bluuebunny/crossref_metadata_2025_split huggingface dataset:
An approximation method for monotone Lipschitzian operators in Hilbert spaces
Authors: Chidume C. E. 
Published: April 2009

AbstractSuppose H is a complex Hilbert space and K is a nonempty closed convex subset of H. Suppose T: K → H is a monotomc Lipschitzian mapping with constant L ≧ 1 such that, for x in K and h in H, the equation x + Tx Tx = h has a solution q in K. Given x0 in K, let {Cn}∞n=0 be a real sequence satisfying: (i) C0 = 1, (ii) 0 ≦ Cn < L-2 for all n ≧ 1, (iii) ΣnCn(1 − Cn) diverges. Then the sequence {Pn}∞n=0 in H defined by pn = (1 − Cn)xn + CnSxn, n ≧ 0, where {xn}∞n=0 in K is such that, for each n ≧ 1, ∥ xn – Pn−1 ∥ = infx ∈ k ∥ Pn−1 − x ∥, converges strongly to a solution q of x + Tx = h. Explicit error estimates are given. A similar result is also proved for the case when the operator T is locally Lipschitzian and monotone.
On extremal points of the unit ball in the Banach space of Lipschitz continuous functions
Authors: Rolewicz S. 
Published: April 2009

AbstractIt is shown that for arbitrary ε > 0 there is a function x(t, x) defined on the square [0,1] × [0,1] such that x(t, s) represents an extremal point of the unit ball in the space of Lipschitz continuous functions, and the gradient of x(t, s) is equal to 0 except on a set of measure at most ε.
A Riemann integral in a locally compact Hausdorff space
Authors: Ahmed S. I. , Pfeffer W. F. 
Published: April 2009

AbstractWe present a systematic and self-contained exposition of the generalized Riemann integral in a locally compact Hausdorff space, and we show that it is equivalent to the Perron and variational integrals. We also give a necessary and sufficient condition for its equivalence to the Lebesgue integral with respect to a suitably chosen measure.
A Property of completely monotonic functions
Authors: O'Cinneide Colm 
Published: April 2009

AbstractA non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.
Subnormal subgroups in direct products of groups
Authors: Hauck Peter 
Published: April 2009

AbstractA groupGis callednormally (subnormally) detectableif the only normal (subnormal) subgroups in any direct productG1× … ×Gnof copies ofGare just the direct factorsGi. We give an internal characterization of finite subnormally detectable groups and obtain analogous results for associative rings and for Lie algebras. The main part of the paper deals with a study of normally detectable groups, where we verify a conjecture of T. O. Hawkes in a number of special cases.
Mal'cev products of varieties of completely regular semigroups
Authors: Jones P. R. 
Published: April 2009

AbstractWhilst the Mal'cev product of completely regular varieties need not again be a variety, it is shown that in many important instances a variety is in fact obtained. However, unlike the product of group varieties this product is nonassociative.Two important operators introduced by Reilly are studied in the context of Mal'cev products. These operators are shown to generate from any given variety one of the networks discovered by Pastijn and Trotter, enabling identities to be provided for the varieties in the network. In particular the join O V BG of the varieties of orthogroups and of bands of groups is determined, answering a question of Petrich.
Smooth derivations on abelian C*-dynamical systems
Authors: Robinson Derek W. 
Published: April 2009

AbstractLet (A, R, σ) be an abelian C*-dynamical system. Denote the generator of σ by δ0 and define A∞ = ∩n>1D (δ0n). Further define the Lipschitz algebra
.If δ is a *-derivation from A∞ into A½, then it follows that δ is closable, and its closure generates a strongly continuous one-parameter group of *-automorphisms of A. Related results for local dissipations are also discussed.
A concrete realization of the dual space of L1-spaces of certain vector and operator-valued measures
Authors: Ricker Werner 
Published: April 2009

AbstractFor a given vector measure n, an important problem, but in practice a difficult one, is to give a concrete description of the dual space of L1(n). In this note such a description is presented for an important class of measures n, namely the spectral measures (in the sense of N. Dunford) and certain other vector and operator-valued measures that they naturally induce. The basic idea is to represent the L1-spaces of such measures as a more familiar space whose dual space is known.
On the measure of the one-skeleton of the sum of convex compact sets
Authors: Dalla Leoni 
Published: April 2009

AbstractFor any two compact convex sets in a Euclidean space, the relation between the volume of the sum of the two sets and the volume of each of them is given by the Brünn-Minkowski inequality. In this note we prove an analogous relation for the one-dimensional Hausdorff measure of the one-skeleton of the above sets. Also, some counterexamples are given which show that the above results are the best possible in some special cases.
Exact coverings of triples with specified longest block length
Authors: Stanton R. G. , Allston J. L. 
Published: April 2009

AbstractA minimal (1,3; ν) covering occurs when we have a family of proper subsets selected from ν elements with the property that every triple occurs exactly once in the family and no family of smaller cardinality possesses this property. Woodall developed a lower bound W for the quantity g(k)(1, 3; ν) which represents the cardinality of a minimal family with longest block of length k. The Woodall bound is only accurate in the region when k ≥ ν/2. We develop an expression for the excess of the true value over the Woodall bound and apply this to show that, when k ≥ ν/2, the value of g(1,3; ν) = W + 1 when k is even and W + 1 + when k is odd.
Fibre bundles and Yang-Mills fields
Authors: Smrz P. K. 
Published: April 2009

Since 1954, when Yang and Mills [7] presented their idea of isotopic gauge transformation, the method of introducing interactions into field theories by using general gauge invariance has been extensively studied.A general formalism was presented by Utiyama [6]. Reference [6] also contains the first application of the formalism to the theory of gravitation. A more general approach to the Young-Mills formalism applied to general relativity was described by Kibble [3]. In a special case of interacting Dirac field the gauge invariance group can still be enlarged, leading to the possibility of describing short-range interactions together with gravitation and electromagnetism [5]. It is, therefore important to have a definite formulation of the common geometrical content of such theories.
Modular inverse semigroups
Authors: Johnston Katherine G. , Jones Peter R. , Hall T. E. 
Published: April 2009

AbstractAn inverse semigroup S is said to be modular if its lattice 𝓛𝓕 (S) of inverse subsemigroups is modular. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a semigroup S is modular if and only if (I) S is combinatorial, (II) its semilattice E of idempotents is “Archimedean” in S, (III) its maximum group homomorphic image G is locally cyclic and (IV) the poset of idempotents of each 𝓓-class of S is either a chain or contains exactly one pair of incomparable elements, each of which is maximal. Thus in view of earlier results of the second author a simple modular inverse semigroup is “almost” distributive. The bisimple modular inverse semigroups are explicitly constructed. It is remarkable that exactly one of these is nondistributive.
Congruences and Green's relations on eventually regular semigroups
Authors: Edwards P. M. , Hall T. E. 
Published: April 2009

AbstractA semigroup is eventually regular if each of its elements has some power that is regular. Let 𝓚 be one of Green's relations and let ρ be a congruence on an eventually regular semigroupS. It is shown for 𝓚 = 𝓛, 𝓡 and 𝓓 that ifAandBare regular elements ofS/ρ that are 𝓚-related inS/ρ then there exist elementsa∈A,b∈Bsuch thataandbare 𝓚-related inS. The result is not true for 𝓗 or 𝓙.
On the Spectrum of almost periodic solutions of an abstract differential equation
Authors: Rao Aribindi Satyanarayan , Hengartner Walter 
Published: April 2009

AbstractIf a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.
A class of hypergeometric polynomials
Authors: Srivastava H. M. 
Published: April 2009

AbstractThe object of the present paper is first to derive an interesting unification (and generalization) of a fairly large number of finite summation formulas including, for example, those that appeared in this Journal recently. We then briefly remark on its various (known or new) special cases which are associated with certain classes of hypergeometric polynomials in one and two variables. We also give several further generalizations (involving multiple series with essentially arbitrary terms) which are shown to be applicable in the derivation of analogous summation formulas for hypergeometric series (and polynomials) in three and more variables. Finally, with a view to presenting relevance of these types of results in various seemingly diverse areas of applied sciences and engineering, some indication of applicability is provided.
Coin tossing and sum sets
Authors: Brown Gavin , Williamson John H. 
Published: April 2009

AbstractWe consider the distribution μ of numbers whose binary digits are generated from infinitely many tosses of a biased coin. It is shown that, if E has positive μ measure, then some n-fold sum of E with itself must contain an interval. This contrasts with the known result that all convolution powers of μ are singular.
The Hadamard conjecture and integer lattices
Authors: McCall J. , Little C. H. C. 
Published: April 2009

AbstractLet L be an integer lattice, and S a set of lattice points in L. We say that S is optimal if it minimises the number of rectangular sublattices of L (including degenerate ones) which contain an even number of points in S. We show that the resolution of the Hadamard conjecture is equivalent to the determination of |S| for an optimal set S in a (4s-1) × (4s-1) integer lattice L. We then specialise to the case of 1 × n integer lattices, characterising and enumerating their optimal sets.
Convolutions of Distributions With Exponential and Subexponential Tails
Authors: Cline Daren B. H. 
Published: April 2009

Distribution tails F(t) = F(t, ∞) are considered for which and as t → ∞. A real analytic proof is obtained of a theorem by Chover, Wainger and Ney, namely that .In doing so, a technique is introduced which provides many other results with a minimum of analysis. One such result strengthens and generalizes the various known results on distribution tails of random sums.Additionally, the closure and factorization properties for subexponential distributions are investigated further and extended to distributions with exponential tails.
An Inequality Implicit Function Theorem
Authors: Ng Kung-Fu 
Published: April 2009

AbstractLet f be a continuous function, and u a continuous linear function, from a Banach space into an ordered Banach space, such that f − u satisfies a Lipschitz condition and u satisfies an inequality implicit-function condition. Then f also satisfles an inequality implicit-function condition. This extends some results of Flett, Craven and S. M. Robinson.
On Dual Radicals and Ring Elements
Authors: De La Rosa B. , Wiegandt R. 
Published: April 2009

AbstractIf a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero P-element is a dual radical in the sense of Andrunakievič, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical.
Sampling Without Replacement: Approximation to the Probability Distribution
Authors: Darroch J. N. , Jirina M. , Speed T. P. 
Published: April 2009

AbstractLet P be the probability distribution of a sample without replacement of size n from a finite population represented by the set N={1,2,…N}. For each r=0, 1, …, an approximation Pr is described such that the uniform norm ‖P − Pr‖ is of order (n2/N)r+1 if n2/N→0. The approximation Pr is a linear combination of uniform probability product-measures concentrated on certain subspaces of the sample space Nn.
Variation of Fixed-Point and Coincidence Sets
Authors: Gauld David 
Published: April 2009

AbstractTopologise the set of continuous self-mappings of a Hausdorff space by the graph topology. When the set of closed subsets of the space is given the upper semi-finite topology then the function which assigns to a map its fixed-point set is continuous. In many familiar cases this is the largest such topology. Related results also hold for the function which assigns to each pair of maps their coincidence set.
Injective Modules Over Non-Artinian Serial Rings
Authors: Hill David A. 
Published: April 2009

AbstractA module is uniserial if its lattice of submodules is linearly ordered, and a ring R is left serial if R is a direct sum of uniserial left ideals. The following problem is considered. Suppose the injective hull of each simple left R-module is uniserial. When does this imply that the indecomposable injective left R-modules are uniserial? An affirmative answer is known when R is commutative and when R is Artinian. The following result is proved.Let R be a left serial ring and suppose that for each primitive idempotent e, eRe has indecomposable injective left modules uniserial. The following conditions are equivalent. (a) The injective hull of each simple left R-module is uniserial. (b) Every indecomposable injective left R-module is univerial. (c) Every finitely generated left R-module is serial.The rest of the paper is devoted to a study of some non-Artinian serial rings which serve to illustrate this theorem.
LECs, Local Mixers, Topological Groups and Special Products
Authors: Borges Carlos R. 
Published: April 2009

AbstractWe prove that every (locally) contractible topological group is (L)EC and apply these results to homeomorphism groups, free topological groups, reduced products and symmetric products. Our main results are: The free topological group of a θ-contractible space is equiconnected. A paracompact and weakly locally contractible space is locally equiconnected if and only if it has a local mixer. There exist compact metric contractible spaces X whose reduced (symmetric) products are not retracts of the Graev free topological groups F(X) (A(X)) (thus correcting results we published ibidem).
Certain Finitely Generated Compact Zero Dimensional Semigroups
Authors: Hunter R. P. 
Published: April 2009

AbstractConsider a compact zero dimensional (profinite) monoid. While the group of units must be open, a regular D-class need not be open in the ideal it generates. This is the case if and only if the semigroup contains infinitely many copies of a certain semilattice composed of an increasing sequence of idempotents converging to an upper bound.Using compactifications of free products, two generator compact monoids with these properties are constructed.
Characterizations of Quasi-Metrizable Bitopological Spaces
Authors: Raghavan T. G. , Reilly I. L. 
Published: April 2009

AbstractIn this paper we prove that a pairwise Hausdorff bitopological space is quasi-metrizable if and only if for each point x ∈ X and for i, j = 1,2, i ≠ j, one can assign nbd bases { S(n, i; x) | n = 1, 2,… } such that (i) y ∉ S (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) y ∈ S (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.
Vector lattices over subfields of the reals
Authors: Bixler P. , Conrad P. , Powell W. B. , Tsinakis C. 
Published: April 2009

AbstractIn this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity ofl-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a non-linearl-automorphism and more than one scalar multiplication. It is also shown that eachl-group contains a largest archimedean convexl-subgroup which admits a unique scalar multiplication.
Groups with many permutable subgroups
Authors: Curzio Mario , Lennox John , Rhemtulla Akbar , Wiegold James 
Published: April 2009

AbstractWe consider the influence on a group G of the condition that every infinite set of cyclic subgroups of G contains a pair that permute and prove (Theorem 1) that finitely generated soluble groups with this condition are centre-by-finite, and (Theorem 2) that torsion free groups satisfying the condition are abelian.
Multipliers on weighted Hardy spaces over locally compact Vilenkin groups, I
Authors: Onneweer C. W. , Quek T. S. 
Published: April 2009

AbstractLet G denote a locally compact Vilenkin group with dual group Γ. We give sufficient conditions for a function ϕ ∈ L∞ (Γ) to be a multiplier from the power-weighted Hardy space to itself or the corresponding power-weighted Lebesgue space
Subgroups of the Schur multiplier
Authors: Higgs R. J. 
Published: April 2009

AbstractTwo subgroups ME(G) and MI(G) of the Schur multiplier M(G) of a finite group G are introduced: ME(G) contains those cohomology classes [α] of M(G) for which every element of G is α-regular, and MI(G) consists of those cohomology classes of M(G) which contain a G-invariant cocycle. It is then shown that under suitable circumstances, such as when G has odd order, that each element of MI(G) can be expressed as the product of an element of ME(G) and an element of the image of the inflation homomorphism from M(G/G′) into M(G).
A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems
Authors: Shih Mau-Hsiang , Tan Kok-Keong 
Published: April 2009

AbstractA geometric property of convex sets which is equivalent to a minimax inequality of the Ky Fan type is formulated. This property is used directly to prove minimax inequalities of the von Neumann type, minimax inequalities of the Fan-Kneser type, and fixed point theorems for inward and outward maps.
Bounded spherical functions for abstract operators
Authors: Cohen Joel M. 
Published: April 2009

AbstractThe aim of this paper is to study the spherical functions associated to an operator. These functions can be thought of abstractly as being eigenfunctions of the operator which can be expressed in terms of the operator. The meaning of these properties will be made precise as will a notion of boundedness. The results are obtained by studying a specific shift operator on the algebra of functionals on the complex polynomial ring. For the class studied, we obtain ellipses of eigenvalues for which there exist bounded spherical functions. As an application of the results, we study radial functions on discrete groups.
Cartan subalgebras of regular extensions of von Neumann algebras
Authors: Sutherland Colin E. 
Published: April 2009

AbstractWe analyse the structure of a regular extension ℳ ⋊ γ, υQ of a von Neumann algebra ℳ by an action (modulo inner automorphisms) γ of a discrete group Q, and a nonabelian 2-cycle υ for γ, under the assumption that the “action” γ of Q is cocycle conjugate to an “action”, α which leaves globally invariant a cartan subalgebra of ℳ. we show that ℳ ⋊ γ, υQ is isomorphic with the algebra of the left regular projective representation of a certain discrete, non-principal groupoid ℜ V Q determined by the action of Q on the given cartan subalgebrs, where ℜ is the Takesaki relation associated to the pair (ℳ, ) we apply this description to give a decomposition of the regular representation of a group G into irreducibles, where G is a split extension of a type I group K by an abelian group Q, and work out the details of the author's earlier abstract plancherel theorem in the case when K is abelian.
The characterization of elliptic curves over finite fields
Authors: Hirschfeld J. W. P. , Voloch J. F. 
Published: April 2009

AbstractIn a finite Desarguesian plane of odd order, it was shown by Segre thirty years ago that a set of maximum size with at most two points on a line is a conic. Here, in a plane of odd or even order, sufficient conditions are given for a set with at most three points on a line to be a cubic curve. The case of an elliptic curve is of particular interest.
Oscillation criteria for second order differential equations with damping
Authors: Grace S. R. 
Published: April 2009

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.
Sharp function estimates for fractional integrals and related operators
Authors: Kurtz Douglas S. 
Published: April 2009

AbstractThis paper considers analogs of results on integral operators studied by Hörmander. Using the sharp function introduced by Fefferman and Stein, we prove weighted norm inequalities on kernel operators which map an Lp space into an Lq space, with q not equal to p. The techniques recover known results about fractional integral operators and apply to multiplier operators which satisfy a generalization of the Hörmander multiplier condition.
Eigenelements of perturbed operators
Authors: Limaye B. V. , Nair M. T. 
Published: April 2009

AbstractLet λ0 be a semisimple eigenvalue of an operator T0. Let Γ0 be a circle with centre λs0 containing no other spectral value of T0. Some lower bounds are obtained for the convergence radius of the power series for the spectral projection P(t) and for trace T(t)P(t) associated with linear perturbation family T(t) = T0 + tV0 and the circle Γ0. They are useful when T0 is a member of a sequence (Tn) which approximates an operator T in a collectively compact manner. These bounds result from a modification of Kato's method of majorizing series, based on an idea of Redont. I λ0 is simple, it is shown that the same lower bound are valid for the convergence radius of a power series yielding an eigenvector of T(t).
Fundamental systems and solutions of nonhomogeneous equations for a pair of mixed linear ordinary differential equations
Authors: Venkatesulu M. , Bhaskar T. Gnana 
Published: April 2009

AbstractTwo different ordinary differential operators L1 and L2 (not of the same order) defined on two adjacent intervals I1 and I2, respectively, with certain mixed conditions at the interface are considered. These problems are encountered in the study of ‘acoustic waveguides in ocean’, ‘transverse vibrations in nonhomogeneous strings’, etc. A complete set of physical conditions on the system give rise to three types of (selfadjoint) boundary value problems associated with the pair (L1, L2). In a series of papers, a systematic study of these new classes of problems is being developed. In the present paper, we construct the fundamental systems and exhibit the forms of solutions of nonhomogeneous problems associated with the pair (L1, L2).
The maximum distribution of a Gaussian stochastic process indexed by a local field
Authors: Evans Steven N. 
Published: April 2009

AbstractWe consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.