bluuebunny/crossref_metadata_2025 huggingface dataset:
On Diagrams of Vector Spaces
Authors: Brenner Sheila , Butler M. C. R.
Published: April 2009

We record here two further remarks about the systems, studied in [1] and [2], consisting of a vector space U and a set K of subspaces of U. In § 1, we show that such a system may be viewed as a module over a suitable artinian ring; the results of [1] and [2] thus serve to illustrate the complexity of structure of these modules. The main idea, a little wider than one introduced by Mitchell in Chapter IX of [3], is to view a diagram of vector spaces, with a small category as the scheme of the diagram, as a module over the ‘category ring’ of the category.
Spherical Modifications and the Strong Category of Manifolds
Authors: Mielke M. V.
Published: April 2009

Using the notion of spherical modification and results from Morse theory a general technique is described for constructing manifolds whose strong category is small (≦ 3) but whose homological structure is complex.
On Characteristic Morphisms: In Memoriam Thomas Macfarland Cherry
Authors: Neumann B. H.
Published: April 2009

This note is concerned with a translation of some concepts and results about characteristic subgroups of a group into the language of categories. As an example, consider strictly characteristic and hypercharacteristic subgroups of a group: the subgroup H of the group G is called strictly characteristic in G if it admits all ependomorphisms of G; that is all homomorphic mappings of G onto G; and H is called hypercharacteristic2 in G if it is the least normal subgroup with factor group isomorphic to G/H, that is if H is contained in every normal subgroup K of G with G/K ≅ G/H.
ℒ-Realcompactifications and Normal Bases
Authors: Alo R. A. , Shapiro H. L.
Published: April 2009

In a recent paper (see [2]), Orrin Frink introduced a method to provide Hausdorff compactifications for Tychonoff or completely regular T1 spaces X. His method utilized the notion of a normal base. A normal base ℒ for the closed sets of a space X is a base which is a disjunctive ring of sets, disjoint members of which may be separated by disjoint complements of members of ℒ.
Distributions associated with the factors of Wilks' Λ in discriminant analysis
Authors: Kshirsagar A. M.
Published: April 2009

Exact tests, based on factorization of Wilks' Λ were derived by Williams (1952, 1955) and Bartlett (1951), for testing the goodness of fit of a single hypothetical discriminant function, in the case of several groups. An analytical derivation of the distributions associated with these tests was given by the author (1964 a), after expressing the test statistics in canonical forms. Wilks' Λ to cover the case of s (s > 1) hypothetical discriminant functions. Radcliffe, in his paper, states that an analytical derivation of the distributions, as well as of the independence of the factors of Λ is desirable. This is done in the present paper, by expressing the test criteria in simpler forms and using matrix transformations in the multivariate Beta distribution (Kshirsager 1961). This is a straightforward extension of the author's paper (1964 a), which dealt with only one hypothetical discriminant function.
The enumeration of rooted trees by total height
Authors: Riordan John , Sloane N. J. A.
Published: April 2009

The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one of us (N.J.A.S.), where the enumeration of greatest interest is that of trees with all points distinctly labeled.
Stability of a pair of first order linear differential equations
Authors: Brace Alan , Daykin D. E.
Published: April 2009

Consider the simultaneous real differential equations , where the dot indicates differentiation with respect to time, and a, b, c, d are functions about which the only thing that we know is that they are uniformly bounded, .
The three kernels of a compact semiring
Authors: Pearson K. R.
Published: April 2009

A topological semiring is a system (S, +, ⋅) where S is a Hausdorff space, (S, +) and (S, ⋅) are topological semigroups (i.e., + and ⋅ are continuous associative binary operations on S) and the distributive laws , hold for all x, y, z in S. The operations + and ⋅ are called addition and multiplication respectively.
Compact Semirings Which are Multiplicatively 0-Simple
Authors: Pearson K. R.
Published: April 2009

A topological semiring is a system (S, +, ⋅) where (S, +) and (S, ⋅) are topological semigroups and the distributive laws , hold for all x, y, z in S; + and ⋅ are called addition and multiplication respectively.
Application of the Ritz method to non-standard eigenvalue problems
Authors: Andrew A. L.
Published: April 2009

There is an extensive literature on application of the Ritz method to eigenvalue problems of the type where L1, L2 are positive definite linear operators in a Hilbert space (see for example [1]). The classical theory concerns the case in which there exists a minimum (or maximum) eigenvalue, and subsequent eigenvalues can be located by a well-known mini-max principle [2; p. 405]. This paper considers the possibility of application of the Ritz method to eigenvalue problems of the type (1) where the linear operators L1L2 are not necessarily positive definite and a minimum (or maximum) eigenvalue may not exist. The special cases considered may be written with the eigenvalue occurring in a non-linear manner.
Decomposition of representation algebras
Authors: Wallis W. D.
Published: April 2009

Throughout this paper g is a finite group and f is a complete local principal ideal domain of characteristic p where p divides |g|. The notations of [5] are adopted; moreover we shall denote the isomorphism-class of an f g-representation module ℳ by M, the class of ℳx by Mx and the class of ℳR by MR for suitable groups K and R.
A diffusion problem with spherical symmetry: Temperature distribution for different initial conditions
Authors: Brown A.
Published: April 2009

The present paper extends some earlier work [1] on heat flow in a composite system, in which a central, high-temperature region loses heat to a surrounding medium. An example of the type of situation in mind is the intrusion of igneous rock into a mass of cooler sedimentary material. As an idealization, spherical symmetry is assumed and the outer region is taken to be infinite in extent. In the earlier work, the central region and the surrounding medium were each taken to be at a constant temperature initially. The present paper gives solutions for a number of alternative situations. The temperature in the outer region is still taken to be constant initially but the temperature in the central region is represented by functions of type rn or (1/r) sin kr, where r is the distance from the centre of the system. As the system of equations for the temperature is linear, and any continuous function can be approximated arbitrarily closely by a polynomial or a Fourier series, the solutions given here can be superposed to give a solution for any continuous initial temperature distribution in the central region.
On some Schreier varieties of universal algebras
Authors: Meskin Stephen
Published: April 2009

Let ω =(ω1) Where ω1 is a set of non-empty sets (called operations) and ω0 is a set of elements (called constants) none of which is a function whose domain belongs to ω1. An ω-ALGEBRA is a set C and a function e (the effect) from the disjoint union of ω0 and ω∈ω1Cω to C, where Cω is the set of all functions from ω to C. Let P be a set of groups Pω of permutations on ω, one group fro each ω∈ω1. A Ρ-ω-ALGEBRA is an ω-algebra such that (ρf)e = (f)e, for all ω ∈ ω1, ρ ∈ Ρω and f ∈ Cω.
On algebraic differential equations satisfied by automorphic functions
Authors: Mahler K.
Published: April 2009

In the present note, I investigate the question whether automorphic functions of the Fuchsian type can satisfy algebraic differential equations of the second order. Under rather general restrictions on the corresponding group, it is proved that there is no such differential equation.
A faithful matrix representation for certain centre-y-metabelian groups
Authors: Gupta C. K.
Published: April 2009

It is a well-known result of W. Magnus [3] that there is a faithful matrix representation for metabelian groups i.e the groups satisfying the law ‘x, y; u, v’. The work in this paper arose in an attempt by the author to find a faithful matrix representation for centre-by-metabelian groups i.e. the groups satisfying the law ‘ x, y; u, v].
Soluble groups with complemented subnormal subgroups
Authors: Kochendörffer R.
Published: April 2009

A subgroup A of a group G is said to be complemented in G if G contains a subgroup C such that . Every subgroup C with its property is called a complement of A in G. Various results have been obtained about groups in which each member of a given set of subgroups is complemented. Some of these results state, roughly speaking, that the existence of complements of all members of a given set of subgroups implies that all members of larger set are also complements. In this paper we derive another theorem of this kind.
The Hughes Problem and others
Authors: Macdonald I. D.
Published: April 2009

Let X be a finite þ-group with the anti-Hughes property . (Notation is set forth in Section 2.) Any element of a finite þ-group G not in Hp (G) has order þ, hence either G/Hp(G) is non-abelian or Hp(G) ≧ (G). Therefore X has the property ; all its elements of maximal order lie in Φ (X).
Commutator subgroups of finite p-groups
Authors: Wiegold James
Published: April 2009

Within five minutes of the start of my first meeting with Bernhard Neumann as his research student, late in 1954, he suggested the following problem to me. Let G be a group in which the cardinals of the classes of conjugate elements are boundedly finite with maximum η, say. Then the commutator subgroup G′ is finite [6], Is the order |G′| of G′ bounded in terms of n? I distinctly recall these words of Neumann: “That should provide us with a start, I think”. He was right: more than just a start, the problem has been a continuing stimulus to a study of questions in fields as far apart as permutation group theory ([7], [11], [12], [14], and some unpublished work of Peter M. Neumann) and multiplicator theory ([13], [2]), as well as attracting interest in its own right.
On a combinatorial generalization of 27 lines associated with a cubic surface
Authors: Ahrens R. W. , Szekeres G.
Published: April 2009

Given integers 0 < λ < κ < ν, does there exist a nontrivial graph G with the following properties: G is of order ν (i.e. has ν vertices), is regular of degree κ (i.e. every vertex is adjacent to exactly κ other vertices), and every pair of vertices is adjacent to exactly λ others? Two vertices are said to be adjacent if they are connected by an edge. We call a graph with the above properties a symmetric (ν, κ, λ) graph and refer to the last of the properties as the A-condition. The complete graph of order v is a trivial example of a symmetric (ν, ν— 1, ν — 2) graph, but we are of course only interested in non-trivial constructions.
A non-cyclic one-relator group all of whose finite quotients are cyclic
Authors: Baumslag Gilbert
Published: April 2009

Let G be a group on two generators a and b subject to the single defining relation a = [a, ab]: . As usual [x, y] = x−1y−1xy and xy = y−1xy if x and y are elements of a group. The object of this note is to show that every finite quotient of G is cyclic. This implies that every normal subgroup of G contains the derived group G′. But by Magnus' theory of groups with a single defining relation G′ ≠ 1 ([1], §4.4). So G is not residually finite. This underlines the fact that groups with a single defining relation need not be residually finite (cf. [2]).
On the semigroup of differentiable mappings
Authors: Yamamuro Sadayuki
Published: April 2009

The purpose of this paper is to improve a result in [2] on the automorphisms of the semigroup D = D(E) of all (Fréchet)-differentiable mappings of a real Banach space E into itself.
A characterisation of the ellipsoid
Authors: Aitchison P. W.
Published: April 2009

The ellipsoid is characterised among all convex bodies in n-dimensional Euclidean space, Rn, by many different properties. In this paper we give a characterisation which generalizes a number of previous results mentioned in [2], p. 142. The major result will be used, in a paper yet to be published, to prove some results concerning generalizations of the Minkowski theory of reduction of positive definite quadratic forms.
The semigroup of endomorphisms of a Boolean ring
Authors: Magill Kenneth D.
Published: April 2009

The family (R) of all endomorphisms of a ring R is a semigroup under composition. It follows easily that if R and T are isomorphic rings, then (R) and (T) are isomorphic semigroups. We devote ourselves here to the converse question: ‘If (R) and (T) are isomorphic, must R and T be isomorphic?’ As one might expect, the answer is, in general, negative. For example, the ring of integers has precisely two endomorphisms – the zero endomorphism and the identity automorphism. Since the same is true of the ring of rational numbers, the two endomorphism semigroups are isomorphic while the rings themselves are certainly not.
Changing the order of integration
Authors: Love E. R.
Published: April 2009

Repeated improper Riemann integrals arise in a variety of contexts, and the validity of changing the order of integration is often in question. Fubini's theorem ensures the equality of two repeated Lebesgue integrals when one of them is absolutely convergent. For many years I have assumed that an analogous test is applicable to repeated improper R-integrals, since they will be absolutely convergent and therefore in agreement with the corresponding L-integrals.
On the laws of certain finite groups
Authors: Cossey John , MacDonald Sheila Oates , Street Anne Penfold
Published: April 2009

In recent years a great deal of attention has been devoted to the study of finite simple groups, but one aspect which seems to have been little considered is that of the laws they satisfy. In a recent paper [3], the first two of the present authors gave a basis for laws ofPSL(2, 5). The techniques of [3] can be used to show that (modulo certain classification problems) a basis for the laws ofPSL(2, pn) can be made up from laws of the following types:

(1) an exponent law,

(2) laws which determine the Sylow subgroups,

(3) laws which determine the normalisers of the Sylow subgroups,

(4) in certain special cases, laws which determine subvarieties of smaller exponent, e.g. the subvariety of exponent 12 for thosePSL(2,pn) which containS4,

(5) a law implying local finiteness.
Derivations related to a separable element of an algebra
Authors: Martin James , Leavitt W. G.
Published: April 2009

Let R be a C-algebra over a commutative ring C of zero characteristic. An element a ∈ R will be called separable if there exists p ∈ C[x] for which p(a) = 0 and such that p′(a) is invertible, where p′ is the formal derivative of p. Call A the C-algebra generated by aR and aL the right and left multiplications by a, and write Da for the inner derivation defined by a. It will be shown that when a is separable there exists φ ∈ A such that [p′(a)]−1φ Da is idempotent. As a consequence it follows that the additive group of R may be decomposed into a direct sum of Ker Da and Im Da. Another result is that for an arbitrary C-derivation δ there exists d ∈ Im Da such that aδ = aDd. Thus Ker Da (and also Im Da) is a δ-subgroup of R+ if and only if aδ = 0.
The isoperimetric problem on some singular surfaces
Authors: Cotton Andrew , Freeman David , Gnepp Andrei , Ng Ting , Spivack John , Yoder Cara
Published: April 2009

We characterize least-perimeter enclosures of prescribed area on some piecewise smooth manifolds, including certain polyhedra, double spherical caps, and cylindrical cans.
Boundedness of sign-preserving charges, regularity, and the completeness of inner product spaces
Authors: Chetcuti Emmanuel , Dvurečenskij Anatolij
Published: April 2009

We introduce sign-preserving charges on the system of all orthogonally closed subspaces, F(S), of an inner product space S, and we show that it is always bounded on all the finite-dimensional subspaces whenever dim S = ∞. When S is finite-dimensional this is not true. This fact is used for a new completeness criterion showing that S is complete whenever F(S) admits at least one non-zero sign-preserving regular charge. In particular, every such charge is always completely additive.
Random fixed point theorems for contractive type multifunctions
Authors: Mustafa Ghulam
Published: April 2009

Some new random coincidence point and random fixed point theorems for multivalued mappings in separable complete metric spaces are proved. The results presented in this paper are the stochastic versions of corresponding results of Chang and Peng and extend the result of the author.
Class number formulae in the form of a product of determinants in function fields
Authors: Ahn Jaehyun , Choi Soyoung , Jung Hwanyup
Published: April 2009

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

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

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

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

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

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

In this paper we present a short definition of the Witten invariants of 3-manifolds. We also give simple proofs of invariance of those obtained for r = 3 and r = 4. Our definition is extracted from the 1993 paper of Lickorish and the Prasolov-Sossinsky book, where it is dispersed over 20 pages. We show by several examples that it is indeed convenient for calculations.
Homogeneous quasi-invariant subspaces of the fock space
Authors: Guo Kunyu
Published: April 2009

In this paper, we prove that two homogeneous quasi-invariant subspaces are similar only if they are equal. Moreover, we exhibit an example to show how to determine the similarity orbits of quasi-invariant subspaces.
On Ψ direct sums of Banach spaces and convexity
Authors: Kato Mikio , Saito Kichi-Suke , Tamura Takayuki
Published: April 2009

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

Convexity and weak closeness of the set of Φ-superharmonic functions in a bounded Lipschitz domain in Rn is considered. By using the fact of that Φ-superharmonic functions are just the solutions to an obstacle problem and establishing some special properties of the obstacle problem, it is shown that if Φ satisfies Δ2-condition, then the set is not convex unless Φ(r) = Cr2 or n = 1. Nevertheless, it is found that the set is still weakly closed in the corresponding Orlicz-Sobolev space.
On Permutational Products of Groups:Part 2-amalgamated products
Authors: Gregorac R. J.
Published: April 2009

The standard methods of constructing generalized free products of groups (with a single amalgamated subgroup) and permutational products of groups are to consider groups of permutations onsets. Although there is an apparent similarity between these two constructions, the exact nature of the relationship is not clear. The following addendum to [4] grew out of an attempt to determine this relationship. By noting that the original construction of permutational products (B. H. Neumann [7]) deals with a group of permutations on agroup(although the group structure has been previously ignored; see [7], [8]) we here give an extension of the original permutational product-construction which yields both the generalized free product and the permutational products as groups of permutations ongroups. A generalized free product is represented as a group of permutations on the ordinary free product of the constituents of the underlying group amalgam and a permutational product is a group of permutations on the direct product of the constituents of the amalgam.
On Laplace Transform
Authors: Kwee B.
Published: April 2009

In this paper we suppose that the function s(x) is integrable in the Lebesgue sense for every finite interval of x ≥ 0. If exists, we say that the integral exists.
Generators for Alternating and Symmetric Groups
Authors: Dey I. M. S. , Wiegold James
Published: April 2009

Let Γ denote the modular group, that is, the free product of a group of order 2 and a group of order 3. Morris Newman investigates in [2] the factor-groups of Γ and calls them Γ-groups for short; thus a group is a Γ-group if and only if it has a generating set consisting of an element of order dividing 2 and an element of order dividing 3. Newman's interest centres on finite simple Γ-groups. He proves that the linear fractional groups LF(2,p) for primes p are Γ -groups, and poses the problem of deciding which of the alternating groups enjoy this property.
A Note on the Absolute Nörlund Summability of Conjugate Fourier Series
Authors: Dikshit G. D.
Published: April 2009

Let σan be an infinite series, with sequence of partial sums {un}. Let {pn} be a sequence of constants, real or complex, and write Pn = po+p1+ … +pn The sequence-to-sequence transformation defines the sequence {tn} of Nörlund means of the sequence {u}, generated by the sequence {pn}. The series σan is said to be surnmable (N, pn), to sum s, if limn→∞ tn = s. It is said to be absolutely sum.mable (N, pn), or summable |N, pn|, if {tn} ∈BV.
An Abstract Formulation of the Lebesgue Decomposition Theorem
Authors: Ficker V.
Published: April 2009

Some concepts in measure theory can be generalized by means of classes of null sets. When measures are considered then the classes of all sets of measure zero play the role of classes of null sets. The purpose of this paper is to give an abstract formulation and proof of the Lebesgue decomposition theorem.
On a Characterisation of Differentiability of the Norm of a Normed Linear Space
Authors: Giles J. R.
Published: April 2009

The purpose of this paper is to show that the various differentiability conditions for the norm of a normed linear space can be characterised by continuity conditions for a certain mapping from the space into its dual. Differentiability properties of the norm are often more easily handled using this characterisation and to demonstrate this we give somewhat more direct proofs of the reflexivity of a Banach space whose dual norm is strongly differentiable, and the duality of uniform rotundity and uniform strong differentiability of the norm for a Banach space.
Matrix-variate Kummer-Beta distribution
Authors: Nagar Daya K. , Gupta Arjun K.
Published: April 2009

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

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

For each positive integer n let N2, n denote the variety of all groups which are nilpotent of class at most 2 and which have exponent dividing n. For positive integers m and n, let N2, mN2, n denote the variety of all groups which have a normal subgroup in N2, m with factor group in N2, n. It is shown that if G ∈N2, mN2, n, where m and n are coprime, then G has a finite basis for its identities.
Irreducible subgroups of symplectic groups in characteristic 2
Authors: Parker Christopher , Rowley Peter
Published: April 2009

Suppose that V is a finite dimensional vector space over a finite field of characteristic 2, G is the symplectic group on V and a is a non-zero vector of V. Here we classify irreducible subgroups of G containing a certain subgroup of O2(StabG(a)) all of whose non-trivial elements are 2-transvections.
Some classes of pseudo-BL algebras
Authors: Georgescu George , Leuştean Laurenţiu
Published: April 2009

Pseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to l-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL algebras.
On the mass formula of supersingular abelian varieties with real multiplications
Authors: Yu Chia-Fu
Published: April 2009

A geometric mass concerning supersingular abelian varieties with real multiplications is formulated and related to an arithmetic mass. We determine the exact geometric mass formula for superspecial abelian varieties of Hubert-Blumenthal type. As an application, we compute the number of the irreducible components of the supersingular locus of some Hubert-Blumenthal varieties in terms of special values of the zeta function.
On Local Embedding Properties of Injectors of Finite Soluble Groups
Authors: Reifferscheid Stephanie
Published: April 2009

In the present paper we consider Fitting classes of finite soluble groups which locally satisfy additional conditions related to the behaviour of their injectors. More precisely, we study Fitting classes 1 ≠⊆such that an-injector of G is, respectively, a normal, (sub)modular, normally embedded, system permutable subgroup of G for all G ∈.

Locally normal Fitting classes were studied before by various authors. Here we prove that some important results—already known for normality—are valid for all of the above mentioned embedding properties. For instance, all these embedding properties behave nicely with respect to the Lockett section. Further, for all of these properties the class of all finite soluble groups G such that an x-injector of G has the corresponding embedding property is not closed under forming normal products, and thus can fail to be a Fitting class.
On the completion of latin rectangles to symmetric latin squares
Authors: Bryant Darryn , Rodger C. A.
Published: April 2009

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n−1)-edge colouring of Kn (n even), and for n-edge colouring of Kn (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.
Positive solutions of some quasilinear singular second order equations
Authors: Goncalves J. V. , Santos C. A. P.
Published: April 2009

In this paper we study the existence and uniqueness of positive solutions of boundary vlue problems for continuous semilinear perturbations, say f: [0, 1) × (0, ∞) → (0, ∞), of class of quasilinear operators which represent, for instance, the radial form of the Dirichlet problem on the unit ball of RN for the operators: p-Laplacian (1 < p < ∞) ad k-Hessian (1 ≤ k ≤ N). As a key feature, f (r, u) is possibly singular at r = 1 or u =0, Our approach exploits fixed point arguments and the Shooting Method.
Finite graphs of valency 4 and girth 4 admitting half-transitive group actions
Authors: Marušič Dragan , Nedela Roman
Published: April 2009

Finite graphs of valency 4 and girth 4 admitting ½-transitive group actions, that is, vertex- and edge- but not arc-transitive group actions, are investigated. A graph is said to be ½-transitiveif its automorphism group acts ½-transitively. There is a natural orientation of the edge set of a ½-transitive graph induced and preserved by its automorphism group. It is proved that in a finite ½-transitive graph of valency 4 and girth 4 the set of 4-cycles decomposes the edge set in such a way that either every 4-cycle is alternating or every 4-cycle is directed relative to this orientation. In the latter case vertex stabilizers are isomorphic to Z2.
The Lindelöf principle and angular derivatives in convex domains of finite type
Authors: Abate Marco , Tauraso Roberto
Published: April 2009

We describe a generalization of the classical Julia-Wolff-Carathéodory theorem to a large class of bounded convex domains of finite type, including convex circular domains and convex domains with real analytic boundary. The main tools used in the proofs are several explicit estimates on the boundary behaviour of Kobayashi distance and metric, and a new Lindelöf principle.
The Schur and (weak) Dunford-Pettis properties in Banach lattices
Authors: Kamińska Anna , Mastyło Mieczysław
Published: April 2009

We study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.
Analyse conforme sur les algèbres de Jordan
Authors: Pevzner M.
Published: April 2009

We construct the Weil representation of the Kantor-Koecher-Tits Lie algebra g associated to a simple real Jordan algebraV. Later we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformal groupGof the Jordan algebraV. The decomposition of L2(V) in the case of Jordan algebra of real square matrices is given using this construction.
On uniform bounds of primeness in matrix rings
Authors: Beidar Konstantin I. , Wisbauer Robert
Published: April 2009

A subset S of an associative ring R is a uniform insulator for R provided a S b ≠ 0 for any nonzero a, b ∈ R. The ring R is called uniformly strongly prime of bound m if R has uniform insulators and the smallest of those has cardinality m. Here we compute these bounds for matrix rings over fields and obtain refinements of some results of van den Berg in this context.

More precisely, for a field F and a positive integer k, let m be the bound of the matrix ring Mk(F), and let n be dimF(V), where V is a subspace of Mk(F) of maximal dimension with respect to not containing rank one matrices. We show that m + n = k2. This implies, for example, that n = k2 − k if and only if there exists a (nonassociative) division algebra over F of dimension k.
Composition operators in Orlicz spaces
Authors: Cui Yunan , Hudzik Henryk , Kumar Romesh , Maligranda Lech
Published: April 2009

Composition operators Cτ between Orlicz spaces Lϕ (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function ϕ and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.
The Exponential Representation of Holomorphic Functions of Uniformly Bounded Type
Authors: Quang Thai Thuan
Published: April 2009

It is shown that if E, F are Fréchet spaces, E ∈ (Hub), F ∈ (DN) then H(E, F) = Hub(E, F) holds. Using this result we prove that a Fréchet space E is nuclear and has the property (Hub) if and only if every entire function on E with values in a Fréchet space F ∈ (DN) can be represented in the exponential form. Moreover, it is also shown that if H(F*) has a LAERS and E ∈ (Hub) then H(E × F*) has a LAERS, where E, F are nuclear Fréchet spaces, F* has an absolute basis, and conversely, if H(E × F*) has a LAERS and F ∈ (DN) then E ∈ (Hub).
Nuclear and integral polynomials
Authors: Cilia Raffaella , Gutiérrez Joaquín M.
Published: April 2009

Let E be a Banach space whose dual E* has the approximation property, and let m be an index. We show that E* has the Radon-Nikodým property if and only if every m-homogeneous integral polynomial from E into any Banach space is nuclear. We also obtain factorization and composition results for nuclear polynomials.
The generalized condition numbers of bounded linear operators in Banach spaces
Authors: Chen Guoliang , Wei Yimin , Xue Yifeng
Published: April 2009

For any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.
Strong duality for metacyclic groups
Authors: Quackenbush R. , Szabó C. S.
Published: April 2009

Davey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).
Extremal partitions and distortion under the Montel bounded univalent maps
Authors: Vasil'ev Alexander
Published: April 2009

Extremal partitions of domains into configurations of certain to pological form are studied. The extremal value of the weighted sum of reduced moduli of circular domains and digons is obtained. These results are applied to some problems about distortion under bounded conformal maps of the unit disk with two preassigned values.
Dense subsemigroups of generalised transformation semigroups
Authors: Wasanawichit Amorn , Kemprasit Yupaporn
Published: April 2009

In 1986, Higgins proved thatT(X), the semigroup (under composition) of all total transformations of a setX, has a proper dense subsemigroup if and only ifXis infinite, and he obtained similar results for partial and partial one-to-one transformations. We consider the generalised transformation semigroupT(X, Y) consisting of all total transformations fromXintoYunder the operation α * β = αθβ, where θ is any fixed element ofT(Y, X). We show that this semigroup has a proper dense subsemigroup if and only ifXandYare infinite and |Yθ| = min{|X|,|Y|}, and we obtain similar results for partial and partial one-to-one transformations. The results of Higgins then become special cases.
Dense subgroups of finite groups
Authors: Gagen Terence M. , Weichsel Paul M.
Published: April 2009

It is well known that in the category of all groups and homomorphisms, every epimorphism is onto. This result does not hold for certain other categories of groups. The condition that an epimorphism θ:G → A is not onto is equivalent to the condition that θ(G) is a proper subgroup A with the property that any two homomorphisms α, β on A which agree elementwise on θ(G) must agree on A. Such a subgroup can be called dense (see e.g. [1]). Naturally the existence of such homomorphisms α and β depend on the particular class of groups that is available. We will choose to work within the context of varieties even though many of the results will hold true for more modest classes of groups.
L-semirings
Authors: Selden John
Published: April 2009

By a topological semiring I mean a Hausdorff space together with two continuous associative operations, addition and multiplication, such that the multiplication distributes across the addition from both sides.
The number of pairs of generalized integers with L.C.M. ≦ x
Authors: Suryanarayana D. , Prasad V. Siva Rama
Published: April 2009

Generalized integers are defined in {2] as follows: Suppose there is given a finite or infinite sequence {p} of real numbers which are called generalized primes such that 1 < p1 < p2 < …. Form the set {l} of all possible p-products, i.e. the products of the form where are integers ≧ 0 of which all but a finite number are 0. Call these numbers generalized integers and suppose that no two generalized integers are equal if their α's are different. Then arrange {l} in an increasing sequence I = l1 < l2 < l3 < … < ln < ….
Minimal prime ideals and compactifications
Authors: Rubinstein J. H.
Published: April 2009

Following on from the work of T. P. Speed [1], we will deal with some obvious conjectures, using particularly results 3.3 and 8.5 of [1].
Primitive idempotent measures on compact semitopological semigroups
Authors: Choy Stephen T. L.
Published: April 2009

For a semigroup S let I(S) be the set of idempotents in S. A natural partial order of I(S) is defined by e ≦ f if ef = fe = e. An element e in I(S) is called a primitive idempotent if e is a minimal non-zero element of the partially ordered set (I(S), ≦). It is easy to see that an idempotent e in S is primitive if and only if, for any idempotent f in S, f = ef = fe implies f = e or f is the zero element of S. One may also easily verify that an idempotent e is primitive if and only if the only idempotents in eSe are e and the zero element. We let П(S) denote the set of primitive idempotent in S.
Some classes of E-Compactness
Authors: Blefko Robert L.
Published: April 2009

Mrowka and Engleking [1] have recently introduced a notion more general than that of compactness. Perhaps the most convenient direction at departure is the following: for spaces X and E, X is said to be E-compact if X is topologically embeddable as a closed subset of a product Em for some cardinal m, in which case we write X ⊂cl Em. More generally, X is said to be E-completely regular if X is topologically embeddable in a product Em for some m. For example, if we take E to be the unit interval I, we obtain the class of compact spaces and completely regular spaces, respectively, as is well-known. The question then arises, of course, given a space E, what spaces are compact with respect to it? A related question, to which we address ourselves in this note, is the following. Denote by K[E] all those topological spaces which are E-compact. Then we ask: are there very many distinct E-compact classes? It will develop that there are indeed quite a large number of such classes.
On ergodic theorem for a Banach valued random sequence
Authors: Pop-Stojanovic Zoran R.
Published: April 2009

In this paper we shall deal with a probability space (S, Σ, P), a separable Banach space X having its strong dual X* and a strictly stationary random sequence defined as in [7], where are X-valued, Gelfand-Pettis (weakly) integrable [6], [9], and strongly measurable random variables. In the case when Yk's are Bochner (strongly) integrable random variables one can find the ergodic theorem for such a sequence and, with respect to strong convergence in X, in the papers [7], [8].
On a type of Sasakian space
Authors: Chaki M. C. , Ghosh D.
Published: April 2009

A Sasakian space [1]Mn (n = 2m + 1) is a Riemannian n-space with a positive definite metric tensor gij and a unit Killing vector field η which satisfies where the comma denotes covariant differentiation with respect to the metic tensor. In a recent paper [2] M. C. Chaki and A. N. Roy Chowdhury studied conformally recurrent spaces of second order, or briefly conformally 2-recurrent spaces, that is, non-flat Riemannian spaces Vn (n > 3) defined by where is the conformal curvature tensor: and alm is a tensor not identically zero.
Some questions about rotundity and renormings in Banach spaces
Authors: Aizpuru A. , Garcia-Pacheco F. J.
Published: April 2009

In this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.
Special involutions and bulky parabolic subgroups in finite Coxeter groups
Authors: Pfeiffer Götz , Röhrle Gerhard
Published: April 2009

The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.
On non-cross varieties of groups
Authors: Kovács L. G. , Newman M. F.
Published: April 2009

Our title has become something of a misnomer, however we retain it since drafts of this note have been quoted with it.
Subgroups of free solvable groups
Authors: Lewin Jacques , Lewin Tekla
Published: April 2009

A consequence of Schreier's formula is that if G is a subgroup of the free group F of rank n < 1 and rank G ≦ n, then G = F or G is of infinite index in F. However, if S is a free sovlvable group of derived length I < 1 and H is a subgroup of S which is free solvable of the same length, then the rank of H does not exceed the rank of S. These observations led G. Baumslag to conjecture that if H is of finite index in S then H = S. In fact, we have sharper results in two directions. If H and S are free solvable of the same length, not only is H of infinite index in S, but δ1−1(S)/δ1−1(H) is torsion-free. In another direction we need not assume that S is free solvable, only that s is torsion-free and of derived length l (l > 1) and that H is not cyclic. Thus Stallings' theorem [11] that a finitely generated torsionfree group with a free subgroup of finite index is itself free has an even stronger counterpart in the variety of groups solvable of length at most l (l > 1): a torsionfree group in that variety with a non-cyclic free subgroup of finite index coincides with this subgroup. The proof relies on the following theorem: If S is a free solvable group, J is the group of automorphisms of S which induce the identity on S/S', and I is the group of inner automorphisms of S, then J/I is torsion-free. The proofs of these theorems form the bulk of the first four sections.
On the equivalence of cancellative extensions of commutative cancellative semigroups by groups
Authors: Heuer Charles V.
Published: April 2009

In [1] D. W. Miller and the author established necessary and sufficient conditions for the existence of a cancellative (ideal) extension of a commutative cancellative semigroup by a cyclic group with zero. The purpose of this paper is to extend these results to cancellative extensions by any finitely generated Abelian group with zero and to establish in this general case conditions under which two such extensions are equivalent.
The category of representations of a completely 0-simple semigroup
Authors: McAlister D. B.
Published: April 2009

A. H. Clifford [1], [2] has shown that all finite dimensional representations of a completely 0-simple semigroup S over a field Φ.phi; can be obtained as extensions of those of its maximal subgroups and has given a method for constructing all such representations. This representation theory depends strongly on the fact the representations under consideration are finite dimensional and is not adequate to deal with the infinite dimensional case or with representations over arbitrary rings. In order to determine the structure of the (contracted) algebra Φ(S) of S modulo its radical, one has to consider representations which are not finite dimensional or over fields; c.f. ‘6’. Hence Clifford's theory does not suffice for this purpose.