bluuebunny/crossref_metadata_2025_split huggingface dataset:
Homomorphisms of Lie Algebras of Algebraic Groups and Analytic Groups
Authors: Nahlus Nazih 
Published: December 2010

AbstractLet be a Lie algebra homomorphism from the Lie algebra of G to the Lie algebra of H in the following cases: (i) G and H are irreducible algebraic groups over an algebraically closed field of characteristic 0, or (ii) G and H are linear complex analytic groups. In this paper, we present some equivalent conditions for ϕ to be a differential in the above two cases. That is, ϕ is the differential of a morphism of algebraic groups or analytic groups as appropriate.In the algebraic case, for example, it is shown that ϕ is a differential if and only if ϕ preserves nilpotency, semisimplicity, and integrality of elements. In the analytic case, ϕ is a differential if and only if ϕ maps every integral semisimple element of into an integral semisimple element of , where G0 and H0 are the universal algebraic subgroups of G and H. Via rational elements, we also present some equivalent conditions for ϕ to be a differential up to coverings of G in the algebraic case, and for ϕ to be a differential up to finite coverings of G in the analytic case.
Weak Normalization of Power Series Rings
Authors: Dobbs David E. , Roitman Moshe 
Published: December 2010

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

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

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

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

AbstractLet A be a bounded linear operator on a Hilbert space H. Assume that A is selfadjoint in the indefinite inner product defined by a selfadjoint, bounded, invertible linear operator G on H; [x,y] := (Gx,y). In the first part of the paper we define two orders of neutrality for the pair (G, A) and a connection is made with the "types" of numbers in the point and approximate point spectrum of A. The main results of the paper are in the second part and they deal with strong and uniform definitizability of a bounded selfadjoint operator on a Pontrjagin space. They state:A) Let A be a bounded strongly definitizable operator on a Pontrjagin space ΠK, then A is uniformly definitizable.B) A bounded selfadjoint operator A on a Pontrjagin space ΠK is uniformly definitizable if and only if all the eigenvalues of A are of definite type and all the nonisolated eigenvalues of A are of positive type.Some applications to the theory of linear selfadjoint operator pencils are given.
On the Unicity Conjecture for Markoff Numbers
Authors: Baragar Arthur 
Published: December 2010

AbstractIn 1913 Frobenius conjectured that for any positive integer m, there exists at most one pair of integers (x, y) with 0 ≤ x ≤ y ≤ m such that (x, y, m) is a solution to the Markoff equation: x2 + y2 + m2 = 3xym. We show this is true if either m, 3m — 2 or 3m + 2 is prime, twice a prime or four times a prime.
Division Graded Algebras in the Brauer-Wall Group
Authors: Coghlan Francis , Hoffman Peter 
Published: December 2010

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

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

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

AbstractLet R be a prime ring with involution and d, δ be derivations on R. Suppose that xd(x)—δ(x)x is central for all symmetric x or for all skew x. Then d = δ = 0 unless R is a commutative integral domain or an order of a 4-dimensional central simple algebra.
Slice Maps and Multipliers of Invariant Subspaces
Authors: Nakazi Takahiko 
Published: December 2010

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

AbstractLet h∞(Dn) denote the space of all bounded n-harmonic functions on the unit polydisk Dn of Cn. In this paper we prove that the Bourgain algebra h∞(Dn)b and h∞(Dn)bb relative to the Lebesgue space L∞(Dn) are of the following forms:Here V(Dn) is the space of those functions such that , where denotes the characteristic function of a subset E of Dn.
Conjugacy Separability of Certain Polygonal Products
Authors: Kim Goansu 
Published: December 2010

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

AbstractThe Abbena-Thurston manifold (M,g) is a critical point of the functional where Q is the Ricci operator and R is the scalar curvature, and then the index of I(g) and also the index of — I(g) are positive at (M,g).
The Failure of Approximate Inner Conjugacy for Standard Diagonals in Regular Limit Algebras
Authors: Donsig Allan P. , Power S. C. 
Published: December 2010

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

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

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

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

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

RésuméLet B1 and B2 be the open unit balls of ℂn1 and ℂn2 for the norms ‖. ‖1 and ‖ . ‖2. Let f: B1 → B2 be a holomorphic mapping such that f(0) = 0. It is well known that, for every z ∈ B1, ‖f(z)‖2 ≤ ‖z‖1, and ‖f′(0)‖ ≤ 1.In this paper, I prove the converse of this result. Let f : B1 → B2 be a holomorphic mapping such that f'(0) is an isometry. If B2 is strictly convex, I prove that f(0)=0 and that f is linear. I also define the rank of a point x belonging to the boundary of B1 or B2. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that f(0)=0 and that f'(0) is an isometry is linear.
Polynomials of Quadratic Type Producing Strings of Primes
Authors: Mollin R. A. , Goddard B. , Coupland S. 
Published: December 2010

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

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

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

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

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

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

AbstractIf A is a subring of a commutative ring B and if n is a positive integer, a number of sufficient conditions are given for “A[[X]] is n-root closed in B[[X]]” to be equivalent to “A is n-root closed in B.” In addition, it is shown that if S is a multiplicative submonoid of the positive integers ℙ which is generated by primes, then there exists a one-dimensional quasilocal integral domain A (resp., a von Neumann regular ring A) such that S = {n ∊ ℙ | A is n-root closed} (resp., S = {n ∊ ℙ | A[[X]] is n-root closed}).
A New Cohomological Criterion for the p-Nilpotence of Groups
Authors: Brunetti Maurizio 
Published: December 2010

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

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

AbstractWe study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.
On a Problem of Rubel Concerning the Set of Functions Satisfying All the Algebraic Differential Equations Satisfied by a Given Function
Authors: Shackell John 
Published: December 2010

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

AbstractIt is known that the Toeplitz algebra associated with any flow which is both minimal and uniquely ergodic always has a trivial K1-group. We show in this note that if the unique ergodicity is dropped, then such K1-group can be non-trivial. Therefore, in the general setting of minimal flows, even the K-theoretical index is not sufficient for the classification of Toeplitz operators which are invertible modulo the commutator ideal.
Oscillatory Integrals with Nonhomogeneous Phase Functions Related to Schrödinger Equations
Authors: Kolasa Lawrence A. 
Published: December 2010

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

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

AbstractA closed convex subset of c0 has the fixed point property (fpp) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of c0 are known to have the fpp. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the fpp.
Fermat Jacobians of Prime Degree over Finite Fields
Authors: González Josep 
Published: December 2010

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

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

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

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.
Rings With Comparability
Authors: Ferrero Miguel , Sant’Ana Alveri 
Published: December 2010

AbstractThe class of rings studied in this paper properly contains the class of right distributive rings which have at least one completely prime ideal in the Jacobson radical. Amongst other results we study prime and semiprime ideals, right noetherian rings with comparability and prove a structure theorem for rings with comparability. Several examples are also given.
Commutators and Analytic Dependence of Fourier-Bessel Series on (0, ∞)
Authors: Guadalupe José J. , Pérez Mario , Varona Juan L. 
Published: December 2010

AbstractIn this paper we study the boundedness of the commutators [b, Sn] where b is a BMO function and Sn denotes the n-th partial sum of the Fourier-Bessel series on (0, ∞). Perturbing the measure by exp(2b) we obtain that certain operators related to Sn depend analytically on the functional parameter b.
On Benson’s Definition of Area in Minkowski Space
Authors: Thompson A. C. 
Published: December 2010

AbstractLet (X, ‖ . ‖) be a Minkowski space (finite dimensional Banach space) with unit ball B. Various definitions of surface area are possible in X. Here we explore the one given by Benson [1], [2]. In particular, we show that this definition is convex and give details about the nature of the solution to the isoperimetric problem.
On the Moduli Space of a Spherical Polygonal Linkage
Authors: Kapovich Michael , Millson John J. 
Published: December 2010

AbstractWe give a “wall-crossing” formula for computing the topology of the moduli space of a closed n-gon linkage on 𝕊2. We do this by determining the Morse theory of the function ρn on the moduli space of n-gon linkages which is given by the length of the last side—the length of the last side is allowed to vary, the first (n − 1) side-lengths are fixed. We obtain a Morse function on the (n − 2)-torus with level sets moduli spaces of n-gon linkages. The critical points of ρn are the linkages which are contained in a great circle. We give a formula for the signature of the Hessian of ρn at such a linkage in terms of the number of back-tracks and the winding number. We use our formula to determine the moduli spaces of all regular pentagonal spherical linkages.