bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Deterministic and Asymptotic σ-Algebras of a Markov Operator
Authors: Krengel Ulrich , Lin Michael
Published: December 2010

Let P be a Markov operator on L∞(X, Σ, m) which does
not disappear (i.e., P1A ≡ 0 => 1A ≡ 0 ) . We study the relationship
between the σ-algebras

(the deterministicσ-algebra), and the asymptoticσ-algebra

When m is a σ-finite invariant measure, measurable iff p*npnf = f, and also iff Pnf has the same distribution as f . The case of a convolution operator on a locally compact group is considered.
A Note on the Rn,k Property for L1 (μ E)
Authors: Rao T. S. S. R. K.
Published: December 2010

In this paper we show that for a Banach space X having the Rn,k property and such that X is constrained in a dual space having the Radon-Nikodým property, the space of X-valued Bochner integrable functions has the Rn,k property.
Isomorphic Group Rings Over Domains
Authors: Adjaero Isabelle , Spiegel Eugene
Published: December 2010

Let R and S be rings, G and H abelian groups, and RG and SH the goup rings of G and H over R and S respectively. In this note we consider what relations must hold between G and H or between R and S if the group rings RG and SH are isomorphic. For example, it is shown that if R and S are integral domains of characteristic zero, G and H torsion abelian groups such that if G has an element of order p then p is not invertible in R, and RG and SH are isomorphic, then the rings R and 5 are isomorphic and the groups G and H are isomorphic.
Fixed Point Theorems for Lipspchitzian Semigroups
Authors: ishihara Hajime
Published: December 2010

Let U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups
On the Distribution of the Sequence {nd*(n)}
Authors: Abbott H. L. , Subbarao M. V.
Published: December 2010

Let d*(n) denote the number of unitary divisors of the positive integer n. For x > 1, let B(x) denote the number of integers n for which nd*(n) ≦ x. Balasubramanian and Ramachandra proved that there exists a positive constant β such that . In this note we give an explicit expression for β as an infinite product, namely where the product is over all primes p.
The Conjugate Function on the Finite Dimensional Torus
Authors: Asmar Nakhle
Published: December 2010

We consider the group Ta, its group of characters Za, and an arbitrary order P on Za. For x ∊ Za, let sgnpx be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp(Ta), 1 < p < ∞, it is known that there is a function in Lp(Ta) such that for all X in Za. Summability methods for are also available. In this paper, we obtain summability methods for that apply for in L1(Ta), and we show how various properties of can be derived from our construction.
A Parametric Gauss-Green Theorem in Several Variables
Authors: Ortel M. , Schneider W.
Published: December 2010

We present a short, computational proof of the parametric Gauss-Green theorem for a broad class of closed chains. The proof involves only measure theory and the basic theory of differential forms: in particular, no constructions from topology are used. For completeness, the standard properties of winding numbers are also established by methods from analysis.
On Weighted Geometric Means
Authors: Alzer Horst
Published: December 2010

The aim of this paper is two-fold: First we prove the Radotype inequality Here denote the weighted geometric means of

with where the pi are positive weights. Thereafter we investigate under which conditions the sequence

is convergent as n → ∞
Properties of the Product of Two Derivations of a C*-Algebra
Authors: Mathieu Martin
Published: December 2010

Let δ1,δ2 be two derivations of a C*-algebra. We characterize when δ1δ2 is a derivation, a compact, or a weakly compact operator
A Note on Hardy-Orlicz Spaces
Authors: Jianzhong Zhang
Published: December 2010

W. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).
Unruly Hilbert Domains
Authors: Mott J. L. , Zafrullah M.
Published: December 2010

We give a simple construction of non-Noetherian Hilbert domains whose maximal ideals are all finitely generated. Such domains we call unruly Hilbert domains.
Half-Silvered Mirrors and Wythoff's Game
Authors: Porta Horacio , Stolarsky Kenneth B.
Published: December 2010

We propose the following problem. Given an array of vertical mirrors that simultaneously transmit and reflect, and a single incoming ray of light, describe the configuration of all light rays that are generated. We solve the problem here for a certain infinite configuration of mirrors; the solution involves the winning positions (a(n), b(n)) of Wythoff's game.
Coefficient Bounds in the Lorentz Representation of a Polynomial
Authors: Lubinsky D. S. , Ziegler Z.
Published: December 2010

Each polynomial P(x) has a "Lorentz representation", of the form This representation becomes unique if we insist that n equals the degree of P. Motivated partly by questions involving polynomials with integer coefficients, we investigate the relationship between
Determining Units in Some Integral Group Rings
Authors: Goodaire E. G. , Jespers E. , Parmenter M. M.
Published: December 2010

In this brief note, we will show how in principle to find all units in the integral group ring ZG, whenever G is a finite group such that and Z(G) each have exponent 2, 3, 4 or 6. Special cases include the dihedral group of order 8, whose units were previously computed by Polcino Milies [5], and the group discussed by Ritter and Sehgal [6]. Other examples of noncommutative integral group rings whose units have been computed include , but in general very little progress has been made in this direction. For basic information on units in group rings, the reader is referred to Sehgal [7].
A (Modest) Generalization of the Theorems of Wilson and Fermat
Authors: Moser W. O. J.
Published: December 2010

We show that is an integer. Special cases include the theorems of Wilson and Fermat.
On Supersolvable Groups and a Theorem of Huppert
Authors: Mukherjee N. P. , Bhattacharya Prabir
Published: December 2010

We obtain the following generalization of a well known result of Huppert. If p is the largest primer divisor of the order of a finite group G and q is any prime distinct from p, then G is supersolvable if and only if every maximal subgroup whose index is relatively prime to either p or q, has prime index.
Sidon Sets
Authors: Abbott H. L.
Published: December 2010

Denote by g(n) the largest integer m such that every set of integers of size n contains a subset of size m whose pairwise sums are distinct. It is shown that g(n) > cn1/2 for any constant c < 2/25 and all sufficiently large n.
Powers of Genus two in Free Groups
Authors: Edmunds Charles C. , Rosenberger Gerhard
Published: December 2010

The general problem is to express an element of the derived group of a free group as a product of a minimal number of commutators. An old conjecture is settled in the negative, and a new conjecture and a number of related questions are posed.
Sample Path Properties of lp -Valued Ornstein-Uhlenbeck Processes
Authors: Schmuland B.
Published: December 2010

We give conditions under which a vector valued Ornstein Uhlenbeck process has continuous sample paths in lp for 1 ≦ p < ∞. We also show when the space lp is not entered at all, i.e., when it has zero capacity.
A Note on Dubins' Theorem
Authors: Babu Gutti Jogesh
Published: December 2010

Let p be the space of probability measures on a compact Hausdorff space. Recently Dubins has characterized the continuous funcitons on p using operator theory. We shall prove the same using probabilistic
arguments.
Uncountably Many Non-Binary Shifts on the Hyperfinite II1-Factor
Authors: Enomoto Masatoshi , Choda Marie , Watatani Yasuo
Published: December 2010

We shall construct uncountably many nonconjugate nonbinary shifts with index two on the hyperfinite II1-factor R using rational functions over a finite field.
A Characterization of Ideals of C* -Algebras
Authors: Kusuda Masaharu
Published: December 2010

Let A be a C*-algebra and let I be a C*-subalgebra of A. Denote by an extension of a state φ of B to a state of A. It is shown that I is an ideal of A if and only if there exists a homomorphism Q from A** onto I** such that Q is the identity map on I** and for every state φ on I. Furthermore it is also shown that I is an essential ideal of A if and only if there exists an injective homomorphism from A into the multiplier algebra of I which is the identity map on I.
Spherical Mean and the Fundamental Group
Authors: Adachi Toshiaki
Published: December 2010

We investigate some properties of spherical means on the universal covering space of a compact Riemannian manifold. If the fundamental group is amenable then the greatest lower bounds of the spectrum of spherical Laplacians are equal to zero. If the fundamental group is nontransient so are geodesic random walks. We also give an isoperimetric inequality for spherical means.
On Soluble Groups of Automorphism of Riemann Surfaces
Authors: Gromadzki Grzegorz
Published: December 2010

Let G be a soluble group of derived length 3. We show in this paper that if G acts as an automorphism group on a compact Riemann surface of genus g ≠ 3,5,6,10 then it has at most 24(g — 1) elements. Moreover, given a positive integer n we show the existence of a Riemann surface of genus g = n4 + 1 that admits such a group of automorphisms of order 24(g — 1), whilst a surface of specified genus can admit such a group of automorphisms of order 48(g — 1), 40(g — 1), 30(g — 1) and 36(g — 1) respectively.
Smooth Norms in Orlicz Spaces
Authors: Maleev R. P. , Troyanski S. L.
Published: December 2010

Equivalent norms with best order of Frechet and uniformly Frechet differentiability in Orlicz spaces are constructed. Classes of Orlicz which admit infinitely many times Frechet differentiable equivalent norm are found.
The Projective Antecedent of the Three Reflection Theorem
Authors: Sherk F. A.
Published: December 2010

A complete answer is given to the question: Under what circumstances is the product of three harmonic homologies in PG(2, F) again a harmonic homology ? This is the natural question to ask in seeking a generalization to projective geometry of the Three Reflection Theorem of metric geometry. It is found that apart from two familiar special cases, and with one curious exception, the necessary and sufficient conditions on the harmonic homologies produce exactly the Three Reflection Theorem.
A Remark on a Paper of Walter and Zayed
Authors: Xie T. F. , Zhou S. P.
Published: December 2010

One result concerning the series representation for the continuous Jacobi transform in Walter and Zayed [1] is improved, the same thought also can be applied to the related results in [1].
Poorly Approximated ℤ2-Cocycles For Transformations With Rational Discrete Spectrum
Authors: Fieldsteel Adam
Published: December 2010

Let T be an ergodic automorphism with rational discrete spectrum and ϕ a ℤ2-cocyle for T. We show that the resulting two-point extension of T is cohomologous to a Morse cocycle if ϕ is approximated with speed o(1/n).

On the other hand, we show by example that this is in general false when the speed of approximation is O(1/n).
Elliptic Curves and Modular Forms
Authors: Ram Murty M.
Published: December 2010

This is a survey of some recent developments in the theory of elliptic curves. After an informal discussion of the main theorems of the arithmetic side of the theory and the open problems confronting the subject, we describe the recent work of K. Rubin, V. Koly vagin, K. Murty and the author which establishes the finiteness of the Shafarevic-Tate group for modular elliptic curves of rank zero and one.
Classification of Maximal Fuchsian Subsgroups of Some Bianchi Groups
Authors: Vulakh L. Ya.
Published: December 2010

Let d = 1,2, or p, prime p ≡ 3 (mod 4). Let Od be the ring of integers of an imaginary quadratic field A complete classification of conjugacy classes of maximal non-elementary Fuchsian subgroups of PSL(2, Od) in PGL(2, Od) is given.
A Note on Brauer Character Degrees of Solvable Groups
Authors: Wang You-Qiang
Published: December 2010

Let G be a finite solvable group. Fix a prime integer p and let t be the number of distinct degrees of irreducible Brauer characters of G with respect to the prime p. We obtain the bound 3t — 2 for the derived length of a Hall p'-subgroup of G. Furthermore, if |G| is odd, then the derived length of a Hall p'-subgroup of G is
bounded by /.
PL Link Isotopy, Essential Knotting and Quotients of Polynomials
Authors: Rolfsen Dale
Published: December 2010

Piecewise-linear (nonambient) isotopy of classical links may be regarded as link theory modulo knot theory. This note considers an adaptation of new (and old) polynomial link invariants to this theory, obtained simply by dividing a link's polynomial by the polynomials of the individual components. The resulting rational functions are effective in distinguishing isotopy classes of links, and in demonstrating that certain links are essentially knotted in the sense that every link in its isotopy class has a knotted component. We also establish geometric criteria for essential knotting of links.
A Moore Strongly Rigid Space
Authors: Tzannes V.
Published: December 2010

It is proved that for every Hausdorff space ℝ and for every Hausdorff (regular or Moore) space X, there exists a Hausdorff (regular or Moore, respectively) space S containing X as a closed subspace and having the following properties:

la)

Every continuous map of S into ℝ is constant.

b)

For every point x of S and every open neighbourhood U of x there exists an open neighbourhood V of x, V ⊆ U such that every continuous map of V into ℝ is constant.

2)

Every continuous map f of S into S (f ≠ identity on S) is constant.

In addition it is proved that the Fomin extension of the Moore space S has these properties.
On Projective Varieties with Projectively Equivalent Zero-Dimensional Linear Sections
Authors: Ballico E.
Published: December 2010

Here we give a partial classification of varieties X ⊂ Pn such that any two general zero-dimensional linear sections are projectively equivalent. They exist (with deg(X) > codim(X) + 2) only in positive characteristic.
Krasnoselski-Mann Iterations in Normed Spaces
Authors: Borwein Jonathan , Reich Simeon , Shafrir Itai
Published: December 2010

We provide general results on the behaviour of the Krasnoselski-Mann iteration process for nonexpansive mappings in a variety of normed settings.
A Stability Property of a Class of Banach Spaces Not Containing c0
Authors: Dowling Patrick N.
Published: December 2010

Let E be a Banach ideal space and X be a Banach space. The Banach function space E(X) does not contain a copy of C0 if and only if neither E nor X contains a copy of c0. Some extensions of this result are also noted.
Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations
Authors: Erbe Lynn H. , Yan Pengxiang
Published: December 2010

We consider the self-adjoint second-order scalar difference equation (1) Δ(rnΔxn) +pnXn+1 = 0 and the matrix system (2) Δ(RnΔXn) + PnXn+1 = 0, where are seQuences of real numbers (d x d Hermitian matrices) with rn > 0(Rn > 0). The oscillation and nonoscillation criteria for solutions of (1) and (2), obtained in [3, 4, 10], are extended to a much wider class of equations by Riccati and averaging techniques.
The Centers of a Radical Ring
Authors: Du Xiankun
Published: December 2010

It is shown that the nth center of a radical ring coincides with that of its adjoint group, from which a result of Jennings is sharpened and a conjecture of his is confirmed.
A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces
Authors: Ebanks B. R. , Kannappan PL. , Sahoo P. K.
Published: December 2010

We determine the general solutions of the functional equation for ƒi: G → F (i = 1,2,3,4), where G is a 2-divisible group and F is a commutative field of characteristic different from 2. The motivation for studying this equation came from a result due to Dry gas [4] where he proved a Jordan and von Neumann type characterization theorem for quasi-inner products. Also, this equation is a generalization of the quadratic functional equation investigated by several authors in connection with inner product spaces and their generalizations. Special cases of this equation include the Cauchy equation, the Jensen equation, the Pexider equation and many more. Here, we determine the general solution of this equation without any regularity assumptions on ƒi.
Trace-Class Operators in CSL Algebras
Authors: Rosenoer Shlomo
Published: December 2010

In this note we show that if 𝓛 is a commutative subspace lattice, then every trace-class operator in Alg 𝓛 lies in the norm-closure of the span of rank-one operators in Alg 𝓛. We also give an elementary proof of a recent result of Davidson and Pitts that if 𝓛 is a CSL generated by completely distributive lattice and finitely many commuting chains, then 𝓛 is compact in the strong operator topology if and only if 𝓛 is completely distributive.
On a Sum of Divisors
Authors: Yokota Hisashi
Published: December 2010

Let l(N, r) be the minimum number of terms needed to express r as a sum of distinct divisors of N. Let l(N) = max{l(N, r) : 1 ≤ r ≤ N}. Then for Vose's sequence improving the result of M. Vose.
Hilbert Rings Arising as Pullbacks
Authors: Anderson David F. , Dobbs David E. , Fontana Marco
Published: December 2010

Let R be the pullback A ×cB, where B → C is a surjective homomorphism of commutative rings and A is a subring of C. It is shown that R and C are Hilbert rings if and only if A and B are Hilbert rings. Applications are given to the D + XE[X], D + M, and D + (X1,..., Xn)Ds[X1,..., Xn] constructions. For these constructions, new examples are given of Hilbert domains R which are unruly, in the sense that R is non-Noetherian and each of its maximal ideals is finitely generated. Related examples are also given.
Centralizing Automorphisms of Lie Ideals in Prime Rings
Authors: Mayne Joseph H.
Published: December 2010

Let R be a prime ring of characteristic not equal to two and let T be an automorphism of R. If U is a Lie ideal of R such that T is nontrivial on U and xxT — xTx is in the center of R for every x in U, then U is contained in the center of R.
Connection Coefficients of Orthogonal Polynomials
Authors: Szwarc Ryszard
Published: December 2010

Let be polynomials orthogonal with respect to different distributions. Conditions are given which imply that the coefficients in the expansion of Pn in terms of Q0, Q1,..., Qn are non-negative.
On a Maximality Property of Partition Regular Systems of Equations
Authors: Lefmann Hanno , Kaddour Hamza Si
Published: December 2010

In this note we will study the following problem. For a given partition regular system of equations, which equations can be added to this system without introducing new variables, such that the new augmented system is again partition regular. It turns that the Hindman system on finite sums as well as the Deuber-Hindman system on finite sums of (m, p, c)-sets are maximal in this sense.
Discriminants of Metacyclic Fields
Authors: Mayer Daniel C.
Published: December 2010

Some formulas for multiplicities of pure cubic discriminants are generalized to the case of a pure field of arbitrary odd prime degree.
Classification and Enumeration of Real Quadratic Fields Having Exactly One Non-Inert Prime Less Than a Minkowski Bound
Authors: Mollin R. A. , Williams H. C.
Published: December 2010

We will classify those real quadratic fields K having exactly one noninert prime less than where Δ is the discriminant of K. Moreover, we will list all such K and prove that the list is complete with one possible exceptional value remaining (whose existence would be a counterexample to the Riemann hypothesis).
Comparison Theorems for Linear Elliptic Equations
Authors: Headley V.B.
Published: December 2010

TWO comparison theorems, one of pointwise type and one of integral type, will be obtained for linear elliptic equations of order 2m on an exterior domain in Rn
Weighted Polynomial Approximation of Entire Functions on Unbounded Subsets of the Complex Plane
Authors: Mhaskar H. N.
Published: December 2010

We study the asymptotic behavior of the n-widths of a class of entire functions in weighted approximation on subsets of the complex plane.
Isomorphism Classes of Solenoidal Algebras I
Authors: Brenken Berndt
Published: December 2010

Each g ∊ ℤ[x] defines a homeomorphism of a compact space We investigate the isomorphism classes of the C*-crossed product algebra Bg associated with the dynamical system An isomorphism invariant Eg of the algebra Bg is shown to determine the algebra Bg up to * or * anti-isomorphism if degree g ≤ 1 and 1 is not a root of g or if degree g = 2 and g is irreducible. It is also observed that the entropy of the dynamical system is equal to the growth rate of the periodic points if g has no roots of unity as zeros. This slightly extends the previously known equality of these two quantities under the assumption that g has no zeros on the unit circle.
Subsocles Supporting Isotype and Balanced Subgroups
Authors: Hill Paul , Megibben Charles
Published: December 2010

We identify a condition, which we refer to as cohesiveness, on a subgroup S of the socle G[p] — {x ∊ G : px = 0} of an abelian p-group G which is necessary for S to be the socle of an isotype subgroup of G. It is shown, when S is countable, that this condition is both necessary and sufficient. A further restriction, definable in terms of the coset valuation on G/S, leads to the notion of S being completely cohesive in G. When S is countable, this latter condition is both necessary and sufficient for S to serve as the socle of a balanced subgroup of G. Also noteworthy is the fact that if H and K are, respectively, balanced and isotype subgroups of G with H[p] = K[p], then K is necessarily balanced in G.
The Lichtenbaum-Quillen Conjecture for Fields
Authors: Jardine J. F.
Published: December 2010

I want to say immediately that, despite the authoritative-sounding title, I am not claiming a proof of anything like the Lichtenbaum-Quillen conjecture. My intent here is only to explain the conjecture in various special cases, but maybe from an idiosyncratic point of view.

This paper is based on the text of the Coxeter-James Lecture given at the Winter Meeting of the Canadian Mathematical Society at Montreal in December, 1992.1 would like to thank the Society for awarding me the honour of giving this talk.
A Note on Hardy's Inequality
Authors: Klemes Ivo
Published: December 2010

We prove a two-sided version of Hardy's inequality by methods arising from the proof of the Littlewood conjecture.
Hankel Operators Associated with Analytic Crossed Products
Authors: Imina Yoshiki , Saito Kichi-Suke
Published: December 2010

We introduce the notion of Hankel operators associated with analytic crossed products and consider the Nehari problem in this setting.
Locally Compact Hughes Planes
Authors: Stroppel Markus
Published: December 2010

Among the eight-dimensional stable planes, the compact connected generalized Hughes planes and the geometries induced on the outer points are characterized by the property that these planes admit an effective action of the group SL3 ℂ.
Projective Orthomodular Lattices
Authors: Bruns Gunter , Roddy Michael
Published: December 2010

We introduce sectional projectivity, which appears to be the correct notion of projectivity when working with orthomodularlattices. We prove some positive results for varieties of OMLs satisfying various finiteness conditions, namely that every finite OML in such a variety is sectionally projective. In contrast, we prove that the eight element modular ortholattice, MO 3, is not projective in the variety of modular ortholattices.
Units of Integral Group Rings of Some Metacyclic Groups
Authors: Jespers Eric , Leal Guilherme , Milies C. Polcino
Published: December 2010

In this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.
Measures Below Outer Measures
Authors: Watson Stephen
Published: December 2010

We give a simple proof that, for any ॉ > 0, there is an outer measure μ* on a finite set X such that, for any measure Thus there is a non-zero outer (finitely subadditive) measure v* on the clopen subsets of the Cantor set such that, if v ≤ v* is a finitely additive measure on the clopen subsets of the Cantor set, then v ≡ 0.
On Semiperfect FPF-Rings
Authors: Yousif Mohamed
Published: December 2010

We show that a semiperfect right FPF-ring is right self-injective if and only if J(R) — Z(RR), extending a well-known result due to Carl Faith on semiperfect right FPF-rings with nil Jacobson radical.
Continuity of Attractors and Invariant Measures for Iterated Function Systems
Authors: Centore P. M. , Vrscay E. R.
Published: December 2010

We prove the "folklore" results that both the attractor A and invariant measure μ of an N-map Iterated Function System (IFS) vary continuously with variations in the contractive IFS maps as well as the probabilities. This represents a generalization of Barnsley's result showing the continuity of attractors with respect to variations of a parameter appearing in the IFS maps. Some applications are presented, including approximations of attractors and invariant measures of nonlinear IFS, as well as some novel approximations of Julia sets for quadratic complex maps.
Distortion Theorems for Diffeomorphisms
Authors: Hengartner W. , Poulin D.
Published: December 2010

Generalizations of the Koebe distortion theorem to a class of diffeomorphisms are given. They are applied to univalent harmonic mappings.
The Residual Finiteness of Polygonal Products—Two Counterexamples
Authors: Allenby R. B. J. T.
Published: December 2010

We show that, even under very favourable hypotheses, a polygonal product of finitely generated torsion free nilpotent groups amalgamating infinite cyclic subgroups is, in general, not residually finite, thus answering negatively a question of C. Y. Tang. A second example shows similar kinds of limitations apply even when the factors of the product are free abelian groups.
The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds
Authors: Heil Wolfgang , Whitten Wilbur
Published: December 2010

The Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1, if π1M is infinite and does not contain Z2 * Z2 as a subgroup, and if π1M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z2 * Z2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but they satisfy Thurston's Geometrization Conjecture. We then reformulate the statement of the (nonorientable) SFS-conjecture and obtain a torus theorem for nonorientable manifolds.
An Approximation Theorem for Coarse V-Topologies on Rings
Authors: Marshall Murray A.
Published: December 2010

An approximation theorem for V-topologies on not necessarily commutative rings is proved. This holds for a certain class of rings (called rings with enough units) and a certain class of V-topologies (called coarse V-topologies). This has application, for example, to V-topologies induced by orderings.
On the Range of an Integral Transformation
Authors: Rooney P. G.
Published: December 2010

The range of the transformation, defined by

is characterized on the spaces Lμ,p defined by the norm

for
Bicyclic Units in some Integral Group Rings
Authors: Jespers E.
Published: December 2010

A description is given of the unit group for the two groups G = D12 and G = D8 × C2. In particular, it is shown that in both cases the bicyclic units generate a torsion-free normal complement. It follows that the Bass-cyclic units together with the bicyclic units generate a subgroup of finite index in for all n ≥ 3.
Isometric Stability Property of Certain Banach Spaces
Authors: Koldobsky Alexander
Published: December 2010

Let E be one of the spaces C(K) and L1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F
Periodic Orbits for Generalized Gradient Flows
Authors: Schwartzman Sol
Published: December 2010

Let Mn be an n-dimensional compact oriented connected Riemannean manifold. It is proved that either of the following conditions is sufficient to insure that the flow defined by a generalized gradient vector field in Mn has either a stationary point or a periodic orbit:

a)Mn is the product of a circle with an (n — 1 ) dimensional manifold of non-zero Euler characteristic.

b)The (n — 1) dimensional Stiefel-Whitney class of Mn is different from zero and in addition Mn possesses no one-dimensional 2-torsion.
Semiprime Goldie Generalised Matrix Rings
Authors: Clase Michael V.
Published: December 2010

Necessary and sufficient conditions are given for a generalised matrix ring to be semiprime right Goldie.
Isometries of Noncompact Lipschitz Spaces
Authors: Weaver Nik
Published: December 2010

We show that under reasonable restrictions on the metric spaces X and Y, every surjective isometric isomorphism between Lip(X) and Lip(Y) arises in a simple manner from an isometry between X and Y. Our result differs from several previous results along these lines in that we do not require X and Y to be compact.
On the Adjoint Group of a Radical Ring
Authors: Amberg Bernhard , Dickenschied Oliver
Published: December 2010

The relations between the adjoint group and the additive group of a radical ring and its nilpotency are investigated. It is shown that certain finiteness conditions carry over from the adjoint group to the additive group and that the converse holds for the class of minimax groups.
Weighted Lacunary Maximal Functions on Curves
Authors: Bak Jong-Guk
Published: December 2010

Let γ(t) = (t, t2,..., tn) + a be a curve in Rn, where n ≥ 2 and a ∊ Rn. We prove LP-Lq estimates for the weighted lacunary maximal function, related to this curve, defined by

If n = 2 or 3 our results are (nearly) sharp.
Polynômes Anisotropes Modulo p2
Authors: Hanine El Mostafa
Published: December 2010

Nous proposons de construire des polynômes à coefficients p-adiques, de degré D, sans terme constant, ayant plus que 2D + 1 variables. Ces polynômes n'ont dans Zp que le zéro trivial modulo p2. Le but que nous cherchons à atteindre, à partir des polynômes ainsi construit, est de minorer les valeurs de p pour lesquelles l'équation F(x1,...,X2D+1) ≡ 0 (mod p2) admet une solution primitive, F est un élément de Zp[X1,... ,X2D+1] de degré D sans term constant.
The Tensor Product Formula for Reflexive Subspace Lattices
Authors: Harrison K. J.
Published: December 2010

We give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.
Torsion Units in Integral Group Rings
Authors: Juriaans Stanley Orlando
Published: December 2010

Special cases of Bovdi's conjecture are proved. In particular the conjecture is proved for supersolvable and Frobenius groups. We also prove that if is finite, α ∊ VℤG a torsion unit and m the smallest positive integer such that αm ∊ G then m divides .
On the Duality of Operator Spaces
Authors: Le Merdy Christian
Published: December 2010

We prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.
A Characterization of Left Perfect Rings
Authors: Zhou Yiqiang
Published: December 2010

In this note, we show that a ring R is a left perfect ring if and only if every generating set of each left R-module contains a minimal generating set. This result gives a positive answer to a question on left perfect rings raised by Nashier and Nichols.
Similarity of Nests in Lp, 1 ≤ p ≠ 2 < ∞
Authors: Arias Alvaro , Müller Paul
Published: December 2010

In this note we prove that one aspect of the similarity theory, for the Volterra nest in Lp(0,1 ) for 1 < p ≠ 2 < ∞, is like that for p = 1 ; we thus answer a question from [ALWW].
A Note on Geometric Factoriality
Authors: Bhatwadekar S. M. , Russell K. P.
Published: December 2010

Let k: be a perfect field such that is solvable over k. We show that a smooth, affine, factorial surface birationally dominated by affine 2-space is geometrically factorial and hence isomorphic to . The result is useful in the study of subalgebras of polynomial algebras. The condition of solvability would be unnecessary if a question we pose on integral representations of finite groups has a positive answer.
CR Mappings of Circular CR Manifolds
Authors: Boivin André , Dwilewicz Roman
Published: December 2010

Let M be a circular CR manifold and let N be a rigid CR manifold in some complex vector spaces. The problem of the existence of local CR mappings from M into N is considered. Conditions are given which ensure that the space of such CR mappings depends on a finite number of parameters. The idea of the proof of the main result relies on a Bishop type equation for CR mappings. Roughly speaking, we look for CR mappings from M into N in the form F = (ƒ,g), we assume that g is given, then we find ƒ in terms of g and some parameters, and finally we look for conditions on g. It works independently of assumptions on the Levi forms of M and N, and there is also some freedom on the codimension of the manifolds.
Stably Free Modules Over Rings of Generalised Integer Quaternions
Authors: Chatters A. W. , Parmenter M. M.
Published: December 2010

In this note, we obtain, in a rather easy way, examples of stably free non-free right ideals. We also give an example of a stably free non-free two-sided ideal in a maximal ℤ-order. These are obtained as applications of a theorem giving necessary and sufficient conditions for H/nH to be a complete 2 x 2 matrix ring, when H is a generalised quaternion ring.
Cut and Paste in 2-Dimensional Projective Planes and Circle Planes
Authors: Polster B. , Steinke G. F.
Published: December 2010

We describe two methods to combine sets of lines of different 2-dimensional projective planes into line sets of new 2-dimensional projective planes. Using these methods we describe several ways in which sets of circles of different 2-dimensional circle planes can be combined into circle sets of new 2-dimensional circle planes.
Mutual Infective Hulls
Authors: Jain S. K. , López-Permouth S. R. , Raza Syed S.
Published: December 2010

The mutual injective hull of an arbitrary family of modules is constructed. Applications to the calculations of quasi-injective and π-injective hulls of direct sums are given.
On the Linear Invariance of Lindelöf Numbers
Authors: Baars Jan , Gladdines Helma
Published: December 2010

Let X and Y be Tychonov spaces and suppose there exists a continuous linear bijection from Cp(X)to CP(Y). In this paper we develop a method that enables us to compare the Lindelöf number of Y with the Lindelöf number of some dense subset Z of X. As a corollary we get that if for perfect spaces X and Y, CP(X) and Cp(Y)are linearly homeomorphic, then the Lindelöf numbers of Jf and Fare equal. Another result in this paper is the following. Let X and Y be any two linearly ordered perfect Tychonov spaces such that Cp(X)and Cp(Y)are linearly homeomorphic. Let be a topological property that is closed hereditary, closed under taking countable unions and closed under taking continuous images. Then X has isproperty if and only if Y has. As examples of such properties we consider certain cardinal functions.
Bernstein-Type Inequalities with Bombieri Norm
Authors: Beaucoup Franck , Souchon Catherine
Published: December 2010

If is an univariate polynomial with degree n then Bombieri norm of P is defined by

where denotes the binomial coefficient.

In the present paper we give, under assumptions on the roots of P, optimal Bernsteintype inequalities for the ratio between Bombieri norm of P and that of its derivative P′.

We also give such inequalities for the polar derivatives of P defined by
On Joint Eigenvalues of Commuting Matrices
Authors: Bhatia R. , Elsner L.
Published: December 2010

A spectral radius formula for commuting tuples of operators has been proved in recent years. We obtain an analog for all the joint eigenvalues of a commuting tuple of matrices. For a single matrix this reduces to an old result of Yamamoto.
Some Rings of Invariants that are Cohen-Macaulay
Authors: Smith Larry
Published: December 2010

Let be a representation of the finite group G over the field . If the order |G| of G is relatively prime to the characteristic of or n = 1 or 2, then it is known that the ring of invariants is Cohen-Macaulay. There are examples to show that need not be Cohen-Macaulay when |G| is divisible by the characteristic of . In all such examples is at least 4. In this note we fill the gap between these results and show that rings of invariants in three variables are always Cohen-Macaulay.
On the Decomposition of Nonsingular CS-Modules
Authors: Clark John , Dung Nguyen Viet
Published: December 2010

It is shown that if M is a nonsingular CS-module with an indecomposable decomposition M = ⊕i∊I Mi, then the family {Mi | i € I} is locally semi-T"- nilpotent. This fact is used to prove that any nonsingular self-generator Σ-CS module is a direct sum of uniserial Noetherian quasi-injective submodules. As an application, we provide a new proof of Goodearl's characterization of non-singular rings over which all nonsingular right modules are projective.
A Full Descriptive Definition of the Gage Integral
Authors: Bongiorno B. , Pfeffer W. F. , Thomson B. S.
Published: December 2010

We consider a specific Riemann type integral, called thegage integral. Using variational measures, we characterize all additive functions of intervals that are indefinite gage integrals. The characterization generalizes the descriptive definition of the classical Denjoy-Perron integral to all dimensions.
Une Caractérisation des Polynômes Prenant des Valeurs Entières Sur Tous les Nombres Premiers
Authors: Chabert Jean-Luc
Published: December 2010

We give a characterization of polynomials with rational coefficients which take integral values on the prime numbers: to test a polynomial of degreen, it is enough to consider its values on the integers from 1 to 2n —1.
On Strongly Normal Functions
Authors: Chen Huaihui , Gauthier Paul M.
Published: December 2010

Loosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.
On Bodies Associated with a Given Convex Body
Authors: Makai Endre , Martini Horst
Published: December 2010

Let d ≥ 2, and K ⊂ ℝd be a convex body with 0 ∈ int K. We consider the intersection body IK, the cross-section body CK and the projection body ΠK of K, which satisfy IK ⊂ CK ⊂ ΠK. We prove that [bd(IK)] ∩ [bd(CK)] ≠ (a joint observation with R. J. Gardner), while for d ≥ 3 the relation [CK] ⊂ int(ΠK) holds for K in a dense open set of convex bodies, in the Hausdorff metric. If IK = c ˙ CK for some constant c > 0, then K is centred, and if both IK and CK are centred balls, then K is a centred ball. If the chordal symmetral and the difference body of K are constant multiples of each other, then K is centred; if both are centred balls, then K is a centred ball. For d ≥ 3 we determine the minimal number of facets, and estimate the minimal number of vertices, of a convex d-polytope P having no plane shadow boundary with respect to parallel illumination (this property is related to the inclusion [CP] ⊂ int(ΠP)).
When X* is a P′-Space
Authors: Swardson Mary Anne , Szeptycki Paul J.
Published: December 2010

In [7,3.1 ] the authors show that if a space X is realcompact and locally compact, then X* is a P′-space. In this paper we show that the hypothesis of realcompactness can be weakened. We also look at other conditions on X that are sufficient to guarantee that X* is a P′-space.
A Note on Un × Um Modular Invariants
Authors: Kechagias Nondas E.
Published: December 2010

We consider the rings of invariants RG, where R is the symmetric algebra of a tensor product between two vector spaces over the field Fp andG = Un × Um. A polynomial algebra is constructed and these invariants provide Chern classes for the modular cohomology of Un+m.
Cauchy’s Problem for Harmonic Functions with Entire Data on a Sphere
Authors: Khavinson Dmitry
Published: December 2010

We give an elementary potential-theoretic proof of a theorem of G. Johnsson: all solutions of Cauchy’s problems for the Laplace equations with an entire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.
Generalized Siegel Modular Forms and Cohomology of Locally Symmetric Varieties
Authors: Lee Min Ho
Published: December 2010

We generalize Siegel modular forms and construct an exact sequence for the cohomology of locally symmetric varieties which plays the role of the Eichler-Shimura isomorphism for such generalized Siegel modular forms.
Une caractérisation des corps satisfaisant le théorème de l'axe principal
Authors: Movahhedi A. , Salinier A.
Published: December 2010

On caractérise les corps K satisfaisant le théorème de l’axe principal à l’aide de propriétés des formes trace des extensions finies de K. Grâce à la caract érisation de ces mêmes corps due à Waterhouse, on retrouve à partir de là, de façon élémentaire, un résultat de Becker selon lequel un pro-2-groupe qui se réalise comme groupe de Galois absolu d’un tel corps K est engendré par des involutions.
The Trigonometry of Hyperbolic Tessellations
Authors: Coxeter H. S. M.
Published: December 2010

For positive integerspandqwith (p− 2)(q− 2) > 4 there is, in the hyperbolic plane, a group [p, q] generated by reflections in the three sides of a triangleABCwith angles π/p, π/q, π/2. Hyperbolic trigonometry shows that the sideAChas length ψ, where cosh ψ =c/s, c = cos π/q,s= sin π/p. For a conformal drawing inside the unit circle with centreA, we may take the sidesABandACto run straight along radiiwhileBCappears as an arc of a circle orthogonal to the unit circle. The circle containing this arc is found to have radius 1/ sinh ψ =s/z, where z =, while its centre is at distance 1/ tanh ψ = c/z fromA. In the hyperbolic triangleABC, the altitude fromABto the right-angled vertex C is ζ, where sinh ζ = z.
Non-Uniqueness for the p-Harmonic Flow
Authors: Hungerbühler Norbert
Published: December 2010

If f0: Ω ⊂ ℝm → Sn is a weakly p-harmonic map from a bounded smooth domain Ω in ℝm (with 2 < p < m) into a sphere and if f0 is not stationary p-harmonic, then there exist infinitely many weak solutions of the p-harmonic flow with initial and boundary data f0, i.e., there are infinitely many global weak solutions f :Ω × ℝ → ⊂ Sn of

We also show that there exist non-stationary weakly (m − 1)-harmonic maps f0: Bm → Sm−1.
Asymptotic Theory and the Foundations of Statistics
Authors: Reid N.
Published: December 2010

Statistics in the 20th century has been enlivened by a passionate, occasionally bitter, and still vibrant debate on the foundations of statistics and in particular on Bayesian vs. frequentist approaches to inference. In 1975 D. V. Lindley predicted a Bayesian 21st century for statistics. This prediction has often been discussed since, but there is still no consensus on the probability of its correctness. Recent developments in the asymptotic theory of statistics are, surprisingly, shedding new light on this debate, and may have the potential to provide a common middle ground.
Finite Groups with Large Automizers for their Abelian Subgroups
Authors: Bechtell H. , Deaconescu M. , Silberberg Gh.
Published: December 2010

This note contains the classification of the finite groups G satisfying the condition NG(H)/CG(H) ≅ Aut(H) for every abelian subgroup H of G.
Amalgamated Products and the Howson Property
Authors: Kapovich Ilya
Published: December 2010

We show that if A is a torsion-free word hyperbolic group which belongs to class (Q), that is all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is a Burns subgroup of A. This, in particular, implies that if B is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated) then A *UB, ⧼A, t | Ut = V⧽ are also Howson groups. Finitely generated free groups, fundamental groups of closed hyperbolic surfaces and some interesting 3-manifold groups are known to belong to class (Q) and our theorem applies to them. We also describe a large class of word hyperbolic groups which are not Howson.
A New Proof of a Theoremof Magnus
Authors: Liriano Sal
Published: December 2010

Using naive algebraic geometric methods a new proof of the following celebrated theorem of Magnus is given: Let G be a group with a presentation having n generators and m relations. If G also has a presentation on n − m generators, then G is free of rank n − m.
On the Non-Vanishing of a Certain Class of Dirichlet Series
Authors: Narayanan Sridhar
Published: December 2010

In this paper, we consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1. We establish criteria for such a Dirichlet series to be nonvanishing on the line of convergence. We also show that our results can be applied to yield non-vanishing results for a subclass of the Selberg class and the Sato-Tate conjecture.
On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line
Authors: Clemence Dominic P.
Published: December 2010

For the perturbed Hill’s equation on the line,

we study the behaviour of the matrix m-function at the spectral gap endpoints. In particular, we extend the result of Hinton, Klaus and Shaw that En, a gap endpoint, is a half-bound state (HBS) if and only if (E − En)½m(E) approaches a nonzero constant as E → En, to the present case.
Gorenstein Graded Algebras and the Evaluation Map
Authors: Félix Yves , Murillo Aniceto
Published: December 2010

We consider graded connected Gorenstein algebras with respect to the evaluation map . We prove that if evG ≠ 0, then the global dimension of G is finite.