bluuebunny/crossref_metadata_2025_split huggingface dataset:
Concerning Metrizability of Pointwise Paracompact Moore Spaces
Authors: Traylor D. R. 
Published: December 2010

Although it is known that there exists a pointwise paracompact Moore space which is not metrizable (1), very little seems to be known about the metrizability of pointwise paracompact Moore spaces. This paper is devoted to determining some of the conditions under which a pointwise paracompact Moore space is metrizable.The statement that 5 is a Moore space means that there exists a sequence of collections of regions in 5 satisfying Axiom 0 and the first three parts of Axiom 1 of (2). A Moore space is complete if and only if it satisfies all of Axiom 1 of (2).
Finite Groups with All Maximal Subgroups of Prime or Prime Square Index
Authors: Kohler Joseph 
Published: December 2010

In this paper finite groups with the property M, that every maximal subgroup has prime or prime square index, are investigated. A short but ingenious argument was given by P. Hall which showed that such groups are solvable.B. Huppert showed that a finite group with the property M, that every maximal subgroup has prime index, is supersolvable, i.e. the chief factors are of prime order. We prove here, as a corollary of a more precise result, that if G has property M and is of odd order, then the chief factors of G are of prime or prime square order. The even-order case is different. For every odd prime p and positive integer m we shall construct a group of order 2apb with property M which has a chief factor of order larger than m.
The Maximum Number of Disjoint Permutations Contained in a Matrix of Zeros and Ones
Authors: Fulkerson D. R. 
Published: December 2010

A well-known consequence of the König theorem on maximum matchings and minimum covers in bipartite graphs (5) or of the P. Hall theorem on systems of distinct representatives for sets (4) asserts that an n by n (0, 1)-matrix A having precisely p ones in each row and column can be written as a sum of p permutation matrices:Our main objective is a generalization of (1.1) along the following lines. Let A be an arbitrary m by n (0, 1)-matrix. Call an m by n (0, 1)-matrix P a permutation matrix if PPT = I, where PT is the transpose of P and I is the identity matrix of order m.
Generalized Hadamard Matrices and Orthogonal Arrays of Strength Two
Authors: Shrikhande S. S. 
Published: December 2010

The purpose of this note is to point out some connexions between generalized Hadamard matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine resolvable balanced incomplete block designs (1), and orthogonal arrays of strength two (2). Some constructions for these arrays are also indicated.A balanced incomplete block design (BIBD) with parameters v, b, r, k, λ is an arrangement of v symbols called treatments into b subsets called blocks of k < v distinct treatments such that each treatment occurs in r blocks and any pair of treatments occurs in λ blocks.
On Generalized Powers of the Difference Operator
Authors: Unni K. R. 
Published: December 2010

Sumner (3) discussed for arbitrary real λ and h, where the averaging operator ∇h is defined by(1.1)when f(z) is an entire function of exponential type <2π/|h|. Boas (2) gave an alternative definition of ∇h which gave Sumner's results quickly and showed that his definition is equivalent to that of Sumner.
Tauberian Estimates Concerning the Regular Hausdorff and [J, f(x)] Transformations
Authors: Meir A. 
Published: December 2010

Denote by {t(x)} some linear transform of the sequenceof the formwhere x attains continuous or only integer values. The problem of estimating |t(x) — sm| as x and m tend to ∞ with some connection between them was considered first by H.
The Generation of the Lower Central Series
Authors: Gallagher P. X. 
Published: December 2010

Let G be a finite group with commutator subgroup G′. In an earlier paper (4) it was shown that each element of G′ is a product of n commutators, if 4n ≥ |G′|. The object of this paper is to improve this result in two directions:Theorem 1a. If (n + 2)!n! > 2|G′| — 2, then each element of G′ is a product of n commutators.Theorem 1b. If G is a p-group, with |G′| = pa, and if n(n + 1) > a, then each element of G′ is a product of n commutators.
Lattice-Ordered Rings of Quotients
Authors: Anderson F. W. 
Published: December 2010

R. E. Johnson (10), Utumi (18), and Findlayand Lambek (7) have defined for each ring R a unique maximal "ring of right quotients" Q. When R is a commutative integral domain (in this paper an integral domain need not be commutative) or an Ore domain, then Q is the usual division ring of quotients of R. Moreover, it is well known that in these special cases, if R is totally ordered, then so is Q.The main purpose of this paper is to study the ring of quotients Q, and in particular its order properties, for certain lattice-ordered rings R.
Convexity Properties for Weak Solutions of Some Differential Equations in Hilbert Spaces
Authors: Zaidman S. 
Published: December 2010

In this work we obtain a simultaneous extension of Theorems 1.6 and 1.7 in Agmon and Nirenberg (1), together with a partial extension of the result on backward unicity for parabolic equations by Lions and Malgrange (4).Let H be a Hilbert space. (·) and | | are the notations for the scalar product and the norm in this space. Consider in H a family B(t), 0 ≤ t ≤ T, of closed linear operators with dense domain DB(t) (varying) with t. Let L2(0, T, H) be the space of Bochner square-integrable vector-valued functions with values in H. Our main result is the following
A Characterization of the Hughes Planes
Authors: Ostrom T. G. 
Published: December 2010

Baer (1) introduced the term "(p,L)-collineation" to denote a central collineation with centre p and axis L. We shall find it convenient to use a modification of the related notion of "(p, L)-transitivity."Definition. Let π0 be a subplane of the projective plane π. Let L be a fixed line of π0, and let p be a fixed point of π0. Let r and s be any two points of π0 that are collinear with p, distinct from p, and not on L. If, for each such choice of r and s, there is a (p, L)-collineation of π that (1) carries π0 into itself and (2) carries r into s, we shall say that π is (p, L, π0)-transitive.
On the Average Number of Trees in Certain Maps
Authors: Mullin R. C. 
Published: December 2010

For a formal definition of “map” the reader is referred to (7, §2). The maps in this paper are rooted by specifying an orientation for one of the edges. This also specifies a root vertex, the negative end of the root, and a root face, the face on the left of the root edge. Counting is, as usual, defined on isomorphism classes.Regular maps of even valence have been enumerated in a recent paper by Tutte. In this paper we determine the average number of trees in such maps, and include similar results for regular tri valent maps, that is, maps with three edges incident on every vertex. In the development for the latter, a formula for the number of trivalent maps with 2t vertices is produced.
A Relationship between Arbitrary Positive Matrices and Stochastic Matrices
Authors: Sinkhorn Richard 
Published: December 2010

The author (2) has shown that corresponding to each positive square matrix A (i.e. every aij > 0) is a unique doubly stochastic matrix of the form D1AD2, where the Di are diagonal matrices with positive diagonals. This doubly stochastic matrix can be obtained as the limit of the iteration defined by alternately normalizing the rows and columns of A.In this paper, it is shown that with a sacrifice of one diagonal D it is still possible to obtain a stochastic matrix. Of course, it is necessary to modify the iteration somewhat. More precisely, it is shown that corresponding to each positive square matrix A is a unique stochastic matrix of the form DAD where D is a diagonal matrix with a positive diagonal. It is shown further how this stochastic matrix can be obtained as a limit to an iteration on A.
A Stieltjes–Volterra Integral Equation Theory
Authors: Hinton D. B. 
Published: December 2010

Suppose S = [a, b] is a number interval and F is a function from S X S to a normed algebraic ring N with multiplicative identity I. We consider the problem of finding, for appropriate conditions on F, a function M from S X S to N such that for all t and x,where the integral is a Cauchy-left integral.
On the Smoothness of General Kernels
Authors: Barros-Neto Jose 
Published: December 2010

In (3, §2), the writer and F. E. Browder stated briefly, without proof, some results concerning general distribution kernels. It is our aim here to prove and complete those results.The terminology and notations are introduced in §1.In §2 we define the notion of domain of dependence with respect to the kernel Kx,y (Definition 1) as well as the notion of smoothness of a distribution kernel at a point (Definition 2). Theorem 1 states that the set of points, where the distribution kernel is smooth, is open and the kernel is a smooth function in this set. Theorems 2 and 3 are the converse of Theorem 1.
Replaceable Nets, Net Collineations, and Net Extensions
Authors: Ostrom T. G. 
Published: December 2010

A net of degree k and order n is a set of n2 points and nk designated sets of points, called lines, such that(1) The lines fall into k disjoint parallel classes, i.e. each line occurs in exactly one parallel class.(2) Lines in the same parallel class have no points in common; lines in different parallel classes have exactly one point in common.(3) Each point lies on exactly one line of each parallel class.
The Reconstruction of a Tree from its Maximal Subtrees
Authors: Harary Frank , Palmer Ed 
Published: December 2010

One of the many interesting conjectures proposed by S. M. Ulam in (5) can be stated as follows:If G and H are two graphs with p points vi and ui respectively (p ⩾ 3) such that for all i, G — vi is isomorphic with H — ui then G and H are themselves isomorphic.P. J. Kelly (3) has shown this to be true for trees. The conjecture is, of course, not true for p = 2, but Kelly has verified by exhaustion that it holds for all of the other graphs with at most six points. Harary and Palmer (2) found the same to be true of the seven-point graphs.In (1) Harary reformulated the conjecture as a problem of reconstructing G from its subgraphs G — vi and derived several of the invariants of G from the collection G — vi.
On Rigid Undirected Graphs
Authors: Hedrlín Z. , Pultr A. 
Published: December 2010

By an undirected graph we mean a couple (X, R), where X is a set and R is a subset of X × X such that (x, y) ∈ R implies (y, x) ∈ R. The cardinal of X, denoted by |X|, will be called the cardinal of the graph.A mapping f:X → X is called an endomorphism of (X, R) if (x, y) ∈ R implies that (f(x), f(y)) ∈ R for all x, y ∈ R.An undirected graph (X, R) is called rigid if there is only one endomorphism of (X, R), namely the identity mapping of X.P. Erdös communicated orally that, using probability methods, it is possible to prove that almost all finite undirected graphs are rigid.
Connectivity in Matroids
Authors: Tutte W. T. 
Published: December 2010

An edge of a 3-connected graph G is called essential if the 3-connection of G is destroyed both when the edge is deleted and when it is contracted to a single vertex. It is known (1) that the only 3-connected graphs in which every edge is essential are the “wheel-graphs.” A wheel-graph of order n, where n is an integer ⩾3, is constructed from an n-gon called its “rim” by adding one new vertex, called the “hub,” and n new edges, or “spokes” joining the new vertex to the n vertices of the rim; see Figure 4A.A matroid can be regarded as a generalized graph. One way of developing the theory of matroids is therefore to generalize known theorems about graphs. In the present paper we do this with the theorem stated above.
New Approximations for Wiener Integrals, with Error Estimates
Authors: Finlayson Henry C. 
Published: December 2010

The principal theorem of this paper, a generalization of a theorem given by R. H. Cameron (2), provides a means of approximating certain Wiener integrals to any desired degree of accuracy by an (n + 1)-fold Riemann integral with sufficiently large n. The generalization is in the use of a general complete orthonormal set of functions, whereas Cameron's paper used only the odd harmonic set.Let C′ be the class of real-valued functions x(t) defined on [0, 1] and such that x(0) = 0 and which are continuous except perhaps for one left continuous jump. Let C be the class of continuous members of C′.
On Partitions of an Equilateral Triangle
Authors: Graham R. L. 
Published: December 2010

Let T denote a closed unit equilateral triangle. For a fixed integer n, let dn denote the infimum of all those x for which it is possible to partition T into n subsets, each subset having a diameter not exceeding x. We recall that the diameter of a plane set A is given bywhere ρ (a, b) is the Euclidean distance between a and b.In this note we determined dn for some small values of n. Typical values of dn are given in Table I. These values were obtained by three methods. As would be expected, as the value of n increases, the complexity of the argument needed to obtain dn also increases. We begin with the simplest case.
On the Number of Spheres Which can Hide a Given Sphere
Authors: Heppes Aladár 
Published: December 2010

Several years ago H. Hornich suggested the following problem: find the minimal number of unit spheres which can hide a unit sphere in the sense that each ray emanating from the centre of that sphere meets at least one of the hiding spheres, with no two of the spheres overlapping. We shall call any set of spheres which hide a given unit sphere acloud.The first result concerning this and related questions can be found in a paper of Fejes Tóth (4 ; see also 5, 7, 8, 6, and 1 ). With respect to the original problem, Fejes Tóth has given a lower estimate for the minimal numberNof the spheres of a cloud.
Lower Bounds for Solutions of Parabolic Differential Inequalities
Authors: Ogawa Hajimu 
Published: December 2010

Let P be the parabolic differential operatorwhere E is a linear elliptic operator of second order on D × [0, ∞), D being a bounded domain in Rn. The asymptotic behaviour of solutions u(x, t) of differential inequalities of the form1has been investigated by Protter (4). He found conditions on the functions ƒ and g under which solutions of (1), vanishing on the boundary of D and tending to zero with sufficient rapidity as t → ∞, vanish identically for all t ⩾ 0. Similar results have been found by Lees (1) for parabolic differential inequalities in Hilbert space.
On Homotopic Harmonic Maps
Authors: Hartman Philip 
Published: December 2010

Let M, M′ be C∞ Riemann manifolds such that(1.0) M is compact;(1.1) M′ is complete and its sectional curvatures are non-positive.In terms of local coordinates x = (x1, … , xn) on M and y = (y1, … , ym) on M′, let the respective Riemann elements of arc-length beand Γijk, Γ′αβγ be the corresponding Christoffel symbols. When there is no danger of confusion, x (or y) will represent a point of M (or M′) or its coordinates in some local coordinate system.
Rational Surfaces with Exceptional Unodes
Authors: Val Patrick du 
Published: December 2010

Many years ago, I defined (8) three types of exceptional unode on an algebraic surface, which I called U*8, U*9, U*10, corresponding, on a non-singular model of the surface, to sets of six, seven, and eight rational curves, each of grade — 2, with the intersection patterns represented by the Coxeter-Dynkin graphs now usually known as E6, E7, E8:where each dot represents a curve, and linked dots intersecting curves. In each case we shall denote the curves in the horizontal sequence by S1, s2, … from left to right, and the extra curve meeting s3 by s*.
Orthogonal Matrices with Zero Diagonal
Authors: Goethals J. M. , Seidel J. J. 
Published: December 2010

The central problem in the present paper is the construction of symmetric and of skew-symmetric ( = skew) matricesCof orderv,with diagonal elements 0 and other elements + 1 or — 1, satisfyingThe following necessary conditions are known:v≡ 2 (mod 4) andaandbintegers, for symmetric matricesC(Belevitch (1, 2), Raghavarao (14)), andv =2 orv≡ 0 (mod 4) for skew matricesC.
Some Remarks on Semigroup Presentations
Authors: Neumann B. H. 
Published: December 2010

Let a semigroupAbe given by generators a1, a2, … , adand defining relationsu1= v1, u2= v2, … ,ue=vebetween these generators, theui,vibeing words in the generators. We then have apresentationofA, and writeThe same generators with the same relations can also be interpreted as the presentation of a group, for which we write
Commutativity for Matrices of Quaternions
Authors: Carlson R. E. , Cullen C. G. 
Published: December 2010

For any ring we shall denote by the ring of all n × n matrices with elements from and by the set of all polynomials in x with coefficients from . will denote the non-commutative four-dimensional division algebra of real quaternions with 1, i1, i2, i3 as generators
A Tauberian Theorem and Analogues of the Prime Number Theorem
Authors: Davison T. M. K. 
Published: December 2010

In 1945 Ingham (3) proved the following Tauberian theorem: if ƒ is a non-decreasing, non-negative function on [1, ∞) and1then ƒ(x) ∼ cx. His proof is based on the non-vanishing of the Riemann zeta-function, ζ (s), on the line , and uses Pitt's form of Wiener's Tauberian theorem; (see, e.g., 5, Theorem 109, p. 211).
Semi-Homomorphisms of Groups
Authors: Herstein I. N. 
Published: December 2010

A mapping ϕ from one group, G, into another, H, is said to be a semi-homomorphism of G if ϕ(aba) = ϕ(a) ϕ(b) ϕa) for all a, b ∊G. Clearly any homomorphism or anti-homomorphism is a semi-homomorphism; the converse, however, need not be true in general. It is perfectly clear what one intends by a semi-isomorphism or semi-automorphism.Our purpose here is to show that for a rather general situation a semi-homomorphism turns out to be a homomorphism or an anti-homomorphism. In (2) we proved that any semi-automorphism of a simple group which contains an element of order 4 must automatically be either an automorphism or an anti-automorphism.
The Classification of Algebras by Dominant Dimension
Authors: Mueller Bruno J. 
Published: December 2010

Nakayama proposed to classify finite-dimensional algebras R over a field according to how long an exact sequenceof projective and injective R-R-bimodules Xi they allow. He conjectured that if there exists an infinite sequence of this type, then R must be quasi-Frobenius; and he proved this when R is generalized uniserial (17).
Natural Partial Orders
Authors: Dean R. A. , Keller Gordon 
Published: December 2010

Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).
On The Determination of Sets by Sets of Sums of Fixed Order
Authors: Ewell John A. 
Published: December 2010

The present investigation is based on two papers: “On the determination of numbers by their sums of a fixed order,” by J. L. Self ridge and E. G. Straus (4), and “On the determination of sets by the sets of sums of a certain order,” by B. Gordon, A. S. Fraenkel, and E. G. Straus (2).First of all, we explain the terms implicit in the above titles. Throughout these considerations we use the term “set” to mean “a totality having possible multiplicities,” so that two sets will be counted as equal if, and only if, they have the same elements with identical multiplicities. In the most general sense the term “numbers” of (4) can be replaced by “elements of any given torsioniree Abelian group.”
On the Diameter of a p-Cyclic Strongly Connected Digraph
Authors: Stuart Lynn M. 
Published: December 2010

In this paper we follow the notation of (2). In (5), Luce showed, in other terminology, that if d is the diameter of a strongly connected digraph, D, on n vertices with m edges, then1.1this inequality being sharp; from (1.1) one may immediately derive sharp upper bounds for d in terms of m and n, this being a generalization of the obvious and well-known inequality1.2
Some Tauberian Theorems for the Logarithmic Method of Summability
Authors: Kwee B. 
Published: December 2010

The series is said to be summable (L) to s if the sequence {sn}, where sn = a0 + a1 + … + an, is L-convergent to s, i.e., ifIf the sequence {sn} is l-convergent to s, i.e., if the sequence {tn}, where1
Hereditary Radicals and Derivations of Algebras
Authors: Anderson T. 
Published: December 2010

In the Amitsur-Kurosch theory of radicals in rings (2), an important problem is to determine the relationship between the radical of a ring and the radical of each of its ideals. The first result on this problem was by Amitsur who proved that if β is a hereditary radical in the sense that ideals of β-radical rings are β-radical, then for each associative ring R and ideal I of R, β(I) = I ∩ β(R), where β(R) denotes the β-radical of R; see (2).Later, Suliński, Divinsky, and the author proved that if β is any radical and R is an associative or alternative ring, then β(I) ⊆ I∩ β(R) for each ideal I of R; see (3). Since every hereditary radical β has the property β(I) ⊇ I ∩ β(R), this result provided another proof of Amitsur's theorem and extended that theorem to alternative rings. Of course, this raises the question of whether Amitsur's theorem is true for Lie or Jordan rings.
Generalized Frattini Subgroups of Finite Groups. II
Authors: Beidleman James C. 
Published: December 2010

The theory of generalized Frattini subgroups of a finite group is continued in this paper. Several equivalent conditions are given for a proper normal subgroup H of a finite group G to be a generalized Frattini subgroup of G. One such condition on H is that K is nilpotent for each normal subgroup K of G such that K/H is nilpotent. From this result, it follows that the weakly hyper-central normal subgroups of a finite non-nilpotent group G are generalized Frattini subgroups of G.Let H be a generalized Frattini subgroup of G and let K be a subnormal subgroup of G which properly contains H. Then H is a generalized Frattini subgroup of K.Let ϕ(G) be the Frattini subgroup of G. Suppose that G/ϕ(G) is nonnilpotent, but every proper subgroup of G/ϕ(G) is nilpotent. Then ϕ(G) is the unique maximal generalized Frattini subgroup of G.
A Note on the Caradus Class of Bounded
Linear Operators on a Complex Banach Space
Authors: Ruston A. F. 
Published: December 2010

1. In a recent paper (1) on meromorphic operators, Caradus introduced the class of bounded linear operators on a complex Banach space X. A bounded linear operator T is put in the class if and only if its spectrum consists of a finite number of poles of the resolvent of T. Equivalently, T is in if and only if it has a rational resolvent (8, p. 314).Some ten years ago (in May, 1957), I discovered a property of the class g which may be of interest in connection with Caradus' work, and is the subject of the present note.2. THEOREM. Let X be a complex Banach space. If T belongs to the class, and the linear operator S commutes with every bounded linear operator which commutes with T, then there is a polynomial p such that S = p(T).