bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Anti-Commutative Algebras with an Invariant Form
Authors: Sagle Arthur A. 
Published: December 2010

In this paper we consider anti-commutative algebras with an invariant form, that is, an algebra A over a field F such thatand A possesses a symmetric bilinear form f(x, y) such thatLie and Malcev algebras (2, 3) are examples of such algebras and we shall consider generalizations of these algebras obtained by introducing commutation, x o y = xy — yx, as a new multiplicative operation in the non-commutative Jordan algebras of (1).
Homotopy and Isotopy Properties of Topological Spaces
Authors: Gottlieb Daniel H. 
Published: December 2010

In 1961, S. T. Hu published a paper (1) in which he discussed the desirability of discovering those topological properties which are preserved under homotopy and isotopy equivalences. In that paper he gave general tests in terms of weakly hereditary and hereditary topological properties for homotopy and isotopy properties.In this paper, general tests for homotopy and isotopy properties in terms of weakly hereditary properties and of a class of properties which the author calls open properties are given. In the last sections, we shall show the strong role played by the notions of dimension and separating subsets in forming isotopy properties.
On Covering of Balanced Incomplete Block Designs
Authors: Hanani Haim 
Published: December 2010

Given a set E of v elements and given positive integers k (k ≤ v) and λ, we understand by balanced incomplete block design (BIBD) B [k, λ, v] a system of blocks (subsets of E) having k elements each such that every pair of elements of E is contained in exactly λ blocks.A necessary condition for the existence of a design B [k, λ, v] is known to be (4)
Collineations of Projective Moulton Planes
Authors: Pierce William A. 
Published: December 2010

In the article "Moulton Planes" (10), I studied F. R. Moulton's construction over any field containing a multiplicative subgroup of index 2. In "Collineations of Affine Moulton Planes" (11), I determined the collineations between two arbitrary affine Moulton planes.The purpose now is to describe the collineations between two projective Moulton planes. Since the affine collineations are known from (11), we are concerned with collineations mapping ideal lines onto ordinary lines. Notations and conventions of (10) and (11) are retained.
The Structure of Powers of Non-Negative Matrices
Authors: Dulmage A. L. , Mendelsohn N. S. 
Published: December 2010

The theory of non-negative matrices was initiated by Perron (7) and Frobenius (4). Wielandt in (11) gives an elegant exposition of the subject.It is well known to workers in the field that if a matrixAhas all its entries non-negative real numbers, then the pattern of zeros and non-zeros ofAcompletely determines the pattern of zeros and non-zeros in every power ofA. Ptak in (8) and Ptak and Sedlacek in (9) describe this behaviour in terms of some combinatorial constructs.
Paths, Trees, and Flowers
Authors: Edmonds Jack 
Published: December 2010

A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An edge is said to join its end-points.A matching in G is a subset of its edges such that no two meet the same vertex. We describe an efficient algorithm for finding in a given graph a matching of maximum cardinality. This problem was posed and partly solved by C. Berge; see Sections 3.7 and 3.8.
Maxima for Graphs and a New Proof of a Theorem of Turán
Authors: Motzkin T. S. , Straus E. G. 
Published: December 2010

Maximum of a square-free quadratic form on a simplex. The following question was suggested by a problem of J. E. MacDonald Jr. (1):Given a graph G with vertices 1, 2, . . . , n. Let S be the simplex in En given by xi ≥ 0, Σxi = 1. What is
On Multipliers of Difference Sets
Authors: McFarland Robert , Mann H. B. 
Published: December 2010

Multipliers are useful in constructing difference sets as well as in impossibility proofs. The existence of a fixed set facilitates their application, so that the results of this paper should prove to be useful in numerical work concerning difference sets.Let G be a group which we shall write multiplicatively. For any set A of elements of G, we define(1)
On Anti-Commutative Algebras and Analytic Loops
Authors: Sagle Arthur A. 
Published: December 2010

In (4) Malcev generalizes the notion of the Lie algebra of a Lie group to that of an anti-commutative "tangent algebra" of an analytic loop. In this paper we shall discuss these concepts briefly and modify them to the situation where the cancellation laws in the loop are replaced by a unique two-sided inverse. Thus we shall have a set H with a binary operation xy defined on it having the algebraic properties(1.1) H contains a two-sided identity element e;(1.2) for every x ∊ H, there exists a unique element x-1 ∊ H such that xx-1 = x-1x = e;
Sur L'Indice de Certains Réseaux de R4 Permis Pour un Octaèdre
Authors: Bantegnie Robert 
Published: December 2010

Si un réseau G de Rn contient Zn et est permis pour l'«octaèdre généralisé» Ωn d'équationl'indice de Zn dans G est borné supérieurement par n! d'après les théorèmes généraux de Minkowski.
Finite Groups in Which Sylow 2-Subgroups are Abelian and Centralizers of Involutions are Solvable
Authors: Gorenstein Daniel 
Published: December 2010

The purpose of this paper is to establish the following theorem :Theorem 1. Let be a finite group with abelian Sylow 2-subgroups in which the centralizer of every involution is solvable. Then either is solvable or else /O is isomorphic to a subgroup of PΓL(2, q) containing PSL(2, q), where either q = 3 or 5 (mod 8), q ≥ 5, or q = 2n, n ≥ 2.
Undirected Graphs Realizable as Graphs of Modular Lattices
Authors: Alvarez Laurence R. 
Published: December 2010

If (L, ≥) is a lattice or partial order we may think of its Hesse diagram as a directed graph, G, containing the single edge E(c, d) if and only if c covers d in (L, ≥). This graph we shall call the graph of (L, ≥). Strictly speaking it is the basis graph of (L, ≥) with the loops at each vertex removed; see (3, p. 170).We shall say that an undirected graph Gu can be realized as the graph of a (modular) (distributive) lattice if and only if there is some (modular) (distributive) lattice whose graph has Gu as its associated undirected graph.
Determination of a Subset from Certain Combinatorial Properties
Authors: Cantor David G. , Mills W. H. 
Published: December 2010

Let N be a finite set of n elements. A collection ﹛S1, S2, … , Sm﹜ of subsets of N is called a determining collection if an arbitrary subset T of N is uniquely determined by the cardinalities of the intersections Si ⋂ T, 1 ≤ i ≤ m. The purpose of this paper is to study the minimum value D(n) of m for which a determining collection of m subsets exists.This problem can be expressed as a coin-weighing problem (1; 7).In a recent paper Cantor (1) showed that D(n) = O(n/log log n), thus proving a conjecture of N. J. Fine (3) that D(n) = o(n). More recently Erdös and Rényi (2), Söderberg and Shapiro (7), Berlekamp, Mills, and Leo Moser have independently found proofs that D(n) = O(n/log n).
The Number of Circular Patterns Compatible with a Pseudo-Symmetric Connected Graph
Authors: Baum L. E. , Eagon J. A. 
Published: December 2010

In this paper we prove:Theorem. Let be an ordered pseudo-symmetric connected graph with l lines and v vertices. Let there be aij lines directed from vertex i to vertex j, i, j = 1, 2, … , v. Let gcd(aij) = d, and define
Modular Annihilator Algebras
Authors: Barnes Bruce A. 
Published: December 2010

In a recent paper (7) Yood developed the beginnings of a theory of modular annihilator algebras. In this paper we extend his work on these algebras.The definition of modular annihilator algebra is algebraic in nature (see §4) ; in fact the algebra need not be assumed even topological. However, a significant number of important normed algebras are modular annihilator algebras. A list of examples is given in §8.The theory of modular annihilator algebras is related to the theory of certain important topological algebras. In §5 we consider the relationships between dual and annihilator algebras and modular annihilator algebras, and in §7, the relationship between completely continuous normed algebras and modular annihilator algebras.
Engel Congruences in Groups of Prime-Power Exponent
Authors: Glauberman George , Krause Eugene F. , Struik Ruth Rebekka 
Published: December 2010

In this paper a simplified proof of a theorem of Sanov (4) is given. No mention is required of Lie elements or of the Baker-Hausdorff formula, both of which played central roles in Sanov's proof.Let G be a group. Define, for all x, y ∈ G,
On the Representation of Integers as Sums of Distinct Terms from a Fixed Sequence
Authors: Folkman Jon 
Published: December 2010

Let A = (a1, a2, a3, …) be a sequence of positive integers. We letdenote the set of integers that are sums of distinct terms of A. If P(A) contains all sufficiently large integers, we say that A is complete. We shall show that certain classes of sequences that are characterized by their rate of growth are complete.
On the Permanent of a Doubly Stochastic Matrix
Authors: Wilf Herbert S. 
Published: December 2010

If is an n X n matrix, the permanent of A, Per A, is defined by1where the sum is over all permutations. If A is doubly stochastic (i.e., nonnegative with row and column sums all equal to 1), then it has been conjectured that Per A ⩾ n!/nn. When confronted with a vaguely similar problem about determinants, M. Kac (1) observed that the computation of minima can often be aided by knowledge of various averages. In this spirit we calculate here the average permanent of a class of doubly stochastic matrices and thereby obtain upper bounds for the minima. These turn out to be surprisingly sharp.
P and D in P-1XP = dg(λ, … , λn) = D As Matrix Functions of X
Authors: Rinehart R. F. 
Published: December 2010

Let be the algebra of n X n matrices over the complex field C, X = ‖xrs‖ a matrix of , and f(X) = ‖(frs(x11, x12, … , xnn)‖ a function with domain and range in . If the frs are differentiable with respect to each of the xij on some open set R of , then the differential df(X) = ‖dfrs(xij)‖ exists, and, moreover, f(X) is Hausdorff-differentiable (HD) (1, 3, 7) i.e. df(X)is expressible in the formwhere dX = ‖dxrs‖, and the matrices Ai Bi are independent of dX. The Hausdorff derivative fI(X) is defined to bei.e. the value of df(X) for dX = I, the identity matrix (2).
Singular Perturbations of Non-Linear Elliptic and Parabolic Variational Boundary-Value Problems
Authors: Ton Bui An 
Published: December 2010

Singular perturbations of linear elliptic and parabolic boundary-value problems have been studied extensively by Visik and Lyusternik (7), Huet (5), and others. It is the purpose of this paper to extend the results of (5) to the non-linear elliptic and parabolic variational boundary-value problems considered during the last few years by Browder (2, 4).In §1, we give the notations and state the main assumptions on the nonlinearity of the elliptic operators. In §2 we study the singular perturbations of non-linear elliptic variational boundary problems. In §3, we consider the case of non-linear parabolic variational boundary problems with a small parameter.
A Mountain-Climbing Problem
Authors: Whittaker James V. 
Published: December 2010

Suppose that two men stand at the same elevation on opposite sides of a mountain range and begin to climb in such a way that their elevations remain equal at all times. Will they ever meet along the way? It is this question, restated in mathematical terms, that we shall consider. We replace the mountain range by the graph of a continuous, real-valued function f(x) defined for x ∈ [0, 1], where f(0) = f(1) = 0, and we ask whether there exist continuous mappings ϕ(t), ψ(t) from [0, 1] into [0, 1] such that12
Topologies of Lattice Products
Authors: Alo Richard A. , Frink Orrin 
Published: December 2010

A number of different ways of defining topologies in a lattice or partially ordered set in terms of the order relation are known. Three of these methods have proved to be useful and convenient for lattices of special types, namely theidealtopology, theintervaltopology, and thenew intervaltopology of Garrett Birkhoff. In another paper (2) we have shown that these three topologies are equivalent for chains (totally ordered sets), where they reduce to the usual intrinsic topology of the chain.Since many important lattices are either direct products of chains or sublattices of such products, it is natural to ask what relationships exist between the various order topologies of a direct product of lattices and those of the lattices themselves.
Minimal Regular Graphs of Girths Eight and Twelve
Authors: Benson Clark T. 
Published: December 2010

In (3) Tutte showed that the order of a regular graph of degree d and even girth g > 4 is greater than or equal toHere the girth of a graph is the length of the shortest circuit. It was shown in (2) that this lower bound cannot be attained for regular graphs of degree > 2 for g ≠ 6, 8, or 12. When this lower bound is attained, the graph is called minimal. In a group-theoretic setting a similar situation arose and it was noticed by Gleason that minimal regular graphs of girth 12 could be constructed from certain groups. Here we construct these graphs making only incidental use of group theory. Also we give what is believed to be an easier construction of minimal regular graphs of girth 8 than is given in (2). These results are contained in the following two theorems.
The L(r, t) Summability Transform
Authors: Powell Robert E. 
Published: December 2010

In a recent article Cheney and Sharma (1) studied the linear operator Pn defined bywherehere Lj(n)(t) denotes the Laguerre polynomial of degree j. Cheney and Sharma proved that if f is continuous on [0, 1], then Pn(f, x) converges uniformly to f(x) on [0, a] where 0 < a < 1.
The Steiner Point of a Convex Polytope
Authors: Shephard G. C. 
Published: December 2010

Associated with each bounded convex set K in n-dimensional euclidean space En is a point s(K) known as its Steiner point. First considered by Steiner in 1840 (6, p. 99) in connection with an extremal problem for convex regions, this point has been found useful in some recent investigations (for example, 4) because of the linearity property1Addition on the left is vector addition of convex sets.
Un Théorème Sur L'Arithmétique des Groupes Ordonnés
Authors: Aubert K. E. 
Published: December 2010

La caractérisation fondamentale des sous-groupes du groupe additif R des nombres réels en tant que groupes ordonnés est la suivante:A. Un groupe abélien totalement ordonné G est isomorphe à un sous-groupe de R si et seulement si G est archimédien.Nous nous proposons ici de donner une nouvelle caractérisation des sousgroupes de R qui nous semble présenter un certain intérêt pour plusieurs raisons. D'abord elle est très différente de la caractérisation A ci-dessus, bien que notre démonstration utilise A. Puis elle ajoute un nouveau théorème de r-groupe à ceux déjà connus. Finalement, en employant les caractérisations des anneaux de valuation généraux et discrets données dans (1), le théorème en question possède quelques corollaires parmi lesquels se trouve le théorème de s-groupe pour un domaine d'intégrité (“s-Gruppensatz” dans la terminologie de Krull (5)).
Oscillation Criteria for Matrix Differential Equations
Authors: Howard H. C. 
Published: December 2010

We shall be concerned at first with some properties of the solutions of the matrix differential equation1.1whereis an n × n symmetric matrix whose elements are continuous real-valued functions for 0 < x < ∞, and Y(x) = (yij(x)), Y″(x) = (y″ ij(x)) are n × n matrices. It is clear such equations possess solutions for 0 < x < ∞, since one can reduce them to a first-order system and then apply known existence theorems (6, Chapter 1).
Permutability of Semilattice Congruences on Lattices
Authors: Fujiwara Tsuyoshi 
Published: December 2010

Many authors have studied lattice congruences on lattices, but it seems that there are few studies concerning semilattice congruences on lattices. However, it seems that the semilattice congruences on lattices are closely connected with their structure. In this paper, we shall study the characterizations of modular, distributive, and relatively complemented lattices by the permutability of semilattice congruences.We can obtain the dual statements of the following discussion, but we shall not write them as a rule to avoid double descriptions.
A General Perron Integral, II
Authors: Bullen P. S. 
Published: December 2010

This paper continues work begun in a previous paper of the same title (7), which will be called I; results from I will be referred to as Theorem 1.4, Axiom 1.1 etc. The notation used in the present paper will, except where noted, be that of I, to which reference should be made for further details.In § 2, certain ideas presented in I are modified to give a neater and more general theory and then some new results of this theory are added. The remaining two sections develop some of the examples mentioned in I, § 5.
Nearly Regular p-Groups
Authors: Hobby C. R. 
Published: December 2010

A finite p-group G is said to be regular if for every pair of elements a, b in G,1where c is an element of the derived group of the subgroup generated by a and b. We shall say that G is nearly regular if (i) there is a central element z of order p such that G/⧼z⧽ is regular, and (ii) the subgroup generated by x and y is regular whenever x ∈ G and y ∈ G′, the derived group of G.
Sieve-Generated Sequences with Translated Intervals
Authors: Buschman R. G. , Wunderlich M. C. 
Published: December 2010

Consider the following sieve process. Let A(1) be the sequence of integers greater than 1. Let A(n+1) be obtained from A(n) = {a1(n), a2(n), …} by eliminating one element from each of the intervals Ik(n), whereWe let an = an(n) and A = {an} be the sequence of integers that survive the sieve. M. C. Wunderlich (8) has found a necessary and sufficient condition for an ∼ n log n and, in a more recent paper, M. Wunderlich and W. E. Briggs (9) have studied a subclass of the sequences defined above for which an ∼ n log n.
A Packing Problem for Measurable Sets
Authors: Sankoff D. , Dawson D. A. 
Published: December 2010

Given a probability measure space (Ω,,P)consider the followingpacking problem.What is the maximum number,b(K,Λ), of sets which may be chosen fromso that each set has measureKand no two sets have intersection of measure larger than Λ <K?In this paper the packing problem is solved for any non-atomic probability measure space. Rather than obtaining the solution explicitly, however, it is convenient to solve the followingminimal paving problem.In a non-atomic a-finite measure space (Ω,,μ)what is the measure,V(b, K,Λ), of the smallest set which is the union of exactlybsubsets of measureKsuch that no subsets have intersection of measure larger than Λ?
Unique Extension and Product Measures
Authors: Luther Norman Y. 
Published: December 2010

Following (2) we say that a measure μ on a ring is semifinite ifClearly every σ-finite measure is semifinite, but the converse fails.In § 1 we present several reformulations of semifiniteness (Theorem 2), and characterize those semifinite measures μ on a ring that possess unique extensions to the σ-ring generated by (Theorem 3). Theorem 3 extends a classical result for σ-finite measures (3, 13.A). Then, in § 2, we apply the results of § 1 to the study of product measures; in the process, we compare the “semifinite product measure” (1; 2, pp. 127ff.) with the product measure described in (4, pp. 229ff.), finding necessary and sufficient conditions for their equality; see Theorem 6 and, in relation to it, Theorem 7.
Symmetric Coordinate Spaces and Symmetric Bases
Authors: Ruckle William 
Published: December 2010

In this paper properties of symmetric coordinate spaces and symmetric bases are investigated. Since a space which possesses a basis is essentially a space of sequences (12, p. 207), the interrelation of these two concepts naturally suggests itself.Section 2 is a summary of the terminology and methods employed, which fall into four categories: (1) set theoretical properties of coordinate spaces such as symmetry and dual spaces; (2) the notion of FK and BK space (12, p. 202; 13); (3) the theory of the Schauder basis in F-space applied to the case when (see § 2) is a basis for a coordinate space; (4) the concept of a sequential norm, which the author introduced in (7) to illustrate the underlying unity of the first three ideas.
A Class of Operators on the Lorentz Space M(ϕ)
Authors: Boyd David W. 
Published: December 2010

In order to deal with certain problems in the theory of interpolation spaces, it is convenient to consider operators of the following form:Let k be a non-negative measurable function on the half-line R+, and let ƒ be a measurable function on R+ with1Then the operator T is defined by2with the domain of T, D(T), consisting of all ƒ which satisfy (1).
On the Number of Associative Triples in an Algebra of n Elements
Authors: Brockwell P. J. 
Published: December 2010

Consider a set of n elements α1, … , αn (denoted by S) and the set of all possible multiplication tables on these elements. The total number of such tables is clearly and each table can be represented by a square matrix [μij] where μij is the product αiαj (μij ∈ S, i = 1, … , n; j = 1, … , n). The triple (αi, αj, αk) is said to be associative if the following equation is satisfied:1.1
Pseudovaluations of Polynomials
Authors: Nelson R. 
Published: December 2010

A valuation of a ring K is a functionwhere A is an archimedean ordered field and W has the properties of the absolute valuation; see (2, chap. X). The theory was extended in 1936 by K. Mahler (1), who introduced the concept of pseudovaluations. Whereas for a valuation we must always havefor a pseudovaluation it is sufficient that
On the Properties of an Entire Function of Two Complex Variables
Authors: Agarwal Arun Kumar 
Published: December 2010

1. Letbe an entire function of two complex variables z1 and z2, holomorphic in the closed polydisk . LetFollowing S. K. Bose (1, pp. 214-215), μ(r1, r2; ƒ ) denotes the maximum term in the double series (1.1) for given values of r1 and r2 and v1{m2; r1, r2) or v1(r1, r2), r2 fixed, v2(m1, r1, r2) or v2(r1, r2), r1 fixed and v(r1r2) denote the ranks of the maximum term of the double series (1.1).
Orthogonal Decompositions of Multivariate Weakly Stationary Stochastic Processes
Authors: Robertson James B. 
Published: December 2010

In this paper we shall study the relations between the ranks of g-variate, discrete-parameter, weakly stationary stochastic processes x, y, and z satisfying the condition1.1and derive from them a characterization for the Wold decomposition and conditions for the concordance of the Wold and the Lebesgue-Cramér decompositions.
A Decomposition of Measures
Authors: Luther Norman Y. 
Published: December 2010

Let X be a set, a σ-ring of subsets of X, and let μ be a measure on . Following (1), we define μ to be semifinite ifWe show (Theorem 1) that every measure can be reduced to a semifinite measure for many practical purposes. In many cases, this reduction can be made even more significantly (Theorems 2 and 3). Finally, necessary and sufficient conditions that a semifinite measure be c-finite are given as a corollary to Theorem 3.
A Characteristic Subgroup of a p-Stable Group
Authors: Glauberman George 
Published: December 2010

Let p be a prime, and let S be a Sylow p-subgroup of a finite group G. J. Thompson (13; 14) has introduced a characteristic subgroup JR(S) and has proved the following results:(1.1) Suppose that p is odd. Then G has a normal p-complement if and only if C(Z(S)) and N(JR(S)) have normal p-complements.