both theorems are essential.
Equivalence classes of inverse orthogonal and unit Hadamard matrices
Authors: Craigen R.
Published: April 2009

In 1867, Sylvester considered n × n matrices, (aij), with nonzero complex-valued entries, which satisfy (aij)(aij−1) = nI Such a matrix he called inverse orthogonal. If an inverse orthogonal matrix has all entries on the unit circle, it is a unit Hadamard matrix, and we have orthogonality in the usual sense. Any two inverse orthogonal (respectively, unit Hadamard) matrices are equivalent if one can be transformed into the other by a series of operations involving permutation of the rows and columns and multiplication of all the entries in any given row or column by a complex number (respectively a number on the unit circle). He stated without proof that there is exactly one equivalence class of inverse orthogonal matrices (and hence also of unit Hadamard matrices) in prime orders and that in general the number of equivalence classes is equal to the number of distinct factorisations of the order. In 1893 Hadamard showed this assertion to be false in the case of unit Hadamard matrices of non-prime order. We give the correct number of equivalence classes for each non-prime order, and orders ≤ 3, giving a complete, irredundant set of class representatives in each order ≤ 4 for both types of matrices.
Representation of type A monoids
Authors: Asibong-Ibe U.
Published: April 2009

A semigroup T consisting of one-one mapping between certain principal left ideals in a type A semigroup S is constructed. T is shown to be a type A semigroup. A representation of S by T is then obtained which is analogous to Vagner-Preston's results on inverse semigroups.
Jordan mappings of semiprime rings II
Authors: Brešar Matej
Published: April 2009

We describe Jordan homomorphisms and Jordan triple homomorphisms onto 2-torsion free semiprime rings in which the annihilator of any ideal is a direct summand.
A note on strong Markuševič of decompositions of Banach spaces
Authors: Jain P.K. , Sinha D.P.
Published: April 2009

The spacel∞ is known to have no Schauder decomposition. It is proved here thatl∞ does not even possess any strong Markuševič decomposition.
The extreme points of a class of functions with positive real part
Authors: Samaris N.
Published: April 2009

Let P1 be the class of holomorphic functions on the unit disc U = {z: |z| < 1} for which f(0) = 1 and Re f > 0. Let also Pn be the corresponding class on the unit disc Un. The inequality |ak| ≤ 2 is known for the Taylor coefficients in the class P1. In this paper, it is generalised for the class Pn. If ρ = (ρ1, ρ2, …, ρn), with ρ1, ρ2, …, ρn nonegative integers whose greatest common divisor is equal to 1, we describe the form of the functions f ∈ Pn under the restriction |aρ| = 2. Under the same restriction, we give conditions for a function to be an extreme point of the class Pn.
Periodic Boehmians II
Authors: Nemzer Dennis
Published: April 2009

A space of periodic generalised functions, called boehmians, is investigated. The space of boehmians contains all periodic distributions. It is known that not every hyperfunction is a boehmian. We show that the converse is also true. We present some theorems which give sufficient conditions for a sequence of complex numbers to be the Fourier coefficients of a boehmian. Sufficient conditions (in terms of the Fourier coefficients) are obtained for a sequence of boehmians to converge. As an application, a Dirichlet problem is discussed.
Finite algebras that generate an injectively complete modular variety
Authors: Kearnes Keith A.
Published: April 2009

We extend Kollár's result on finitely generated, injectively complete congruence distributive varieties to the congruence modular setting. By doing so we show that, given any finite algebra A of finite type, there is an algorithm to decide whether V(A) is an injectively complete, congruence modular variety.
Local integrability of CR-hypersurfaces
Authors: Kwon Kil H. , Song Byeong C.
Published: April 2009

By characterising CR-hypersurfaces of dimensionmhavingmstrongly independent CR-functions, we find the necessary condition for a CR-hypersurface to be locally integrable and show that the same condition is also sufficient if the CR-hypersurface is strongly pseudoconvex and has m strongly independent CR-functions.
Non-isomorphic 2-perfect 6-cycle systems of order 13
Authors: Gower Rebecca A.H.
Published: April 2009

Running a computer search for new, cyclic, 2-perfect 6-cycle systems of order 13 and constructing the quasigroups which arise from such systems enabled the author to establish that there are at most two such non-isomorphic systems. Then by using two-variable laws of the quasigroups it is shown that there are exactly two non-isomorphic 2-perfect 6-cycle systems of order 13 which are cyclic.
The primes of S(R)
Authors: Magill K.D.
Published: April 2009

S(R) is the semigroup, under composition, of all continuous selfmaps of the space R of real numbers. We show that the primes of S(R) are precisely those continuous selfmaps which are surjective and have exactly two local extrema. Additional results are then derived from this. For example, if f is any surjective continuous selfmap of R with n ≥ 2 local extrema, then there exist homeomorphisms from R onto R such that m ≤ 1 + n/2 and

where P is the polynomial defined by P(x) = x3 − x. It follows from this that the homeomorphisms together with the polynomial P generate a dense subsemigroup of S(R) where the topology on S(R) is the compact-open topology.
Small squaring and cubing properties for finite groups
Authors: Berkovich Ya. G. , Freiman G.A. , Praeger Cheryl E.
Published: April 2009

A group G is said to have the small squaring property on k-sets if |K2| < k2 for all k-element subsets K of G, and is said to have the small cubing property on k-sets if |K3| < k3 for all k-element subsets K. It is shown that a finite nonabelian group with the small squaring property on 3-sets is either a 2-group or is of the form TP with T a normal abelian odd order subgroup and P a nontrivial 2-group such that Q = Cp(T) has index 2 in P and P inverts T. Moreover either P is abelian and Q is elementary abelian, or Q is abelian and each element of P − Q inverts Q. Conversely each group of the form TP as above has the small squaring property on 3-sets. As for the nonabelian 2-groups with the small squaring property on 3-sets, those of exponent greater then 4 are classified and the examples are similar to dihedral or generalised quaternion groups. The remaining classification problem of exponent 4 nonabelian examples is not complete, but these examples are shown to have derived length 2, centre of exponent at most 4, and derived quotient of exponent at most 4. Further it is shown that a nonabelian group G satisfies |K2| < 7 for all 3-element subsets K if and only if G = S3. Also groups with the small cubing property on 2-sets are investigated.
A result concerning additive maps on the set of quaternions and an application
Authors: Kobal Damjan , Šemrl Peter
Published: April 2009

We determine all additiveF,G: ℍ → ℝ and multiplicativeM: H → ℝ satisfying the functional equationF(λ) +M(λ)G(λ−1) = 0. As an application we generalise Kurepa's solution of one of Halperin's problem concerning quadratic functionals.
Volume comparison of Bishop-Gromov type
Authors: Lee Sungyun
Published: April 2009

Bishop-Gromov type comparison theorems for the volume of a tube about a sub-manifold of a complete Riemannian manifold whose Ricci curvature is bounded from below are proved. The Kähler analogue is also proved.
Steinhardt's inequality in the Minkowski plane
Authors: Ghandehari Mostafa
Published: April 2009

In a Minkowski plane with unit circle E, the product of the positive circumference of a plane convex body K and that of its polar dual is greater than or equal to the square of the Euclidean length of the polar dual of E. Equality holds if and only if K is a Euclidean unit circle.
Modified Hermite polynomials in the spectral approximation for boundary layer problems
Authors: Adžić Nevenka
Published: April 2009

The solution of the linear boundary layer problem is presented as a sum of the reduced solution and the layer function, which is approximated by a truncated orthogonal series. The layer subinterval is determined through the numerical layer length, which depends on the perturbation parameter and the degree of the spectral approximation. Modified Hermite polynomials are used as an orthogonal basis. Systematic methods are presented to obtain the recurrence relations for the coefficients in modified Hermite series solution of linear differential equations with polynomial coefficients. The upper bound for the error function is constructed and the numerical example is included.
Oscillatory properties of solutions of certain elliptic equations
Authors: Yoshida Norio
Published: April 2009

Certain elliptic equations of higher order are studied and a sufficient condition is given that every solution is oscillatory in an exterior domain. The principal tool is an averaging technique which enables one to reduce the n–dimensional problem to a one-dimensional problem.
Construction of some new Hadamard matrices
Authors: Đoković Dragomir Ž.
Published: April 2009

We prove that there exist skew type Hadamard matrices of order 4n for n = 67, 113, 127, 157, 163, 181 and 241 which have not been constructed so far. In particular there exists a Hadamard matrix of order 4 · 163, which was unknown until now. We mention that very recently we have constructed skew type Hadamard matrices of orders 4n for n = 37 and 43.
Perfect pyramids
Authors: Buchholz Ralph Heiner
Published: April 2009

This paper discusses rational edged tetrahedra, in 3, 4 and n dimensions, with rational volume. The main results are (i) a proof of the existence of infinitely many tetrahedra with rational edge-lengths, face-areas and volume and (ii) a proof that there exist dimensions for which all regular hypertetrahedra with rational edge-lengths have rational hypervolume.
Twists of matrix algebras and some subgroups of Brauer groups
Authors: Chi Wenchen
Published: April 2009

We consider twists of matrix algebras by some continuous characters. There are some subgroups of Brauer groups arising from these twists. Some results regarding these subgroups are proved.
Simultaneous monotone approximation in low-order mean
Authors: Huotari Robert , Sahab Salem
Published: April 2009

Suppose that f, g ∈ L∞[0,1] have discontinuities of the first kind only. Using the measure, max{‖f − h‖p, ‖g − h‖p}, of simultaneous Lp approximation, we show that the best simultaneous approximations, hp, to f and g by nondecreasing functions converge uniformly as p → 1. Part of the proof involves a discussion of discrete simultaneous approximation in a general context. We discuss the inheritance of properties of f and g by hp, and of hp by h1.
A new Banach space without the Kadec-Klee property
Authors: Alexandrov G.A. , Babev V.D.
Published: April 2009

An example of a Banach space is given which does not contain isomorphically l1 and does not admit the Kadec-Klee property.
On a homotopy invariant for simplexes and its application
Authors: Ha Chung-Wei
Published: April 2009

Based on a congruence relation of K. Fan in the integer labelling of pseudomanifolds, we follow an idea of H. Sies and define a mod 2 homotopy invariant d for a class of continuous functions defined on an n-simplex into ℝn+1 ＼ {0} satisfying a certain boundary condition. Using the homotopy invariance of d, generalised coincidence theorems are proved which unify and extend some existence theorems of K. Fan. Our results also contain Kakutani's fixed point theorem and a new covering property of simplexes of Shapley's type.
Characterisations of Galois extensions of prime cubed degree
Authors: Carter James E.
Published: April 2009

Let p be a prime number and let k be a field of characteristic not equal to p. Assuming k contains the appropriate roots of unity, we characterise the non-cyclic Galois extensions of k of degree p3. Concrete examples of such extensions are given for each possible case which can occur, up to isomorphism.
Topological separability and axioms of countability in GPO-spaces
Authors: Alcantud J.C.R.
Published: April 2009

In this paper we obtain characterisations of first and second countability and separability for GPO-spaces, a class of topological spaces that include LOTS and GO-spaces. Some additional results concerning the transmission of these properties to weaker/finer topologies are derived in this framework.