bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Remarks on Rotors in Link Theory
Authors: Jin Gyo Taek , Rolfsen Dale 
Published: December 2010

AbstractWe present examples showing that certain results on the invariance of link polynomials under generalized mutation are the best possible. They show, moreover, that this generalized mutation cannot be effected by a sequence of ordinary mutations. One of the examples also shows that the reduced Jones polynomial can be a more sensitive invariant than the Jones polynomial itself.
Independence for Sets of Topological Spheres
Authors: Pakula Lewis , Schwartzman Sol 
Published: December 2010

AbstractConsider a collection of topological spheres in Euclidean space whose intersections are essentially topological spheres. We find a bound for the number of components of the complement of their union and discuss conditions for the bound to be achieved. This is used to give a necessary condition for independence of these sets. A related conjecture of Griinbaum on compact convex sets is discussed.
A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings
Authors: Xu Hong-Kun 
Published: December 2010

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.
A Divisor Problem for Values of Polynomials
Authors: Mercier Armel , Nowak Werner Georg 
Published: December 2010

AbstractIn this article we investigate the average order of the arithmetical functionwhere p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.
Artin Rings with Two-Generated Ideals
Authors: Rush David E. 
Published: December 2010

AbstractIt is shown that each commutative Artin local ring having each of its ideals generated by two elements is the homomorphic image of a one-dimensional local complete intersection ring which also has each of its ideals generated by two elements. It is indicated how this can be applied to show that the property that each ideal is projective over its endomorphism ring does not pass to homomorphic images, and in determining the commutative group rings with the two-generator property.
Regularity of the Interfaces in the Stefan Problem with a Mushy Region
Authors: Yin Hong-Ming 
Published: December 2010

AbstractThis paper deals with the Stefan-type problem with a zone of coexistence of both phases. We formulate the problem in the enthalpy form and show that the interfaces between the liquid and the mushy, the mushy and the solid phase are smooth. Our approach is to study the structures of the level sets of the solution via Sard's Lemma and the implicit function theorem.
Words without Near-Repetitions
Authors: Currie J. , Bendor-Samuel A. 
Published: December 2010

AbstractWe find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.
Characterization of Eigenfunctions by Boundedness Conditions
Authors: Howard Ralph , Reese Margaret 
Published: December 2010

AbstractSuppose is a sequence of functions on ℝn with Δfk = fk+1 (where Δ is the Laplacian) that satisfies the growth condition: |fk(x)| ≤ Mk{1 + |x|)a where a ≥ 0 and the constants have sublinear growth Then Δf0 = —f0- This characterizes eigenfunctions f of Δ with polynomial growth in terms of the size of the powers Δkf, —∞ < k < ∞. It also generalizes results of Roe (where a = 0, Mk = M, and n = 1 ) and Strichartz (where a = 0, Mk = M for n). The analogue holds for formally self-adjoint constant coefficient linear partial differential operators on ℝn.
A Class of Mellin Multipliers
Authors: McBride A. C. , Spratt W. J. 
Published: December 2010

AbstractWe examine a class of functions which can serve as Mellin multipliers in the
setting of the spaces Fp,μ which we have used
extensively in other papers. The conditions to be satisfied by such a multiplier
h do not involve h′ explicitly.
This means that multipliers involving T-functions can be handled by means of the
asymptotics of Γ(z) alone, without the need to study
ψ = Γ′/Γ, thereby saving effort
in the case of complicated multipliers.
The Kernel of and the 4-Rank of K2(O)
Authors: Berger Ruth I. 
Published: December 2010

AbstractAn upper bound is given for the order of the kernel of the map on Sideal class groups that is induced by For some special types of number fields F the connection between the size of the above kernel for and the units and norms in are examined. Let K2(O) denote the Milnor K-group of the ring of integers of a number field. In some cases a formula by Conner, Hurrelbrink and Kolster is extended to show how closely the 4-rank of is related to the 4-rank of the S-ideal class group of
Constructing Isospectral But Non-Isometric Riemannian Manifolds
Authors: Chen Sheng 
Published: December 2010

AbstractIn this paper we examine the examples of isospectral but non-isometric Riemannian manifolds given by Milnor, Ikeda, and Vignéras. Of these, only Milnor's example is accounted for by Sunada's method of constructing isospectral manifolds, and even then only as an "unnatural" construction.
Congruence Normal Covers of Finitely Generated Lattice Varieties
Authors: Day Alan , Nation J. B. 
Published: December 2010

AbstractWe consider certain pseudovarieties K of lattices which are closed under the doubling of convex sets. For each such K, given an arbitrary finite lattice 𝓛, we describe the covers of the variety V(𝓛) of the form V(𝓛, K) with K a subdirectly irreducible lattice in K.
Second Order Operators with Non-Zero Eta Invariant
Authors: Fegan H. D. 
Published: December 2010

AbstractWe give an example of an elliptic second order pseudodifferential operator with a non-zero eta invariant. The operator is constructed on homogeneous bundles over compact Lie groups and is formed by composing differential operators and an operator of class In general it is not elliptic but in the special case of even dimensional bundles over SU(2) it is elliptic. The eta invariant is calculated in the special case and in the non elliptic case a difference eta invariant is obtained.
Class Number Divisibility in Real Quadratic Function Fields
Authors: Friesen Christian 
Published: December 2010

AbstractLet q be a positive power of an odd prime p, and let Fq(t) be the function field with coefficients in the finite field of q elements. Let denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic . The following theorem is proved: Let n ≧ 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, such that n divides the class number, . The proof constructs an element of order n in the ideal class group.
Finiteness Conditions for Near-Rings
Authors: Heatherly H. E. , Meldrum J. D. P. 
Published: December 2010

AbstractThere have been a number of papers which give necessary conditions for a ring to be finite, and a few, most notably H. E. Bell [1], which do the same for near-rings. We wish to make a contribution to this latter theme. Most of Bell's results concern distributive near-rings. Our main contribution is to extend a number of these results to weakly distributive near-rings.
Constructive Complete Distributivity III
Authors: Rosebrugh Robert , Wood R. J. 
Published: December 2010

AbstractA complete lattice L is constructively completely distributive,(CCD)(L), if the sup map defined on down closed subobjects has a left adjoint. We characterize preservation of this property by left exact functors between toposes using a "logical comparison transformation". The characterization is applied to (direct images of) geometric morphisms to show that local homeomorphisms (in particular, product functors) preserve (CCD) objects, while preserving (CCD) objects implies openness.
Approximate Identities in Banach Algebras of Compact Operators
Authors: Grønbæk Niels , Willis George A. 
Published: December 2010

AbstractLet X be a Banach space and let A be a uniformly closed algebra of compact operators on X, containing the finite rank operators. We set up a general framework to discuss the equivalence between Banach space approximation properties and the existence of right approximate identities in A. The appropriate properties require approximation in the dual X* by operators which are adjoints of operators on X. We show that the existence of a bounded right approximate identity implies that of a bounded left approximate identity. We give examples to show that these properties are not equivalent, however. Finally, we discuss the well known result that, if X* has a basis, then X has a shrinking basis. We make some attempts to generalize this to various bounded approximation properties.
On the p-Thin Problem for Hypersurfaces of Rn With Zero Gaussian Curvature
Authors: Guo Kanghui 
Published: December 2010

AbstractA subset M of Rn is said to be p-thin if T ∊ FLP(Rn) and supp(T) ⊂ M imply T = 0. For a class of smooth (n — 1 )-dimensional submanifolds of Rn, we obtain the optimal result for the p-thin problem, which is applied to give the complete solution to a uniqueness problem of wave equations.
Counterexamples to a Conjecture for Neutral Equations
Authors: Krisztin T. , Mathsen R. M. , Yuantong Xu 
Published: December 2010

AbstractA collection of examples of first order linear neutral differential delay equations having a nonoscillatory solution with lim sup = ∞ and lim inf = 0 at ∞ is given. This disproves a recent conjecture about the asymptotic behavior of solutions to such equations.
Oscillation and Global Attractivity in Stage-Structured Population Models
Authors: Cao Yulin , Freedman H. I. 
Published: December 2010

AbstractStage-structured models of population growth have been considered in the constant delay and state-dependent delay cases, when modeled by retarded functional differential equations. In the first case we settle a conjecture posed by Aiello and Freedman [1] by showing the existence of oscillatory solutions. In the second case, we show that under suitable criteria, all positive solutions tend to a global attractor.
Pairings of Homotopy Sets Over and Under B
Authors: Oda Nobuyuki 
Published: December 2010

AbstractWe define pairings and copairings in the category of topological spaces over and under B. We prove a relation between pairings of homotopy sets induced by a pairing and a copairing of topological spaces over and under B. We obtain some properties of the axes of pairings and the homotopy set of the axes of pairings in the category of topological spaces over and under B. We also prove the dual results.
Complemented c0-Subspaces of a Non-Separable C(K)-Space
Authors: Patterson Wanda M. 
Published: December 2010

AbstractThe non-separable Banach space of right continuous functions with left hand limits and the supremum norm is investigated to find the isomorphic types of complemented subspaces. It is shown that every isometric isomorph of c0 is complemented in this space which may be identified as a non-separable C(K) space. Sufficient conditions are given for other isomorphs of C0 to be complemented in the space and the complement of a C0 subspace is characterized isomorphically.
Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals
Authors: Yue Zhang Nan , Williams Kenneth S. 
Published: December 2010

AbstractThe Hurwitz zeta function ζ(s, a) is defined by the seriesfor 0 < a ≤ 1 and σ = Re(s) > 1, and can be continued analytically to the whole complex plane except for a simple pole at s = 1 with residue 1. The integral functions C(s, a) and S(s, a) are defined in terms of the Hurwitz zeta function as follows:Using integral representations of C(s, a) and S(s, a), we evaluate explicitly a class of improper integrals. For example if 0 < a < 1 we show that
Lp Behavior of the Eigenfunctions of the Invariant Laplacian
Authors: Kwon E. G. 
Published: December 2010

AbstractLet be the invariant Laplacian on the open unit ball B of Cn and let Xλ denote the set of those f € C2(B) such that counterparts of some known results on X0, i.e. on M-harmonic functions, are investigated here. We distinguish those complex numbers λ for which the real parts of functions in Xλ belongs to Xλ. We distinguish those λ for which the Maximum Modulus Priniple remains true. A kind of weighted Maximum Modulus Principle is presented. As an application, setting α ≥ ½ and λ = 4n2α(α — 1), we obtain a necessary and sufficient condition for a function f in Xλ to be represented asfor some F ∊ LP(∂B).
On the Lattice of Existence Varieties of Locally Inverse Semigroups
Authors: Auinger Karl 
Published: December 2010

AbstractThe mapping which assigns to each existence variety of locally inverse semigroups the class of all pseudosemilattices of idempotents of members of is shown to be a complete, surjective homomorphism from the lattice of existence varieties of locally inverse semigroups onto the lattice of varieties of pseudosemilattices.
A Lower Bound for the Class Number of a Real Quadratic Field of ERD-Type
Authors: Mollin R. A. , Zhang L.-C. , Kemp Paula 
Published: December 2010

AbstractIn this paper, we use the Lagrange neighbour and our equivalence theorem for primitive ideals to obtain lower bounds which are sharper than those given in the literature for class numbers of real quadratic fields in general, but applied to greatest advantage when d is of ERD type.
Derivations Whose Iterates are Zero or Invertible On a Left Ideal
Authors: Tilly Ben 
Published: December 2010

AbstractLet n ∊ ℤ+ and R be a ring which possesses a unit element, a left ideal J, and a derivation d such that dn(J) ≠ 0 and dn(r) is 0 or invertible, for all r ∊ J. We prove that either R is primitive, in which case R is Di with 1 ≤ i ≤ n+ 1, where Di is the ring of i × i matrices over a division ring D, or else there exist positive integers i, l and p with p prime and 2 ≤ ipl ≤ n + 1, such that R is where D is a division ring with characteristic p, and furthermore there is a derivation f of Di and a1, a2,..,al ∊ ZDi., the center of Di, such that a ∊ Di thenandfor all 2 ≤ j ≤ l
The Normal Closures of Certain Kummer Extensions
Authors: Waterhouse William C. 
Published: December 2010

AbstractLet F be a field containing a primitive p-th root of unity, let K / F be a cyclic extension with group 〈σ〉 of order pn, and choose a in K. This paper shows how the Galois group of the normal closure of K(a1/p) over F can be determined by computations within K. The key is to define a sequence by applying the operation x ↦ σ(x)/x repeatedly to a. The first appearance of a p-th power determines the degree of the extension and restricts the Galois group to one or two possibilities. A certain expression involving that p-th root and the terms in the sequence up to that point is a p-th root of unity, and the group is finally determined by testing whether that root is 1. When (σ(a)/a G Kp, the results reduce to a theorem of A. A. Albert on cyclic extensions.
The Average Edge Order of 3-Manifold Coloured Triangulations
Authors: Casali Maria Rita 
Published: December 2010

AbstractIf K is a triangulation of a closed 3-manifold M with E0(K) edges and F0(K) triangles, then the average edge order of K is defined to beIn [8], the relations between this quantity and the topology of M are investigated, especially in the case of μ0(K) being small (where the study relies on Oda's classification of triangulations of 𝕊2 up to eight vertices—see [9]). In the present paper, the attention is fixed upon the average edge order of coloured triangulations; surprisingly enough, the obtained results are perfectly analogous to Luo-Stong' ones, and may be proved with little effort by means of edge-coloured graphs representing manifolds.
Nonoscillation of Second Order Superlinear Differential Equations
Authors: Erbe L. H. , Xia H. X. , Wu J. H. 
Published: December 2010

AbstractSome sufficient conditions are given for all solutions of the nonlinear differential equation y″(x) +p(x)f(y) = 0 to be nonoscillatory, where p is positive andfor a quotient γ of odd positive integers, γ > 1.
Trace Classes and Quadratic Forms in the Modular Group
Authors: Fine Benjamin 
Published: December 2010

AbstractThe Modular Group M is PSL2(Z) the group of linear fractional transformations with integral entries and determinant one. M has been of great interest in many diverse fields of Mathematics, including Number Theory, Automorphic Function Theory and Group Theory. In this paper we give an effective algorithm to determine, for each integer d, a complete set of representatives for the trace classes in trace d. This algorithm depends on the combinatorial group theoretic structure of M. It has been subsequently extended by Sheingorn to the general Hecke groups. The number h(d) of trace classes in trace d is equal to the ideal class number of the field The algorithm mentioned above then provides a new straightforward computational procedure for determining h(d). Finally as an outgrowth of the algorithm we present a wide generalization of the Fermat Two-Square theorem. This last result can also be derived from classical work of Gauss.
The Macneille Completion of a Uniquely Complemented Lattice
Authors: Harding John 
Published: December 2010

AbstractProblem 36 of the third edition of Birkhoff's Lattice theory [2] asks whether the MacNeille completion of uniquely complemented lattice is necessarily uniquely complemented. We show that the MacNeille completion of a uniquely complemented lattice need not be complemented.
Linear Operators Preserving Similarity Classes and Related Results
Authors: Li Chi-Kwong , Pierce Stephen 
Published: December 2010

AbstractLet Mn be the algebra of n × n matrices over an algebraically closed field of characteristic zero. For A ∊ Mn, denote by the collection of all matrices in Mn that are similar to A. In this paper we characterize those invertible linear operators ϕ on Mn that satisfy , where for some given A1,..., Ak ∊ Mn and denotes the (Zariski) closure of S. Our theorem covers a result of Howard on linear operators mapping the set of matrices annihilated by a given polynomial into itself, and extends a result of Chan and Lim on linear operators commuting with the function f(x) = xk for a given positive integer k ≥ 2. The possibility of weakening the invertibility assumption in our theorem is considered, a partial answer to a conjecture of Howard is given, and some extensions of our result to arbitrary fields are discussed.
Matrix Operators on lp to lq
Authors: Borwein David , Gao Xiaopeng 
Published: December 2010

AbstractWorkable necessary and sufficient conditions for a non-negative matrix to be a bounded operator from lp to lq when 1 < q ≤ p < ∞ are discussed. Alternative proofs are given for some known results, thereby filling a gap in the proof of the case p = q of a result of Koskela's. The case 1 < q < p < ∞ of Koskela's result is refined, and a weakened form of the Vere-Jones conjecture concerning matrix operators on lp is shown to be false.
Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
Authors: Manne Per E. 
Published: December 2010

AbstractLet L1, L2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L1 ∩ L2 = {0}. We show that continuous functions on L1 ∪L2 allow Carleman approximation by entire functions if and only if L1 ∪L2 is polynomially convex. If the latter condition is satisfied, then a function f:L1 ∪L2 —> C such that f|LiCk(Li), i = 1,2, allows Carleman approximation of order k by entire functions if and only if f satisfies the Cauchy-Riemann equations up to order k at the origin.
Topological Transitivity on the Torus
Authors: Schwartzman Sol 
Published: December 2010

AbstractT. Ding has shown that a topologically transitive flow on the torus given by a real analytic vector field is orbitally equivalent to a Kronecker flow on the torus, modified so as to have a finite number of fixed points, provided the original flow had only a finite number of fixed points. In this paper it is shown that the assumption that there are only finitely many fixed points is unnecessary.
Gradient Estimates on Rd
Authors: Wang Feng-Yu 
Published: December 2010

AbstractThis paper uses both the maximum principle and coupling method to study gradient estimates of positive solutions to Lu = 0 on Rd, wherewith (aij) uniformly positive definite and aij,bi € C1(Rd). We obtain some upper bounds of |∇u|/u and ∥∇u∥∞/∥u∥∞, which imply a Harnack inequality and improve the corresponding results proved in Cranston [4]. Besides, two examples show that our estimates can be sharp.
Vanishing of Hochschild Cohomologies for Local Rings with Embedding Dimension Two
Authors: Hoshino Mitsuo 
Published: December 2010

AbstractLet S = k[[x,y]] be a formal power series ring in two variables x, y over a field k and I an (x, y)-primary ideal of S. We show that S/I is selfinjective if Hi(S/I, S/I ⊗k S/I) = 0 for i = 1 and 2.
The Characterisation of Modular Group Algebras Having Unit Groups of Nilpotency Class 3
Authors: Anwar Rao M. , Sandling Robert 
Published: December 2010

AbstractThe unit group of the modular group algebra of a finite p-group in characteristic p is nilpotent. The p-groups for which it is of nilpotency class 3 were determined in work of Coleman, Passman, Shalev and Mann when p ≥ 3. We resolve the p = 2 case here which completes the classification.
A Leopoldt-Type Result for Rings of Integers of Cyclotomic Extensions
Authors: Bley W. 
Published: December 2010

AbstractLet p be a prime number and let m, r denote positive integers with r ≥ 1 if p > 3 (resp. r ≥ 2 if p = 2) and m ≥ 1. We put and Γ = Gd1(N/M). Then the associated order of N/M is the unique maximal order M in the group ring MΓ and ON is a free, rank one module over M. A generator of ON over M is explicitly given.
A Jordan-Hölder Theorem for Finitary Groups
Authors: Wehrfritz B. A. F. 
Published: December 2010

AbstractLet V be any left vector space over any division ring D and let G be any group of finitary linear maps of V. Then the D — G bimodule V satisfies a Jordan- Hölder theorem. Specifically, there is a bijection between the G-nontrivial factors in two composition series of V such that corresponding factors are isomorphic as D — G bimodules. This cannot be extended to cover the G-trivial factors.
Two-Weighted Inequalities for Singular Integrals
Authors: Edmunds David E. , Kokilashvili Vakhtang M. 
Published: December 2010

AbstractWe consider operators T of the form Tf = {Tjfj}, where Tjfj(x) = (p. v) ∫Rn kj(x — y)fj(y) dy. Under appropriate conditions on the kj, two-weighted estimates for T are obtained, the weights being radial and suitably linked.
The Hausdorff Completion of the Space of Closed Subsets of a Module
Authors: Johnson E. W. , Johnson Johnny A. 
Published: December 2010

AbstractIn this paper, we show that the lattice of closed subsets of the completion, in the Jacobson radical topology, of a finitely generated module M is isomorphic to the completion, under the Hausdorff topology, of the lattice of closed subsets of M. This extends submodule-theoretic results for complete modules to modules satisfying Chevalley's Theorem. We show that the lattice of submodules of every finitely generated module over a semi-local ring R is complete in the Hausdorff topology if and only if R is complete in the Jacobson radical topology.