on the lebesgue measure of li yorke pairs for interval maps we investigate the prevalence of li yorke pairs for c2 and c3 multimodal maps f with non flat critical points we show that every measurable scrambled set has zero lebesgue measure and that all strongly wandering sets have zero lebesgue measure as does the set of pairs of asymptotic but not asymptotically periodic points

on the continuity of the multivariate pade operator abstract continuity of the univariate pade operator was proved in 5 6 we discuss the limitations of a multivariate generalization and prove a multivariate analogon of the continuity property

singular rules for the calculations of non normal multivariate pade approximants abstract section 1 describes the univariate situation in the case of non normal pade approximants and cordellier s extension of the famous five star identity of wynn section 2 repeats our definition of multivariate pade approximants and proves a number of theorems that remain valid when going from the univariate to the multivariate case these theorems and more new results given in section 3 will finally also copy cordellier s extension from the univariate to the multivariate case

multivariate rational approximants for multiclass closed queuing networks closed markovian networks of queues with multiclass customers and having a product form equilibrium state probability distribution are useful in the performance evaluation and design of computer and telecommunication systems therefore the efficient computation of the normalizing function the key element of the solution in product form has attracted considerable effort we consider a network that consists of one infinite server is station and one processor sharing ps or fcfs single server station we use multivariate newton pade approximants computed from data for small numbers of customers in each class to estimate the normalizing function for a larger population in the network the effectiveness and tremendous gain in computing time of this procedure are illustrated through various numerical experiments

the d 2 transformation for infinite double series and the d 2 transformation for infinite double integrals new transformations for accelerating the convergence of infinite double series and infinite double integrals are presented these transformations are generalizations of the univariate d and d transformations the d 2 transformation for infinite double integrals is efficient if the integrand satisfies a p d e of a certain type similarly the d 2 transformation for double series works well for series whose terms satisfy a difference equation of a certain type in both cases the application of the transformation does not require an explicit knowledge of the differential or the difference equation asymptotic expansions for the remainders in the infinite double integrals and series are derived and nonlinear transformations based upon these expansions are presented finally numerical examples which demonstrate the efficiency of these transformations are given

brief stochastic optimal control via bellman s principle this paper presents a strategy for finding optimal controls of non linear systems subject to random excitations the method is capable to generate global control solutions when state and control constraints are present the solution is global in the sense that controls for all initial conditions in a region of the state space are obtained the approach is based on bellman s principle of optimality the cumulant neglect closure method and the short time gaussian approximation problems with state dependent diffusion terms non closeable hierarchies of moment equations for the states and singular state boundary condition are considered in the examples the uncontrolled and controlled system responses are evaluated by creating a markov chain with a control dependent transition probability matrix via the generalized cell mapping method in all numerical examples excellent controlled performances were obtained

explicit construction of multivariate pade approximants we explicitly construct both homogeneous and nonhomogeneous multivariate pade approximants to some functions which satisfy some simple functional equations by using the residue theorem and the functional equation method which has been used successfully by borwein 1988 to construct one variable pade approximants to the q elementary functions

a multivariate convergence theorem of the de montessus de ballore type abstract the univariate theorem of de montessus de ballore proves the convergence of column sequences of pade approximants for functions f z meromorphic in a disk in case the number of poles of f z and their multiplicity is known in advance we prove here a multivariate anologon for the case of simple poles and for the general order pade approximants as introduced by cuyt and verdonk 1984

non linear quadratic gaussian controlf abstract algebraic necessary conditions for the minimization of a quadratic cost function are derived for non linear stochastic regulator systems on the assumption that the statistics of the state and output random variables can be represented satisfactorily by a gaussian distribution this non linear quadratic gaussian nqg technique is related to the use of statistical linearization and lqg theory in particular the cases of perfect state measurement and incomplete and noisy measurement are addressed

multivariate pade approximation multivariate pade approximation is considered in the framework of the theory developed by a cuyt 1982 the denominators are determined from determinants of matrices whose entries are homogeneous polynomials the main difference to the univariate case is a typical shift of the degree of the polynomials singularities atx 0 are analyzed since it is the rule rather than the exception that simultaneous zeros of the numerator and the denominator cannot be removed

attractors for graph critical rational maps we call a rational map f graph critical if any critical point either belongs to an invariant finite graph g or has minimal limit set or is non recurrent and has limit set disjoint from g we prove that for any conformal measure either for almost every point of the julia set j f its limit set coincides with j f or for almost every point of j f its limit set coincides with the limit set of a critical point of f

generalizations of orthogonal polynomials we give a survey of recent generalizations of orthogonal polynomials that includes multidimensional matrix and vector orthogonal polynomials and multivariate versions multipole orthogonal rational functions variants and extensions of the orthogonality conditions multiple orthogonality most of these generalizations are inspired by the applications in which they are applied we also give a glimpse of these applications which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role moment problems numerical quadrature rational approximation linear algebra recurrence relations and random matrices

the qd algorithm and multivariate pade approximants the quotient difference qd algorithm can be used to construct univariate pade approximants 1 in this paper we see that it can also be used to construct the multivariate pade approximants introduced in 3 just by reformulating the quotient difference algorithm as in sect 1 the multivariate pade approximants and the multivariate qd scheme are treated in the sects 2 and 3 respectively thus for this type of multivariate pade approximants a link with the theory of multivariate continued fractions is established

use of particle filters in an active control algorithm for noisy nonlinear structural dynamical systems the problem of active control of nonlinear structural dynamical systems in the presence of both process and measurement noises is considered the focus of the study is on the use of particle filters for state estimation in feedback control algorithms for nonlinear structures when a limited number of noisy output measurements are available the control design is done using the state dependent riccati equation sdre method the stochastic differential equations sdes governing the dynamical systems are discretized using explicit forms of ito taylor expansions the bayesian bootstrap filter and that based on sequential important sampling sis are employed for state estimation the simulation results show the feasibility of using particle filters and sdre techniques in control of nonlinear structural dynamical systems

identification of discontinuous nonlinear systems via a multivariate pade approach we present a nonlinear system identification technique based on multi dimensional rational polynomials a multi dimensional pade legendre approximation is developed to circumvent challenges in dealing with sharp shocks the purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems particularly systems with a non smooth response surface this identification approach utilizes the generalized form of a pade legendre approximation for studying multivariable functions in the studied problems the nonlinearity is a function of state variables displacement and velocity which requires multi dimensional formulation furthermore a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface this study presents different types of nonlinearities including smooth irregular and hysteretic functions in order to demonstrate the performance of the approach under different conditions in order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation a nonlinear system with a sharp discontinuous restoring force surface is considered the performance of both approaches is investigated for different degrees of sharpness in addition the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system computed on the basis of the identified model from data sets corresponding to different excitations than those used for identification purposes it is shown that the proposed approach provides a robust identification technique for a broad class of highly nonlinear systems and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties

two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series two new classes of nonlinear transformations the d transformation to accelerate the convergence of infinite integrals and the d transformation to accelerate the convergence of infinite series are presented in the course of the development of these transformations two interesting asymptotic expansions one for infinite integrals and the other for infinite series are derived the transformations d and d can easily be applied to infinite integrals 0f t dt whose integrands f t satisfy linear differential equations of the form f t s m k 1p k t f k t and to infinite series s r 1f r w terms f r satisfy a linear difference equation of the form f r s m k 1p k r d kf r such that in both cases the p k have asymptotic expansions in inverse powers of their arguments in order to be able to apply these transformations successfully one need not know explicitly the differential equation that the integrand satisfies or the difference equation that the terms of the series satisfy mere knowledge of the existence of such a differential or difference equation and its order m is enough this broadens the areas to which these methods can be applied the connection between the d and d transformations with some known transformations in shown the use and the remarkable efficiency of the d and d transformations are demonstrated through several numerical examples the computational aspects of these transformations are described in detail

on a diagonal pade approximation in two complex variables a special type diagonal pade approximation for a class of hermitian power series in two variables is related to a canonical strong operator topology finite rank approximation of cyclic operators the expected convergence of the process uniform or in measure is derived from operator theory facts

general order multivariate pade approximants for pseudo multivariate functions ii although general order multivariate pade approximants were introduced some decades ago very few explicit formulas for special functions have been given we explicitly construct some general order multivariate pade approximants to the class of so called pseudo multivariate functions using the pade approximants to their univariate versions we also prove that the constructed approximants inherit the normality and consistency properties of their univariate relatives which do not hold in general for multivariate pade approximants examples include the multivariate forms of the exponential and the q exponential functions

on lagrange and hermite interpolation in rk a method for the construction of a set of data of interpolation in several variables is given the resulting data which are either function values or directional derivatives values give rise to a space of polynomials in such a way that unisolvence is guaranteed the interpolating polynomial is calculated using a procedure which generalizes the newton divided differences formula for a single variable

general order newton pade approximants for multivariate functions pade approximants are a frequently used tool for the solution of mathematical problems one of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off x 1 x p therefore multivariate newton pade approximants are introduced their computation will only use the value off at some points in sect 1 we shall repeat the univariate newton pade approximation problem which is a rational hermite interpolation problem in sect 2 we sketch some problems that can arise when dealing with multivariate interpolation in sect 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate newton pade approximants in sect 4 a numerical example is given in sect 5 together with the proof that forp 1 the classical newton pade approximants for a univariate function are obtained

brief paper a stochastically averaged optimal control strategy for quasi hamiltonian systems with actuator saturation a stochastic optimal control strategy for quasi hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programming principle first the partially completed averaged ito stochastic differential equations for the energy processes of individual degree of freedom are derived by using the stochastic averaging method for quasi hamiltonian systems then the dynamical programming equation is established by applying the stochastic dynamical programming principle to the partially completed averaged ito equations with a performance index the saturated optimal control consisting of unbounded optimal control and bounded bang bang control is determined by solving the dynamical programming equation numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang bang control

error formulas for multivariate rational interpolation and pade approximation the univariate error formulas for pade approximants and rational interpolants which are repeated in section 2 are generalized to the multivariate case in section 4 we deal with general order multivariate pade approximants and rational interpolants where the numerator and denominator polynomials as well as the equations expressing the approximation order can be chosen by the user of these multivariate rational functions

kronecker type theorems normality and continuity of the multivariate pade operator for univariate functions the kronecker theorem stating the equivalence between the existence of an infinite block in the table of pade approximants and the approximated function f being rational is well known in lubi88 lubinsky proved that if f is not rational then its pade table is normal almost everywhere for an at most countable set of points the taylor series expansion of f is such that it generates a non normal pade table this implies that the pade operator is an almost always continuous operator because it is continuous when computing a normal pade approximant wuyt81 in this paper we generalize the above results to the case of multivariate pade approximation we distinguish between two different approaches for the definition of multivariate pade approximants the general order one introduced in levi76 cuve84 and the so called homogeneous one discussed in cuyt84

semi active optimal control of linearized systems with multi degree of freedom and application abstract a semi active optimal control method for non linear multi degree of freedom systems and its application to a building structure for random response reduction are presented in this paper a structural system with semi active control devices under random loading is modelled as a controlled randomly excited and dissipated hamiltonian system of multi degree of freedom the control force produced by a semi active control device is split into semi active part and passive part incorporated in the uncontrolled system applying the statistical linearization method to the non linear multi degree of freedom system with passive control force components yields quasi linear equations of motion which can tend to corresponding linear ones with system response reduction by applying the dynamical programming principle to the controlled linearized system a dynamical programming equation is established and in particular for a non filtering white noise excitation is solved as an optimal regulation problem to determine the quasi linear quadratic optimal control law and furthermore semi active optimal control law according to the variational principle then the semi active optimal control of a tall building structure with magnetorheological tuned liquid column damper mr tlcd under random wind excitation is performed by using the proposed method the non linear model of the structural system with semi active mr tlcd is formulated in structural mode space and uncoupled between structural and mr fluid accelerations the quasi linear equations for system states are derived from the model and the dynamical programming equation for the system is obtained in the case that the random wind excitation with the davenport power spectrum cannot be modelled as a linear filtering white noise the dynamical programming equation is solved as an optimal regulation problem to obtain the semi active optimal control force on which the clipping treatment may be performed to ensure the control force implementable actually eventually the response statistics of the semi actively controlled structure under random wind excitation are evaluated by using the statistical linearization method and are compared with those of the passively controlled structure to determine the control efficacy numerical results illustrate the high control effectiveness of the proposed semi active optimal control method for building structures with mr tlcds

convergence of diagonal pade approximants for functions analytic near 0 for functions analytic in a neighbourhood of 0 we show that at least for a subsequence of the diagonal pade approximants the point 0 attracts a zero proportion of the poles the same is true for every sufficiently dense diagonal subsequence consequently these subsequences have a convergence in capacity type property which is possibly the correct analogue of the nuttallpommerenke theorem in this setting

julia fatou sullivan theory for real one dimensional dynamics our aim is to show that the julia fatou sullivan structure theory for the dynamics of rational maps is also valid for smooth endomorphisms of the circle and of the interval under extremely mild smoothness and non flatness conditions in order to stress the similarity between real and complex one dimensional dynamics let us recall the main results from the fatou julia sullivan theory if f is a rational map then there is a dynamical decomposition of the riemann sphere into the disjoint union of two totally invariant i e both forward and backward invariant sets j f f f here f f is the domain of normality of the family of iterates of f and is called the fatou set its complement which is called the julia set off is a compact set which contains all the complications of the dynamics off the connected components of the open set f f are mapped onto each other by f hence the orbit of a component of f f is the union of some components of f f julia proved in the beginning of the century that if a component of f f is periodic and contains an attracting periodic point then the orbit of this component must contain a critical point sullivan in the remarkable paper su showed via quasi conformal deformations that the components are eventually periodic and fall into finitely many orbits let n be either the circle s j or a compact interval of the real line and f n n be a smooth endomorphism a critical point of f is a point where the derivative vanishes a critical point is non flat if some higher derivative is non zero a critical point is an inflection point if it has a neighbourhood where f is monotone otherwise it is called a turning point assume f is not a homeomorphism i f f is a homeomorphism then these maps correspond to degree 1 rational maps of the riemann sphere and the situation is

a direct approach to convergence of multivariate nonhomogeneous pade approximants we present a direct approach for proving convergence in measure product capacity of multivariate nonhomogeneous pade approximants previous approaches have involved projection onto pade type approximation in one variable and only yielded convergence in lebesgue measure

convergence analysis for a generalized richardson extrapolation process with an application to the d 1 transformation on convergent and divergent logarithmic sequences in an earlier work by the author the generalized richardson extrapolation process grep was introduced and some of its convergence and stability properties were discussed in a more recent work by the author a special case of grep which we now call grep 1 was considered and its properties were reviewed with emphasis on oscillatory sequences in the first part of the present work we give a detailed convergence and stability analysis of grep 1 as it applies to a large class of logarithmic sequences both convergent and divergent in particular we prove several theorems concerning the columns and the diagonals of the corresponding extrapolation table these theorems are very realistic in the sense that they explain the remarkable efficiency of grep 1 in a very precise manner in the second part we apply this analysis to the levin sidi d 1 transformation as the latter is used with a new strategy to accelerate the convergence of infinite series that converge logarithmically or to sum the divergent extensions of such series this is made possible by the observation that when the proper analogy is drawn the d 1 transformation is in fact a grep 1 we append numerical examples that demonstrate the theory

extension of a multivariate convergence theorem of the de montessus de ballore type to multipoles abstract in this journal 1990 we proved a multivariate version of the de montessus de ballore theorem stating the convergence of general order pade approximants for multivariate meromorphic functions with so called simple poles that result is extended here to the case of multipoles

an lqr lqg theory for systems with saturating actuators an extension of the lqr lqg methodology to systems with saturating actuators referred to as slqr slqg where s stands for saturating is obtained the development is based on the method of stochastic linearization whereby the saturation is replaced by a gain calculated as a function of the variance of the signal at its input using the stochastically linearized system and the lagrange multiplier technique solutions of the slqr slqg problems are derived these solutions are given by standard riccati and lyapunov equations coupled with two transcendental equations which characterize both the variance of the signal at the saturation input and the lagrange multiplier associated with the constrained minimization problem it is shown that under standard stabilizability and detectability conditions these equations have a unique solution which can be found by a simple bisection algorithm when the level of saturation tends to infinity these equations reduce to their standard lqr lqg counterparts in addition the paper investigates the properties of closed loop systems with slqr slqg controllers and saturating actuators in this regard it is shown that slqr slqg controllers ensure semi global stability by appropriate choice of a parameter in the performance criterion finally the paper illustrates the techniques developed by a ship roll damping problem

nuttall pommerenke theorems for homogeneous pade approximants we investigate nuttall pommerenke theorems for several variable homogeneous pade approximants using ideas of goncar karlsson and wallin

multivariate reciprocal differences for branched thiele continued fraction expansion etude des differences reciproques multivariables pour les developpements en fractions continues de thiele ramifiees

how well can the concept of pade approximant be generalized to the multivariate case what we know about multivariate pade approximation has been developed in the last 25 years in the next sections we compare and discuss many of these results it will become clear that simple properties or requirements such as the uniqueness of the pade approximant and consequently its consistency property can play a crucial role in the development of the multivariate theory a separate section is devoted to a discussion of the convergence properties at the end we include an extensive reference list on the topic

hausdorff dimension and conformal measures of feigenbaum julia sets 1 1 statement of the results one of the first questions usually asked about a fractal subset of r is whether it has the maximal possible hausdorff dimension n it certainly happens if the set has positive lebesgue measure on the other hand it is easy to construct fractal sets of zero measure but of dimension n moreover this phenomenon is often observable for fractal sets produced by conformal dynamical systems iterated rational functions or kleinian groups in particular the analogy with kleinian groups suggested that the julia sets of feigenbaum maps should have hausdorff dimension two in this paper we will show that this is not always the case a quadratic polynomial or more generally a quadratic like map is called feigenbaum if it is infinitely renormalizable of bounded combinatorial type with a priori bounds see 2 for a precise definition feigenbaum polynomials are remarkable dynamical systems whose geometry has been a focus of research for the past 25 years by analogy with kleinian groups it was anticipated that their julia sets have dimension 2 and this problem has been around for a while however in this paper we will show that this is not always the case

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

iterative procedures in application of the lqg approach to control problems for polynomial stochastic systems the problem of the determination of quasi optimal control for polynomial stochastic dynamic systems using the lqg technique and linearization methods is considered in this paper we present some sufficient conditions of convergence for iterative procedures used in evaluation of quasi optimal control scalar and vector systems are treated separately obtained results are illustrated by numerical examples

nested multivariate pade approximants abstract a new class of multivariate pade approximants is introduced when dealing with two variables x and y the approach consists in applying the pade approximation with respect to y to the coefficients of the pade approximation with respect to x this technique has a natural extension to n variables and is well adapted to programming in any usual language the advantage of the method is that the algorithm uses only univariate pade approximation as a consequence only small systems need to be solved and the computation of the approximant is much faster if m is the number of derivatives with respect to x and y the algorithm requires o m 4 operations instead of o m 6 when matrix methods are used for solving the coefficients problem or o m 3 operations instead of o m 4 if staircase methods are used another important feature is that the reliable methods which have been developed for choosing the degrees of the numerator and the denominator in the univariate case can be straightforwardly used in the multivariate case

backward stability for polynomial maps with locally connected julia sets we study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability then we deduce from this that a polynomial f with a locally connected julia set is backward stable outside any neighborhood of its attracting and neutral cycles for a conformal measure this easily implies that one of the following holds 1 for a e x e j f x j f 2 for a e x j f x c x for a critical point c x depending on x

a stochastic optimal semi active control strategy for er mr dampers abstract a stochastic optimal semi active control strategy for randomly excited systems using electrorheological magnetorheological er mr dampers is proposed a system excited by random loading and controlled by using er mr dampers is modelled as a controlled stochastically excited and dissipated hamiltonian system with n degrees of freedom the control forces produced by er mr dampers are split into a passive part and an active part the passive control force is further split into a conservative part and a dissipative part which are combined with the conservative force and dissipative force of the uncontrolled system respectively to form a new hamiltonian and an overall passive dissipative force the stochastic averaging method for quasi hamiltonian systems is applied to the modified system to obtain partially completed averaged ito stochastic differential equations then the stochastic dynamical programming principle is applied to the partially averaged ito equations to establish a dynamical programming equation the optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of er mr damping forces and the fully completed averaged ito equations are obtained from the partially completed averaged ito equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces finally the response of semi actively controlled system is obtained from solving the final dynamical programming equation and the fokker planck kolmogorov equation associated with the fully completed averaged ito equations of the system two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi active control strategy

birkhoff gustavson normal form and the semiclassical energies of a double pendulum although the double pendulum is a well known system the literature is sparse with regard to the study of its full dynamical behaviour as a simple conservative system that displays both ordered and chaotic motion it poses an interesting problem for the study of classical quantum correspondence in this work we present its birkhoff gustavson normal form and semiclassical energies obtained from the normal form the pade summation technique is used to re sum the normal form series

multidimensional integral inversion with applications in shape reconstruction in shape reconstruction the celebrated fourier slice theorem plays an essential role it allows one to reconstruct the shape of a quite general object from the knowledge of its radon transform s helgason the radon transform birkhauser boston boston 1980 in other words from the knowledge of projections of the object in case the object is a polygon g h golub p milanfar and j varah siam j sci comput 21 1999 pp 1222 1243 or when it defines a quadrature domain in the complex plane b gustafsson c he p milanfar and m putinar inverse problems 16 2000 pp 1053 1070 its shape can also be reconstructed from the knowledge of its moments essential tools in the solution of the latter inverse problem are quadrature rules and formal orthogonal polynomials in this paper we show how shape reconstruction from the knowledge of moments can also be realized in the case of general compact objects not only in two but also in higher dimensions to this end we use a less known homogeneous pade slice property again integral transforms in our case the multivariate stieltjes transform and univariate markov transform formal orthogonal polynomials in the form of pade denominators and multidimensional integration formulas or cubature rules play an essential role we emphasize that the new technique is applicable in all higher dimensions and illustrate it through the reconstruction of several two and three dimensional objects

a recursive computation scheme for multivariate rational interpolants we derive here a recursive computation scheme for the rational interpolation method introduced in 7 explicit formulas for these multivariate rational interpolants are repeated in 2 while the recursive algorithm is described in 3 a number of interesting special cases such as the univariate rational interpolation problem and the multivariate pade approximants introduced in 6 and 10 are dealt with in 4 for some of these rational approximants other recursive schemes were described previously finally 5 contains the numerical results the multivariate rational interpolants described here are compared with multivariate polynomial interpolants interpolating branched continued fractions introduced by cuyt and verdonk 8 interpolating branched continued fractions introduced by siemaszko 12 and several multivariate pade approximants 6 3 10 besides the fact that our multivariate rational interpolants allow a large degree of freedom in the choice for the numerator and denominator in ord

pade approximation for stochastic discrete event systems we show that pade approximation can be effectively used for approximation of performance functions in discrete event systems the method is 1 obtaining the maclaurin coefficients of the performance function and 2 finding a pade approximant from the maclaurin coefficients and use it to approximate the function we use the method with the expected number of renewals in a random interval gi g 1 systems and inventory systems the results are very good

a stochastic optimal control strategy for partially observable nonlinear quasi hamiltonian systems abstract a stochastic optimal control strategy for partially observable nonlinear quasi hamiltonian systems is proposed the optimal control force consists of two parts the first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system the second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system the response of the optimally controlled quasi hamiltonian system is predicted by solving the averaged fokker planck kolmogorov equation associated with the optimally controlled completely observable linear system and solving the riccati equation for the estimate errors of system states an example is given to illustrate the procedure and effectiveness of the proposed control strategy

conservative exact rational maps of the sphere abstract in this paper we investigate conditions for conservativity and exactness ofd to 1 endomorphisms we prove that all rational maps of degree greater than 1 are either conservative and exact with respect to normalized lebesgue measure on the sphere or have an attracting property inside the julia set we provide examples of rational maps which can be shown to be conservative and exact by using the previous result which was not formerly known to have this property

multivariate pade approximants to a meromorphic function abstract we explicitly construct the general multivariate pade approximants to the function g q x y j 1 1 xy q j x q 2j q 1 q c by using the residue theorem and the functional equation method then we prove some convergence properties of the approximants

multivariate pade approximants abstract for an operator f r n r analytic in the origin the notion of abstract multivariate pade approximant apa is introduced by making use of abstract polynomials the classical pade approximant n 1 is a special case of the multivariate theory and many interesting properties of classical pade approximants remain valid such as covariance properties and the block structure annie a m cuyt j oper theory6 2 1981 207 209 of the pade table also a projection property for multivariate pade approximants is proved

multivariate frobenius pade approximants properties and algorithms the aim of this paper is to construct rational approximants for multivariate functions given by their expansion in an orthogonal polynomial system this will be done by generalizing the concept of multivariate pade approximation after defining the multivariate frobenius pade approximants we will be interested in the two following problems the first one is to develop recursive algorithms for the computation of the value of a sequence of approximants at a given point the second one is to compute the coefficients of the numerator and denominator of the approximants by solving a linear system for some particular cases we will obtain a displacement rank structure for the matrix of the system we have to solve the case of a tchebyshev expansion is considered in more detail

wild attractors of polymodal negative schwarzian maps we study wild attractors of polymodal negative schwarzian interval maps and prove that they are it super persistently recurrent a polymodal version of persistent recurrence we also prove that if a map has an attractor which is a cycle of intervals then at almost every point of this cycle the map has properties similar to the markov property introduced by martens thus the lack of super persistent recurrence at a critical point c can be considered as a mild topological expanding property and this expansion prevents c from being a wild attractor in the previous paper we have shown that it also prevents the map from being c2 stable

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

grobner bases and generalized pade approximation it is shown how to find general multivariate pade approximation using the grobner basis technique this method is more flexible than previous approaches and several examples are given to illustrate this advantage when the number of variables is small compared to the degree of approximation the grobner basis technique is more efficient than the linear algebra methods in the literature

newton pade approximations for multivariate functions abstract we modify cuyt and verdonk s approach to multivariate newton pade approximations explicit formulas are given for coefficients which can be computed once for given system of nodes and the linear system of equations to find multivariate newton pade approximants can be written using simple formulas with those coefficients and the newton series of interpolated function