bluuebunny/crossref_metadata_2025 huggingface dataset:
The Failure of Cancellation Laws for Equidecomposability Types
Authors: Truss J. K.
Published: December 2010

Let B be a Boolean algebra and G a group of automorphisms of B. Define an equivalence relation ∼ on B by letting x ∼ y if there are x1, x2,…,xn, y1, y2, …yn in B such that x is the disjoint union of the xi, y is the disjoint union of the yi, and for each i there is a member of G taking xi to yi. The equivalence classes under ∼ are called equidecomposability types. Addition of equidecomposability types is given by (x) + (y) = (x V y) provided x ∧ y = 0. An example is given of a complete Boolean algebra B and a group G of automorphisms of B with X, Y ∊ B such that (X) + (X) = (Y) + (Y) but (X) ≠ (Y), answering a question of Wagon (see [5 p. 231 problem 14]). Moreover B may be taken to be the algebra of Borel subsets of Cantor space modulo sets of the first category. It is also remarked that in this case equidecomposability types do not form a weak cardinal algebra.
Commuting Dilations and Uniform Algebras
Authors: Nakazi Takahiko
Published: December 2010

Let X be a compact Hausdorff space, let C(X) be the algebra of complex-valued continuous functions on X, and let A be a uniform algebra on X. Fix a nonzero complex homomorphism τ on A and a representing measure m for τ on X. The abstract Hardy space Hp = Hp(m), 1 ≤ p ≤ ∞, determined by A is defined to the closure of Lp = Lp(m) when p is finite and to be the weak*-closure of A in L∞ = L∞(m) p = ∞.
Stochastic Fubini Theorem for Semimartingales in Hilbert Space
Authors: León Jorge A.
Published: December 2010

In this paper we will study the Fubini theorem for stochastic integrals with respect to semimartingales in Hilbert space.

Let (Ω, , P) he a probability space, (X, , μ) a measure space, H and G two Hilbert spaces, L(H, G) the space of bounded linear operators from H into G, Z an H-valued semimartingale relative to a given filtration, and φ: X × R+ × Ω → L(H, G) a function such that for each t ∈ R+ the iterated integrals are well-defined (the integrals with respect to μ are Bochner integrals). It is often necessary to have sufficient conditions for the process Y1 to be a version of the process Y2 (e.g. [1], proof of Theorem 2.11).
More on the Waiting Time Till Each of Some Given Patterns Occurs as a Run
Authors: Móri Tamás F.
Published: December 2010

Let H be a finite set; we can suppose H = { 1, 2, …,d } . Consider Hn, the set of length n words over the alphabet H. For every A ∈ Hn define the waiting time for A as the number of experiments needed till A appears as a connected sub-sequence of random elements of H. Formally, let X1, X2,... be i. i. d. random variables, P(X1 = i) = d−1, 1 ≤ i ≤ d then
The Pseudo-Orbit Shadowing Property for Markov Operators in the Space of Probability Density Functions
Authors: Boyarsky Abraham , Góra Pawel
Published: December 2010

Let X be a space with two metrics d1 and d2. Let S :(X, d1) → (X, d2) be continuous. We say S has the generalized pseudoorbit shadowing property with respect to the metrics d1 and d2 if for every every δ-pseudo-orbit in d1 can be ∊-shadowed by a true orbit in d2, i.e., if {x0, x1,…} satisfies for all i ≧ 0, then for all i ≧ 0. The main result of this note shows that certain Markov operators P : L1→ L1 have the generalized shadowing property on weakly compact subsets of the space of probability density functions, where d1 is the metric of norm convergence and d2 is the metric of weak convergence. An important class of such operators are the Frobenius-Perron operators induced by certain expanding and nonexpanding maps on the interval. When there is exponential convergence of the iterates to the density, we can express δ in terms of ∊. We also show that, unlike the situation in the space X itself, the generalized shadowing property is valid for all parameters in families of maps and that there is stability of the shadowing property.
A Mean Ergodic Theorem for Multiparameter Superadditive Processes on Banach Lattices
Authors: Lee Felix
Published: December 2010

LetEbe a Banach Lattice. We will considerEto be weakly sequentially complete and to have a weak unitu. Thus we may representEas a lattice of real valued functions defined on a measure space (χ,,μ). There is a setR⊂χsuch thatRsupports a maximal invariant functionΦfor a postive contractionTonE[5]. LetN=χ—Rbe the complement ofR. Akcoglu and Sucheston showed thatwhereE+is the positive cone ofE. If in addition a monotone condition (UMB) is satisfied, then the same authors showed [4] thatconverges in norm.
Free Objects in Certain Varieties of Inverse Semigroups
Authors: Margolis S. W. , Meakin J. C. , Stephen J. B.
Published: December 2010

In this paper it is shown how the graphical methods developed by Stephen for analyzing inverse semigroup presentations may be used to study varieties of inverse semigroups. In particular, these methods may be used to solve the word problem for the free objects in the variety of inverse semigroups generated by the five-element combinatorial Brandt semigroup and in the variety of inverse semigroups determined by laws of the formxn=xn+ 1. Covering space methods are used to study the free objects in a variety of the form∨whereis a variety of inverse semigroups andis the variety of groups.
Butler Modules Over Valuation Domains
Authors: Fuchs L. , Monari-Martinez E.
Published: December 2010

Let R be a commutative domain with 1, Q its field of quotients, and M a torsion-free R module. By a balanced submodule of M is meant an RD-submodule N [i.e. rN = N ∩ rM for each r ∈ R] such that, for every R-submodule J of Q, every homomorphism η : J → M/N can be lifted to a homomorphism χ:J → M. This definition extends the notion of balancedness as introduced in abelian groups (see e.g. [10, p. 113]). The balanced-projective R-modules can be characterized as summands of completely decomposable R-modules (i.e. summands of direct sums of submodules of Q). If R is a valuation domain, then such summands are again completely decomposable; see [12, p. 275].
One-Parameter Automorphism Groups of the Injective Factor of Type II1 With Connes Spectrum Zero
Authors: Kawahigashi Yasuyuki
Published: December 2010

We construct a one-parameter automorphism group of the injective type II1 factor with Connes spectrum ﹛0﹜ which is not stably conjugate to an infinite tensor product action. We construct a countable family of one-parameter automorphism groups of the injective type II1 factor such that all are stably conjugate but no two are cocycle conjugate.
Group Rings With Hypercentral Unit Groups
Authors: Riley David M.
Published: December 2010

Let KG be the group ring of a group G over a field K and let U(KG) be its group of units. If K has characteristic p > 0 and G contains p-elements, then it is proved that U(KG) is hypercentral if and only if G is nilpotent and G′ is a finite p-group.
Minimal and Maximal Operator Theory With Applications
Authors: Wong M. W.
Published: December 2010

LetXbe a complex Banach space andAa linear operator fromXintoXwith dense domain. We construct the minimal and maximal operators of the operatorAand prove that they are equal under reasonable hypotheses on the spaceXand operatorA. As an application, we obtain the existence and regularity of weak solutions of linear equations on the spaceX. As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.
Pairwise Balanced Designs with Block Sizes Three and Four
Authors: Colbourn Charles J. , Rosa Alexander , Stinson Douglas R.
Published: December 2010

Given integers ν, a and b, when does a pairwise balanced design on ν elements with a triples and b quadruples exist? Necessary conditions are developed, and shown to be sufficient for all v ≥ 96. An extensive set of constructions for pairwise balanced designs is used to obtain the result.
Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators
Authors: Droste M. , Holland W. C. , Macpherson H. D.
Published: December 2010

A partially ordered set (T, ≤) is called a tree if it is semilinearly ordered, i.e. any two elements have a common lower bound but no two incomparable elements have a common upper bound, and contains an infinite chain and at least two incomparable elements. Let k ∈ ℕ. We say that a partially ordered set (T, ≤) is k-homogeneous, if each isomorphism between two k-element subsets of T extends to an automorphism of (T, ≤), and weakly k-transitive, if for any two k-element subchains of T there exists an automorphism of (T, ≤) taking one to the other.
Periods and the Asymptotics of a Diophantine Problem II
Authors: Lichtin Ben
Published: December 2010

Let P(z1,…, zn) be a polynomial with positive coefficients. For positive x define A classical diophantine problem is to describe the asymptotic behavior of N1(x) as x → ∞. More generally, one can introduce a second polynomial φ satisfying the condition (0.1) Sign φ (m) is constant for all m outside at most a finite subset of ℕn.
Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2
Authors: Michler G. O. , Olsson J. B.
Published: December 2010

In his fundamental paper [1] J. L. Alperin introduced the idea of a weight in modular representation theory of finite groups G. Let p be a prime. A p-subgroup R is called a radical subgroup of G if R = Op(NG(R)). An irreducible character φ of NG(R) is called a weight character if φ is trivial on R and belongs to a p-block of defect zero of NG(R)/R. The G-conjugacy class of the pair (R, φ) is a weight of G. Let b be the p-block of NG(R) containing φ, and let B be p-block of G. A weight (R, φ) is a B-weight for the block B of G if B = bG, which means that B and b correspond under the Brauer homomorphism. Alperin's conjecture on weights asserts that the number l*(B) of B-weights of a p-block B of a finite group G equals the number l(B) of modular characters of B.
Nongaussian Limit Distributions of Lacunary Trigonometric Series
Authors: Berkes I.
Published: December 2010

It is a well known fact that for rapidly increasing nkthe sequence , behaves like a sequence of independent random variables; in particular has a limiting Gaussian distribution as N → ∞. Under a certain critical speed this result breaks down and becomes strongly dependent. The purpose of this paper is to investigate the asymptotic behavior of normed sums in the strongly dependent domain; specifically, we construct a large class of nongaussian limit distributions of such sums.
Fluctuations Pour Des Équations De Boltzmann Scalaires
Authors: Ferland René
Published: December 2010

Kac [22] a montré, pour sa caricature d'un gaz de Boltzmann, que la solution de l'équation de Boltzmann généralisée correspondante peut être obtenue comme limite d'une suite de lois empiriques induites par des processus markoviens . Pour un entier n donné, le processus (Xn(t))t≥0 décrit le comportement d'un gaz à n molécules où des collisions binaires ont lieu à des instants imprévisibles. Ce processus est gouverné par un générateur Gn qui est défini à l'aide de l'opérateur de collision apparaissant dans la version de Kac de l'équation de Boltzmann.
Existence de Solutions au Sens de Carathéodory Pour le Problème de Neumann y″ = f(t, y, y′)
Authors: Guennoun Zine E. A.
Published: December 2010

We announce some existence results and their consequences for the Neumann problem of the nonlinear differential equation: where f: [0, 1] x ℝ2 → ℝ is a Carathéodory function and can grow very rapidly in the y′ variable.
Gaussian and Non–Gaussian Distribution–Valued Ornstein–Uhlenbeck Processes
Authors: Bojdecki Tomasz , Gorostiza Luis G.
Published: December 2010

Generalized (distribution-valued) Ornstein-Uhlenbeck processes, which by definition are solutions of generalized Langevin equations, arise in many investigations on fluctuation limits of particle systems (eg. Bojdecki and Gorostiza [1], Dawson, Fleischmann and Gorostiza [5], Fernández [7], Gorostiza [8,9], Holley and Stroock [10], Itô [12], Kallianpur and Pérez-Abreu [16], Kallianpur and Wolpert [14], Kotelenez [17], Martin-Löf [19], Mitoma [22], Uchiyama [25]). The state space for such a process is the strong dual Φ′ of a nuclear space Φ. A generalized Langevin equation for a Φ′-valued process X ≡ {Xt} is a stochastic evolution equation of the form

where {At} is a family of linear operators on Φ and Z ≡ {Zt} is a Φ'-valued semimartingale (in some sense) with independent increments. Equations of the type (1.1) where Z does not have independent increments also arise in applications (eg. [9,14,20]) but here we are interested precisely in the case when Z has independent increments (we restrict the term generalized Langevin equation to this case in accordance with the classical Langevin equation).
Inflection Points of Bessel Functions of Negative Order
Authors: Lorch Lee , Muldoon Martin E. , Szego Peter
Published: December 2010

We consider the positive zeros j″vk, k = 1, 2,…, of the second derivative of the Bessel function Jν(x). We are interested first in how many zeros there are on the interval (0,jν1), where jν1 is the smallest positive zero of Jν(x). We show that there exists a number ƛ = —0.19937078… such that and . Moreover, j″v1 decreases to 0 and j″ν2 increases to j″01 as ν increases from ƛ to 0. Further, j″vk increases in —1 < ν< ∞, for k = 3,4,… Monotonicity properties are established also for ordinates, and the slopes at the ordinates, of the points of inflection when — 1 < ν < 0.
Coloring Ordered Sets to Avoid Monochromatic Maximal Chains
Authors: Duffus D. , Rodl V. , Sauer N. , R. Woodrow
Published: December 2010

This paper is devoted to settling the following problem on (infinite, partially) ordered sets: Is there always a partition (2-coloring) of an ordered set X so that all nontrivial maximal chains of X meet both classes (receive both colors)? We show this is true for all countable ordered sets and provide counterexamples of cardinality N3. Variants of the problem are also considered and open problems specified.
Group C*-Algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold
Authors: Sunada Toshikazu
Published: December 2010

The spectrum of the Laplacian or more generally of a Schrödinger operator on an open manifold may have possibly a complicated aspect. For example, a Cantor set in the real axis may appear as the spectrum even for an innocent looking potential on a standard Riemannian manifold (see J. Moser [10]). The fundamental result of the spectral theory of periodic Schrödinger operators, however, says that the picture of the spectrum of a Schrödinger operator on ℝn with a periodic potential is simple; indeed the spectrum consists of a series of closed intervals of the real axis without accumulation, separated in general by gaps outside the spectrum (see M. Reed and B. Simon [13] or M. M. Skriganov [15] for instance).
The Structure of the Sequence Spaces of Maddox
Authors: Karl-Goswin  , Grosse-Erdmann
Published: December 2010

The sequence of spaces of Maddox, c0(p), c(p)and l∞(p), are investigated. Here, p — (pk) is a bounded sequence of strictly positive numbers. It is observed that C0(P) is an echelon space of order 0 and that l∞(p) is a co-echelon space of order ∞, while clearly c(p) = c0(p) ⊗ 〈 (1,1,1,…) 〉. This sheds a new light on the topological and sequence space structure of these spaces: Based on the highly developed theory of (co-) echelon spaces all known and various new structural properties are derived.
Extreme and Exposed Points in Orlicz Spaces
Authors: Grzaślewicz R. , Hudzik H. , Kurc W.
Published: December 2010

Extreme points of the unit sphere in any Orlicz space over a measure space that contains no atoms of infinite measure are characterized. In the case of a finite-valued Orlicz function and a nonatomic measure space, exposed points of the unit sphere in these spaces are characterized too. Some corollaries and examples are also given.
Lie Ideals and Central Identities With Derivation
Authors: Lanski Charles
Published: December 2010

In this paper we consider various degree two central polynomials with derivation, holding for Lie ideals in prime rings. The results give substantial generalizations of the existing ones on central and semi-centralizing derivations, and show essentially that there are no central identities of the form p(x,y) = c1xyD + C2XDy + c3yxD + C4yDx, where D is a nonzero derivation of the prime ring R.
The Heat Equation on the Spaces of Positive Definite Matrices
Authors: Sawyer P.
Published: December 2010

The main topic of this paper is the study of the fundamental solution of the heat equation for the symmetric spaces of positive definite matrices, Pos(n,R).

Our first step is to develop a “False Abel Inverse Transform” which transforms functions of compact support on an euclidean space into integrable functions on the symmetric space. The transform is shown to satisfy the relation is the usual Laplacian with a constant drift).

Using this transform, we find explicit formulas for the heat kernel in the cases n = 2 and n = 3. These formulas allow us to give the asymptotic development for the heat kernel as t tends to infinity. Finally, we give an upper and lower bound of the same type for the heat kernel.
Extreme Points of Positive Functionals and Spectral States on Real Banach Algebras
Authors: Srivastav Anand
Published: December 2010

Extreme points of positive functionals and spectral states on real commutative Banach algebras are investigated and characterized as multiplicative functionals extending the well-known results from complex to real Banach algebras. As an application a new and short proof of the existence of the Shilov boundary of a real commutative Banach algebra with nonempty maximal ideal space is given.
An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
Authors: Swarttouw René F.
Published: December 2010

In this paper a q-analogue of Gegenbauer's addition formula for Bessel functions is obtained by using the orthogonality relation for the q-Ultraspherical polynomials of Rogers'. Also some product formulas and an integral representation for the Hahn-Exton q-Bessel functions are obtained.
Bruhat Order and Transfer for Complex Reductive Groups
Authors: Andler Martin
Published: December 2010

Let G be a complex reductive group, and G^ its set of irreducible admissible representations. The Bruhat order on G^ is defined in a natural way. We prove that this Bruhat order is preserved by transfer. This gives new proofs of some results by the author on L-functions.
Frames with Block Size Four
Authors: Rees Rolf S. , Stinson Douglas R.
Published: December 2010

We investigate the spectrum for frames with block size four, and discuss
several applications to the construction of other combinatorial designs.

Our main result is that a frame of type hu, having blocks of size four, exists if and
only if u ≥ 5, h ≡ 0 mod 3 and h(u — 1) ≡ 0 mod 4, except possibly where

(i)

h = 9 and u ∈ ﹛13,17,29,33,93,113,133,153,173,193﹜;

(ii)

h ≡ 0 mod 12 and u ∈ ﹛8,12﹜,

h = 36 and u ∈ ﹛7,18,23,28,33,38,43,48﹜,

h = 24 or 120 and u ∈ ﹛7﹜,

h = 72 and u ∈ 2Z+ U ﹛n : n ≡ 3 mod4 and n ≤527﹜ U ﹛563﹜; or

(iii)

h ≡ 6mod l2 and u ∈ (﹛17,29,33,563﹜ U ﹛n : n ≡ 3 or 11 mod 12 and
n ≤ 527﹜ U ﹛n : n ≡ 7 mod 12 and n ≤ 259﹜), h = 18.

Additionally, we give a new recursive construction for resolvable group-divisible designs from frames: if there is a resolvable k-GDD of type gu, a k-frame of type ﹛mg)v where u ≥ m + 1, and a resolvable TD(k, mv) then there is a resolvable k-GDD of type (mg)uv. We use this to construct some new resolvable GDDs with group size three and block size four.
Combinatorial Local Planarity and the Width of Graph Embeddings
Authors: Mohar Bojan
Published: December 2010

Let G be a graph embedded in a closed surface. The embedding is “locally planar” if for each face, a “large” neighbourhood of this face is simply connected. This notion is formalized, following [RV], by introducing the width ρ(ψ) of the embedding ψ. It is shown that embeddings with ρ(ψ) ≥ 3 behave very much like the embeddings of planar graphs in the 2-sphere. Another notion, “combinatorial local planarity”, is introduced. The criterion is independent of embeddings of the graph, but it guarantees that a given cycle in a graph G must be contractible in any minimal genus embedding of G (either orientable, or non-orientable). It generalizes the width introduced before. As application, short proofs of some important recently discovered results about embeddings of graphs are given and generalized or improved. Uniqueness and switching equivalence of graphs embedded in a fixed surface are also considered.
Oscillations in Higher-Order Neutral Differential Equations
Authors: Philos CH. G. , Purnaras I. K. , Sficas Y. G.
Published: December 2010

Consider the n-th order (n ≥ 1 ) neutral differential equation where σ1 < σ 2 < ∞ and μ and η are increasing real-valued functions on [Ƭ1, Ƭ2] and [σ1, σ2] respectively. The function μ is assumed to be not constant on [Ƭ1, Ƭ2] and [Ƭ1, Ƭ2] for every Ƭ ∈ (Ƭ1, Ƭ2) similarly, for each σ ∈ (σ1, σ2), it is supposed that r\ is not constant on [σ1 , σ] and [σ, σ2]. Under some mild restrictions on Ƭ1,- and σ1, (ι = 1,2), it is proved that all solutions of (E) are oscillatory if and only if the characteristic equation of (E) has no real roots.
Curvature Pinching Based on Integral Norms of the Curvature
Authors: Lovrić Miroslav
Published: December 2010

A compact Riemannian manifold (M, g) of dimension 3 or higher admits a metric of constant (positive or negative) sectional curvature if the following conditions hold: the diameter is bounded from above, the part of the Ricci curvature which lies below some fixed negative number is bounded in LP norm for p > n/2, and the metric is almost spherical or almost hyperbolic in the LP sense. The idea of the proof is to obtain stronger (i.e. L∞) pinching by deforming the initial metric using the Ricci flow, thus reducing the problem to the theorems of Gromov in the case rg < 0 and of Grove, Karcher and Ruh in the case rg > 0. The reduced curvature tensor changes along the flow according to the heat equation, which implies a weak nonlinear parabolic inequality for its norm. The iteration method of De Giorgi, Nash and Moser is applied to obtain the estimate for the maximum norm of the reduced curvature tensor. The crucial step in the iteration consists of controlling the Sobolev constant of the appropriate imbedding (which also changes along the flow, but behaves well) by the isoperimetric constant, which, in turn, can be bounded in terms independent of the particular manifold.
Cubic Analogues of the Jacobian Theta Function θ(z, q)
Authors: Hirschhorn Michael , Garvan Frank , Borwein Jon
Published: December 2010

There are three modular forms a(q), b(q), c(q) involved in the parametrization of the hypergeometric function analogous to the classical θ2(q), θ3(q), θ4(q) and the hypergeometric function We give elliptic function generalizations of a(q), b(q), c(q) analogous to the classical theta-function θ(z, q). A number of identities are proved. The proofs are self-contained, relying on nothing more than the Jacobi triple product identity
Commutativity Preserving Mappings of Von Neumann Algebras
Authors: Brešar Matej , Robert Miers C.
Published: December 2010

A map θ: M —> N where M and N are rings is said to preserve commutativity in both directions if the elements a,b ∊ M commute if and only if θ(a) and θ(b) commute. In this paper we show that if M and N are von Neumann algebras with no central summands of type I1 or I2 and θ is a bijective additive map which preserves commutativity in both directions then θ(x) = cφ(x) +f(x) where c is an invertible element in ZN, the center of N, φ M —> N is a Jordan isomorphism of M onto N, and f is an additive map of M into ZN.
Degenerate Cases of Uniform Approximation by Solutions of Systems with Surjective Symbols
Authors: Gauthier P. M. , Tarkhanov N. N.
Published: December 2010

We prove that each (vector-valued) function in Sobolev space on a compact set K, which in the interior K0 of K satisfies a system of differential equations, can be approximated by solutions in a neighbourhood of K plus sums of potentials of measures supported on the boundary of K. We discuss the particular case where, for all compact sets K, one can dispense with potentials in such approximations
Quantizations of the Module of Tensor Fields Over the Witt Algebra
Authors: Liu Ke-Qin
Published: December 2010

After introducing the q-analogue of the enveloping algebra of the Witt algebra, we construct q-analogues of the module of tensor fields over the Witt algebra and prove a partial q-analogue of Kaplansky's Theorem concerning this module of tensor fields.
Propagation Of Singularities for Semilinear Hyperbolic Equations
Authors: Liu Linqi
Published: December 2010

In this paper we use a particular kind of weighted Sobolev space and pseudo-differential operators to study H3s propagation of singularities for the solution u ∊ Hs of the equations with second order.
Projective and Injective Hopf Algebras Over the Dyer-Lashof Algebra
Authors: Goerss Paul G.
Published: December 2010

The purpose of this paper is to discuss the existence, structure, and properties of certain projective and injective Hopf algebras in the category of Hopf algebras that support the structure one expects on the homology of an infinite loop space. As an auxiliary project, we show that these projective and injective Hopf algebras can be realized as the homology of infinite loop spaces associated to spectra obtained from Brown-Gitler spectra by Spanier-Whitehead duality and Brown-Comenetz duality, respectively. We concentrate mainly on indecomposable projectives and injectives, and we work only at the prime 2.
Sensitivity and Controllability of Systems Governed by Integral Equations Via Proximal Analysis
Authors: Yezza A.
Published: December 2010

In this paper, we are concerned with the basic problem defined in [9]. Formulas for δV(0)and δ∞V(0),respectively the generalized and asymptotic gradient of the value function at zero, corresponding to an L2 -additive perturbation of dynamics are given. Under the normality condition, δV(0)turns out to be a compact subset of L2, formed entirely of arcs, and V is locally finite and Lipschitz at 0. Moreover, estimations of the generalized directional derivative and Dini's derivative of V at 0 are derived. Supplementary conditions imply that Dini's derivative of V at 0 exists, and V is actually strictly differentiate at this point.
A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
Authors: Mueller C.
Published: December 2010

We give a modulus of continuity for solutions of the wave equation with a noise term:

utt = Δu + a(u) + b(u)G, x ∈ ℝ3

where G is a Gaussian noise. This case is more difficult than in lower dimensions because the fundamental solution of the wave equation is singular.
Cohomology of Quantum Groups: the Quantum Dimension
Authors: Parshall Brian , Wang Jian-Pan
Published: December 2010

This paper uses the notion of the quantum dimension to obtain new results on the cohomology and representation theory of quantum groups at a root of unity. In particular, we consider the elementary theory of support varieties for quantum groups.
Distance Matrices and Ridge Function Interpolation
Authors: Reid Les , Sun Xingping
Published: December 2010

A geometric characterization is given for a collection of points in ℝd to produce a singular l1 -distance matrix. Some quantitative results are established in terms of "characteristic matrices". The results in this paper generalize those of Dyn, Light and Cheney and have application to ridge function interpolation.
Circulant Graphs and 4-Ranks of Ideal Class Groups
Authors: Hurrelbrink Jurgen
Published: December 2010

This is about results on certain regular graphs that yield information about the structure of the ideal class group of quadratic number fields associated with these graphs. Some of the results can be formulated in terms of the quadratic forms x2+ 27y2, x2+ 32y2, x2+ 64y2.
The Spectrum of Orthogonal Steiner Triple Systems
Authors: Colbourn Charles J. , Gibbons Peter B. , Mathon Rudolf , Mullin Ronald C. , Rosa Alexander
Published: December 2010

Two Steiner triple systems (V, 𝓑) and (V, 𝓓) are orthogonal if they have no triples in common, and if for every two distinct intersecting triples {x,y,z} and {x, y, z} of 𝓑, the two triples {x,y,a} and {u, v, b} in (𝓓 satisfy a ≠ b. It is shown here that if v ≡ 1,3 (mod 6), v ≥ 7 and v ≠ 9, a pair of orthogonal Steiner triple systems of order v exist. This settles completely the question of their existence posed by O'Shaughnessy in 1968.
Unipotent Orbital Integrals of Hecke Functions for GL(n)
Authors: Herb Rebecca A.
Published: December 2010

Let G = GL(n, F) where F is a p-adic field, and let 𝓗(G) denote the Hecke algebra of spherical functions on G. Let u1,..., up denote a complete set of representatives for the unipotent conjugacy classes in G. For each 1 ≤ i ≤ p, let μi be the linear functional on such that μi(f) is the orbital integral of f over the orbit of ui. Waldspurger proved that the μi, 1 ≤ i ≤ p, are linearly independent. In this paper we give an elementary proof of Waldspurger's theorem which provides concrete information about the Hecke functions needed to separate orbits. We also prove a twisted version of Waldspurger's theorem and discuss the consequences for SL(n, F).
Multiparameter Weighted Ergodic Theorems
Authors: Jones Roger L. , Olsen James
Published: December 2010

In this paper we show that multi-dimensional bounded Besicovitch weights are good weights for the pointwise ergodic theorem for Dunford-Schwartz operators and positively dominated contractions of LP. This in particular implies new weighted results for multi-parameter measure preserving point transformations. The proofs show that Besicovitch weights are a very natural class when considered from the operator point of view. We also show that for 1 ≤ r < ∞, the r-bounded Besicovitch classes are all the same, generalizing a result of Bellow and Losert.
New Tauberian Theorems from Old
Authors: Parameswaran Mangalam R.
Published: December 2010

A new and very general and simple, yet powerful approach is introduced for obtaining new Tauberian theorems for a summability method V from known Tauberian conditions for V, where V is merely assumed to be linear and conservative. The technique yields the known theorems on the weakening of Tauberian conditions due to Meyer-König and Tietz and others and also improves many of them. Several new results are also obtained, even for classical methods of summability, including analogues of Tauber's second theorem for the Borel and logarithmic methods. The approach yields also new Tauberian conditions for the passage from summability by a method V to summability by a method V', as well as to more general methods of summability like absolute summability or summability in abstract spaces; the present paper however confines itself to ordinary summability.
When is a Distribution of Signs Locally Completable?
Authors: Acquistapace F. , Broglia F. , Fortuna E.
Published: December 2010

Let V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.
Real Projective Representations of SNand AN
Authors: Huang John Q.
Published: December 2010

Three main results are obtained in this paper: one generalizes the Atiyah-Bott-Shapiro periodicity equivalence on the category of real Clifford modules, (Theorem 2.2); another establishes the existence of two algebras for real projective representations of the symmetric groupSnand the alternating groupAn, (Theorem 3.2) and determines their structure, (Theorem 6.1); the third describes all the real projective representations ofSnandAnexcept for some small numbersn, (Theorem 7.2).
Conjugacy Classes of Maximal Tori in Simple Real Algebraic Groups and Applications
Authors: Doković Dragomir Ž. , Thăńg Nguyêñ Quôć
Published: December 2010

Let G be an almost simple complex algebraic group defined over R, and let G(R) be the group of real points of G. We enumerate the G(R)-conjugacy classes of maximal R-tori of G. Each of these conjugacy classes is also a single G(R)˚-conjugacy class, where G(R)˚ is the identity component of G(R), viewed as a real Lie group. As a consequence we also obtain a new and short proof of the Kostant-Sugiura's theorem on conjugacy classes of Cartan subalgebras in simple real Lie algebras.

A connected real Lie group P is said to be weakly exponential (w.e.) if the image of its exponential map is dense in P. This concept was introduced in [HM] where also the question of identifying all w.e. almost simple real Lie groups was raised. By using a theorem of A. Borel and our classification of maximal R-tori we answer the above question when P is of the form G(R)˚.
Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution
Authors: Drensky Vesselin , Giambruno Antonio
Published: December 2010

Let M2(K, *) be the algebra of 2 × 2 matrices with involution over a field K of characteristic 0. We obtain the exact values of the cocharacters, codimensions and Hilbert series of the *-T-ideal of the polynomial identities for M2(K, *).
Homomorphisms on Function Algebras
Authors: Garrido M. I. , Gómez Gil J. , Jaramillo J. A.
Published: December 2010

Let A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-analytic functions, or Cm-functions) on a Banach space, we provide a positive answer for a wide class of spaces, including separable spaces and super-reflexive spaces (with nonmeasurable cardinal).
Formulas for Brown-Peterson Operations
Authors: Li Zaiqing
Published: December 2010

We introduce a new method to calculate compositions of Brown-Peterson operations. We derive a formula for rn1 and a formula for commutators.
Representations of Quantum Heisenberg Algebras
Authors: Fabbri Marc A. , Okoh Frank
Published: December 2010

A Lie algebra is called a Heisenberg algebra if its centre coincides with its derived algebra and is one-dimensional. When is infinite-dimensional, Kac, Kazhdan, Lepowsky, and Wilson have proved that -modules that satisfy certain conditions are direct sums of a canonical irreducible submodule. This is an algebraic analogue of the Stone-von Neumann theorem. In this paper, we extract quantum Heisenberg algebras, q(), from the quantum affine algebras whose vertex representations were constructed by Frenkel and Jing. We introduce the canonical irreducible q()-module Mq and a class Cq of q()-modules that are shown to have the Stone-von Neumann property. The only restriction we place on the complex number q is that it is not a square root of 1. If q1 and q2 are not roots of unity, or are both primitive m-th roots of unity, we construct an explicit isomorphism between q1() and q2(). If q1 is a primitive m-th root of unity, m odd, q2 a primitive 2m-th or a primitive 4m-th root of unity, we also construct an explicit isomorphism between q1() and q2().
The Stability Theorems for Subgroups of and
Authors: Lari-Lavassani Ali , Lu Yung-Chen
Published: December 2010

In singularity theory, J. Damon gave elegant versions of the unfolding
and determinacy theorems for geometric subgroups of . and . In this work, we propose a unified treatment of the smooth stability of germs and the structural stability of versai unfoldings for a large class of such subgroups.
The Structure of C*-Convex Sets
Authors: Morenz Phillip B.
Published: December 2010

Compact C*-convex subsets of Mn correspond exactly to n-th matrix ranges of operators. The main result of this paper is to discover the “right” analog of linear extreme points, called structural elements, and then to prove a generalised Krein-Milman theorem for C*-convex subsets of Mn. The relationship between structural elements and an earlier attempted generalisation, called C*-extreme points, is examined,
solving affirmatively a conjecture of Loebl and Paulsen [8]. An improved bound for a C* -convex version of the Caratheodory theorem for convex sets is also given.
Algebraic Cycles in Families of Abelian Varieties
Authors: Abdulali Salman
Published: December 2010

If the Hodge *-operator on the L2-cohomology of Kuga
fiber varieties is algebraic, then the Hodge conjecture is true for all abelian
varieties.
Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules
Authors: Brown Lawrence G. , Mingo James A. , Shen Nien-Tsu
Published: December 2010

This paper considers Hilbert C*-bimodules, a
slight generalization of imprimitivity bimodules which were introduced by Rieffel
[20]. Brown, Green, and Rieffel [7] showed that every imprimitivity bimodule X can
be embedded into a certain C*-algebra L, called the
linking algebra of X. We consider arbitrary embeddings of Hilbert
C*-bimodules into
C*-algebras; i.e. we describe the relative position of
two arbitrary hereditary C*-algebras of a
C*-algebra, in an analogy with Dixmier's description
[10] of the relative position of two subspaces of a Hilbert space.

The main result of this paper (Theorem 4.3) is taken from the doctoral
dissertation of the third author [22], although the proof here follows a different
approach. In Section 1 we set out the definitions and basic properties (mostly
folklore) of Hilbert C*-bimodules. In Section 2 we show
how every quasi-multiplier gives rise to an embedding of a bimodule. In Section 3
we show that , the enveloping
C*-algebra of the
C*-algebraA with its product perturbed by a positive
quasi-multiplier , is isomorphic to
the closure (Proposition 3.1).
Section 4 contains the main theorem (4.3), and in Section 5 we explain the analogy
with the relative position of two subspaces of a Hilbert spaces and present some
complements.
The Königsberg Bridge Problem for Peano Continua
Authors: Bula W. , Nikiel J. , Tymchatyn E. D.
Published: December 2010

Peano continua which are images of the unit interval [0,1] or the circle
S under a continuous and irreducible map are
investigated. Necessary conditions for a space to be the irreducible image of
[0,1] are given, and it is conjectured that these conditions are sufficient as
well. Also, various results on irreducible images of [0,1] and
S are given within some classes of regular curves.
Some of them involve inverse limits of inverse sequences of Euler graphs with
monotone bonding maps.
Asymptotics of the Exit Distribution for Markov Jump Processes; Application to
Atm
Authors: Iscoe I. , Mcdonald D. , Qian K.
Published: December 2010

We approximate the exit distribution of a Markov jump process into a set of
forbidden states and we apply these general results
to an ATM multiplexor. In this case the forbidden
states represent an overloaded multiplexor. Statistics for this overload or busy
period are difficult to obtain since this is such a rare event. Starting from the
approximate exit distribution, one may simulate the busy period without wasting
simulation time waiting for the overload to occur.
Geometric Characterization of Interpolating Varieties for the (FN)-Space A0p of Entire Functions
Authors: Berenstein Carlos A. , Li Bao Qin , Vidras Alekos
Published: December 2010

A necessary and sufficient geometric characterization and a necessary and sufficient analytic characterization of interpolating varieties for the space of entire functions will be obtained in the paper, which as an application will also give a generalization of the well-known Pólya-Levinson density theorem.
Restricted Lie Algebras and Their Envelopes
Authors: Riley D. M. , Shalev A.
Published: December 2010

Let L be a restricted Lie algebra over a field of characteristic p. Denote by u(L) its restricted enveloping algebra and by ωu(L) the augmentation ideal of u(L). We give an explicit description for the dimension subalgebras of L, namely those ideals of L defined by Dn(L) - L∩ωu(L)n for each n ≥ 1. Using this expression we describe the nilpotence index of ωU(L). We also give a precise characterisation of those L for which ωu(L) is a residually nilpotent ideal. In this case we show that the minimal number of elements required to generate an arbitrary ideal of u(L) is finitely bounded if and only if L contains a 1-generated restricted subalgebra of finite codimension. Subsequently we examine certain analogous aspects of the Lie structure of u(L). In particular we characterise L for which u(L) is residually nilpotent when considered as a Lie algebra, and give a formula for the Lie nilpotence index of u(L). This formula is then used to describe the nilpotence class of the group of units of u(L).
Topological Properties of the Set of Norm-Attaining Linear Functionals
Authors: Debs Gabriel , Godefroy Gilles , Raymond Jean Saint
Published: December 2010

If X is a separable non-reflexive Banach space, then the set NA of all norm-attaining elements of X* is not a w*-Gδ subset of X*. However if the norm of X is locally uniformly rotund, then the set of norm attaining elements of norm one is w*-Gδ. There exist separable spaces such that NA is a norm-Borel set of arbitrarily high class. If X is separable and non-reflexive, there exists an equivalent Gâteaux-smooth norm on X such that the set of all Gâteaux-derivatives is not norm-Borel.
Reducibility for Non-Connected p-Adic Groups, With G° Of Prime Index
Authors: Goldberg David
Published: December 2010

We determine the structure of representations induced from discrete series of parabolic subgroups of quasi-split p-adic groups G with G/G° a cyclic group of prime order. We attach to each such representation an R-group which extends the definition of the Knapp-Stein R-group. We show that this R-group has the properties predicted by Arthur. We apply our results to the case of Orthogonal groups.
Fixed Points of Automorphisms of Free Pro-p Groups of Rank 2
Authors: Herfort Wolfgang N. , Ribes Luis , Zalesskii Pavel A.
Published: December 2010

Let p be a prime number, and let F be a free pro-p group of rank two. Consider an automorphism α of F of finite order m, and let FixF(α) = {x ∈ F | α(x) = x} be the subgroup of F consisting of the elements fixed by α. It is known that if m is prime to p and α = idF, then the rank of FixF(α) is infinite. In this paper we show that if m is a finite power pr of p, the rank of FixF(α) is at most 2. We conjecture that if the rank of F is n and the order of a is a power of α, then rank (FixF(α)) ≤ n.
Analytic Range Functions of Several Variables
Authors: Cheng R.
Published: December 2010

Let C be a separable Hilbert Space, and let Λ be the halfplane {(m, n) ∈ Ζ2 : m ≥ 1} ∪ {(0, n) ∈ Ζ2 : n ≥ 0} of the integer lattice. Consider the subspace ℳc(Λ) of on the torus spanned by the C-valued trigonometric functions {Ceims+int : с ∈ C, (m, n) ∈ Λ}. The notion of a Λ-analytic operator on ℳc(Λ) is defined with respect to the family of shift operators {Smn}Λ on ℳC(Λ) given by (Smnƒ)(eis, eit) = eims+intƒ(eis, eit). The corresponding concepts of inner function, outer function and analytic range function are explored. These ideas are applied to the spectral factorization problem in prediction theory.
Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory
Authors: Hwangk Yoon Sung , Jacob Bill
Published: December 2010

Let F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.
Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices
Authors: Moody R. V. , Patera J.
Published: December 2010

We give a uniform description, in terms of Coxeter diagrams, of the Voronoi domains of the root and weight lattices of any semisimple Lie algebra. This description provides a classification not only of all the facets of these Voronoi domains but simultaneously a classification of their dual or Delaunay cells and their facets. It is based on a much more general theory that we develop here providing the same sort of information in the setting of chamber geometries defined by arbitrary reflection groups. These generalized kaleidoscopes include the classical spherical, Euclidean, and hyperbolic kaleidoscopes as special cases. We prove that under certain conditions the Delaunay cells are Voronoi cells for the vertices of the Voronoi complex. This leads to the description in terms of Wythoff polytopes of the Voronoi cells of the weight lattices.
On the Existence and the Classification of Critical Points for Non-Smooth Functionals
Authors: Fang G.
Published: December 2010

We extend the min-max methods used in the critical point theory of differentiable functionals on smooth manifolds to the case of continuous functionals on a complete metric space. We study the topological properties of the min-max generated critical points in this new setting by adopting the methodology developed by Ghoussoub in the smooth case. Many old and new results are extended and unified and some applications are given.
Markov Processes Associated With Positivity Preserving Coercive Forms
Authors: Ma Zhi-Ming , Röckner Michael
Published: December 2010

Coercive closed forms on L2-spaces are studied whose associated L2-semigroups are positivity preserving. Earlier work by other authors is extended by further developing the potential theory of such forms and completed by proving an analytic characterization of those of these forms which have a probabilistic counterpart, i.e., are associated with (special standard) Markov processes. Examples with finite and infinite dimensional state spaces are discussed.
Cliques of Irreducible Representations, Quotient Groups, and Brauer's Theorems on Blocks
Authors: Ellers Harald
Published: December 2010

Assumekis an algebraically closed field of characteristicpandGis a finite group. IfPis ap-subgroup ofGsuch thatG=PCG(P), and ifHis a normal subgroup ofGwithP≤H, then the number ofH-cliques of irreduciblek[G]-modules is the same as the number ofH/P-cliques of irreduciblek[G/P]-modules.
Consistency of Moment Systems
Authors: Lewis A. S.
Published: December 2010

An important question in the study of moment problems is to determine when a fixed point in ℝn lies in the moment cone of vectors , with μ a nonnegative measure. In associated optimization problems it is also important to be able to distinguish between the interior and boundary of the moment cone. Recent work of Dachuna-Castelle, Gamboa and Gassiat derived elegant computational characterizations for these problems, and for related questions with an upper bound on μ. Their technique involves a probabilistic interpretation and large deviations theory. In this paper a purely convex analytic approach is used, giving a more direct understanding of the underlying duality, and allowing the relaxation of their assumptions.
Proof, Disproof and Advances Concerning Certain Conjectures on Real Quadratic Fields
Authors: Mollin R. A. , Williams H. C.
Published: December 2010

The purpose of this paper is to address conjectures raised in [2]. We show that one of the conjectures is false and we advance the proof of another by proving it for an infinite set of cases. Furthermore, we give hard evidence as to why the conjecture is true and show what remains to be done to complete the proof. Finally, we prove a conjecture given by S. Louboutin, for Mathematical Reviews, in his discussion of the aforementioned paper.