bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Results on Totally Isotropic Subspaces and Five-Dimensional Quadratic Forms Over GF(q)
Authors: Cordes Craig M. 
Published: December 2010

In [5] Pall denned a partitioning of a quadratic space over a field of characteristic not 2 to be a collection of disjoint (except for ﹛0﹜ ) maximal totally isotropic subspaces whose union formed the set of isotropic vectors. Clearly isometric quadratic spaces simultaneously do or do not have partitionings. Pall exhibited the existence of partitionings for the spaces associated withover formally real fields for n = 1, 2, 4, 8 and over Z/(p), p prime, for n = 1, 2. Using the latter, he was able to find a new proof for Jacobi's formula for the number of representations of a positive integer as the sum of four integral squares.
A Variational Technique for Bounded Starlike Functions
Authors: Barnard R. W. 
Published: December 2010

Let KM = {z : \z\ < M}, 1 ≦ M < ∞ and K = K1. Let S denote the collection of functions f(z) = z + a2z2 + a3s3 + … that are regular and univalent in K. We write, for 1 < M < ∞,S(M) = ﹛f : f ∞ S, f (K) ⊂ KM ﹜,S*(M) = ﹛f : f ∞ S(M), f(K) is starlike with respect to the origin﹜.In this paper we develop a variational technique for slit domains and give some applications with respect to finding theand thefor any nonconstant entire function ᶲ(w) and a given z ∊ K.
A Minimax Equality Related to the Longest Directed Path in an Acyclic Graph
Authors: Vidyasankar K. , Younger D. H. 
Published: December 2010

As an analog of a recently established minimax equality for directed graphs [1], I. Simon has suggested that the following be investigated.1.1. For a finite acyclic directed graph G, a minimum collection of directed coboundaries whose union is the edge set of G has cardinality equal to that of a maximum strong matching of G.This minimax equality is here proved, using a characterization of a maximum strong matching of an acyclic graph as the set of edges of a longest directed path in the graph.The terms employed in the above theorem are defined as follows. Let G be a finite directed graph with vertex set VG and edge set eG
The n-Dimensional Distributional Hankel Transformation
Authors: Koh E. L. 
Published: December 2010

The Hankel transformation was extended to certain generalized functions of one dimension [1; 2; 3]. In this paper, we develop the n-dimensional case corresponding to [1]. The procedure in [1] is briefly as follows:A test function space Hμ is constructed on which the μth order Hankel transformation hμ defined byis an automorphism whenever μ ≧ —1/2. The generalized transformation hμ' is then defined on the dual Hμ' as the adjoint of hμ through a Parseval relation, i.e.
On a Theorem of Arhangel'skiĭ Concerning Lindelöf P-Spaces
Authors: Hodel R. E. 
Published: December 2010

1. Introduction. In [4] Arhangel'skiĭ proved the remarkable result that every regular space which is hereditarily a Lindelöf p-space has a countable base. As a consequence of the main theorem in this paper, we obtain an analogue of Arhangel'skiĭs result, namely that every regular space which is hereditarily an ℵi-compact strong ∑-space has a countable net. Under the assumption of the generalized continuum hypothesis (GCH), the main theorem also yields an affirmative answer to Problem 2 in Arhangel'skiĭs paper.In § 3 we introduce and study a new cardinal function called the discreteness character of a space. The definition is based on a property first studied by Aquaro in [1], and for the class of T1 spaces it extends the concept of Kicompactness to higher cardinals.
A Note on Certain Spaces with Bases (mod K)
Authors: Bennett Harold R. , Martin Harold W. 
Published: December 2010

In this note all spaces are assumed to be regular T1 spaces and all undefined terms and notations may be found in [8], In particular let cl(A) denote the closure of the set A and let Z+ denote the set of natural numbers.Definition 1. Let X be a topological space and a covering of X by compact sets. An open covering of X is said to be a basis (mod K) if whenever and an open set V contains Kx, then there exists such that . In such a case X is written as the ordered triple .
The Convergence of Series for Various Choices of Sign in Banach Spaces
Authors: Shirey James 
Published: December 2010

1. Let (xn, Xn) denote a basis for a Banach space (X, ∥ • ∥) of measurable functions in (0, 1).It is shown in [2] and [9] that the equivalence of the normsand ∥ • ∥ is equivalent to the unconditionality of the basis (xn, Xn). In [8] a weaker relationship between these norms is exploited to establish the existence of an element of L1(E) for each E ⊂ (0, 1), |£| > 0, whose Haar series expansion is conditionally convergent in the norm of L\(E).In this note, a Lemma of Orlicz [7] is generalized to provide a relationship between , and the changes in sign that are tolerated in without disruption of norm convergence.
A Remark on Colimits
Authors: Osofsky Barbara L. 
Published: December 2010

Let MR be a right module over the associative ring R (with 1). Assume one has an expression for M as a colimit (direct limit) of a systemover the (directed) poset D. A natural way to get M as a colimit of the family ﹛F∞ —” Fβ|∞, fβ ∈ E﹜ for some subset £ of D is to take E cofinal in D. However, if one is concerned about the cardinality of the set E, cofinal subsets may be too large. Let us look at a specific example. Lazard [3] has shown that any flat MR is a direct limit of finitely generated free R-modules. The cardinality of his indexing set depends on the cardinality of M.
On Infinite Systems of Linear Differential Equations
Authors: McClure J. P. , Wong R. 
Published: December 2010

Let A = [αtj] (i,j = 1, 2, …) be an infinite matrix with complex entries, and let z = (ζj) (j = 1, 2, …) be a sequence of complex numbers. In this paper we wish to investigate the existence, uniqueness and asymptotic behavior of solutions to the infinite system of linear differential equationswith the initial conditions
Synthese Harmonique Des Sous-Groupes Discrets
Authors: Lohoué N. 
Published: December 2010

Dans [4] C. S. Herz soulève la question suivante:Soit G = SL(2, R) le groupe des matrices réelles d'order deux, de déterminant un; soit H = SL(2, Z) le sous-groupe discret de G, formé des matrices à coefficients entiers. Existe-t-il une constante absolue c > 0 telle que pour toute function f de At(H) à support fini, on puisse trouver une function de AP(G), à support compact dont la restriction à H coïncide a vec f et
A General Asymptotic Result for Partitions
Authors: Richmond Bruce 
Published: December 2010

In this paper we are concerned with partition functions pϒ(n) that have generating functions of the formwhere γ(n) ≧ 0. We shall obtain an asymptotic relation for pϒ(n) under suitable restrictions on ϒ (see Theorem 1.1). These restrictions are weaker than those of Brigham [2] who considered this problem previously.
Oscillation of Elliptic Equations in General Domains
Authors: Noussair E. S. 
Published: December 2010

Oscillation criteria will be obtained for the linear elliptic partial differential equationin an unbounded domain G of general type in n-dimensional Euclidean space En. The differential operator D is defined as usual by where each α (i), i = 1, … , n, is a non-negative integer.
A Note on the Dirichlet Condition for Second-Order Differential Expressions
Authors: Everitt W. N. 
Published: December 2010

Let M denote the formally symmetric, second-order differential expression given by, for suitably differentiable complex-valued functions ƒ,The coefficients p and q are real-valued, Lebesgue measurable on the halfclosed, half-open interval [a, b) of the real line, with - ∞ < a < b ≦ ∞, and satisfy the basic conditions:
Split Subdirect Products and Piecewise Domains
Authors: Fuelberth John , Kuzmanovich James 
Published: December 2010

Throughout this paper all rings will have unity and all modules will be unital.If X ⊂ R, then r(X) (respectively, l(X)) denotes the right (left) annihilator of x.An element d of R is called right (left) regular if r(d) = 0 (1(d) = 0). An element which is both right and left regular is called regular.
On a Structural Property of the Groups of Alternating Links
Authors: Mayland E. J. , Murasugi Kunio 
Published: December 2010

In this paper, we will prove, as a consequence of the main theorem,THEOREM A. (See Corollary 2.6). The group of an alternating knot, for which the leading coefficient of the knot polynomial is a prime power, is residually finite and solvable.
Value Distribution of Biaxially Symmetric Harmonic Polynomials
Authors: D'Archangelo J. , McCoy P. A. 
Published: December 2010

Consider the biaxially symmetric potential equationwhere α, β > — 1/2. If 2α + 1 and 2 β + 1 are non-negative integers and if X corresponds to the hypercirclethen the biaxisymmetric Laplace equation in E2(α+ β+2),and (1.1) are equivalent.
Matrices Doubly Stochastic by Blocks
Authors: Fischer Pal , Holbrook John A. R. 
Published: December 2010

The present work stems from the following classical result, due to G. H. Hardy, J. E. Littlewood, G. Pólya [7], and R. Rado [10].THEOREM 1. Concerning a pair of n-tuples x, y ϵ Rn, the following four statementsare equivalent:(a) for every continuous, convex function f : R → R
Changes of Variables Preserving Fourier-Stieltjes Transforms on Simply Connected Nilpotent Lie Groups
Authors: Drury S. W. 
Published: December 2010

In [1] Beurling and Helson prove the following theorem.THEOREM. Let φ: R → R be a continuous map such thatThen φ is affine. (Here denotes the space of Fourier-Stieltjes transforms on R.)
Even Whitehead Squares are Not Projective
Authors: James Milgram R. , Zvengrowski Peter 
Published: December 2010

The projectivity of the Whitehead square wn = [in, in] in π2n-1(SN) has been studied by Randall [6] who proved that if wn is projective then n must be a power of 2 or one less than a power of 2. Here we solve the question in the even case, proving by means of bo homology:Theorem. if and only if n = 1, 2, 4.
A Failure of Stability Under Complex Interpolation
Authors: Connett William C. , Schwartz Alan L. 
Published: December 2010

Let denote the spaces of Bessel potentials as denned and discussed in [6]. When 1 < q < ∞ and α is an integer , the Sobolev space which consists of functions Fin Lq with α derivatives in Lq and with norm If now we make the change of variables x = ev, f(x) = F (In x) it is easily seen that the ratio
Geometry on the Unit Ball of a Complex Hilbert Space
Authors: Hahn Kyong T. 
Published: December 2010

Furnishing the open unit ball of a complex Hilbert space with the
Carathéodory-differential metric, we construct a model which plays a
similar role as that of the Poincaré model for the hyperbolic geometry.
In this note we study the question whether or not through a point in the
model not lying on a
given line there exists a unique perpendicular, and give a necessary and
sufficient condition for the existence of a unique perpendicular. This enables us
to divide a triangle into two right triangles. Many trigonometric identities in a
general triangle are easy consequences of various identities which hold on a right
triangle.
Functionals on Real C(S)
Authors: Farnum Nicholas , Whitley Robert 
Published: December 2010

The maximal ideals in a commutative Banach algebra with identity have been
elegantly characterized [5; 6] as
those subspaces of codimension one which do not contain invertible elements. Also,
see [1]. For a function algebra
A, a closed separating subalgebra with constants of
the algebra of complex-valued continuous functions on the spectrum of
A, a compact Hausdorff space, this characterization
can be restated: Let F be a linear functional on
A with the property:
(*) For each ƒ in A there is a point
s, which may depend on f,
for which F(f) = f(s).
Planar Sublattices of a Free Lattice. I
Authors: Rival Ivan , Sands Bill 
Published: December 2010

There are three lattice-theoretic properties that are generally used to open a discussion on sublattices of a free lattice:(W) for all a, b, c, d, a Λ b ≦ c V d implies a A b ≦ c, a Λ b g rf, a ≦cVd,orb ≦ c V d;(SDv) for all a, b, c, a V b = a V c implies a V b = a V (b Λ c ) ;(SDΛ) for all a, b, c, a Λ b = a Λ c implies a Λ b = a Λ (b V c).
The Density of Zeros of Dirichlet's L-Functions
Authors: Heath-Brown D. R. 
Published: December 2010

Let L(s, χ) be a Dirichlet L-function and let N(σ, T, χ) denote the number of zeros ρ of L(s, χ), counted according to multiplicity, in the rectangle σ ≦ Re(ρ) ≦ 1, |Im(ρ)| ≦ T, (T ≦ 1). In this paper we shall prove several new estimates for the sumwhere Σ* denotes summation over primitive characters only. These estimates will all be of the type(1)where denotes any fixed positive quantity.
On Certain Polynomials of Gaussian Type
Authors: Reich Daniel 
Published: December 2010

Introduction. We shall consider functions of the formwhere {ri} and {si} are sets of positive integers. Such functions were studied by E. Grosswald in [2], who took {si} to be pairwise relatively prime, and asked the following two questions:(a) When is ƒ(t) a polynomial?(b) When does ƒ(t) have positive coefficients?These questions arise naturally from the work of Allday and Halperin, who show in [1] that under suitable circumstance ƒ(t) will be the Poincare polynomial of the orbit space of a certain Lie group action. Grosswald gives a complete answer to (a), but (b) is a much harder question, and a complete answer is provided only for the case m = 2. His treatment involves the representation of the coefficients of ƒ(t) by partition functions, and uses a classical description by Sylvester of the semigroup generated by {si}.
Mean Values of Character Sums
Authors: Montgomery H. L. , Vaughan R. C. 
Published: December 2010

For a non-principal Dirichlet character χ modulo q,Let the Pólya-Vingradov inequality asserts that M(x) < q1/2 log q see [7]. in the opposite direction it is a trivial consequence of lemma 1 below and 1. Parseval's identity that if χ is primitive modulo q, thenWe show that on average the latter of these estimates is the more precise.THEOREM 1. For any real k > 0where the summation is over all non-principal characters modulo q.THEOREM 2. For any k > 0,
Noether Lattices Representable as Quotients of the Lattice of Monomially Generated Ideals of Polynomial Rings
Authors: Anderson D. D. , Johnson E. W. , Johnson J. A. 
Published: December 2010

Noether lattices were introduced by R. P. Dilworth in [5] and constitute a natural abstraction of the lattice of ideals of a Noetherian ring. In his definitive work, Dilworth showed that a minimal prime of an element generated by n principal elements has rank ≦ n. Following standard ring theoretical terminology, a local Noether lattice with (unique) maximal element M is said to be regular if M has rank n and can be generated by n principal elements.In [3], K. P. Bogart showed that a distributive regular local Noether lattice of Krull dimension n is isomorphic to RLn, the sublattice of all ideals generated by monomials of any polynomial ring (k a field). In a later paper [4], Bogart extended his results on distributive regular local Noether lattices by showing that any distributive local Noether lattice is the image of a multiplicative map θ which preserves joins, and can in fact be thought of as the related congruence lattice.
Localization, Algebraic Loops and H-Spaces II
Authors: Shar Albert O. 
Published: December 2010

In a previous work [6] it was shown that by imposing certain finiteness conditions on a nilpotent loop certain algebraic results yielded properties about [X, Y] where X is finite CW and Y is an H-Space. In this sequel we further restrict the category of nilpotent loops to a full subcategory called H-loops which still contains all loops of the form [X, Y], We prove that on this category there is a unique and universal P-localization if P ≠ ∅ which corresponds to topological localization. We also show that if the H-loop is a group then the two concepts of localization agree.The first section of this paper is devoted to the definition and basic properties of H-loops. In the second section we develop the localization construction and prove uniqueness. Finally, in the third section we consider the topological and group theoretic situations.
Combinatorial Oriented Maps
Authors: Tutte W. T. 
Published: December 2010

An orientable map is often presented as a realization of a finite connected graphGin an orientable surface so that the complementary domains ofG, the “faces” of the map are topological open discs. This is not the definition to be used in the paper. But let us contemplate it for a while.On each edge ofGwe can recognize two opposite directed edges, or “darts”. Letθbe the permutation of the dart-setSthat interchanges each dart with its opposite. The darts radiating from a vertexvoccur in a definite cyclic order, fixed by a chosen positive sense of rotation on the surface. The cyclic orders at the various vertices are the cycles of a permutationPofS. The choice ofPrather thanP–l, which corresponds to the other sense of rotation, makes the map “oriented”.
On a Uniqueness Theorem
Authors: Niimura Mikio 
Published: December 2010

The classical uniqueness theorems of Riesz and Koebe show an important characteristic of boundary behavior of analytic functions in the unit disc. The purpose of this note is to discuss these uniqueness theorems on hyperbolic Riemann surfaces. It will be necessary to give additional hypotheses because Riemann surfaces can be very nasty. So, in this note the Wiener compactification will be used as ideal boundary of Riemann surfaces. The Theorem, Corollaries 1, 2 and 3 are of Riesz type, Riesz-Nevanlinna type, Koebe type and Koebe-Nevanlinna type respectively. Corollaries 4 and 5 are general forms of Corollaries 2 and 3 respectively.Let f be a mapping from an open Riemann surface R into a Riemann surface R′.
Equivalence of Topologically-Algebraic and Semi-Topological Functors
Authors: Herrlich H. , Nakagawa R. , Strecker G. E. , Titcomb T. 
Published: December 2010

Throughout let be faithful.1.1. A U-morphism with domain X is a pair (e, A), where e ∈ Hom (X, UA). A [U-morphism (e, A) is called U-epi ( = generating) provided that r, s ∈ Hom (A, A’) and (Ur)e = (Us)e imply that r = s.1.2. A U-source is a pair (X, (fi,Ai)I), (written more simply (X, (fi,Ai)I),, where (fi,Ai)I 7 is a family of U-morphisms each with domain X.1.3. A factorization of a U-source (X,fi,Ai)I is a triple (e,A,gi)I such that (e, A) is a U-morphisms with domain X and for each i ∈ I gi ∈ Hom (A,Ai) and (Ugi)e = fi.
A Characterization of Sharply Transferable Lattices
Authors: Grätzer G. , Platt C. R. 
Published: December 2010

A lattice L is called transferable if and only if, whenever L can be embedded in the ideal lattice I(K) of a lattice K, L can be embedded in K. L is called sharply transferable if and only if, for every lattice embedding ψ(x) , there exists an embedding such that for x, y ϵ L, if and only if x ≤ y. Finite sharply transferable lattices were characterized in [3]. In this paper we extend the characterization to the infinite case. We begin by revising some of the terminology of [3].1.1. Definition, (a) Let 〈P; ≧〉 be a poset and X, Y ⊆ P. Then X dominates Y (written X Dom Y) if and only if, for every y ∈ F, there exists x ∈ X such that y ∈ x. Dually, X supports Y (written X Spp Y) if and only if, for every y ∈ Y, there exists x ∈ X such that x ≦ y.
SL(2,5) and Frobenius Galois Groups Over Q
Authors: Sonn Jack 
Published: December 2010

A finite transitive permutation group G is called a Frobenius group if every element of G other than 1 leaves at most one letter fixed, and some element of G other than 1 leaves some letter fixed. It is proved in [20] (and sketched below) that if k is a number field such that SL(2, 5) and one other nonsolvable group Ŝ5 of order 240 are realizable as Galois groups over k, then every Frobenius group is realizable over k. It was also proved in [20] that there exists a quadratic (imaginary) field over which these two groups are realizable. In this paper we prove that they are realizable over the rationals Q, hence we ObtainTHEOREM 1. Every Frobenius group is realizable as the Galois group of an extension of the rational numbersQ.
Rational Approximation to xn II
Authors: Newman D. J. , Reddy A. R. 
Published: December 2010

Introduction. In 1858 Chebyshev showed that xn+l can be approximated uniformly on [–1, 1] by polynomials of degree at most n with an error 2–n. Let 0 ≦ σ ≦ (n + l)tan2(π/2n + 2). In 1868 Zolotarev established that x n + 1σxn can be approximated uniformly on [ –1, 1] by polynomials of degree at most (n – 1) with an error 2–n(l + σ/n + l)n+1. It is interesting to note that for the case σ = 0, Zolotarev's result includes Chebyshev's result. Achieser ([1], p. 279) proved the following analogue for rational approximation. Let a0 ≠ 0, a1, a2, a3, …, an be any given real numbers. Then for every N > n,where λ is numerically the smallest root of the polynomialwith
On a Class of One-Relator Groups
Authors: Brunner A. M. 
Published: December 2010

In this paper, we consider the class of groups G(l, m; k) which are defined by the presentationwhere k, l, m are integers, and |l| > m > 0, k > 0. Groups in this class possess many properties which seem unusual, especially for one-relator groups. The basis for the results obtained below is the determination of endomorphisms.For certain of the groups, we are able to calculate their automorphism groups. One consequence of this is to produce examples of one-relator groups with infinitely generated automorphism groups. This answers a question raised by G. Baumslag (in a colloquium lecture at the University of Waterloo). Our examples are, perhaps, the simplest possible; J. Lewin [10] has found an example of a finitely presented group with an infinitely generated automorphism group.
Incompressible Surfaces in the Boundary of a Handlebody–an Algorithm
Authors: Lyon Herbert C. 
Published: December 2010

Our first result is a decomposition theorem for free groups relative to a set of elements. This enables us to formulate several algebraic conditions, some necessary and some sufficient, for various surfaces in the boundary of a 3-dimensional handlebody to be incompressible. Moreover, we show that there exists an algorithm to determine whether or not these algebraic conditions are met.Many of our algebraic ideas are similar to those of Shenitzer [3]. Conversations with Professor Roger Lyndon were helpful in the initial development of these results, and he reviewed an earlier version of this paper, suggesting Theorem 1 (iii) and its proof. Our notation and techniques are standard (cf. [1], [2]). A set X of elements in a finitely generated free group F is a basis if it is a minimal generating set, and X±l denotes the set of all elements in X, together wTith their inverses.
Blocking Sets and Skew Subspaces of Projective Space
Authors: Bruen Aiden A. 
Published: December 2010

In what follows, a theorem on blocking sets is generalized to higher dimensions. The result is then used to study maximal partial spreads of odd-dimensional projective spaces.Notation. The number of elements in a set X is denoted by |X|. Those elements in a set A which are not in the set Bare denoted by A — B. In a projective space Σ = PG(n, q) of dimension n over the field GF(q) of order q, ┌d(Ωd, Λd, etc.) will mean a subspace of dimension d. A hyperplane of Σ is a subspace of dimension n — 1, that is, of co-dimension one.A blocking set in a projective plane π is a subset S of the points of π such that each line of π contains at least one point in S and at least one point not in S. The following result is shown in [1], [2].