bluuebunny/crossref_metadata_2025_split huggingface dataset:
Rigidity of Decomposition laws and number fields
Authors: Klingen Norbert 
Published: April 2009

AbstractWe speak of rigidity, if partial information about the prime decomposition in an extension of number fields K¦k determines the decomposition law completely (and hence the zeta function ζK), or even fixes the field K itself. Several concepts of rigidity, depending on the degree of information we start from, are introduced and studied. The strongest concept (absolute rigidity) was only known to hold for the ground field and all quadratic extensions. Here a complete list of all Galois quartic extensions which are absolutely rigid is given. For the weaker concept of rigidity, all rigid situations among the fields of degree up to 8 are determined.
A dual approach to embedding the complement of two lines in a finite projective plane
Authors: Batten Lynn Margaret 
Published: April 2009

AbstractLet S be a finite linear space on v ≥ n2 –n points and b = n2+n+1–m lines, m ≧ 0, n ≧ 1, such that at most m points are not on n + 1 lines. If m ≧ 1, except if m = 1 and a unique point on n lines is on no line with two points, then S embeds uniquely in a projective plane of order n or is one exceptional case if n =4. If m ≦ 1 and if v ≧ n2 – 2√n + 3, + 6, the same conclusion holds, except possibly for the uniqueness.1991 Mathematics subject classification (Amer. Math. Soc.) 05 B 05, 51 E 10.
Congruence networks for completely simple semigroups
Authors: Petrich Mario 
Published: April 2009

AbstractThe operators K, k, T and t are defined on the lattice of congruences on a Rees matrix semigroup S as follows. For ρ ∈ (S), ρK and ρk (ρT and ρt) are the greatest and the least congruences with the same kernel (trace) as ρ, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence ρ ∈ (S) and the lattice generated by it. The latter is then represented by generators and relations.
A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold
Authors: Carreras Francisco J. , Giménez Fernando , Miquel Vicente 
Published: April 2009

AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.
Lattice-ordered power series fields
Authors: Redfield R. H. 
Published: April 2009

AbstractA lattice-ordered power series algebra of a totally ordered field over a rooted abelian group may be constructed in a way that is arbitrary only in requiring that a factor set be chosen in the field and an extended total order be chosen on the group modulo its torsion subgroup. The resulting algebra is a field if and only if the subalgebra of elements with torsion support form a field. It follows that if the torsion subgroup may be independently embedded in the algebraic closure of the totally ordered field, or if the resulting algebra has no zero-divisors, then the algebra is a field. The set of supporting subsets for the power series may be characterized abstractly in such a way that previous representation theorems of lattice-ordered fields into power series algebras may be applied to produce representations into power series fields.
The lattice of ideals of MR(R2)Ra commutative pir
Authors: Maxson C. J. , Van Wyk L. 
Published: April 2009

AbstractIn this paper we characterize the ideals of the centralizer near-ring N = MR(R2), where R is a commutative principle ideal ring. The characterization is used to determine the radicals Jυ(N) and the quotient structures N/ Jv(N), v = 0, 1, 2.
On the spectrum of C1 as an operator on bv0
Authors: Okutoyi J. I. 
Published: April 2009

AbstractIn 1985 John Reade determined the spectrum of C1 regarded as an operator on the space c0 of all null sequences normed by ║x║ = supn≧0|xn|. It is the purpose of this paper to determine the spectrum of C1 regarded as an operator on the space bv0 of all sequences x such that xk → 0 as k → ∞ and .
Preorders on canonical families of modules of finite length
Authors: Fixman Uri , Okoh Frank 
Published: April 2009

AbstractLet R be an artinian ring. A family, ℳ, of isomorphism types of R-modules of finite length is said to be canonical if every R-module of finite length is a direct sum of modules whose isomorphism types are in ℳ. In this paper we show that ℳ is canonical if the following conditions are simultaneously satisfied: (a) ℳ contains the isomorphism type of every simple R-module; (b) ℳ has a preorder with the property that every nonempty subfamily of ℳ with a common bound on the lengths of its members has a smallest type; (c) if M is a nonsplit extension of a module of isomorphism type II1 by a module of isomorphism type II2, with II1, II2 in ℳ, then M contains a submodule whose type II3 is in ℳ and II1 does not precede II3. We use this result to give another proof of Kronecker's theorem on canonical pairs of matrices under equivalence. If R is a tame hereditary finite-dimensional algebra we show that there is a preorder on the family of isomorphism types of indecomposable R-modules of finite length that satisfies Conditions (b) and (c).
The second dual of C0 (S, A)
Authors: Choy Stephen T. L. , Wong James C. S. 
Published: April 2009

AbstractThe second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.
Twisted crossed products by coactions
Authors: Phillips John , Raeburn Iain 
Published: April 2009

AbstractWe consider coactions of a locally compact group G on a C*-algebra A, and the associated crossed product C*-algebra A× G. Given a normal subgroup N of G, we seek to decompose A× G as an iterated crossed product (A× G/ N) × N, and introduce notions of twisted coaction and twisted crossed product which make this possible. We then prove a duality theorem for these twisted crossed products, and discuss how our results might be used, especially when N is abelian.
Harmonic analysis for groups acting on triangle buildings
Authors: Cartwright Donald I. , MŁotkowski Wojciech 
Published: April 2009

AbstractLet Δ be a thick building of type Ã2, and letbe its set of vertices. We study a commutative algebraof ‘averaging’ operators acting on the space of complex valued functions on. This algebra may be identified with a space of ‘biradial functions’ on, or with a convolution algebra of bi-K-invariant functions onG, ifGis a sufficiently large group of ‘type-rotating’ automorphisms of Δ, andKis the subgroup ofGfixing a given vertex. We describe the multiplicative functionals onand the corresponding spherical functions. We consider theC*-algebra induced byonl2, find its spectrum Σ, prove positive definiteness of a kernelkzfor eachz∈ Σ, find explicity the spherical Plancherel formula for any groupGof type rotating automorphisms, and discuss the irreducibility of the unitary representations appearing therein. For the class of buildings ΔJarising from the groups ΓJintroduced in [2], this involves proving that the weak closure ofis maximal abelian in the von Neumann algebra generated by the left regular representation of ΓJ.
Linear operators in l2 with a universality property
Authors: Edelstein Michael , Holmes Raymond D. 
Published: April 2009

AbstractA collection P of bounded linear operators in l2 is constructed in such a manner that given any separable metric space X, and any countable collection F of continuous self-maps of X, there is a homeomorphism h of X onto a subset of l2 such that for each f ∈ F there is P ∈ P with hf = Ph.While similar results were obtained by Baayen and Dc Groot, our construction makes it possible to impose additional conditions on h (depending on F). For example, if all the members of F are uniformly continuous then h too can be made uniformly continuous.
Coherent Monoids
Authors: Gould Victoria 
Published: April 2009

AbstractThis paper is concerned with a new notion of coherency for monoids. A monoid S is right coherent if the first order theory of right S-sets is coherent; this is equivalent to the property that every finitely generated S-subset of every finitely presented right S-set is finitely presented. If every finitely generated right ideal of S is finitely presented we say that S is weakly right coherent. As for the corresponding situation for modules over a ring, we show that our notion of coherency is related to products of flat left S-sets, although there are some marked differences in behaviour from the case for rings. Further, we relate our work to ultraproducts of flat left S-sets and so to the question of axiomatisability of certain classes of left S-sets.We show that a monoid S is weakly right coherent if and only if the right annihilator congruence of every element is finitely generated and the intersection of any two finitely generated right ideals is finitely generated. A similar result describes right coherent monoids. We use these descriptions to recognise several classes of (weakly) right coherent monoids. In particular we show that any free monoid is weakly right (and left) coherent and any free commutative monoid is right (and left) coherent.
Total chromatic number of graphs of high degree, II
Authors: Yap H. P. , Chew K. H. 
Published: April 2009

AbstractWe prove Theorem 1: suppose G is a simple graph of order n having Δ(G) = n − k where k ≥ 5 and n ≥ max (13, 3k −3). If G contains an independent set of k − 3 vertices, then the TCC (Total Colouring Conjecture) is true. Applying Theorem 1, we also prove that the TCC is true for any simple graph G of order n having Δ(G) = n −5. The latter result together with some earlier results confirm that the TCC is true for all simple graphs whose maximum degree is at most four and for all simple graphs of order n having maximum degree at least n − 5.
The Toeplitz operator proof of noncommutative Bott periodicity
Authors: Phillips N. Christopher 
Published: April 2009

AbstractWe adapt the Toeplitz operator proof of Bott periodicity to give a short direct proof of Bott periodicity for the representable K-theory of σ-C*-algebras. We further show how the use of this proof and the right definitions simplifies the derivation of the basic properties of representable K-theory.
On pairwise paracompactness
Authors: Ganster M. , Reilly I. L. 
Published: April 2009

AbstractThis paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.
Embeddings of quaternion space in S4
Authors: Katanaga Atsuko , Saeki Osamu 
Published: April 2009

AbstractConsider a (real) projective plane which is topologically locally flatly embedded in S4. It is known that it always admits a 2-disk bundle neighborhood, whose boundary is homeomorphic to the quaternion space Q, the total space of the nonorientable S1-bundle over RP2 with Euler number ± 2, with fundamental group isomorphic to the quaternion group of order eight. Conversely let f: Q → S4 be an arbitrary locally flat topological embedding. Then we show that the closure of each connected component of S4 − f(Q) is always homeomorphic to the exterior of a topologically locally flatly embedded projective plane in S4. We also show that, for a large class of embedded projective planes in S4, a pair of exteriors of such embedded projective planes is always realized as the closures of the connected components of S4 − f(Q) for some locally flat topological embedding f: Q → S4.
Non-expansive derived horseshoes
Authors: Sakai Kazuhiro 
Published: April 2009

AbstractFor a two parameter family of C3 diffeomorphisms having a homoclinic orbit of tangency derived from a horseshoe, the relationship between the measure of the parameter values at which the diffeomorphism (restricted to a certain compact invariant set containing the horseshoe) is not expansive and the Hausdorff dimension of the horseshoe associated to the homoclinic orbit of tangency is investigated. This is a simple application of the Newhouse-Palis-Takens-Yoccoz theory.
Time-isolated Singularities of Temperatures
Authors: Watson Neil A. 
Published: April 2009

AbstractWe study singularities of solutions of the heat equation, that are not necessarily isolated but occur only in a single characteristic hyperplane. We prove a decomposition theorem for certain solutions on D+ = D ∩ (Rn × ]0. ∞[), for a suitable open set D, with singularities at compact subset K of Rn × {0}, in terms of Gauss-Weierstrass integrals. We use this to prove a representation theorem for certain solutions on D+, with singularities at K, as the sums of potentials and Dirichlet solutions. We also give conditions under which K is removable for solutions on D∖K.
Extensions of G-posets and Quillen's complex
Authors: Segev Yoav , Webb Peter 
Published: April 2009

AbstractWe develop techniques to compute the homology of Quillen's complex of elementary abelian p-subgroups of a finite group in the case where the group has a normal subgroup of order divisible by p. The main result is a long exact sequence relating the homologies of these complexes for the whole group, the normal subgroup, and certain centralizer subgroups. The proof takes place at the level of partially-ordered sets. Notions of suspension and wedge product are considered in this context, which are analogous to the corresponding notions for topological spaces. We conclude with a formula for the generalized Steinberg module of a group with a normal subgroup, and give some examples.
Numerical Range of the Derivation of an Induced Operator
Authors: Holmes Randall R. , Li Chi-Kwong , Tam Tin-Yau 
Published: April 2009

AbstractLet V be an n–dimensional inner product space over , let H be a subgroup of the symmetric group on {l,…, m}, and let x: H → be an irreducible character. Denote by (H) the symmetry class of tensors over V associated with H and x. Let K (T) ∈ End((H)) be the operator induced by T ∈ End(V), and let DK(T) be the derivation operator of T. The decomposable numerical range W*(DK(T)) of DK(T) is a subset of the classical numerical range W(DK(T)) of DK(T). It is shown that there is a closed star-shaped subset of complex numbers such that⊆ W*(DK(T)) ⊆ W(DK(T)) = con where conv denotes the convex hull of . In many cases, the set is convex, and thus the set inclusions are actually equalities. Some consequences of the results and related topics are discussed.
Distance to the convex hull of an orbit under the action of a compact Lie group
Authors: Holmes Randall R. , Tam Tin-Yau 
Published: April 2009

AbstractFor a real vector space V acted on by a group K and fixed x and y in V, we consider the problem of finding the minimum (respectively, maximum) distance, relative to a K-invariant convex function on V, between x and elements of the convex hull of the K-orbit of y. We solve this problem in the case where V is a Euclidean space and K is a finite reflection group acting on V. Then we use this result to obtain an analogous result in the case where K is a maximal compact subgroup of a reductive group G with adjoint action on the vector component ρ of a Cartan decomposition of Lie G. Our results generalize results of Li and Tsing and of Cheng concerning distances to the convex hulls of matrix orbits.
On Pascal ovals
Authors: Fernandes Olga 
Published: April 2009

AbstractIn this paper we prove that if an oval in a finite projective plane of order n ≡ 3 (mod 4) has the four point Pascal property and if each of its tangents and secants has the five point Pascal property, then the plane is Pappian and the oval is a conic.We also establish results concerning Ostrom conics and ovals with the three point and four point Pascal properties.
Periodic and fixed point theorems in a quasi-metric space
Authors: Ćirić Ljubomir 
Published: April 2009

AbstractGeneral periodic and fixed point theorems are proved for a class of self maps of a quasi-metric space which satisfy the contractive definition (A) below. Two examples are presented to show that the class of mappings which satisfy (A) is indeed wider than a class of selfmaps which satisfy Caristi's contractive definition (C) below. Also a common fixed point theorem for a pair of maps which satisfy a contractive condition (D) below is established.
On the number of real roots of a random algebraic equation
Authors: Pratihari D. , Panda R. K. , Pattanaik B. P. 
Published: April 2009

AbstractLet Nn(ω) be the number of real roots of the random algebraic equation Σnv = 0 avξv (ω)xv = 0, where the ξv(ω)'s are independent, identically distributed random variables belonging to the domain of attraction of the normal law with mean zero and P{ξv(ω) ≠ 0} > 0; also the av 's are nonzero real numbers such that (kn/tn) = 0(log n) where kn = max0≤v≤n |av| and tn = min0≤v≤n |av|. It is shown that for any sequence of positive constants (εn, n ≥ 0) satisfying εn → 0 and ε2nlog n → ∞ there is a positive constant μ so that for all n0 sufficiently large.
Minimal ideals in near-rings and localized distributivity conditions
Authors: Birkenmeier Gary , Heatherly Henry 
Published: April 2009

AbstractLetB, S, andTbe subsets of a (left) near-ringRwithBandTnonempty. We sayBis (S, T)-distributiveifs(b1+b2)t=sb1t+sb2t, for eachs∈S,b1,2∈B,t∈T. Basic properties for this type of ‘localized distributivity’ condition are developed, examples are given, and applications are made in determining the structure of minimal ideals.Theorem. IfIis a minimal ideal ofRandIkis (Im,In)-distributive for somek,n≧ 1,m≧ 0, then eitherI2= 0 orIis a simple, nonnilpotent ring with every element ofIdistributive inR. Theorem. LetRkbe (Rm,Rn)-distributive, for somek,n≧ 1, m ≧ 0; ifRis semiprime or is a subdirect product of simple near-rings, thenRis a ring. Connections are established with near-rings which satisfy a permutation identity and with weakly distributive near-rings. IfR→A→ 0 is an exact sequence of near-rings, then conditions onAare given which will impose conditions on the minimal ideals ofR.
Full coactions on Hilbert C*-modules
Authors: Bui Huu Hung 
Published: April 2009

AbstractWe introduce a natural notion of full coactions of a locally compact group on a Hilbert C*-module, and associate each full coaction in a natural way to an ordinary coaction. We also introduce a natural notion of strong Morita equivalence of full coactions which is sufficient to ensure strong Morita equivalence of the corresponding crossed product C*-algebras.
Asymptotic properties of rooted 3-connected maps on surfaces
Authors: Bender Edward A. , Gao Zhicheng , Richmond L. Bruce , Wormald Nicholas C. 
Published: April 2009

AbstractIn this paper we obtain asymptotics for the number of rooted 3-connected maps on an arbitrary surface and use them to prove that almost all rooted 3-connected maps on any fixed surface have large edge-width and large face-width. It then follows from the result of Roberston and Vitray [10] that almost all rooted 3-connected maps on any fixed surface are minimum genus embeddings and their underlying graphs are uniquely embeddable on the surface.
The Appell transform and the semigroup property for temperatures
Authors: Kochneff Elizabeth , Sagher Yoram 
Published: April 2009

AbstractWe prove that if u(x, t) is a solution of the one dimensional heat equation and if A u(x, t) is its Appell transform, then u(x, t) has the semi-group (Huygens) property in a domain D if and only if A u(x, t) has the semi-group property in a dual region. We apply this result to simplify and extend some results of Rosenbloom and Widder.
Franel integrals of order four
Authors: McIntosh Richard J. 
Published: April 2009

AbstractLet ((x)) =x−⌊x⌋−1/2 be the swatooth function. Ifa, b, cand e are positive integeral, then the integral or ((ax)) ((bx)) ((cx)) ((ex)) over the unit interval involves Apolstol's generalized Dedekind sums. By expressing this integral as a lattice-point sum we obtain an elementary method for its evaluation. We also give an elementary proof of the reciprocity law for the third generalized Dedekind sum.
On the component group of the automorphism group of a Lie group
Authors: Chen P. B. , Wu T. S. 
Published: April 2009

AbstractLetGbe a Lie group,Gothe connected component ofGthat contains the identity, and AutGthe group of all topological automorphisms ofG. In the case whenG/Gois finite andGhas a faithful representation, we obtain a necessary and sufficient condition forGso that AutGhas finitely many components in terms of the maximal central torus inGo.
Rates of convergence to normality for samples from a finite set of random variables
Authors: John R. D. , Robinson J. 
Published: April 2009

AbstractRates of convergence to normality ofO(N-½) are obtained for a standardized sum ofmrandom variables selected at random from a finite set ofNrandom variables in two cases. In the first case, the sum is randomly normed and the variables are not restricted to being independent. The second case is an alternative proof of a result due to von Bahr, which deals with independent variables. Both results derive from a rate obtained by Höglund in the case of sampling from a finite population.
Laguerre geometries and some connections to generalized quadrangles
Authors: Brown Matthew R. 
Published: April 2009

AbstractA Laguerre plane is a geometry of points, lines and circles where three pairwise non-collinear points lie on a unique circle, any line and circle meet uniquely and finally, given a circle C and a point Q not on it for each point P on C there is a unique circle on Q and touching C at P. We generalise to a Laguerre geometry where three pairwise non-collinear points lie on a constant number of circles. Examples and conditions on the parameters of a Laguerre geometry are given.A generalized quadrangle (GQ) is a point, line geometry in which for a non-incident point, line pair (P. m) there exists a unique point on m collinear with P. In certain cases we construct a Laguerre geometry from a GQ and conversely. Using Laguerre geometries we show that a GQ of order (s. s2) satisfying Property (G) at a pair of points is equivalent to a configuration of ovoids in three-dimensional projective space.
A note on Beukers' integral
Authors: Hata Masayoshi 
Published: April 2009

AbstractThe aim of this note is to give a sharp lower bound for rational approximations to ζ(2) = π2/6 by using a specific Beukers' integral. Indeed, we will show that π2 has an irrationality measure less than 6.3489, which improves the earlier result 7.325 announced by D. V. Chudnovsky and G. V. Chudnovsky.
Regular skew group rings
Authors: Alfaro Ricardo , Ara Pere , Río Angel Del 
Published: April 2009

AbstractLet G be a group acting on a ring R. We study the problem of determining necessary and sufficient conditions in order that the skew group ring RG be von Neumann regular. Complete characterizations are given in some particular situations, including the case where all idempotents of R are central. For a regular ring R admitting a G-invariant pseudo-rank function N, with G finite, we obtain a necessary condition for RG being regular in terms of the induced action of G on the N-completion of R.