bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semibounded Extensions of Singular Ordinary Differential Operators
Authors: Krall Allan M. 
Published: December 2010

AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.
On Levi-Like Properties and some of Their Applications in Riesz Space Theory
Authors: Buskes G. , Labuda I. 
Published: December 2010

AbstractLet (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.
Injective and Weakly Injective Rings
Authors: Gardner B. J. , Stewart P. N. 
Published: December 2010

AbstractLet V be a variety of rings and let A ∊ V. The ring A is injective in V if every trianglewith C ∊ V, m a monomorphism and f a homomorphism has a commutative completion as indicated. A ring which is injective in some variety (equivalently, injective in the variety it generates) is called injective. When only triangles with f surjective are considered we obtain the notion of weak injectivity. Directly indecomposable injective and weakly injective rings are classified.
Non-Standard, Normal Subgroups and Non-Normal, Standard Subgroups of the Modular Group
Authors: Mason A.W. 
Published: December 2010

AbstractLet R be a commutative ring with identity. A subgroup S of GLn(R), where n ≥ 2, is said to be standard if and only if S contains all the q-elementary matrices and all conjugates of those matrices by products of elementary matrices, where q is the ideal in R generated by Xij,xii — Xjj(i ≠ j), for all (xij) ∊ S. It is known that, when n ≧ 3, the standard subgroups of GLn(R) are precisely those normalized by the elementary matrices. To demonstrate how completely this result can break down for n = 2 we prove that GL2(Z), where Z is the ring of rational integers, has uncountably many non-normal, standard subgroups and uncountably many non-standard, normal subgroups.
Montel Subspaces in the Countable Projective Limits of Lp(μ)-Spaces
Authors: Díaz J. C. 
Published: December 2010

AbstractLet us suppose one of the following conditions: (a) p ≧ 2 and F is a closed subspace of a projective limit (b) p = 1 and F is a complemented subspace of an echelon Köthe space of order 1, Λ(X,β,μ,gk); and (c) 1 > p > 2 and F is a quotient of a countable product of Lp(μn) spaces. Then, F is Montel if and only if no infinite dimensional subspace of F is normable.
Solutions of Specific Diophantine Equations and their Relationship to Complex Multiplication
Authors: Wajngurt Clara 
Published: December 2010

AbstractIn this paper we establish a relationship between the rational solutions (x(t), y(t)), over C(t), of the diophantine equation:and the solutions which parametrize the elliptic curve E, y2 = 4x3 — g2x — g3 admitting complex multiplication by λ. We first characterize the form of all rational solutions of diophantine equation (1). The rational solutions are derivable from the subsititutionsin which μ = 0,ω1,ω2,ω1 + ω2 = ω3. Using techniques established in elliptic function theory, we prove that the complex multiplier λ, associated with a unique rational solution (x(t), y(t)), must be of a certain form. Next we construct all rational solutions of diophantine equation (1) by using the addition theorems valid for the Weierstrass function, Specific examples are finally worked out for the cases
A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property
Authors: Hare D. E. G. 
Published: December 2010

AbstractWe introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.
Moore G-Spaces Which are not Co-Hopf G-Spaces
Authors: Doman Ryszard 
Published: December 2010

AbstractLet G be a finite group. By a Moore G-space we mean a G-space X such that for each subgroup H of G the fixed point space XH is a simply connected Moore space of type (MH,n), where MH is an abelian group depending on H, and n is a fixed integer. By a co-Hopf G-space we mean a G-space with a G-equivariant comultiplication. In this note it is shown that, in contrast to the non-equivariant case, there exist Moore G-spaces which are not co-Hopf G-spaces.
A Group Theoretic Characterization of the 2-Dimensional Spherical Groups
Authors: Miller Andy 
Published: December 2010

AbstractIt is shown that for a finite group G to be isomorphic to a subgroup of SO(3) (or, equivalently, of PSL(2, C)) it is necessary and sufficient that G satisfies the property that the normalizer of every cyclic subgroup is either cyclic or dihedral.
On the Davison Convolution of Arithmetical Functions
Authors: Haukkanen Pentti 
Published: December 2010

AbstractThe Davison convolution of arithmetical functions f and g is defined by where K is a complex-valued function on the set of all ordered pairs (n, d) such that n is a positive integer and d is a positive divisor of n. In this paper we shall consider the arithmetical equations f(r) = g, f(r) = fg, f o g = h in f and the congruence (f o g)(n) = 0 (mod n), where f(r) is the iterate of f with respect to the Davison convolution.
Projective Socles
Authors: Stewart Patrick N. 
Published: December 2010

AbstractNicholson and Watters have recently investigated rings with projective socles and they have shown, among other things, that a ring R has a projective socle if and only if each matrix ring Mn(R), n > 1, has a projective socle. We generalize this result by showing that if S is an excellent extension of R, then the socle of R is projective if and only if the socle of S is projective. Examples of excellent extensions include, as well as matrix rings Mn(R), skew group rings R * G where G is a finite group and the order of G is invertible in R.
Families of Sequences of 0s and 1s In FK-Spaces
Authors: Sember John 
Published: December 2010

AbstractA characterization is given of those families ℱ of subsets of the positive integers for which σ(ℓ1, ) is sequentially complete, where denotes the linear span of the characteristic functions of ℱ. Consequences include some known matrix results, such as Hahn's Theorem and conditions required for a matrix to "sum" the characteristic functions of the lacunary sets.
Dependent Random Variables with Independent Subsets - II
Authors: Wang Y. H. 
Published: December 2010

AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.
A Banach Space in Which a Ball is Contained in the Range of Some Countably Additive Measure is Superreflexive
Authors: Sun Yeneng 
Published: December 2010

AbstractA nonstandard proof of the fact that a Banach space in which a ball is contained in the range of a countably additive measure is superreflexive is given. The proof is an application of a general method in which we first transfer certain standard objects to the nonstandard hull of a Banach space and then, using the quite well developed theory of nonstandard hulls, derive results about the objects in the original Banach space. It also provides us with an example of the applications of the theory of nonstandard hull valued measures.
Extensions that are Submodules of their Quotients
Authors: Okoh F. , Zorzitto F. 
Published: December 2010

AbstractLet 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.
Divisors of Integers in Arithmetic Progression
Authors: Varbanec P. D. , Zarzycki P. 
Published: December 2010

AbstractLet d(n; l, k) be the number of positive divisors of n which lie in the arithmetic progression l mod k. Using the complex integration technique the formula is proved. This formula holds uniformly in l, k and x satisfying 1 ≦ l ≦ k, (lx)1/2 ≦ k ≦ x1-∊; the exponent α ≦ 1/3.
Exemples de Dimension de Krull D'Anneaux de Polynomes
Authors: Ouertani Ahmed 
Published: December 2010

AbstractFor each pair (m, n) of integers such that m+1 ≦ n ≦ 2m+1, we give, by original and straightforward methods, some examples of rings A' such that dim A' = m and dim A'[X] = n.
On the Étale K-Theory of an Elliptic Curve with Complex Multiplication for Regular Primes
Authors: Wingberg Kay 
Published: December 2010

AbstractGeneralizing a result of Soulé we prove that for an elliptic curve E defined over an imaginary quadratic field K with complex multiplication having good ordinary reduction at the prime number p > 3 which is regular for E and the extension F of K contained in K(Ep) the dimensions of the étale K-groups are equal to the numbers predicted by Bloch and Beilinson, i.e.,
On Totally Real Submanifolds in a 6-Sphere
Authors: Bashir M. A. 
Published: December 2010

AbstractThe 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. With respect to this structure S6 is a nearly Kaehlerian manifold. We investigate 2-dimensional totally real submanifolds in S6. We prove that a 2-dimensional totally real submanifold in S6 is flat.
The Hexagonal Packing Lemma and Discrete Potential Theory
Authors: Aharonov Dov 
Published: December 2010

AbstractOne of the questions concerning the Hexagonal Packing Lemma ([1], [3], [4]) is the rate of convergence of Sn. It was suggested in [3] and [4] that Sn = 0(1/n). In the following we prove this conjecture under the additional condition of some "nice" behaviour of the "circle function".
Totally Integrally Closed Azumaya Algebras
Authors: Macoosh R. , Raphael R. 
Published: December 2010

AbstractEnochs introduced and studied totally integrally closed rings in the class of commutative rings. This article studies the same question for Azumaya algebras, a study made possible by Atterton's notion of integral extensions for non-commutative rings.The main results are that Azumaya algebras are totally integrally closed precisely when their centres are, and that an Azumaya algebra over a commutative semiprime ring has a tight integral extension that is totally integrally closed. Atterton's integrality differs from that often studied but is very natural in the context of Azumaya algebras. Examples show that the results do not carry over to free normalizing or excellent extensions.
Binary Trees and the n-Cutset Property
Authors: Arpin Peter , Ginsburg John 
Published: December 2010

AbstractA partially ordered set P is said to have the n-cutset property if for every element x of P, there is a subset S of P all of whose elements are noncomparable to x, with |S| ≤ n, and such that every maximal chain in P meets {x} ∪ S. It is known that if P has the n-cutset property then P has at most 2n maximal elements. Here we are concerned with the extremal case. We let Max P denote the set of maximal elements of P. We establish the following result. THEOREM: Let n be a positive integer. Suppose P has the n-cutset property and that |Max P| = 2n. Then P contains a complete binary tree T of height n with Max T = Max P and such that C ∩ T is a maximal chain in T for every maximal chain C of P. Two examples are given to show that this result does not extend to the case when n is infinite. However the following is shown. THEOREM: Suppose that P has the ω-cutset property and that |Max P| = 2ω. If P — Max P is countable then P contains a complete binary tree of height ω
An Induction Theorem for Units of p-Adic Group Rings
Authors: Bhandari A. K. , Sehgal S. K. 
Published: December 2010

AbstractLet G be a finite group and let C be the family of cyclic subgroups of G. We show that the normal subgroup H of U = U(ZpG) generated by U(ZpC), C ∊ C, where Zp is the ring of p-adic integers, is of finite index in U.
Determination of Grassmann Manifolds Which are Boundaries
Authors: Sankaran Parameswaran 
Published: December 2010

AbstractLetFGn,kdenote the Grassmann manifold of allk-dimensional (left)F-vector subspace ofFnfor F = ℝ, the reals,C, the complex numbers, orHthe quaternions. The problem of determining which of the Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the caseF= ℝ, including a sufficient condition, due to A. Dold, on n and k for ℝGn,kto bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well.
Dimension-Preserving Extensions of Pro-p-Groups
Authors: Würfel Tilmann 
Published: December 2010

AbstractWe investigate extensions of pro-p-groups 1 —> N —> G —> Γ —> 1 where N is pro-p-free and Nab, is a free Zp[Γ]-module. In case Γ is finite we show that such an extension splits modulo the second derived
group N".
Weak Continuity of a Composition Map Between Spaces of Compact Operators and Banach Valued Continuous Functions
Authors: Asthagiri Rajappa K. 
Published: December 2010

AbstractThis paper characterizes the Banach space E for the sequential continuity and the continuity on bounded sets of the composition map m: C(S, E)wk x K{E,F)wk —> C(S,F)wk. Here, K(E,F) denotes the Banach space of compact linear operators on the Banach space E to the Banach space F with the usual operator norm, and for any Banach space E, Ewk denote the Banach space E with the weak topology. Also we denote by C(S, E) the Banach space of E valued continuous functions on a nonvoid compact Hausdorff space S with sup norm.
An Arithmetical Function Associated With the Rank of Elliptic Curves
Authors: Clark David 
Published: December 2010

AbstractWe define an arithmetical function, f(n), which gives a lower bound for the rank of elliptic curves, y2 = x3 + nx, n square-free. Thus, if f(n) is unbounded for square-free values of n, then there are elliptic curves of arbitrarily large rank. We show that f(n) is unbounded as n ranges over all integers.
Mahler's Measure of a Polynomial in Function of the Number of its Coefficients
Authors: Dobrowolski Edward 
Published: December 2010

AbstractMahler's measure of a monic polynomial is equal to the product of modules of its roots which lie outside the unit circle. By classical theorem of Kronecker it is strictly greater than 1 for any polynomial that is not a product of cyclotomic factors. In this case a number of lower bounds of the measure, depending either on the degree of the polynomial or on the number of its non-zero coefficients, has been found. Here is given an improvement of the bound of the latter type previously found by the author, A. Schinzel and W. Lawton.
Nest Algebras of Operators and the Dunford-Pettis Property
Authors: Feeman Timothy G. 
Published: December 2010

AbstractA Banach space X is said to have the Dunford-Pettis Property if every weakly compact linear operator T: X —> Y, where Y is any Banach space, is completely continuous (that is, T maps weakly convergent sequences to strongly convergent ones). In this paper, we prove that if A is a nest algebra of operators on a separable, infinite dimensional Hilbert space, then A fails to have the Dunford-Pettis Property. We also investigate a certain algebra associated to A, analogous to a construction used by Bourgain and others in connection with the Dunford-Pettis Property for function algebras. We show that this algebra must lie between A and the quasi-triangular algebra A + K and we give examples to show that either extreme or something in between is possible. Finally, we consider the algebra of analytic Toeplitz operators and give a result for the corresponding associated algebra which is analogous to a result of Cima, Jansen, and Yale for H∞.
On Mennicke Groups of Deficiency Zero II
Authors: Albar Muhammad A. , Al-Shuaibi Abdul-Aziz A. 
Published: December 2010

AbstractLet M be the group defined by the presentation 〈 x, y, z | xy = xm, yz = yn, zx = zr〉,m,n,r ∊ Z. M is one of the few 3-generator finite groups of deficiency zero. These groups have been considered by Mennicke [3], Macdonald, Wamsley [10], Johnson and Robertson [7], and Albar. Properties like the order of M, the nilpotency and solvability were studied. In this paper we give a better upper bound for M than the one given by Johnson and Robertson [7]. We also describe the structure of some cases of M.
On Rings With Engel Cycles
Authors: Bell H. E. , Klein A. A. 
Published: December 2010

AbstractA ring R is called an EC-ring if for each x, y ∊ R, there exist distinct positive integers m, n such that the extended commutators [x, y]m and [x, y]n are equal. We show that in certain EC-rings, the commutator ideal is periodic; we establish commutativity of arbitrary EC-domains; we prove that a ring R is commutative if for each x, y ∊ R, there exists n > 1 for which [x, y] = [x, y]n.
On Sierpinski's Conjecture Concerning the Euler Totient
Authors: Subbarao M. V. , Yip L. W. 
Published: December 2010

AbstractIf Φk(n) denotes the Schemmel totient (so that Φ1 (n) becomes the Euler totient) we conjecture that for each k ≥ 1 and any given integer n > 1 there exist infinitely many m for which the equation Φk(x) = m has exactly n solutions. For the case k = 1, this gives Sierpinski's conjecture.We prove that on the basis of Schinzel's Hypothesis H, our conjecture holds for any k ≥ 3 of the form where p0 is an odd prime and α ∊ N. In 1961 Schinzel proved the case k = 1 assuming his Hypothesis H.
Pullback-Flat Acts are Strongly Flat
Authors: Bulman-Fleming Sydney 
Published: December 2010

AbstractLet 5 be a monoid. A right S-system A is called strongly flat if the functor A ⊗ — (from the category of left S-systems into the category of sets) preserves pullbacksand equalizers. (This concept arises in B. Stenström, Math. Nachr. 48(1971), 315-334 under the name weak flatness). The main result of the present paper is a proof that for A to be strongly flat it is in fact sufficient that A ⊗ — preserve only pullbacks. The approach taken is to develop an "interpolation" condition for pullback-preservation, and then to show its equivalence to Stenström's conditions for strong flatness.
Multipliers Between Sobolev Spaces
Authors: Fabec R. C. 
Published: December 2010

AbstractA sufficient condition for the boundedness of a multiplier from a Sobolev space of index t > 1 / 4 to one of opposite index — t is obtained. The condition relates the indices of the Sobolev spaces to which the multiplier belongs to the pairs of Sobolev spaces between which the multiplier is bounded. The result is applied to homogeneous multipliers and a description of these multipliers in this setting is presesented. Extensions to higher dimensions are indicated.
Similarité Entre Certains Quotients de A+et des Quotients D'Algèbres Uniformes
Authors: Koua Konin 
Published: December 2010

RésuméLetA(D) be the usual disc algebra, and letA+be the subalgebra ofA(D) consisting in thosef € A(D) which have an absolutely convergent series of Taylor coefficients. Setm1= {f€A(D) |f(1) = 0},m=m1∩A+, letGbe the functionandK = A+∩ I1.We show that the quotient algebrasm1/I1andm/Kare similar in the sense of J. Esterle.
Basic Double Series, Quadratic Transformations and Products of Basic Series
Authors: Nassrallah Bassam 
Published: December 2010

AbstractA basic double series is expressed in terms of two 5ϕ4 series which extends Bailey's transformation of an 8ϕ7 series into two 4ϕ3 's. From this formula we derive some quadratic transformations; one of them is a new q-analogue of a transformation due to Whipple. Product formulas as well as Gasper-Rahman's q-Clausen formula are also given as special cases.
Asymptotics for Semilinear Elliptic Systems
Authors: Noussair Ezzat S. , Swanson Charles A. 
Published: December 2010

AbstractA class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞. Additional results concern the existence and structure of positive solutions u with finite energy in a neighbourhood of infinity.
Note on the Space Bmoa
Authors: Choa Jun Soo 
Published: December 2010

AbstractLet D be the unit disc in the complex plane. It is shown that(i) for 0 < p < 2, there exists an analytic function f ∊	BMOA for which and(ii) for 2 < p < ∞, there exists an analytic function f ∉ BMOA for whichThis settles the question of Stroethoff [5] on BMOA.
A Relation Between S1 and S3-Invariant Homotopy In The Stable Range
Authors: Gilbert Shirley M. F. , Zvengrowski Peter 
Published: December 2010

AbstractFor any X and any q > 0, one has natural inclusions where the groups S1 and S3 act on S4q-1 in the standard way and are the G-invariant homotopy subsets, G = S1 or G = S3. It is proved here that for any space X of the homotopy type of a CW-complex and for π4q-1 (X) in the c3 cl stable range, the inclusion is m fact an equality when localized away from the prime 2.
Finite Lattices of Projections in Factors and Approximately Finite C*-Algebras
Authors: Power S. C. 
Published: December 2010

AbstractA unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.
Automorphisms and Derivations of Skew Polynomial Rings
Authors: Rosen Mary P. , Rosen Jerry D. 
Published: December 2010

AbstractFor a prime ring R and σ ∊ Aut(R), we determine the group of Rstabilizing automorphisms of the skew polynomial ring R[x; σ]. In the case where R is simple, we characterize the X-inner automorphisms of R[x; σ]. We also provide necessary and sufficient conditions for a σ -commuting derivation of a prime ring R to extend to a derivation of R[x; σ].
Module Homomorphisms of the Dual Modules of Convolution Banach Algebras
Authors: Ghahramani F. , Mcclure J. P. 
Published: December 2010

AbstractSuppose that A is either the group algebra L1 (G) of a locally compact group G, or the Volterra algebra or a weighted convolution algebra with a regulated weight. We characterize: a) Module homomorphisms of A*, when A* is regarded an A** left Banach module with the Arens product, b) all the weak*-weak* continuous left multipliers of A**.