finite dimensional vertex algebra modules over fixed point commutative subalgebras abstract let a be a connected commutative c algebra with derivation d g a finite linear automorphism group of a which preserves d and r a g the fixed point subalgebra of a under the action of g we show that if a is generated by a single element as an r algebra and is a galois extension over r in the sense of m auslander and o goldman then every finite dimensional indecomposable vertex algebra r module has a structure of twisted vertex algebra a module

finite dimensional vertex algebra modules over fixed point differential subfields abstract let k be a differential field over c with derivation d g a finite linear automorphism group over k which preserves d and k g the fixed point subfield of k under the action of g we show that every finite dimensional vertex algebra k g module is contained in some twisted vertex algebra k module

from stochastic partial difference equations to stochastic cellular automata through the ultra discretization we derive stochastic cellular automata with finite range interactions from stochastic partial difference equations through the ultra discrete limit a typical example for stochastic cellular automata is the domany kinzel model which is equivalent to mixed site bond oriented percolation as a special case

error estimates in the numerical evaluation of some bem singular integrals in some applications of galerkin boundary element methods one has to compute integrals which after proper normalization are of the form b 2 x y dxdy a 1 x y y where a b 1 1 or a b a 1 or a b 1 b and f x y is a smooth function in this paper we derive error estimates for a numerical approach recently proposed to evaluate the above integral when a p or h p formulation of a galerkin method is used this approach suggests approximating the inner integral by a quadrature formula of interpolatory type that exactly integrates the cauchy kernel and the outer integral by a rule which takes into account the log endpoint singularities of its integrand some numerical examples are also given

on the convergence of product formulas for the evaluation of certain two dimensional cauchy principal value integrals on etablit la convergence des regles de produits de type interpolatoire pour l evaluation numerique de certaines integrales bidimensionnelles a valeur principale de cauchy on obtient quelques estimations du reste pour plusieurs classes de fonctions

quantum operators in classical probability theory iv quasi duality and thinnings of interacting particle systems duality has proved to be a powerful technique in the study of interacting particle systems ips this concept can be enlarged and a quasi duality defined between various pairs of ips previously thought unrelated consequently theorems of a similar style to those involving duality can be deduced the concept of quasi duality follows naturally from our previous studies into the use ofsingle site operators an idea borrowed from quantum physics in paper ii of this series it is shown that a necessary condition for quasi duality is that the eigenvalues of the corresponding two site infinitesimal generators be the same and using this observation a number of quasi dual pairs have been found and studied it is further shown that if two different ips share a common dual then one can be considered as a thinning of the other

on the convergence of an interpolatory product rule for evaluating cauchy principal value integrals etablissement des theoremes de convergence des regles de produits interpolatoires pour l evaluation d integrales singulieres de cauchy avec estimation asymptotique du reste amelioration et generalisation de resultats anterieurs

the geometry of a parameter space of interacting particle systems we study a four parameter family of interacting particle systems containing the basic voter model and contact processes two processes in this family are related by duality or thinning if and only if their parameters belong to the same orbit of a certain one dimensional group of linear mappings this shows that many duals exist

approximation of the hilbert transform on the real line using hermite zeros the authors study the hilbert transform on the real line they introduce some polynomial approximations and some algorithms for its numerical evaluation error estimates in uniform norm are given

convergence of rules based on nodal splines for the numerical evaluation of certain 2d cauchy principal value integrals abstract we consider interpolatory type integration rules for the numerical approximation of certain 2d cauchy principal value integrals based on tensor product of nodal splines we present convergence results which generalize those known in one dimensional case

numerical evaluation of two dimensional cauchy principal value integrals a twelve point cubature formula has been constructed for the numerical evaluation of two dimensional real cauchy principal value cpv integrals some particular cases of this rule have been discussed and the truncation error associated with the rules have been analysed

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

associated generalized jacobi functions and polynomials abstract pointwise estimates are obtained for associated functions and polynomials corresponding to generalized jacobi weights these estimates hold uniformly in the interval of orthogonality

on the convergence of product formulas for the numerical evaluation of derivatives of cauchy principal value integrals product rules of interpolatory type on the zeros of generalized smooth jacobi polynomials for the numerical approximation of cauchy principal value integrals and their derivatives are considered convergence results for these rules are given and some estimates of the remainder are established in relation to the regularity of the density function

spline approximation for cauchy principal value integrals abstract in this paper we prove the uniform convergence of some quadrature formulas based on spline approximation for cauchy principal value integrals of the type f b a w x f k x x y d x k 0 1 and we present some numerical applications in particular we apply our rules to the well known prandtl s integral equation

a new algorithm for cauchy principal value and hadamard finite part integrals an algorithm for the approximate evaluation of integrals defined by cauchy principal value or by hadamard finite part has been proposed the convergence of the procedure is proved the stability of the algorithm is considered and some numerical examples are given

finite dimensional modules for the polynomial ring in one variable as a vertex algebra abstract a commutative associative algebra a over c with a derivation is one of the simplest examples of a vertex algebra however the differences between the modules for vertex algebra a and the modules for associative algebra a are not well understood in this paper i give the classification of finite dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over c as a vertex algebra

properties of interpolatory product integration rules this paper is concerned with the approximate evaluation of int 1 1 k x f x d x where k is lebesgue integrable and f is at least riemann integrable and preferably smooth the integral is approximated by a rule of the form sum nolimits i 1 n w ni k f x ni where the points x ni are chosen in some prescribed way and the weights w ni k are such that the rule is exact if f is any polynomial of degree n for suitable choices of the points and suitable functions k the rule is shown to converge to the exact integral and the companion rule sum w ni k f x ni to int k x f x dx for all riemann integrable functions f the companion property ensures for example that the weights have the asymptotic positivity property if k is positive error bounds are given that guarantee rapid convergence of the rule if f is smooth finally by establishing a connection with mean convergence of lagrangian interpolation some negative theorems are proved in pa

on the weights of certain quadratures for the numerical evaluation of cauchy principal value integrals and their derivatives we consider interpolatory quadrature rules of the type begin gathered frac d k d lambda k int limits 1 1 1 x alpha 1 x beta frac f x x lambda dx sum limits i 1 n w ni k lambda f x ni r n k f hfill k 0 1 alpha beta 0 hfill end gathered where the nodes x ni are the zeros of the jacobi polynomialp n x in particular we prove that sum limits i 1 n left w ni k lambda right o n k log n uniformly in 1 e 1 e furthermore we show that whenk 1 f x c p 1 1 p 1 andf p x h 1 1 0 1 we have r n 1 f o n p mu 1 delta 0 small as we like uniformly in 1 e 1 e

rates of convergence of gaussian quadrature for singular integrands the authors obtain the rates of convergence or divergence of gaussian quadrature on functions with an algebraic or logarithmic singularity inside or at an endpoint of the interval of integration a typical result is the following for a bounded smooth weight function on 1 1 the error in n point gaussian quadrature of f x ix y1 1 is o n 2 28 if y 1 and o n if y e 1 1 provided we avoid the singularity if we ignore the singularityy the error is o n1 23 log n 8 loglog n 8t 1 for almost all choices of y these assertions are sharp with respect to order

on the uniform convergence of gaussian quadrature rules for cauchy principal value integrals and their derivatives the convergence of the aforementioned quadrature rules for integrands possessing h6lder continuous derivatives of an appropriate order is proved to be uniform and not only pointwise the rate of convergence is also established and an application to the numerical solution of singular integral equations is made

numerical evaluation of hypersingular integrals abstract boundary integral equations which employ integrals which exist only if defined in the cauchy principal value sense or as the hadamard finite part are currently used with success to solve many two and three dimensional problems of applied mechanics we will recall definitions and main properties of these integrals examine some numerical approaches for their evaluation and present several new results

a sinc quadrature rule for hadamard finite part integrals a sinc quadrature rule is presented for the evaluation of hadamard finite part integrals of analytic functions integration over a general are in the complex plane is considered special treatment is given to integrals over the interval 1 1 theoretical error estimates are derived and numerical examples are included

the use of spline on spline for the approximation of cauchy principal value integrals in this paper the spline on spline interpolatory polynomials are used to approximate cauchy principal value integrals and their derivatives this technique yields better results than using the derivatives of the traditional single spline functions which has been considered by orsi improved order of convergence for these approximations are discussed

on the evaluation of certain two dimensional singular integrals with cauchy kernels in this paper we consider product formulas of interpolatory type for the two dimensional cauchy principal value integral i f eta 1 eta 2 int limits 1 1 int limits 1 1 omega x y frac f x y x eta 1 y eta 2 dxdy where 1 2 1 1 x y 1 x 2 y and 1 x and 2 x are two absolutely integrable weight functions the integral is approximated by f n m f eta 1 eta 2 sum limits i 0 n sum limits j 0 m a i 1 eta 1 a j 2 eta 2 f x i y i where the nodes x i and y j are the zeros of the chebyshev polynomials of the first kind commonly named classical abscissas or the clenshaw points often called practical abscissas we present convergence results for these rules

error expansion of trapezoidal rule for certain two dimensional cauchy principal value integrals abstract in this article we discuss the classical composite trapezoidal rule for the computation of two dimensional singular integrals the purpose is to obtain the convergence results o h 2 which is the same as the riemann integral convergence rate at certain points of the classical composite trapezoidal rule with the error functional of trapezoidal rule for computing two dimensional singular integrals we get the superconvergence phenomenon when the special function in error functional is equal to zero at last some numerical examples are reported to illustrate our theoretical analysis which agree with it very well

self duality for multi state probabilistic cellular automata with finite range interactions in this paper we study a criterion of self duality for multi state probabilistic cellular automata with finite range interactions and give some models which satisfy this criterion

convergence of product formulas for the numerical evaluation of certain two dimensional cauchy principal value integrals we consider product rules of interpolatory type for the numerical approximation of certain two dimensional cauchy principal value integrals we present convergence results which generalize those known in the one dimensional case

the convergence of several algorithms for solving integral equations with finite part integrals ii we establish the uniform convergence and obtain convergence rates for several algorithms for solving a class of hadamard singular integral equations these results improve on the mean square convergence shown in 2

interlacing properties of the zeros of the orthogonal polynomials and approximation of the hilbert transform abstract in this paper starting from interlacing properties of the zeros of the orthogonal polynomials the authors propose a new method to approximate the finite hilbert transform for this method they give error estimates in uniform norm

spline product quadrature rules for cauchy singular integrals abstract in this paper product quadrature rules based on cubic spline interpolation are obtained for the numerical evaluation of cauchy singular integrals and an error bound is proposed some numerical examples that test the performance of the rules are given

mean convergence of hermite fejer interpolation abstract weighted l p convergence of hermite fejer interpolation based on the zeros of generalized jacobi polynomials is investigated the main result of the paper gives necessary and sufficient conditions for such convergence for all continuous functions

quantum operators in classical probability theory ii the concept of duality in interacting particle systems duality has proved to be a powerful tool in the theory of interacting particle systems the approach in this paper is algebraic rather than via harris diagrams a form of duality is found which includes coalescing and annihilating duality as special cases this enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived

the numerical evaluation of a 2 d cauchy principal value integral arising in boundary integral equation methods in this paper we consider the problem of computing 2 d cauchy principal value integrals of the form

on the convergence of interpolatory type quadrature rules for evaluating cauchy integrals the aim of this work is to analyse the stability and the convergence for the quadrature rule of interpolatory type based on the trigonometric approximation for the discretization of the cauchy principal value integrals 11 f t d we prove that the quadrature rule has almost optimal stability property behaving in the form o logn 1 sin2x x cos t using this result we show that the rule has an exponential convergence rate when the function f is differentiable enough when f possesses continuous derivatives up to order p 0 and the derivative f p t satisfies holder continuity of order we can also prove that the rule has the convergence rate of the form o a b log n n2 np p where is as small as we like a and b are constants depending only on x

representations of vertex operator algebra v l for rank one lattice l we classify the irreducible modules for the fixed point vertex operator subalgebra v l of the vertex operator algebra v l associated to a positive definite even lattice of rank 1 under the automorphism lifted from the 1 isometry of l

error expansion of piecewise constant interpolation rule for certain two dimensional cauchy principal value integrals the classical composite rectangle midpoint rule for the computation of two dimensional singular integrals is discussed with the error functional of rectangle rule for computing two dimensional singular integrals the local coordinate of certain point and the convergence results o h2 are obtained when the local coordinate is coincided with certain priori known coordinates we get the convergence rate the same as the riemann integral at certain point at last numerical examples are presented to illustrate our theoretical analysis which agree with it very well

invariant measures and decay of correlations for a class of ergodic probabilistic cellular automata we give new sufficient ergodicity conditions for two state probabilistic cellular automata pca of any dimension and any radius the proof of this result is based on an extended version of the duality concept under these assumptions in the one dimensional case we study some properties of the unique invariant measure and show that it is shift mixing also the decay of correlation is studied in detail in this sense the extended concept of duality gives exponential decay of correlation and allows to compute explicitly all the constants involved

approximation of the hilbert transform on the real semiaxis using laguerre zeros the authors propose two new algorithms for the computation of cauchy principal value integrals on the real semiaxis the proposed quadrature rules use zeros of laguerre polynomials theoretical error estimates are proved and some numerical examples are showed