bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Quadratic and Cubic Summation Formulas for Basic Hypergeometric Series
Authors: Rahman Mizan 
Published: December 2010

AbstractAn identity of L. Carlitz for a bibasic hypergeometric series is used to find some summation formulas for series in which the bases are either q and q2 or q and q3,0 < q < 1 In general, these series are neither balanced nor very-well-poised in the usual sense
Contributions to a General Theory of View-Obstruction Problems
Authors: Dumir V. C. , Hans-Gill R. J. , Wilker J. B. 
Published: December 2010

AbstractIn the original view-obstruction problem congruent closed, centrally symmetric convex bodies centred at the points of the set are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size and this value is known for balls in dimensions n = 2,3 and for symmetrically placed cubes in dimensions n = 2, 3, 4In order to explain fully the distinction between rational and irrational rays in the original problem, we extend consideration to the blocking of subspaces of all dimensions. In order to appreciate the special properties of balls and cubes, we give a discussion of the convex body with respect to reflection symmetry, lower dimensional sections, and duality. We introduce topological considerations to help understand when the critical parameter of the theory is an attained maximum and we add substantially to the list of known values of this parameter. In particular, when the dimension is n = 2 our dual body considerations furnish a complete solution to the view-obstruction problem
Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians
Authors: Ge Zhong 
Published: December 2010

AbstractWe study the asymptotic behavior of the Laplacian on functions when the underlying Riemannian metric is collapsed to a Carnot-Carathéodory metric. We obtain a uniform short time asymptotics for the trace of the heat kernel in the case when the limit Carnot-Carathéodory metric is almost Heisenberg, the limit of which is the result of Beal-Greiner-Stanton, and Stanton-Tartakoff.
Sur les Opérations Partielles Implicites et Leur Relation Avec la Surjectivité Des Épimorphismes
Authors: Hébert Michel 
Published: December 2010

AbstractLet K be a category of structures with all its homomorphisms, Uα K → Set the α-th power of its forgetful functor U An α-ary implicit partial operation (O.P.I.) in K is a diagram of natural transformations and functors. We first study various properties which O P I's can have, as maximality, definability and closure under products or equalizers. Revisiting various concepts and results of Isbell, Linton, Bacsich and Herrera, we note, among other things, that the dominion (resp. the stable dominion) of a subset of a structure K is its closure under O P I's (resp. under equalizer-closed O P I's), and we show that in a variety, all epis are surjective (resp. all monos are regular) iff all limit-closed (resp. product-closed) O P I's are restrictions of total implicit operations.
Second-Order Gâteaux Differentiable Bump Functions and Approximations in Banach Spaces
Authors: McLaughlin D. , Poliquin R. , Vanderwerff J. , Zizler V. 
Published: December 2010

AbstractIn this paper we study approximations of convex functions by twice Gâteaux differentiate convex functions. We prove that convex functions (respectively norms) can be approximated by twice Gâteaux differentiate convex functions (respectively norms) in separable Banach spaces which have the Radon-Nikody m property and admit twice Gâteaux differentiable bump functions. New characterizations of spaces isomorphic to Hilbert spaces are shown. Locally uniformly rotund norms that are limits of Ck-smooth norms are constructed in separable spaces which admit Ck-smooth norms.
Polynomials with a Prescribed Zero and the Bernstein's Inequality
Authors: Olivier P. F. , Watt A. O. 
Published: December 2010

AbstractLet be the class of all polynomials/? of degree at most n such that In view of the example zn it follows from Bernstein's inequality for polynomials that at each point z0 of the unitcirle. It was shown by A. Giroux and Q. I. Rahman [2] that if denotes the subclass of polynomials in which vanish at 1, thenwhere c1 and c2 are constants not depending on n. Here we find the exact value of which has some special significance and also at certain other points of the unit circle.
Group Actions on Flag Manifolds and Cobordism
Authors: Sankaran P. , Varadarajan K. 
Published: December 2010

AbstractIn this paper we show that any(respectively α є Ωm) can be represented by a closed smooth (respectively closed, oriented smooth) manifoldMmadmitting a smooth (Z/2)m(respectivelyS1)-action with a finite stationary set. We also completely determine the Grassman manifoldswhich are oriented boundaries as well as those which represent non-torsion elements in Ω*.
Jacobi Matrices and the Spectrum of the Neumann Operator on a Family of Riemann Surfaces
Authors: Edward Julian 
Published: December 2010

AbstractThe Neumann operator is an operator on the boundary of a smooth manifold which maps the boundary value of a harmonic function to its normal derivative. The spectrum of the Neumann operator is studied on the curves bounding a family of Riemann surfaces. The Neumann operator is shown to be isospectral to a direct sum of symmetric Jacobi matrices, each acting on l2(ℤ). The Jacobi matrices are shown to be isospectral to generators of bilateral, linear birth-death processes. Using the connection between Jacobi matrices and continued fractions, it is shown that the eigenvalues of the Neumann operator must solve a certain equation involving hypergeometric functions. Study of the equation yields uniform bounds on the eigenvalues and also the asymptotics of the eigenvalues as the curves degenerate into a wedge of circles.
Mod Odd Modular Coinvariants, Homology Operations, and Limit Spaces
Authors: Kechagias Nondas E. 
Published: December 2010

AbstractWe compute the homology of limn->∞(Gn ≀ X), where (Gn) is a system of subgroups of Σpn containing a p-Sylow subgroup (Σpn p) and satisfying certain properties. We show that H*(limn->∞(Gn, ≀ X);Z/pZ) is built naturally over homology operations related to (Gn). We describe this family of operations using modular coinvariants.
Analytic Taf Algebras
Authors: Peters J. R. , Poon Y. T. , Wagner B. H. 
Published: December 2010

AbstractA strongly maximal triangular AF algebra which is defined by a realvalued cocycle is said to be analytic. Formulas for generic cocycles are given separately for both the integer-valued case and the real-valued coboundary case, and also for certain nest algebras. In the case of an integer-valued cocycle, there is an associated partial homeomorphismof the maximal ideal space of the diagonal. If the partial homeomorphism extends to a homeomorphism, then the algebra embeds in a crossed product. This occurs for a large class of subalgebras of UHF algebras, but an example shows that this does not always occur. An example is given of a triangular AF algebra which is analytic via a coboundary but is not a nest algebra; also, it is shown that a nest algebra need not be analytic
A Specialised Continued Fraction
Authors: Van Der Poorten A. J. , Shallit J. 
Published: December 2010

AbstractWe display a number with a surprising continued fraction expansion and show that we may explain that expansion as a specialisation of the continued fraction expansion of a formal series: A series ΣchX-h has a continued fraction expansion with partial quotients polynomials in X of positive degree (other, perhaps than the 0-th partial quotient). Simple arguments, let alone examples, demonstrate that it is noteworthy if those partial quotients happen to have rational integer coefficients only. In that special case one may replace the variable X by an integer ≥ 2; that is: one may 'specialise' and thereby proceed to obtain the regular continued fraction expansion of values of the series. And that is significant because, generally, it is difficult to obtain the explicit continued fraction expansion of a number presented in different shape. Our example leads to a series with a specialisable continued fraction expansion and, a little surprisingly, our arguments suggest that the phenomenon of specialisability for series of the kind appearing here may be reserved to just the special subclass of series we happen to have stumbled upon.
Oscillation Criteria for Second Order Nonlinear Differential Equations Involving Integral Averages
Authors: Wong James S. W. 
Published: December 2010

AbstractConsider the second order nonlinear differential equationy" + a(t)f(y) = 0where a(t) ∈ C[0,∞),f(y) GC1 (-∞, ∞),ƒ'(y) ≥ 0 and yf(y) > 0 for y ≠ 0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function f(y) = |γ|γ sgny with γ > 1 and 0 < γ < 1 known as the Emden-Fowler case. The coefficient a(t) is allowed to be negative for arbitrarily large values of t. Oscillation criteria involving integral averages of a(t) due to Wintner, Hartman, and recently Butler, Erbe and Mingarelli for the linear equation are shown to remain valid for the general equation, subject to certain nonlinear conditions on f(y). In particular, these results are therefore valid for the Emden-Fowler equation.
Location of Zeros of Chromatic and Related Polynomials of Graphs
Authors: Brenti Francesco , Royle Gordon F. , Wagner David G. 
Published: December 2010

AbstractWe consider the location of zeros of four related classes of polynomials, one of which is the class of chromatic polynomials of graphs. All of these polynomials are generating functions of combinatorial interest. Extensive calculations indicate that these polynomials often have only real zeros, and we give a variety of theoretical results which begin to explain this phenomenon. In the course of the investigation we prove a number of interesting combinatorial identities and also give some new sufficient conditions for a polynomial to have only real zeros.
Norm Convergence in Ergodic Theory and the Behavior of Fourier Transforms
Authors: Rosenblatt Joseph 
Published: December 2010

AbstractThe Lp-norm convergence of weighted averages μnf is ergodic theory is equivalent to the pointwise convergence of the Fourier transforms . If h(γ) = , then the behavior of h determines when the Lp-norm limit of μnf is ∫f dm. The nature of such limit functions h is the focus of this article.
Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators
Authors: Xuebo Luo 
Published: December 2010

AbstractIn this paper the Corwin's conjecture is proved, which says that if d is a function analytic near ∞, then the hypoellipticity of the convolution operator Ad, defined by for every u ∊ S'(ℝn), implies that P(x)/ logx → ∞ as x → ∞, where P(x) is the distance from x ∊ ℝn to the set of complex zeros of d.
Equivalences D'Homotopie et Crochet de Whitehead
Authors: Didierjean G. , Legrand A. 
Published: December 2010

RésuméL'homotopie de l'espace des équivalences homotopie fibrées, est limite d'une suite spectrale dont on calcule ici la première différentielle. On montre, sous des hypothèses assez générales et dans le cas où le fibré admet une section, que cette différentielle est la somme des trois opérations suivantes:une opération produit tensoriel d'une opération cohomologique type carré de Steenrod avec une opération homotopique de Hopfune opération définie par le "Brace-product" du fibréune opération définie par les crochets de Whitehead de la fibreLa différentielle de la suite spectrale associée à l'homotopie de l'espace des équivalences d'homotopie d'un espace s'obtient en prenant la base réduite à un point. Ce calcul prolonge certains résultats de [KA 69], [CO-HA].
Geometry of Spaces of Vector-Valued Harmonic Functions
Authors: Dowling Patrick N. , Hu Zhibao , Smith Mark A. 
Published: December 2010

AbstractIt is shown that the space hp(D,X) has the Kadec-Klee property with respect to pointwise norm convergence in the Banach space X if and only if X has the Radon-Nikodym property and every point of the unit sphere of X is a denting point of the unit ball of X. In addition, it is shown that hp(D,X) is locally uniformly rotund if and only if X is locally uniformly rotund and has the Radon-Nikodym property.
Some Applications of Artamonov-Quillen-Suslin Theorems to Metabelian Inner Rank and Primitivity
Authors: Gupta C. K. , Gupta N. D. , Noskov G. A. 
Published: December 2010

AbstractFor any variety of groups, the relative inner rank of a given groupG is defined to be the maximal rank of the -free homomorphic images of G. In this paper we explore metabelian inner ranks of certain one-relator groups. Using the well-known Quillen-Suslin Theorem, in conjunction with an elegant result of Artamonov, we prove that if r is any "Δ-modular" element of the free metabelian group Mn of rank n > 2 then the metabelian inner rank of the quotient group Mn/(r) is at most [n/2]. As a corollary we deduce that the metabelian inner rank of the (orientable) surface group of genus k is precisely k. This extends the corresponding result of Zieschang about the absolute inner ranks of these surface groups. In continuation of some further applications of the Quillen-Suslin Theorem we give necessary and sufficient conditions for a system g = (g1,..., gk) of k elements of a free metabelian group Mn, k ≤ n, to be a part of a basis of Mn. This extends results of Bachmuth and Timoshenko who considered the cases k = n and k < n — 3 respectively.
Additive Automorphic Functions and Bloch Functions
Authors: Aulaskari Rauno , Lappan Peter 
Published: December 2010

AbstractA function f analytic in the unit disk D is said to be strongly uniformly continuous hyperbolically, or SUCH, on a set E ⊂ D if for each ∊ > 0 there exists a δ > 0 such that |f(z) — f(z')| < ∊ whenever z and z' are points in E and the hyperbolic distance between z and z' is less than δ. We show that f is a Bloch function in D if and only if |f| is SUCH in D. A function f is said to be additive automorphic in D relative to a Fuchsian group F if, for each γ ∊ Γ, there exists a constant Aγ such that f(γ(z)) =f(z) + Aγ. We show that if an analytic function f is additive automorphic in D relative to a Fuchsian group Γ, where Γ is either finitely generated or if the fundamental region F of Γ has the right kind of structure, and if |f| is SUCH in F, then f is a Bloch function. We show by example that some restrictions on Γ are needed.
Singularities and Higher Torsion in Symplectic Cobordism
Authors: Botvinnik Boris I. , Kochman Stanley O. 
Published: December 2010

AbstractIn this paper we construct higher two-torsion elements of all orders in the symplectic cobordism ring. We begin by constructing higher torsion elements in the symplectic cobordism ring with singularities using a geometric approach to the Adams- Novikov spectral sequence in terms of cobordism with singularities. Then we show how these elements determine particular elements of higher torsion in the symplectic cobordism ring.
Isometric Shift Operators on C(X)
Authors: Farid F. O. , Varadarajan K. 
Published: December 2010

AbstractRecently A. Gutek, D. Hart, J. Jamison and M. Rajagopalan have obtained many significiant results concerning shift operators on Banach spaces. Using a result of Holsztynski they classify isometric shift operators on C(X) for any compact Hausdorff space X into two (not necessarily disjoint) classes. If there exists an isometric shift operator T: C(X) → C(X) of type II, they show that X is necessarily separable. In case T is of type I, they exhibit a paticular infinite countable set of isolated points in X. Under the additional assumption that the linear functional Γ carrying f ∊ C(X) to Tf(p) ∊ is identically zero, they show that D is dense in X. They raise the question whether D will still be dense in X even when Γ ≠ 0. In this paper we give a negative answer to this question. In fact, given any integer l ≥ 1, we construct an example of an isometric shift operator T: C(X) —> C(X) of type I with X \ having exactly / elements, where is the closure of D in X.
Isometric Characterizations of ℓnp Spaces
Authors: Komorowski Ryszard 
Published: December 2010

AbstractThe paper establishes some characterizations of spaces in terms of p-summing or p-nuclear norms of the identity operator on the given space E.In particular, for an n-dimensional Banach space E and I ≤ p < 2, E is isometric to if and only if πp(E*) ≥ n1/p and E* has cotype p' with the constant one.Furthermore, spaces are characterized by inequalities for p-summing norms of operators related to the John's ellipsoid of maximal volume contained in the unit ball of E.
Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities
Authors: Lakey Joseph D. 
Published: December 2010

AbstractWiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates
Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
Authors: Young Wo-Sang 
Published: December 2010

AbstractLet S2jf be the 2j-th partial sum of the Vilenkin-Fourier series of f ∊ L1, and set S2-1f = 0. For , we show that the ratiois contained between two bounds (independent of f) . From this we obtain the Marcinkiewicz multiplier theorem for Vilenkin-Fourier series.
Products of Decomposable Positive
Operators
Authors: Quinn Terrance 
Published: December 2010

AbstractIn recent years there has been a growing interest in problems of factorization for bounded linear operators. We first show that many of these problems properly belong to the category of C*-algebras. With this interpretation, it becomes evident that the problem is fundamental both to the structure of operator algebras and the elements therein. In this paper we consider the direct integral algebra with separable and infinite dimensional. We generalize a theorem of Wu (1988) and characterize those decomposable operators which are products of non-negative decomposable operators. We do this by first showing that various results on operator ranges may be generalized to “measurable fields of operator ranges”.
Finite Clones Containing All Permutations
Authors: Haddad L. , Rosenberg I. G. 
Published: December 2010

AbstractLet A be a finite set with |A| > 2. We describe all clones on A containing the set SA of all permutations of A among its unary operations. (A clone on A is a composition closed set of finitary operations on A containing all projections). With a few exceptions such a clone C is either essentially unary or cellular i.e. there exists a monoid M of self-maps of A containing SA such that either C = (= all essentially unary operations agreeing with some f ∊ M) or C = ∪ Гh where 1 < h ≤ |A| and Гh consists of all finitary operations on A taking at most h values. The exceptions are subclones of Burle's clone or of its variant (provided |A| is even).
Weakly Projective and Weakly Injective Modules
Authors: Jain S. K. , López-Permouth S. R. , Oshiro K. , Saleh M. A. 
Published: December 2010

AbstractA module M is said to be weakly N-projective if it has a projective cover π: P(M) ↠M and for each homomorphism : P(M) → N there exists an epimorphism σ:P(M) ↠M such that (kerσ) = 0, equivalently there exists a homomorphism :M ↠N such that σ= . A module M is said to be weakly projective if it is weakly N-projective for all finitely generated modules N. Weakly N-injective and weakly injective modules are defined dually. In this paper we study rings over which every weakly injective right R-module is weakly projective. We also study those rings over which every weakly projective right module is weakly injective. Among other results, we show that for a ring R the following conditions are equivalent:(1) R is a left perfect and every weakly projective right R-module is weakly injective.(2) R is a direct sum of matrix rings over local QF-rings.(3) R is a QF-ring such that for any indecomposable projective right module eR and for any right ideal I, soc(eR/eI) = (eR/eJ)n for some positive integer n.(4) R is right artinian ring and every weakly injective right R-module is weakly
projective.(5) Every weakly projective right R-module is weakly injective and every weakly injective right R-module is weakly projective.
Unification in Varieties of Groups: Nilpotent Varieties
Authors: Albert Michael H. , Lawrence John 
Published: December 2010

Abstract
In this paper we show that any system of equations over a free nilpotent
group of class c is either unitary or miliary. In fact,
such a system either has a most general solution (akin to the most general
solution of a system of linear dipohantine equations), or every solution has a
proper generalization. In principle we provide an algorithm for determining
whether or not a most general solution exists, and exhibiting it if it
does.
Exponential Boundedness and Amenability of Open Subsemigroups of Locally
Compact Groups
Authors: Jaworski Wojciech 
Published: December 2010

Abstract
Let G be a connected amenable locally compact
group with left Haar measure λ. In an earlier work Jenkins claimed that
exponential boundedness of G is equivalent to each of
the following conditions: (a) every open subsemigroup S
⊆ G is amenable; (b) given and a compact
K ⊆ G with nonempty
interior there exists an integer n such that (c) given a signed
measure of compact support
and nonnegative nonzero f ∈ L
∞(G), the condition
v * f ≥ 0 implies
v(G) ≥ 0. However,
Jenkins‚ proof of this equivalence is not complete. We give a complete proof. The
crucial part of the argument relies on the following two results: (1) an open
σ-compact subsemigroup S ⊆ G
is amenable if and only if there exists an absolutely continuous probability
measure μ on S such that lim
for every
s ∈ S; (2) G is
exponentially bounded if and only if for every nonempty
open subset U ⊆ G.
A Lower Bound for the Real Genus of a Finite Group
Authors: May Coy L. 
Published: December 2010

Abstract
Let G be a finite group. The real
genus ρ(G) is the minimum algebraic
genus of any compact bordered Klein surface on which G
acts. Here we obtain a good general lower bound for the real genus of the group
G. We use the standard representation of
G as a quotient of a non-euclidean crystallographic
group by a bordered surface group. The lower bound is used to determine the real
genus of several infinite families of groups; the lower bound is attained for some
of these families. Among the groups considered are the dicyclic groups and some
abelian groups. We also obtain a formula for the real genus of the direct product
of an elementary abelian 2-group and an “even” dicyclic group. In addition, we
calculate the real genus of an abstract family of groups that includes some
interesting 3-groups. Finally, we determine the real genus of the direct product
of an elementary abelian 2-group and a dihedral group.
Zeros of Iterated Integrals of Polynomials
Authors: Borwein Peter B. , Chen Weiyu , Dilcher Karl 
Published: December 2010

AbstractThe operator Im is defined as m-fold indefinite integration with zero constants of integration. The zero distribution of Im(p) for polynomials p is studied in general, and for two special classes of polynomials in detail. The main results are: (i) The zeros of In(Pn), where Pn(𝑧) is the n-th Legendre polynomial, converge to a certain algebraic curve; (ii) the zeros of an integer) converge to pieces of a circle and of two "Szegö curves".