bluuebunny/crossref_metadata_2025_split huggingface dataset:
Strong Extensions vs. Weak Extensions of C*-Algebras
Authors: Cho S. J. 
Published: December 2010

Let be a separable complex infinite dimensional Hilbert space, the algebra of bounded operators in the ideal of compact operators, and the quotient map. Throughout this paper A denotes a separable nuclear C*-algebra with unit. An extension of A is a unital *-monomorphism of A into . Two extensions τ1 and τ2 are strongly (weakly) equivalent if there exists a unitary (Fredholm partial isometry) U in such thatfor all a in A.
Some Smoothness Properties of Measures on Topological Spaces
Authors: Hegde Shankar 
Published: December 2010

AbstrctV. S. Varadarajan has classified the bounded linear functional on the algebra C(X) of bounded continuous functions on a topological space X, according to the properties of their smoothness and related this classification to the corresponding natural classification of finitely additive regular measures on the zero sets of X. In this paper, some of these results are extended to the linear functionals on an arbitrary uniformly closed algebra A of bounded functions on a set X.
On a Result of Levitzki
Authors: Felzenszwalb B. 
Published: December 2010

A well known result of Levitzki [2, Lemma 1.1] is the following:Theorem. Let R be a ring and U a non-zero one-sided ideal of R. Suppose that given a∈U, an = 0 for a fixed integer n ≥ 1; then R has a non-zero nilpotent ideal.The purpose of this note is to observe some additional results which are related to the above.Theorem 1. Let R be a ring with no non-zero nil ideals and U an ideal of R. Suppose that a∊R is such that for every x∊U, axn(x) = 0 where n(x) ≥ 1 depends on x; then aU= Ua = 0.
Unipotent Matrix Groups Over Division Rings
Authors: Mochizuki H. Y. 
Published: December 2010

AbstractIf G is a unipotent group of n×n matrices over a division ring of characteristic 0 or prime p greater than (n- 1) (n-[n/2]) where [n/2] is the greatest integer less than or equal to n/2, then it is proved that G can be simultaneously triangularized.
A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order
Authors: Al-Abedeen Ahmed Z. , Arora H. L. 
Published: December 2010

AbstractWe extend the Picard's theorem to ordinary differential equation of generalized order α, 0 ≤ α ≤ l, and prove a global existence and uniqueness theorem by using the Banach contraction principle.
Certain nth Order Differential Inequalities in the Complex Plane
Authors: Al-Amiri H. S. 
Published: December 2010

AbstractLet w(z) be regular in the unit disc U:|z|<l, with w(0) = 0 and let h(r, s, t) be a complex function defined in a domain D of C3. The author determines conditions on h such that ifz∈U, then |w(z)|< 1 for z ∈ U and n= 0, 1, 2, …. Here Dnw(z) = (z/(l-z)n+1*w(z), where * stands for the Hadamard product (convolution). Some applications of the results to certain differential equations are given.
Determination of [nθ] by its Sequence of*Differences
Authors: Fraenkel A. S. , Mushkin M. , Tassa U. 
Published: December 2010

AbstractFor any real numberθletwhere [x] denotes the greatest integer not exceedingx.A method is given for computingfθfrom its first few terms. A similar method is given for computing the characteristic functiongθ(n)of[nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequencesfθand gθdetermines the sequence[nθ] (n = 1, 2,…).
Properties of Hereditary Hypergraphs and Middle Graphs
Authors: Cockayne E. J. , Hedetniemi S. T. , Miller D. J. 
Published: December 2010

AbstractThe middle graph of a graph G=( V, E) is the graph M(G) = (V∪E, E′), in which two vertices u, v are adjacent if either M is a vertex in V and v is an edge in E containing u, or u and v are edges in E having a vertex in common. Middle graphs have been characterized in terms of line graphs by Hamada and Yoshimura [7], who also investigated their traversability and connectivity properties. In this paper another characterization of middle graphs is presented, in which they are viewed as a class of intersection (representative) graphs of hereditary hypergraphs. Graph theoretic parameters associated with the concepts of vertex independence, dominance, and irredundance for middle graphs are discussed, and equalities relating the chromatic number of a graph to these parameters are obtained.
A Lower Bound for the Number of Negative Zeros of Power Series
Authors: Gawronski W. 
Published: December 2010

In this paper we are concerned with power series of the type1which admit unique analytic extension onto a domain containing the negative real axis. Our primary object is to establish a general theorem giving a lower estimate for the number of different zeros of (1) on the negative real axis. W. Jurkat and A. Peyerimhoff showed that for a certain class of coefficient functions a(z) the number of negative zeros of (1) is closely related to the behaviour of a(z) at z = 0. In particular they proved the following theorem [4, p. 219, Theorem 4].
A Criterion for Taylor Summability of Fourier Series
Authors: Holland A. S. B. , Sahney B. N. , Tzimbalario J. 
Published: December 2010

Let {ank} be a matrix defined by1and n taking only non-negative integer values.Let f(x) ∈ L [0, 2π] and be periodic with period 2π outside this interval. Let the Fourier series associated with the function f(x) be given byand letwhere s is a constant.
Approximation on Boundary Sets
Authors: Wang James Li-Ming 
Published: December 2010

AbstractLet U be a bounded open subset of the complex plane. By a well known result of A. M. Davie, C(bU) is the uniformly-closed linear span of A(U) and the powers (z-zi)-n, n = 1, 2, 3, … with zi a point in each component of U. We show that if A(U) is a Dirichlet algebra and bU is of infinite length, then one power of (z - zi) is superfluous.
Strongly Monotone Solutions of Retarded Differential Equations
Authors: Sficas Y. G. 
Published: December 2010

Let us consider the retarded differential equation1for which the following assumptions are made:(i) p: [t0, ∞) → [0, ∞) is continuous and not identically zero for all large t.(ii) σ [t0, ∞)→ ℝ is continuous, strictly increasing,(iii) φ: ℝ → ℝ is continuous, non-decreasing and
A Commutattvity Theorem for Rings and Groups
Authors: Nicholson W. K. , Yaqub Adil 
Published: December 2010

AbstractThe following theorem is proved: Suppose R is a ring with identity which satisfies the identities xkyk = ykxk and xlyl = ylxl, where k and l are positive relatively prime integers. Then R is commutative. This theorem also holds for a group G. Furthermore, examples are given which show that neither R nor G need be commutative if either of the above identities is dropped. The proof of the commutativity of R uses the fact that G is commutative, where G is taken to be the group R* of units in R.
A Note on a Theorem of Ky Fan
Authors: Lin Tzu-Chu 
Published: December 2010

Fan ([2, Theorem 2]) has proved the following theorem:Let K be a nonempty compact convex set in a normed linear space X. For any continuous map f from K into X, there exists a point u∈K such thatIn this note, we prove that the above theorem is true for a continuous condensing map defined on a closed ball in a Banach space. We also prove that it is true for a continuous condensing map defined on a closed convex bounded subset of a Hilbert space.
On Some Generalization of Inequalities of Opial, Yang and Shum
Authors: Lee Cheng-Shyong 
Published: December 2010

In 1960, Z. Opial [20] proved the following interesting integral inequality:Theorem A. If u is a continuously differentiable function on [0, b], and if u(0) = u(b) = 0, and u(x)>0 for x∊(0, b), then1where the constant b/4 is the best possible.
Fixed Point Theorems for Multi-Valued Mappings
Authors: Hu Thakyin 
Published: December 2010

AbstractTwo fixed point theorems for multi-valued mappings in a complete, ε-chainable metric space are proved. The theorems, thus established, extend result of M. Edelstein, Peter K. F. Kuhfittig, Hwei-mei Ko and Yueh-hsia Tsai, S. B. Nadler, Jr. and S. Reich.
Irréductibilité des Polynömes Sur un Corps Fini
Authors: Agou S. 
Published: December 2010

Dans ce qui suit f(X) désigne un polynöme irréductible de degré n de et un polynöme de tel que a≠0 et r désigne un entier non nul.On montre dans cet article que les polynÔmes ne sont pas irréductibles sur pour m≥3.
Decomposition of Kn into Dragons
Authors: Huang C. , Schonheim J. 
Published: December 2010

AbstractIt is shown that if 1<n ≡ 0 or 1 (mod 2 m), then the edges of Kn may be partitioned into isomorphic copies of a graph D3(m) and also of a graph D4(m), graphs consisting respectively of a triangle with an attached path of m - 3 edges or a quadrilateral with an attached path of m - 4 edges. If m is a power of 2 then the above condition is shown to be necessary and sufficient for the existence of such a partition.
On the Boundedness and Range of the Extended Hankel Transformation
Authors: Rooney P. G. 
Published: December 2010

For l≤p<∞ μ∈ℝ, let ℒμ.p denote the collection of functions f, measurable on (0, ∞) and such thatLet C0 be the collection of functions continuous and compactly supported on (0, ∞); it is known that C0 is dense in ℒμ.p—see [2; Lemma 2.2]. If X and Y are Banach spaces, denote by [X, Y] the collection of bounded linear operators from X into Y, abbreviating [X, X] to [X].
Gaps between Spheres in Normed Linear Spaces
Authors: Lohman Robert H. 
Published: December 2010

AbstractThe geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.
An Ultrafilter Completion of a Nearness Space
Authors: Carlson John W. 
Published: December 2010

AbstractAn ultrafilter completion is constructed for a nearness space. It is shown to preserve the Tl separation axiom. Characterizing conditions are given for it to be topological or for its topology to be compact. It is shown to have the simple extension topology and for a given Hausdorff space a compatible nearness structure is found for which its ultrafilter completion is homeomorphic to the Katetov H-closed extension.
The Zeroes of Functions Related to Dirichlet L-Functions
Authors: Weinstein Lenrd 
Published: December 2010

Hecke, [3], has shown for x a real Dirichlet character modulo q, the associated Dirichlet L-function L(s, x) has infinitely many zeroes on the line Here, using a method of Polya, [5], we show that both the real and imaginary parts of a function associated to L(s, x) through the functional equation, have infinitely many zeroes on any line
Operator Topologies and Invariant Operator Ranges
Authors: Ong Sing-Cheong 
Published: December 2010

AbstractThe invariant operator range lattices of a wide class of uniformly closed algebras (including C*-algebras) are stable under weak closures. There is an algebra whose invariant operator range lattice contains properly the corresponding lattice of its norm closure. An operator range transitive algebra is operator range n -transitive for all n. A normal operator is algebraic if and only if each of its invariant operator ranges is the range of some operator commuting with it.
Conditions for the Uniqueness of the Fixed Point in Kakutani's Theorem
Authors: Schirmer Helga 
Published: December 2010

AbstractKakutani's Theorem states that every point convex and use multifunction ϕ defined on a compact and convex set in a Euclidean space has at least one fixed point. Some necessary conditions are given here which ϕ must satisfy if c is the unique fixed point of ϕ. It is e.g. shown that if the width of ϕ(c) is greater than zero, then ϕ cannot be lsc at c, and if in addition c lies on the boundary of ϕ(c), then there exists a sequence {xk} which converges to c and for which the width of the sets ϕ(xk) converges to zero. If the width of ϕ(c) is zero, then the width of ϕ(xk) converges to zero whenever the sequence {xk} converges to c, but in this case ϕ can be lsc at c.
Summability of Matrix Transforms of Subsequences
Authors: Keagy Thomas A. 
Published: December 2010

AbstractD. F. Dawson has considered several questions of the following nature. Suppose T is a regular matrix summability method. If A is a regular matrix and x is a sequence having a finite limit point, then there exists a subsequence y of x such that each finite limit point of x is a T-limit point of Ay. In the present paper, we show the regularity condition for A may be replaced by the requirement that A be a limit preserving bv to c map. This leads to summability characterizations for several classes of sequences.
On the Cohomological Dimension of Soluble Groups
Authors: Gildenhuys D. , Strebel R. 
Published: December 2010

AbstractIt is known that every torsion-free soluble group G of finite Hirsch number hG is countable, and its homological and cohomological dimensions over the integers and rationals satisfy the inequalitiesWe prove that G must be finitely generated if the equality hG = cdQG holds. Moreover, we show that if G is a countable soluble group of finite Hirsch number, but not necessarily torsion-free, and if hG = cdQG, then hḠ = cdQḠ for every homomorphic image Ḡ of G.
Reflexive Topological Semilattices
Authors: Hong S. S. , Nel L. D. 
Published: December 2010

The duality between compact 0-dimensional semilattices and discrete semilattices studied by K. H. Hofmann et al. [2] is here extended to larger categories of topological semilattices.We regard topological semilattices as objects in the category CvSl of convergence semilattices, believing CvSl to be the appropriate setting for this study. The referee objected to this at first, which prompted us to set forth more carefully our reasons for doing so, as follows.
Bivectors over a Finite Field
Authors: MacDougall J. A. 
Published: December 2010

AbstractLet U be an n -dimensional vector space over a finite field of q elements. The number of elements of Λ2U of each irreducible length is found using the isomorphism of Λ2U with Hn, the space of n x n skew-symmetric matrices, and results due to Carlitz and MacWilliams on the number of skew-symmetric matrices of any given rank.
Remark on Irreducible Factorizations of Polynomials in Several Variables*
Authors: Rodman Leiba 
Published: December 2010

AbstractIt is proved that a polynomial on several complex variables, whose coefficients depend analytically on a parameter ε, admits a factorization which is irreducible for every value of the parameter, with the possible exception of an analytic set of points. Moreover, the coefficients of the irreducible factors can be chosen to depend analytically on ε in a neighborhood of every point not belonging to this analytic set.
Remarks on Two Weak Forms of Continuity
Authors: Espelie M. Solveig , Joseph James E. 
Published: December 2010

AbstractNew characterizations of weakly-continuous andθ-continuous functions are presented, andθ-continuity is applied to characterizeH(i) spaces; a recent characterization of closed graph functions is utilized to characterizeH-closed spaces. Noiri has shown that a function λ which is almost-continuous in the sense of Husain is weakly-continuous if cl(λ−1(W)) ⊂ λ−1(cl(W)) for all openW. It is established here that almost-continuity is superfluous in this statement.
Integral Representation by Boundary Vector Measures
Authors: Saab Paulette 
Published: December 2010

AbstractIn this paper we show that if X is a compact Hausdorff space, A is an arbitrary linear subspace of C(X, C), and if E is a Banach space, then each element L of (A ⊗ E)* can be represented by a boundary E*-valued vector measure of the same norm as L.
A New Proof of the Snake Theorem
Authors: Keener Lee L. 
Published: December 2010

AbstractThe Snake Theorem (terminology of Krein), due to Karlin in its original form, has been periodically improved. The theorem shows under appropriate conditions the existence of a function p* from a Tchebycheff space T, with a graph that alternately "touches" the graphs of functions f and g where f < g and f ≤ p* ≤ g on a compact interval [a, b]. The number of "touchings" depends upon the dimension of T. In this paper the conditions assumed are not the weakest known (see Gopinath and Kurshan, J. of Approximation Theory 21 (1977), 151–173), but the apparently new proof offered is elementary and fairly short. f and g are not assumed continuous.
A Note on Asymptotic Normal Structure and Close-to-Normal Structure
Authors: Tan Kok-Keong 
Published: December 2010

AbstractA closed convex subset X of a Banach space E is said to have (i) asymptotic normal structure if for each bounded closed convex subset C of X containing more than one point and for each sequence in C satisfying ‖xn − xn + 1‖ → 0 as n → ∞, there is a point x ∈ C such that ; (ii) close-to-normal structure if for each bounded closed convex subset C of X containing more than one point, there is a point x ∈ C such that ‖x − y‖ < diam‖ ‖(C) for all y ∈ C While asymptotic normal structure and close-to-normal structure are both implied by normal structure, they are not related. The example that a reflexive Banach space which has asymptotic normal structure but not close-to normal structure provides us a non-empty weakly compact convex set which does not have close-to-normal structure. This answers an open question posed by Wong in [9] and hence also provides us a Kannan map defined on a weakly compact convex set which does not have a fixed point.
Opérateurs à Itérés Uniformement Bornés
Authors: Nieto José I. 
Published: December 2010

RésuméDans un espace de Banach complexe (X, | |) on considère un opérateur linéaire borné A de spectre σ(A) et de rayon spectral r(A) = 1. On établit des conditions, en termes du spectre périphérique de A: σπ(A) = {λ ∊ σ(A): |λ| = 1}, qui garantissent l'existence d'une norme | |0, équivalente à | |, définie par un produit scalaire si | | l'est et telle que ‖A‖0 = Sup{|Ax|0: x|0 = 1} = 1. Si A est à itérés uniformément bornés (‖An‖ ≤ M pour n = 1, 2, …) une telle norme peut ne pas exister.
On the Number of Binomial Coefficients which are Divisible by their Row Number
Authors: Robbins Neville 
Published: December 2010

AbstractIf n is a natural number, let A(n) be the number of integers, k, such that 0 < k < n and n divides . Then ϕ(n) ≤ A(n) ≤ n - 1 - 2ω(n) + ɛ, where ?(n) denotes the number of distinct prime factors of n, and ɛ = 0 unless n is twice a prime, in which case ɛ = 1.
Almost Continuous Functions with Closed Graphs
Authors: Berner Andrew J. 
Published: December 2010

AbstractA function f:X → Y is almost continuous if for every x ∊ X and for each open set V ⊂ Y containing f(x), Cl(f-l(V)) is a neighborhood of x. Various conditions are given that guarantee that an almost continuous function is continuous. The main theorem states that if f:X → Y is almost continuous with a closed graph (closed in X × Y) and X and Y are complete metric spaces, then f is continuous.
Strong and Quasistrong Disconjugacy
Authors: London David , Schwarz Binyamin 
Published: December 2010

AbstractA complex linear homogeneous differential equation of the nth order is called strong disconjugate in a domain G if, for every n points z1,…, zn in G and for every set of positive integers, k1…, kl, k1 + … + kl = n, the only solution y(z) of the equation which satisfiesis the trivial one y(z) = 0. The equation y(n)(z) = 0 is strong disconjugate in the whole plane and for every other set of conditions of the form y(mk(zk) = 0, k = 1 , . . . , n, m1 ≤ m2... mn, there exist, in any given domain, points z1 , . . . , zn and nontrivial polynomials of degree smaller than n, which satisfy these conditions. An analogous results holds also for real disconjugate differential equations.
Rings with Automorphisms Leaving no Nontrivial Proper Ideals Invariant
Authors: Shamsuddin Ahmad 
Published: December 2010

AbstractIf an automorphism a on a ring R (with 1) leaves no non-trivial proper ideals of R invariant then we say that R is σ-simple. We construct examples of σ-simple rings and prove that finitely generated σ-simple algebras over fields are regular. A geometric interpretation of these concepts is also discussed.
A Characterization of the Topological Dimension
Authors: Rodé Gerd 
Published: December 2010

AbstractThis paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.
A Self-Dual Equational Basis for Boolean Algebras
Authors: Padmanabhan R. 
Published: December 2010

AbstractThe principle of duality for Boolean algebra states that if an identity ƒ = g is valid in every Boolean algebra and if we transform ƒ = g into a new identity by interchanging (i) the two lattice operations and (ii) the two lattice bound elements 0 and 1, then the resulting identity ƒ = g is also valid in every Boolean algebra. Also, the equational theory of Boolean algebras is finitely based. Believing in the cosmic order of mathematics, it is only natural to ask whether the equational theory of Boolean algebras can be generated by a finite irredundant set of identities which is already closed for the duality mapping. Here we provide one such equational basis.
An Oscillation Criterion for nth Order Non-Linear Differential Equations with Functional Arguments
Authors: Grace S. R. , Lalli B. S. 
Published: December 2010

AbstractAn oscillation criterion for an even order equation: x(n) + q(t)ƒ(x(t)), x[g(t)]) = 0 is provided. This criterion is an extension of a result established by Yeh for the second order equation ẍ + q(t)ƒ(x(t)), x[g(t)]) = 0.
Large Sets not Containing Images of a Given Sequence
Authors: Komjáth Péter 
Published: December 2010

AbstractIn the first part we construct a subsetHof positive measure in the unit interval and a zero-sequence {an} so thatHcontains no homothetic copy of {an}. In Theorem 2 we prove that if ε > 0 and a zero-sequence {an} are given then there exists a setAof measure less than ε so thatcovers the interval. An application of this result is Theorem 3: for any sequence {an} and ε > 0 there is a set H of measure 1 - ε such that for noNandcis {an+ c}n ≥ Ncontained byH.
On Lattice Analogues of Absolutely Summing Constants*
Authors: Szulga J. 
Published: December 2010

AbstractLet E be a Banach lattice,where x1, …, xn ∊ E. We study properties of constantsA characterization of AM-spaces is obtained which generalizes the result of Abramocič, Positselskiĭ, Yanovskii. Asymptotic estimates of φp for some classical finite dimensional lattices are given.
On the Rank of a p-Group of Class 2
Authors: Webb U. H. M. 
Published: December 2010

AbstractLet d(G) denote the minimal number of generators of the finite p-group G, r(G) the maximum over all subgroups H of G of d(H) and ra(G) the maximum over all abelian subgroups H of G of d(H). If G is of class two it is clear thatBy considering properties of the stability number of graphs we construct examples which show that any value of r(G) within these bounds can occur.
Embedding Theorems in Group C*-Algebras†
Authors: Lee Tan-Yu 
Published: December 2010

AbstractLet G be a locally compact group and H an open subgroup of G. The embeddings of group C*-algebras associated with H into the group C*-algebras associated with G are studied. Three conditions for the embeddings given in terms of C*-norms of the group algebras, group representations and positive definite functions are shown to be equivalent. As corollary, we prove that the full C*-algebra of H can be embedded into the full C*-algebra of G in a natural way as well as the case for the reduced group C*-algebras. We also show that the embeddings hold for their duals and double duals.