bluuebunny/crossref_metadata_2025_split huggingface dataset:
Equal Integrals of Functions
Authors: Cater F. S. 
Published: December 2010

AbstractLet f1, . . . , fk be finitely many L1-functions on a measurable set E, and let d and r be numbers such that ∫E, fj, — d > r > 0 for all j. Then there is a measurable subset S of E such that ∫s fj = r for all j.
A Local Ergodic Theorem for Multiparameter Superadditive Processes
Authors: Sato Ryotaro 
Published: December 2010

AbstractIn this paper a local ergodic theorem is proved for positive (multiparameter) superadditive processes with respect to (multiparameter) semiflows of nonsingular point transformations on a a-finite measure space. The theorem obtained here generalizes Akcoglu-Krengel's [2] local ergodic theorem for superadditive processes with respect to semiflows of measure preserving transformations. The proof is a refinement of Akcoglu-Krengel's argument in [2]. Also, ideas of Feyel [3] and the author [4], [5] are used.
Relations Between the Genera and Between the Hasse-Witt Invariants of Galois Coverings of Curves
Authors: Kani Ernst 
Published: December 2010

AbstractLet G ⊂ Aut (C) be a (finite) group of automorphisms of a curve C defined over a field K and, for each subgroup H ≤ G, let gH denote the genus of the quotient curve CH = C/H (briefly: quotient genus of H).In this paper we show that certain idempotent relations in the rational group ring [G] imply relations between the quotient genera {gH}H=G this generalizes two theorems of Accola. Moreover, we show that in the case of char (K) = p ≠ 0, a similar statement holds for the Hasse-Witt invariants σH of the curves CH
Which Rationals are Ratios of Pisot Sequences?
Authors: Boyd David 
Published: December 2010

AbstractA Pisot sequence is a sequence of integers defined recursively by the formula - . If 0 < a0 < a1 then an+1/an converges to a limit θ. We ask whether any rational p/q other than an integer can ever occur as such a limit. For p/q > q/2, the answer is no. However, if p/q < q/2 then the question is shown to be equivalent to a stopping time problem related to the notorious 3x + 1 problem and to a question of Mahler concerning the powers of 3/2. Although some interesting statistical properties of these stopping time problems can be established, we are forced to conclude that the question raised in the title of this paper is perhaps more intractable than it might appear.
The Cohomology of the Units in Certain Zp-Extensions
Authors: Kisilevsky H. 
Published: December 2010

AbstractFor K/k a Zp-extension with Galois group Γ Iwasawa in [4], poses the question of determining the cohomology groups Hn (Γ, E) of the unit group E of K. In this article we compute the cohomology of the units (up to finite groups) for a certain class of Zp-extensions.
Products of Elations and Harmonic Homologies
Authors: Ellers Erich W. 
Published: December 2010

AbstractThe projective special linear group PSL(V) is generated by dations. Among all factorizations of p ∈ PSL(V) into dations there will be one (or more) with the least number of factors. We determine this number, i.e. we solve the length problem for the projective special linear group. We solve a similar problem for the projective unimodular group which is generated by harmonic homologies. The projective special linear group and the projective unimodular group are the most important special cases of projective hyperreflection groups. We also solve the length problem for the general case.
Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class
Authors: Johnson Charles R. , Pierce Stephen 
Published: December 2010

AbstractLet T be a linear transformation acting on the space of n x n complex matrices. Let G(k) be the set of all hermitian matrices with k positive and n — k negative eigenvalues. Let T map some indefinite inertia class G(k) onto itself. We classify all such T. The possibilities are congruence, congruence followed by transposition, and, if n = 2k, it is possible that — T can be a congruence or a congruence followed by transposing. In other words, negation is an admissible transformation when n = 2k.
On the Analytic Determination of the Trace Form
Authors: Perlis Robert 
Published: December 2010

AbstractThe Dedekind zeta function of an algebraic number field E determines the rational equivalence class of the trace form of E. The Hasse symbols of the trace form are related to the local Artin root numbers of the zeta function by formulas of Serre and Deligne. This is used to settle the question of which families of complex numbers appear as the local Artin root numbers of a continuous real representation of the absolute Galois group of ℚ.
On the Criteria of D.D. Anderson for Invertible and Flat Ideals
Authors: Dobbs David E. 
Published: December 2010

AbstractLet R be an integral domain. It is proved that if a nonzero ideal I of R can be generated by n < ∞ elements, then I is invertible (i.e., flat) if and only if I(∩ Rai) = ∩ Iai for all { a1, . . ., a n﹜ ⊂ I. The article's main focus is on torsion-free R-modules E which are LCM-stable in the sense that E(Ra ∩ Rb) = Ea ∩ Eb for all a, b ∈ R. By means of linear relations, LCM-stableness is shown to be equivalent to a weak aspect of flatness. Consequently, if each finitely generated ideal of R may be 2-generated, then each LCM-stable R-module is flat. Finally, LCM-stableness of maximal ideals serves to characterize Prüfer domains, Dedekind domains, principal ideal domains, and Bézout domains amongst suitably larger classes of integral domains.
Co-Rank of a Composition Operator
Authors: Harrington David J. 
Published: December 2010

AbstractA composition operator CT on L2(X, Σ,m) is a bounded linear transformation induced by a mapping T : X → X via CTf = f∘ T.If m has no atoms then the co-rank of CT (i.e., dim is either zero or infinite. As a corollary, when m has no atoms, CT is a Fredholm operator iff it is invertible.
An Optimization Problem Related to the Zeta-function
Authors: Guiasu Silviu 
Published: December 2010

AbstractS. Golomb noticed that Riemann's zeta function ζ induces a probability distribution on the positive integers, for any s > 1, and studied some of its properties connected to divisibility. The object of this paper is to show that the probability distribution mentioned above is the unique solution of an entropy-maximization problem.
A Generalization of Smith's Determinant
Authors: McCarthy P. J. 
Published: December 2010

AbstractWe shall evaluate the determinants ofnxnmatrices of the form[f(i,j)],wheref (w, r)is an even function of m (modr).Among the examples of determinants of this kind are H. J. S. Smith's determinant det[(i,j)],where(m, r)is the greatest common divisor ofmandr,and a generalization of Smith's determinant due to T. M. Apostol.
On Complete Intersections Over an Algebraically Non-Closed Field
Authors: Marinari Maria Grazia , Raimondo Mario 
Published: December 2010

AbstractWe give a criterion in order that an affine variety defined over any field has a complete intersection (ci.) embedding into some affine space. Moreover we give an example of a smooth real curve C all of whose embeddings into affine spaces are c.i.; nevertheless it has an embedding into ℝ3 which cannot be realized as a c.i. by polynomials.
Fixed Point Theorems for Proximately Nonexpansive Semigroups
Authors: Kiang Mo Tak , Tan Kok-Keong 
Published: December 2010

AbstractA commutative semigroup G of continuous, selfmappings on (X, d) is called proximately nonexpansive on X if for every x in X and every (β > 0, there is a member g in G such that d(fg(x),fg(y)) ≤ (1 + β) d (x, y) for every f in G and y in X. For a uniformly convex Banach space it is shown that if G is a commutative semigroup of continuous selfmappings on X which is proximately nonexpansive, then a common fixed point exists if there is an x0 in X such that its orbit G(x0) is bounded. Furthermore, the asymptotic center of G(x0) is such a common fixed point.
Groups Admitting only Finitely Many Nilpotent Ring Structures
Authors: Feigelstock Shalom 
Published: December 2010

AbstractThe abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.
Remarks on the Intersection of Finitely Generated Subgroups of a Free Group
Authors: Burns R. G. , Imrich Wilfried , Servatius Brigitte 
Published: December 2010

AbstractThe first result gives a (modest) improvement of the best general bound known to date for the rank of the intersectionU ∩ Vof two finite-rank subgroups of a free groupFin terms of the ranks ofUandV. In the second result it is deduced from that bound that ifAis a finite-rank subgroup ofFandB < Fis non-cyclic, then the index ofA ∩ BinB, if finite, is less than 2(rank(A) - 1), whence in particular if rank (A) = 2, thenB ≤ A. (This strengthens a lemma of Gersten.) Finally a short proof is given of Stallings' result that ifU, V(as above) are such thatU ∩ Vhas finite index in bothUandV, then it has finite index in their join 〈U, V〉.
The Nilpotency Class Of The p-Sylow Subgroups of GL(n, q) Where (p, q) = 1
Authors: Bialostocki Arie 
Published: December 2010

AbstractFormulae for the nilpotency class of the p-sylow subgroups of GL(n, q) where (p, q) = 1 are derived. These formulae are used in author's following paper: “On the other pα qβ theorem of Burnside”.
Lattice Partitions with a Straight Line
Authors: Brownrigg D. R. K. 
Published: December 2010

AbstractIn [1], the solution of a problem of distinct digital filter enumeration was expressed in terms of enumerating partitions of a rectangular set of lattice points with a straight line, under certain restrictions. Here, firstly, an explicit expression is derived for the number of such partitions in that and a more general case. Secondly, the asymptotic ratio of partitions to square of lattice dimensions is derived for a square lattice.
A Method for Constructing Square Roots in Finite Full Transformation Semigroups
Authors: Higgins Peter M. 
Published: December 2010

AbstractLet Tn denote the full transformation semigroup on the set X = {1,2,. . .,n}, that is the set of all mappings from X to X, the semigroup operation being composition of mappings. The aim of this paper is to provide a method for the construction of all square roots of an arbitrary element α ∈ Tn, by employing a representation of the members of Tn as special directed graphs.
Generalized Solutions of Autonomous Algebraic Differential Equations
Authors: Rubel Lee A. 
Published: December 2010

AbstractIn an earlier paper, the author introduced the notions of N-solutions and IN-solutions of algebraic differential equations (ADE's). Here it is shown, in contradistinction to the situation for Cn solutions, that every N-solution of an ADE is an N-solution of an autonomous ADE. The corresponding result also holds for IN-solutions.
Homogeneous Bundles and Universal Potentials
Authors: Fegan H. D. 
Published: December 2010

AbstractThis paper studies complex potentials on homogeneous bundles over a compact Lie group. It extends the previous work of V. Guillemin and A. Uribe on potentials isospectral to the zero potential. Then the notion of a universal potential is introduced, that is a potential which acts on sections by a group representation rather than as a scalar. Finally the inverse question of whether the spectral data of a complex potential on all bundles over S2 determines the potential is answered negatively.
The Meet Operator in the Lattice of Group Topologies
Authors: Clark Bradd , Schneider Victor 
Published: December 2010

AbstractIt is well known that the lattice of topologies on a set forms a complete complemented lattice. The set of topologies which make G into a topological group form a complete lattice L(G) which is not a sublattice of the lattice of all topologies on G.Let G be an infinite abelian group. No nontrivial Hausdorff topology in L(G) has a complement in L(G). If τ1 and τ2 are locally compact topologies then τ1Λτ2 is also a locally compact group topology. The situation when G is nonabelian is also considered.
Examples of Factorial Rings in Algebraic Geometry
Authors: Bochnak Jacek , Kucharz Wojciech 
Published: December 2010

AbstractWe show that the ring of complex-valued regular functions on an affine irreducible nonsingular real algebraic variety X is factorial if dim X = 1 or dim X = 2 and X has no compact connected components or X is compact and the second cohomology group of X with integral coefficients vanishes.
SP Transform and Uniform Convergence of Laurent and Power Series
Authors: Settu S.A. 
Published: December 2010

AbstractIf the Laurent seriesis transformed toit is shown that convergence of the former at z = 1 implies the uniform convergence of the latter on a symmetric arc of |z - 1/P| = 1/P - 1 not containing z = 1 and that the uniform convergence of the former over a symmetric arc of |z| = 1 containing z = 1 implies uniform convergence of the latter on the entire circle |z — 1/P| = 1/P — 1.
Intersection of Two Invariant Subspaces
Authors: Nakazi Takahiko 
Published: December 2010

AbstractIt is shown that, if F and G are inner functions, (H2 ⊖ FH2)/(H2 ⊖ FH2) ∩ GH2 is n-dimensional if and only if G is a Blaschke product of degree n. This is an extension of the well known result for the case (H2 ⊖ FH2) ∩ GH2 = {0}.
Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs
Authors: Assani I. 
Published: December 2010

AbstractLet (αn.k) be a sequence of positive numbers. We define a regular sequence (resp. a weakly regular sequence) and then show the existence of a unitary operator (resp. a contraction T) L2[0, 1] → L2[0, 1] and a function f ∊ L2[0, 1] such that the pointwise convergence of the sequence of functions is not satisfied almost surely. As a first corollary the pointwise convergence of the Abel means of a contraction from L2 into L2 does not hold necessarily almost surely. As a second corollary there exists a contraction T for which the means (and powers) of Brunei's operator A do not converge pointwise a.s. We also show that, for P > 1 fixed, there exists a sequence of positive numbers αn.k for which we have the pointwise convergence in LP of the sequence of polynomials where T is a contraction of L1 and Lα. The dominated theorem does not, however, always hold for such LP-contractions.
On GL2 of a Local Ring in Which 2 is Not a Unit
Authors: Mason A. W. 
Published: December 2010

AbstractLet A be a local ring with maximal ideal m, let N(m ) be the order of the residue field A/m and let N be a subgroup of GLn (A) which is normalized by SLn(A). It follows from results of Klingenberg that N is normal in GLn(A) when n ≥ 3 or . Results of Lacroix show that this is also true when n = 2 and N(m) = 3, provided that N∩2(A) ≠ SL2(A)'.The principal aim of this paper is to provide examples of non-normal subgroups of GL2(A) which are normalized by SL2(A). In the process we extend results of Lacroix and Levesque on GL2(A)-normalized subgroups of GL2(A), where 2 ∊ m and N(m) > 2.
Uniqueness of Invariant Densities for Certain Random Maps of The Interval
Authors: Boyarsky Abraham 
Published: December 2010

AbstractA random map is a discrete time process in which one of a number of maps, 𝓜, is chosen at random at each stage and applied. In this note we study a random map, where 𝓜 is a set of piecewise linear Markov maps on [0, 1]. Sufficient conditions are presented which allow the determination of the unique absolutely continuous invariant measure of the process.
A Note on M-Summands in Dual Spaces
Authors: Feeman Timothy 
Published: December 2010

AbstractA theorem concerning M-summands in dual spaces is used to prove that certain known M-ideals are not M-summands. In some cases where this information was already known, our procedure greatly simplifies the earlier proofs. Finally, we give a condition to determine which M-ideals in dual spaces are M-summands and which are not.
Empty Simplices in Euclidean Space
Authors: Bárány Imre , Füredi Zoltán 
Published: December 2010

AbstractLet P - {p1,p2,. . . ,pn} be an independent point-set in ℝd (i.e., there are no d + 1 on a hyperplane). A simplex determined by d + 1 different points of P is called empty if it contains no point of P in its interior. Denote the number of empty simplices in P by fd(P). Katchalski and Meir pointed out that . Here a random construction Pn is given with , where K(d) is a constant depending only on d. Several related questions are investigated.
Projections in Spaces of Bimeasures
Authors: Graham Colin C. , Bertram M. Schreiber  
Published: December 2010

AbstractLet X and Y be metrizable compact spaces and μ and v be nonzero continuous measures on X and Y, respectively. Then there is no bounded operator from the space of bimeasures BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1 (μ X v); in particular, if X and Fare nondiscrete locally compact groups, then there is no bounded projection from BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1(X X Y).
Recouvrements Ponctuellements Dénombrables
par des Ensembles Négligeables
Authors: Burke Maxim R. 
Published: December 2010

RésuméNous allons démontrer la consistance avec la théorie des ensembles ZFC de l'existence d'un recouvrement de R par une collection d'ensembles négligeables, telle que pour tout est mesurable.
On an Extremal Problem Involving Harmonic Functions
Authors: Georg Schmidt E. J. P. 
Published: December 2010

AbstractGiven a domain D in R” and two specified points P0 and P1 in D we consider the problem of minimizing u(p1) over all functions harmonic in D with values between 0 and 1 normalised by the requirement u(P0) = 1/2. We show that when D is suitably regular the problem has a unique solution u* which necessarily takes on boundary values 0 or 1 almost everywhere on the boundary. In the process we prove that it is possible to separate P0 and P1by a harmonic function whose boundary value is supported in an arbitrary set of positive measure. These results depend on the fact that (under suitable regularity conditions) a harmonic function which vanishes on an open subset of the boundary has a normal derivative which is almost everywhere non-vanishing in that set.
Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations
Authors: Eloe P. W. , Saintignon P. L. 
Published: December 2010

AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.
The Number of Rooted Convex Polyhedra
Authors: Bender Edward A. , Wormald Nicholas C. 
Published: December 2010

AbstractLet pij be the number of rooted convex polyhedra with i + 1 vertices and j + 1 faces. We express pij as a singly indexed summation whose terms decrease geometrically. From this we deduce thatuniformly as max(i, j) → ∞.
Derivations with Invertible Values on a Lie Ideal
Authors: Bergen Jeffrey , Carini L. 
Published: December 2010

AbstractLet R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u ∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0. We also examine for which division rings D, D2 can possess such a derivation and study when this derivation must be inner.
Counterexamples Concerning Support Theorems for Convex Sets in Hilbert Space
Authors: Phelps R. R. 
Published: December 2010

AbstractThe Bishop-Phelps theorem guarantees the existence of support points and support functionals for a nonempty closed convex subset of a Banach space; equivalently, it guarantees the existence of subdifferentials and points of subdifferentiability of a proper lower semicontinuous convex function on a Banach space. In this note we show that most of these results cannot be extended to pairs of convex sets or functions, even in Hilbert space. For instance, two proper lower semicontinuous convex functions need not have a common point of subdifferentiability nor need they have a subdifferential in common. Negative answers are also obtained to certain questions concerning density of support points for the closed sum of two convex subsets of Hilbert space.
Reduced Sobolev Inequalities
Authors: Adams R. A. 
Published: December 2010

AbstractThe Sobolev inequality of ordermasserts that ifp≧ 1,mp<nand1/q = 1/p — m/n,then the Lq-norm of a smooth function with compact support in Rnis bounded by a constant times the sum of theLp-norms of the partial derivatives of ordermof that function. In this paper we show that that sum may be reduced to include only the completely mixed partial derivatives or orderm,and in some circumstances even fewer partial derivatives.
The Focal Locus of a Riemannian 4-Symmetric Space
Authors: Alfredo Jimenez J. 
Published: December 2010

Abstractcompact Riemannian 4-symmetric space M can be regarded as a fibre bundle over a Riemannian 2-symmetric space with totally geodesic fibres isometric to a 2-symmetric space. Here the result of R. Crittenden for conjugate and cut points in a 2-symmetric space is extended to the focal points of the fibres of M. Also the restriction of the exponential map of M up to the first focal locus in the normal bundle of a fibre is proved to yield a covering map onto its image. It is shown that for the noncompact dual M*, the fibres have no focal points and hence the exponential map of M* restricted to the normal bundle of a fibre is a covering map. The classification of the compact simply connected 4-symmetric spaces G/L with G classical simple provides a large class of examples of these fibrations.
Local Connectedness of the stone-Čech Compactification
Authors: Baboolal D. 
Published: December 2010

AbstractA uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage V ⊂ U such that V[x] is connected for each x ∈ X. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.
Derivations on a Lie Ideal
Authors: Mauceri Silvana , Misso Paola 
Published: December 2010

AbstractIn this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.
Indecomposable Positive Maps in Matrix Algebras
Authors: Tanahashi Kôtarô , Tomiyama Jun 
Published: December 2010

AbstractWe prove that Choi's map in M3 cannot be written as the sum of a 2-positive map and a 2-copositive map. We also provide other examples of positive maps in Mn which cannot be written as the sum of an n-positive map and a 2-copositive map.
A New Proof of a Watson's Formula
Authors: Stempak Krzysztof 
Published: December 2010

AbstractA new proof of a product formula for Laguerre polynomials, due originally to Watson, is given. Considering the commutative Banach algebra of radial functions on the Heisenberg groups Hn, n ≧ 2, we observe that Watson's formula holds for z = 1,2, 3, …. Then, applying a complex function theory argument, we establish the validity of this formula for other complex values of z, i.e. for Re z > - 1/2.