bluuebunny/crossref_metadata_2025_split huggingface dataset:
Irreducible representations of the group of movements of the Euclidean plane
Authors: Symons James 
Published: April 2009

It is well known that a wide range of Special Function Theory can be realized by considering unitary representations of certain topological groups.In this approach it is very important to determine all irreducible continuous unitary representations of the group in question.For the group of movements this problem was initiated by Vilenkin [6]. Rather restrictive conditions were imposed in this paper and while he returned to the problem in [7], it was still not solved in full generality (among other things the representation space was assumed separable). The first complete solution appears to have been given by Thoma [5]. Here, the method was to show each irreducible continuous unitary representation equivalent to a particular representation in a space of square integrable functions.
On multiplicative representations of integers
Authors: Erdös P. , Szemerédi A. 
Published: April 2009

AbstractLet 1 ≦ a1 < … < ak ≦ x; b1 < … b1 ≦ x. Assume that the number of solutions of a1b1 = m is less than c. The authors prove that then . They also give a simple proof of Szemerédi's theorem: If the products aibj are all distinct then . They conjecture that (2) holds for c2 = 1 + ε if x > x0(ε). Several other unsolved problems are stated.
Hadamard matrices of Williamson type
Authors: Whiteman Albert Leon 
Published: April 2009

AbstractLet p be a prime ≡ 1 (mod 4) and put v = p(p + 1)/2. It is proved in this paper that there exist four symmetric circulant matrices A, B, C, D of order υ such that where Iv is the identity matrix of order υ. This result is used to construct Hadamard matrices of order 4υ that are of the type originally prescribed by Williamson.
On the permanent of Schur's matrix
Authors: Graham R. L. , Lehmer D. H. 
Published: April 2009

AbstractSchur's matrix Mnis ordinarily defined to be thenbynmatrix (εjk), 0 ≦j, k < n, where ε = exp (2 πi/n). This matrix occurs in a variety of areas including number theory, statistics, coding theory and combinatorics. In this paper, we investigatePn, thepermanentofMn, which is define bywhere π ranges over alln! permutations on {0,1, …,n– 1}.Pnoccurs, for example, in the study of circulants. Specifically, letXndenote thenbyncirculant matrix(xi, j)withxi, j= xi, j, where the subscript is reduced modulon. The determinant ofXnis a homogeneous polynomial of degreenin thexiand can be written asThenPn= A(1,1, … 1). Typical of the results established in this note are: (i)P2n= 0 for alln, (ii)Pp≡p! (modp3)forpa prime >3. (iii) IfpadividesnthendividesPn. Also, a table of values ofPnis given for 1 ≦n≦ 23.
Nilpotent and semi-n-abelian groups
Authors: Kowol G. 
Published: April 2009

AbstractA group G is called semi-n-abelian, if for every g ∈ G there exists at least one a(g) ∈ G-which depends only on g-such that (gh)n = a-1(g)gnhna(g) for all h ∈ G; a group G is called n-abelian, if a(g) = e for all g ∈ G. According to Durbin the following holds for n-abelian groups: If G is n-abelian for at lesast 3 consecutive integers, then G in n-abelian for all integers and these groups are exactly the abelian groups. In this paper this problem is generalized to the semi-n-abelian case: If a finite group G is semi-n-abelian for at least 4 consecutive integers then G is semi-n-abelian for all integers and these groups are exactly the nilpotent groups, where the Sylow-2-subgroup is abelian, the Sylow-3-subgroup is any element of the Levi-variety ([[g, h], h] = e ∀ g, h ∈ G) and the Sylow-p-subgroup (p < 3) is of class <2. As a consequence we get a description of all finite (3-)groups, which are elements of the Levi-variety.
Remarks on multipliers on certain function spaces on groups
Authors: Yamaguchi Hiroshi 
Published: April 2009

AbstractLet G be LCA group with an algebraically ordered dual Ĝ. Suppose also that the semigroup P of positive elements in Ĝ is not dense in Ĝ. Subspaces (G) (1 < s < ∞) are defined analogous to the Hardy spaces on the circle group, and the question whether every multiplier from into can be extended to a multiplier from L3(G) into Lq(G) is investigated. If we suppose that s ≠ ∞, the it is shown that such an extension is possible if and only if (s, q) ∈ (1, ∞) × [1, ∞] ∪ {(1, ∞)}. (the negative result for (1, 1) was obtained in a previous paper.)
Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups
Authors: Mcalister D. B. 
Published: April 2009

AbstractA partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that {} has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.
On the Schur-Baer property
Authors: Moghaddam Mohammad Reza R. 
Published: April 2009

AbstractIn 1957 P. Hall conjectured that every (finitely based) variety has the property that, for every group G, if the marginal factor-group is finite, then the verbal subgroup is also finite. The content of this paper is to present a precise bound for the order of the verbal subgroup of a G when the marginal factor-group is of order Pn (p a prime and n > 1) with respect to the variety of polynilpotent groups of a given class row. We also construct an example to show that the bound is attained and furthermore, we obtain a bound for the order of the Baer-invariant of a finite p-group with respect to the variety of polynilpotent groups.
Growth sequences of finite groups V
Authors: Meier D. , Wiegold James 
Published: April 2009

AbstractA short and easy proof that the minimum number of generators of the nth direct power of a non-trival finite group of order s having automorphism group of order a is more than logsn + logsa, n > 1. On the other hand, for non-abelian simple G and large n, d(Gn) is within 1 + e of logsn + logsa.
Some topological properties of vector measures and their integral maps
Authors: Anantharaman R. , Garg K. M. 
Published: April 2009

AbstractIn the present paper we prove that every finite dimensional non-atomic measure ν is open and monotone (viz. ν–1 preserves connected sets) relative to the usual Fréchet-Nikodým topology on its domain and the relative topology on its range. An arbitrary finite dimensional measure is found on the other hand to be biquotient.Given a vector measure ν, we further investigate the properties of its integral map Tν: φ → ∫ φdν defined on the set of functions φ in L1(|ν|) for which φ(s) ∈ [0,1] |ν|-almost everywhere. When ν is finite dimensional, Tν is found to be always open. In general, when Tν is open, the set of extreme points of the closed convex hull of the range of ν is proved to be closed, and when ν and Tν are both open, the range of ν in itself is closed.
Non-tall compact groups admit infinite Sidon sets
Authors: Hutchinson M. F. 
Published: April 2009

AbstractRiesz polynomials are employed to give a sufficient condition for a non-abelian compact group G to have an infinite uniformly approximable Sidon set. This condition is satisfied if G admits infinitely many pairwise inequivalent continuous irreducible unitary representations of the same degree. Consequently a compact Lie group admits an infinite Sidon set if and only if it is not semi-simple.
Generalized Semi-Fredholm transformations
Authors: Tacon D. G. 
Published: April 2009

AbstractThe class ϕ+(X, Y) of semi-Fredholm transformations consists of those transformationsT:X→Yfor which α(T) = dim kerT< ∞ and for whichT(X) is closed. It forms an open subset of B (X, Y) closed under perturbation by compact transformations and is a particularly important class of transformation sinceTis Fredholm if and only ifT∈ ϕ+(X, Y) andT′ ∈ ϕ+(Y′.X′). The realization that elements of ϕ+(X, Y) have very simple nonstandard characterizations lead the author to consider the possibility of finding an analogous open class of transformation which is closed under perturbation by weakly compact transformations. Consequently this paper investigates two related classes which contain ϕ+(X, Y). The first such class coincides with the class of Tauberian transformations whilst the second consists of those transformations which have Tauberian extensions on the nonstandard hulls. The Tauberian transformations are closed under perturbation by weakly compact transformations but in general are not open. The “super” Tauberian transformations are closed under perturbation by super weakly compact transformations and in fact form an open subset of B(X, Y).
Boundedness and completeness in locally convex spaces and algerbras
Authors: Joseph Gerard A. 
Published: April 2009

AbstractThe set of bounded elements of a unital l.m.c. algebra is characterised as the union of certain naturally defined normed subalgebras, and an analogous characterisation is given for algebras of quotient-bounded operators on a locally convex space. Pseudocomplete l.m.c. algebras are characterised in terms of the completeness of these subalgebras, and the equivalence of this condition with the pseudocompleteness of the quotient-bounded operator algebras established. The scalar multiples of the identity in a unital l.m.c. algebra are characterised in terms of certain boundedness conditions.
On the concept of length in the sense of Lausch-Nöbauer and its generalizations
Authors: Eigenthaler Günther , Wiesenbauer Johann 
Published: April 2009

AbstractIn this paper the concept of length as defined for groups by Lausch–Nöbauer in their book Algebra of Polynomials (North Holland, Amsterdam, 1973) is generalized in several ways. It turns out that the main results of Lausch-Nöbauer concerning it remain valid for this generalization.
An infinite family of Williamson matrices
Authors: Spence Edward 
Published: April 2009

AbstractIn this paper the following result is proved. Suppose there exists a C-matrix of order n + 1. Then if n≡1 (mod 4) there exists a Hadamard matrix of order 2nr(n + 1), while if n≡3 (mod 4) there exists a Hadamard matrix of order nr(n + 1) for all r ≧0. If n≡1 (mod 4) is a prime power, the method is adapted to prove the existence of a Hadamard matrix of the Williamson type, of order 2nr(n + 1), for all r ≧0.
On the enumeration of homeomorphism classes of finite topologies
Authors: Krishnamurthy V. 
Published: April 2009

AbstractAn algorithm called UNLABEL is devised to uniquely label an unlabelled transitive digraph. This is used to construct a one-one correspondence between homeomorphism classes of finite nondiscrete To-topologies and certain generalised Young tableaux of shape-type α. For sets of cardinality 2, 3, 4 and 5 these classes are enumerated and classified in several ways. The notion of a generalised descriptor graph is then introduced to enumerate the homeomorphism classes of all topologies on these sets.
Starter-adder methods in the construction of Howell designs
Authors: Anderson B. A. , Gross K. B. 
Published: April 2009

AbstractThe powerful starter-adder theorems for constructing Howell Designs are improved and consequently many types of Howell Designs that previously could only be constructed by multiplicative techniques are shown amenable to a modified starter-adder method. The existence question for Howell Designs of many new types H(s, 2n) is settled affirmatively. For prime powers pn, p ≧ 7, we reduce the entire existence question for designs of type H*(pn, 2r), pn + 1 ≦ 2r ≦ 2pn to the corresponding question for designs of type H*(p, 2m), p + 1 ≦ 2m≦2p. If these designs exist, s has no prime divisors ≤ 7 and t odd is “close” to 1, a design H * (s, s + t) is shown to exist.
On tensor product graphs
Authors: Sampathkumar E. 
Published: April 2009

AbstractThe tensor product G ⊕ H of graphs G and H is the graph with point set V(G) × V(H) where (υ1, ν1) adj (υ2, ν2) if, and only if, u1 adj υ2 and ν1 adj ν2. We obtain a characterization of graphs of the form G ⊕ H where G or H is K2.
Closed subalgebras of homogeneous Banach algebras
Authors: Tseng Ching-Nan , Wang Hawi-Chiuan 
Published: April 2009

AbstractRudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.
Embedding the affine complement of three intersecting lines in a finite projective plane
Authors: Mullin R. C. , Singhi N. M. , Vanstone S. A. 
Published: April 2009

AbstractAn (r, 1)–design is a pair (V, F) where V is a v–set and F is a family of non-null subsets of V (b in number) which satisfy the following. (1) Every pair of distinct members of V is contained in precisely one member of F. (2) Every member of V occurs in precisely r members of F. A pseudo parallel complement PPC(n,α) is an (n + 1, 1)–design with v = n2 – αn and b ≦ n2 + n − α in which there are at least n – α a blocks of size n. A pseudo intersecting complement PIC(n, α) is an (n + 1, 1)–design with v = n2 − αn + α − 1 and b ≦ n2 + n – α in which there are at least n − α + 1 blocks of size n − 1. It has previously been shown that for α ≧ 4, every PIC(n, α) can be embedded in a PPC(n, α − 1) and that for n > (α4 − 2α3 + 2α2 + α − 2)/2, every PPC(n, α) can be embedded in a finite projective plane of order n. In this paper we investigate the case of α = 3 and show that any PIC(n, 3) is embeddable in a PPC(n,2) provided n ≥ 14.
Semilattices with a transitive automorphism group
Authors: Pastijn F. 
Published: April 2009

AbstractIf L is any semilattice, let TL denote the Munn semigroup of L, and Aut (L) the automorphism group of L.We show that every semilattice L can be isomorphically embedded as a convex subsemilattice in a semilattice L' which has a transitive automorphism group in such a way that (i) every partial isomorphism α of L can be extended to an automorphism of L', (ii) every partial isomorphism: α: eL → fL of L can be extended to a partial isomorphism αL′: eL′ → fL′ of L′ such that TL → TL′, α → αL′ embeds TL' isomorphically in TL′, (iii) every automorphism γ of L can be extended to an automorphism γL′ of L′ such that Aut (L) → Aut (L′), γ → γL embeds Aut (L) isomorphically in Aut (L′).
An inequality from applied probability
Authors: Henderson W. 
Published: April 2009

AbstractJ. F. C. Kingman (1967) proved that if {φn}, n = 1, 2, …, N is any set of Radon-Nikodym derivatives of λn w.r.t. μn, when λn, μn are the restrictions of λ, μ respectively to a sub σ-algebra Gn of G then where bn ≧ 0 ∀n and .
Monodromy in local groups
Authors: Atkin C. J. 
Published: April 2009

AbstractA monodromy theorem for homomorphisms of local groups into groups is proved. It follows that under suitable conditions the universal group of the local group depends only on the germ of the local group (up to natural isomorphism).1980 Mathematics subject classification (Amer. Math. Soc.): 22 E 05.
Local and global extrema for functions of several variables
Authors: Calvert Bruce , Vamanamurthy M. K. 
Published: April 2009

AbstractLet p: R2 → R be a polynomial with a local minimum at its only critical point. This must give a global minimum if the degree of p is < 5, but not necessarily if the degree is ≥ 5. It is an open question what the result is for cubics and quartics in more variables, except cubics in three variables. Other sufficient conditions for a global minimum of a general function are given.1980 Mathematics subject classification (Amer. Math. Soc.): 26 B 99, 26 C 99.
Thue's equation over function fields
Authors: Schmidt Wolfgang M. 
Published: April 2009

AbstractSuppose we are given a “Thue equation” f(x, y) = 1, where f is a binary form with coefficients in a function field K of characteristic zero. A typical result is that if f is of degree at least 5 and has no multiple factors, then every solution x = (x, y) of the equation with components in K has H(x)≤90H(f) + 250g. Here g is the genus of K and H(x), H(f) are suitably defined heights. No assumption is made that x be “integral” in some sense. As an application, bounds are derived for “integral” solutions of hyperelliptic equations over K.
Simultaneous approximation of numbers connected with the exponential function
Authors: Waldschmidt Michel 
Published: April 2009

AbstractWe give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo|+ |ea– ξ1|, whereais any non-zero complex number, and ξ are two algebraic numbers. We also improve the estimate of the so-called Franklin Schneider theorem concerning |b– ξ | + |a– ξ | + |ab– ξ. We deduce these results from an estimate for linear forms in logarithms.
Weak compactness of Fréchet-derivatives: application to composition operators
Authors: Dierolf Peter , Voigt Jürgen 
Published: April 2009

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.
An extremal problem in graph theory II
Authors: Abbott H. L. , Katchalski M. , Liu A. C. 
Published: April 2009

AbstractWe contine our study of the following combinatorial problem: What is the largest integer N = N (t, m, p) for which there exists a set of N people satisfying the following conditions: (a) each person speaks t languages, (b) among any m people there are two who speak a common language and (c) at most p speak a common language. We obtain bounds for N(t, m, p) and evaluate N(3, m, p) for all m and infintely many values of p.
Positive values of inhomogeneous 5-ary quadratic forms of type (3, 2)
Authors: Hans-Gill R. J. , Raka Madhu 
Published: April 2009

AbstractLet Q(x, y, z, t, u) be a real indefinite 5-ary quadratic form of type (3,2) and determinant D(> 0). Then given any real numbers x0, y0, z0, t0, u0 there exist integers x, y, z, t, u such that 0 < Q(x+x0,y+y0,z+z0,t+t0,u+u0)≦(16D)1/5. All the critical forms are also determined.
Maximal subfields of algebraically closed fields
Authors: Guralnick Robert M. , Miller Michael D. 
Published: April 2009

AbstractLet K be an algebraically closed field of characteristic zero, and S a nonempty subset of K such that S Q = Ø and card S < card K, where Q is the field of rational numbers. By Zorn's Lemma, there exist subfields F of K which are maximal with respect to the property of being disjoint from S. This paper examines such subfields and investigates the Galois group Gal K/F along with the lattice of intermediate subfields.
Regular semigroups, fundamental semigroups and groups
Authors: McAlister D. B. 
Published: April 2009

AbstractIn this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ:S→Tbetween regular semigroups. This is a mapping such that (ab)θ ≦ aθ bθin the natural partial order onT.
Random Fourier series on compact abelian hypergroups
Authors: Fournier John J. F. , Ross Kenneth A. 
Published: April 2009

AbstractRandom Fourier series are studied for a class of compact abelian hypergroups. The randomizing factors are assumed to be independent and uniformly subgaussian. In the presence of a natural teachnical hypothesis, an entropy condition of Dudley is shown to be sufficient for almost sure continuity. The classical results on almost sure membership in Lp, where p < ∞, are generalized to this setting. As an application, it is shown that a simple condition on the dual object implies that the de Leeuw-Kahane-Katznelson phenomenon occurs. Another application is the analogue of a classical sufficient condition for almost sure continuity. Examples illustrating the general theory are given for the hypergroup of conjugacy classes of SU(2) and for a class of compact countable hypergroups.
The Lindelöf degree of scattered spaces and their products
Authors: Gewand Marlene E. 
Published: April 2009

AbstractDifferent methods are used to show that a finite or countable product of Lindelöf scattered spaces is Lindelöf. Also, a technique of Kunen is modified to yield results concerning the Lindelöf degree of the Gδ and Gα-topologies on the countable product of compact scattered spaces.
Maps on D1 and D2 spaces
Authors: Potoczny H. B. 
Published: April 2009

AbstractA space X is said to be D1 provided each closed set has a countable basis for the open sets containing it. It is said to be D2 provided there is a countable base {Un} such that each closed set has a countable base for the open sets containing it, which is a subfamily of {Un}. In this paper, we give a separation theorem for D1 spaces, and provide a characterization of D1 and D2 spaces in terms of maps.
A Commutativity theorem for semiprime rings
Authors: Gupta Vishnu 
Published: April 2009

AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.
Orthodox semirings and rings
Authors: Zeleznikow John 
Published: April 2009

AbstractWe show that in a regular ring (R, +, ·), with idempotent setE, the following conditions are equivalent: (i)(ii) (R, ·) is orthodox. (iii) (R, ·) is a semilattice of groups. These and other conditions are also considered for regular semigroups, and for semirings (S, +, · ), in which (S, +) is an inverse semigroup. Examples are given to show that they are not equivalent in these cases.
Coextensions of pseudo-Inverse semigroups by rectangular bands
Authors: Meakin John 
Published: April 2009

AbstractWe say that a regulär semigroup S is a coetension of a (regular) semigroup T by rectangular bands if there is a homomorphism ϕ: S → T from S onto T such that, for each e = e2 ∈ S, e(ϕ ϕ-1) is a rectangular band. Regular semigroups which are coextesions of pseudo-inverse semigroups by rectangular bands may be characterized as those regular semigroups S with the property that, for each e = e2 ∈ S, ω(e) = {f = f2 ∈ S: ef = f} and ωl(e) = {f = f2 ∈ S: fe = f} are bands: this paper is concerned with a study of such semigroups.
Orthomorphisms of a commutative W*-algebra
Authors: Dodds P. G. 
Published: April 2009

AbstractIf M is a commutative W*-algebra of operators and if ReM is the Dedekind complete Riesz space of self-adjoint elements of M, then it is shown that the set of densely defined self-adjoint transformations affiliated with ReM is a Dedekind complete, laterally complete Riesz algebra containing ReM as an order dense ideal. The Riesz algebra of densely defined orthomorphisms on ReM is shown to coincide with , and via the vector lattice Randon-Nikodym theorem of Luxemburg and Schep, it is shown that the lateral completion of ReM may be identified with the extended order dual of ReM.
Biordered sets are biordered subsets of idempotents of semigroups
Authors: Easdown David 
Published: April 2009

AbstractA new arrow notation is used to describe biordered sets. Biordered sets are characterized as biordered subsets of the partial algebras formed by the idempotents of semigroups. Thus it can be shown that in the free semigroup on a biordered set factored out by the equations of the biordered set there is no collapse of idempotents and no new arrows.