on locating all zeros of an analytic function within a bounded domain by a revised delves lyness method the method of delves and lyness math comp 21 1967 pp 543 560 561 577 on locating all the zeros of an analytic function in a bounded domain is revised such that no division of the region is needed the method used here is the homotopy continuation method also discussed here is how the continuation curves can be followed efficiently in this particular setting

on stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls abstract the paper discusses stabilizing effects of some time delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations first we derive explicit delay dependent stability conditions that are applicable to a family of time delayed systems with simultaneously triangularizable system matrices then using this criterion and other argumentation we employ diagonal delayed feedback controls of conventional and pyragas type to stabilize unstable steady states of the studied autonomous system more precisely we formulate explicit non improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization as an illustration we stabilize the unstable steady states of the rossler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior also we consider a non diagonal feedback control whose rotational gain matrix involving a feedback strength and phase commutes with the jacobi matrix of the uncontrolled system and show its larger stabilization potential with respect to the appropriate diagonal control the obtained results are tested by numerical experiments and confronted with the existing results as a supplement we provide matlab codes supporting theoretical conclusions

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

the gpl stability of rosenbrock methods for delay differential equation this paper deals with the stability analysis of the rosenbrock method for the numerical solution of delay differential equation the stability behavior of rosenbrock method is analyzed for the solutions of linear test equation we will give that the rosenbrock method is gpl stable if and only if it is l stable

an error analysis of two related quadrature methods for computing zeros of analytic functions we present an error analysis for two related quadrature methods the delves lyness method and its modification by kravanja sakurai and van barel for computing all the zeros of an analytic function that lie inside the unit circle we consider the forward as well as the backward approximation error in case the integrals are computed via the trapezoidal rule on the unit circle contrary to the delves lyness method the quadrature error that arises from the zeros located inside the unit circle does not affect the results of the approach of kravanja et al numerical experiments illustrate our main results

asymptotic stability of neutral differential systems with many delays we are concerned with delay independent asymptotic stability of linear system of neutral differential equations we first establish a sufficient and necessary condition for the system to be delay independently asymptotically stable and then give some equivalent stability conditions this paper improves many recent results on the asymptotic stability in the literature one example is given to show that the sufficient and necessary condition is easy to verify

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

on parallel complexity of analytic functions abstract in this paper we study the parallel complexity of analytic functions we investigate the complexity of computing the derivatives integrals and zeros of n c or logarithmic space computable analytic functions where n c denotes the complexity class of sets acceptable by polynomial size polylogarithmic depth uniform boolean circuits it is shown that the derivatives and integrals of n c or logarithmic space computable analytic functions remain n c or respectively logarithmic space computable we also study the problem of finding all zeros of an nc computable analytic function inside an n c computable jordan curve and show that under a uniformity condition on the function values on the jordan curve all zeros can be found in nc

stability of discrete delay systems boundary criteria this paper deals with the stability of linear discrete delay systems two stability criteria that are described by evaluating a corresponding harmonic function on the boundary of a torus region are presented testing these criteria can be proved to be much easier than those reported in the literature

on good eq algebras a special algebra called eq algebra has been recently introduced by vilem novak its original motivation comes from fuzzy type theory in which the main connective is fuzzy equality eq algebras have three binary operations meet multiplication and fuzzy equality and a unit element they open the door to an alternative development of fuzzy many valued logic with the basic connective being a fuzzy equality instead of an implication this direction is justified by the idea presented by g w leibniz that a fully satisfactory logical calculus must be an equational one in this paper we continue the study of eq algebras and their special cases we introduce and study the prefilters and filters of separated eq algebras we give great importance to the study of good eq algebras as we shall see in this paper the goodness property and thus separateness is necessary for reasonably behaving algebras we enrich good eq algebras with a unary operation d the so called baaz delta fulfilling some additional assumptions that are heavily used in fuzzy logic literature we show that the characterization theorem obtained until now for representable good eq algebras also hold for the enriched algebra

asymptotic stability for the system of neutral delay differential equations abstract this paper deals with the asymptotic stability of the system of neutral delay differential equations in an angle which has fewer reports stability regions are presented geometrically as well as two criteria which are obtained through the evaluation of a harmonic function on the boundary of a certain region numerical experiments on various circumstances are shown to locate the specific region which can make the system unstable so as to exclude it from the whole complex plane

non linear hierarchical models for monitoring compliance as biomarkers transformable by specific drug agents increasingly become available so their usefulness also increases for monitoring compliance in clinical and prevention trials and for subsequent monitoring in the general population if a treatment is found successful marker levels measured over the course of a treatment yield a longitudinal trajectory that is typically non linear with varying velocities during the phase in and steady state periods of treatment followed by decays back to normal in the presence of non compliance there is often considerable between individual variability both in the mean parameters of the trajectory and the variability over time an example is the biomarker mean corpuscular volume mcv which increases by 20 per cent from the drug zidovudine azt and has been used to monitor compliance to azt using mcv data from a previous aids clinical trial as an example we describe a non linear hierarchical growth model suitable for biomarkers that exhibit sigmoidal and or asymptotic growth behaviour and show how such models can be supplemented with a change point to identify potential times of non compliance we perform a fully bayesian analysis to obtain a variety of posterior summaries for the behaviour of the longitudinal trajectory and the times of non compliance and describe how to obtain predictions of non compliance for new individuals

delay independent stability criteria for discrete delay systems several sufficient conditions for stability of linear discrete delay systems are derived since these conditions are independent of the delay and possess simple forms they will provide useful tools to check stability of the systems at the first stage

a new approach to the derivation of exact analytical formulae for the zeros of sectionally analytic functions abstract a new method for the analytical determination of zeros of sectionally analytic functions in the cut complex plane or of poles of sectionally meromorphic functions based only on the first plemelj formula is proposed this method like the analogous earlier methods of burniston and siewert and of the senior author leads to the determination of these zeros or poles as the roots of a polynomial the coefficients of this polynomial contain regular integrals along the discontinuity interval which can be computed by appropriate usually gaussian quadrature rules the advantage of the present approach over the existing ones is its simplicity as a concept and ease during the application to particular sectionally analytic or meromorphic functions

homotopies for solving polynomial systems within a bounded domain abstract the problem considered in this paper is the computation of all solutions of a given polynomial system in a bounded domain proving rouche s theorem by homotopy continuation concepts yields a new class of homotopy methods the so called regional homotopy methods these methods rely on isolating a part of the system to be solved which dominates the rest of the system on the border of the domain as the dominant part has a sparser structure it is easier to solve it will be used as start system in the regional homotopy the paper further describes practical homotopy construction methods by presenting estimators to obtain bounds for polynomials over a bounded domain applications illustrate the usefulness of the approach

a reliable argument principle algorithm to find the number of zeros of an analytic function in a bounded domain the argument principle is a natural and simple method to determine the number of zeros of an analytic functionf z in a bounded domaind n the number of zeros counting multiplicities off z is 1 2 times the change in argf z asz moves along the closed contour d since the range of argf z is a critical point in the computational procedure is to assure that the discretization of d z i i 1 m is such that delta text z i text text z i 1 text arg f z leqq pi discretization control which may violate this inequality can lead to an unreliable algorithm mathematical theorems derived for the discretization of d lead to a completely reliable algorithm to computen this algorithm also treats in an elementary way the case when a zero is on or near the contour d numerical examples are given for the reliable algorithm formulated here and it is pointed out in these examples how inadequate discretization control can lead to failure of other algorithms

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

eq algebras from the point of view of generalized algebras with fuzzy equalities eq algebras introduced by novak are algebras of truth values for a higher order fuzzy logic fuzzy type theory in this paper the compatibility of multiplication w r t the fuzzy equality in an arbitrary eq algebra is examined particularly an example indicates that the compatibility axiom does not always hold and then a class of eq algebras satisfying the compatibility axiom is characterized by introducing a residuated integral meet semilattice ordered monoid valued fuzzy algebra called a generalized algebra with a fuzzy equality

on the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane abstract a family of higher order iterative methods for the simultaneous determination of all simple or multiple zeros of an analytic function inside a simple smooth closed contour is obtained using earlier results of the author with the help of circular arithmetic the interval variant of this family is proposed many parallel iterative methods of the literature are special cases of this family

a modification of the delves lyness method for locating the zeros of analytic functions abstract a new formula is proposed for the calculation of the integrals involved in the application of the delves lyness method for locating the zeros of analytic functions inside an arbitrary simple smooth contour this formula does not contain the derivative of the analytic function whose zeros are sought and moreover is free from multivaluedness problems for the integrand

quotients with respect to similarity relations abstract the problem of the quotient w r t a similarity relation is closely related to poincare s paradox and central problems in cluster analysis amazingly this problem remains open for more than 30 years as a generalization of strong m categories we introduce the concept of m valued sets which leads to the definition of the category m set in m set we give a complete solution of the quotient problem

delay independent exponential stability criteria for time varying discrete delay systems derives delay independent exponential stability conditions for linear nonlinear time varying discrete delay systems since these conditions are of delay independence and easily verifiable they may provide handy tools for the stability analysis

solution of equations involving analytic functions abstract the location by the method of delves and lyness of the roots of the equation z 0 for analytic is examined new formulas are proposed for calculating the integrals involved in the application of the method these formulas do not require the evaluation of z and are more accurate than some existing ones a highly reliable but not completely foolproof procedure for computing the number of zeros of in a given region is also proposed

asymptotic and numerical stability of systems of neutral differential equations with many delays we are concerned with the asymptotic stability of a system of linear neutral differential equations with many delays in the form y t ly t email protected i 1dm iy email protected i email protected i 1dn iy email protected i where l m i n email protected c n x n i 1 2 d are constant complex matrices t i 0 i 1 2 d are constant delays and y t y 1 t y 2 t y n t t is an unknown vector valued function for t 0 we first establish a new result for the distribution of the roots of its characteristic function next we obtain a sufficient condition for its asymptotic stability and then we investigate the corresponding numerical stability of linear multistep methods applied to such systems one numerical example is given to testify our numerical analysis

eq algebras we introduce a new class of algebras called eq algebras an eq algebra has three basic binary operations meet multiplication and a fuzzy equality and a top element these algebras are intended to become algebras of truth values for a higher order fuzzy logic a fuzzy type theory ftt the motivation stems from the fact that until now the truth values in ftt were assumed to form either an imtl bl or mv algebra all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation multiplication and its residuum the latter is a natural interpretation of implication in fuzzy logic the equivalence is then interpreted by the biresiduum a derived operation the basic connective in ftt however is a fuzzy equality and therefore it is not natural to interpret it by a derived operation this defect is expected to be removed by the class of eq algebras introduced and studied in this paper from the algebraic point of view the class of eq algebras generalizes in a certain sense the class of residuated lattices and so they may become an interesting class of algebraic structures as such

numerical algorithms based on analytic function values at roots of unity let f z be an analytic or meromorphic function in the closed unit disk sampled at the n th roots of unity based on these data how can we approximately evaluate f z or f m z at a point z in the disk how can we calculate the zeros or poles of f in the disk these questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations partial differential equations and large scale linear algebra we analyze some of the possibilities and emphasize the distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of cauchy integrals we then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension finally we highlight the power of rational in comparison with polynomial approximations for some of these problems

numerical stability of the t methods for systems of differential equations with several delay terms abstract consider the following two dimensional delay differential equation dde u t a 1 u t b 1 v t d 2 v t a 2 v t b 2 u t d 1 t t 0 with the initial conditions u t u 0 t t 0 d 1 t t 0 v t v 0 t t 0 d 2 t t 0 where a j b j c d j 0 and u 0 t 0 t are continuous and complex valued the author give the sufficient conditions for the asymptotic stability of equation 0 1 the numerical stabilities of the linear method and the one leg method are investigated by analysing their stabilities behaviour in the solutions of 0 1 it is shown that the linear method is gp stable if and only if 1 2 1 and that the one leg method is gp stable if and only if 1

simple stability criteria for nonlinear time varying discrete systems abstract we present two sufficient conditions for asymptotic stability of nonlinear time varying discrete systems our main results generalize mori s result for linear discrete time invariant systems to nonlinear time varying systems

stability of neutral delay differential systems boundary criteria this paper deals with the delay dependent stability of linear invariant neutral delay differential systems with a positive constant delay six criteria that are described by evaluating a corresponding harmonic function on the boundary of a certain rectangular region are presented

on bayesian analysis of mixtures with an unknown number of components discussion author s reply new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

a reliable algorithm for computing the topological degree of a mapping in r2 abstract in this paper we present a method to reliably compute the topological degree of a mapping in the plane over a simple closed polygon the method is based on henrici s argument principle and computes the degree using the winding number concept in range arithmetic the algorithm is then applied to the root computation of a univariate polynomial the proposed algorithms are demonstrated with examples

stability of linear neutral systems with multiple delays boundary criteria the stability of linear neutral delay differential systems with multiple delays is investigated the delay dependent stability criteria are presented through the evaluation of the corresponding harmonic functions on the boundary of a certain half circular region and such criteria are extensions of some results in literature an example is given to illustrate the stability criteria

computable stability criterion of linear neutral systems with unstable difference operators abstract this paper is concerned with linear neutral systems with unstable difference operators all the unstable characteristic roots of the linear neutral systems are located in a bounded half circular region then based on the argument principle a computable stability criterion is derived which is necessary and sufficient for asymptotic stability of the neutral systems furthermore the number of the unstable characteristic roots is given the main results of the present paper extend those in literature numerical experiments are provided to illustrate the main results

computation of closed loop eigenvalues associated with the optimal regulator problem for functional differential equations a solution of the linear quadratic control problem involving functional differential equations gives a linear feeback which modifies the original system dynamics under certain assumptions the eigenvalues of the modified system constitute a stable part of the spectrum of a certain hamiltonian operator these eigenvalues can be computed without solving the infinite dimensional riccati equation in this note we present a method to compute the eigenvalues directly from a characteristic equation of the optimal closed loop system numerical results are presented for three examples and compared to those obtained by a finite dimensional approximation of a functional differential equation

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

the numerical solution of discrete delay systems in this note we consider the numerical solution of initial value discrete delay systems an interpolation procedure is introduced to compute the numerical solution the convergence and stability of the interpolation procedure for the discrete delay systems is discussed

algebras with fuzzy equalities an algebra with fuzzy equality is a set with operations on it that is equipped with similarity i e a fuzzy equivalence relation such that each operation f is compatible with described verbally compatibility says that each f yields similar results if applied to pairwise similar arguments on the one hand algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic and have been studied from this point of view before on the other hand they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones the present paper aims at developing fundamental points of algebras with fuzzy equalities we introduce the notion of an algebra with fuzzy equality present natural examples compare the notion with other approaches and introduce and develop basic structural notions subalgebras morphisms products direct unions in a follow up paper vychodil direct limits and reduced products of algebras with fuzzy equalities submitted for publication we deal with advanced topics in algebras with fuzzy equalities direct limits reduced products

the numerical solution of discrete delay systems abstract in this note we consider the numerical solution of initial value discrete delay systems an interpolation procedure is introduced to compute the numerical solution the stability of the interpolation procedure for linear discrete delay systems is discussed

locating the zeros of an analytic function abstract a numerical technique is presented for locating the zeros of an analytic function in the complex plane the methods used are not new the important content of this paper is the development and testing of a method to a point where it may be used with confidence and reliability an application considered here is the location of the eigenvalues of the orr sommerfeld equation for plane poiseuille flow in a specified portion of the complex eigenvalue plane

a new simple approach to the derivation of exact analytical formulae for the zeros of analytic functions a very simple method for the construction of the polynomial whose zeros coincide with the zeros of an analytic function inside and along a simple closed contour in the complex plane based on an appropriate application of the cauchy theorem in complex analysis is proposed the present method was motivated by the classical burniston siewert method based on the theory of the riemann hilbert boundary value problem for the construction of the aforementioned polynomial but although essentially equivalent to the burniston siewert method it is much simpler

stability analysis for delay differential equations with multidelays and numerical examples in this paper we are concerned with the asymptotic stability of the delay differential equation x t a 0 x t a k x t k where a 0 a k c d d are constant complex matrices and x t k x 1 t k1 x 2 t k2 x d t kd t kl 0 stand for n x d constant delays k 1 n i 1 d we obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region we also get similar results for the neutral delay differential equation x t lx t m i x t i n j x t j where l m i and nj e c d d are constant complex matrices and i j 0 stands for constant delays i 1 m j 1 n numerical examples on various circumstances are shown to check our results which are more general than those already reported

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

numerical integration error method for zeros of analytic functions it is shown that a globally convergent zero finding method named the numerical integration error method niem can be applied to functions in a certain class of analytic functions including exponential type some results of numerical experiments are given

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi