bluuebunny/crossref_metadata_2025 huggingface dataset:
Artin Rings with Two-Generated Ideals
Authors: Rush David E.
Published: December 2010

It 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

This 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

We 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

Suppose 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.
An Extremal Problem for Harmonic Functions in the Ball
Authors: Khavinson Dmitry
Published: December 2010

In this note we obtain a sharp estimate for a radial derivative of bounded harmonic functions in the ball.
A Class of Mellin Multipliers
Authors: McBride A. C. , Spratt W. J.
Published: December 2010

We 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

An 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

In 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

We 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

We 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

Let 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.
Sandwich Theorems for Semicontinuous Operators
Authors: Borwein J. M. , Théra M.
Published: December 2010

We provide vector analogues of the classical interpolation theorems for lower semicontinuous functions due to Dowker and to Hahn and Katetov-Tong.
Finiteness Conditions for Near-Rings
Authors: Heatherly H. E. , Meldrum J. D. P.
Published: December 2010

There 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

A 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

Let 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

A 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

A 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

Stage-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

We 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.
Regions Cut by Arrangements of Topological Spheres
Authors: Pakula Lewis
Published: December 2010

We define an arrangement of pseudohyperplanes as an image of a topological sphere arrangement with appropriate intersections, and prove that the complement components are then homologically trivial. We apply this to extend a formula of Winder and Zaslavsky.
Complemented c0-Subspaces of a Non-Separable C(K)-Space
Authors: Patterson Wanda M.
Published: December 2010

The 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

The Hurwitz zeta function ζ(s, a) is defined by the series

for 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

Let 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 as

for some F ∊ LP(∂B).
On the Lattice of Existence Varieties of Locally Inverse Semigroups
Authors: Auinger Karl
Published: December 2010

The 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.
Corrections à: Quelques Formules Exactes Pour des Moyennes de Fonctions L de Dirichlet
Authors: Louboutin Stéphane
Published: December 2010

Cette note corrige un erreur commise dans [Lou, Théorème 4].
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

In 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

Let 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 then

and

for all 2 ≤ j ≤ l
The Normal Closures of Certain Kummer Extensions
Authors: Waterhouse William C.
Published: December 2010

Let 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

If 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 be

In [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

Some 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 and

for a quotient γ of odd positive integers, γ > 1.
Trace Classes and Quadratic Forms in the Modular Group
Authors: Fine Benjamin
Published: December 2010

The 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

Problem 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.
Normal-Preserving Linear Mappings
Authors: Brešar Matej , Šemrl Peter
Published: December 2010

Let H be a Hilbert space, dim H ≥ 3, and B(H) the algebra of all bounded linear operators on H. We characterize bijective linear mappings on B(H) that preserve normal operators.
Linear Operators Preserving Similarity Classes and Related Results
Authors: Li Chi-Kwong , Pierce Stephen
Published: December 2010

Let 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

Workable 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.
On Modules Having Small Cofinite Irreducibles
Authors: Johnson E. W. , Johnson Johnny A. , Taylor Monty B.
Published: December 2010

In this paper we obtain several new characterizations of modules having small cofinite irreducibles. One of these characterizations involves a metric topology defined on the submodule lattice.
Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
Authors: Manne Per E.
Published: December 2010

Let 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

T. 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

This paper uses both the maximum principle and coupling method to study gradient estimates of positive solutions to Lu = 0 on Rd, where

with (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.
The Group of Eigenvalues of a Rank One Transformation
Authors: Choksi J. R. , Nadkarni G.
Published: December 2010

In this paper, several characterizations are given of the group of eigenvalues of a rank one transformation. One of these is intimately related to the corresponding expression for the maximal spectral type of a rank one transformation given in an earlier paper.
Vanishing of Hochschild Cohomologies for Local Rings with Embedding Dimension Two
Authors: Hoshino Mitsuo
Published: December 2010

Let 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

The 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

Let 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

Let 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

We 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

In 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.
Homomorphisms of Lie Algebras of Algebraic Groups and Analytic Groups
Authors: Nahlus Nazih
Published: December 2010

Let be a Lie algebra homomorphism from the Lie algebra of G to the Lie algebra of H in the following cases: (i) G and H are irreducible algebraic groups over an algebraically closed field of characteristic 0, or (ii) G and H are linear complex analytic groups. In this paper, we present some equivalent conditions for ϕ to be a differential in the above two cases. That is, ϕ is the differential of a morphism of algebraic groups or analytic groups as appropriate.

In the algebraic case, for example, it is shown that ϕ is a differential if and only if ϕ preserves nilpotency, semisimplicity, and integrality of elements. In the analytic case, ϕ is a differential if and only if ϕ maps every integral semisimple element of into an integral semisimple element of , where G0 and H0 are the universal algebraic subgroups of G and H. Via rational elements, we also present some equivalent conditions for ϕ to be a differential up to coverings of G in the algebraic case, and for ϕ to be a differential up to finite coverings of G in the analytic case.
Weak Normalization of Power Series Rings
Authors: Dobbs David E. , Roitman Moshe
Published: December 2010

It is proved that if r* is the weak normalization of an integral domain r, then the weak normalization of the power series ring r[[x1,....xn]] is contained in R*[[X1,....Xn]]. Consequently, if R is a weakly normal integral domain, then R[[X1,....Xn]] is also weakly normal.
A Note on Derivations of Group Rings
Authors: Ferrero Miguel , Giambruno Antonio , Milies César Polcino
Published: December 2010

LetRGdenote the group ring of a groupGover a semiprime ringR. We prove that, if the center ofGis of finite index and some natural restrictions hold, then everyR-derivation ofRGis inner. We also give an example of a groupGwhich is both locally finite and nilpotent and such that, for every fieldF, there exists anF-derivation ofFGwhich is not inner.
Comparaison de Deux Mesures de Polynômes
Authors: Flammang V.
Published: December 2010

L'objet de cet article est d'une part la comparaison de la mesure de Mahler et de la longueur d'un polynôme à coefficients entiers dont toutes les racines sont réelles positives. Nous comparons ensuite la mesure de Mahler d'un polynôme à coefïîcients entiers ayant toutes ses racines réelles à une mesure généralisant la longueur.
The Genus of the Coxeter Graph
Authors: Mitchell Jane M. O.
Published: December 2010

In [1], Biggs stated that the Coxeter graph can be embedded in an orientable surface of genus 3. The purpose of this note is to point out that Biggs' embedding is in fact into a non-orientable surface. Further, it is shown that the orientable genus is 3 and the non-orientable genus is 6.
Definitizable Operators on a Krein Space
Authors: Zizler Petr
Published: December 2010

Let A be a bounded linear operator on a Hilbert space H. Assume that A is selfadjoint in the indefinite inner product defined by a selfadjoint, bounded, invertible linear operator G on H; [x,y] := (Gx,y). In the first part of the paper we define two orders of neutrality for the pair (G, A) and a connection is made with the "types" of numbers in the point and approximate point spectrum of A. The main results of the paper are in the second part and they deal with strong and uniform definitizability of a bounded selfadjoint operator on a Pontrjagin space. They state:

A) Let A be a bounded strongly definitizable operator on a Pontrjagin space ΠK, then A is uniformly definitizable.

B) A bounded selfadjoint operator A on a Pontrjagin space ΠK is uniformly definitizable if and only if all the eigenvalues of A are of definite type and all the nonisolated eigenvalues of A are of positive type.

Some applications to the theory of linear selfadjoint operator pencils are given.
On the Unicity Conjecture for Markoff Numbers
Authors: Baragar Arthur
Published: December 2010

In 1913 Frobenius conjectured that for any positive integer m, there exists at most one pair of integers (x, y) with 0 ≤ x ≤ y ≤ m such that (x, y, m) is a solution to the Markoff equation: x2 + y2 + m2 = 3xym. We show this is true if either m, 3m — 2 or 3m + 2 is prime, twice a prime or four times a prime.
A Continuity-Like Property of Derivatives
Authors: Bullen P. S. , Sarkhel D. N.
Published: December 2010

In this paper a refinement of property Z of Zahorski-Weil is defined and shown to be, like the weaker property Z, satisfied by all common derivatives.
Division Graded Algebras in the Brauer-Wall Group
Authors: Coghlan Francis , Hoffman Peter
Published: December 2010

We show that every element in the Brauer-Wall group of a field with characteristic different from 2 is represented uniquely by a division graded algebra, (i.e. homogeneous elements are invertible) but, of course, not necessarily by a graded (division algebra). This is a fairly direct consequence of Wall's structure theory for central simple Z/2-graded algebras.
Surjective Linear Maps Between Root Systems with Zero
Authors: Đoković D. Ž. , Thãńg Nguyêñ Q.
Published: December 2010

If R1 and R2 are root systems and there is a linear map which maps R1 ∪{0} onto R2∪{0} we write R1 —> R2. We determine all pairs (R1, R2) of irreducible root systems such that R1 —> R2.
The Doob-Meyer Decomposition Revisited
Authors: Bass Richard F.
Published: December 2010

A new proof is given of the Doob-Meyer decomposition of a supermartingale into martingale and decreasing parts. Although not the most concise proof, the proof is elementary in the sense that nothing more sophisticated than Doob's inequality is used. If the supermartingale is bounded and the jump times are totally inaccessible, then it is shown that discrete time approximations converge to the decreasing part in L2. The general case is handled by reduction to the above special case.
Central *-Differential Identities in Prime Rings
Authors: Lee P. H. , Wong T. L.
Published: December 2010

Let R be a prime ring with involution and d, δ be derivations on R. Suppose that xd(x)—δ(x)x is central for all symmetric x or for all skew x. Then d = δ = 0 unless R is a commutative integral domain or an order of a 4-dimensional central simple algebra.
Further on the Points of Inflection of Bessel Functions
Authors: Lorch Lee , Szego Peter
Published: December 2010

We offer here a substantial simplification and shortening of a proof of the monotonicity of the abscissae of the points of inflection of Bessel functions of the first kind and positive order.
Slice Maps and Multipliers of Invariant Subspaces
Authors: Nakazi Takahiko
Published: December 2010

Let be the closed bidisc and T2 be its distinguished boundary. For be a slice map, that is, and Then ker Φαβ is an invariant subspace, and it is not difficult to describe ker Φαβ and In this paper, we study the set of all multipliers for an invariant subspace M such that the common zero set of M contains that of ker Φαβ.
Bourgain Algebras of Spaces of n-Harmonic Functions in the Unit Polydisk
Authors: Izuchi Keiji , Kasuga Kazuhiro , Matsugu Yasuo
Published: December 2010

Let h∞(Dn) denote the space of all bounded n-harmonic functions on the unit polydisk Dn of Cn. In this paper we prove that the Bourgain algebra h∞(Dn)b and h∞(Dn)bb relative to the Lebesgue space L∞(Dn) are of the following forms:

Here V(Dn) is the space of those functions such that , where denotes the characteristic function of a subset E of Dn.
Conjugacy Separability of Certain Polygonal Products
Authors: Kim Goansu
Published: December 2010

We show that polygonal products of polycyclic-by-finite groups amalgamating central cyclic subgroups, with trivial intersections, are conjugacy separable. Thus polygonal products of finitely generated abelian groups amalgamating cyclic subgroups, with trivial intersections, are conjugacy separable. As a corollary of this, we obtain that the group A1 *〈a1〉A2 *〈a2〉 • • • *〈am-1〉Am is conjugacy separable for the abelian groups Ai.
The Abbena-Thurston Manifold as a Critical Point
Authors: Park Joon-Sik , Oh Won Tae
Published: December 2010

The Abbena-Thurston manifold (M,g) is a critical point of the functional where Q is the Ricci operator and R is the scalar curvature, and then the index of I(g) and also the index of — I(g) are positive at (M,g).
Derivations of Higher Order in Prime Rings
Authors: Ye Youpei , Luh Jiang
Published: December 2010

Let R be a prime ring of characteristic not 2 and d a derivation of R. It is shown that if d2n is a derivation of R, where n is a positive integer, then d2n-1 = 0.
The Failure of Approximate Inner Conjugacy for Standard Diagonals in Regular Limit Algebras
Authors: Donsig Allan P. , Power S. C.
Published: December 2010

AF C*-algebras contain natural AF masas which, here, we call standard diagonals. Standard diagonals are unique, in the sense that two standard diagonals in an AF C*-algebra are conjugate by an approximately inner automorphism. We show that this uniqueness fails for non-selfadjoint AF operator algebras. Precisely, we construct two standard diagonals in a particular non-selfadjoint AF operator algebra which are not conjugate by an approximately inner automorphism of the non-selfadjoint algebra.
A Generalization of an Inequality of Bhattacharya and Leonetti
Authors: Hurri-Syrjänen Ritva
Published: December 2010

We show that bounded John domains and bounded starshaped domains with respect to a point satisfy the following inequality

where F: [0, ∞) → [0, ∞) is a continuous, convex function with F(0) = 0, and u is a function from an appropriate Sobolev class. Constants b and K do depend at most on D. If F(x) = xp, 1 ≤ p < ∞, this inequality reduces to the ordinary Poincaré inequality.
The Wallace Problem: A Counterexample from MaCountableandp-Compactness
Authors: Tomita Artur H.
Published: December 2010

We construct, under MAcountable, a countably compact topological subsemigroup ofwhich is not a group, hence a counterexample for the Wallace problem. We also show that there is nop-compact counterexample for the Wallace problem, answering a question of D. Grant. Finally, we show that—in some sense—our counterexample for the Wallace problem constructed under MAcountablecannot be done in ZFC.
The Multidirectional Mean Value Theorem in Banach Spaces
Authors: Radulescu M. L. , Clarke F. H.
Published: December 2010

Recently, F. H. Clarke and Y. Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certain Banach spaces, namely those that admit a C1-Lipschitz continuous bump function.
The Transfer of a Commutator Law from a Nil-Ring to its Adjoint Group
Authors: Riley David M. , Tasić Vladimir
Published: December 2010

For every field F of characteristic p ≥ 0, we construct an example of a finite dimensional nilpotent F-algebra R whose adjoint group A(R) is not centreby- metabelian, in spite of the fact that R is Lie centre-by-metabelian and satisfies the identities x2p = 0 when p > 2 and x8 > 0 when p = 2. The existence of such algebras answers a question raised by A. E. Zalesskii, and is in contrast to positive results obtained by Krasilnikov, Sharma and Srivastava for Lie metabelian rings and by Smirnov for the class Lie centre-by-metabelian nil-algebras of exponent 4 over a field of characteristic 2 of cardinality at least 4.
Un lemme de Schwarz pour les boules-unités ouvertes
Authors: Vigué Jean-Pierre
Published: December 2010

Let B1 and B2 be the open unit balls of ℂn1 and ℂn2 for the norms ‖. ‖1 and ‖ . ‖2. Let f: B1 → B2 be a holomorphic mapping such that f(0) = 0. It is well known that, for every z ∈ B1, ‖f(z)‖2 ≤ ‖z‖1, and ‖f′(0)‖ ≤ 1.

In this paper, I prove the converse of this result. Let f : B1 → B2 be a holomorphic mapping such that f'(0) is an isometry. If B2 is strictly convex, I prove that f(0)=0 and that f is linear. I also define the rank of a point x belonging to the boundary of B1 or B2. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that f(0)=0 and that f'(0) is an isometry is linear.
The Class A∞+(g) and the One-Sided Reverse Hölder Inequality
Authors: Cruz-Uribe David
Published: December 2010

We give a direct proof that wis an A∞+(g) weight if and only if w satisfies a one-sided, weighted reverse Hölder inequality.
The J0-Radical of a Matrix Nearring can be Intermediate
Authors: Meldrum J. D. P. , Meyer J. H.
Published: December 2010

An example is constructed to show that the J0-radical of a matrix nearring can be an intermediate ideal. This solves a conjecture put forward in [1].
Polynomials of Quadratic Type Producing Strings of Primes
Authors: Mollin R. A. , Goddard B. , Coupland S.
Published: December 2010

The primary purpose of this paper is to provide necessary and sufficient conditions for certain quadratic polynomials of negative discriminant (which we call Euler-Rabinowitsch type), to produce consecutive prime values for an initial range of input values less than a Minkowski bound. This not only generalizes the classical work of Frobenius, the later developments by Hendy, and the generalizations by others, but also concludes the line of reasoning by providing a complete list of all such primeproducing polynomials, under the assumption of the generalized Riemann hypothesis (GRH).We demonstrate how this prime-production phenomenon is related to the exponent of the class group of the underlying complex quadratic field. Numerous examples, and a remaining conjecture, are also given.
On Semiregular Rings whose Finitely Generated Modules Embed in Free Modules
Authors: Rada Juan , Saorin Manuel
Published: December 2010

We consider rings as in the title and find the precise obstacle for them not to be Quasi-Frobenius, thus shedding new light on an old open question in Ring Theory. We also find several partial affirmative answers for that question.
Non-Real Periodic Points of Entire Functions
Authors: Bergweiler Walter
Published: December 2010

It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.
The Stable and Unstable Types of Classifying Spaces
Authors: Lee Hyang-Sook
Published: December 2010

The main purpose of this paper is to study groupsG1,G2such thatH*(BG1,Z/p)is isomorphic toH*(BG2,Z/p)in U, the category of unstable modules over the Steenrod algebra A, but not isomorphic as graded algebras overZ/p.
Which 3-Manifolds Embed in Triod × I × I?
Authors: Rolfsen Dale , Zhongmou Li
Published: December 2010

We classify the compact 3-manifolds whose boundary is a union of 2-spheres, and which embed in T ×I ×I, where T is a triod and I the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any 3-manifold in T × I × I embeds in a punctured handlebody.
Elliptic Units and Class Fields of Global Function Fields
Authors: Bae Sunghan , Kang Pyung-Lyun
Published: December 2010

Elliptic units of global function fields were first studied by D. Hayes in the case that deg ∞ is assumed to be 1, and he obtained some class number formulas using elliptic units. We generalize Hayes’ results to the case that deg ∞ is arbitrary.
On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence
Authors: Carpenter Jenna P.
Published: December 2010

This paper studies how the local root numbers and the Weil additive characters of the Witt ring of a number field behave under reciprocity equivalence. Given a reciprocity equivalence between two fields, at each place we define a local square class which vanishes if and only if the local root numbers are preserved. Thus this local square class serves as a local obstruction to the preservation of local root numbers. We establish a set of necessary and sufficient conditions for a selection of local square classes (one at each place) to represent a global square class. Then, given a reciprocity equivalence that has a finite wild set, we use these conditions to show that the local square classes combine to give a global square class which serves as a global obstruction to the preservation of all root numbers. Lastly, we use these results to study the behavior of Weil characters under reciprocity equivalence.
Matrix Transformations Based on Dirichlet Convolution
Authors: Selvaraj Chikkanna , Selvaraj Suguna
Published: December 2010

This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as ℓ − ℓ and G − G mappings. The strength of the Af-matrix is also discussed.
Root Closure in Integral Domains, III
Authors: Anderson David F. , Dobbs David E.
Published: December 2010

If A is a subring of a commutative ring B and if n is a positive integer, a number of sufficient conditions are given for “A[[X]] is n-root closed in B[[X]]” to be equivalent to “A is n-root closed in B.” In addition, it is shown that if S is a multiplicative submonoid of the positive integers ℙ which is generated by primes, then there exists a one-dimensional quasilocal integral domain A (resp., a von Neumann regular ring A) such that S = {n ∊ ℙ | A is n-root closed} (resp., S = {n ∊ ℙ | A[[X]] is n-root closed}).
Simple Conditions for Matrices to be Bounded Operators on lp
Authors: Borwein David
Published: December 2010

The two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on lp. The theorems are applied to Nörlund and weighted mean matrices.
A New Cohomological Criterion for the p-Nilpotence of Groups
Authors: Brunetti Maurizio
Published: December 2010

Let G be a finite group, H a copy of its p-Sylow subgroup, and K(n)*(−) the n-th Morava K-theory at p. In this paper we prove that the existence of an isomorphism between K(n)*(BG) and K(n)*(BH) is a sufficient condition for G to be p-nilpotent.
On the Clarke Subdifferential of an Integral Functional on Lp, 1 ≤ p < ∞
Authors: Giner E.
Published: December 2010

Given an integral functional defined on Lp, 1 ≤ p < ∞, under a growth condition we give an upper bound of the Clarke directional derivative and we obtain a nice inclusion between the Clarke subdifferential of the integral functional and the set of selections of the subdifferential of the integrand.
Stability of Weighted Darma Filters
Authors: Harrison K. J. , Ward J. A. , Eaton L-J.
Published: December 2010

We study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.
Smooth Partitions of Unity on Banach Spaces
Authors: Fry R.
Published: December 2010

It is shown that if a Banach space X admits a Ck-smooth bump function, and X* is Asplund, then X admits Ck-smooth partitions of unity.
On a Problem of Rubel Concerning the Set of Functions Satisfying All the Algebraic Differential Equations Satisfied by a Given Function
Authors: Shackell John
Published: December 2010

For two functions ƒ and g, define g ≪ ƒ to mean that g satisfies every algebraic differential equation over the constants satisfied by ƒ . The order ≪ was introduced in one of a set of problems on algebraic differential equations given by the late Lee Rubel. Here we characterise the set of g such that g ≪ ƒ, when ƒ is a given Liouvillian function.
On Certain K-Groups Associated with Minimal Flows
Authors: Xia Jingbo
Published: December 2010

It is known that the Toeplitz algebra associated with any flow which is both minimal and uniquely ergodic always has a trivial K1-group. We show in this note that if the unique ergodicity is dropped, then such K1-group can be non-trivial. Therefore, in the general setting of minimal flows, even the K-theoretical index is not sufficient for the classification of Toeplitz operators which are invertible modulo the commutator ideal.
Note on the Support of Sobolev Functions
Authors: Bagby Thomas , Gauthier P. M.
Published: December 2010

We prove a topological restriction on the support of Sobolev functions.
A Simple Ring over which Proper Cyclics are Continuous is a PCI-Ring
Authors: Barthwal S. , Jhingan S. , Kanwar P.
Published: December 2010

It is shown that simple rings over which proper cyclic right modules are continuous coincide with simple right PCI-rings, introduced by Faith.
Oscillatory Integrals with Nonhomogeneous Phase Functions Related to Schrödinger Equations
Authors: Kolasa Lawrence A.
Published: December 2010

In this paper we consider solutions to the free Schrödinger equation in n + 1 dimensions. When we restrict the last variable to be a smooth function of the first n variables we find that the solution, so restricted, is locally in L2, when the initial data is in an appropriate Sobolev space.
Embedding the Hopf Automorphism Group into the Brauer Group
Authors: Van Oystaeyen Fred , Zhang Yinhuo
Published: December 2010

Let H be a faithfully projective Hopf algebra over a commutative ring k. In [8, 9] we defined the Brauer group BQ(k, H) of H and an homomorphism π from Hopf automorphism group AutHopf(H) to BQ(k,H). In this paper, we show that the morphism π can be embedded into an exact sequence.
The Fixed Point Property in c0
Authors: Llorens-Fuster Enrique , Sims Brailey
Published: December 2010

A closed convex subset of c0 has the fixed point property (fpp) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of c0 are known to have the fpp. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the fpp.
The Moments of the Sum-Of-Digits Function in Number Fields
Authors: Gittenberger Bernhard , Thuswaldner Jörg M.
Published: December 2010

We consider the asymptotic behavior of the moments of the sum-of-digits function of canonical number systems in number fields. Using Delange’s method we obtain the main term and smaller order terms which contain periodic fluctuations.
Fermat Jacobians of Prime Degree over Finite Fields
Authors: González Josep
Published: December 2010

We study the splitting of Fermat Jacobians of prime degree l over an algebraic closure of a finite field of characteristic p not equal to l. We prove that their decomposition is determined by the residue degree of p in the cyclotomic field of the l-th roots of unity. We provide a numerical criterion that allows to compute the absolutely simple subvarieties and their multiplicity in the Fermat Jacobian.
Points of Weak*-Norm Continuity in the Unit Ball of the Space WC(K; X)*
Authors: Rao T. S. S. R. K.
Published: December 2010

For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak*-norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property.
Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology
Authors: Baker Andrew
Published: December 2010

Hecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions
Authors: Bonet José , Dománski Paweł , Lindström Mikael
Published: December 2010

Every weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.