bluuebunny/crossref_metadata_2025 huggingface dataset:
The Poincaré Dual of a Geodesic Algebraic Curve in a Quotient of the 2-Ball
Authors: Kudla Stephen S. , Millson John J.
Published: December 2010

We shall consider an irreducible, non-singular, totally geodesic holomorphic curve N in a compact quotient M = Γ\D of the unit ball D = {(z, w):|z|2 + |w|2 < 1} in C2 with the Kahler structure provided by the Bergman metric. The main result of this paper is an explicit construction of the harmonic form of type (1,1) which is dual to N. Our construction is as follows. Let p:D → Γ\D be the universal covering map. Choose a component D1 in the inverse image of N under p. The choice of D1 corresponds to choosing an embedding of the fundamental group of N into Γ. We denote the image by Γ1. Let π : D → D1 be the fiber bundle obtained by exponentiating the normal bundle of D1 in D. Let μ be the volume form of D1.
Maximal Quotient Rings of Endomorphism Rings of E(RR)-Torsionfree Generators
Authors: Izawa Tatsuo
Published: December 2010

Let R be a ring with identity and let H = End (E(RR)) and Q = Dou(E(RR)) = End(HE(RR)). Then Lambek [11] showed that Q is always isomorphic to Qm(R), the maximal right quotient ring of R. And Johnson [10] and Wong-Johnson [26] proved that Qm(R) is regular and right self-injective if and only if R is right non-singular, and then H is isomorphic to Qm(R), too. Moreover, Sandomierski [18] showed that Qm(R) is semi-simple Artinian if and only if R is right finite dimensional and right non-singular. And it is well known that Qm(R) is a quasi-Frobenius ring if and only if E(RR) is a rational extension of RR and the ACC holds on right annihilators of subsets of E(RR).

The purpose of this paper is to give some module-theoretic generalizations of these results. Let PR be an E(PR)-torsionless generator, and let S = End(PR), H = End(E(PR)) and Q = Dou(E(PR)).
Diameters of Random Graphs
Authors: Klee Victor , Larman David
Published: December 2010

For two nodes x and y of a graph G, the distance δG(x,y) is the smallest integer k such that k edges form a path from x to y; δG(x, x) = 0, and δG(x,y) = ∞ when x ≠ y and there is no path from x to y. The diameter δG is the maximum of δG(x, y) as x and y range over the nodes of G. When G is connected, δ(G) is the smallest integer k such that any two nodes of G can be joined by a path formed from at most k edges. When G is not connected, δ(G) = ∞ and there is interest in δc(G), the maximum of δ(G) over the components C of G.

For 2 ≧ n < ∞ and 0 ≧ E ≧ n(n − l)/2, let denote the set of all loopless undirected graphs with the node-set {1, …, n} and exactly E edges.
Power-Rich and Power-Deficient LCA Groups
Authors: Khan M. A.
Published: December 2010

In [4], Edwin Hewitt denned a-rich LCA (i.e., locally compact abelian) groups and classified them by their algebraic structure. In this paper, we study LCA groups with some properties related to a-richness. We define an LCA group G to be power-rich if for every open neighbourhood V of the identity in G and for every integer n > 1, λ(nV) > 0, where nV = {nx ∈ G : x ∈ V} and λ is a Haar measure on G. G is power-meagre if for every integer n > 1, there is an open neighbourhood V of the identity, possibly depending on n, such that λ(nV) = 0. G is power-deficient if for every integer n > 1 and for every open neighbourhood V of the identity such that is compact, . G is dual power-rich if both G and Ĝ are power-rich. We define dual power-meagre and dual power-deficient groups similarly.
Compact Perturbations of Reflexive Algebras
Authors: Davidson Kenneth R.
Published: December 2010

In this paper we study lattice properties of operator algebras which are invariant under compact perturbations. It is easy to see that if and are two operator algebras with contained in , then the reverse inclusion holds for their lattices of invariant subspaces. We will show that in certain cases, the assumption thats is contained in , where is the ideal of compact operators, implies that the lattice of is “approximately” contained in the lattice of . In particular, supposed and are reflexive and have commutative subspace lattices containing “enough” finite dimensional elements. We show (Corollary 2.8) that if is unitarily equivalent to a subalgebra of , then there is a unitary operator which carries all “sufficiently large” subspaces in lat into lat .
Hypermetric Spaces and the Hamming Cone
Authors: Avis David
Published: December 2010

We denote by d = (d12, …, d1n, d23, …, dn-1,n) a vector of distances between n points. Such a vector d is called a metric if it satisfies the triangle inequalities

(1)

The set of all metrics on n points forms a convex polyhedral cone, the extremal properties of which are discussed in [4]. We will be concerned with a sub-cone that is spanned by metrics of the form

(2)

where t ≧ 0, V is a proper subset of {1, 2, …, n}; and the symbol ⊥ is used for “exclusive or”: i ⊥ j ∈ V means i ∈ V, j ∉ V or i ∉ V,j∉ V.
On Derivations Induced by p-Adic Fields
Authors: Heerema N. , Morrison T.
Published: December 2010

This paper is concerned with a question which occurs in [6, p. 346] and uses the notation of that article. Thus K ⊃ K0 are p-adic fields (p ≠ 2) with residue fields k ⊃ k0 and having respective rings of integers R ⊃ R0, G0 = G0(K/K0) is the group of inertial automorphisms of K over K0,I(K/K0) is the R module of integral derivations on K over K0 and Ī(K/K0) is the k space of derivations on k induced by I(K/K0). The question here dealt with is the following. Given fields k ⊃ k0 of characteristic p(≠0, 2) with k/k0 finitely generated, which subspaces of the k space, Der(k/k0), of derivations on k over k0 have the form Ī(K/K0) for some pair of p-adic fields K ⊃ K0 having k ⊃ k0 as residue fields. We note the following connection between Ī(K/K0) and G0(K/K0).
The Word Problem for Orthogroups
Authors: Gerhard J. A. , Petrich Mario
Published: December 2010

A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a-l for a ∈ S be the group inverse of a in the maximal subgroup of S to which a belongs. This unary operation satisfies the identities

(1)

(2)

(3)

In fact a completely regular semigroup can be defined as a unary semigroup (a semigroup with an added unary operation) satisfying these identities. An orthogroup can be characterized as a completely regular semigroup satisfying the additional identity

(4)
Systemes Fondamentaux D'Unites De Certains Composes De Deux Corps Quadratiques, I
Authors: Levesque Claude
Published: December 2010

Lorsque est un composé de deux corps quadratiques réels, nous pouvons calculer explicitement un système fondamental d'unités de L4 (cf. [3], [2] et [5]), en considérant les unités fondamentales η2, δ2 et ∈2 des trois sous-corps quadratiques L2, F2 et K2 de L4.
Locally Compact Hjelmslev Planes and Rings
Authors: Lorimer J. W.
Published: December 2010

Affine and projective Hjelmslev planes are generalizations of ordinary affine and projective planes where two points (lines) may be joined by (may intersect in) more than one line (point). The elements involved in multiple joinings or intersections are neighbours, and the neighbour relations on points respectively lines are equivalence relations whose quotient spaces define an ordinary affine or projective plane called the canonical image of the Hjelmslev plane. An affine or projective Hjelmslev plane is a topological plane (briefly a TH-plane and specifically a TAH-plane respectively a TPH-plane) if its point and line sets are topological spaces so that the joining of non-neighbouring points, the intersection of non-neighbouring lines and (in the affine case) parallelism are continuous maps, and the neighbour relations are closed.

In this paper we continue our investigation of such planes initiated by the author in [38] and [39].
Gyclotomic Division Algebras
Authors: Mollin R. A.
Published: December 2010

Let K be a field of characteristic zero. The Schur subgroup S(K) of Brauer group B(K) consists of those equivalence classes [A] which contain an algebra which is isomorphic to a simple summand of the group algebra KG for some finite group G. It is well known that the classes in S(K) are represented by cyclotomic algebras, (see [16]). However it is not necessarily the case that the division algebra representatives of these classes are themselves cyclotomic. The main result of this paper is to provide necessary and sufficient conditions for the latter to occur when K is any algebraic number field.

Next we provide necessary and sufficient conditions for the Schur group of a local field to be induced from the Schur group of an arbitrary subfield. We obtain a corollary from this result which links it to the main result. Finally we link the concept of the stufe of a number field to the existence of certain quaternion division algebras in S(K).
Elements of Spectral Theory for Generalized Derivations II : The Semifredholm Domain
Authors: Fialkow Lawrence A.
Published: December 2010

Let and denote infinite dimensional Hilbert spaces and let denote the space of all bounded linear operators from to . For A in and B in , let τAB denote the operator on defined by τAB(X) = AX – XB. The purpose of this note is to characterize the semi-Fredholm domain of τAB (Corollary 3.16). Section 3 also contains formulas for ind(τAB – λ). These results depend in part on a decomposition theorem for Hilbert space operators corresponding to certain “singular points” of the semi-Fredholm domain (Theorem 2.2). Section 4 contains a particularly simple formula for ind(τAB – λ) (in terms of spectral and algebraic invariants of A and B) for the case when τAB – λ is Fredholm (Theorem 4.2). This result is used to prove that (τBA) = –ind(τAB) (Corollary 4.3). We also prove that when A and B are bi-quasi-triangular, then the semi-Fredholm domain of τAB contains no points corresponding to nonzero indices.
On Reflexivity of Algebras
Authors: Radjabalipour Mehdi
Published: December 2010

For each natural number n we define to be the class of all weakly closed algebras of (bounded linear) operators on a separable Hilbert space H such that the lattice of invariant subspaces of and (alg lat )(n) are the same. (If A is an operator, A(n) denotes the direct sum of n copies of A; if is a collection of operators,. Also, alg lat denotes the algebra of all operators leaving all invariant subspaces of invariant.) In the first section we show that . In Section 2 we prove that every weakly closed algebra containing a maximal abelian self adjoint algebra (m.a.s.a.) is , and that . It is also shown that certain algebras containing a m.a.s.a. are necessarily reflexive.
A Subsemilattice of the Lattice of Varieties of Lattice Ordered Groups
Authors: Reilly Norman R.
Published: December 2010

Each variety of lattice ordered groups determines a variety of groups, namely the variety of groups generated by the groups i n . In this paper a completely new and different correspondence between varieties of groups and varieties of lattice ordered groups is developed. It is known that the variety of representable lattice ordered groups is defined by the law z+ Λ u-1z-u = 1. Here we consider the varieties defined by laws of this form where u is restricted to lie in some fully invariant subgroup of the free group Fx on a countable set X. All the varieties considered contain the variety of representable l-groups and therefore the free group with appropriate ordering.
Symbolic Powers of Regular Primes
Authors: Ishibashi Yasunori
Published: December 2010

In a recent paper [6], P. Seibt has obtained the following result: Let k be a field of characteristic 0, k[T1, … , Tr] the polynomial ring in r indeterminates over k, and let P be a prime ideal of k[T1, … , Tr]. Then a polynomial F belongs to the n-th symbolic power P(n) of P if and only if all higher derivatives of F from the 0-th up to the (n – l)-st order belong to P.

In this work we shall naturally generalize this result so as to be valid for primes of the polynomial ring over a perfect field k. Actually, we shall get a generalization as a corollary to a theorem which asserts: For regular primes P in a k-algebra R of finite type, a certain differential filtration of R associated with P coincides with the symbolic power filtration (P(n))n≧0.
Necessary Conditions for Universal
Interpolation in
Authors: Squires W. A.
Published: December 2010

Let be the space of Fourier transforms of distributions with compact support, or equivalently, the space of entire functions h satisfying the growth condition

(1)

where p(z) = |Imz| + log (1 + |z|2) and A, B are constants depending only on h. A sequence with |zk| ↑ ∞ is said to be a universal interpolation sequence for if for all such that

(2)

for constants A, B independent of k, there exists such that f(zk) = ak. In this note we will consider necessary conditions for universal interpolation in and more general subspaces of the entire functions.
Stability and Categoricity of Lattices
Authors: Smith Kenneth W.
Published: December 2010

This paper is a contribution to applied stability theory. Our purpose is to investigate the complexity of lattices by determining the stability of their first order theories.

Stability measures the complexity of a theory T by counting the number of different “kinds” of elements in models of T. The notion of ω-stability was introduced by Morley [26] in 1965 and generalized by Shelah [31] in 1969. Shelah classified all first order theories according to their stability properties.

Stability and -categoricity are closely related (see [26] and [1]). In fact, the notions of stable, superstable and ω-stable can be regarded as successive approximations of -categorical. -categoricity is a very strong property while stability, superstability and ω-stability facilitate the classification of more “complex” theories.
Modeles Bifiltres: Une Plaque Tournante en Homotopie Rationnelle
Authors: Felix Yves
Published: December 2010

A chaque c.w. complexe X, 1-connexe, de type fini, est associé une
algèbre différentielle graduée commutative (ΛZ, d) qui est un modèle dans le sens de Sullivan [10] et représente donc le type d'homotopie rationnelle de X.

ΛZ est munie d'une seconde graduation Z = ⊕q≧0Zq. La différentielle d se décompose alors sous la forme et d0(Zp) ⊂ (Λ2Z)p–1 et di(Zp) ⊂ Zp–i, i ≧ 1. En particulier d0 est purement quadratique tandis que di est du premier degré, i ≧ 1.

L'algèbre ΛZ et la partie quadratique d0 ne dépendent que des nombres de Betti de X. Les différents types d'homotopie rationnelle de nombres de Betti donnés sont donc paramétrés par les déformations di. La partie d1 exprime la structure multiplicative de l'algèbre de cohomologie rationnelle de X, les parties d2, d3, d4. … les structures algébriques plus complexes du type d'homotopie rationnelle.
Krull Semigroups and Divisor Class Groups
Authors: Chouinard II Leo G.
Published: December 2010

R. Matsuda has shown that a group ring is a Krull domain if and only if the coefficient ring is a Krull domain and the group is a torsion-free abelian group satisfying the ascending chain condition (ace) on cyclic subgroups [6]. D. F. Anderson has used this to obtain a partial determination of when a semigroup ring is a Krull domain, and under certain circumstances to describe the divisor class group of such a ring ([1], [2]). Using some of Anderson's techniques, but taking a different approach, we arrive at a complete answer of a different nature to these questions. We call a semigroup satisfying the major new conditions arising a Krull semigroup, and define its divisor class group.

In particular, every abelian group is the divisor class group of such a ring, and it follows that every abelian group is the divisor class group of a quasi-local ring, which seems to be a new result.
On the Homotopy Property of Nussbaum's Fixed Point Index
Authors: Fournier Gilles , Fournier Reine
Published: December 2010

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.

In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.
Root Systems and Cartan Matrices
Authors: Moody R. V. , Yokonuma T.
Published: December 2010

This paper is concerned with two things. The first is a (primarily) geometric axiomatic description for the systems of real roots of Lie algebras arising from (generalized) Cartan matrices. The description is base free and is a natural extension of the well-known axiomatic description of finite root systems. The primary component of our description is an open convex cone which, following Looijenga [3], we call the Tits cone. In fact it was Looijenga's paper that led to this axiomatic formulation. Unlike his construction, the dimension of the Tits cone is not tightly connected to the dimension of the Cartan matrix which it eventually yields. This leads us to the second part of the paper which concerns the construction of Cartan matrices of low row rank. We can show that if we have an l × l Cartan matrix of row rank n, then we can model an axiomatic description of it with a cone of dimension n + 1.
Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate
Authors: John David
Published: December 2010

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.

A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.
Primitive Generators for Algebras
Authors: Kochman Stanley O.
Published: December 2010

LetHbe a graded commutative algebra with a nice set of algebra generators. LetHalso be a comodule over a Hopf algebraA. In Section 2 we give conditions under which certain of these generators ofHcan be rechosen to be primitive. In addition we give explicit formulas expressing these primitive generators in terms of the original set of generators.

In Section 3 we apply the theory of Section 2 to the modphomology of the Thorn spectraMO, MUandMSp.In particular we give two explicit descriptions of the image of the Hurewicz homomorphism forMO.One of these makes explicit the recursive computation of E. Brown and F. Peterson [1].

In Section 4 we give a variation of the theory of Section 2 which computes primitive generators of certain Hopf algebras. This theory is applied to study the primitive elements ofH*(BU)andH*(SO;Z2).
Additivity of the Pn-Integral (2)
Authors: Cross G. E.
Published: December 2010

The problem of additivity of the Pn-integral on abutting intervals was considered in [2] and in [5]. It was noted in [2] that the necessary and sufficient conditions for additivity for the P2-integral obtained by Skvorcov in [5] could be completely generalized to the Pn-integral, n > 2, if a key lemma (corresponding to Skvorcov's Lemma 3 [6]) could be proved. We provide a proof of that lemma in this paper and hence obtain the general additivity result.

The definitions and notation of [2] are used in the following, except that we shall take the following as the definition of Pn-major and minor functions:

Definition 1.1. Let f(x) be a function defined in [a, b] and let a1, i = 1, 2, …, n, be fixed points such that a = a1 < a2 < … < an = b.
The Application of Lagrangian Methods to the Enumeration of Labelled Trees with Respect to Edge Partition
Authors: Goulden I. P. , Jackson D. M.
Published: December 2010

In an earlier paper [6] we considered the application of Lagrangian methods to the enumeration of plane rooted trees with given colour partition. We obtained an expression which generalised Tutte’s result [9], and a correspondence, which, when specialised, gives the de Bruijn-van Aardenne Ehrenfest-Smith-Tutte Theorem [1]. A corollary of these results is a one-to-one correspondence [4], between trees and generalised derangements, for which no combinatorial description has yet been found.

In this paper we extend these methods to the enumeration of rooted labelled trees to demonstrate how another pair of well-known and apparently unrelated theorems may be obtained as the result of a single enumerative approach. In particular, we show that a generalisation of Good's result [3], also considered by Knuth [7], and the matrix tree theorem [8] have a common origin in a single system of functional equations, and that they correspond to different coefficients in the power series solution.
Bounds on Betti Numbers
Authors: Ramras Mark
Published: December 2010

The Betti numbers βn(k) of the residue class field k = R/m of a commutative local ring (R, m) have been studied for about 20 years, primarily as the coefficients of the Poincaré series of E . Several authors have obtained results about the growth of the sequence {βn(k)}.For example, Gulliksen [3] showed that when R is non-regular, the sequence is non-decreasing. More recently, Avramov [1] studied asymptotic properties of {βn(k)} and found that under certain conditions the growth is exponential, i.e., there is a natural number p such that for all n, βpn(k) ≧ 2n.

In this paper, we examine the sequence {βn(M)} for arbitrary finitely generated non-free modules M over any commutative local artin ring R. We establish the following bounds:

1

2

3

where l(X) is the length of X.
Resolution D'Equations Associees a un Systeme de Tchebycheff
Authors: Dubuc Serge , Savoie Jean
Published: December 2010

Soit {f1(x),f2(x), …,fm(x)} un système de Tchebycheff de dimension m, c'est-à-dire les fonctions fj(x) sont des fonctions réelles continues définies sur un intervalle ouvert (a, b) et toute fonction de la forme admet au plus m — 1 racines dans (a, b) lorsqu'au moins un des coefficients Cj diffère de 0. Notre point de départ est un théorème dû à Krein [3]. On se limite au cas où la dimension m est paire, m = 2n. Ce théorème dit que la totalité Ω des points de R2n qui se représentent ainsi sont n points distincts de (a, b) et où pi > 0, 1 ≦ i≦n, forme effectivement un ouvert convexe de R2n. Les systèmes d'équations que nous voulons traiter sont justement les équations:

I
A Stickelberger Condition on Cyclic Galois Extensions
Authors: Childs L. N.
Published: December 2010

LetRbe a commutative ring,Ca finite abelian group,Sa Galois extension ofRwith groupC, in the sense of [1]. ViewingSas anRC-module defines the Picard invariant map [4] from the Harrison group Gal (R,C) of isomorphism classes of Galois extensions ofRwith groupCto CI (RC), the class group ofRC. The image of the Picard invariant map is known to be contained in the subgrouphCl (RC) of primitive elements of CI (RC) (for definition see below). Characterizing the image of the Picard invariant map has been of some interest, for the image describes the extent of failure of Galois extensions to have normal bases.

LetRbe the ring of integers of an algebraic number fieldK.
Semi-Prime Rings Whose Homomorphic Images are Serial
Authors: Levy Lawrence S. , Smith Patrick F.
Published: December 2010

A theorem of Eisenbud, Griffith, and Robson states that if R is hereditary and noetherian (on both the left and right) then every proper homomorphic image of R is a generalized unserial ring (see, for example, [3, p. 244]). Singh [11, p. 883] states a converse: If R is a right bounded, noetherian prime ring, all of whose proper homomorphic images are generalized uniserial rings, then (every divisible right R-module is injective, so) R is right hereditary. (Actually, Singh omitted the clearly necessary “bounded” condition.) Singh's theorem generalizes results of [9, Proposition 15], [2, Theorem 2.1], and [8], about commutative rings.

We will call a semi-prime ring R essentially right bounded if each essential right ideal contains a two-sided ideal which is essential as a right ideal. In case R is prime, “essentially right bounded” coincides with “right bounded”.
Orthomodular Lattices Which can be Covered by Finitely Many Blocks
Authors: Bruns Günter , Greechie Richard
Published: December 2010

In our paper [3] we considered four nniteness conditions for an orthomodular lattice (abbreviated: OML) L and conjectured their equivalence. The only question left open in that paper was whether an OML L which can be covered by finitely many blocks (maximal Boolean subalgebras) has only finitely many blocks. In this paper we give an affirmative answer to this question, in fact, we prove the slightly stronger result:
Perfect Sets of Uniqueness on the Group 2ω
Authors: Yoneda Kaoru
Published: December 2010

Let ω0, ω1, … denote the Walsh-Paley functions and let G denote the dyadic group introduced by Fine [3]. Recall that a subset E of G is said to be a set of uniqueness if the zero series is the only Walsh series ∑ akωk which satisfies

A subset E of G which is not a set of uniqueness is called a set of multiplicity.

It is known that any subset of G of positive Haar measure is a set of multiplicity [5] and that any countable subset of G is a set of uniqueness [2]. As far as uncountable subsets of Haar measure zero are concerned, both possibilities present themselves. Indeed, among perfect subsets of G of Haar measure zero there are sets of multiplicity [1] and there are sets of uniqueness [5].
Degree One Maps and a Realization Theorem
Authors: Shastri Anant R.
Published: December 2010

In [8] we classified degree one maps denned on Sp × Sg × Sr. In this paper we shall study degree one maps defined on the n-dimensional torus T = Sl × Sl × … × S1 as well as certain general properties of degree one maps. Theorem 1.1 must be known to experts; however we could not find it in the literature. Theorem 1.5 b) says that a Poincaré complex is nilpotent if it admits a degree one map from another nilpotent Poincaré complex. Theorem 1.5 a) means that certain stable properties are preserved by degree one maps and we use it later in Section 2.
Isometries of Weighted Bergman Spaces
Authors: Kolaski Clinton J.
Published: December 2010

In [2], [8] and [10], Forelli, Rudin and Schneider described the isometries of the Hp spaces over balls and polydiscs. Koranyi and Vagi [6] noted that their methods could be used to describe the isometries of the Hp spaces over bounded symmetric domains. Recently Kolaski [4] observed that the algebraic techniques used above and Rudin's theorem on equimeasurability extended to the Bergman spaces over bounded Runge domains. In this paper we use the same general argument to characterize the onto linear isometries of the weighted Bergman spaces over balls and polydiscs, (all isometries referred to are assumed to be linear).

2. Preliminaries. Horowitz [3] first defined the weighted Bergman space Ap,α(0 < p < ∞, 0 < α < ∞) to be the space of holomorphic functions f in the disc which satisfy

(1)
On an Inequality of S. Bernstein
Authors: Frappier C. , Rahman Q. I.
Published: December 2010

Let R > 1 and denote by ℰR the ellipse

(1)

If Pn is a polynomial of degree at most n such that

(2)

then ([2]; also see [13, p. 337] and [9, p. 158, Prob. No. 270])

(3)

The standard proof of this well known result runs as follows. The function

(4)

is entire and in view of (2) we have

Hence by the maximum modulus principle

(5)

which is clearly equivalent to (3).
Symbole Holomorphe
Authors: Meril A.
Published: December 2010

Soit T un endomorphisme continu de , nous montrons qu'il existe une fonction entière S sur Cn × Cn telle que ζ → S(x, ζ) soit de type exponential sur Cn avec croissance controlée uniformément lorsque x parcourt un compact de Cn, de telle sorte que pour on ait

( désigne la transformée de Fourier-Borel d'une fonctionnelle analytique). Une telle fonction S sera dite un symbole holomorphe sur Cn. Réciproquement nous montrons que si S est une fonctionnelle analytique, la formule précédente permet de définir un endomorphisme continu (encore noté S) de .
Brauer Groups, Class Groups and Maximal Orders for a Krull Scheme
Authors: Lee Heisook , Orzech Morris
Published: December 2010

In a previous paper [13] one of us considered Brauer groups Br(C) and class groups Cl(C) attached to certain monoidal categories C of divisorial R-lattices. That paper showed that the groups arising for a suitable pair of categories C1 ⊆ C2 could be related by a tidy exact sequence

It was shown that this exact sequence specializes to a number of exact sequences which had formerly been handled separately. At the same time the conventional setting of noetherian normal domains was replaced by that of Krull domains, thus generalizing previous results while also simplifying the proofs. This work was carried out in an affine setting, and one aim of the present paper is to carry these results over to Krull schemes. This will enable us to recover the non-affine version of an exact sequence obtained by Auslander [1, p. 261], as well as to introduce a new, non-affine version of a different sequence derived by the same author [2, Theorem 1].
Coefficients in Expansions of Certain Rational Functions
Authors: Evans Ronald , Ismail Mourad E. H. , Stanton Dennis
Published: December 2010

The constant term of certain rational functions has attracted much attention recently. For example the Dyson conjecture; that the constant term of

is the multinomial coefficient

has spawned many generalizations (see [2], [7]). In this paper we consider some other families of rational functions which have interesting constant terms. For example, Corollary 4 states that the constant term of

(1.1)

is . Here, and throughout this paper, A and B denote fixed positive integers.

In order to prove this result, we consider the rational function in two variables
Systemes Fondamentaux D'unites de Certains Corps de Degre 4 et de Degre 8 Sur Q
Authors: Levesque Claude
Published: December 2010

Lorsque Kn = Q(ω) est une extension algébrique de degré n sur Q telle que

avec D ∈ N, d ∈ Z, d|D2 et D2 + 4d > 0, nous avons prouvé [1] en utilisant certaines idées de Halter-Koch et Stender [2] que si

alors

est un système indépendant d'unités de Kn.
Solvable and Nilpotent Subgroups of GL(n,qm)
Authors: Wolf Thomas R.
Published: December 2010

Let V ≠ 0 be a vector space of dimension n over a finite field of order qm for a prime q. Of course, GL(n, qm) denotes the group of -linear transformations of V. With few exceptions, GL(n, qm) is non-solvable. How large can a solvable subgroup of GL(n, qm) be? The order of a Sylow-q-subgroup Q of GL(n, qm) is easily computed. But Q cannot act irreducibly nor completely reducibly on V.

Suppose that G is a solvable, completely reducible subgroup of GL(n, qm). Huppert ([9], Satz 13, Satz 14) bounds the order of a Sylow-q-subgroup of G, and Dixon ([5], Corollary 1) improves Huppert's bound. Here, we show that |G| ≦ q3nm = |V|3. In fact, we show that

where
Group Rings with Units of Bounded Exponent over the Center
Authors: Coelho Sônia P.
Published: December 2010

Let KG be the group ring of a group G over a field K, and U its group of units. Given a group H, we shall denote by ξ(H) the center of H and by T(H) the set of all its torsion elements.

The following question appears in [5, p. 231]: When is Un ⊂ ξ (U), for some n? It was considered by G. Cliff and S. K. Sehgal in [1], where G is assumed to be a solvable group. A complete answer at characteristic zero is given there. Also they obtain partial results at characteristic p ≠ 0, with certain restrictions on the exponent n.
Prime Numbers in Short Intervals and a Generalized Vaughan Identity
Authors: Heath-Brown D. R.
Published: December 2010

1. Introduction. Many problems involving prime numbers depend on estimating sums of the form ΣΛ(n)f(n), for appropriate functions f(n), (here, as usual, Λ(n) is the von Mangoldt function). Three distinct general methods have been used to estimate such sums. The earliest is due to Vinogradov (see [13, Chapter 9]); the second involves zerodensity bounds for Dirichlet L–functions (see [8, Chapters 15 and 16] for example); and the third, due to Vaughan (see [12] for example) uses an arithmetical identity as will be explained later. The second and third methods are much simpler to apply than the first. On the other hand Vinogradov's technique is at least as powerful as Vaughan's and occasionally more so. In many cases Vaughan's identity yields better bounds than the use of zero–density estimates, but sometimes they are worse. The object of this paper is to present a simple extension of Vaughan's method which is essentially as powerful as any of the techniques mentioned above, to discuss its general implications, and to apply it to the proof of the following result of Huxley [4], which has previously only been within the scope of the zero density method.
A Further Generalization of an Irreducibility Theorem of A. Cohn
Authors: Michael Filaseta
Published: December 2010

Let dndn–1 … d0 be the b-ary representation of a positive integer N. Call the polynomial obtained from N base b. In the case the base is 10, f(x) will be called the polynomial obtained from N. Pólya and Szegö attribute the following theorem to A. Cohn [2, b. 2, VIII, 128]:

THEOREM 1. A polynomial obtained from a prime is irreducible.

This theorem was generalized in two different ways by John Brillhart, Andrew Odlyzko, and myself [1]. One way was by proving the theorem remains true regardless of the base being used. The second way was by permitting the coefficients of f(x) to be different from digits. Thus, for example, if , where 0 ≦ dk ≦ 167 for all k, and if f(10) is prime, then f(x) is irreducible. In this paper, Theorem 1 will be generalized in another way by considering composite N.
Sufficiency of Weierstrass Jets
Authors: Kirschenbaum Marc , Lu Yung-Chen
Published: December 2010

1. Introduction. Let C(r+1)(2, 1) be the set of all (r + 1)-time continuously differentiable mappings f: R2 → R with . Two maps f and g ∈ C(r+1)(2, 1) are said to be equivalent of order r at , if at , their Taylor expansions up to and including the terms of degree ≦ r are identical. An r-jet, denoted j(r)(f), is the equivalence class of f with f being called a realization of j(r)(f). The set of all r-jets is denoted Jr(2, 1).

Definition. An r-jet Z ∈ Jr(2, 1) is called C0-sufficient (in C(r+1)(2, 1)), if for any two C(r+1)(2, 1) functions f, g which realize Z, there exists a local homeomorphism h: R2 → R2, for which f(h(x, y)) = g(x, y) in a neighborhood of . I.e., the following diagram commutes.
l′-Isolated Maps and Localizations
Authors: Hurvitz Sara
Published: December 2010

Let P be the set of primes, l ⊆ P a subset and l′ = P – l Recall that an H0-space is a space the rational cohomology of which is a free algebra.

Cassidy and Hilton defined and investigated l′-isolated homomorphisms between locally nilpotent groups. Zabrodsky [8] showed that if X and Y are simply connected H0-spaces either with a finite number of homotopy groups or with a finite number of homology groups, then every rational equivalence f : X → Y can be decomposed into an l-equivalence and an l′-equivalence.

In this paper we define and investigate l′-isolated maps between pointed spaces, which are of the homotopy type of path-connected nilpotent CW-complexes. Our definition of an l′-isolated map is analogous to the definition of an l′-isolated homomorphism. As every homomorphism can be decomposed into an l-isomorphism and an l′-isolated homomorphism, every map can be decomposed into an l-equivalence and an l′-isolated map.
Representations of Well-Founded Preference Orders
Authors: Cenzer Douglas , Mauldin R. Daniel
Published: December 2010

A preference order, or linear preorder, on a set X is a binary relation which is transitive, reflexive and total. This preorder partitions the set X into equivalence classes of the form . The natural relation induced by on the set of equivalence classes is a linear order. A well-founded preference order, or prewellordering, will similarly induce a well-ordering. A representation or Paretian utility function of a preference order is an order-preserving map f from X into the R of real numbers (provided with the standard ordering). Mathematicians and economists have studied the problem of obtaining continuous or measurable representations of suitably defined preference orders [4, 7]. Parametrized versions of this problem have also been studied [1, 7, 8]. Given a continuum of preference orders which vary in some reasonable sense with a parameter t, one would like to obtain a continuum of representations which similarly vary with t.
Polynomials with Coefficients from a Division Ring
Authors: Bray Una , Whaples George
Published: December 2010

Let R be any division ring and let

1

be a polynomial, in the indeterminate X, with coefficients in R. Note that the powers of X are always to the right of the coefficients. We denote the set of all such polynomials by R[X].

B. Beck [3] proved the following theorem for the generalized quaternion division algebra; i.e., any division ring of dimension 4 over its center:

THEOREM 1. If f(X) is of degree n then f(X) has either infinitely many or at most n zeros in R.

Under a reasonable definition of multiplicity Beck also proved:

THEOREM 2. Let (c1, c2, …, cn) be a set of pairwise non-conjugate elements of R, and (m1, …, mN) positive integers such that Σmi = n = deg f(x).
p-Adic Eigen-Eunctions for Kubert Distributions
Authors: Koblitz Neal
Published: December 2010

Functions onR(or onR/Z, orQ/Z, or the interval (0,1)) which satisfy the identity

1.1

for positive integersmand fixed complexs,appear in several branches of mathematics (see [8], p. 65-68). They have recently been studied systematically by Kubert [6] and Milnor [12]. Milnor showed that for each complexsthere is a one-dimensional space of even functions and a one-dimensional space of odd functions which satisfy (1.1). These functions can be expressed in terms of either the Hurwitz partial zeta-function or the polylogarithm functions.

My purpose is to prove an analogous theorem forp-adic functions. Thep-adic analog is slightly more general; it allows for a Dirichlet characterχ0(m) in front ofms–lin (1.1). The functions satisfying (1.1) turn out to bep-adic “partial DirichletL-functions”, functions of twop-adic variables (x, s) and one character variableχ0which specialize to partial zeta-functions whenχ0is trivial and to Kubota-LeopoldtL-functions whenx= 0.
The Poisson Integral of a Singular Measure
Authors: Ahern Patrick
Published: December 2010

Let σ be a finite positive singular Borel measure defined on Euclidean space RN. For w ∈ RN and y > 0, its Poisson integral is defined by the formula

where CN is chosen so that

Since σ is singular, almost everywhere with respect to Lebesgue measure on RN. On the other hand, almost everywhere dσ. It follows that for all sufficiently small y,

is a non-empty open subset of RN. If σ has compact support then |Ey| → 0 as y → 0, where |Ey| denotes the Lebesgue measure of Ey. In this paper we give a lower bound on the rate at which |Ey| may go to zero. The lower bound depends on the smoothness of the measure; the smoother the measure, the more slowly |Ey| may approach 0.
Obtaining Prescribed Rates of Convergence for the Ergodic Theorem
Authors: O'Brien G. L.
Published: December 2010

Let {Yn, n ∊ Z} be an ergodic strictly stationary sequence of random variables with mean zero, where Z denotes the set of integers. For n ∊ N = {1, 2, …}, let Sn = Y1 + Y2 + … + Yn. The ergodic theorem, alias the strong law of large numbers, says that n–lSn → 0 as n → ∞ a.s. If the Yn's are independent and have variance one, the law of the iterated logarithm tells us that this convergence takes place at the rate in the sense that

1

It is our purpose here to investigate what other rates of convergence are possible for the ergodic theorem, that is to say, what sequences {bn, n ≧ 1} have the property that

2

for some ergodic stationary sequence {Yn, n ∊ Z}.
Rayon de Regularite Dans Les Algebres Infrasequentielles
Authors: Oudadess Mohamed
Published: December 2010

Nous commençons par caractériser les algèbres infraséquentielles (cf [11]) à l'aide du rayon de régularité. Nous montrons qu'une algèbre topologique (E, τ) est infraséquentielle si, et seulement si, le rayon de régularité β est borné (i.e., l'image, par β, de tout borné de (E, τ) est un borné de R+). Nous dirons qu'une telle algèbre est β-régulière. Nous montrons qu'une algèbre β-régulière pseudo-complète (cf [3]) a tous ses caractères bornés. En fait nous obtenons que l'ensemble des caractères (algébriques) M*, de E, est équiborné. Ce résultat recouvre et généralise ceux de T. Husaïn et S.B. Ng ([12]), de G.A. Joseph ([13]) et de T. Husaïn. ([11]). Dans le cas des algèbres séquentielles pseudo-complètes, nous montrons que tout caractère est séquentiellement continu. Nous obtenons des résultats analogues sur les formes faiblement positives.
Tangent Spaces of a Normal Surface with Hyperelliptic Sections
Authors: Edge W. L.
Published: December 2010

A rational normal curve C of order n in [n] has, at each point P, a nest of osculating spaces

as P moves on C the [n — 2] generates a primal Dn-1 of order 2n — 2.

Hilbert [3] found the multiplicities on Dn-1 not only of the vμ+1 generated by Dμ for each lesser value of μ but also those of all submanifolds common to these various Dμ.

A surface Φ in higher space has, as explained [4] by del Pezzo, a nest of tangent spaces

of respective dimensions

they raise the problem of finding the orders of manifolds generated by them and the multiplicity of each on the higher manifolds to which it belongs: the task does not seem to have been attempted, but it may well be eased if Φ is rational and normal.
Normal Semimodules: A Theory of Generalized Convex Cones
Authors: Marcus Daniel A.
Published: December 2010

In [3], C. Davis showed that if a convex polyhedral cone C (the positive span of a finite set of vectors in Euclidean space) contains no nonzero linear subspace, then C is linearly isomorphic to the set V+ of nonnegative points in a linear subspace V of Rn. Moreover n can be taken to be the number of facets (maximal proper faces) of C.
How Many Matrices Have Roots?
Authors: Borwein J. M. , Richmond B.
Published: December 2010

In many basic linear algebra texts it is shown that various classes of square matrices (normal, positive, invertible) possess square roots. In this note we characterize those n × n matrices with complex entries which possess at least one square root without any restriction on the class of root or matrix involved. We then use this characterization to obtain asymptotic estimates for the relative profusion of such matrices.

In Section 1 we characterize those n × n matrices with entries in C (or any algebraically complete field) which have square roots over C. This characterization is in terms of similarity classes. In Section 2 we give asymptotic estimates for the number of Jordan forms of nilpotent n × n matrices which are squares. Section 3 is given over to numerical results concerning the actual and asymptotic frequency of such forms.
Semigroupe des Parties et Relations de Green
Authors: Pin J. E.
Published: December 2010

Dans cet article, tous les semigroupes sont supposés finis, sauf dans le cas d'un semigroupe ou d'un monoïde libre. Les références de base sont [1, 2].

L'objet de cet article est de poursuivre l'étude du semigroupe des parties d'un semigroupe, étude qui a connu récemment des développements inattendus [3, 4, 5, 6, 8, 10, 11, 12]. Putcha [10] avait caractérisé les semigroupes S tels que le semigroupe des parties soit apériodique, autrement dit -trivial. Je donne ici une nouvelle démonstration du théorème de Putcha basée sur le théorème de Ramsey et je caractérise les semigroupes S tels que soit -trivial (resp. ℒ-trivial, ℐ-trivial): ce sont les semigroupes apériodiques tels que es = ese (se = ese, es = se) pour tout s ∊ S et pour tout idempotent e ∊ S. Il en résulte que la variété des semigroupes V2 (resp V3, V1) définie par ces conditions est la variété maximale V telle que la variété PV engendrée par les , S ∊ V, soit contenue dans la variété des monoïdes -triviaux (ℒ-trivial, ℐ-trivial).
A Canonical Decomposition in Mixed Exterior Algebra
Authors: Vanstone J. R.
Published: December 2010

Let E be a vector space of dimension n ∊ N over a field Γ, of characteristic 0. Choose E*, dual to E, and form

the space of exterior powers of E, as well as ΛE*. Finally, let
Interior Estimates for Elliptic Partial Differential Equations in the ℒ(q,λ) Spaces of Strong Type
Authors: Ono Akira
Published: December 2010

Recently the ℒ(q,λ) spaces have been investigated by many authors and the theory of these spaces has proved to be particularly important for research in partial differential equations (see for example [15], [16] and [18]).

The equations of elliptic type in these spaces were first studied by C. B. Morrey [8], [9], who applied his well-known imbedding theorems, and afterwards by S. Campanato [3], [4] with the aid of isomorphism theorems and the so-called fundamental inequalities due to him.

On the other hand, G. Stampacchia introduced the ℒ(q,λ) spaces of strong type [17], the structures of which are more general and complicated than those of ℒ(q,λ) Spaces in the usual sense, and greater part of them were characterized by him, L. C. Piccinini, Y. Furusho, the author and others (see [5], [11]-[14], [16] and [17]).
A Note on Divisibility in H∞(X)
Authors: Forelli Frank
Published: December 2010

Let X be a Riemann surface, and H∞(X) the ring of bounded holomorphic functions in X. We offer here a question on divisibility in H∞(X), and then give in Section 2 a condition in which the answer is yes (Corollary 2 to Lemma 1). In Section 3 we use part 2 to prove a theorem on the separation of points by H∞(X). In Section 4 we study X/H∞(X).

If f is meromorphic in X and z ∈ X, then by o(f, z) we mean the order of f at z. (We agree that o(f, z) = ∞ if f ≡ 0.) Let h be memomorphic in X; then h might be said to be of bounded type if h = f/g where f,g ∈ H∞(X), g ≠ 0.
Fonction De Green Et Surfaces Nodales Des Fonctions Propres De L'hamiltonien − ½ Δ + V
Authors: Vauthier J.
Published: December 2010

On étudie, dans ce travail, l'hamiltonien − ½ Δ + V suivant deux points de vue distincts. Le premier, dans le paragraphe 1, consiste à faire une hypothèse de nature asymptotique sur le potentiel V : on suppose qu'en dehors d'une boule B, il est à croissance au plus polynômiale. On étudie la fonction de Green de H dans le complémentaire de la boule B précédente. La méthode consiste à utiliser le processus de générateur ½V stoppé sur le bord de B avec V jouant un rôle de création ou d'annihilation. On projette par une fonction d'exhaustion et on utilise un théorème de comparaison. C'est par un calcul élémentaire sur une équation du second ordre que l'on calcule les poids des espaces entre lesquels opère la fonction de Green du complémentaire de B définie par H.
Spherical Harmonics, the Weyl Transform and the Fourier Transform on the Heisenberg Group
Authors: Geller Daryl
Published: December 2010

In the early days of quantum mechanics, Weyl asked the following question. Let λ be a non-zero real number, ℋa separable Hilbert space. Given certain (unbounded) operators W1,…,Wn,W1+, …, Wn+ on ℋ satisfying

(on a dense subspace D of ℋ) with all other commutators vanishing. Given also a function where ζ ∈ Cn. Let W = (W1 …, Wn) W+ = (W1+ …, Wn+). How does one associate to f an operator f(W, W+)? (Actually, Weyl phrased the question in terms of p = Re ζ, q = Im ζ, P = Re W, Q = Im W+ which represent momentum and position. In this paper, however, we wish to exploit the unitary group on Cn and so prefer complex notation.)