bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Parametric Gauss-Green Theorem in Several Variables
Authors: Ortel M. , Schneider W. 
Published: December 2010

AbstractWe 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.
A Note on Hardy-Orlicz Spaces
Authors: Jianzhong Zhang 
Published: December 2010

AbstractW. 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).
Half-Silvered Mirrors and Wythoff's Game
Authors: Porta Horacio , Stolarsky Kenneth B. 
Published: December 2010

AbstractWe 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.
On Supersolvable Groups and a Theorem of Huppert
Authors: Mukherjee N. P. , Bhattacharya Prabir 
Published: December 2010

AbstractWe 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.
Sample Path Properties of lp -Valued Ornstein-Uhlenbeck Processes
Authors: Schmuland B. 
Published: December 2010

AbstractWe 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 Characterization of Ideals of C* -Algebras
Authors: Kusuda Masaharu 
Published: December 2010

AbstractLet 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

AbstractWe 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

AbstractLet 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.
The Projective Antecedent of the Three Reflection Theorem
Authors: Sherk F. A. 
Published: December 2010

AbstractA 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.
Poorly Approximated ℤ2-Cocycles For Transformations With Rational Discrete Spectrum
Authors: Fieldsteel Adam 
Published: December 2010

AbstractLet 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

AbstractThis 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

AbstractLet 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

AbstractLet 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

AbstractPiecewise-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

AbstractIt 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.
Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations
Authors: Erbe Lynn H. , Yan Pengxiang 
Published: December 2010

AbstractWe 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.
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

AbstractWe 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

AbstractIn 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

AbstractLet 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

AbstractLet 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

AbstractLet 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.
On a Maximality Property of Partition Regular Systems of Equations
Authors: Lefmann Hanno , Kaddour Hamza Si 
Published: December 2010

AbstractIn 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.
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

AbstractWe 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).
Isomorphism Classes of Solenoidal Algebras I
Authors: Brenken Berndt 
Published: December 2010

AbstractEach 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

AbstractWe 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.
Projective Orthomodular Lattices
Authors: Bruns Gunter , Roddy Michael 
Published: December 2010

AbstractWe 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

AbstractIn 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

AbstractWe 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.
Continuity of Attractors and Invariant Measures for Iterated Function Systems
Authors: Centore P. M. , Vrscay E. R. 
Published: December 2010

AbstractWe 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.
The Residual Finiteness of Polygonal Products—Two Counterexamples
Authors: Allenby R. B. J. T. 
Published: December 2010

AbstractWe 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

AbstractThe 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

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

AbstractA 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

AbstractLet 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

AbstractLet 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.
Isometries of Noncompact Lipschitz Spaces
Authors: Weaver Nik 
Published: December 2010

AbstractWe 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.
Weighted Lacunary Maximal Functions on Curves
Authors: Bak Jong-Guk 
Published: December 2010

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

RésuméNous 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.
Torsion Units in Integral Group Rings
Authors: Juriaans Stanley Orlando 
Published: December 2010

AbstractSpecial 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

AbstractWe 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.
Similarity of Nests in Lp, 1 ≤ p ≠ 2 < ∞
Authors: Arias Alvaro , Müller Paul 
Published: December 2010

AbstractIn 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

AbstractLet 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

AbstractLet 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

AbstractIn 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.