bluuebunny/crossref_metadata_2025_split huggingface dataset:
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.
Polynomials with Coefficients from a Division Ring
Authors: Bray Una , Whaples George 
Published: December 2010

Let R be any division ring and let1be 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 identity1.1for 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 formulawhere CN is chosen so thatSince 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 that1It 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 that2for some ergodic stationary sequence {Yn, n ∊ Z}.
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 spacesas 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 spacesof respective dimensionsthey 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.
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).
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.
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.)
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 bywas 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 thatSuch an integral operator is called a Carleman integral operator if for almost every x ∊ X the functionis 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 notationThere is a natural duality between S and the space ϕ of sequences which are eventually ϕ given by the equationThe series has only a finite number of nonzero terms since t is in ϕ.A subset B of ϕ is called S-bounded iffor 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 withThere 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 identityof 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 thatLet 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.
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.