on the definition of temperature using time averages abstract this paper is a natural continuation of a previous one by the author which was concerned with the foundations of statistical thermodynamics far from equilibrium one of the problems left open in that paper was the correct definition of temperature in the literature temperature is in general defined through the mean kinetic energy of the particles of a given system in this paper instead temperature is defined a la caratheodory the system being coupled to a heat bath and temperature being singled out as the right integrating factor of the exchanged heat as a byproduct the right expression for the entropy is also obtained in particular in the case of a q distribution the entropy turns out to be that of tsallis

a parameter uniform implicit difference scheme for solving time dependent burgers equations abstract a numerical study is made for solving one dimensional time dependent burgers equation with small coefficient of viscosity burgers equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows for high coefficient of viscosity a number of solution methodology exist in the literature 6 7 8 9 and 14 but for the sufficiently low coefficient of viscosity the exist solution methodology fail and a discrepancy occurs in the literature in this paper we present a numerical method based on finite difference which works nicely for both the cases i e low as well as high viscosity coefficient the method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh the quasilinearzation process is used to tackle the non linearity an extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter to illustrate the method numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity

temporal extensivity of tsallis entropy and the bound on entropy production rate the tsallis entropy which is a generalization of the boltzmann gibbs entropy plays a central role in nonextensive statistical mechanics of complex systems a lot of efforts have recently been made on establishing a dynamical foundation for the tsallis entropy they are primarily concerned with nonlinear dynamical systems at the edge of chaos here it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by carati a carati physica a 348 110 2005 that whenever relevant the tsallis entropy indexed by q is temporally extensive linear growth in time i e finite entropy production rate then the universal bound on the entropy production rate is shown to be 1 absolute value 1 q the property of the associated probabilistic process i e the sojourn time distribution determining randomness of motion in phase space is also analyzed

a numerical solution of burgers equation by finite element method constructed on the method of discretization in time abstract in this paper the galerkin finite element method constructed on the method of discretization in time was applied to solve the one dimensional nonlinear burgers equation the system of nonlinear equations obtained for each time step was solved by using the newton method in order to show the efficiency of the presented method the numerical solutions obtained for various values of viscosity were compared with the exact solutions it was seen that they were in excellent agreement

interactive fuzzy decision making for multiobjective nonlinear programming usingaugmented minimax problems an interactive fuzzy decision making method for solving multiobjective nonlinear programming problems is presented in this paper by assuming that the decision maker dm has fuzzy goals for each of the objective functions the fuzzy goals of the dm are quantified by eliciting corresponding membership functions through the interaction with the dm having determined the membership functions if the dm specifies his reference membership values the augmented minimax problem is solved and the dm is supplied with the corresponding pareto optimal solution together with the trade off rates between the membership functions then by considering the current values of the membership functions as well as the trade off rates the dm responds by updating his reference membership values in this way the compromise or satisficing solution for the dm can be derived efficiently from among a pareto optimal solution set on the basis of the proposed method a time sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs

interactive stability of vector optimization problems abstract this paper presents a solution method for multiobjective nonlinear programming monlp problems and the stability of this solution the method called interactive stability compromise programming iscp offers a practical solution to monlp problems by deriving the compromise weights and combining judgement with an automatic optimization technique in fuzzy decision making this is achieved by using the method of compromise programming and the method of compromise weights and we obtain the stability for the solution in each step of the algorithm a numerical example illustrates various aspects of the results developed in this paper

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

fractal geometry information growth and nonextensive thermodynamics abstract this is a study of the information evolution of complex systems by a geometrical consideration we look at chaotic systems evolving in fractal phase space the entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement due to the incompleteness of the state number counting at any scale on fractal support the incomplete normalization i p i q 1 is applied throughout the paper where q is the fractal dimension divided by the dimension of the smooth euclidean space in which the fractal structure of the phase space is embedded it is shown that the information growth is nonadditive and is proportional to the trace form i p i i p i q which can be connected to several nonadditive entropies this information growth can be extremized to give power law distributions for these nonequilibrium systems it can also be used for the study of the thermodynamics derived from tsallis entropy for nonadditive systems which contain subsystems each having its own q it is argued that within this thermodynamics the stefan boltzmann law of blackbody radiation can be preserved

interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters this paper presents interactive decision making methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters on the basis of the level sets of the fuzzy numbers the concept of multiobjective programming and local m pareto optimality is introduced through the interaction with the decision maker dm the fuzzy goals of the dm for each of the objective functions in multiobjective programming are quantified by eliciting the corresponding membership functions after determining the membership functions in order to generate a candidate for the local satisficing solution which is also local m pareto optimal if the dm specifies the degree of the level sets and the reference membership values the augmented minimax problem is solved and the dm is supplied with the corresponding local m pareto optimal solution together with the trade off rates among the values of the membership functions and the degree then by considering the current values of the membership functions and as well as the trade off rates the dm responds by updating his her reference membership values and or the degree in this way the local satisficing solution for the dm can be derived efficiently from among an m pareto optimal solution set based on the proposed methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated

thermodynamics and time averages abstract for a dynamical system far from equilibrium one has to deal with empirical probabilities defined through time averages and the main problem then is how to formulate an appropriate statistical thermodynamics the common answer is that the standard functional expression of boltzmann gibbs for the entropy should be used the empirical probabilities being substituted for the gibbs measure other functional expressions have been suggested but apparently with no clear mechanical foundation here it is shown how a natural extension of the original procedure employed by gibbs and khinchin in defining entropy with the only proviso of using the empirical probabilities leads to a functional expression for the entropy which is in general different from that of boltzmann gibbs in particular the gibbs entropy is recovered for empirical probabilities of the poisson type while the tsallis entropies are recovered for a deformation of the poisson distribution

an implicit scheme for solving the convection diffusion reaction equation in two dimensions in this paper we consider a passive scalar transported in two dimensional flow the governing equation is that of the convection diffusion reaction equation for purposes of computational efficiency we apply an alternating direction implicit scheme akin to that proposed by polezhaev use of this implicit operator splitting scheme allows the application of a tridiagonal thomas solver to obtain the solution within each solution step a semidiscretization scheme is applied to discretize the differential equation in one dimension we approximate the time derivative term using a forward time stepping scheme the resulting inhomogeneous differential equation has only the spatial derivative terms and is solved using a newly proposed nodally exact steady state convection diffusion reaction scheme details on the development of the flux discretization scheme are provided modified equation analysis fourier stability analysis and a study on scheme monotonicity are also performed to shed further light on the proposed transient scheme to validate the proposed scheme we first consider test problems which are amenable to analytic solutions good agreement is obtained with both one and two dimensional steady unsteady problems thus demonstrating the validity of the method c 2000 academic press

stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints the aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent in addition the related dual problems for which the set of feasible parameters and the solvability set are studied these fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers the existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of a pareto optimality an illustrative example is given to clarify the obtained results

a perturbational h 4 exponential finite difference scheme for the convective diffusion equation a perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation four numerical examples including one to three dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes the h4 accuracy of the perturbational scheme is verified using double precision arithmetic

decomposition of the fuzzy parametric space in multiobjective nonlinear programming problems this paper deals with a method for decomposing the fuzzy parametric space in multiobjective nonlinear programming problems using the generalized tchebycheff norm this approach is simpler than the corresponding one using the nonnegative weighted sum of objectives also several results are introduced which relate two fuzzy programs with each other one with fuzzy parameters in the constraints and the other with fuzzy parameters in both objective functions and constraints these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the decomposition of parametric space in multiobjective convex programs using the generalized tchebycheff norm are reformulated to study under the concept of pareto optimality such results make the study of the first type of problems rather simple three illustrated examples are presented in the paper which clarify the developed theory

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

a numerical solution of burgers equation in this paper the burgers equation which is one dimensional quasi linear parabolic partial differential equation was solved by a variational method constructed on the method of discretization in time the numerical results obtained by these ways for various values of viscosity have been compared with the exact solution it was seen that they were in good agreement with each other

exponential methods for one dimensional reaction diffusion equations abstract non iterative exponential time linearization and iterative exponential quasilinearization techniques for one dimensional reaction diffusion equations based on the discretization of the time derivative the freezing of the coefficients of the resulting linear ordinary differential equations and the piecewise analytical solution of these ordinary differential equations are presented and applied to the nagumo and fisher equations these techniques yield three point finite difference expressions that depend in an exponential manner on either the diffusion reaction and transient terms or the diffusion and reaction terms it is shown that first order accurate in time exponential time linearization and exponential quasilinearization methods which account for reaction and diffusion processes in the ordinary differential operator are more robust than standard second order accurate techniques even for very large time steps and grid sizes and yield results in excellent accord with those obtained by means of non standard finite difference schemes and nodal integral formulations for the nagumo and fisher equations unlike non standard finite difference methods the exponential schemes presented in this paper do not require any knowledge of the exact solution of the differential equation and can be easily derived in a rather systematic manner compared with nodal integral formulations the exponential techniques presented here only require the solution of second order ordinary differential equations

a fourth order compact adi method for solving two dimensional unsteady convection diffusion problems n this article an exponential high order compact ehoc alternating direction implicit adi method in which the crank nicolson scheme is used for the time discretization and an exponential fourth order compact difference formula for the steady state 1d convection diffusion problem is used for the spatial discretization is presented for the solution of the unsteady 2d convection diffusion problems the method is temporally second order accurate and spatially fourth order accurate which requires only a regular five point 2d stencil similar to that in the standard second order methods the resulting ehoc adi scheme in each adi solution step corresponds to a strictly diagonally dominant tridiagonal matrix equation which can be inverted by simple tridiagonal gaussian decomposition and may also be solved by application of the one dimensional tridiagonal thomas algorithm with a considerable saving in computing time the unconditionally stable character of the method was verified by means of the discrete fourier or von neumann analysis numerical examples are given to demonstrate the performance of the method proposed and to compare mostly it with the high order adi method of karaa and zhang and the spatial third order compact scheme of note and tan

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

stability of possibilistic multiobjective nonlinear programming problems without differentiability abstract this paper deals with multiobjective nonlinear programming problems with possibilistic variables and without differentiability for the considered objective functions the concept of possibly optimal solution is specified for the parametric approach with possibility data a necessary and sufficient condition for such a solution is established the basic notions like the solvability set and the stability sets of the first second third and fourth kind have been defined and analyzed without differentiability assumptions on the considered functions under the concept of possibly feasible solution

numerical treatment of moving and free boundary value problems with the tau method this paper reports numerical experiments on the implementation of the operational formulation of the tau method for moving and free boundary value problems we consider problems defined by linear and nonlinear ordinary differential equations and by linear partial differential equa tions we compare the accuracy attainable with the technique introduced in this paper with that of standard numerical techniques we find that the tau method provides accurate results even using approximations of a low degree this paper reports numerical experiments on the implementation of the operational formulation of the tan method for the numerical treatment of moving and free boundary value problems we consider first problems involving linear and nonlinear ordinary differential equations and develop on them basic strategies for their tau method approximate solution we then discuss a tau lines formulation of these techniques and apply it to the approximate solution of a moving boundary value problem for partial differential equations the problem considered is related to a model for the diffusion and absorption of oxygen in biological tissue we compare our results with those obtained in the related literature using seven different numerical techniques we find that the tan method provides accurate results even using low degree polynomial approximations

modified nystrom methods for semi discrete hyperbolic differential equations first and second order nystrom type methods are derived for second order differential equations without first derivatives possessing the following properties i the stability interval equals 4m 2 m denoting the number of stages per integration step ii the method is internally stable irrespective of the value of m iii the storage requirements are limited and iv the costs per integration step are one right hand side evaluation one evaluation of the jacobian matrix and m 1 matrix vector multiplications these four properties are of interest in the integration of the usually very large systems of ordinary differential equations resulting from the semi discretization of partial differential equations which are of hyperbolic type and of second order in time

optimal solutions in optimization problem with objective function depending on fuzzy parameters in this paper we first introduce a broad class of fuzzy optimization problems with an objective function depending on fuzzy parameters fo problems and introduce the concept a maximal solutions of fo problems with respect to some fuzzy relation we derive a simple and natural sufficient condition for a feasible solution to be an a maximal solutions of fo problem later on we define possibly and necessarily a maximal solutions of fo problems and prove that any possibly or necessarily a maximal solution of fo problem is an a maximal solution with respect to the possibilistic fuzzy relation or necessity fuzzy relation respectively the introduced concepts and results are illustrated and discussed on two numerical examples

stability analysis and design of takagi sugeno fuzzy systems this work presents stable composite control criteria for multivariable takagi sugeno t s fuzzy systems on the basis of the linear matrix inequality lmi control strategy and parametric optimization the composite fuzzy control algorithms are derived unlike earlier studies of fuzzy control systems on an lmi framework this investigation develops a supervisory control approach such that a fuzzy controller can be synthesized more efficiently moreover a robust control scheme is applied to the t s fuzzy model with parametric uncertainties the sufficient conditions are deduced in the form of reduced lmis and adaptive tuning rules finally numeric simulations are given to validate the proposed approach

interactive stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints this paper deals with an interactive stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the qualitative analysis of stability set of the first kind are reformulated to study this stability set of first kind under the concept of pareto optimality an interactive algorithm for obtaining the best compromise solution and obtaining any subset of the parametric space which has the same corresponding pareto optimal solution is also presented an illustrative example is given to clarify the obtained results

numerical methods for nonlinear second order hyperbolic partial differential equations i time linearized finite difference methods for 1 d problems abstract a three parameter family of finite difference methods for one dimensional hyperbolic equations with damping and nonlinearities based on the introduction of a new dependent variable and three implicitness parameters for the time discretization and the diffusion and reaction terms is presented and shown to result in two time level semi discrete equations second order accurate spatial discretizations and time linearization of the nonlinear source terms are shown to result in three time level linear finite difference equations which are second order accurate in time whenever the reaction and diffusion terms are allocated in the proportion 1 2 1 to the past current and future time levels second order accurate in time time linearized three point compact operator methods for the spatial derivatives which only involve three time levels and three grid points and are fourth order accurate in space are also presented and their linear stability analyzed an exhaustive comparison between analytical and numerical results indicates that the accuracy of time linearized methods increases as the time step and grid spacing are decreased and is nearly independent of the order of the spatial discretization when there is a sufficient number of grid points to resolve the wave structure and the best accuracy is achieved when the three implicitness parameters are equal to 1 2 it is also shown that the accuracy of time linearized methods is a strong function of the wave speed as the wave speed is increased and the wave equation tends to a parabolic one the methods are still three time level techniques which may not preserve the positivity of the solution whereas a crank nicolson discretization of the corresponding parabolic equation does preserve this property provided that there are no mathematical incompatibilities between the initial and the boundary conditions it is also shown that for one dimensional wave equations with monotonic kinetics and time dependent forcing there are very few differences between second and first order time accurate discretizations of the diffusion terms provided that the time step and grid size are sufficiently small and the discretization of the reaction terms plays a less important rule than that of the diffusion terms

on diffusive methods and exponentially fitted techniques liouville s transformations are employed to reduce a one dimensional time dependent convection diffusion reaction operator to a diffusion reaction one which upon a control volume second order accurate discretization results in the same finite difference methods as those of exponentially fitted techniques two variants of these techniques are considered depending on the continuity and or smoothness of the analytical albeit approximate solution to the ordinary differential equations that result upon discretization of the time variable time linearization and piecewise spatial linearization of linear equations it is shown that these exponential techniques include those of allen and southwell il in and el mistikawy and werle for steady linear convection diffusion operators and are linearly stable and monotonic it is also shown that exponentially fitted techniques account for the characteristic times of reaction diffusion and residence and the time step employed in the discretization of the time variable can use adaptive refinement techniques and can account for the convection diffusion and reaction the convection and diffusion the reaction and diffusion and the diffusion processes however the latter three require iterative techniques to find the numerical solution

stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints abstract the purpose of the paper is to investigate the stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints these fuzzy parameters are characterized by fuzzy numbers for such problems concept and notion of the stability set of the first kind in parametric nonlinear programming problems are redefined and analyzed qualitatively under the concept of pareto optimality an algorithm for the determination of any subset of the parametric space which has the same corresponding pareto optimal solution is proposed a numerical example is given to illustrate the method developed in the paper

stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints this paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraint functions these fuzzy parameters are characterized by fuzzy numbers qualitative and quantitative analysis of the basic notions like the set of feasible parameters the solvability set the stability sets of the first kind and of the second kind will be reformulated under the concept of pareto optimality an illustrative example is given to clarify the obtained results

a parametric study of multiobjective nlp problems with fuzzy parameters in the objective functions abstract this paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the qualitative analysis of the notions solvability set stability sets of the first kind and of the second kind in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality an algorithm for obtaining any subset of the parametric space which has the same corresponding pareto optimal solution is also presented an illustrative example is given to clarify the obtained results

on some applications of the superposition principle with fourier basis this paper presents several applications of local fourier basis combined with corrector techniques via the superposition principle to compute solutions of boundary value problems our methodology is inspired by the well known corrector technique used in asymptotic singular perturbation theory see for example w eckhaus asymptotic analysis of singular perturbations north holland amsterdam 1979 we build solvers for time dependent boundary value problems and or singular perturbation problems using fourier expansions combined to additional convenient set of time independent basis functions to enforce the boundary conditions the algorithms are very well suited for parallel computing because they rely mainly on ffts and basis functions given analytically or computed in parallel once and for all our method can be spectral accurate for simple geometry we obtain in addition interesting new results for boundary value problems with complex geometry we describe in this paper the implementation of the method and the numerical results for many linear and nonlinear problems our goal is to test the advantages and the limits of our approach in order to motivate further theoretical investigations our method applied to steady one dimensional problems is similar to the work of israeli vozovoi and averbuch j sci comput 8 1993 pp 135 149 on domain decomposition with local fourier basis for the helmotz problem however our methodology for time dependent problem and or two space dimensions geometry is rather different in its spirit and complements previous investigations of israeli vozovoi and averbuch

shooting methods for 1d steady state free boundary problems in this note we present two numerical methods based on shooting methods to solve steady state diffusion absorption models

order reduction and how to avoid it when explicit runge kutta nystrom methods are used to solve linear partial differential equations in this paper we study the order reduction which turns up when explicit runge kutta nystrom methods are used to discretize linear second order hyperbolic equations by means of the method of lines the order observed in practice including its fractional part is obtained it is also proved that the order reduction can be completely avoided taking the boundary values of the intermediate stages of the time semidiscretization the numerical experiments confirm that the optimal order can be reached

a comparison of time discretization linearization approaches for the incompressible navier stokes equations abstract this paper presents a numerical study of two ways for discretizing and linearizing the time dependent incompressible navier stokes equations one approach consists in first applying a semi discretization in time by a fully implicit scheme then in each discrete time the equations are linearized by a fixed point iteration the number of iterations to reach a given stopping criterion is a priori unknown in this approach in the second approach rosenbrock schemes with s stages are used as temporal discretization the non linearity of the navier stokes equations is treated internally in the rosenbrock methods in each discrete time exactly s linear systems of equations have to be solved the numerical study considers five two dimensional problems with distinct features four implicit time stepping schemes and five rosenbrock methods are involved

a numerical solution of burgers equation by modified adomian method in this paper the modified adomian s decomposition method for calculating a numerical solution of the one dimensional quasi linear the burgers equation is presented time discretization has been used in decomposition without using any transformation in the burgers equation such as hopf cole transformation the numerical results obtained by this way for various values of viscosity have been compared with the exact solution to show the efficiency of the method

linearly implicit approximate factorization exponential methods for multi dimensional reaction diffusion equations abstract linearly implicit approximate factorization methods are used to reduce the solution of multi dimensional reaction diffusion equations to a sequence of two point boundary value problems in ordinary differential equations which are solved analytically in a piecewise manner it is shown that depending on the allocation of the transient diffusion and reaction terms to the second order ordinary differential operators several families of piecewise exponential methods can be obtained when only diffusion is included a quadratic analytical solution is obtained whereas if transient and diffusion diffusion and reaction and transient diffusion and reaction terms are included piecewise exponential methods result it is shown that exponential methods that only account for reaction and diffusion in the differential operator may result in ill conditioned systems of algebraic equation whereas if diffusion transient and reaction are included ill conditioning is avoided if the time step is sufficiently small it is also shown that the most robust exponential method is that that accounts for transient and diffusion terms in the differential operator and this method provides solutions in good accord with those of a linearly implicit approximate factorization technique which employs a three point second order accurate discretization of the diffusion terms it is also shown that a hybrid exponential method that solves the transient reaction and diffusion terms at odd time levels and the transient and diffusion terms at even time levels also provides very accurate solutions

on the fractal dimension of orbits compatible with tsallis statistics abstract in a previous paper a carati physica a 348 2005 110 120 it was shown how for a dynamical system the probability distribution function of sojourn times in phase space defined in terms of the dynamical orbits up to a given observation time induces unambiguously a statistical ensemble in phase space in the present paper the p d f of the sojourn times corresponding to a tsallis ensemble is obtained this by the way requires the solution of a problem of a general character disregarded in paper a carati physica a 348 2005 110 120 in particular some qualitative properties such as the fractal dimension of the dynamical orbits compatible with the tsallis ensembles are indicated

equivalence of c0 and c1 methods for ode s in this paper it is proved that exponentially fitted c 0 techniques based on piecewise linearization on two adjacent intervals which employ conditions as the three points in this interval and yield piecewise analytical solutions also provide piecewise smooth solutions everywhere the proof is based on the use of exponential c 1 methods based on the piecewise linearization of nonlinear ordinary differential equations in two adjacent nonoverlapping intervals and the imposition of continuity conditions at the end points of these intervals plus the condition of smoothness at the common boundary point of these adjacent intervals it is also shown that this smoothness requirement comes at the expense of a loss in accuracy of c 1 methods and that the resulting piecewise smooth method is only first order accurate for small values of the perturbation parameter

shooting methods for one dimensional diffusion absorption problems in this paper a numerical algorithm is presented and analyzed based on the shooting method to approximate the solution of a model for the diffusion and absorption of oxygen in living tissue the model is a variant of one originally proposed by crank and gupta j inst math appl 10 1972 pp 19 33 in that article the rate of consumption of oxygen is assumed to be constant in this paper this rate is assumed to be a function of the distance to the outer surface of the tissue this allows for an inhomogeneous medium i e the oxygen consumption rate could vary from point to point

discrete transparent boundary conditions for schrodinger type equations we present a general technique for constructing nonlocal transparent boundary conditions for one dimensional schrodinger type equations our method supplies boundary conditions for the family of implicit one step discretizations of schrodinger s equation in time the use of mikusi ski s operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner

simulations of transverse vibrations of an axially moving string a modified difference approach a modified finite difference approach to simulate transverse vibrations of an axially moving string is presented the stress is treated as a new unknown in discretization of the spatial variable a set of differential algebraic equations is established based on the discreted governing equation and the constitutive relation for linear vibrations a conserved functional is employed to test the algorithm and the 1 2 3 4 term truncated modal analytical solutions are compared with the numerical solution for the free nonlinear vibration a new conserved functional is used to check the algorithm effects of the transport speed on the free and forced nonlinear vibrations are numerically investigated

smoothing and rothe s method for stefan problems in enthalpy form the classical two phase stefan problem as well as its weak variational formulation model the connection between the different phases of the considered material by interface conditions at the occurring free boundary or by a jump of the enthalpy one way to treat the corresponding discontinuous variational problems consists in its embedding into a family of continuous ones and applying some standard techniques to the chosen approximation problems the aim of the present paper is to analyze a semi discretization via rothe s method and its convergence behavior in dependence of the smoothing parameter while in grossmann et al optimization in preparation the treatment of the stefan problem is based on the given variable i e the temperature here first a transformation via the smoothed enthalpy is applied numerical experiments indicate a higher stability of the discretization by rothe s method in addition to avoid inner iterations a frozen coefficient approach as common in literature is used

a new sinc galerkin method for convection diffusion equations with mixed boundary conditions abstract a new sinc galerkin method is developed for approximating the solution of convection diffusion equations with mixed boundary conditions on half infinite intervals the method avoids differentiation of the coefficients of the pde rendering it appropriate as a forward solver in an inverse coefficient problem the method has the advantage that no functions are appended to the sinc basis in the discretization an error analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system we demonstrate the exponential convergence of the method on several test problems

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

on the boltzmann entropy of non equilibrium systems abstract boltzmann defined the entropy of a macroscopic system in a macrostate m as the log of the volume of phase space number of microstates corresponding to m this agrees with the thermodynamic entropy of clausius when m specifies the locally conserved quantities of a system in local thermal equilibrium lte here we discuss boltzmann s entropy involving an appropriate choice of macro variables for systems not in lte we generalize the formulas of boltzmann for dilute gases and of resibois for hard sphere fluids and show that for macro variables satisfying any deterministic autonomous evolution equation arising from the microscopic dynamics the corresponding boltzmann entropy must satisfy an h theorem

a study of fuzzy parametric on multiobjective nonlinear programming problems without differentiability this paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions without differentiability these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the stability notions of parametric convex programs are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality without differentiability on the functions considered

numerical methods for nonlinear second order hyperbolic partial differential equations ii rothe s techniques for 1 d problems abstract two families of rothe s methods that are based on the discretization of the time variable and keeping the spatial one continuous for the solution of second order hyperbolic equations with damping and nonlinear source terms are presented the first family is based on time integration and results in a volterra integro differential equation which upon approximating certain time integrals can be written as an ordinary differential equation in space upon discretizing the spatial derivatives by means of finite difference formula this family results in nonlinear algebraic equations which contain exponential terms that depend on the time step and its accuracy is shown to be lower than that of an explicit second order accurate discretization in both space and time of second order hyperbolic equations the second family of methods is based on the discretization of the time derivatives and time linearization and results in linear ordinary differential equations in space upon freezing the coefficients of these equations one can integrate analytically the resulting linear ordinary differential equations to obtain piecewise exponential solutions which are continuous in space and three point finite difference equations which depend exponentially on the time step spatial grid size and the diffusion relaxation damping and reaction times the finite difference equations are shown to result in non diagonally dominant matrices unless the time step is smaller than the characteristic relaxation diffusion damping and reaction times to avoid this problem two rothe s techniques that do not account for the jacobian of the reaction terms in the ordinary differential operator are developed and it is shown that the rothe s techniques belonging to the second family are as accurate as the linearly implicit methods presented in part i provided that the relaxation time is smaller than the critical time and the solution does not oscillate in space when the relaxation time is greater than the critical one rothe s methods have been found to be less accurate than the finite difference techniques of part i the rothe s techniques belonging to the second family are generalized to systems of nonlinear second order hyperbolic equations and mixed systems of parabolic and second order hyperbolic partial differential equations