bluuebunny/crossref_metadata_2025 huggingface dataset:
Groups with the Subnormal Join Property
Authors: Smith Howard
Published: December 2010

A group G is said to have the subnormal join property (s.j.p.) if the join of two (and hence of finitely many) subnormal subgroups of G is always subnormal in G. Following Robinson [6], we shall denote the class of groups having this property by . A particular subclass of is , consisting of those groups G in which the join of two subnormals is again subnormal in G and has defect bounded in terms of the defects of the constituent subgroups (for a more precise definition see Section 7 of [6]).

In [16], Wielandt showed that groups which satisfy the maximal condition for subnormal subgroups have the s.j.p. Many further results on groups with the s.j.p. were proved in [6] and [7]. In Sections 2 and 3 of this paper, it will be shown that several of these results can be exhibited as corollaries of a few rather more general theorems on the classes , .
On Hankel Transformable Spaces and a Cauchy Problem
Authors: Pathak R. S.
Published: December 2010

The classical Hankel transform of a conventional function ϕ on (0, ∞) defined formally by

was extended by Zemanian [21-23] to certain generalized functions of one dimension. Koh [9, 10] extended the work of [21] to n-dimensions, and that of [22] to arbitrary real values of μ. Motivated from the work of Gelfand and Shilov [6], Lee [11] introduced spaces of type Hμ and studied their Hankel transforms. The results of Lee [11] and Zemanian [21] are special cases of recent results obtained by the author and Pandey [14]. The aforesaid extensions are accomplished by using the so-called adjoint method of extending integral transforms to generalized functions. Dube and Pandey [2], Pathak and Pandey [15, 16] applied a more direct method, the so-called kernel method, for extending the Hankel and other related transforms.
The Orbit-Stabilizer Problem for Linear Groups
Authors: Dixon John D.
Published: December 2010

Let G be a subgroup of the general linear group GL(n, Q) over the rational field Q, and consider its action by right multiplication on the vector space Qn of n-tuples over Q. The present paper investigates the question of how we may constructively determine the orbits and stabilizers of this action for suitable classes of groups. We suppose that G is specified by a finite set {x1, …, xr) of generators, and investigate whether there exist algorithms to solve the two problems:

(Orbit Problem) Given u, v ∊ Qn, does there exist x ∊ G such that ux = v; if so, find such an element x as a word in x1, …, xr and their inverses.

(Stabilizer Problem) Given u, v ∊ Qn, describe all words in x1, …, xr and their inverses which lie in the stabilizer
Compactness Properties of Carleman and Hille-Tamarkin Operators
Authors: Schep Anton R.
Published: December 2010

In this paper we study integral operators with domain a Banach function space Lρ1 and range another Banach function space Lρ2 or the space L0 of all measurable functions. Recall that a linear operator T from Lρ1 into L0 is called an integral operator if there exists a μ × v-measurable function T(x, y) on X × Y such that

Such an integral operator is called a Carleman integral operator if for almost every x ∊ X the function

is an element of the associate space L′ρ1, i.e.,
Generalized Gradients, Lipschitz behavior and Directional Derivatives
Authors: Treiman Jay S.
Published: December 2010

In the study of optimization problems it is necessary to consider functions that are not differentiable. This has led to the consideration of generalized gradients and a corresponding calculus for certain classes of functions. Rockafellar [16] and others have developed a very strong and elegant theory of subgradients for convex functions. This convex theory gives point-wise criteria for the existence of extrema in optimization problems.

There are however many optimization problems that involve functions which are neither differentiable nor convex. Such functions arise in many settings including optimal value functions [15]. In order to deal with such problems Clarke [3] defined a type of subgradient for nonconvex functions. This definition was initially for Lipschitz functions on R”. Clarke extended this definition to include lower semicontinuous (l.s.c.) functions on Banach spaces through the use of a directional derivative, the distance function from a closed set and tangent and normal cones to closed sets.
The Strong ϕ Topology on Symmetric Sequence Spaces
Authors: Ruckle William H.
Published: December 2010

The strong ϕ topology. Let S be a linear space of real sequences written in functional notation

There is a natural duality between S and the space ϕ of sequences which are eventually ϕ given by the equation

The series has only a finite number of nonzero terms since t is in ϕ.

A subset B of ϕ is called S-bounded if

for each s in S.
Metrizability of Finite Dimensional Spaces with a Binary Convexity
Authors: Vel M. Van de
Published: December 2010

A convex structure consists of a set X, together with a collection of subsets of X, which is closed under intersection and under updirected union. The members of are called convex sets, and is a convexity on X. Fox A a subset of X, h (A) denotes the (convex) hull of A. If A is finite, then h(A) is called a polytope, is called a binary convexity if each finite collection of pairwise intersecting convex sets has a nonempty intersection. See [8], [21] for general references.

If X is also equipped with a topology, then the corresponding weak topology is the one generated by the convex closed sets. It is usually assumed that at least all polytopes are closed. is called normal provided that for each two disjoint convex closed sets C, D there exist convex closed sets C′, D′, with
Some Order Properties of the Lattice of Varieties of Commutative Semigroups
Authors: Almeida Jorge
Published: December 2010

The most complete work on the structure of the lattice of varieties of commutative semigroups available to this date is [12]. Nevertheless, it fails to give the structure of this lattice. In the positive direction, it shows in particular that the order structure of is determined by the order structure of well-known lattices of integers together with the sublattice of varieties of commutative nil semigroups.

In the present work, we study from the point of view of order. Perkins [13] has shown that has no infinite descending chains and is countable. The underlying questions we consider here arose from the results of Almeida and Reilly [1] in connection with generalized varieties. There, it is observed that the best-known part of consisting of the
varieties all of whose elements are abelian groups is in a sense very wide: it contains infinite subsets of mutually incomparable elements and allows the construction of uncountably many generalized varieties and infinite descending chains of generalized varieties.
Derivations from Hereditary Subalgebras of C*-Algebras
Authors: Lazar A. J. , Tsui S.-K. , Wright S.
Published: December 2010

Let A be a C*-algebra, B a C*-subalgebra of A, δ:B → A a derivation, i.e., a linear map with

There has been considerable interest for several years now in the question of when δ can be extended from B to a derivation of A (see, for example, [8], Section 4, [1], [5], [4], [6], [9], [10], [11]). The paper before the reader will be concerned with this extension problem when B is a hereditary C*-subalgebra of A.

Our work takes its cue from the paper [6] of George Elliott. We prove in Section 2 of the present paper that derivations as described above of a unital hereditary C*-subalgebra always extend whenever A is either simple, AW*, separable and AF, or separable with continuous trace, thus generalizing and extending Theorem 4.5 of [6].
On a Family of Distributions obtained from Orbits
Authors: Arthur James
Published: December 2010

Suppose that G is a reductive algebraic group defined over a number field F. The trace formula is an identity

of distributions. The terms on the right are parametrized by “cuspidal automorphic data”, and are defined in terms of Eisenstein series. They have been evaluated rather explicitly in [3]. The terms on the left are parametrized by semisimple conjugacy classes and are defined in terms of related G(A) orbits. The object of this paper is to evaluate these terms.

In previous papers we have already evaluated in two special cases. The easiest case occurs when corresponds to a regular semisimple conjugacy class in G(F). We showed in Section 8 of [1] that for such an , could be expressed as a weighted orbital integral over the conjugacy class of σ. (We actually assumed that was “unramified”, which is slightly more general.) The most difficult case is the opposite extreme, in which corresponds to {1}.
Frame Fields on Manifolds
Authors: Ng Tze Beng
Published: December 2010

Consider the following stable secondary cohomology operations associated with the relations in the mod 2 Steenrod algebra:

such that

Let ψ5 be a stable tertiary cohomology operation associated with the above relation. We assume that (ϕ4, ϕ5) and ψ5 are chosen to be spin trivial in the sense of Theorem 3.7 of [14].

Let ϕ0,0, ϕ1,1 be the stable Adams basic secondary cohomology operations associated with the relations:

respectively.
Bezout Domains and Rings with a Distributive Lattice of Right Ideals
Authors: Brungs H. H.
Published: December 2010

It is the purpose of this paper to discuss a construction of right arithmetical (or right D-domains in [5]) domains, i.e., integral domains R for which the lattice of right ideals is distributive (see also [3]). Whereas the commutative rings in this class are precisely the Prüfer domains, not even right and left principal ideal domains are necessarily arithmetical. Among other things we show that a Bezout domain is right arithmetical if and only if all maximal right ideals are two-sided.

Any right ideal of a right noetherian, right arithmetical domain is two-sided. This fact makes it possible to describe the semigroup of right ideals in such a ring in a satisfactory way; [3], [5].
Boundary Value Problems for Harmonic Functions on the Heisenberg Group
Authors: Dunkl Charles F.
Published: December 2010

Analysis on the Heisenberg group has become an important area with strong connections to Fourier analysis, group representations, and partial differential operators. We propose to show in this work that special functions methods can also play a significant part in this theory. There is a one-parameter family of second-order hypoelliptic operators Lγ, (γ ∊ C), associated to the Laplacian L0 (also called the subelliptic or Kohn Laplacian). These operators are closely related to the unit ball for reasons of homogeneity and unitary group invariance. The associated Dirichlet problem is to find functions with specified boundary values and annihilated by Lγ inside the ball (that is, Lγ-harmonic). This is the topic of this paper.

Gaveau [9] proved the first positive result, showing that continuous functions on the boundary can be extended to L0-harmonic functions in the ball, by use of diffusion-theoretic methods. Jerison [15] later gave another proof of the L0-result. Hueber [14] has recently obtained some results dealing with special values of the Poisson kernel for L0.
Ensembles Reconnaissables de Mots Biinfinis
Authors: Nivat Maurice , Perrin Dominique
Published: December 2010

Introduction. La théorie des automates finis fait partie de ce que l'on appelle aujourd'hui les mathématiques de l'informatique. Comme pour les autres spécialités de ce domaine, elle est née des travaux de logiciens et, pour les automates finis, c'est à Kleene que l'on doit le premier théorème. Cette théorie s'est considérablement développée depuis la période des fondations. La direction principale est l'étude des automates reconnaissant des suites finies ou mots. Elle présente des aspects mathématiques qui la rapprochent de domaines classiques comme par exemple la théorie combinatoire des groupes. Parallèlement, plusieurs auteurs ont étudié le comportement des automates finis sur des objets plus généraux que les mots. C'est le cas notamment pour la théorie des automates reconnaissant des arbres. C'est aussi le cas pour les automates reconnaissant des mots infinis qui sont le sujet de cet article.
Small Compact Actions on Chainable Continua
Authors: Toledo Juan A.
Published: December 2010

1. Introduction. In 1931, Newman [9] showed that a connected manifold cannot accept arbitrarily small period-n homeomorphisms, for any n > 1. In this paper we are concerned with the existence of chainable continua with arbitrarily small homeomorphisms.

For a long time the only known periodic homeomorphisms of chainable continua had periods 1, 2 or 4 [4]. Recently, Wayne Lewis [8] showed that the pseudo-arc admits periodic homeomorphisms of every order, as well as p-adic cantor group actions. We will see that such homeomorphisms can be made arbitrarily small.

In Section 4, a different chainable indecomposable continuum accepting arbitrarily small period-2 homeomorphisms is constructed.
An integral Representation of a 10ϕ9 and Continuous Bi-Orthogonal 10ϕ9 Rational Functions
Authors: Rahman Mizan
Published: December 2010

1. Introduction. One of the most remarkable q-extensions of the classical beta integral was recently introduced by Askey and Wilson [1]

(1.1)

where |q| < 1 and the pairwise products of {a, b, c, d} as a multiset do not belong to the set {qj, j = 0, – 1, – 2, …}. The contour C is the unit circle described in the positive direction, but with suitable deformations to separate the sequences of poles converging to zero from the sequences of poles diverging to infinity. The symbol (A; q)∞ is an infinite product defined by

(1.2)

whenever it converges.
A Note on Small Baire Spaces
Authors: Shelah Saharon , Todorcevic Stevo
Published: December 2010

A Baire space is a topological space which satisfies the Baire Category Theorem, i.e., in which the intersection of countably many dense open sets is dense. In this note we shall be interested in the size of Baire spaces, so to avoid trivialities we shall consider only non-atomic spaces, that is, spaces X whose regular open algebras ro(X) are non-atomic. All natural examples of Baire spaces, such as complete metric spaces or compact spaces, seem to have sizes at least 2ℵ0. So a natural question, asked first by W. Fleissner and K. Kunen [5], is whether there exists a Baire space of the minimal possible size ℵ1. The purpose of this note is to show that such a space need not exist by proving the following result.
(KK)-Properties, Normal Structure and Fixed Points of Nonexpansive Mappings in Orlicz Sequence Spaces
Authors: van Dulst D. , de Valk V.
Published: December 2010

In this paper we investigate Orlicz sequence spaces with regard to certain geometric properties that have proved to be important in fixed point theory. In particular, we shall consider various Kadec-Klee type properties, and weak and weak* normal structure. It turns out that many of these properties, though generally distinct, coincide in Orlicz sequence spaces and that all of them are intimately related to the so-called Δ2-condition. Some of our results extend to vector-valued Orlicz sequence spaces. For example, we prove a rather powerful theorem on the preservation of weak normal structure under the formation of substitution spaces. There is also a fixed point theorem: the Orlicz sequence space hM has the fixed point property if the complementary Orlicz function M* satisfies theΔ2-condition. Another one of our results implies that, under this assumption on M*, hM has weak normal structure if and only if M also satisfies the Δ2-condition.
A Semigroup Approach to Linear Algebraic Groups III. Buildings
Authors: Putcha Mohan S.
Published: December 2010

Introduction. Let K be an algebraically closed field, G = SL(3, K) the group of 3 × 3 matrices over K of determinant 1. Let denote the monoid of all 3 × 3 matrices over K. If e is an idempotent in , then

are opposite parabolic subgroups of G in the usual sense [1], [28]. However the map

does not exhaust all pairs of opposite parabolic subgroups of G. Now consider the representation ϕ:G → SL(6, K) given by
Monomorphisms of Semigroups of Local Dendrites
Authors: Magill K. D.
Published: December 2010

When we speak of the semigroup of a topological space X, we mean S(X) the semigroup of all continuous self maps of X. Let h be a homeomorphism from a topological space X onto a topological space Y. It is immediate that the mapping which sends f ∊ S(X) into h º f º h−1 is an isomorphism from the semigroup of X onto the semigroup of Y. More generally, let h be a continuous function from X into Y and k a continuous function from Y into X such that k º h is the identity map on X. One easily verifies that the mapping which sends f into h º f º k is a monomorphism from S(X) into S(Y). Now for “most” spaces X and Y, every isomorphism from S(X) onto S(Y) is induced by a homeomorphism from X onto Y. Indeed, a number of the early papers dealing with S(X) were devoted to establishing this fact.
Nilpotent Extensions of Abelian p-GROUPS
Authors: Buckley Joseph , Wiegold James
Published: December 2010

This paper arose out of an attempt to solve the following problem due to Suprunenko [5, Problem 2.77]. For which pairs of abelian groups A, B is every extension of A by B nilpotent? We obtain complete answers when A and B are p-groups and (a) A has finite exponent or (b) B is divisible or (c) A has infinite exponent, is countable and B is non-divisible. The structure of a basic subgroup of A plays a central role in cases (b) and (c).

At the outset we must say that the problem is too difficult to solve in complete generality. If G/A ≅ 2?, then the nilpotency of G depends solely on properties of the associated homomorphism θ.B → Aut A. Thus for instance if A is torsion-free and B finite, G is nilpotent if and only if the extension is a central one, and we would need detailed information on finite subgroups of the group Aut A.
On Periodicity in Topological Surgery
Authors: Kwasik Slawomir
Published: December 2010

One of the distinguishing features of the topological category is the following periodicity in the set of homotopy TOP structures on X.

THEOREM (Siebenmann). Let Xm, m ≦ 5, be a connected compact topological manifold with non-empty boundary. Then

It was conjectured by Siebenmann (see [3], p. 283) that the analogous periodicity should also exist for noncompact manifolds.

The purpose of this paper is to prove that this is indeed the case, namely:

THEOREM 1. Let Let Xm, m ≦ 6, be a connected noncompact topological manifold with non-empty boundary. Then
Some Supercuspidal Representations of Sp4(k)
Authors: Asmuth Charles
Published: December 2010

The purpose of this paper is to produce explicit realizations of supercuspidal representations of Sp4(k) where k is a p-adic field with odd residual characteristic. These representations will be constructed using the Weil representation of Sp4(k) associated with a certain 4-dimensional compact orthogonal group OQ over k. The main problem addressed in this paper is the analysis of this representation; we need to find how the supercuspidal summands decompose into irreducible pieces.

The problem of decomposing Weil representations has been studied quite a bit already. The Weil representations of SL2(k) associated to 2-dimensional orthogonal groups were used by Casselman [4] and Shalika [9] to produce all supercuspidals of SL2(k). The explicit formulas for these representations were used by Sally and Shalika ([10]) to compute the characters and finally to write down a Plancherel formula for that group.
Multipliers for Amalgams and the Algebra S0(G)
Authors: Torres De Squire Maria L.
Published: December 2010

Throughout the whole paper G will be a locally compact abelian group with Haar measure m and dual group Ĝ. The difference of two sets A and B will be denoted by A ∼ B, i.e.,

For a function f on G and s ∊ G, the functions f′ and fs will be defined by
On Representations of Grothendieck Toposes
Authors: Barr Michael , Makkai Michael
Published: December 2010

Results of a representation-theoretic nature have played a major role in topos theory since the beginnings of the subject. For example, Deligne's theorem on coherent toposes, which says that every coherent topos has a continuous embedding into a topos of the form SetI for a discrete set I, is a typical result in the representation theory of toposes. (A continuous functor between toposes is the left adjoint of a geometric morphism. For Grothendieck toposes, it is exactly the same as a continuous functor between them, considered as sites with their canonical topologies. By a continuous functor between sites on left exact categories, we mean a left exact functor taking covers to covers.)

A representation-like result for toposes typically asserts that a topos that satisfies some abstract conditions is related to a topos of some concrete kind; the relation between them is usually an embedding of the first topos in the second (concrete) one, for which the embedding satisfies some additional properties (fullness, etc.).
High Level Occupation Times for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
Authors: Lawniczak Anna T.
Published: December 2010

Let X be a complete separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I(·) if there exists a function I(·) from X into [0, ∞] satisfying:

(i)

0 ≦ I(x) ≦ ∞ for all x ∊ X.

(ii)

I(·) is lower semicontinuous.

(iii)

For each l < ∞ the set {x:I(x) ≦ l} is a compact set in X.

(iv)

For each closed set C ⊂ X

(v)

For each open set C ⊂ X
The Multivalent Class of Geometrically Close-to-Convex Functions
Authors: Lyzzaik Abdallah
Published: December 2010

The class of univalent close-to-convex functions, K, was introduced by Kaplan [4] and first studied by him. The first important extension to the class of multivalent close-to-convex functions, K(p) where p is a positive integer, was considered by Livingston [7]. Somewhat later, Styer [15] introduced the more general class, Kw(p), of weakly close-to-convex functions by simply taking the closure of Livingston's class K(p) in the topology of locally uniform convergence in B = {z: |z| ≤ 1}.

In 1936 Biernacki [2] introduced his class of linearly accessible functions. A function f is linearly accessible if f is univalent in B, f(0) = 0, and C – f(B) where C is the complex plane, is a union of closed (Euclidean) rays with disjoint interiors. In an interesting result, Lewandowski [6] showed that the classes of univalent close-to-convex functions and linearly accessible functions are equal.
On the Distribution of the Sequence n2θ (mod 1)
Authors: Friedlander J. B. , Iwaniec H.
Published: December 2010

In a paper with the above title H. Heilbronn [4] proved that, given any real θ, there exist infinitely many positive integers n such that the distance ║θn2║ from θn2 to its nearest integral neighbour satisfies the bound

He actually proved a somewhat stronger statement which shows that the integers n occur with some regularity and he suggested that perhaps the exponent may be replaced by . This theorem has attracted considerable attention and spawned a number of generalizations (see [1], [7] and the references therein), yet no essential improvement has been given for the original problem (but see [6], [8]).
The Empty Sphere
Authors: Erdahl R. M. , Ryshkov S. S.
Published: December 2010

In 1924 at the Toronto meeting of the International Congress of Mathematicians, B. N. Delone introduced his empty sphere method for lattices. We have titled our paper after this method as a tribute to his memory.

We have studied the sets of integer solutions of equations of the form

1

where f satisfies the following condition in which Z denotes the integers,

2

and have resolved this problem using the theory of L-types of lattices [3, 4, 11]. We have been able to give a complete description of all such integer solutions when n ≦ 4.
Classification Theory and Stationary Logic
Authors: Mekler Alan H.
Published: December 2010

Stationary logic L(aa) is obtained for Lωω by adding a quantifier aa which ranges over countable sets and is interpreted to mean “for a closed unbounded set of countable subsets”. The dual quantifier for aa is stat, i.e., stat sφ(s) is equivalent to ¬aa s ¬φ(s). In the study of the L(aa)-model theory of structures a particular well behaved class was isolated, the finitely determinate structures. These are structures in which the quantifier “stat” can be replaced by the quantifier “aa” without changing the validity of sentences. Many structures such as R and all ordinals are finitely determinate. In this paper we will be concerned with finitely determinate first order theories, i.e., those theories all of whose models are finitely determinate.

Example 0.1. [5] The theory of dense linear orderings is not finitely determinate. Let S be a stationary costationary subset of ω1 and

where
Semilinear Elliptic Problems with Pairs of Decaying Positive Solutions
Authors: Noussair Ezzat S. , Swanson Charles A.
Published: December 2010

Our main objective is to prove the existence of a pair of positive, exponentially decaying, classical solutions of the semilinear elliptic eigenvalue problem

1.1

in a smooth unbounded domain Ω ⊂ RN, N ≧ 2, where λ is a positive parameter and L is a uniformly elliptic operator in Ω defined by
The MultipleQ-Construction
Authors: Jardine J. F.
Published: December 2010

Products, and closely associated questions of infinite loop space structure, have always been a source of trouble in higher algebraicK-theory. From the first description of the product in terms of the plus construction, up to the current tendency to let the infinite loop space machines do it, the constructions have never been completely explicit, and many mistakes have resulted.

Since Waldhausen introduced the doubleQ-construction [16], there has been the tantalizing prospect of an infinite loop space structure for the nerveof theQ-constructionof an exact category, which would be understandable to the man on the street, and which also would be well-behaved with respect to products induced by biexact pairings. Gillet [3] showed that most of these conditions could be met with his introduction of the multipleQ-construction. Shimakawa [14] filled in some of the details later.
THE C1-Invariance of the Godbillon-Vey Map in Analytical K-Theory
Authors: Natsume Toshikazu
Published: December 2010

An action α of a discrete group Γ on the circle S1 as orientation preserving C∞-diffeomorphisms gives rise to a foliation on the homotopy quotient S1Γ, and its Godbillon-Vey invariant is, by definition, a cohomology class of S1Γ([1]). This cohomology class naturally defines an additive map from the geometric K-group K0(S1, Γ) into C, through the Chern character from K0(S1, Γ) to H*(S1, Γ Q).

Using cyclic cohomology, Connes constructed in [2] an additive map, GV(α), which we shall call the Godbillon-Vey map, from the K0-group of the reduced crossed product C*-algebra C(S1) ⋊ αΓ into C. He showed that GV(α) agrees with the geometric Godbillon-Vey invariant through the index map μ from K0(S1, Γ) to K0(C(S1) ⋊ αΓ).
Fuchsian Embeddings in the Bianchi Groups
Authors: Fine Benjamin
Published: December 2010

If d is a positive square free integer we let Od be the ring of integers in and we let Γd = PSL2(Od), the group of linear fractional transformations

and entries from Od {if d = 1, ad – bc = ±1}. The Γd are called collectively the Bianchi groups and have been studied extensively both as abstract groups and in automorphic function theory {see references}. Of particular interest has been Γ1 – the Picard group. Group theoretically Γ1, is very similar to the classical modular group M = PSL2(Z) both in its total structure [4, 6], and in the structure of its congruence subgroups [8]. Where Γ1 and M differ greatly is in their action on the complex place C. M is Fuchsian and therefore acts discontinuously in the upper half-plane and every subgroup has the same property.
Weak Mixing Manifold Homeomorphisms Preserving an Infinite Measure
Authors: Alpern Steve , Prasad Vidhu
Published: December 2010

Let denote the group of all homeomorphisms of a σ-compact manifold which preserve a σ-finite, nonatomic, locally positive and locally finite measure μ. In two recent papers [4, 5] the possible ergodicity of a homeomorphism h in was shown to be related to the homeomorphism h* induced by h on the ends of M. An end of a manifold is, roughly speaking, a distinct way of going to infinity. Those papers demonstrated in particular that always contains an ergodic homeomorphism, paralleling the similar result of Oxtoby and Ulam [11] for compact manifolds with finite measures. Unfortunately the techniques used in [4] and [5] rely on the fact that a skyscraper construction with an ergodic base transformation is ergodic, a result which cannot be extended to finer properties than ergodicity.
N Subspaces
Authors: Sunder V. S.
Published: December 2010

It is a well-known fact (cf., for instance Lemma 7.3.1 of [8], and also [2] and [4] ) that if M and N are closed subspaces of a finite-dimensional Hilbert space, and if M and N are in ‘generic’ position (i.e., any two of the four subspaces M, M⊥, N, N⊥ have trivial intersection), then N is the graph of a linear isomorphism of M onto M⊥ . To be sure, there exist infinite-dimensional versions of this, where one must allow for unbounded operators in case the ‘gap’ between M and N is zero, in the sense of Kato [7]. (There is an extensive literature on pairs of subspaces, [2], [3], [4], [6] and [7], to cite a few; for a fairly extensive bibliography, see [3].)

This paper addresses itself to the case of n (2 ≦ n < ∞) subspaces.
Irreducibility Criteria for Polynomials with non-negative Coefficients
Authors: Filaseta Michael
Published: December 2010

In [7, b.2, VIII, 128] Pólya and Szegö state the following theorem of A. Cohn:

THEOREM 1. Let dndn−x … d0 be the decimal representation of a prime. Then

is irreducible.

Thus, for example, since 1289 is prime, x3 + 2x2 + 8x + 9 is irreducible. Brillhart, Odlyzko, and the author generalized Cohn's Theorem in three different directions. As examples of these types of generalizations, we note the following results, the first two of which are special cases of a result in [1] and the third of a result in [3].

THEOREM 2. Let dndn−x … d0 be the base b representation of a prime where b is an integer ≧2. Then

is irreducible.

THEOREM 3. Let

be such that f(10) is prime and 0 ≦ dj ≦ 167 for j = 0, 1, …, n. Then f(x) is irreducible.
On an F-Algebra of Holomorphic Functions
Authors: Kim Hong Oh
Published: December 2010

The complex maximal theorem of Hardy and Little-wood states:

(Mp). For 0 < p < ∞, there exists a positive constant Cp such that if f is holomorphic in the unit disc U of the complex plane then

where

The corresponding statement to the limiting case p = 0 can be stated as follows:

(M0) There exists a positive constant C0 such that if f is holomorphic in U

where log+t = max(log t, 0).

The statement (M0) is false as the following example shows.
Convergence of Interpolation to Transforms of Totally Positive Kernels
Authors: Dyn N. , Lubinsky D. S.
Published: December 2010

Convergence of exponential sums

that interpolate to Laplace transforms

(1.1)

have been studied by several authors [3, 6, 8, 15]. For rational functions that interpolate to Markov functions (also called Hamburger or Stieltjes Series or Hilbert Transforms)

(1.2)

far more detailed convergence results are available (see [10, 11, 16] and references therein). Both (1.1) and (1.2) are special cases of the transform

(1.3)

where K(x, t) is a strictly totally positive kernel.
Choquet Boundary for Real Function Algebras
Authors: Kulkarni S. H. , Arundhathi S.
Published: December 2010

The concepts of Choquet boundary and Shilov boundary are well-established in the context of a complex function algebra (see [2] for example). There have been a few attempts to develop the concept of a Shilov boundary for real algebras, [4], [6] and [7]. But there seems to be none to develop the concept of Choquet boundary for real algebras.

The aim of this paper is to develop the theory of Choquet boundary of a real function algebra (see Definition (1.8)) along the lines of the corresponding theory for a complex function algebra.

In the first section we define a real-part representing measure for a continuous linear functional ϕ on a real function algebra A with the property ║ϕ║ = 1 = ϕ(1). The elements of A are functions on a compact, Hausdorff space X. The Choquet boundary is then defined as the set of those points x ∊ X such that the real part of the evaluation functional, Re(ex), has a unique real part representing measure.
Some Remarks on IA Automorphisms of Free Groups
Authors: McCool J.
Published: December 2010

Let An be the automorphism group of the free group Fn of rank n, and let Kn be the normal subgroup of An consisting of those elements which induce the identity automorphism in the commutator quotient group . The group Kn has been called the group of IA automorphisms of Fn (see e.g. [1]). It was shown by Magnus [7] using earlier work of Nielsen [11] that Kn is finitely generated, with generating set the automorphisms

and

where x1, x2, …, xn, is a chosen basis of Fn.
Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group
Authors: Anderson John T.
Published: December 2010

If K is a compact subset of Cn, will denote the polynomial hull of K:

arises in the study of uniform algebras as the maximal ideal space of the algebra P(K) of uniform limits on K of polynomials (see [3]). The condition (K is polynomially convex) is a necessary one for uniform approximation on K of continuous functions by polynomials (P(K) = C(K)). If K is not polynomially convex, the question of existence of analytic structure in is of particular interest. For n = 1, is the union of K and the bounded components of C\K. The determination of in dimensions greater than one is a more difficult problem. Among the special classes of compact sets K whose polynomial hulls have been determined are those invariant under certain group actions on Cn.
Oscillations of Second Order Neutral Equations
Authors: Ladas G. , Partheniadis E. C. , Sficas Y. G.
Published: December 2010

Consider the second order neutral differential equation

1

where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is

2

The main result in this paper is the following necessary and sufficient condition for all solutions of Eq. (1) to oscillate.

THEOREM. The following statements are equivalent:

(a) Every solution of Eq. (1) oscillates.

(b) Equation (2) has no real roots.
General Heredity and Strength for Radical Classes
Authors: Sands A. D. , Stewart P. N.
Published: December 2010

An H-relation, as introduced by Rossa and Tangeman [4], is a relation σ on the class of associative rings with their subrings satisfying the following conditions:

(1) IσR implies that I is a subring of R;

(2) if IσR and f is a homomorphism of R, then (If)σ(Rf);

(3) if IσR and J is an ideal of R, then (I∩J)σJ.

Puczylowski [3] imposes also the condition

(4) if J is an ideal of R, then JσR.

A further condition satisfied by many familiar H-relations is the following:

(5) if f is a homomorphism from a ring R onto a ring S and BσS, then there
exists a subring A of R such that AσR and Af = B.
Moyennes Galoisiennes des Valeurs de Fonctions L
Authors: Vignéras Marie-France
Published: December 2010

On se propose d'étendre un résultat de Rorhlich [5] concernant les moyennes galoisiennes des valeurs en s = 1 des fonctions L associées à une forme modulaire de poids 2, tordue par certains caractères de Dirichlet. On considérera une représentation automorphe parabolique π de GL(n), n≦2, sur un corps de nombres K, et l'on s'intéressera aux valeurs des fonctions L(S,πχ) et de leurs dérivées L(m)(s, πχ), m ≧1, où χ parcourt certains caractères de Hecke de K, d'ordre fini, et où s appartient à la bande a < Re s < 1 — a, où a mesure la déviation de n par rapport à la conjecture de Petersson généralisée.
C-Valuations and Normal C-Orderings
Authors: Chacron M.
Published: December 2010

Let D stand for a division ring (or skewfield), let G stand for an ordered abelian group with positive infinity adjoined, and let ω: D → G. We call to a valuation of D with value group G, if ω is an onto mapping from D to G such that

(i) ω(x) = ∞ if and only if x = 0,

(ii) ω(x1 + x2) = min(ω (x1), ω (x2)), and

(iii) ω (x1 x2) = ω (x1) + ω (x2).

Associated to the valuation ω are its valuation ring

R = ﹛x ∈ Dω(x) ≧ 0﹜,

its maximal ideal

J = ﹛x ∈ |ω(x) > 0﹜, and its residue division ring D = R/J.The invertible elements of the ring R are called valuation units. Clearly R and, hence, J are preserved under conjugation so that 1 + J is also preserved under conjugation. The latter is thus a normal subgroup of the multiplicative group Dm of D and hence, the quotient group D˙/1 + J makes sense (the residue group of ω). It enlarges in a natural way the residue division ring D (0 excluded, and addition “forgotten“).
Introduction to the Schwartz Space of T\G
Authors: Casselman W.
Published: December 2010

LetGbe the group of R-rational points on a reductive group defined over Q andTan arithmetic subgroup. The aim of this paper is to describe in some detail the Schwartz space(whose definition I recall in Section 1) and in particular to explain a decomposition of this space into constituents parametrized by the T-associate classes of rational parabolic subgroups ofG.This is analogous to the more elementary of the two well known decompositions ofL2(T\G)in [20](or [17]), and a proof of something equivalent was first sketched by Langlands himself in correspondence with A. Borel in 1972. (Borel has given an account of this in [8].)Langlands’ letter was in response to a question posed by Borel concerning a decomposition of the cohomology of arithmetic groups, and the decomposition I obtain here was motivated by a similar question, which is dealt with at the end of the paper.
Rewritable Products In Fc-By-Finite Groups
Authors: Blyth Russell D. , Rhemtulla Akbar H.
Published: December 2010

Let n be an integer greater than 1. The group G has the property Q„, or is n-rewritable, if for each «-element subset ﹛x1 x 2… ,x n﹜ of G, there exist permutations such that If one of ᓂ,τ can always be chosen to be the identity, then G has Pn, or is totally n-rewritable. We also use Pn and Qn to denote the classes of groups having these properties. Making use of the obvious inclusions, we define
Congruences on Completely Regular Semigroups
Authors: Petrich Mario
Published: December 2010

There are two subjects in the literature on semigroups which have recently attracted great attention: the class of completely regular semigroups (that is semigroups which are unions of their subgroups) and congruences on regular semigroups. In completely regular semigroups, the most popular subject is that of varieties, even though other aspects of them, such as structure, congruences, amalgamation, received their due attention. On the other hand, the treatment of congruences on regular semigroups became especially interesting with the emergence of the kernel-trace approach. This method proved quite successful in the case of inverse semigroups, see [6], whereas the analysis for the general regular semigroups encounters considerable difficulties, see [4].
Topological Properties of Cyclic Coverings Branched Along an Ample Divisor
Authors: Lanteri Antonio , Struppa Daniele C.
Published: December 2010

Let X’ → X be a finite morphism between two complex connected projective k-folds. Since Π is surjective, the Betti numbers of X and X’ are related as follows

(0.1) bi(X) ≦ bi(X’).

In particular, if Π is a cyclic covering and the branch locus A is an ample divisor, (0.1) is in fact an equality for i ≦ k — 1 (see 1.10 or, more generally, [5] ). It seems natural to look for such coverings satisfying

(0.2) bk(X)= bk(X’).

Let us see what happens for k = 2. In this case (0.2) can be rephrased as

(0.3) 2x(Ox) + h1,1 (X) + g(Δ) = 2,
Generalized Matrices
Authors: Roesler Friedrich
Published: December 2010

Similar to the multiplication of square matrices one can define
multiplications for three dimensional matrices, i.e., for the "cubes" of the vector
space

where I denotes a finite set of indices and Kis any field. The multiplications shall imitate the matrix multiplication: To obtain the coefficient γxyzof the product (γxyz) — (αxyz)( βxyz),all coefficients axij, ij∈ I, of the horizontal plane with index xof (αxyz)are multiplied with certain coefficients βhgzof the vertical plane with index z of (βxyz)and the results are added:
Lyndon Words, Free Algebras and Shuffles
Authors: Melançon Guy , Reutenauer Christophe
Published: December 2010

A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of the quotients of the lower central series of a free group or, equivalently, bases of the free Lie algebra [2], [7]. They have also many combinatorial properties, with applications to semigroups, pi-rings and pattern-matching, see [1], [10].

We study here the Poincaré-Birkhoff-Witt basis constructed on the Lyndon basis (PBWL basis). We give an algorithm to write each word in this basis: it reads the word from right to left, and the first encountered inversion is either bracketted, or straightened, and this process is iterated: the point is to show that each bracketting is a standard one: this we show by introducing a loop invariant (property (S)) of the algorithm. This algorithm has some analogy with the collecting process of P. Hall [5], but was never described for the Lyndon basis, as far we know.
Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series
Authors: Krattenthaler Christian
Published: December 2010

Let be a pair of a formal series (fps) in z1 and z2 of the form where is an fps with for i = 1,2. Then there exists a unique pair of fps which is also of the form (1.1), with This pair is called the inverse of f(z1,z2 ).
Classifying Algebras for the K-Theory of σ-C*-Algebras
Authors: Phillips N. Christopher
Published: December 2010

In topology, the representable K-theory of a topological space X is defined by the formulas RK0(X) = [X,Z x BU] and RKl(X) = [X, U], where square brackets denote sets of homotopy classes of continuous maps, is the infinite unitary group, and BU is a classifying space for U. (Note that ZxBU is homotopy equivalent to the space of Fredholm operators on a separable infinite-dimensional Hilbert space.) These sets of homotopy classes are made into abelian groups by using the H-group structures on Z x BU and U. In this paper, we give analogous formulas for the representable K-theory for α-C*-algebras defined in [20].
An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas
Authors: Gasper George , Rahman Mizan
Published: December 2010

Let denote the q-shifted factorial, and set Recently, Gasper [7] showed that some bibasic summation formulas derived by Carlitz [5], Al-Salam and Verma [1], and Wm. Gosper could be extended to the indefinite bibasic summation formula where p and q are independent bases and a, b, c are arbitrary parameters.
Lawrence Polytopes
Authors: Bayer Margaret , Sturmfels Bernd
Published: December 2010

In 1980 Jim Lawrence suggested a construction Λ which assigns to a given rank r oriented matroid M on n points a rank n + r oriented matroid Λ(M) on 2n points such that the face lattice of Λ(M) is polytopal if and only if M is realizable. The Λ-construction generalized a technique used by Perles to construct a nonrational polytope [10]. It was used by Lawrence to prove that the class of polytopal lattices is strictly contained in the class of face lattices of oriented matroids (unpublished) and by Billera and Munson to show that the latter class is not closed under polarity. See [4] for a discussion of this construction and both of these applications.
Acyclicity of Certain Homeomorphism Groups
Authors: Sankaran P. , Varadarajan K.
Published: December 2010

The concept of a mitotic group was introduced in [3] by Baumslag, Dyer and Heller who showed that mitotic groups were acyclic. In [8] one of the authors introduced the concept of a pseudo-mitotic group, a concept weaker than that of a mitotic group, and showed that pseudo-mitotic groups were acyclic and that the group Gnof homeomorphisms of Rn with compact support is pseudo-mitotic. In our present paper we develop techniques to prove pseudomitoticity of certain other homeomorphism groups. In [5] Kan and Thurston observed that the group of set theoretic bijections of Q with bounded support is acyclic. A natural question is to decide whether the group of homeomorphisms of Q (resp. the irrationals I ) with bounded support is acyclic or not. In the present paper we develop techniques to answer this question in the affirmative.
Samelson Products In Spaces of Self-Homotopy Equivalences
Authors: Møller Jesper Michael
Published: December 2010

The homotopy groups of any group-like space are equipped with a Samelson product satisfying, up to sign, the identities of a graded Lie bracket. We shall compute the Samelson product in two kinds of spaces of selfhomotopy equivalences arising when adding a homotopy or a homology group to a space.

First, let A→ X be a cofibration with a Moore space M(G,n) as cofibre. For the monoid autA (X) of maps under A homotopic (rel. A) to the identity, the Samelson product is a pairing

πn+i(G;X)⨂πn+j(G;X) → πn+i+j(G;X)

of homotopy groups with coefficients [1] in G. Theorem 2.1 computes this pairing in terms of a homomorphism associated to a α ∈ πi(autAX)).
Total Categories and Solid Functors
Authors: Börger Reinhard , Tholen Walter
Published: December 2010

Totality of a category as introduced by Street and Walters [17] is known to be a strong cocompleteness property (cf. also [21]) which goes far beyond ordinary (small) cocompleteness. It implies compactness in the sense of Isbell [11] and therefore hypercompleteness [7], that is: the existence of limits of all those (not necessarily small) diagrams which are not prevented from having a limit merely from size-considerations with respect to the homsets. In particular, arbitrary intersections of monomorphisms exist in a total category; which is part of Street's [16] characterization of totality and is used in establishing the interrelationship with topoi (cf. also [15]).
Automorphisms of Free Nilpotent Lie Algebras
Authors: Drensky Vesselin , Gupta C. K.
Published: December 2010

Let Fm be the free Lie algebra of rank m over a field K of characteristic 0 freely generated by the set ﹛x1,… ,xm﹜, m ≧ 2. Cohn [7] proved that the automorphism group Aut Fm of the K-algebra Fm is generated by the following automorphisms: (i) automorphisms which are induced by the action of the general linear group GLm (= GLm(K)) on the subspace of Fm spanned by ﹛x1, … ,xm﹜; (ii) automorphisms of the form x1 → x1 +f(x2,… ,xm),Xk → xk, k ≠ 1, where the polynomial f(x2,…,xm) does not depend on x1.
A Generalization of Moak's q-Laguerre Polynomials
Authors: Koekoek Roelof
Published: December 2010

In [6] we studied the polynomials which are generalizations of the classical (generalized) Laguerre polynomials These polynomials were shown to be orthogonal on the interval [0, ∞) with respect to the inner product where a > — 1,M ≧0 and N ≧0.