bluuebunny/crossref_metadata_2025_split huggingface dataset:
A construction for certain classes of supplementary difference sets
Authors: Cooper Joan 
Published: April 2009

AbstractLet ν = ef + 1 be a prime power, and consider G the cyclic group of order ν − 1 with e cosets Ci, of order f defined as Ci = {xej+i: 0 ≦ j ≦ f − 1} and 0 ≦ i ≦ e − 1, where x is a primitive element of GF(pα) and a generator of G. By using these cosets we give a simple construction for certain classes of Supplementary Difference Sets, Difference Sets, and Szekeres Difference Sets. These classes are not new, but the simple method of construction is original.
p-Groups with an Abelian Maximal Subgroup and Cyclic Center
Authors: Conlon S. B. 
Published: April 2009

AbstractAll such nonabelian finite p-groups are classified. They coincide with the class of nonabelian finite p-subgroups of GL(p, F), where F is a field, not of characteristic p, which contains all p power roots of 1, or agian with the class of all nonabelian finite subgroups of Zp= wr Zp. Various automorphism groups associated to them and their representations are calculated. Two such subgroups of GL(p, F) are conjugate as subgroups of GL(p, F) iff they are isomorphic.
The hulls of representablel-groups andf-rings
Authors: Conrad Paul 
Published: April 2009

A lattice-ordered group (“l-group”)Gwill be calledaP-groupifG=g″ ⊕g′ for eachg∈G(projectable)anSP-groupifG=C⊕C′ for each polarCofG(strongly projectable)anL-groupif each disjoint subset has a 1. u. b. (laterally complete)anO groupif it is both anL-groupand aP-group (orthocomplete).Gisrepresentableif it is anl-subgroup of a cardinal product of totally ordered groups. It follows that aP-group must be representable and henceSP-groups andO-groups are also representable.
On the value distribution of f2f(k)
Authors: Huang Xiaojun , Gu Yongxing 
Published: April 2009

AbstractIn this paper, we prove that for a transcendental meromorphic function f(z) on the complex plane, the inequality T(r, f) < 6N (r, 1/(f2 f(k)−1)) + S(r, f) holds, where k is a positive integer. Moreover, we prove the following normality criterion: Let ℱ be a family of meromorphic functions on a domain D and let k be a positive integer. If for each ℱ ∈ ℱ, all zeros of ℱ are of multiplicity at least k, and f2 f(k) ≠ 1 for z ∈ D, then ℱ is normal in the domain D. At the same time we also show that the condition on multiple zeros of f in the normality criterion is necessary.
U-Operators
Authors: Bernal-González L. , Prado-Tendero J. A. 
Published: April 2009

AbstractInspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Müller about the existence of universal entire functions with gap power series is also strengthened.
On the existence of sulutions of the equationLx∞Nxand a coincidence degree theory
Authors: Tarafdar E. , Teo Suat Khoh 
Published: April 2009

The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equationLx = NxwhereL: domL⊂X→Zis a linear Fredholm mapping of index zero andis a (possiblv nonlinear) mapping and Ω is a bounded open subset ofX, XandZbeing normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation, whereL: domL⊂X→Zis a linear Fredholm mapping of index zero,andX, Zand Ω are as above,CK(Z)being the set of compact convex subsets ofZ.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.
Free groups, symmetric and reduced products
Authors: Borges Carlos R. 
Published: April 2009

AbstractWe show that, for any Tychonoff space X with base point θ, the infinite symmetric product SP∞ X of X is a subspace of an abelian group A(X) generated by X. (This clarifies the continuity of the multiplication in SP∞ X.) Furthermore, SP∞ X is a retract of A(X). Analogous results hold for reduced product spaces, with respect to non-abelian groups.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 99; secondary 54 B 15.
Universal functions in several complex variables
Authors: Chee P. S. 
Published: April 2009

AbstractIt is proved that there exists a universal good inner function in the open unit polydisc Un, that is its non Euclidean translates are dense in the closed unit ball of H∞ (Un) and that there exists a universal function in the open unit ball Bn of Cn. These generalize Heins' result on universal Blaschke products.1980 Mathematics subject classification (Amer. Math. Soc.): primary 32 A 10.
Weak convergence on non-separable metric spaces
Authors: Pollard David 
Published: April 2009

AbstractFor certain problems in the weak convergence theory of probability measures on non-separable metric spaces it is convenient to consider measures defined on a σ-field B0 smaller than the Borel σ-field. A suitable theory has been developed by Dudley and Wichura. In this paper it is shown that some of the key results in that theory can be deduced directly from the better known weak convergence theory for Borel measures. This is achieved by a remetrization of the underlying space to make it separable. The σ-field B0 contains the new Borel σ-field and weak convergence in Dudley's sense becomes equivalent to convergence of restrictions of the measures to the latter σ-field.1980 Mathematics Subject Classification (Amer. Math. Soc.): primary 60 B 10, 60 B 05.
On semigroups and groups of local polynomial functions
Authors: Nöbauer Wilfried 
Published: April 2009

AbstractLet Zn be the factor ring of the integers mod n and t be a positive integer. In this paper some results are given on the structure of the semigroup of all mappings from Zn into Zn and on the structure of the group of all permutations on Zn, which, for any t elements, can be represented by a polynomial function. If n = ab and a, b are relatively prime, then this (semi)group is isomorphic to the direct product of the respective (semi)groups for a and b. Thus it is sufficient to consider only the case where n = pe, p being a prime. In this case it is proved, that the (semi)group is isomorphic to the wreath product of a certain sub(semi)group of the symmetric (semi)group on Zpe−1 by the symmetric (semi)group on Zp. Some remarks on these sub(semi)groups are given.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 B 99, 13 B 25.
Zero-set ultrafilters and Gδ-closures in uniform spaces
Authors: Curzer Howard , Hager Anthony W. 
Published: April 2009

AbstractThe paper examines the classes K1 and Γ1 of Hausdorff uniform spaces which are Gδ-closed in their Samuel compactifications, or completions. It is shown that the classes are epi-reflective, the reflections K1 and Γ are described, K1 and Γ1 are represented as epi-reflective hulls, membership in the classes is described by fixation of certain zero-set ultrafilters, and it is shown that k1 = Γ1 exactly on spaces without discrete sets of measurable power. The results include familiar facts about realcompact and topologically complete topological spaces and are closely connected with the theory of metric-fine uniform spaces.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 50, 54 E 15, 18 A 40; secondary 54 B 05, 54 B 10, 54 C 10, 54 C 30.
Covering a polygon with triangles: a Caratheodory-type theorem
Authors: Baker M. J. C. 
Published: April 2009

AbstractGeneralizations are proved for theorems of Carathéodory (1907), Kirchberger (1903) and Watson (1973), the theme of these results being how thickly the convex hull of a family of points is covered by simplexes whose vertices are chosen from the points of the family.Subject classification (Amer. Math. Soc. (MOS) 1970): 52A35.
Unambiguous evaluations of bidecic Jacobi and Jacobsthal sums
Authors: Evans Ronald J. 
Published: April 2009

AbstractFor a class of primes p ≡ 1 (mod 20) for which 2 is a quintic nonresidue, unambiguous evaluations of parameters of bidecic Jacobi and Jacobsthal sums (mod p) are presented, in terms of the partition p = a2+5b2+5c2+5d2, ab = d2–c2–cd. Similar results for sums of others orders have been obtained by E. Lehmer and by K. S. Williams.Subject classification (Amer. Math. Soc. (MOS) 1970): 10 G 05.
On two-bridged knot polynomials
Authors: Hartley R. I. 
Published: April 2009

AbstractThe extended diagram of a two-bridged knot is introduced, and it is shown how the coefficients of the Alexander polynomial of the knot may be read straight from this diagram. Using this result, it is shown by diagram manipulation that a conjecture of Fox about the coefficients of the Alexander polynomial of an alternating knot is true at least for two-bridged knots (which are all alternating).1980 Mathematics subject classification (Amer. Math. Soc.): 57 M 25.
Finitely presented groups of Fibonacci type. part II
Authors: Campbell Colin M. , Robertson Edmund F. 
Published: April 2009

AbstractA class of cyclically presented groups with n generators and n Fibonacci type relations is discussed. Conditions are given for these groups to be finite and metacyclic. With these conditions the presentations are reduced to the standard form for metacyclic groups with trivial Schur multiplicator. This enables certain ismorphisms between the groups to be found.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 F 05.
Cubic symmetric graphs of order twice an odd prime-power
Authors: Feng Yan-Quan , Kwak Jin Ho 
Published: April 2009

AbstractAn automorphism group of a graph is said to be s-regular if it acts regularly on the set of s-arcs in the graph. A graph is s-regular if its full automorphism group is s-regular. For a connected cubic symmetric graph X of order 2pn for an odd prime p, we show that if p ≠ 5, 7 then every Sylow p-subgroup of the full automorphism group Aut(X) of X is normal, and if p ≠3 then every s-regular subgroup of Aut(X) having a normal Sylow p-subgroup contains an (s − 1)-regular subgroup for each 1 ≦ s ≦ 5. As an application, we show that every connected cubic symmetric graph of order 2pn is a Cayley graph if p > 5 and we classify the s-regular cubic graphs of order 2p2 for each 1≦ s≦ 5 and each prime p. as a continuation of the authors' classification of 1-regular cubic graphs of order 2p2. The same classification of those of order 2p is also done.
Mappings on matrices: invariance of functional values of matrix products
Authors: Chan Jor-Ting , Li Chi-Kwong , Sze Nung-Sing 
Published: April 2009

AbstractLetMn, be the algebra of alln × nmatrices over a field F, wheren≧ 2. LetSbe a subset ofMncontaining all rank one matrices. We study mappings φ:S → Mn, such thatF(φ (A)φ (B)) =F(A B)for various families of functionsFincluding all the unitary similarity invariant functions on real or complex matrices. Very often, these mappings have the form A ↦ μ(A)S(σ (aij))S-1for allA= (aij) ∈Sfor some invertibleS ∈ Mn, field monomorphism σ of F, and an F*-valued mapping μ defined onS. For real matrices, σ is often the identity map; for complex matrices, σ is often the identity map or the conjugation map: z ↦ z. A key idea in our study is reducing the problem to the special case whenF:Mn→ {0, 1} is defined byF(X)= 0, ifX= 0, andF(X)= 1 otherwise. In such a case, one needs to characterize φ:S → Mnsuch that φ(A) φ (B) = 0 if and only ifAB= 0. We show that such a map has the standard form described above on rank one matrices inS.
A Dirichlet series expansion for the p-adic zeta-function
Authors: Delbourgo Daniel 
Published: April 2009

AbstractWe prove that the p-adic zeta-function constructed by Kubota and Leopoldt has the Dirichlet series expansion Where the convergence of the first summation is for the p-adic topology. The proof of this formula relates the values of p(–s, ω1+σ) for s ∈ Zp, with a branch of the ‘sth-fractional derivative’, of a suitable generating function.
Cotorsion modules and relative pure-injectivity
Authors: Mao Lixin , Ding Nanqing 
Published: April 2009

AbstractLet R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C) = 0 for any flat right R-module F. In this paper, we first characterize those rings satisfying the condition that every cotorsion right (left) module is injective with respect to a certain class of right (left) ideals. Then we study relative pure-injective modules and their relations with cotorsion modules.
Homomorphisms of the algebra of locally integrable functions on the half line
Authors: Grabiner Sandy 
Published: April 2009

AbstractLet φ be a continuous nonzero homomorphism of the convolution algebra L1loc(R+) and also the unique extension of this homomorphism to Mloc(R+). We show that the map φis continuous in the weak* and strong opertor topologies on Mloc, considered as the dual space of Cc(R+) and as the multiplier algebra of L1loc. Analogous results are proved for homomorphism from L1 [0, a) to L1 [0, b). For each convolution algebra L1 (ω1), φ restricts to a continuous homomorphism from some L1 (ω1) to some L1 (ω2), and, for each sufficiently large L1 (ω2), φ restricts to a continuous homomorphism from some L1 (ω1) to L1 (ω2). We also determine which continuous homomorphisms between weighted convolution algebras extend to homomorphisms of L1loc. We also prove results on convergent nets, continuous semigroups, and bounded sets in Mloc that we need in our study of homomorphisms.
Automatic continuity for Banach algebras with finite-dimensional radical
Authors: Pham Hung Le 
Published: April 2009

AbstractThe paper [3] proved a necessary algebraic condition for a Banach algebra A with finite-dimensional radical R to have a unique complete (algebra) norm, and conjectured that this condition is also sufficient. We extend the above theorem. The conjecture is confirmed in the case where A is separable and A/R is commutative, but is shown to fail in general. Similar questions for derivations are discussed.
Generalized Gaussian estimates and riesz means of Schrödinger groups
Authors: Blunck Sönke 
Published: April 2009

AbstractWe show that generalized Gaussian estimates for selfadjoint semigroups (e-tA)t∈ R+ onL2implyLpboundedness of Riesz means and other regularizations of the Schrödinger group (eitA)t∈ R. This generalizes results restricted to semigroups with a heat kernel, which are due to Sjöstrand, Alexopoulos and more recently Carron, Coulhon and Ouhabaz. This generalization is crucial for elliptic operators A that are of higher order or have singular lower order terms since, in general, their semigroups fail to have a heat kernel.
The weighted g-Drazin inverse for operators
Authors: Dajić A. , Koliha J. J. 
Published: April 2009

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29 (1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.
Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups
Authors: Dvurečenskij Anatolij 
Published: April 2009

AbstractWe introduce perfect effect algebras and we show that every perfect algebra is an interval in the lexicographical product of the group of all integers with an Abelian directed interpolation po-group. To show this we introduce prime ideals of effect algebras with the Riesz decomposition property (RDP). We show that the category of perfect effect algebras is categorically equivalent to the category of Abelian directed interpolation po-groups. Moreover, we prove that any perfect effect algebra is a subdirect product of antilattice effect algebras with the RDP.
On systems of diagonal forms
Authors: Knapp Michael P. 
Published: April 2009

AbstractIn this paper we consider systems of diagonal forms with integer coefficients in which each form has a different degree. Every such system has a nontrivial zero in every p-adic field Qp provided that the number of variables is sufficiently large in terms of the degrees. While the number of variables required grows at least exponentially as the degrees and number of forms increase, it is known that if p is sufficiently large then only a small polynomial bound is required to ensure zeros in Qp. In this paper we explore the question of how small we can make the prime p and still have a polynomial bound. In particular, we show that we may allow p to be smaller than the largest of the degrees.
Intersections of α-spaces
Authors: Fowler Northrup 
Published: April 2009

AbstractLet be an infinite r.e. repère, an infinite dimensional r.e. space such that ≦ L(). A condition is derived that is both necessary and sufficient for the existence of an infinite subset β ⊂ such that L(β)∪ is not an α-space. Examples which satisfy this condition are exhibited, proving that the class of α-spaces is not closed under intersections.
Delay differential equations of odd order satisfying property Pk
Authors: Terry Raymond D. 
Published: April 2009

AbstractThe property Pk(K = 0,1,…,n) is formulated. For k = 0, n this property reduces to conditions A and B defined by Kiguradze (1962) for a class of ordinary differential equations. Sufficient conditions are then given which guarentee that a class of delay differential equations of odd order possesses property Pk. The property PK is also seen to be useful in reducing the number of types of positve solutions of a related nonhomogeneous delay differential equation.
Rudin-Shapiro sequences for arbitrary compact groups
Authors: McMullen J. R. , Price J. F. 
Published: April 2009

AbstractLet G be a compact group. A sequence of functions in L∞ (G) is said to be a Rudin-Shapiro sequence (briefly, an RS-sequence) if the following conditions hold: (1) (2) (3) The main purpose here is to prove the following theorem: Theorem: Theorem. Let G be an infinite compact group. Then G has an RS-sequence consisting of trigonometric polynomials.
Some sequence spaces and almost convergence
Authors: Nanda Sudarsan 
Published: April 2009

AbstractIn this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper is to introduce the spaces of strongly almost summable sequences which happen to be complete paranormed spaces under certain conditions. Some topological results, characterisation of strongly almost regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed.
Hadamard matrices and submatrices
Authors: Vijayan K. 
Published: April 2009

AbstractShrinkande and Bhagwan Das (1970) showed how to extend a (4t – 1, 4t) row-orthogonal matrix with entries ± 1 to a Hadamard matrix of order 4t. Using a slightly different approach we consider extensions of (4t – k, 4t) row-orthogonal matrix to a Hadamard matrix of order 4t.
The Schur-Zassenhaus theorem in locally finite groups
Authors: Hartley B. 
Published: April 2009

AbstractLet L = HK be a semidirect product of a normal locally finite π′-group H by a locally finite π′-group K, where π, is a set of primes. Suppose CK(H) = 1 and L is Sylow π-sparse (which in the countable case just says that the Sylow π-subgroups of L are conjugate). This paper completes the characterization of those groups which can occur as K—this had previously been obtained under the assumption that L is locally soluble. The answer is the same—essentially that the groups occurring are those having a subgroup of finite index which is a subdirect product of so-called “pinched” groups.
A generalization of a theorem of Totten
Authors: Mullin R. C. , Vanstone S. A. 
Published: April 2009

AbstractAn (r, 1) system is 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.(i) Every pair of distinct members of V occur in precisely one member of F;(ii) Every member of V occurs in precisely r members of F.A pseudo parallel complement PPC(n, α) is an (n+1, 1) system with ν = n2 – αn and b ≦ n2 + n – α in which there are at least n – α blocks of size n. A pseudo intersection complement PIC (n, α) is an (n+1, 1) system with ν=n2 – αn + α – 1 b ≦ n2+n – α in which there are at least n – α+1 blocks of size n-1. It is 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 every PPC(n, α) can be embedded in a projective plant of order n. The latter generalizes a result of Totten (who proves the result for α = 1).
The subdirect decomposition theorem for classes of structures closed under direct limits
Authors: Caicedo Xavier 
Published: April 2009

AbstractBy a theorem of G. Birkhoff, every algebra in an equationally defined class of algebras K is a subdirect product of subdirectly irreducible algebras of K. In this paper we show that this result is true for any class of structures. not necessarily algebraic, closed under isomorphisms and direct limits. Quasivarieties in the sense of Malcev are examples of such classes of structures. This includes Birkhoffs result as a particular case.
Linear spaces with line range {n−1, n, n + 1} and at most n2 points
Authors: Batten Lynn Margaret 
Published: April 2009

AbstractWe characterize all finite linear spaces with p ≤ n2 points where n ≥ 8 for p ≠ n2 − 1 and n ≥ 23 for p = n2−1, and the line range is {n−1, n, n+1}. All such linear spaces are shown to be embeddable in finite projective planes of order a function of n. We also describe the exceptional linear spaces arising from p < n2−1 and n ≥ 4.
Random labelled trees and their branching networks
Authors: Grimmett G. R. 
Published: April 2009

AbstractA random rooted labelled tree on n vertices has asymptotically the same shape as a branching-type process, in which each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation. In this note we use this probabilistic representation to deduce the asymptotic distribution of the distance from the root to the nearest endertex other than itself.
Lattice-ordered modules of quotients
Authors: Steinberg Stuart A. 
Published: April 2009

AbstractLet Q be the ring of quotients of the f-ring R with respect to a positive hereditary torsion theory and suppose Q is a right f-ring. It is shown that if the finitely-generated right ideals of R are principal, then Q is an f-ring. Also, if QR is injective, Q is an f-ring if and only if its Jacobson radical is convex. Moreover, a class of po-rings is introduced (which includes the classes of commutative po-rings and right convex f-rings) over which Q(M) is an f-module for each f-module M.
C-Commutativity
Authors: Cheatham T. , Enochs E. 
Published: April 2009

AbstractAn associative ring R with identity is said to be c-commutative for c ∈ R if a, b ∈ R and ab = c implies ba = c. Taft has shown that if R is c-commutative where c is a central nonzero divisor]can be omitted. We show that in R[x] is h(x)-commutative for any h(x) ∈ R [x] then so is R with any finite number of (commuting) indeterminates adjoined. Examples adjoined. Examples are given to show that R [[x]] need not be c-commutative even if R[x] is, Finally, examples are given to answer Taft's question for the special case of a zero-commutative ring.