cylindrical cellular automata a one dimensional cellular automaton with periodic boundary conditions may be viewed as a lattice of sites on a cylinder evolving according to a local interaction rule a technique is described for finding analytically the set of attractors for such an automaton given any one dimensional automaton rule a matrixa is defined such that the number of fixed points on an arbitrary cylinder size is given by the trace ofa n where the powern depends linearly on the cylinder size more generally the number of strings of arbitrary length that appear in limit cycles of any fixed period is found as the solution of a linear recurrence relation derived from the characteristic equation of an associated matrix the technique thus makes it possible for any rule to compute the number of limit cycles of any period on any cylinder size to illustrate the technique closed form expressions are provided for the complete attractor structure of all two neighbor rules the analysis of attractors also identifies shifts as a basic mechanism underlying periodic behavior every limit cycle can be equivalently defined as a set of strings on which the action of the rule is a shift of sizes h i e each string cyclically shifts bys sites inh iterations of the rule the study of shifts provides detailed information on the structure and number of limit cycles for one dimensional automata

stability and stabilization of delay differential systems the delay systems considered here are represented by linear delay differential equations the system parameters and the delays are assumed to be imperfectly known the instantaneous state vector is perturbed by a bounded external disturbance vector the problem addressed is that of characterizing conditions that guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints it is shown that the positive invariance property can be used to solve this problem and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system the possible use of these results for the control of a multiple delay mimo differential model is then presented finally an example is given

graph theoretical characterization of invertible cellular automata abstract a cellular automaton is defined to be invertible if its induced global rule is surjective on the set of all finite configurations it is shown that all one dimensional invertible cellular automata are obtainable from invertible nearest pair ones i e cellular automata given by a rule matrix for these an algorithm is proposed which runs in a time which is a polynomial function of the number of letters of the alphabet the result is expressed in a graph theoretical way the cellular automaton is invertible if and only if two graphs constructed by the algorithm have no edges in common it follows that if the number of letters in the alphabet is a prime the only invertible cellular automata are those for which every row or column of the rule matrix is a permutation of the alphabet for composite alphabet cardinalities several methods analytical and computational ones to obtain more complicated invertible cellular automata are proposed and used to construct examples all four letter invertible automata are constructed

effect of the numerical scheme resolution on quasi 2d simulation of an automotive radial turbine under highly pulsating flow automotive turbocharger turbines usually work under pulsating flow because of the sequential nature of engine breathing however existing turbine models are typically based on quasi steady assumptions in this paper a model where the volute is calculated in a quasi 2d scheme is presented the objective of this work is to quantify and analyse the effect of the numerical resolution scheme used in the volute model the conditions imposed upstream are isentropic pressure pulsations with different amplitude and frequency the volute is computed using a finite volume approach considering the tangential and radial velocity components the stator and rotor are assumed to be quasi steady in this paper different integration and spatial reconstruction schemes are explored the spatial reconstruction is based on the muscl method with different slope limiters fulfilling the tvd criterion the model results are assessed against 3d u rans calculations the results show that under low frequency pressure pulses all the schemes lead to similar solutions but for high frequency pulsation the results can be very different depending upon the selected scheme this may have an impact in noise emission predictions

study of iterative methods through the cayley quadratic test many iterative methods for solving nonlinear equations have been developed recently the main advantage claimed by their authors is the improvement of the order of convergence in this work we compare their dynamical behavior on quadratic polynomials with the one of newton s scheme this comparison is defined in what we call cayley quadratic test cqt which can be used as a first test to check the efficiency of such methods moreover we make a brief insight in cubic polynomials

on convergence of a new secant like method for solving nonlinear equations in this paper we prove that the order of a new secant like method presented recently with the so called order of 2 618 is only 2 414 some mistakes in the derivation leading to such a conclusion are pointed out meanwhile under the assumption that the second derivative of the involved function is bounded the convergence radius of the secant like method is given and error estimates matching its convergence order are also provided by using a generalized fibonacci sequence

influence of gravity on generalized magneto thermoelastic medium for three phase lag model the three phase lag model and green naghdi theory without energy dissipation are applied to study the effect of the gravity field and a magnetic field on a wave propagation in a generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed the medium is a homogeneous isotropic thermoelastic in the half space the exact expressions of the displacement components temperature and stress components are obtained by using normal mode analysis numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of a magnetic field as well as the gravity field

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

an optimization algorithm for solving the rich vehicle routing problem based on variable neighborhood search and tabu search metaheuristics this paper presents a novel optimization algorithm that consists of metaheuristic processes to solve the problem of the capillary distribution of goods in major urban areas taking into consideration the features encountered in real life time windows capacity constraints compatibility between orders and vehicles maximum number of orders per vehicle orders that depend on the pickup and delivery and not returning to the depot with the intention of reducing the wide variety of constraints and complexities known as the rich vehicle routing problem this algorithm proposes feasible alternatives in order to achieve the main objective of this research work the reduction of costs by minimizing distances and reducing the number of vehicles used as long as the service quality to customers is optimum and a load balance among vehicles is maintained

newton like methods for the computation of fixed points abstract the celebrated banach fixed point theorem provides conditions which assure that the method of successive substitution is convergent the convergence however may take place very slowly so that it may be desirable to use a newton like method for the computation of the fixed point if newton s method itself is applied one ignores the additional information that the problem arises from a frixed point problem with a contraction mapping in the present note some variants of newton s method are discussed which make use of this contraction information it turns out that the convergence of newton s method can be accelerated without any relevant additional computational labour

on an iterative algorithm with superquadratic convergence for solving nonlinear operator equations we study an iterative method with order 1 2 for solving nonlinear operator equations in banach spaces algorithms for specific operator equations are built up we present the received new results of the local and semilocal convergence in case when the first order divided differences of a nonlinear operator are holder continuous moreover a quadratic nonlinear majorant for a nonlinear operator according to the conditions laid upon it is built a priori and a posteriori estimations of the method s error are received the method needs almost the same number of computations as the classical secant method but has a higher order of convergence we apply our results to the numerical solving of a nonlinear boundary value problem of second order and to the systems of nonlinear equations of large dimension

decision model for siting transport and logistic facilities in urban environments in this study based on the use of a geographic information system gis we define a decision model for determining the possible optimal locations of various facilities in an urban setting which can be used by the transport infrastructure or logistics sector the proposed methodology is based on the superposition of layers in gis software thereby enabling the prioritization or exclusion of certain areas depending on whether they meet specific requirements defined in each of the layers this formulation assigns one degree of decision to each area of the map and it then classifies all of the areas to obtain the best solution according to the jenks optimization method we provide five case studies of transport related facilities including an example where the location of a hydrogen refueling station is determined using the proposed methodology

a technique to choose the most efficient method between secant method and some variants abstract a few variants of the secant method for solving nonlinear equations are analyzed and studied in order to compute the local order of convergence of these iterative methods a development of the inverse operator of the first order divided differences of a function of several variables in two points is presented using a direct symbolic computation the computational efficiency and the approximated computational order of convergence are introduced and computed choosing the most efficient method among the presented ones furthermore we give a technique in order to estimate the computational cost of any iterative method and this measure allows us to choose the most efficient among them

output feedback stabilization for a discrete time system with a time varying delay this study employs the free weighting matrix approach to investigate the output feedback control of a linear discrete time system with an interval time varying delay first the delay dependent stability is analyzed using a new method of estimating the upper bound on the difference of a lyapunov function without ignoring any terms and based on the results a design criterion for a static output feedback sof controller is derived since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility sof control problem furthermore the problem of designing a dynamic output feedback controller is formulated as one of designing an sof controller numerical examples demonstrate the effectiveness of the method and its advantage over existing methods

mathematical analysis of a biochemical oscillator with delay in this work we analyze a nonlinear delay differential equation dde model with negative feedback and constant time delay the model is constructed from a previously studied biochemical reaction network of gene transcription and protein synthesis linear analysis of the associated dde model gives a critical time delay beyond which a periodic motion is born in a hopf bifurcation the method of multiple scales is then used to analyze the nonlinear system to obtain expressions for the amplitude and frequency of oscillation as a function of the system parameters we use our closed form analytical expressions to study the importance of a well balanced ratio between synthesis and degradation rates in the existence of periodic solutions we show that our theoretical results are in agreement with numerical simulations and with experimental evidence found in the biological literature

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

high performance computing of the matrix exponential this work presents a new algorithm for matrix exponential computation that significantly simplifies a taylor scaling and squaring algorithm presented previously by the authors preserving accuracy a matlab version of the new simplified algorithm has been compared with the original algorithm providing similar results in terms of accuracy but reducing processing time it has also been compared with two state of the art implementations based on pade approximations one commercial and the other implemented in matlab getting better accuracy and processing time results in the majority of cases

semilocal convergence of secant like methods for differentiable and nondifferentiable operator equations abstract from well known secant like methods we observe that we can construct a new family of secant like methods that includes the secant method and kurchatov s method we analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators finally we apply our results to conservative problems

robust observer based h controller design for linear uncertain time delay systems in this note we present a robust observer based h control design method for linear time delay systems with norm bounded time varying uncertainties using the riccati equation based approach we design observer based feedback control laws which guarantee the quadratic stability of the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

moving meshes to solve the time dependent neutron diffusion equation in hexagonal geometry to simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time dependent neutron diffusion equation inside the reactor core here the spatial discretization of this equation is done using a finite element method that permits h p refinements for different geometries this means that the accuracy of the solution can be improved refining the spatial mesh h refinement and also increasing the degree of the polynomial expansions used in the finite element method p refinement transients involving the movement of the control rod banks have the problem known as the rod cusping effect previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties the present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells the performance of the moving mesh scheme is tested studying one dimensional and three dimensional benchmark problems the simulation of transients on nuclear reactors involving control rods movements present the rod cusping problem to avoid this problem a moving mesh scheme based on hp finite element method is proposed for the time dependent neutron diffusion equation 1d and 3d benchmarks have been studied obtaining accurate results for coarse mesh discretizations

predecessor states for certain cellular automata evolutions this paper reports the solution of the problem of finding which inputs for a function of discrete variables will result in any specified output for the set of binomially determined nearest neighbor additive cellular automata defined on finite or half infinite sequences in computing the solution to this problem a process which is the discrete analog to backward integration is defined this process is determined in terms of an operator which exhibits an interesting period multiplying property

newton like method with modification of the right hand side vector this paper proposes a new newton like method which defines new iterates using a linear system with the same coefficient matrix in each iterate while the correction is performed on the right hand side vector of the newton system in this way a method is obtained which is less costly than the newton method and faster than the fixed newton method local convergence is proved for nonsingular systems the influence of the relaxation parameter is analyzed and explicit formulae for the selection of an optimal parameter are presented relevant numerical examples are used to demonstrate the advantages of the proposed method

efficient numerical integration of n th order non autonomous linear differential equations we consider the numerical integration of high order linear non homogeneous differential equations written as first order homogeneous linear equations and using exponential methods integrators like magnus expansions or commutator free methods belong to the class of exponential methods showing high accuracy on stiff or oscillatory problems but the computation of the exponentials or their action on vectors can be computationally costly the first order differential equations to be solved present a special algebraic structure associated with the companion matrix which allows to build new methods hybrid methods between magnus and commutator free methods the new methods are of similar accuracy as standard exponential methods with a reduced complexity additional parameters can be included into the scheme for optimization purposes we illustrate how these methods can be obtained and present several sixth order methods which are tested in several numerical experiments

on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

on efficient weighted newton methods for solving systems of nonlinear equations in this study we present iterative methods of convergence order four and six for solving systems of nonlinear equations the fourth order scheme is composed of two steps namely newton iteration as the first step and weighted newton iteration as the second step the sixth order scheme is composed of three steps the first two steps are same as that of fourth order scheme whereas the third step is again based on weighted newton iteration computational efficiency in its general form is discussed comparison between the efficiencies of proposed techniques and existing techniques is made it is proved that for large systems the new methods are more efficient numerical tests are performed which confirm the theoretical results moreover theoretical order of convergence is verified in the examples

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

algorithms for computing preimages of cellular automata configurations this paper investigates pre images ancestors or past configurations of specified configurations of one dimensional cellular automata both counting and listing of pre images are discussed the main graphical tools used are the de bruijn diagram and its extension the pre image network which is created by concatenating de bruijn diagrams the counting of pre images is performed as the multiplication of topological matrices of de bruijn diagrams listing of pre images is described using two algorithms the first algorithm traces paths in the pre image network and focuses on local knowledge of the network the second performs a complete analysis of the network before proceeding with listing

secant like methods for solving nonlinear integral equations of the hammerstein type we consider a one parametric family of secant type iterations for solving nonlinear equations in banach spaces we establish a semilocal convergence result for these iterations by means of a technique based on a new system of recurrence relations this result is then applied to obtain existence and uniqueness results for nonlinear integral equations of the hammerstein type we also present a numerical example where the solution of a particular hammerstein integral equation is approximated by different secant type methods

on the local convergence of a family of two step iterative methods for solving nonlinear equations a local convergence analysis for a generalized family of two step secant like methods with frozen operator for solving nonlinear equations is presented unifying earlier methods such as secant s newton chebyshev like steffensen and other new variants the family of iterative schemes is built up where a profound and clear study of the computational efficiency is also carried out numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root finally a study comparing the order efficiency and elapsed time of the methods suggested supports the theoretical results claimed

a non linear quasi 3d model with flux corrected transport for engine gas exchange modelling modelling has proven to be an important tool in the design of manifolds and silencers for internal combustion engines although simple 1d models are generally sufficiently precise in the case of manifold models they would usually fail to predict the high frequency behaviour of modern compact manifold designs and of course of a complex shaped silencing system complete 3d models are able to account for transversal modes and other non 1d phenomena but at a high computational cost a suitable alternative is provided by time domain non linear quasi 3d models whose computational cost is relatively low but still providing an accurate description of the high frequency behaviour of certain elements in this paper a quasi 3d model which makes use of a non linear second order time and space discretization based on finite volumes is presented as an alternative for avoiding overshoots at discontinuities a flux corrected transport technique has been adapted to the quasi 3d method in order to achieve convergence and avoid numerical dispersion it is shown that the combination of dissipation via damping together with the phoenical form of the anti diffusion term provides satisfactory results

the majorant method in the theory of newton kantorovich approximations and generalized lipschitz conditions we provide a semilocal as well as a local convergence analysis for newton s and modified newton s methods in order to approximate a locally unique solution of a nonlinear equation in a banach space setting we use more precise majorizing sequences than in earlier studies such as appell et al 1997 appell et al 1991 argyros 2004 argyros and hilout 2009 kantorovich and akilov 1982 ortega and rheinboldt 1970 and generalized lipschitz continuity conditions our sufficient convergence conditions are weaker than before and our convergence analysis is tighter special cases and numerical examples are also given in this study

letter to the editor frozen divided difference scheme for solving systems of nonlinear equations the development of an inverse first order divided difference operator for functions of several variables as well as a direct computation of the local order of convergence of an iterative method is presented a generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

on the gauss helmert model with a singular dispersion matrix where b q is of smaller rank than b the case of a singular dispersion matrix within the gauss helmert model has been considered before usually assuming a sufficiently small rank deficiency in order to guarantee a unique solution for both the residual vector as well as the estimated parameter vector of type best linear uniformly unbiased estimate bluue in this contribution the emphasis is shifted towards establishing necessary and sufficient conditions for a unique residual vector along with a unique estimate of type best linear uniformly minimum bias estimate blumbe for the parameter vector should uniformly unbiased estimates exist the blumbe obviously becomes the bluue

predecessors of cellular automata states ii pre images of finite sequences abstract graph theoretic techniques are used to derive algorithms which determine all pre images of any given finite sequence s under one dimensional cellular automata rules defined over z 2 it is also shown that for a given rule q the number of pre images of any finite sequence is determined by an algebraic form in the components of q this extends results of jen on the enumeration of pre images we also show that the set of k site rules for which a given sequence s has no pre images is determined by the solution set of a non linear diophantine equation

numerical solution of burgers equation with high order splitting methods in this work high order splitting methods have been used for calculating the numerical solutions of burgers equation in one space dimension with periodic dirichlet neumann and robin boundary conditions however splitting methods with real coefficients of order higher than two necessarily have negative coefficients and cannot be used for time irreversible systems such as burgers equations due to the time irreversibility of the laplacian operator therefore the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed if we consider the system as the perturbation of an exactly solvable problem or one that can be easily approximated numerically it is possible to employ highly efficient methods to approximate burgers equation the numerical results show that both the methods with complex time steps having one set of coefficients real and positive say a i r and b i c and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of burgers equation

on stability independent of delay for linear systems a new criterion for asymptotic stability of solutions of certain linear differential difference equations independent of the delay duration is given in terms of solutions of a complex lyapunov matrix equation

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

delay dependent robust h control of uncertain linear systems with time varying delays abstract this paper proposes an optimization based approach to the robust h control problem of uncertain continuous or discrete time linear time invariant systems with different time varying delays in the state vector and control input of the dynamic equation and controlled output sufficient delay dependent conditions are derived for the control stabilization problem where both the size of the time varying delay and the size of its time derivative in the continuous time case play a crucial role for the closed loop stability with a guaranteed h performance index the solutions that are proposed for the h control problem are similar or less conservative when compared to other recent approaches

h sub infinity analysis and synthesis of discrete time systems with time varying uncertainty the problems of h sub infinity analysis and synthesis of discrete time systems with block diagonal real time varying uncertainty are considered it is shown that these problems can be converted into scaled h sub infinity analysis and synthesis problems the problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case the results on synthesis are established for general linear dynamic output feedback control

on the convergence of efficient king werner type methods of order 1 2 we present a local as well as a semilocal convergence analysis of some efficient king werner type methods of order 1 2 in order to approximate a locally unique solution of a nonlinear equation in a banach space setting our results compare favorably to earlier results using the same or stronger hypotheses mcdougall and wotherspoon 2014 werner 1979 1982 numerical examples are also presented to illustrate the theoretical results

stability of x t ax t bx t tau a stability criterion for linear time delay systems described by a differential difference equation of the form dx t ax t bx t tau is proposed the result obtained includes information on the size of the delay and therefore can be a delay dependent stability condition its relation to existing delay independent stability criteria is also discussed

the king werner method for solving nonsymmetric algebraic riccati equation for the nonsymmetric algebraic riccati equation arising from transport theory we concern about solving its minimal positive solution in 1 lu transferred the equation into a vector form and pointed out that the minimal positive solution of the matrix equation could be obtained via computing that of the vector equation in this paper we use the king werner method to solve the minimal positive solution of the vector equation and give the convergence and error analysis of the method numerical tests show that the king werner method is feasible to determine the minimal positive solution of the vector equation

h control of discrete time linear systems with time varying delays in state this paper deals with the h control problems for discrete time linear systems with time varying delays in state in this paper the h control law is assumed to be a memoryless state feedback and the size of time varying delays considered is upper bounded the solution of the h control problem for discrete time linear systems with time varying delays in state can be obtained by solving an h control problem for auxiliary discrete time linear systems with no time delays

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

nearest neighbor cellular automata over z 2 with periodic boundary conditions abstract one dimensional nearest neighbor cellular automata defined over z 2 are characterized in terms of a set of eight non additive basis operators which act on the automaton state space every evolution rule for such automata can be expressed as an operator which is a direct sum of the basis operators this approach allows decomposition of automata rules into additive and non additive parts as a result it is simple to determine fixed points those states for which the rule reduces to the identity and shift cycles sets of states on which the rule reduces to a shift sets of states on which any given nearest neighbor automaton reduces to an identity or a shift are characterized and maximum tree heights are computed for certain cases the formalism is used to explore and generalize a relationship recently studied by ito we conclude by indicating a connection to the invariance matrix approach to cellular automata which has been developed by jen

periodic seeded arrays and automorphisms of the shift the automorphism group autfsy of the full 2 shift is conjectured to be generated by the shift and involutions we approach this problem by studying a certain family of automorphisms whose order was unknown but which we show to be finite and for which we find factorizations as products of involutions the result of this investigation is the explicit construction of a subgroup z of aut z2 z is generated by certain involutions g and turns out to have a number of curious properties for example gn and gk commute unless n and k are consecutive integers the order of gn k o o gk is independent of k and z contains elements of all orders the investigation is aided by the development of results about certain new types of arrays of o s and l s called periodic seeded arrays as well as the use of boyle and krieger s work on return numbers and periodic points

on the convergence of a damped newton like method with modified right hand side vector we present a convergence analysis for a damped newton like method with modified right hand side vector in order to approximate a locally unique solution of a nonlinear equation in a banach spaces setting in the special case when the method is defined on r m our method provides computable error estimates based on the initial data such estimates were not given in relevant studies such as numerical examples further validating the theoretical results are also presented in this study

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

semilocal convergence of a secant type method under weak lipschitz conditions in banach spaces abstract the semilocal convergence of double step secant method to approximate a locally unique solution of a nonlinear equation is described in banach space setting majorizing sequences are used under the assumption that the first order divided differences of the involved operator satisfy the weaker lipschitz and the center lipschitz continuity conditions a theorem is established for the existence uniqueness region along with the estimation of error bounds for the solution our work improves the results derived in ren and argyros 2015 in more stringent lipschitz and center lipschitz conditions and gives finer majorizing sequences also an example is worked out where the conditions of ren and argyros 2015 fail but our s work numerical examples including nonlinear elliptic differential equations and integral equations are worked out it is found that our conditions enlarge the convergence domain of the solution finally taking a nonlinear system of m equations the efficiency index e i and the computational efficiency index c e i of double step secant method are computed and its comparison with respect to other similar existing iterative methods are summarized in the tabular forms

the inverse eigenvalue problem for a hermitian reflexive matrix and the optimization problem the inverse eigenvalue problem and the associated optimal approximation problem for hermitian reflexive matrices with respect to a normal k 1 potent matrix are considered first we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them then when such a solution exists an expression for the solution to the corresponding optimal approximation problem is obtained

on a two step optimal steffensen type method relaxed local and semi local convergence analysis and dynamical stability abstract in this paper we study on the local and semi local convergence and dynamic of an iterative optimal two step steffensen s method we study local convergence by using lipschitz conditions and continuity of differentiable function f we also obtain semi local convergence by using majorizing sequences by this approach we can obtain the convergence of the method by minimum of auxiliary sequences and few initial conditions moreover we analyze the stability of the method via julia sets and parameter planes that is a novelty for steffensen type methods we extend this method for obtaining the sign function of a matrix numerical examples are given to confirm our theoretical results

a steffensen type method of two steps in banach spaces with applications this paper is devoted to the analysis of a steffensen type of two steps with order of convergence at least three the main advantage of this method is that it does not need to evaluate any frechet derivative or any bilinear operator the method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration we prove using recurrence relations a semilocal convergence result in banach spaces and do a detailed study of the domain of parameters associated to this result finally some numerical results including differentiable and nondifferentiable operators are presented special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing

wolfram s class iv automata and good life abstract a comprehensive discussion of wolfram s four classes of cellular automata is given with the intention of relating them to conway s criteria for a good game of life although it is known that such classifications cannot be entirely rigorous much information about the behavior of an automaton can be gleaned from the statistical properties of its transition table still more information can be deduced from the mean field approximation to its state densities in particular from the distribution of horizontal and diagonal tangents of the latter in turn these characteristics can be related to the presence or absence of certain loops in the de bruijn diagram of the automaton

comparative experiment on the numerical solutions of hammerstein integral equation arising from chemical phenomenon in this paper efficient numerical techniques have been proposed to solve nonlinear hammerstein integral equation arising from chemical phenomenon the following integral equation forms the basis for the conductor like screening model for real solvent which appeared in chemical phenomenon our aim is to solve the hammerstein nonlinear integral equation s r t ln p s exp e i n t s r t d where r is the gas constant t is the temperature and the term e i n t denotes the interaction energy expression for the segments with screening charge density and respectively the molecular interaction in solvent is p s and the chemical potential of the surface segments is described by s which is to be determined this cosmo rs integral equation has been solved by bernstein collocation method haar wavelet method and sinc collocation method these methods reduce the integral equation to nonlinear system of algebraic equations and then this algebraic system has been solved numerically by newton s method comparison has been done for these methods illustrative examples have been discussed to demonstrate the validity and applicability of bernstein collocation method haar wavelet method and sinc collocation method

periodic points and automorphisms of the shift on etudie le groupe d automorphisme d un decalage de markov topologique a l aide des points periodiques et des ensembles instables

predecessors of cellular automata states i additive automata abstract let e be the space of right half infinite sequences with entries in z 2 and let q be the global transition rule for the one dimensional cellular automaton q e for which e is the state space the predecessor problem for q e is to find all solutions of the equation q where is an arbitrary element of e in this paper we consider the case in which the operator q represents an additive rule the predecessor equation is solved in closed form for all two and three site rules in particular for rules 90 and 150 and a technique is introduced which generates a closed form solution for many higher site values this is demonstrated with several examples

on the convergence of king werner type methods of order 1 2 free of derivatives we present a semilocal and local convergence analysis of some efficient king werner type methods of order 1 2 free of derivatives in a banach space setting numerical examples are presented to illustrate the theoretical results

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

robust h control for linear discrete time systems with norm bounded time varying uncertainty the problem of robust h analysis and synthesis for linear discrete time systems with norm bounded time varying uncertainty is studied in this paper it will be shown that this problem is equivalent to the problem of h analysis and synthesis of an auxiliary system the necessary and sufficient conditions for the equivalency are proved thus the original problem can be solved by existing h control methods

solving random mixed heat problems this paper develops a random mean square fourier transform approach to solve random partial differential heat problems with nonhomogeneous boundary value conditions random mean square operational rules for the random fourier sine and cosine transforms are stated and illustrative examples are included

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

improved local convergence of newton s method under weak majorant condition we provide a local convergence analysis for newton s method under a weak majorant condition in a banach space setting our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than before 14 special cases and numerical examples are also provided in this study

a semilocal convergence analysis for directional newton methods a semilocal convergence analysis for directional newton methods in n variables is provided in this study using weaker hypotheses than in the elegant related work by y levin and a ben israel and introducing the center lipschitz condition we provide under the same computational cost as in levin and ben israel a semilocal convergence analysis with the following advantages weaker convergence conditions larger convergence domain finer error estimates on the distances involved and an at least as precise information on the location of the zero of the function a numerical example where our results apply to solve an equation but not the ones in levin and ben israel is also provided in this study

bayesian prediction for flowgraph models with covariates an application to bladder carcinoma statistical flowgraph models are an efficient tool to model multi state stochastic processes they support both frequentist and bayesian approaches inclusion of covariates is also available in this paper we propose an easy way to perform a bayesian approach with covariates results are presented with an application to bladder carcinoma data

a compact difference scheme for numerical solutions of second order dual phase lagging models of microscale heat transfer dual phase lagging dpl models constitute a family of non fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient these lags may need to be considered when modeling microscale heat transfer and thus dpl models have found application in the last years in a wide range of theoretical and technical heat transfer problems consequently analytical solutions and methods for computing numerical approximations have been proposed for particular dpl models in different settings in this work a compact difference scheme for second order dpl models is developed providing higher order precision than a previously proposed method the scheme is shown to be unconditionally stable and convergent and its accuracy is illustrated with numerical examples

an efficient derivative free family of fourth order methods for solving systems of nonlinear equations we present a derivative free two step family of fourth order methods for solving systems of nonlinear equations using the well known traub steffensen method in the first step in order to determine the local convergence order we apply the first order divided difference operator for functions of several variables and direct computation by taylor s expansion computational efficiencies of the methods of new family are considered and compared with existing methods of similar structure it is showed that the new family is especially efficient in solving large systems four numerical examples are given to compare the proposed methods with existing methods and to confirm the theoretical results

on graphs associated to sets of rankings in this paper we analyze families of rankings by studying structural properties of graphs given a finite number of elements and a set of rankings of those elements two elements compete when they exchange their relative positions in at least two rankings and we can associate an undirected graph to a set of rankings by connecting elements that compete we call this graph a competitivity graph competitivity graphs have already appeared in the literature as co comparability graphs f graphs or intersection graphs associated to a concatenation of permutation diagrams we introduce certain important sets of nodes in a competitivity graph for example nodes that compete among them form a competitivity set and nodes connected by chains of competitors form a set of eventual competitors these sets are analyzed and a method to obtain sets of eventual competitors directly from a set of rankings is shown

constructing positive reliable numerical solution for american call options a new front fixing transformation is applied to the black scholes equation for the american call option pricing problem the transformed non linear problem involves homogeneous boundary conditions independent of the free boundary the numerical solution by an explicit finite difference method is positive and monotone stability and consistency of the scheme are studied the explicit proposed method is compared with other competitive implicit ones from the points of view accuracy and computational cost

stability study of eighth order iterative methods for solving nonlinear equations in this paper we study the stability of the rational function associated to a known family of eighth order iterative schemes on quadratic polynomials the asymptotic behavior of the fixed points corresponding to the rational function is analyzed and the parameter space is shown in which we find choices of the parameter for which there exists convergence to cycles or even chaotical behavior showing the complexity of the family moreover some elements of the family with good stability properties are obtained

some supplementary results on the 1 sqrt 2 order method for the solution of nonlinear equations recently an iterative method for the solution of systems of nonlinear equations having at leastr order 1 sqrt 2 for simple roots has been investigated by the author 7 this method uses as many function evaluations per step as the classical newton method in the present note we deal with several properties of the method such as monotone convergence asymptotic inclusion of the solution and convergence in the case of multiple roots

the automorphism group of a shift of finite type let xt at be a shift of finite type and g aut vt denote the group of homeomorphisms of xt commuting with t we investigate the algebraic properties of the countable group g and the dynamics of its action on xt and associated spaces using marker constructions we show g contains many groups such as the free group on two generators however g is residually finite so does not contain divisible groups or the infinite symmetric group the doubly exponential growth rate of the number of automorphisms depending on n coordinates leads to a new and nontrivial topological invariant of crt whose exact value is not known we prove that modulo a few points of low period g acts transitively on the set of points with least at period n using padic analysis we generalize to most finite type shifts a result of boyle and krieger that the gyration function of a full shift has infinite order the action of g on the dimension group of at is investigated we show there are no proper infinite compact g invariant sets we give a complete characterization of the g orbit closure of a continuous probability measure and deduce that the only continuous g invariant measure is that of maximal entropy examples questions and problems complement our analysis and we conclude with a brief survey of some remaining open problems

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

the sums of powers theorem for commuting block maps a block map is a map f 0 1 0 1 for some n 2 1 a block map f induces an endomorphismfto of the full 2 shift x a composition of block maps is defined in such a way that f o g o fo o go in this paper some recent results concerning the set g i g o f f o g for certain types of block maps f are extended it has been shown 2 theorem 3 4 that the endomorphisms of the shift dynamical system over 0 1 can be studied via block maps an n block is a sequence b bn where b1 e 0 11 for 1 i n and an n block map is a function from the set of n blocks to the set 0 11 two endomorphisms commute if and only if the corresponding block maps commute there is a 1 1 relationship between n block maps and polynomial functions in n variables over z2 2 theorem 19 1 the commuting block maps problem has been solved in 1 for linear block maps and for block maps with polynomials of the form

predecessors of cellular automata states iii garden of eden classification of cellular automata abstract a procedure is given which determines all finite sequences without pre images for any one dimensional cellular automata with entries in z 2 on this basis we determine some properties of such sequences and classify all three site rules categories defined by this classification are compared to other phenomenological classifications introduced by wolfram gutowitz and jen