Imprimitive Q-polynomial Association Schemes

It is well known that imprimitive P-polynomial association schemes with are either bipartite or antipodal, i.e., intersection numbers satisfy either for all for all . In this paper, we show that imprimitive -polynomial association schemes with are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either .     

On Dirichlet Processes Associated with Second Order Divergence Form Operators

Let be a d - dimensional Markov family corresponding to a uniformly elliptic second order divergence form operator. We show that for any quasi continuous in the Sobolev space the process (X) admits under P ^x a decomposition into a martingale additive functional (AF) M and a continuous AF A of zero quadratic variation for almost every starting point x if q=2, for quasi every x if q>2 and for every if is continuous, d=1 and or d>1 and q>d. Our decomposition enables us to show that in the case of symmetric operator the energy of A equals zero if q=2 and that the decomposition of (X) into the martingale AF M and the AF of zero energy A is strict if for some q>d. Moreover, our decomposition provides a probabilistic representation of A .     

Initial and Internal Limits of Supertemperatures

Let D and E be open subsets of which meet , with E bounded and D, and let . Given a non-negative supertemperature u on D ₊, we express its restriction to E ₊ as the sum of a temperature that vanishes at time 0, and a potential on that vanishes for all negative time. This enables us to use initial limit theorems about such potentials to prove similar results for u.     

Polynômes Harmoniques sur L'Espace du Bruit Blanc

Let denote the space of harmonic polynomial of . We study some properties of on the white noise space. We show that harmonic polynomials are characterized by an invariance property with respect to the S-transform, and that the closure (S)harm of harm in Hida's test-functionnals topology is exactly the kernel of the Gross Laplacian G. Lastly we show that Ker G is strictly contained in the space of functionnals of (S) which remain fixed under S-transform.     

Two New Infinite Families of 3-Designs from Kerdock Codes over Z4

In this paper we show that the support of the codewords of each type in the Kerdock code of length 2^m over Z₄ form 3-designs for any odd integer . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer , whose parameters are ,and .     

On posets with isomorphic interval posets

Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].     

Brownian Martingales and Some New Results on Interpolation of Hardy Spaces

Let H₁( ) be the usual Hardy space on . We show that the couple (H₁( ), L( ) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH₁( ) +L( ) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H₁( ) to L₁( ) and also from L( ) to L( ); (ii) V(Nf)=f, V is similtaneously bounded from L₁( ) to H₁( ) and from L( ) to L( ) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (L_p( ), BMO ( )) for every 1相似文献   

Spin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let and denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of with respect to p. By a hyper-duality of , we mean an automorphism of such that for all ; and is a duality of . is said to be hyper-self-dual whenever there exists a hyper-duality of . We say that is strongly hyper-self-dual whenever there exists a hyper-duality of which can be expressed as conjugation by an invertible element of . We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra.     

Stochastic Partial Differential Equations on Manifolds~II. Nonlinear Filtering

The conditional law of an unobservable component x(t) of a diffusion (x(t),y(t)) given the observations {y(s):s[0,t]} is investigated when x(t) lives on a submanifold of . The existence of the conditional density with respect to a given measure on is shown under fairly general conditions, and the analytical properties of this density are characterized in terms of the Sobolev spaces used in the first part of this series.     

Convex Subgroups of Partially Right-Ordered Groups

We study into the question of whether a partial order can be induced from a partially right-ordered group onto a space of right cosets of w.r.t. some subgroup of . Examples are constructed showing that the condition of being convex for in is insufficient for this. A necessary and sufficient condition (in terms of a subgroup and a positive cone of ) is specified under which an order of can be induced onto . Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups for which is partially ordered for every convex subgroup , and properties of the class of groups such that is partially ordered for every partial right order on and every subgroup that is convex under .     

Path-Integral Calculations for the First Excited State of Hydrogen Atom

Consider a path-integral which is the solution to a diffusion version of the generalized Schro¨dinger's equation . Here , where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process . For and V replaced by one obtains , which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of by generating a large number of trajectories of an ergodic diffusion process.     

Varieties Defined by Permutations

We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form . A criterion is given determining whether a cyclic variety is interpretable in . For a permutation without fixed elements, it is stated that a set of primes for which is interpretable in in the lattice is finite. It is also proved that for distinct primes , the Helly number of a type in coincides with dimension of the dual type and equals .     

K-Theory for the Banach Algebra of Operators on James''s Quasi-reflexive Banach Spaces

We prove that the K-groups of the Banach algebra of bounded, linear operators on the pth James space , where 1 < p < , are given by and . Moreover, for each Banach space and each non-zero, closed ideal contained in the ideal of inessential operators, we show that and . This enables us to calculate the K-groups of for each Banach space which is a direct sum of finitely many James spaces and -spaces.     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

Equational Theories for Classes of Finite Semigroups

It is proved that there exists an infinite sequence of finitely based semigroup varieties such that, for all i, an equational theory for and for the class of all finite semigroups in is undecidable while an equational theory for and for the class of all finite semigroups in is decidable. An infinite sequence of finitely based semigroup varieties is constructed so that, for all i, an equational theory for and for the class of all finite semigroups in is decidable whicle an equational theory for and for the class of all finite semigroups in is not.     

Spectral Properties of Solutions of the Burgers Equation with Small Dissipation

We study the asymptotic behavior as of the Sobolev norm of the solution to the Cauchy problem for the one-dimensional quasilinear Burgers type equation (It is assumed that the problem is , the boundary conditions are periodic, and .) We show that the locally time-averaged Sobolev norms satisfy the estimate . The estimates obtained as a consequence for the Fourier coefficients justify Kolmogorov's spectral theory of turbulence for the case of the Burgers equation.     

Conditions of Local Asymptotic Normality for Gaussian Stationary Processes

Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let be the -algebra induced by the random variables {\bold x}[], D(R¹), and let _t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by (f) the Gaussian measure on generated by {\bold x}. Let _t(f) be the restriction of (f) to _t. Let f and g be nonnegative functions such that the measures _t(f) and _t(g) are absolutely continuous. Put

Capacitary Estimates for Solutions of the Dirichlet Problem for Second Order Elliptic Equations in Divergence Form

We consider the Dirichlet problem for A-harmonic functions, i.e. the solutions of the uniformly elliptic equationdiv( in an n-dimensional domain , n 3. The matrix A is assumed to have bounded measurable entries. We obtain pointwise estimates for the A-harmonic functions near a boundary point. The estimates are in terms of the Wiener capacity and the so called capacitary interior diameter. They imply pointwise estimates for the A-harmonic measure of the domain , which in turn lead to a sufficient condition for the Hölder continuity of A-harmonic functions at a boundary point. The behaviour of A-harmonic functions at infinity and near a singular point is also studied and theorems of Phragmén–Lindelöf type, in which the geometry of the boundary is taken into account, are proved. We also obtain pointwise estimates for the Green function for the operator -div( in a domain and for the solutions of the nonhomogeneous equation -div with measure on the right-hand side.     

λ-Divergence of the Fourier Series of Continuous Functions of Several Variables

In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices for which for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity such that its Fourier series is -divergent everywhere for any .