bluuebunny/crossref_metadata_2025_split huggingface dataset:
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 , thenare opposite parabolic subgroups of G in the usual sense [1], [28]. However the mapdoes not exhaust all pairs of opposite parabolic subgroups of G. Now consider the representation ϕ:G → SL(6, K) given by
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. ThenIt 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 boundHe 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 form1where f satisfies the following condition in which Z denotes the integers,2and 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 andwhere
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 problem1.1in 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 transformationsand 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.
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. Thenis 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. Thenis irreducible.THEOREM 3. Letbe 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 thenwhereThe 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 Uwhere 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 sumsthat 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 automorphismsandwhere 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 equation1where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is2The 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.
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 ringR = ﹛x ∈ Dω(x) ≧ 0﹜,its maximal idealJ = ﹛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“).
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
spacewhere 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.
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 pairingπn+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)).
The Failure of Cancellation Laws for Equidecomposability Types
Authors: Truss J. K. 
Published: December 2010

AbstractLet B be a Boolean algebra and G a group of automorphisms of B. Define an equivalence relation ∼ on B by letting x ∼ y if there are x1, x2,…,xn, y1, y2, …yn in B such that x is the disjoint union of the xi, y is the disjoint union of the yi, and for each i there is a member of G taking xi to yi. The equivalence classes under ∼ are called equidecomposability types. Addition of equidecomposability types is given by (x) + (y) = (x V y) provided x ∧ y = 0. An example is given of a complete Boolean algebra B and a group G of automorphisms of B with X, Y ∊ B such that (X) + (X) = (Y) + (Y) but (X) ≠ (Y), answering a question of Wagon (see [5 p. 231 problem 14]). Moreover B may be taken to be the algebra of Borel subsets of Cantor space modulo sets of the first category. It is also remarked that in this case equidecomposability types do not form a weak cardinal algebra.
Stochastic Fubini Theorem for Semimartingales in Hilbert Space
Authors: León Jorge A. 
Published: December 2010

In this paper we will study the Fubini theorem for stochastic integrals with respect to semimartingales in Hilbert space.Let (Ω, , P) he a probability space, (X, , μ) a measure space, H and G two Hilbert spaces, L(H, G) the space of bounded linear operators from H into G, Z an H-valued semimartingale relative to a given filtration, and φ: X × R+ × Ω → L(H, G) a function such that for each t ∈ R+ the iterated integrals are well-defined (the integrals with respect to μ are Bochner integrals). It is often necessary to have sufficient conditions for the process Y1 to be a version of the process Y2 (e.g. [1], proof of Theorem 2.11).