numerical solution of fractional differential equations with a collocation method based on muntz polynomials this paper presents a computational technique based on the collocation method and muntz polynomials for the solution of fractional differential equations an appropriate representation of the solution via the muntz polynomials reduces its numerical treatment to the solution of a system of algebraic equations the main advantage of the present method is its superior accuracy and exponential convergence consequently one can obtain good results even by using a small number of collocation points the accuracy and performance of the proposed method are examined by means of some numerical experiments

spectral methods for weakly singular volterra integral equations with smooth solutions we propose and analyze a spectral jacobi collocation approximation for the linear volterra integral equations vies of the second kind with weakly singular kernels in this work we consider the case when the underlying solutions of the vies are sufficiently smooth in this case we provide a rigorous error analysis for the proposed method which shows that the numerical errors decay exponentially in the infinity norm and weighted sobolev space norms numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence

schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

ls svr based solving volterra integral equations abstract in this paper a novel hybrid method is presented for solving the second kind linear volterra integral equations due to the powerful regression ability of least squares support vector regression ls svr we approximate the unknown function of integral equations by using ls svr in intervals with known numerical solutions the trapezoid quadrature is used to approximate subsequent integrations in intervals with unknown numerical solutions the feasibility of the proposed method is examined on some integral equations experimental results of comparison with analytic and repeated modified trapezoid quadrature method s solutions show that the proposed algorithm could reach a very high accuracy the proposed algorithm could be a good tool for solving the second kind linear volterra integral equations

on orthonormal muntz laguerre filters when the muntz szasz 1953 condition holds the muntz laguerre filters form a uniformly bounded orthonormal basis in hardy space this has consequences in terms of optimal pole cancellation schemes and it also allows for a generalization of lerch s theorem

on orthogonal polynomials with respect to varying measures on the unit circle let io d i be a system of orthonormal polynomials on the unit circle with respect to d l and yi m dli be a system of orthonormal polynomials on the unit circle with respect to the varying measures d u l iw z 2 z eio where wn z is a sequence of polynomials deg w n whose zeros wn i n lie in izi 1 the asymptotic behavior of the ratio of the two systems on and outside the unit circle is obtained

some mu ntz orthogonal systems abstract let 0 1 be a given sequence of complex numbers such that i 1 and re i j 1 0 for each i and j for muntz polynomials p x i 0npix i and q x j 0mqjx j we define an inner product p q by p q 0 1 p q x d x x 2 where p q x i 0 n j 0 m p i q j x i j we obtain the muntz polynomials qn x orthogonal with respect to this inner product and connect them with the malmquist rational functions w z v 0 n 1 z 1 v v 0 n z v orthogonal on the unit circle with respect to the inner product u v 1 2 i 1 u z v z d z z several interesting properties of polynomials qn x are given

on maximal weight solutions of two matricial moment problems in the nondegenerate case abstract we first revisit the question of existence and uniqueness of maximal weight solutions of the truncated trigonometric matrix moment problem problem ttm in the nondegenerate case the starting point of the consideration is a specialized representation of the matrix weight assigned at each point on the unit circle for the solutions of nondegenerate problem ttm our approach is essentially self contained and different from the existing methods moreover based on this approach we also derive some important weight features of the so called n extremal solutions within the whole solution set of nondegenerate problem ttm and the discrete structure of them in the second part these observations inspire us to look for the corresponding weight features of the solutions of a nondegenerate moment problem for rational matrix valued functions problem r where only the theory of orthogonal matrix polynomials on the unit circle is involved

numerical solution of linear volterra integral equations of the second kind with sharp gradients collocation methods are a well developed approach for the numerical solution of smooth and weakly singular volterra integral equations in this paper we extend these methods through the use of partitioned quadrature based on the qualocation framework to allow the efficient numerical solution of linear scalar volterra integral equations of the second kind with smooth kernels containing sharp gradients in this case the standard collocation methods may lose computational efficiency despite the smoothness of the kernel we illustrate how the qualocation framework can allow one to focus computational effort where necessary through improved quadrature approximations while keeping the solution approximation fixed the computational performance improvement introduced by our new method is examined through several test examples the final example we consider is the original problem that motivated this work the problem of calculating the probability density associated with a continuous time random walk in three dimensions that may be killed at a fixed lattice site to demonstrate how separating the solution approximation from quadrature approximation may improve computational performance we also compare our new method to several existing gregory sinc and global spectral methods where quadrature approximation and solution approximation are coupled

asymptotic behavior of muntz christoffel functions at the endpoints we establish asymptotics for christoffel functions of muntz systems at the endpoints x 0 and x 1 of 0 1 assuming that there exists a r 0 such that the muntz exponents l k satisfy limk l kk r

numerical solution of volterra fredholm integral equations using the collocation method based on a special form of the muntz legendre polynomials abstract this paper presents a computational technique based on a special family of the muntz legendre polynomials to solve a class of volterra fredholm integral equations the relationship between the jacobi polynomials and muntz legendre polynomials in a particular state are expressed the proposed method reduces the integral equation into algebraic equations via the chebyshev gauss lobatto points so that the system matrix coefficients are obtained by the least squares approximation method the useful properties of the jacobi polynomials are exploited to analyze the approximation error the performance and accuracy of our method are examined with some illustrative examples

stability criteria for certain third order delay differential equations in this paper we study the asymptotic stability of the zero solution of third order linear delay differential equations of the form y t p1y t p2y t q1y t q2y t v1y t v2y t where p1 p1 q1 q2 v1 and v2 are certain constants here 0 is a constant delay in proving our results we make use of pontryagin s theory for quasi polynomials

muntz galerkin methods and applications to mixed dirichlet neumann boundary value problems solutions for many problems of interest exhibit singular behaviors at domain corners or points where the boundary condition changes type for these types of problems direct spectral methods with the usual polynomial basis functions do not lead to a satisfactory convergence rate we develop in this paper a muntz galerkin method which is based on specially tuned muntz polynomials to deal with the singular behaviors of the underlying problems by exploring the relations between jacobi polynomials and muntz polynomials we develop efficient implementation procedures for the muntz galerkin method and provide optimal error estimates as an example of applications we consider the poisson equation with mixed dirichlet neumann boundary conditions whose solution behaves like o r 1 2 near the singular point and demonstrate that the muntz galerkin method greatly improves the rates of convergence of the usual spectral method

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

asymptotic and exponential stability of certain third order non linear delayed differential equations frequency domain method we use the frequency domain method to prove that the zero solution of certain third order nonlinear delayed differential equations is asymptotically stable when there is no forcing term we also prove the existence of a bounded solution which is exponentially stable when there is a bounded forcing term the situation for which the non linear term is delayed is also proved

moment problems and orthogonal functions abstract the caratheodory coefficient problem for an infinite sequence c n can be formulated as follows find a caratheodory function f z i e an analytic function mapping the unit disk d z z into the right half plane p w re w 0 whose taylor coefficients at a fixed points in d for convenience the origin are the c n this problem is equivalent to the trigonometric moment problem find a measure on such that e i n d c n for n 0 1 2 these problems are closely related to the theory of szego polynomials i e orthogonal polynomials on the unit circle t z z 1 let n be an arbitrary given sequence of not necessarily distinct points in d and let w n be a given sequence of numbers the nevanlinna pick problem for this situation is to find a caratheodory function f z with the interpolation property f n w n for all n when points n are repeated the interpolation property involves the appropriate number of taylor coefficients also this problem is connected with the problem of finding a measure generating moments the nevanlinna pick problem is related to a theory of rational functions which are orthogonal on t with poles at the points 1 n this relationship is analogous to and generalizes the relationship between the caratheodory coefficient problem or trigonometric moment problem and polynomials orthogonal on t the situation when points n are given on the boundary t or d is also briefly discussed

on the convergence of the rational interpolation approximant of carathe odory functions let zn m nm 1 with zn m 1 n 1 2 be an arbitrary sequence of complex numbers we study the convergence of the rational functionpn 1 qn which interpolates the caratheodory function f z 1 2 2 0u u z d t u eit at zn m 1 zn m nm 1 where d is a finite positive measure on the unit circle we also consider the relations between pn 1 qn and the orthogonal polynomials with respect to varying measures

on the asymptotic stability for nonautonomous functional differential equations by lyapunov functionals sufficient conditions are given for the asymptotic stability and uniform asymptotic stability of the zero solution of the nonautonomous fde s whose right hand sides can be unbounded functions of the time the theorems are based upon lyapunov krasovskii functionals whose derivatives with respect to the equations are negative semidefinite and can vanish at long intervals the functionals and their derivatives are estimated by either x t the norm of the instantaneous value of the solutions or x t 2 the l 2 norm of the phase segment of the solutions examples are given to show that the conditions are sharp and the main theorems with the two different types of estimates are independent and improve earlier results the theorems are applied to linear and nonlinear retarded fde s with one delay and with distributed delays

on the convergence of rational functions orthogonal on the unit circle rational functions orthogonal on the unit circle with prescribed poles are studied we establish some convergence theorems for the orthogonal rational functions we generalize some of the results for szego polynomials to rational orthogonal functions

numerical solution of a class of fractional order integro differential algebraic equations using muntz jacobi tau method abstract this paper presents a spectral tau method based on muntz jacobi basis functions for approximating the solutions of fractional order volterra integro differential algebraic equations we examine the solvability of the considered equation and we show that the exact solutions suffer from a singularity at the origin numerical solvability and convergence analysis of the proposed approximate approach are also studied and the error bounds are obtained in a weighted l 2 norm some illustrative examples are presented to validate the theoretical results

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

szego functions and multipoint pade approximation abstract rational functions analogous to szego polynomials are introduced and their application in multipoint pade approximation is discussed

on the orthogonal rational functions with arbitrary poles and interpolation properties let zn mm 1n with zn m 1 n 1 2 be an arbitrary sequence of complex numbers we generalize the orthogonal rational functions with poles at we study the weak convergence and the interpolation properties of the orthogonal rational functions

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

language based performance prediction for distributed and mobile systems we present a framework for performance prediction of distributed and mobile systems we rely on process calculi and their structural operational semantics the dynamic behaviour is described through transition systems whose transitions are labelled by encodings of their proofs that we then map into stochastic processes we enhance related works by allowing general continuous distributions resorting to a notion of enabling between transitions we also discuss how the number of resources available affects the overall model finally we introduce a notion of bisimulation that takes stochastic information into account and prove it to be a congruence when only exponential distributions are of interest our equivalence induces a lumpable partition on the underlying markov process

orthogonal rational functions with poles on the unit circle let n be a sequence of not necessarily distinct points on the unit circle t z c z 1 set ln span 1 1 1 1 n l n 0ln where we have used the notation n nk 1 z k let m be a positive linear functional defined on the space l l with m r real for functions that are real on t define r s m r z s 1 z for r s l in particular if m is given as m r r ei d for some measure then r s r ei s ei d let the orthogonal system n be obtained from 1 n by orthogonalization three term recurrence relations quadrature formulas moment theory and interpolation properties connected with the functional m and the system n are discussed

favard theorem for reproducing kernels abstract consider for n 0 1 the nested spaces l n of rational functions of degree n at most with given poles 1 i i i 1 n let l 0 l n given a finite positive measure on the unit circle we associate with it an inner product on l by g g d suppose kn z w is the reproducing kernel for l n i e z k n z w w for all l n w then it is known that they satisfy a coupled recurrence relation in this paper we shall prove a favard type theorem which says that if you have a sequence of kernel functions kn z w which are generated by such a recurrence then there will be a measure supported on the unit circle so that kn is the reproducing kernel for ln the measure is unique under certain extra conditions on the points i

numerical solution of nonlinear volterra fredholm hammerstein integral equations via tau collocation method with convergence analysis in this paper we consider the nonlinear volterra fredholm hammerstein integral equations the approximate solution for the nonlinear volterra fredholm hammerstein integral equations is obtained by using the tau collocation method to do this the nonlinear volterra fredholm hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form thus by solving this system unknown coefficients are obtained the spectral rate of convergence for the proposed method is established in the l 2 norm the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the tau collocation method is of high accuracy more convenient and efficient for solving nonlinear volterra fredholm hammerstein integral equations

reversibility in the higher order π calculus the notion of reversible computation is attracting increasing interest because of its applications in diverse fields in particular the study of programming abstractions for reliable systems in this paper we continue the study undertaken by danos and krivine on reversible ccs by defining a reversible higher order calculus called rho we prove that reversibility in our calculus is causally consistent and that the causal information used to support reversibility in rho is consistent with the one used in the causal semantics of the calculus developed by boreale and sangiorgi finally we show that one can faithfully encode rho into a variant of higher order substantially improving on the result we obtained in the conference version of this paper

a causal semantics for ccs via rewriting logic we consider two operational semantics for ccs defined in the literature the first exploits proved transition systems pts and the second rewriting logic rl we show that the interleaving interpretation of both semantics agree in that they define the same transitions and exhibit the same non deterministic structure in addition we study causality in ccs computations we recall its treatment via pts exhibiting the notion of causality presented in the literature and we show how to recast it in the rl semantics via suitable axioms also in this case the two semantics agree

on a class of extremal solutions of a moment problem for rational matrix valued functions in the nondegenerate case ii the main theme of this paper is the discussion of a family of extremal solutions of a finite moment problem for rational matrix functions in the nondegenerate case we will point out that each member of this family is extremal in several directions thereby the investigations below continue the studies in fritzsche et al in press 1 in doing so an application of the theory of orthogonal rational matrix functions with respect to a nonnegative hermitian matrix borel measure on the unit circle is used to get some insights into the structure of the extremal solutions in question in particular we explain characterizations of these solutions in the whole solution set in terms of orthogonal rational matrix functions we will also show that the associated riesz herglotz transform of such a particular solution admits specific representations where orthogonal rational matrix functions are involved

relative growth of linear iterations and orthogonal polynomials on several intervals assume a c2 2 and y0 c2 let yn yn a y0 be defined by thelinear iteration yn ayn 1 n 1 2 then for every p 0 and for every norm in c2 there is a constant c depending only on p and such that sup a 1 y0 0 yl a y0 p lk 0 yk a y0 p cl l 1 2 where a denotes the spectral radius of a applications to orthogonal polynomials pn with respect to a positive borel measure on several intervals are studied in particular the growth of orthogonal polynomials relative to their sums satisfies limn supx supp pn x p n 1k 0 pk x p 0 provided that the three term recurrence coefficients of pn are asymptotically periodic

convergence of orthogonal rational functions outside of the unit circle rational functions orthogonal on the unit circle with prescribed poles lying outside the unit circle are studied we study the asymptotic behaviors for the orthogonal rational functions outside of the unit circle

muntz systems and orthogonal muntz legendre polynomials the muntz legendre polynomials arise by orthogonalizing the muntz system xio x l with respect to lebesgue measure on 0 1 in this paper differential and integral recurrence formulae for the muntz legendre polynomials are obtained interlacing and lexicographical properties of their zeros are studied and the smallest and largest zeros are universally estimated via the zeros of laguerre polynomials the uniform convergence of the christoffel functions is proved equivalent to the nondenseness of the muntz space on 0 1 which implies that in this case the orthogonal muntz legendre polynomials tend to 0 uniformly on closed subintervals of 0 1 some inequalities for muntz polynomials are also investigated most notably a sharp l2 markov inequality is proved

on the stability of solutions of certain fourth order delay differential equations the paper gives sufficient conditions for the asymptotic stability of the zero solutions of systems 1 and 2 by constructing lyapunov functionals we obtained the results in a very simple form

foreword to the proceedings of the orthoquad 2014 conference orthoquad 2014 was an international symposium on orthogonality quadrature and related topics held on january 20 24 2014 in puerto de la cruz tenerife spain it was held in memory of professor pablo gonzalez vera 1955 2012

numerical solution of volterra fredholm integral equations using parameterized pseudospectral integration matrices the main purpose of this work is to provide parameterized pseudospectral integration matrices ppims for solving volterra fredholm integral equations we present an exact efficient and stable approach for computing ppims furthermore we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the jacobi type points in both l and l 2 spaces numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes

stable evaluations of fractional derivative of the muntz legendre polynomials and application to fractional differential equations abstract the aim of this paper is to present efficient and stable methods to compute caputo fractional derivative cfd of the muntz legendre polynomials based on three term recurrence relations and gauss jacobi quadrature rules this approach with collocation method at chebyshev gauss lobatto points has been applied for solving linear and nonlinear fractional multi order differential equations fdes described in caputo sense the main characteristic of spectral collocation method is that the problems reduce to linear or nonlinear systems of algebraic equations in this work for the first time we present the new rates of convergence for projection error which are more accurate than the rate presented by shen and wang in shen and wang 2016 moreover we present convergence rate for spectral collocation method for linear fdes with initial value on a finite interval and endpoint singularities also we propose an error analysis for jacobi gauss type quadrature and present a way to accelerate the convergence rate for singular integrands applied in this paper finally the stability and applicability of the numerical approach and convergence analysis is demonstrated by some numerical examples

local variability of non smooth functions abstract with the help of muntz powers a formula of the taylor type for non smooth functions is presented the approximation provides a local study for the variability of some curves which do not have a derivative the approach includes the classical case but at the same time other non analytical and non differentiable mappings in the first place a muntz curve representing the local variability of a function is defined the coefficient and exponent of the model allow a numerical characterization of the relative extremes and differentiability of the map the introduction of exponents of higher order provides a generalization of the taylor s formula including some cases of non differentiability in the last part a series expansion of non necessarily integer powers representing the function is presented several properties of convergence continuity integrability and density are studied

rates of convergence of multipoint rational approximants and quadrature formulas on the unit circle abstract in this paper multipoint rational approximants to the riesz herglotz transform of a borel measure supported on are considered we give estimates for the rate of convergence of these approximants these estimates are obtained from the asymptotic behaviour of a sequence of rational functions orthogonal with respect to and having prescribed poles 1 k where k 1 is a sequence of complex numbers compactly contained in the open unit disk as an application we also give the rate of convergence of rational szego quadrature formulas for integrals with respect to

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

non interleaving semantics for mobile processes abstract this paper studies causality in the calculus our notion of causality combines the dependencies given by the syntactic structure of processes with those originated by passing names our studies show that two transitions not causally related may however occur in a fixed ordering in any computation i e the calculus may implicitly express a precedence between actions the same partial order of transitions is associated with all the computations that are obtained by shuffling transitions that are concurrent i e related neither by causality nor by precedence other non interleaving semantics are investigated and compared the presentation takes advantage of a parametric definition of process behaviour given in sos style that permits us to take almost for free the interleaving theory and tools finally we extend our approach to higher order calculus enriched with a spawn operation

some congruence properties for p calculus bisimilarities both for interleaving and for non interleaving semantics several variants of a pi calculus bisimilarity can be given which differ on the requirements imposed on name instantiations examples are the em late early open and em ground variants the ground variant is the simplest because it places no requirements on name instantiations with the exception of open bisimilarities none of the bisimilarity considered in the literature is a congruence relation on the full pi calculus language we show that in the case of certain forms of the non interleaving em causal bisimulation the late early open and ground variants coincide and are congruence relations in the sublanguage of the pi calculus without matching we also show that to obtain the same results in the case of the interleaving bisimilarity in addition to forbidding matching it is necessary to constrain the output prefix

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

typed event structures and the linear π calculus we propose a typing system for the true concurrent model of event structures that guarantees the interesting behavioural properties known as conflict freeness and confusion freeness conflict freeness is the true concurrent version of the notion of confluence a system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components ours is the first typing system to control behaviour in a true concurrent model to demonstrate its applicability we show that typed event structures give a semantics of linearly typed version of the p calculi with internal mobility the semantics we provide is the first event structure semantics of the p calculus and generalises winskel s original event structure semantics of ccs

local approximation of functions with several variables abstract this paper presents the problem of local approximation of scalar functions with several variables including points of non differentiability the procedure considers that the mapping displays rates of change of power type with respect to linear changes in the coordinate domain and the exponents are not necessarily integer the approach provides a formula describing the local variability of scalar fields which contains and generalizes taylor s formula of first order the functions giving the contact are muntz polynomials the knowledge of their coefficients and exponents enables the finding of local extremes including cases of non smoothness sufficient conditions for the existence of global maxima and minima of concave convex functions are obtained as well

gaussian type quadrature rules for muntz systems a method for constructing the generalized gaussian quadrature rules for muntz polynomials on 0 1 is given such quadratures possess several properties of the classical gaussian formulae for polynomial systems such as positivity of the weights rapid convergence etc they can be applied to the wide class of functions including smooth functions as well as functions with end point singularities such as those in boundary contact value problems integral equations with singular kernels complex analysis potential theory etc the constructive method is based on an application of orthogonal muntz polynomials introduced by badalyan it akad nauk armyan ssr izv fiz mat estest tehn nauk 8 1955 pp 1 28 9 1956 pp 3 22 russian armenian summary and studied intensively by borwein erdelyi and zhang it trans amer math soc 342 1994 pp 523 542 as well as by milovanovic on a numerical procedure for evaluation of such polynomials with high precision it muntz orthogonal polynomials and their numerical evaluation in applications and computation of orthogonal polynomials internat ser numer math 131 w gautschi g h golub and g opfer eds birkhauser basel 1999 pp 179 194 the method is numerically stable some numerical examples are included

solutions of the strong hamburger moment problem abstract the strong hamburger moment problem for a bi infinite sequence c n n 0 1 2 can be described as follows 1 find conditions for the existence of a positive measure on such that c n t n d t for all n 2 when there is a solution find conditions for uniqueness of the solution 3 when there is more than one solution describe the family of all solutions in this paper a theory concerning question 3 is developed in particular an analog to the nevanlinna parametrization describing the solutions of the classical hamburger moment problem is given

a sparse fractional jacobi galerkin levin quadrature rule for highly oscillatory integrals abstract levin s quadrature rule is well known for its good performance on numerical treatment with highly oscillatory integrals however most existing work treats with sufficiently smooth integrands in this paper we study levin s quadrature rule for a class of singular and oscillatory integrals based on fractional jacobi polynomials a class of differential equation solvers for levin s equation are developed which leads to the fractional jacobi galerkin levin method the discretized equation is turned into a sparse linear system by properly choosing jacobi polynomials and the inner product furthermore convergence analysis with respect to the oscillation is presented by studying coefficients of the fractional jacobi expansion of the error function numerical experiments indicate that in contrast to existing quadrature rules the new method is efficient for computing oscillatory integrals with stationary points and unknown singular parameters

fredholm volterra integral equation of the first kind and contact problem regular and singular asymptotic methods are applied to one and two dimensional fredholm volterra integral equation f vie of the first kind that arise in the treatment of various two dimensional axisymmetric and three dimensional problems with mixed boundary conditions in the mechanics of continuous media the solution of the integral equation is obtained in the space l 2 w xc 0 t 0

modal logics for mobile processes in process algebras bisimulation equivalence is typically defined directly in terms of the operational rules of action it also has an alternative characterisation in terms of a simple modal logic sometimes calledhennessy milner logic this paper first defines two forms of bisimulation equivalence for the 031 calculus a process algebra which allows dynamic reconfiguration among processes it then explores a family of possible logics with different modal operators it is proven that two of these logics characterise the two bisimulation equivalences also the relative expressive power of all the logics is exhibited as a lattice

muntz spaces and remez inequalities two relatively long standing conjectures concerning muntz polynomials are resolved the central tool is a bounded remez type inequality for non dense muntz spaces

muntz legendre spectral collocation method for solving delay fractional optimal control problems abstract in this paper a numerical method is applied for solving delay fractional optimal control problems dfocps the fractional derivative is described in the caputo sense since the fractional derivative of muntz polynomials can be expressed in terms of the same polynomials those polynomials can accurately represent properties of fractional calculus in some situations such as in the frequency response based analysis of control systems containing a time delay it is necessary to substitute exponential function with an approximation in the form of a rational function the most common approximation is the pade approximation at the first step using pade approximation the delay problem is transformed to a non delay problem next using the operational matrix of the fractional derivative of muntz polynomials and pseudospectral method fractional optimal control problem focp is reduced to a nonlinear programming problem some numerical examples are given to illustrate the effectiveness of the proposed scheme

locality and interleaving semantics in calculi for mobile processes abstract process algebra semantics can be categorised into noninterleaving semantics where parallel composition is considered a primitive operator and interleaving semantics where concurrency is reduced to sequentiality plus nondeterminism the former have an appealing intuitive justification but the latter are mathematically more tractable this paper addresses the study of noninterleaving semantics in the framework of process algebras for mobile systems like calculus 19 17 we focus on location bisimulation in our opinion one of the most convincing non interleaving equivalences which aims to describe the spatial dependencies on processes we introduce in calculus following the definition for ccs given in 5 our main contribution is to show that in calculus can be expressed or implemented within the ordinary interleaving observation equivalence 16 19 by means of a fairly simple and fully abstract encoding thus we can take advantage of the easier theory of observation equivalence to reason about we illustrate this with a few examples including the proof of the congruence properties of we show that in calculus is not a congruence and that the full abstraction of the encoding extends to the induced congruence the results in the paper also shed more light on the expressive power of the calculus

generalized legendre polynomials abstract orthogonal polynomials have been extensively investigated in this paper we construct a sequence of orthogonal dirichlet polynomials which generalize legendre polynomials we show that our new system satisfies a generalized rodrigues formula we also extend a well known result concerning the distribution of the zeros of legendre polynomials

numerical solution of volterra fredholm integral equations based on e svr method in this paper we try to study the numerical methods for solving integral equations from a new perspective machine learning method by means of the idea of kernel e support vector regression machine e svr we construct an optimization modeling for a class of volterra fredholm integral equations and propose a novel numerical method for solving them the proposed method has a certain versatility and can be used to solve some other kinds of integral equations in order to verify the effectiveness of the proposed method we perform a series of comparative experiments with six specific volterra fredholm integral equations and a method proposed in wang et al 2014 experimental results show that the proposed method has a good approximation property

causal static analysis for brane calculi we present here a static analysis based on abstract interpretation8 obtained by defining an abstract version of the causal semantics for the mate bud drip mbd version of brane calculi 7 proposed by busi 6 our analysis statically approximates the dynamic behaviour of mbd systems more precisely the analysis is able to describe the essential behaviour of the represented membranes in terms of their possible interactions furthermore our analysis is able to statically capture the possible causal dependencies among interactions whose determination can be exploited to better understand the modelled biological phenomena finally we apply our analysis to an abstract specification of the receptor mediated endocytosis mechanism

orthogonal laurent polynomials and the strong hamburger moment problem abstract this paper is concerned with the strong hamburger moment problem shmp for a given double sequence of real numbers c c n does there exist a real valued bounded non decreasing function on with infinitely many points of increase such that for every integer n c n t n d t necessary and sufficient conditions for the existence of such a function are given in terms of the positivity of certain hankel determinants associated with c our approach is made through the study of orthogonal and quasi orthogonal laurent polynomials referred to here as l polynomials and closely related gaussian type quadrature formulas in the proof of sufficiency an inner product for l polynomials is defined in terms of the given double sequence c since orthogonal l polynomials are believed to be of interest in themselves some examples of specific systems are considered

generalizations of muntz s theorem via a remez type inequality for muntz spaces the principal result of this paper is a remez type inequality for m untz polynomials p x sum n i 0 a i x lambda i or equivalently for dirichlet sums p t sum n i 0 a i e lambda i t where 0 lambda 0 0 here cdot a denotes the supremum norm on a this remez type inequality allows us to resolve two reasonably long standing conjectures the first due to d j newman and dating from 1978 asserts that if sum infty i 1 1 lambda i infty then the set of products p 1 p 2 p 1 p 2 in text span x lambda 0 x lambda 1 ldots is not dense in c 0 1 the second is a complete extension of m untz s classical theorem on the denseness of m untz spaces in c 0 1 to denseness in c a where a subset 0 infty is an arbitrary compact set with positive lebesgue measure that is for an arbitrary compact set a subset 0 infty with positive lebesgue measure text span x lambda 0 x lambda 1 ldots is dense in c a if and only if sum infty i 1 1 lambda i infty several other interesting consequences are also presented

strong and weak convergence of orthogonal systems of rational functions on the unit circle abstract pan k strong and weak convergence of orthogonal systems of rational functions on the unit circle journal of computational and applied mathematics 46 1993 427 436 we study weak and strong convergence of rational functions that are orthonormal on the unit circle and have all their poles in a given sequence of points outside the unit disk the erd s measures have been characterized as well

convergence of modified approximants associated with orthogonal rational functions abstract let n be a sequence in the unit disk d z c z consisting of a finite number of points cyclically repeated and let l be the linear space generated by the functions b n z k 0 n k z k k 1 k z let n z be orthogonal rational functions obtained from the sequence bn z orthogonalization with respect to a given functional on l and let n z be the corresponding functions of the second kind with superstar transforms n z and n z respectively interpolation and convergence properties of the modified approximants r n z u n v n u n n z v n n z u n n z v n n z that satisfy u n v n are discussed

frequency domain approach to some third order nonlinear differential equations abstract in this work we shall use the frequency domain approach to prove properties p1 the existence of a unique bounded solution which is exponentially stable and p2 existence of periodic respectively almost periodic solution on some third order nonlinear differential equations using a duality principle we shall also give an extension of the results to a dual system

petr nets algebras morphisms and compositionality abstract it is shown how a category of petri nets can be viewed as a subcategory of two sorted algebras over multisets this casts petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition the morphisms here respect the behaviour of nets the categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components for example various forms of parallel composition of petri nets arise naturally from the product in the category this abstract setting makes plain a useful functor from the category of petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of petri nets for instance the coloured and higher level nets of kurt jensen arise through a simple modification of the sorts of the algebras underlying nets further it provides a smooth formal relation with other models of concurrency such as milner s calculus of communicating systems ccs and hoare s communicating sequential processes csp though this is only indicated in this paper

probabilistic and nondeterministic aspects of anonymity the concept of anonymity comes into play in a wide range of situations varying from voting and anonymous donations to postings on bulletin boards and sending emails the protocols for ensuring anonymity often use random mechanisms which can be described probabilistically while the agents behavior may be totally unpredictable irregular and hence expressible only nondeterministically formal definitions of the concept of anonymity have been investigated in the past either in a totally nondeterministic framework or in a purely probabilistic one in this paper we investigate a notion of anonymity which combines both probability and nondeterminism and which is suitable for describing the most general situation in which the protocol and the users can have both probabilistic and nondeterministic behavior we also investigate the properties of the definition for the particular cases of purely nondeterministic users and purely probabilistic users we formulate the notions of anonymity in terms of probabilistic automata and we describe protocols and users as processes in the probabilistic p calculus whose semantics is again based on probabilistic automata throughout the paper we illustrate our ideas by using the example of the dining cryptographers

p calculus internal mobility and agent passing calculi abstract the calculus is a process algebra which originates from ccs and permits a natural modelling of mobility i e dynamic reconfigurations of the process linkage using communication of names previous research has shown that the calculus has a much greater expressiveness than ccs but it also has a much more complex mathematical theory the primary goal of this work is to understand the reasons for this gap another goal is to compare the expressiveness of name passing calculi i e calculi like calculus where mobility is achieved via exchange of names and that of agent passing calculi i e calculi where mobility is achieved via exchange of agents we divide the mobility mechanisms of the calculus into internal and external mobility mechanisms the study of the subcalculus which only uses internal mobility called i suggests that internal mobility is responsible for much of the expressiveness of the calculus whereas external mobility is responsible for many of the semantic complications a pleasant property of i is the full symmetry between input and output constructs internal mobility is strongly related to agent passing mobility by imposing bounds on the order of the types of i and of the higher order calculus sangiorgi 1992 we define a hierarchy of name passing calculi based on internal mobility and one of agent passing calculi we show that there is an exact correspondence in terms of expressiveness between the two hierarchies

rate of relative growth of orthogonal polynomials abstract let 0 p n a n a 2 b n b 0 define a polynomial sequence p n by the recurrence relation xp n x a n 1 x b n p n x a n p n 1 x it was proved that formula this paper investigates the rate of growth of such a sequence relative to its sums in terms of the rate of convergance of n some applications to orthogonal polynomials are given

strong and weak convergence of orthogonal polynomials le cercle unite fonctionnelles continues sur des mesures resultats principaux sur le cercle unite corollaires de convergence faible les parties absolument continues et les parties singulieres d une mesure integrabilite uniforme et inegalite de turan series orthogonales avec trous la ligne reelle convergence forte convergence faible convergence forte pour des moyennes arithmetiques

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

unique solvability of an extended hamburger moment problem abstract r functions are rational functions with no poles in the extended complex plane outside a given set a1 ap of points on the real axis methods from the theory of orthogonal polynomials can be extended to r functions by this means the author solved an extended hamburger moment problem given sequences of real numbers cn i n 1 2 i 1 p find conditions for a distribution function to exist such that d t 1 d t t a i m c m i m 1 2 i 1 p in this paper these methods are extended to treat conditions for the moment problem to have a unique solution the results are related to the classical limit point limit circle situation

a favard theorem for rational functions abstract the space r of r functions consists of all rational functions whose poles are contained in a fixed finite subset of the finite complex plane let qn be a monic regular sequence of elements in r it is shown that qn is an orthogonal sequence with respect to a linear functional on r iff the qn satisfy a certain set of three term recurrence relations

structural operational semantics for stochastic and weighted transition systems we introduce weighted gsos a general syntactic framework to specify well behaved transition systems where transitions are equipped with weights coming from a commutative monoid we prove that weighted bisimilarity is a congruence on systems defined by weighted gsos specifications we illustrate the flexibility of the framework by instantiating it to handle some special cases most notably that of stochastic transition systems through examples we provide weighted gsos definitions for common stochastic operators in the literature

on the stability and boundedness of solutions of a kind of third order delay differential equations abstract in this paper we study eq 1 1 for asymptotic stability of the zero solution when p t x x x 0 and uniformly bounded and uniformly ultimate bounded of all solutions when p t x x x 0

extensions of szego s theory of rational functions orthogonal on the unit circle rational functions orthogonal on the unit circle with prescribed poles lying outside the unit circle are studied we study the asymptotic behaviors for the orthogonal rational functions when the measure does not satisfy the szego condition

interval inversion approach for an improved interpretation of well logs the quality analysis of well logging inversion results has always been an important part of formation evaluation the precise calculation of hydrocarbon reserves requires the most accurate possible estimation of porosity water saturation and shale and rock matrix volumes the local inversion method conventionally used to predict the above model parameters depth by depth represents a marginally overdetermined inverse problem which is rather sensitive to the uncertainty of observed data and limited in estimation accuracy to reduce the harmful effect of data noise on the estimated model we have suggested the interval inversion method in which an increase of the overdetermination ratio allows a more accurate solution of the well logging inverse problem the interval inversion method inverts the data set of a longer depth interval to predict the vertical distributions of petrophysical parameters in a joint inversion procedure in formulating the forward problem we have extended the validity of probe response functions to a greater depth interval assuming the petrophysical parameters are depth dependent and then we expanded the model parameters into a series using the legendre polynomials as basis functions for modeling inhomogeneous formations we solved the inverse problem for a much smaller number of expansion coefficients than data to derive the petrophysical parameters in a stable overdetermined inversion procedure the added advantage of the interval inversion method is that the layer thicknesses and suitably chosen zone parameters can be estimated automatically by the inversion procedure to refine the results of inverse and forward modeling we have defined depth dependent model covariance and correlation matrices to compare the quality of the local and interval inversion results a detailed study using well logs measured from a hungarian gas bearing unconsolidated formation revealed that the greatly overdetermined interval inversion procedure can be effectively used in reducing the estimation errors in shaly sand formations which may refine significantly the results of reserve calculation

least squares approximation method for the solution of volterra fredholm integral equations in this paper an efficient numerical method is developed for solving the volterra fredholm integral equations by least squares approximation method which is based on a polynomial of degree n to compute an approximation to the solution of volterra fredholm integral equations the convergence analysis of the approximation solution relative to the exact solution of the integral equation is proved the reliability and efficiency of the proposed method are demonstrated by some numerical experiments

on orthogonal systems of rational functions on the unit circle and polynomials orthogonal with respect to varying measures abstract we study the recurrence relations of rational functions that are orthonormal on the unit circle and have all their poles in a given sequence of points outside the unit disk these relations enable us to find the recurrence relations and the ratio asymptotic behaviors for the orthonormal polynomials with respect to varying weights d n and d n 1 at the end of this paper we also consider the convergence theorem for multipoint pade approximations of markov type functions