bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cut and Paste in 2-Dimensional Projective Planes and Circle Planes
Authors: Polster B. , Steinke G. F. 
Published: December 2010

AbstractWe 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.
On the Linear Invariance of Lindelöf Numbers
Authors: Baars Jan , Gladdines Helma 
Published: December 2010

AbstractLet 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

AbstractIf is an univariate polynomial with degree n then Bombieri norm of P is defined bywhere 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
Some Rings of Invariants that are Cohen-Macaulay
Authors: Smith Larry 
Published: December 2010

AbstractLet 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

AbstractIt 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

AbstractWe 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

AbstractWe 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

AbstractLoosely 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

AbstractLet 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

AbstractIn [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.
Une caractérisation des corps satisfaisant le théorème de l'axe principal
Authors: Movahhedi A. , Salinier A. 
Published: December 2010

RésuméOn 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

AbstractFor 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

AbstractIf 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 ofWe 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

AbstractStatistics 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.
Amalgamated Products and the Howson Property
Authors: Kapovich Ilya 
Published: December 2010

AbstractWe 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.
On the Non-Vanishing of a Certain Class of Dirichlet Series
Authors: Narayanan Sridhar 
Published: December 2010

AbstractIn 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

AbstractFor 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.
Criteria for Commutativity in Large Groups
Authors: Mohammadi Hassanabadi A. , Rhemtulla Akbar 
Published: December 2010

AbstractIn this paper we prove the following:1.Let m ≥ 2, n ≥ 1 be integers and let G be a group such that (XY)n = (YX)n for all subsets X, Y of size m in G. Thena)G is abelian or a BFC-group of finite exponent bounded by a function of m and n.b)If m ≥ n then G is abelian or |G| is bounded by a function of m and n.2.The only non-abelian group G such that (XY)2 = (YX)2 for all subsets X, Y of size 2 in G is the quaternion group of order 8.3.Let m, n be positive integers and G a group such that for all subsets Xi of size m in G. Then G is n-permutable or |G| is bounded by a function of m and n.
Splitting Patterns and Trace Forms
Authors: Hurrelbrink Jurgen , Rehmann Ulf 
Published: December 2010

AbstractThe splitting pattern of a quadratic form q over a field k consists of all distinct Witt indices that occur for q over extension fields of k. In small dimensions, the complete list of splitting patterns of quadratic forms is known. We show that all splitting patterns of quadratic forms of dimension at most nine can be realized by trace forms.
Automorphisms of Metabelian Groups
Authors: Papistas Athanassios I. 
Published: December 2010

AbstractWe investigate the problem of determining when IA(Fn(AmA)) is finitely generated for all n and m, with n ≥ 2 and m ≠ 1. If m is a nonsquare free integer then IA(Fn(AmA)) is not finitely generated for all n and if m is a square free integer then IA(Fn(AmA)) is finitely generated for all n, with n ≠ 3, and IA(F3(AmA)) is not finitely generated. In case m is square free, Bachmuth and Mochizuki claimed in ([7], Problem 4) that TR(AmA) is 1 or 4. We correct their assertion by proving that TR(AmA) = ∞.
Uniform Approximation to Mahler’s Measure in Several Variables
Authors: Boyd David W. 
Published: December 2010

AbstractIf ƒ (x1,…,xk) is a polynomial with complex coefficients, the Mahler measure of ƒ , M(ƒ) is defined to be the geometric mean of |f| over the k-torus 𝕋k. We construct a sequence of approximations Mn(ƒ) which satisfy −d2−n log 2 + log Mn(ƒ) ≤ log M(ƒ) ≤ log Mn(ƒ). We use these to prove that M(ƒ) is a continuous function of the coefficients of ƒ for polynomials of fixed total degree d. Since Mn(ƒ) can be computed in a finite number of arithmetic operations from the coefficients of ƒ this also demonstrates an effective (but impractical) method for computing M(ƒ) to arbitrary accuracy.
Exponential Sums on Reduced Residue Systems
Authors: Loh W. K. A. 
Published: December 2010

AbstractThe aim of this article is to obtain an upper bound for the exponential sums , where the summation runs from x = 1 to x = q with (x, q) = 1 and e(α) denotes exp(2πiα).We shall show that the upper bound depends only on the values of q and s, where s is the number of terms in the polynomial ƒ(x).
A Note on H1 Multipliers for Locally Compact Vilenkin Groups
Authors: Daly James E. , Phillips Keith L. 
Published: December 2010

AbstractKitada and then Onneweer and Quek have investigated multiplier operators on Hardy spaces over locally compact Vilenkin groups. In this note, we provide an improvement to their results for the Hardy space H1 and provide examples showing that our result applies to a significantly larger group of multipliers.
Lp-Boundedness of a Singular Integral Operator
Authors: Al-Hasan Abdelnaser J. , Fan Dashan 
Published: December 2010

AbstractLet b(t) be an L∞ function on R, Ω(y′) be an H1 function on the unit sphere satisfying the mean zero property (1) and Qm(t) be a real polynomial on R of degree m satisfying Qm(0) = 0. We prove that the singular integral operatoris bounded in Lp(Rn) for 1 < p < ∞, and the bound is independent of the coefficients of Qm(t).
A Mountain Pass to the Jacobian Conjecture
Authors: Chamberland Marc , Meisters Gary 
Published: December 2010

AbstractThis paper presents an approach to injectivity theorems via the Mountain Pass Lemma and raises an open question. The main result of this paper (Theorem 1.1) is proved by means of the Mountain Pass Lemma and states that if the eigenvalues of are uniformly bounded away from zero for x ∊ Rn, where is a class C1 map, then F is injective. This was discovered in a joint attempt by the authors to prove a stronger result conjectured by the first author: Namely, that a sufficient condition for injectivity of class C1 maps F of Rn into itself is that all the eigenvalues of F′(x) are bounded away from zero on Rn. This is stated as Conjecture 2.1. If true, it would imply (via Reduction-of-Degree) injectivity of polynomial mapssatisfying the hypothesis, det F′(x) ≡ 1, of the celebrated Jacobian Conjecture (JC) of Ott-Heinrich Keller. The paper ends with several examples to illustrate a variety of cases and known counterexamples to some natural questions.
The Right Regular Representation of a Compact Right Topological Group
Authors: Moran Alan 
Published: December 2010

AbstractWe show that for certain compact right topological groups, , the strong operator topology closure of the image of the right regular representation of G in L(H), where H = L2(G), is a compact topological group and introduce a class of representations, R , which effectively transfers the representation theory of over to G. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.
On the Construction of Hölder and Proximal Subderivatives
Authors: Borwein J. M. , Girgensohn R. , Wang Xianfu 
Published: December 2010

AbstractWe construct Lipschitz functions such that for all s > 0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.
On the Set of Common Differences in van der Waerden’s Theorem on Arithmetic Progressions
Authors: Brown Tom C. , Graham Ronald L. , Landman Bruce M. 
Published: December 2010

AbstractAnalogues of van derWaerden’s theorem on arithmetic progressions are considered where the family of all arithmetic progressions, AP, is replaced by some subfamily of AP. Specifically, we want to know for which sets A, of positive integers, the following statement holds: for all positive integers r and k, there exists a positive integer n = w′(k, r) such that for every r-coloring of [1, n] there exists a monochromatic k-term arithmetic progression whose common difference belongs to A. We will call any subset of the positive integers that has the above property large. A set having this property for a specific fixed r will be called r-large. We give some necessary conditions for a set to be large, including the fact that every large set must contain an infinite number of multiples of each positive integer. Also, no large set {an : n = 1, 2,…} can have . Sufficient conditions for a set to be large are also given. We show that any set containing n-cubes for arbitrarily large n, is a large set. Results involving the connection between the notions of “large” and “2-large” are given. Several open questions and a conjecture are presented.
Generic Partial Two-Point Sets Are Extendable
Authors: Dijkstra Jan J. 
Published: December 2010

AbstractIt is shown that under ZFC almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K. Kunen and J. vanMill under the assumption that Martin’s Axiom is valid.
The Bockstein Map is Necessary
Authors: Dădărlat Marius , Eilers Søren 
Published: December 2010

AbstractWe construct two non-isomorphic nuclear, stably finite, real rank zero C*-algebras E and E′ for which there is an isomorphism of ordered groups which is compatible with all the coefficient transformations. The C*-algebras E and E0 are not isomorphic since there is no Θ as above which is also compatible with the Bockstein operations. By tensoring with Cuntz’s algebra one obtains a pair of non-isomorphic, real rank zero, purely infinite C*-algebras with similar properties.
Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces
Authors: Kikuchi Masato 
Published: December 2010

AbstractWe shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section 2 the equivalence between Shimogaki’s theorem and some martingale inequalities will be established, and in Section 3 the equivalence between Boyd’s theorem andmartingale inequalities with change of probability measure will be established.
Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups
Authors: Kim Goansu , Tang C. Y. 
Published: December 2010

AbstractWe derive a necessary and sufficient condition for HNN-extensions of cyclic subgroup separable groups with cyclic associated subgroups to be cyclic subgroup separable. Applying this, we explicitly characterize the residual finiteness and the cyclic subgroup separability of HNN-extensions of abelian groups with cyclic associated subgroups. We also consider these residual properties ofHNN-extensions of nilpotent groups with cyclic associated subgroups.
A Real Holomorphy Ring without the Schmüdgen Property
Authors: Marshall Murray A. 
Published: December 2010

AbstractA preordering T is constructed in the polynomial ring A = ℝ[t1, t2, … ] (countablymany variables) with the following two properties: (1) For each f ∈ A there exists an integer N such that −N ≤ f (P) ≤ N holds for all P ∈ SperT(A)). (2) For all f ∈ A, if N + f, N − f ∈ T for some integer N, then f ∈ R. This is in sharp contrast with the Schmüdgen-Wörmann result that for any preordering T in a finitely generated ℝ-algebra A, if property (1) holds, then for any f ∈ A, f > 0 on SperT(A)) f ∈; T. Also, adjoining to A the square roots of the generators of T yields a larger ring C with these same two properties but with ∑C2 (the set of sums of squares) as the preordering.
A Generalized Rao Bound for Ordered Orthogonal Arrays and (t, m, s)-Nets
Authors: Martin W. J. , Stinson D. R. 
Published: December 2010

AbstractIn this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and (t, m, s)-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (i.e., necessary conditions) for existence of these objects.
Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center
Authors: Marubayashi H. , Ueda A. 
Published: December 2010

AbstractLet Q be a simple Artinian ring with finite dimension over its center. An order R in Q is said to be Prüfer if any one-sided R-ideal is a progenerator. We study prime and primary ideals of a Prüfer order under the condition that the center is Prüfer. Also we characterize branched and unbranched prime ideals of a Prüfer order.
A Class of Supercuspidal Representations of G2(k)
Authors: Savin Gordan 
Published: December 2010

AbstractLet H be an exceptional, adjoint group of type E6 and split rank 2, over a p-adic field k. In this article we discuss the restriction of the minimal representation of H to a dual pair PD× × G2(k), where D is a division algebra of dimension 9 over k. In particular, we discover an interesting class of supercuspidal representations of G2(k).
Ramanujan and the Modular j-Invariant
Authors: Berndt Bruce C. , Chan Heng Huat 
Published: December 2010

AbstractA new infinite product tn was introduced by S. Ramanujan on the last page of his third notebook. In this paper, we prove Ramanujan’s assertions about tn by establishing new connections between themodular jinvariant and Ramanujan’s cubic theory of elliptic functions to alternative bases. We also show that for certain integers n, tn generates the Hilbert class field of . This shows that tn is a new class invariant according to H. Weber’s definition of class invariants.
Finite Rank Operators in Certain Algebras
Authors: Bradley Sean 
Published: December 2010

AbstractLet Alg(ℒ) be the algebra of all bounded linear operators on a normed linear space X leaving invariant each member of the complete lattice of closed subspaces L. We discuss when the subalgebra of finite rank operators in Alg(ℒ) is non-zero, and give an example which shows this subalgebra may be zero even for finite lattices. We then give a necessary and sufficient lattice condition for decomposing a finite rank operator F into a sum of a rank one operator and an operator whose range is smaller than that of F, each of which lies in Alg(ℒ). This unifies results of Erdos, Longstaff, Lambrou, and Spanoudakis. Finally, we use the existence of finite rank operators in certain algebras to characterize the spectra of Riesz operators (generalizing results of Ringrose and Clauss) and compute the Jacobson radical for closed algebras of Riesz operators and Alg(ℒ) for various types of lattices.
A Property of Lie Group Orbits
Authors: Božičević Mladen 
Published: December 2010

AbstractLet G be a real Lie group and X a real analytic manifold. Suppose that G acts analytically on X with finitely many orbits. Then the orbits are subanalytic in X. As a consequence we show that the micro-support of a G-equivariant sheaf on X is contained in the conormal variety of the G-action.