bluuebunny/crossref_metadata_2025_split huggingface dataset:
A system of PDEs for Riemannian spaces
Authors: Senarath Padma , Thornley Gillian , van Brunt Bruce 
Published: April 2009

AbstractMatsumoto [10] remarked that some locally projectively flat Finsler spaces of non-zero constant curvature may be Riemannian spaces of non-zero constant curvature. The Riemannian connection, however, must be metric compatible, and this requirement places restrictions on the geodesic coefficients for the Finsler space in the form of a system of partial differential equations. In this paper, we derive this system of equations for the case where the geodesic coefficients are quadratic in the tangent space variablesyi, and determine the solutions. We recover two standard Remannian metrics of non-zero constant curvature from this class of solutions.
Principal solutions of positive linear Hamiltonian systems
Authors: Hinton Don 
Published: April 2009

AbstractThe Hamiltonian system Y′ = BY + CZ, Z′ = – AY – B*Z is considered where the coefficients are continuous on I = [a, ∞, C = C* ≧ 0, and A = A* ≦ 0. A solution (Y, Z) satisfying Y*Z = Z*Y is defined to be principal (coprincipal) provided that (i) Y−1 exists on I (Z−1 exists on I) and (ii) as t→∞ ( as t → ∞). Three conditions are given which are separtely equivalent to the condition that a solution is principal iff it is coprincipal. For a self-adjoint scalar operator L of order 2n, this problem is related to the deficiency index problem and to a problem of Anderson and Lazer (1970) which concerns the number of lnearly independent solutions of L (y) =0 satisfying y(k) ∈ (a, ∞) (k = 0, …, n).
Semi-Markov processes on a general state space: α-theory and quasi-stationarity
Authors: Arjas E. , Nummelin E. , Tweedie R. L. 
Published: April 2009

AbstractBy amalgamating the approaches of Tweedie (1974) and Nummelin (1977), an α-theory is developed for general semi-Markov processes. It is shown that α-transient, α-recurrent and α-positive recurrent processes can be defined, with properties analogous to those for transient, recurrent and positive recurrent processes. Limit theorems for α-positive recurrent processes follow by transforming to the probabilistic case, as in the above references: these then give results on the existence and form of quasistationary distributions, extending those of Tweedie (1975) and Nummelin (1976).
Identities and left cancellation in distributively generated near-rings
Authors: John David 
Published: April 2009

AbstractGiven a semigroup S, we define {N(S), +, ·} to be the ‘free’ distributively generated near-ring. Since all words in N(S) can be expressed as the sum and difference of elements of S, we are able to define a length function on the words of N(S). The following theorems then follow: Theorem 1. N(S) contains a multiplicatice identity e if and only if e ∈ S. Theorem 2. If S is the free semigroup in the cariety of all semi—groups then N(S) is left cancellatice.
Minkowski's fundamental inequality for reduced positive quadratic forms(II)
Authors: Barnes E. S. 
Published: April 2009

AbstractA convex polytope D (α) was defined in Barnes (1978) as the set of Minkowski-reduced forms with prescribed diagonal coefficients α1, α2,…αn. A local minimum of the determinant D(f) over D(α) must occur at a vertex of D(α). Here a criterion is obtained for a given vertex to provide a local minimum, completely analogous to Voronoï's criterion for a perfect form to be extreme.
Some Properties of stochastic compactness
Authors: Maller R. A. 
Published: April 2009

AbstractThe aim of this paper is to show that some of the known properties of distributions in the domain of attraction of a stable law have counterparts for distributions which are stochastically compact in the sense of Feller. This enables us to unify the ideas of Feller and Doeblin, who first studied the concept of stochastic compactness, and give new characterizations of stochastic compactness and the domain of attraction of the normal distribution.
Ramsey numbers for certain k-graphs
Authors: Burr Stefan A. , Duke Richard A. 
Published: April 2009

AbstractWe are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.
Relations, homogeneity and group quotients
Authors: Warner M. W. 
Published: April 2009

AbstractA set with a relation is isomorphic to a group quotient under the condition described as weak homogeneity, and to the quotient of a group with relation preserved by right and left translations if the homogeneity is strengthened. A method of constructing these group quotients and, furthermore, all such very homogeneous spaces, is described and an illustrative example given.
Certain semigroups embeddabable in topological groups
Authors: Dzinotyiweyi Heneri A. M. 
Published: April 2009

AbstractIn this paper we study commutative topological semigroups S admitting an absolutely continuous measure. When S is cancellative we show that S admits a weaker topology J with respect to which (S, J) is embeddable as a subsemigroup with non-empty interior in some locally compact topological group. As a consequence, we deduce certain results related to the existence of invariant measures on S and for a large class of locally compact topological semigroups S, we associate S with some useful topological subsemigroup of a locally compact group.
Topological properties of the scale of a uniform space
Authors: Richardson G. D. , Wolf E. M. 
Published: April 2009

AbstractLet (S. U) be a uniform space. This space can be embedded in a complete, uniform lattice called the scale of (S. U). We prove that the scale is compact if and only if S is finite or U = {S × S}. We prove that this statement remains true if compact is replaced by countably compact, totally bounded. Lindelof, second countable, or separable. In the last section of this paper, we investigate the cardinality of the scale and the retracted scale.
Quotient bounded elements in locally convex algebras
Authors: Bhatt Subhash J. 
Published: April 2009

AbstractThe quotient bounded and the universally bounded elements in a calibrated locally convex algebra are defined and studied. In the case of a generalized B*-algebra A, they are shown to form respectively b* and B*-algebras, both dense in A. An internal spatial characterization of generalized B*-algebras is obtained. The concepts are illustrated with the help of examples of algebras of measurable functions and of continuous linear operators on a locally convex space.
A Fourier inversion method for the estimation of a density and its derivatives
Authors: Blum J. , Susarla V. 
Published: April 2009

During the last two decades a variety of methods have been developed for the problem of estimation of unknown density f wrt Lebesgue measure and its vth dervative g(= f(v)) using i.i.d random variables X1, …, Xn when X1 ∼ f. For example, see Wegman (1972). In almost all the papers on the estimation of f(x) or g(x), various authors assumed the existence of derivatives of f of order r(>v) at x to obtain rates for the mean-square convergences and other desirable properties for their estimators. Here it is shown that ifthen estimators gˇ(x) can be constructed for which E[(gˇ(x)-g(x))2] = O(n−(2a-δ)/(2a+2v+1)) for anygiveng δ > 0. Simiar statements hold for almost sure convergence of gˇ(x). It can also be shown that (gˇ(x1), gˇ(x2)) is asymptotically bivariate normal under certain conditions for x1, ≠ x2. If (Al) is satisfied with a ≦ l, then our estimators have all the desirable properties while other methods are not applicable in this situation since they require differentiability conditions on g. (For example, see Susarla and Kumar (1975) and its references.) Our estimators are defined by using the inversion theorem for some absolutely integrable characteristic functions. The motivation for our estimators is given in O'Bryan and Susarla (1975, 76) and Susarla and O'Bryan (1975).
On doubly transitive permutation groups of degree prime squared plus one
Authors: Chillag David 
Published: April 2009

AbstractA doubly transitive permutation group of degreep2+ 1, pa prime, is proved to be doubly primitive forp≠ 2. We also show that if such a group is not triply transitive then either it is a normal extension ofP S L(2,p2) or the stabilizer of a point is a rank 3 group.
Generalized products of weakly m — n compact spaces, I
Authors: Dissanayake U. N. B. 
Published: April 2009

AbstractA topological space X is said to be weakly-Lindelöf if and only if every open cover of X has a countable sub-family with dense union. We know that products of two Lindelöf spaces need not be weakly-Lindelöf. In this paper we obtain non-trivial sufficient conditions on small sub-products to ensure the producitivity of the property weakly-Lindelöf with respect to arbitrary products.
Reducing two person, zero sum games with underlying symmetry
Authors: Pearson K. R. 
Published: April 2009

AbstractWe consider two person, zero sum games with several symmetries. Where such symmetries are present there is a group acting on the strategies of the game. We show how to use this action to produce a reduced game with a smaller matrix, but having the same value as the original game, and how to obtain optimal strategies for the original game from optimal strategies of the reduced game. An analysis of a simplified version of the popular game Mastermind is given to illustrate the theory developed.
Conformal variation of a hypersurface of constant mean curvature in an einstein space
Authors: Smith Geoffrey Howard 
Published: April 2009

AbstractLet a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.
Almost distributive lattices
Authors: Swamy U. Maddana , Rao G. C. 
Published: April 2009

AbstractThe concept of ‘Almost Distributive Lattices’ (ADL) is introduced. This class of ADLs includes almost all the existing ring theoretic generalisations of a Boolean ring (algebra) like regular rings, P-rings, biregular rings, associate rings, P1-rings, triple systems, etc. This class also includes the class of Baer-Stone semigroups. A one-to-one correspondence is exhibited between the class of relatively complemented ADLs and the class of Almost Boolean Rings analogous to the well-known Stone's correspondence. Many concepts in distributive lattices can be extended to the class of ADLs through its principal ideals which from a distributive lattice with 0. Subdirect and Sheaf representations of an ADL are obtained.
Reducibility for real analytic quasi-periodic linear systems
Authors: O'Brien G. C. 
Published: April 2009

AbstractIn this paper we examine the linear differential equations x′ = Ax + P(φ)x, φ′ = ω where x ∈ Rn, φ ∈ Rm, A and ω are constant and P(φ) is real analytic and periodic in φ. We use the method of accelerated convergence to overcome the small divisors problem and reduce this system to the system y′ = By, φ′ = ω with constant coefficients.This problem has already been examined by Mitropolśki and Samolenko but the calculations and details in their work are formidable and difficult to follow. Besides being simpler our method provides more precise estimates at all stages and can be extended to the differentiable case to provide a significant improvement over previous results.
On strongly exposing functionals
Authors: Lau Ka-Sing 
Published: April 2009

AbstractLet X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K^ of K is a (norm) dense G8 in X* if and only if for any bounded closed convex subset C such that K⊄C, there exists a point x in K which is a strongly exposed point of conv (C ∪ K). As an application, we show that if X* is weakly compact generated, then for any weakly compact subset K in X, the set K^ is a dense G8 in X*.
Abelian Unipotent Subgroups of Finite Unitary and Symplectic Groups
Authors: Wong W. J. 
Published: April 2009

AbstractIf G is the unitary group U(V) or the symplectic group Sp(V) of a vector space V over a finite field of characteristic p, and r is a positive integer, we determine the abelian p-subgroups of largest order in G whose fixed subspaces in V have dimension at least r, with the restriction that we assume p ≠ 2 in the symplectic case. In particular, we determine the abelian subgroups of largest order in a Sylow p-subgroup of G. Our results complement earlier work on general linear and orthogonal groups.
Sur les mesures coniques localisables
Authors: Becker Richard 
Published: April 2009

AbstractLet X be a weakly complete proper cone, contained in an Hausdorff locally convex space E, with continuous dual E′. A positive linear form on the Risz space of functions on X generated by E′ is called a conical measure on X. Let M+ (X) be the set of all conical measures on X. G. Choquet asked the question: when is every conical measure on X given by a Radon measure on (X\0)? Let L be the class of such X. In this paper we show that the fact that X ∈ L only depends, in some sense, on the cofinal subsets of the space E′|x ordered by the order of functions on X. We derive that X ∈ L is equivalent to M+ (M) ∈ L. We show that is closed under denumerable products.
The lattice of stable marriages and permutations
Authors: Hwang J. S. 
Published: April 2009

AbstractRecently, we have introduced the notion of stable permutations in a Latin rectangle L(r×c) of r rows and c columns. In this note, we prove that the set of all stable permutations in L (r×c) forms a distributive lattice which is Boolean if and only if c ≤ 2.
Essential extensions in radical theory for rings
Authors: Heyman G. A. P. , Roos C. 
Published: April 2009

AbstractThe essential coverMkof a classMis defined as the class of all essential extensions of rings belonging toM.Mis called essentially closed ifMk=M. Every classMhas a unique essential closure, i.e. a smallest essentially closed class containingM.LetMbe a hereditary class of (semi)prime rings. ThenMis proved to be a (weakly) special class if and only ifMis essentially closed. A main result is thatMkis the smallest (weakly) special class containingM. Further it is shown that the upper radicalUMdetermined byM, is hereditary if and only ifUMhas the intersection property with respect toMk.
Free topological groups
Authors: Borges Carlos R. 
Published: April 2009

AbstractLet X be any Tychonoff space and βX the Stone—Čech compactification of X. Let F(βX) be the Graev free group of βX and let be the subspace topology on the Graev group F(X). Our results demonstrate that this topology is useful and behaves extremely well; the behavior of the free topology still remains enigmatic.There are various applications, some of which clarify the free topology on F(X), while others improve various results recently published.
An algebraic characterization of groups with soluble word problem
Authors: Boone William W. , Higman Graham 
Published: April 2009

The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem.THEOREM I. A necessary and sufficient condition that a finitely generated group G have a soluble word problem is that there exist a simple group H, and a finitely presented group K, such that G is a subgroup of H, and H is a subgroup of K.
Concerning periodicity in the asymptotic behaviour of partition functions
Authors: Erdös P. , Richmond B. 
Published: April 2009

AbstractLet PA(n) denote the number of partitions of n into summands chosen from the set A = {a1, a2, …}. De Bruijn has shown that in Mahler's partition problem (aν = rν) there is a periodic component in the asymptotic behaviour of PA(n). We show by example that this may happen for sequences that satisfy aν ν and consider an analogous phenomena for partitions into primes. We then consider corresponding results for partitions into distinct summands. Finally we obtain some weaker results using elementary methods.
A class of D-extreme Minkowski-reduced forms
Authors: Trenerry D. W. 
Published: April 2009

AbstractBarnes (1978, 1979) introduced the concept of a -extreme form, which is a Minkowski-reduced positive definite quadratic form having prescribed diagonal coefficients α1, α2, …, αn and providing a local minimum of the determinant of the form over all such forms. Here a class of forms which are -extreme for all α and all n is described.
Regular Wallman compactifications of rim-compact spaces
Authors: Njåstad Olav 
Published: April 2009

AbstractA compact Hausdorff space is regular Wallman if it possesses a separating ring of regular closed sets, an s-ring. It was proved by P. C. Baayen and J. van Mill [General Topology and Appl. 9 (1978), 125–129] that if a locally compact Hausdorff space possesses an s-ring, then every Hausdorff compactification with zero-dimensional remainder is regular Wallman.In this paper the reasoning leading to this result is modified to work in a more general setting. Iet αX be a Hausdorff compactification of a space X, and let be the family of those closed sets in αX whose boundaries are contained in X. A main result is the following: If contains an s-ring for some Hausdorff compactification γX, then every larger Hausdorff compactification αX for which is a base for the closed sets on αX — X, is regular Wallman. Various consequences concerning compactifications of a class of rim-compact spaces (called totally rim-compact spaces) are discussed.
Some results concerning frames, Room squares, and subsquares
Authors: Stinson D. R. 
Published: April 2009

AbstractFrames have been defined as a certain type of generalization of Room square. Frames have proven useful in the construction of Room squares, in particular, skew Room squares.We generalize the definition of frame and consider the construction of Room squares and skew Room squares using these more general frames.We are able to construct skew Room squares of three previously unknown sides, namely 93, 159, and 237. This reduces the number of unknown sides to four: 69, 87, 95 and 123. Also, using this construction, we are able to give a short proof of the existence of all skew Room squares of (odd) sides exceeding 123.Finally, this frame construction is useful for constructing Room squares with subsquares. We can also construct Room squares “missing” subsquares of sides 3 and 5. The “missing” subsquares of sides 3 and 5 do not exist, so these incomplete Room squares cannot be completed to Room squares.
The conjugacy problem and cuclic HNN constructions
Authors: Larsen Leif 
Published: April 2009

AbstractWe consider two related classes of groups. For any group G of the first of these — the smallest class containing all finitely generated free groups and closed under cyclic amalgamations — we show that for any U, W ∈ G we can “effectively describe” the set of all x and y with U* and W* conjugate in G. For the second class, which consists of all groups obtained from the first class through cyclic HNN constructions, we solve the conjugacy and power-conjugacy problems.
Some results on a combinatorial problem of Cordes
Authors: McCarthy D. , Rees G. H. J. van 
Published: April 2009

AbstractCordes (1976) introduced the problem of determining the maximum number of resolution classes of a finite set partitioned into equicardinal subsets such that the number of pairs common to any 2 classes is minimized. A later paper of Mullin and Stanton (1976) investigated those conditions under which the configurations were actually BIBD's. They obtained a bound for these special configurations and conjectured it applied in general. We prove this in the present paper. A recursive and a direct construction are also given for a special class of configurations.
Recursive equivalence types and octahedra
Authors: Dekker J. C. E. 
Published: April 2009

AbstractLet the word “graph” be used in the sense of a countable, connected, simple graph with at least one vertex. We write Qn and Ocn for the graphs associated with the n-cube Qn and the n-octahedron Ocn respectively. In a previous paper (Dekker, 1981) we generalized Qn and Qn to a graph QN and a cube QN, for any nonzero recursive equivalence type N. In the present paper we do the same for Ocn and Ocn. We also examine the nature of the duality between QN and OcN, in case N is an infinite isol. There are c RETs, c denoting the cardinality of the continuum.
N-Semigroups and their translation semigroups
Authors: Tamura Takayuki 
Published: April 2009

AbstractIfhis a homomorphism of anN-semigroup onto anN-semigroupS′, thenhinduces a homomorphismhof the translation semigroup Λ(S) ofSinto Λ(S′) ofS′. We will study the relations between the structures ofS,S′ and Λ(S), Λ(S)′, and will introduce the specialized concepts ofN-semigroupsS. In particular, we will be interested in power-joined steady or endlessN-semigroups. Finally, we will consider admissibility of torsion abelian groups, that is, consider what torsion abelian group can be a structure group of a power-joined steadyN-semigroup.
Recursive constructions for equidistant permutation arrays
Authors: Schellenberg P. J. , Vanstone S. A. 
Published: April 2009

AbstractAn equidistant permutation array (EPA) is a ν ×rarray defined on anr-set,R, such that (i) each row is a permutation of the elements ofRand (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.The first construction uses a resolvable regular pairwise balanced design of ordervto construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.
Maximal quotient rings of prime group algebras. II Uniform right ideals
Authors: Hannah John 
Published: April 2009

AbstractSuppose KG is a prime nonsingular group algebra with uniform right ideals. We show that G has no nontrivial locally finite normal subgroups. If G is soluble or residually finite, or if K has zero characteristic and G is linear, then the maximal right quotient ring of KG is simple Artinian.
Regular graphs and stability
Authors: Holton D. A. , Grant Douglas D. 
Published: April 2009

AbstractWe show that a graph G is semi-stable at vertex v if and only if the set of vertices of G adjacent to v is fixed by the automorphism group of Gv, the subgraph of G obtained by deleting v and its incident edges. This result leads to a neat proof that regular graphs are semi-stable at each vertex. We then investigate stable regular graphs, concentrating mainly on stable vertex-transitive graphs. We conjecture that if G is a non-trivial vertex-transitive graph, then G is stable if and only if γ(G) contains a transposition, offering some evidence for its truth.
Inhomogeneous products of cyclic irreducible nonnegative matrices
Authors: Taylor G. C. 
Published: April 2009

AbstractThe now well-known Coale–Lopez theorem, and variants of it, state that, under certain conditions, the product of the first r members of an infinite inhomogeneous sequence of nonnegative matrices approaches, as r → ∞, the class of matrices which, apart from scalar multiples, have only one distinct column. The aim of the present paper is to lay down conditions under which such products approach the class of matrices which, apart from scalar multiples, have no more than d distinct columns. A stronger result is then obtained by considering stochastic matrices instead of just nonnegative ones.