bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some criteria for the regularity of a direct product of regular p-groups
Authors: Groves J. R. J. 
Published: April 2009

AbstractA sufficient condition, which may also be necessary, for the regularity of the direct product of two finite regular p-groups is obtained. In an attempt to decide the necessity of the condition, we look at two related questions. Firstly, does the regularity of the direct square of a regular p-group imply the regularity of all the finite direct powers; secondly, is the join of two regular varieties regular? Fainally, the results obtained are used to give some precise answers in special cases.
The exceptional case in a theorem of Bose and Shrikhande
Authors: de Witte Paul , Wallis Jennifer Seberry 
Published: April 2009

AbstractIt is shown that (n being an integer) any non-trivial finite linear space with n2- 1 points, all of degree at most n+1, is embeddable in a finite projective plane of order n. This generalizes a theorem of Bose and Shrikhande and settles the unsolved case n = 6.
Commutators and abelian groups
Authors: Rodney D. M. 
Published: April 2009

AbstractIf G is a group, then K(G) is the set of commutators of elements of G. C is the class of groups such that G′ = K(G) is the minimal cardinality of any generating set of dG. We prove: Theorem A. Let G be a nilpotent group of class two such that G' is finite and d(G′) < 4.Then G < G.Theorm B. Let G be a finite group such that G′ is elementary abelian of order p3. Then G ∈ C.Theorem C. Let G be a finite group with an elementary abelian Sylow p-subgroup S, of order p2, such that S ⊆ K(G). Then S ⊆K(G).
Inverse semigroups of homeomorphisms between open subsets
Authors: Baird Bridget Bos 
Published: April 2009

AbstractThe symbolIG(X) denotes the inverse semigroup, under composition of functions, of all homeomorphisms between open subsets of aT1topological spaceX. The first result is that two such semigroupsIG(X) andIG(Y) are isomorphic if and only if the spacesXandYare homeomorphic. Ideals ofIG(X) are next examined and it is shown that for many spacesXthe semigroupIG(X) is 0-simple. We also look at congruences onIG(X); one result is that we determine a congruence which in many instances is the largest proper congruence onIG(X).
Congruence-free right simple semigroups
Authors: Trotter P. G. 
Published: April 2009

AbstractCongruence-free right simple semigroups with idempotents are simple groups or have order 2. It is shown in this paper that there exist congruence-free simple semigroups without idempotents. Some properties of congruences on right simple semigroups, expressed mainly in terms of their unitary and left unitary subsemigroups, are determined. These are used to provide characterizations of congruence-free right simple semigroups.
Some properties of endomorphisms in residually finite groups
Authors: Hirshon Ronald 
Published: April 2009

AbstractIf ε is an endomorphism of a finitely generated residually finite group onto a subgroup Fε of finite index in F, then there exists a positive integer k such that ε is an isomorphism of Fεk. If K is the kernel of ε, then K is a finite group so that if F is a non trivial free product or if F is torsion free, then ε is an isomorphism on F. If ε is an endomorphism of a finitely generated resedually finite group onto a subgroup Fε (not necessatily of ginite index in F) and if the kernel of ε obeys the minimal condition for subgroups then there exists a positive integer k such that ε is an isomorphism on Fεk.
On uniqueness and continuability of the Emden–Fowler equation
Authors: Kwong Man Kam 
Published: April 2009

AbstractThe Emden-Fowler equation x″(t) + a(t)|x|γ sgn x = 0, t ≧ 0, is said to be in the sublinear or superlinear case according to whether γ < 1 or γ > 1. Conditions on a(t) are given to ensure local uniqueness of solutions in the sublinear case and continuability of solutions in the superlinear case. Boundedness of solutions is also studied.
Classes of operators on vector valued integration spaces
Authors: Fleming R. J. , Jamison J. E. 
Published: April 2009

AbstractLet Lp(Ω, K) denote the Banach space of weakly measurable functions F defined on a finite measure space and taking values in a separable Hilbert space K for which ∥ F ∥p = ( ∫ | F(ω) |p)1/p < + ∞. The bounded Hermitian operators on Lp(Ω, K) (in the sense of Lumer) are shown to be of the form , where B(ω) is a uniformly bounded Hermitian operator valued function on K. This extends the result known for classical Lp spaces. Further, this characterization is utilized to obtain a new proof of Cambern's theorem describing the surjective isometries of Lp(Ω, K). In addition, it is shown that every adjoint abelian operator on Lp(Ω, K) is scalar.
The stability index of a cactus
Authors: Grant Douglas D. , Holton D. A. 
Published: April 2009

AbstractWe show that ifGis a connected graph of ordernsuch that no line lies in more than one cycle (in other words,Gis a cactus of ordern), then the stability index ofGis one of the integers 0, 1,n−7,n−6,n−5,n−4 orn.
Rigidity in order-types
Authors: Hickman J. L. 
Published: April 2009

AbstractA totally ordered set (and corresponding order-type) is said to be rigid if it is not similar to any proper initial segment of itself. The class of rigid ordertypes is closed under addition and multiplication, satisfies both cancellation laws from the left, and admits a partial ordering that is an extension of the ordering of the ordinals. Under this ordering, limits of increasing sequences of rigid order-types are well defined, rigid and satisfy the usual limit laws concerning addition and multiplication. A decomposition theorem is obtained, and is used to prove a characterization theorem on rigid order-types that are additively prime. Wherever possible, use of the Axiom of Choice is eschewed, and theorems whose proofs depend upon Choice are marked.
Analysis of the effect of certain forcings on the nonoscillatory solutions of even order equations
Authors: Kartsatos Athanassios G. 
Published: April 2009

AbstractProperties of solutions of, are studied in the causeuH(t, u)>0 foru≠0. It is shown that two inequalities may always be associated with (I) in such a way that if one of these inequalities has a small positive solution and the other inequality has a small negative solution, then (I) is oscillatory. Further asymptotic properties of (I) are studied under assumptions involving intermediate antiderivativesP(i)(t), withP(n)=Q. Several results of this type ensure the non-existence of positive solutions of (I).
On majorizing and cone-absolutely summing mappings
Authors: Wong Yau-Chuen 
Published: April 2009

AbstractThe notions of majorizing mappings and cone-absolutely summing mappings are studied in the locally convex Riesz space setting. It is shown that a locally convex Riesz space Y is an M-space in the sense of Jameson (1970) if and only if, for any locally convex space E, every continuous linear map from E into Y is majorizing. Another purpose of this note is to study the lattice properties of the vector space ℒl(X, Y) of cone-absolutely summing mappings from one locally convex Riesz space into another Y. It is shown that if Y is both locally and boundedly order complete, then ℒl(X, Y) is an l-ideal in Lb(X, Y). This improves a result of Krengel.
Groups with large conjugacy classes
Authors: Balogun Bola O. 
Published: April 2009

AbstractA finite group is called repetition-free if its conjugacy classes have distinct sizes. It is known that a supersolvable repetition-free group is necessarily isomorphie to Sym(3). the symmetric group on three symbols. Thus the question arises as to whether Sym (3) is the only repetition-free group. In this paper it is proved that if mk denotes the minimum of the orders of the centralizers of elements of a repetition-free group G and mk ≦ 4 then G is isomorphie to Sym (3).
Simultaneous Diophantine approximation
Authors: Mack J. M. 
Published: April 2009

AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46¼ = 1/2.6043 ….
The Diophantine equationy2= x(x2+ 21Dx+ 112D2)and the conjectures of Birch and Swinnerton-Dyer
Authors: Rajwade A. R. 
Published: April 2009

AbstractSome of the conjectures of Birch and Swinnerton-Dyer have been verified for curves with complex multiplication by √ — 7. TheL-functionLD(1) of such curves at the points= 1 is written as a finite sum of division values ofp-functions and the integer property ofLD(1) is proved.
Characterization of a family of simple groups by their character table
Authors: Herzog Marcel , Wright David 
Published: April 2009

AbstractThe paper establishes a method for bounding the 2-rank of a simple group with one conjugacy class of involutions, by means of its character table. For many groups of 2-rank ≦ 4, this bound is shown to be exact. The main result is that the simple groups G2(q),(q,6) = 1, are characterized bv their character table.
Weak and unbounded order convergence in Banach lattices
Authors: Wickstead A. W. 
Published: April 2009

AbstractA net (xy) in a vector lattice is unbounded order convergent (uo-convergent) to 0 if u ∧ |xv| order converges to 0 for all u ≧ 0. We consider, in a Banach lattice, the relationship between weak and uo-convergence. We characterise those Banach lattices in which weak convergence implies uo-convergence and those in which uo-convergence of a bounded net implies weak convergence. Finally we combine the results to characterise those Banach lattices in which weak and uo-convergence coincide for bounded nets.
Ideals in autometrized algebras
Authors: Swamy K. L. N. , Rao N. P. 
Published: April 2009

AbstractA notion of a normal autometrized algebra is introduced which generalises the concepts of Boolean geometry. Brouwerian geometry, autometrized lattice ordered groups, semi-Brouwerian geometry, etc. The notions of ideals and congruence relations are introduced in normal autometrized algebras and a one to one correspondence between ideals and congruence relations is established. Some other common properties of the above geometries are also obtained for normal autometrized algebras.
The Moore-Penrose inverse of a sum of matrices
Authors: Hung Ching-Hsiang , Markham Thomas L. 
Published: April 2009

AbstractSuppose U and V are to m × n matrices over the complex field. We obtain a representation for the Moore–Penrose inverse of the sum U + V. A well-known result of Cline is then derived as a special case of a corollary of this representation.
Restricted diophantine approximation
Authors: Worley R. T. 
Published: April 2009

AbstractThe problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.
Proper colourings of K15
Authors: Heinrich Katherine 
Published: April 2009

AbstractWe denote the complete graph on n vertices by Kn. A proper k–colouring of Kn is a way of assigning colours from a set of k colours to the edges of Kn in such a way that no monochromatic triangles are formed. It is known that there are precisely two proper 3-colourings of K16 each of which has exactly one proper 3-colouring of K15 embedded in it. We show that these two are the only proper 3-colourings of K15.
Second order elliptic boundary value problems in spaces with homogeneous norms
Authors: Pryde A. J. 
Published: April 2009

AbstractWe consider the interior and Dirichiet problems and problems with first order boundary conditions, for a second order homogeneous elliptic partial differential operator with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. From there we obtain a priori estimates and regularity results for boundary value problems in Sobolev spaces.
Growth sequences of finite groups IV
Authors: Wiegold James 
Published: April 2009

AbstractThe main result is that d(Ssm) = n+2 for every finite non-abelian two-generator simple group S of order s and every integer n > 0. This is applied to give a very close estimate on d(Gn) for any finite group G whose simple images are two-generator. The article is based on the author's previous papers with similar titles.
Separating conjugates in amalgamated free products and HNN extensions
Authors: Dyer Joan L. 
Published: April 2009

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.
Near-rings of polynomials and polynomial functions
Authors: Pilz Günter , so Yong-Sian 
Published: April 2009

AbstractIn this paper we investigate near-rings of polynomials and polynomial functions. After some results which belong to universal algebra we turn our attention to the familiar case of polynomials and polynomial functions over a commutative ring with identity. We study the relation between ring- and near-ring homomorphisms, and the behaviour of polynomial near-rings when the ring splits into a direct sum. A discussion of the structure of these polynomial near-rings (radical, semisimplicity) finishes this paper. These investigations are motivated by Clay and Doi (1973).
Extensions of orthomorphisms
Authors: Wickstead A. W. 
Published: April 2009

AbstractWe consider, on an Archimedean Riesz space, the spaces of all linear operators lying between two multiples of the identity (for the order), those leaving all ideals invariant and the order bounded orthomorphisms. We find, if E is uniformly complete, necessary and sufficient conditions for all such operators defined on sublattices of E to extend to the whole of E. Examples are given to show the role of uniform completeness. For the space of all orthomorphisms we give a sufficient condition on E for such an extension to exist.
Uniform spaces, spanier quasitopologies, and a duality for locally convex algebras
Authors: Dubuc Eduardo J. , Porta Horacio 
Published: April 2009

AbstractGelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be extended to pro-C*-algebras and separated quasitopologies. The extension is provided by a functional representation of an algebra A as the algebra of all continuous numerical functions on a quasitopological space. The first half of the paper deals with uniform spaces and quasitopologies, and has independent interest.
On characters in the principal 2-block
Authors: Berger Thomas R. , Herzog Marcel 
Published: April 2009

AbstractLet k be a complex number and let u be an element of a finite group G. Suppose that u does not belong to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(1) – X(u) = k for every complex nonprincipal irreducible character X in the principal 2-block of G if and only if G/O(G) is isomorphic either to C2, a cyclic group of order 2, or to PSL (2, 2n), n ≧ 2.
Ideals in simple rings
Authors: Davenport W. Harold 
Published: April 2009

AbstractIn this article, we define the concept of a Malcev ideal in an alternative ring in a manner analogous to Lie ideals in associative rings. By using a result of Kleinfield's we show that a nonassociative alternative ring of characteristic not 2 or 3 is a ring sum of Malcev ideals Z and [R, R] where Z is the center of R and [R, R] is a simple non-Lie Malcev ideal of R. If R is a Cayley algebra over a field F of characteristic 3 then [R, R] is a simple 7 dimensional Lie algebra. A similar result is obtained if R is a simple associative ring.
Sharply two-transitive families of permutations on an immune set
Authors: Dekker J. C. E. 
Published: April 2009

AbstractIt is known that there is a finite affine (or projective) plane of order n if and only if there is a sharply two-transitive set of permutations of degree n. This paper deals with a generalization of this theorem, in which finite sets are replaced by isolated sets, cardinalities by isols and certain effectiveness conditions are imposed on the two systems involved which are trivially satisfied in the finite case.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 02F40, secondary 05B25.
Lie and Jordan structure in operator algebras
Authors: Robinson Derek W. , Størmer Erling 
Published: April 2009

AbstractLet υ be a C*-algebra, α a *-anti-automorphism of order 2, and υα(±1) = {A; A ∈ υ, α(A) = ± A} the spectral subspaces of α. It follows that υα(+ 1) is a Jordan algebra and υα(− 1) is a Lie algebra. We begin the classification of pairs of Jordan and Lie algebras which can occur in this manner by examining υ = ℒ(ℋ), the algebra of bounded operators on a Hilbert space ℋ.
Congruences contained in an equivalence on a semigroup
Authors: Jones P. R. 
Published: April 2009

AbstractThe main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.
Mean Value theorems for multiplicative functions bounded in mean α-power, α >1
Authors: Elliott P. D. T. A. 
Published: April 2009

AbstractOn analogy with functions if Lebesuge class Lα on the real line the author considers those multiplicative arthmetic functions which are bounded in mean α>1. Necessary and sufficient conditions are obtained in order that they should have a mean-value, zero or non-zero. An application is made to Ramanujan's τ-function.
On the continuous linear image of a Banach space
Authors: Cross R. W. 
Published: April 2009

AbstractA subspace of a Banach space is called anoperator rangeif it is the continuous linear image of a Banach space. Operator ranges and operator ideals with fixed range space are investigated. Properties of strictly singular, strictly cosingular, weakly sequentially precompact, and other classes of operators are derived. Perturbation theory and closed semi-Fredholm operators are discussed in the final section.
On closure and factorization properties of subexponential and related distributions
Authors: Embrechts Paul , Goldie Charles M. 
Published: April 2009

AbstractFor a distribution function F on [0, ∞] we say F ∈ if {1 – F(2)(x)}/{1 – F(x)}→2 as x→∞, and F∈, if for some fixed γ > 0, and for each real , limx→∞ {1 – F(x + y)}/{1 – F(x)} ═ e– n. Sufficient conditions are given for the statement F ∈ F * G ∈ and when both F and G are in y it is proved that F*G∈pF + 1(1 – p) G ∈ for some (all) p ∈(0,1). The related classes ℒt are proved closed under convolutions, which implies the closure of the class of positive random variables with regularly varying tails under multiplication (of random variables). An example is given that shows to be a proper subclass of ℒ 0.
Coverings of products of linear topological spaces
Authors: Todd Aaron R. 
Published: April 2009

AbstractAn extension of the Banach-Mackey theorem is used to prove a theorem about countable families of closed balanced convex sets that cover a product of linear topological spaces. This theorem clarifies proofs that certain Baire-type properties, including the unordered Baire-like property, are preserved under products. A modification of the theorem is used to show that a property involving the bounded-absorbing sequences of DeWilde and Houet is also productive. Finally, a question is posed about balanced absorbing sets relating to products of linear Baire spaces.1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 99.
Norm and order properties of Banach lattices
Authors: Bedingfield Susan E. , Wirth Andrew 
Published: April 2009

AbstractThe interrelationships between norm convergence and two forms of convergence defined in terms of order, namely order and relative uniform convergence are considered. The implications between conditions such as uniform convexity, uniform strictness, uniform monotonicity and others are proved. In particular it is shown that a σ-order continuous, σ-order complete Banach lattice is order continuous.1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 40.
Subexponential distribution functions
Authors: Pitman E. J. G. 
Published: April 2009

AbstractA distribution function (F on [0,∞) belongs to the subexponential class if and only if 1−F(2) (x) ~ 2(1−F(x)), as x→ ∞. For an important class of distribution functions, a simple, necessary and sufficient condition for membership of is given. A comparison theorem for membership of and also some closure properties of are obtained.1980 Mathematics subject classification (Amer. Math. Soe.): primary 60 E 05; secondary 60 J 80.
On the relationship between ordinary thin sets and full-thin sets
Authors: Hwang J. S. , Jackson H. L. 
Published: April 2009

AbstractIn this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.
On odd perfect numbers (II), multiperfect numbers and quasiperfect numbers
Authors: Cohen Graeme L. 
Published: April 2009

Let N be a positive integer. This paper is concerned with obtaining bounds for(p prime), when N is an odd perfect number, a multiperfect number, or a quasiperfect number, under assumptions on the existence of such numbers (where none is known) and whether 3 and 5 are divisors. We argue that our new lower bounds in the case of odd perfect numbers are not likely to be significantly improved further. Triperfect numbers are investigated in some detail, and it is shown that an odd triperfect number must have at least nine distinct prime factors.1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 20.
Major arcs in the four cubes problem
Authors: Szekeres George 
Published: April 2009

AbstractThere is an old conjecture that every integer can be decomposed into four (positive or negative) perfect cubes. More specifically one would like to know the asymptotic number of solutions of when a large bound N is placed on the parts mi. Using the circle method it is shown that the number of such representations of n when N → ∞ is asymptotically equal to C(n). N for a certain positive constant C(n), provided that the contribution of the minor arcs can be neglected.
A diophantine equation over a function field
Authors: Cassels J. W. S. 
Published: April 2009

AbstractLet x0, x1, x2, x3 be polynomials in a variable t and with coefficients in a field k of character of characteristic 0. If and , then x0 = x1 = x2 = x3 = 0. This partially answers a question of Pjatetskii-Š;apiro and Šafarevič about the K3-surface . The proof uses a technique of M. R. Christie.