scaling theory for gelling systems work in progress abstract gelation as it arises in the kinetic equations describing irreversible aggregation the so called smoluchowski equations is briefly reviewed the scaling theory near the gel point immediately before the transition is presented the equations presented earlier for the scaling function and the exponent are cast in a form more amenable to numerical study an algorithm to solve them is described and applied to the kernels of the form k x y x y x y a theory for the behaviour immediately after the gel transition is also presented and is found to be verified in one special exactly solved case product kernel with power law initial conditions

robust multiobjective optimization applications in portfolio optimization motivated by markowitz portfolio optimization problems under uncertainty in the problem data we consider general convex parametric multiobjective optimization problems under data uncertainty for the first time this uncertainty is treated by a robust multiobjective formulation in the gist of ben tal and nemirovski for this novel formulation we investigate its relationship to the original multiobjective formulation as well as to its scalarizations further we provide a characterization of the location of the robust pareto frontier with respect to the corresponding original pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier we illustrate our results based on a standard mean variance problem

nonlinear conjugate gradient methods for vector optimization in this work we propose nonlinear conjugate gradient methods for finding critical points of vector valued functions with respect to the partial order induced by a closed convex and pointed cone

an introduction to mathematical models of coagulation fragmentation processes a discrete deterministic mean field approach abstract we summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity an integer multiple of some basic unit size in particular we discuss smoluchowski s equation for aggregation the becker doring model of simultaneous aggregation and fragmentation and more general models involving coagulation and fragmentation

an interior proximal method in vector optimization abstract this paper studies the vector optimization problem of finding weakly efficient points for maps from r n to r m with respect to the partial order induced by a closed convex and pointed cone c r m with nonempty interior we develop for this problem an extension of the proximal point method for scalar valued convex optimization problem with a modified convergence sensing condition that allows us to construct an interior proximal method for solving vop on nonpolyhedral set

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

proximal methods in vector optimization we consider the vector optimization problem of finding weakly efficient points for maps from a hilbert space x to a banach space y with respect to the partial order induced by a closed convex and pointed cone c subset y with a nonempty interior we develop for this problem an extension of the proximal point method for scalar valued convex optimization in this extension the subproblems consist of finding weakly efficient points for suitable regularizations of the original map we present both an exact and an inexact version in which the subproblems are solved only approximately within a constant relative tolerance in both cases we prove weak convergence of the generated sequence to a weakly efficient point assuming convexity of the map with respect to c and c completeness of the initial section in cases where this last assumption fails we still establish that the generating sequence is in a suitable sense a minimizing one we also exhibit a particular instance of the algorithm for which under a mild hypothesis on c the weak limit of the generated sequence is an efficient rather than a weakly efficient point

asymptotic behavior of solutions to the coagulation fragmentation equations ii weak fragmentation the discrete coagulation fragmentation equations are a model for the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones the assumptions made on the fragmentation coefficients have the physical interpretation that surface effects are important our results on the asymptotic behavior of solutions generalize the corresponding results of ball carr and penrose for the becker doring equation

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

metastable decay rates asymptotic expansions and analytic continuation of thermodynamic functions the grand potentialp z kt of the cluster model at fugacityz neglecting interactions between clusters is defined by a power series nqnzn whereqn which depends on the temperaturet is the partition function of a cluster of sizen at low temperatures this series has a finite radius of convergencezs some theorems are proved showing that ifqn considered as a function ofn is the laplace transform of a function with suitable properties thenp z can be analytically continued into the complexz plane cut along the real axis fromzs to and that a the imaginary part ofp z on the cut is apart from a relatively unimportant prefactor equal to the rate of nucleation of the corresponding metastable state as given by becker doring theory and b the real part ofp z on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term

approximate proximal methods in vector optimization abstract this paper studies the vector optimization problem of finding weakly efficient points for mappings in a banach space y with respect to the partial order induced by a closed convex and pointed cone c y with a nonempty interior the proximal method in vector optimization is extended to develop an approximate proximal method for this problem by virtue of the approximate proximal point method for finding a root of a maximal monotone operator in this approximate proximal method the subproblems consist of finding weakly efficient points for suitable regularizations of the original mapping we present both an absolute and a relative version in which the subproblems are solved only approximately weak convergence of the generated sequence to a weak efficient point is established in addition we also discuss an extension to bregman function based proximal algorithms for finding weakly efficient points for mappings

box constrained multi objective optimization a gradient like method without a priori scalarization abstract the aim of this paper is the development of an algorithm to find the critical points of a box constrained multi objective optimization problem the proposed algorithm is an interior point method based on suitable directions that play the role of gradient like directions for the vector objective function the method does not rely on an a priori scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box the key tool to define the mentioned vector field is the notion of vector pseudogradient we prove that the limit points of the solutions of the system satisfy the karush kuhn tucker kkt first order necessary condition for the box constrained multi objective optimization problem these results allow us to develop an algorithm to solve box constrained multi objective optimization problems finally we consider some test problems where we apply the proposed computational method the numerical experience shows that the algorithm generates an approximation of the local optimal pareto front representative of all parts of optimal front

hybrid fuzzy model based control of nonholonomic systems a unified viewpoint this paper proposes a unified hybrid fuzzy model based control scheme for uncertain nonholonomic systems compared with typical hybrid fuzzy control the stability analysis is performed based on a new concept of constructing a semicommon lyapunov function and a new definition called as exponential like model following this advancement provides a strict stability analysis but results in relaxed gain conditions in detail a unified hybrid takagi sugeno fuzzy model is first introduced for representing well known nonholonomic systems with a momentum conservation constraint or a no slip constraint then the hybrid fuzzy controller is derived to ensure robust nonlinear model following control i e an asymptotic convergence with adjustable ultimate bound and arbitrary disturbance attenuation in an gain sense furthermore an iterative linear matrix inequality technique is proposed to guarantee the stability and avoid the need of a common positive definite matrix finally the applications are carried out on a hopping robot and a car like mobile robot numerical simulations and experiment results show the expected performances

robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching this paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system a design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures and the dwell time approach is utilized for the stability analysis then the approach is extended to take into account stochastic switched system with lipschitz nonlinearities and structured uncertainties finally a numerical example is employed to verify the proposed method

the becker doring equations and the lifshitz slyozov theory of coarsening in this paper the relation between the kinetic set of becker doring bd equations and the classical lifshitz slyozov ls theory of coarsening is studied a model that resembles the ls theory but keeps some of the nucleation effects is derived for this model a solution is described that shows how the kinetic effects explain the particular solution selected in the ls theory by means of a renormalization procedure a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the ls theory

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

asymptotic solutions of the becker doring equations with size dependent rate constants we find the large time asymptotic behaviour for a number of physically interesting cases of the becker doring equations allowing both the forward and the backward rates to depend on cluster size in a power law fashion we consider in detail the constant monomer form of the equations in the special case where the powers are equal since the structure of the large time asymptotic behaviour is then richest we then turn to cases in which aggregation and fragmentation have different exponents examining both the fragmentation and coagulation dominated cases again under constant monomer conditions

self similar solutions to a coagulation equation with multiplicative kernel abstract existence of self similar solutions to the oort hulst safronov coagulation equation with multiplicative coagulation kernel is established these solutions are given by s t y s t for t y 0 t 0 where t is some arbitrary positive real number s t 3 t t 1 3 and the parameter ranges in a given interval c 3 in addition the second moment of these self similar solutions blows up at time t as for the profile it belongs to l 1 0 y 2 d y for each c 3 but its behaviour for small and large y varies with the parameter

a triangle of interconnected coagulation models a number of new coagulation models depending on a parameter is derived the dependence is considered in two different ways if the parameter takes its maximal value then in the first case we obtain a new discrete kinetic equation we demonstrate that its continuous version is simply the oort hulst s coagulation model in the second case the maximum of the corresponding parameter yields the smoluchowski coagulation equation at the minimal values of both parameters we arrive at another new kinetic equation these three models form a triangle connecting the two known coagulation equations situated in its vertexes smoluchowski and oort hulst equations via an alteration of the parameters also a comparative analysis of these three models is presented as an advantage of the oort hulst approach we compute the coagulation front and establish a connection between the infringement of the mass conservation law and convergence of the coagulation front to infinity

singular continuation generating piecewise linear approximations to pareto sets via global analysis we propose a strategy for approximating pareto optimal sets based on the global analysis framework proposed by smale global analysis and economics i pareto optimum and a generalization of morse theory in dynamical systems academic press new york 1973 pp 531 544 the method highlights and exploits the underlying manifold structure of the pareto sets approximating pareto optima by means of simplicial complexes the method distinguishes the hierarchy between singular set pareto critical set and stable pareto critical set and it can handle the problem of superposition of local pareto fronts occurring in the general nonconvex case furthermore a quadratic convergence result in a suitable setwise sense is proven and tested in a number of numerical examples

asynchronous filtering for discrete time switched t s fuzzy systems in this paper asynchronous mathcal h infty filtering is studied for discrete time switched takagi sugeno t s fuzzy systems new lyapunov functions are constructed for switched systems with asynchronous switching between subsystems and candidate filters these improved lyapunov functions are dependent on the mode of filters instead of subsystems which are more consistent with the switching mechanism of switched systems with asynchronous switching meanwhile they are quasi time dependent which are effective in achieving more general results than traditional time independent lyapunov functions based on the new lyapunov functions a stability and ell 2 gain criterion is deduced for switched t s fuzzy systems then switched fuzzy filters are designed to guarantee that the filtering error system is globally uniformly asymptotically stable and has a prescribed mathcal h infty performance at last an illustrative example is provided to demonstrate the potentials and advantages of the proposed filtering scheme

epsilon dominating solutions in mean variance portfolio analysis abstract in this paper the problem of finding the effcient set of portfolios in a general constraint set is replaced by finding a set of epsilon dominating protfolios the number of which is determined by the size of epsilon algorithms and associated theory are given together with some possible modifications

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

exact solutions for cluster growth kinetics with evolving size and shape profiles in this paper we construct a model for the simultaneous compaction by which clusters are restructured and growth of clusters by pairwise coagulation the model has the form of a multi component aggregation problem in which the components are cluster mass and cluster diameter following suitable approximations exact explicit solutions are derived which may be useful for the verification of simulations of such systems numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model the solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times

polynomial fuzzy model based control systems stability analysis via piecewise linear membership functions this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems using the sum of squares sos approach the pfmb control system under consideration requires that the polynomial fuzzy model and polynomial fuzzy controller share neither the same premise membership functions nor the same number of fuzzy rules this class of pfmb control systems offers a greater design flexibility to the polynomial fuzzy controller however due to the imperfectly matched membership functions it usually produces more conservative stability conditions by following the traditional stability analysis approach for the fmb control systems to facilitate the stability analysis piecewise linear membership functions plmfs are proposed which offer a nice property that the grades of membership are governed by a finite number of sample points thus it allows the plmfs to be brought to the sos based stability conditions which are applied to the pfmb control systems with the specified plmfs rather than any shapes the system stability can be examined by checking only the pfmb control system at the sample points it is worth mentioning that the plmfs which are not necessarily implemented physically are a mathematical tool to carry out the stability analysis to verify the stability analysis result a simulation example is given to demonstrate the effectiveness of the proposed approach

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

fault estimation and tolerant control for fuzzy stochastic systems this paper deals with the problem of fault estimation and fault tolerant control for takagi sugeno t s fuzzy stochastic systems with sensor failures where the system under consideration contains ito type stochastic disturbances a new robust observer technique is presented to obtain the estimates of the system states and the sensor faults simultaneously and a fuzzy fault tolerant control scheme is developed to guarantee the closed loop system to be exponentially stable in mean square sufficient conditions are obtained for the existence of admissible controllers and it is shown that the reachability of the sliding mode dynamics can be guaranteed under the proposed control techniques finally a numerical example is provided to illustrate the effectiveness and applicability of the theoretic results obtained

analysis and synthesis of robust control systems using linear parameter dependent lyapunov functions this note provides sufficient robust stability conditions for continuous time polytopic systems they are obtained from the frobenius perron theorem applied to the time derivative of a linear parameter dependent lyapunov function and are expressed in terms of linear matrix inequalities lmi they contain as special cases various sufficient stability conditions available in the literature to date as a natural generalization the determination of a guaranteed h2 cost is addressed a new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent lyapunov functions through linear matrix inequalities numerical examples are included for illustration

piecewise sliding mode control for t s fuzzy systems this paper addresses piecewise sliding mode control for takagi sugeno t s fuzzy models a novel sliding mode control smc design approach is developed which is based on individual sliding surface in each local region of the t s fuzzy systems conditions of existence of sliding mode in the associated region are given the chattering effect around region boundaries is analyzed and prevention of such chattering is discussed two illustrative examples are finally given to illustrate the effectiveness and performance of the proposed controller

approach to self similarity in smoluchowski s coagulation equations we consider the approach to self similarity or dynamical scaling in smoluchowski s equations of coagulation for the solvable kernels k x y 2 x y and xy in addition to the known self similar solutions with exponential tails there are one parameter families of solutions with algebraic decay whose form is related to heavy tailed distributions well known in probability theory for k 2 the size distribution is mittag leffler and for k x y and k xyit is a power law rescaling of a maximally skewed stable levy distribution we characterize completely the domains of attraction of all self similar solutions under weak convergence of measures our results are analogous to the classical characterization of stable distributions in probability theory the proofs are simple relying on the laplace transform and a fundamental rigidity lemma for scaling limits c 2004 wiley periodicals inc

finite time stabilization of discrete time switched nonlinear systems without stable subsystems via optimal switching signal design this paper investigates the finite time exponential stability analysis and stabilization problem of discrete time switched nonlinear systems without stable subsystems in the stability analysis the takagi sugeno t s fuzzy model is employed to approximate nonlinear subsystems with two level functions namely crisp switching functions and local fuzzy weighting functions we introduce switched fuzzy systems with approximation errors which inherently contain both the features of the switched systems and t s fuzzy systems by constructing the decreasing jump piecewise lyapunov like functions and minimum dwell time technique a finite time exponential stability of switched fuzzy systems with bounded approximation errors is obtained then based on the finite time exponential stability a multiobjective evolution algorithm nondominated sorting genetic algorithm nsga ii which considers two conflicting objectives such as the average convergence error and the average switching cost is proposed to generate tradeoff switching sequences to stabilize the discrete time switched nonlinear systems over a finite time interval a numerical example and a practical example are provided to illustrate the effectiveness of the stability and the algorithm respectively

asymptotic behaviour of solutions to a simplified lifshitz slyozov equation abstract for the system c u 1 c u 0 c d 0 c d 1 we prove for several classes of initial data c 0 that lim 2 x c x d x h x where h is a known function determined by the behaviour of c 0 near the largest values in its support if c 0 has compact support near whose supremum a it behaves like a q q 1 then h also has compact support near whose supremum it behaves like a q 1 if c 0 goes to zero exponentially fast as a or if its support is infinite and it decays exponentially fast for large then h x is e x if c 0 has infinite support and decays for large like a negative power of then so does h we also give examples of initial data for which the above limit does not exist

the exponential stability and asynchronous stabilization of a class of switched nonlinear system via the t s fuzzy model in this paper we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems the takagi and sugeno t s fuzzy model is employed to approximate the subnonlinear dynamic systems with two level functions namely crisp switching functions and local fuzzy weighting functions we introduce continuous time switched fuzzy systems which inherently contain the features of the switched hybrid systems and t s fuzzy systems by the use of delicately constructed piecewise lyapunov like functions plfs and minimum dwell time method we obtain the exponential stability of the switched fuzzy systems which allows us to have stable and unstable nonlinear subsystems in practice for the control problem it inevitably takes some time to identify the system modes and apply the matched controller the asynchronous phenomena between the system modes switching and the controllers switching generally exists based on the result of stability the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems in addition the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound the stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible finally two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results

convergence properties of nonlinear conjugate gradient methods recently important contributions on convergence studies of conjugate gradient methods were made by gilbert and nocedal siam j optim 2 1992 pp 21 42 they introduce a sufficient descent condition to establish global convergence results although this condition is not needed in the convergence analyses of newton and quasi newton methods gilbert and nocedal hint that the sufficient descent condition which was enforced by their two stage line search algorithm may be crucial for ensuring the global convergence of conjugate gradient methods this paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods consequently convergence results on the fletcher reeves and polak ribiere type methods are established in the absence of the sufficient descent condition to show the differences between the convergence properties of fletcher reeves and polak ribiere type methods two examples are constructed showing that neither the boundedness of the level set nor the restriction beta k geq 0 can be relaxed for the polak ribiere type methods

a survey of numerical solutions to the coagulation equation we present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form aij i j i j and monodisperse initial conditions the results confirm that there are three classes of rate coefficients with qualitatively different solutions for 1 and 1 the numerical solution evolves in an orderly fashion and tends towards a self similar solution at large time t the properties of the numerical solution in the scaling limit agree with the analytic predictions of van dongen and ernst in particular for the subset with 0 and 1 the numerical solution tends towards a self similar solution as t approaches a finite time t0 the mass spectrum nk develops at t0 a power law tail nk k at large masses that violates mass conservation and runaway growth gelation is expected to start at tcrit t0 in the limit the initial number of particles n0 the exponent is in general less than the analytic prediction 3 2 and t0 k 1 n0a11 with k 1 2 if 1 1 for 1 the behaviours of the numerical solution are similar to those found in a previous paper by us they strongly suggest that there are no self consistent solutions at any time and that runaway growth is instantaneous in the limit n0 they also indicate that the time tcrit for the onset of runaway growth decreases slowly towards zero with increasing n0

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

on the minimization of completion time variance with a bicriteria extension we discuss a single machine scheduling problem where the objective is to minimize the variance of job completion times to date the problem has not been solved in polynomial time this paper presents a dynamic programming algorithm that is pseudopolynomial in complexity we also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation furthermore we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time

existence of self similar solutions to smoluchowski s coagulation equation the existence of self similar solutions to smoluchowski s coagulation equation has been conjectured for several years by physicists and numerical simulations have confirmed the validity of this conjecture still there was no existence result up to now except for the constant and additive kernels for which explicit formulae are available in this paper the existence of self similar solutions decaying rapidly at infinity is established for a wide class of homogeneous coagulation kernels

existence of gelling solutions for coagulation fragmentation equations we study the smoluchowski coagulation fragmentation equation which is an infinite set of non linear ordinary differential equations describing the evolution of a mono disperse system of particles in a well stirred solution approximating the solutions of the smoluchowski equations by a sequence of finite markov chains we investigate the qualitative behavior of the solutions we determine a device on the finite chains which can detect the gelation phenomena the density dropping phenomena it shows how the gelation phenomena are reflected on the sequence of finite markov chains using this device we determine various types of gelation kernels and get the bounds of gelation times

metastable states for the becker doring cluster equations the becker doring equations in whichc l t can represent the concentration ofl particle clusters or droplets in say a condensing vapour at timet are begin array 20 c dc l t mathord left vphantom dc l t dt right kern nulldelimiterspace dt j l 1 t j l t l 2 3 end array with j l t a l c 1 t c l t b l 1 c l 1 t and eitherc1 const case a or rho sum limits 1 infty lc l const case b the equilibrium solutions arec l q l z l where q l prod limits 2 l a r 1 mathord left vphantom a r 1 b r right kern nulldelimiterspace b r the density of the saturated vapour defined as rho s sum limits 1 infty lq l z s l wherez s is the radius of convergence of the series is assumed finite it is proved here that subject to some further plausible conditions on the kinetic coefficientsa l andb l there is a class of metastable solutions of the equations withc1 z s small and positive which take an exponentially long time to decay to their asymptotic steady states an exponentially long time means one that increases more rapidly than any negative power of the given value ofc1 z s or in caseb s as the latter tends to zero the main ingredients in the proof are i a time independent upper bound on the solution of the kinetic equations this upper bound is a steady state solution of case a of the equations of the type used in the becker doring theory of nucleation and ii an upper bound on the total concentration of particles in clusters greater than a certain critical size which with suitable initial conditions remains exponentially small until the time becomes exponentially large

petri net representation of switched fuzzy systems switched fuzzy systems can be used to describe the hybrid systems with fuzziness however the languages to describe the switching logic and the fuzzy subsystems are in general different and this difference makes the system analysis and implementation hard in this paper we use differential petri net dpn as a unified model to represent both the discrete logic and fuzzy dynamic processes to exam the rationality of the representation we prove the correctness of the representation for the discrete part and estimate the approximation accuracy of the representation for the dynamic part our work provides a way to analyze the switched fuzzy systems by checking the pn and to use the pn model for further system implementation we demonstrate the benefits of our work via a case study

non self similar behavior in the lsw theory of ostwald ripening the classical lifshitz slyozov wagner theory of domain coarsening predicts asymptotically self similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field here we consider the long time behavior of measure valued solutions for systems in which particle size is uniformly bounded i e for initial measures of compact support we prove that the long time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support we give a necessary criterion for convergence to other self similar solutions and conditional stability theorems for some such solutions for a dense set of initial data convergence to any self similar solution is impossible

the discrete coagulation fragmentation equations existence uniqueness and density conservation the discrete coagulation fragmentation equation describes the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones these models have many applications in pure and applied science ranging from cluster formation in galaxies to the kinetics of phase transformations in binary alloys our results relate to existence uniqueness density conservation and continuous dependence and they generalise the corresponding results in ref 2 for the becker doring equations for which the processes are restricted to clusters gaining or shedding one particle examples are given which illustrate the role of the assumptions on the kinetic coefficients and show the rich set of analytic phenomena supported by the general discrete coagulation fragmentation equations

proof of dynamical scaling in smoluchowski s coagulation equation with constant kernel smoluchowski s coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version open image in new window wherect c1 t is the concentration ofl particle clusters at timet we prove that for initial data satisfyingc1 0 0 and the condition 0 cl 0 0 the solutions behave asymptotically likec1 t t 2 c lt 1 ast withlt 1 kept fixed the scaling function c is 1 gr where rho sum l lc l 0 a conserved quantity is the initial number of particles per unit volume an analous result is obtained for the continuous version of smoluchowski s coagulation equation frac partial partial t c v text t int 0 v du text c v u text t text c u text t 2c v text t int 0 infty du text c u text t wherec v t is the oncentration of clusters of sizev

coagulation diffusion systems derivation and existence of solutions for the diffuse interface structure equations abstract this paper considers an infinite system of partial differential equations the coagulation diffusion equations which add spatial diffusion to the classical coagulation equations the main emphasis is placed on deriving an infinite system of ordinary differential equations which described the structured interface between reacting coagulation and dilute concentration existence of solutions to interfacial equaitons is proven under spatial boundary conditions

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

control of switched nonlinear systems via t s fuzzy modeling this paper is concerned with the control problem for a class of switched nonlinear systems possibly composed of all unstable modes by using time controlled switching signals to tackle the problem a new mode dependent average dwell time mdadt switching property is proposed which is different from the existing one in the literature then the stabilization condition under such mdadt switching signals is established for the switched nonlinear systems with possibly all unstable subsystems by proposing a class of time scheduled multiple quadratic lyapunov function and applying t s fuzzy models to represent the underlying nonlinear subsystems numerically easily verified stabilization conditions are further derived in the form of linear matrix inequalities a numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results

stability and stabilization of nonlinear switched systems under average dwell time in this paper the problems of stability and stabilization of nonlinear discrete time switched systems is investigated firstly in order to implement the lower bound of minimum average dwell time adt of discrete time switched nonlinear systems the open chain and quasi cyclic switching signals are introduced secondly the problem of these underlying nonlinear discrete time switched systems are solved by using the interval type 2 it2 fuzzy modeling approach thirdly a novel delayed it2 fuzzy controller is devised to guarantee the asymptotically stable of the resulting systems finally a numerical simulation example is given to show the merit and effectiveness of the proposed approach

an explicit solution to a discrete fragmentation model the discrete binary fragmentation equation is solved explicitly far a model where tnenetrateoibreakupoiaparlicie oishek o equals k lj k l andthedaughter ri e distribution b lx equals 2 k 1 this system is closely related to a model of polymer degradation considered by simha in which ax i and b is as above in the continuum limit both of these models go over to a continuous fragmentation model in which all particles break with an equal rate a x i and the daughter size distribution is uniform b yl x z x which is at the borderline of the shattering transition

a formula for the post gelation mass of a coagulation equation with a separable bilinear kernel abstract it is well known that solutions of the coagulation equation do not conserve mass if the coagulation kernel grows too rapidly the phenomenon whereby conservation of mass breaks down in finite time is known as gelation and is physically interpreted as being caused by the appearance of an infinite gel or superparticle in this paper we derive a formula for the post gelation mass for the case of a separable bilinear kernel k and investigate the asymptotic behaviour of the solution

switching type h filter design for t s fuzzy systems with unknown or partially unknown membership functions this paper is concerned with the h filter design problem for takagi sugeno t s fuzzy systems with unknown or partially unknown membership functions if the membership functions are allowed to be unknown or partially unknown then a fuzzy system may describe a wide class of nonlinear systems however in this case the filter design of fuzzy systems which is based on parallel distributed compensator strategy is infeasible to tackle this difficulty a switching mechanism which depends on the lower and upper bounds of the unknown membership functions is introduced to construct the h filter with varying gains some examples given in the simulation section show that the proposed method can achieve a better disturbance attenuation performance than a simple fixed gain filter design approach

the becker doring cluster equations basic properties and asymptotic behaviour of solutions existence and uniqueness results are established for solutions to the becker doring cluster equations the density is shown to be a conserved quantity under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined denoting the set of equilibrium solutions byc 0 s the principal result is that if the initial density 0 s then the solution converges strongly toc o while if 0 s the solution converges weak toc s in the latter case the excess density 0 s corresponds to the formation of larger and larger clusters i e condensation the main tools for studying the asymptotic behaviour are the use of a lyapunov function with desirable continuity properties obtained from a known lyapunov function by the addition of a special multiple of the density and a maximum principle for solutions

a subgradient method for vector optimization problems vector optimization problems are a significant extension of scalar optimization and have many real life applications we consider an extension of the projected subgradient method to convex vector optimization which works directly with vector valued functions without using scalar valued objectives we eliminate the scalarization approach a popular strategy for solving vector optimization problems exploring strongly the structure of these kinds of problems under suitable assumptions we show that the sequence generated by the algorithm converges to a weakly efficient optimum point

asymptotic solutions of the becker doring equations we describe the solution of various becker doring models first we analyse equilibrium and steady state solutions together with the large time behaviour of solutions for the case of constant monomer concentration then we solve a weak fragmentation constant mass case by using matched asymptotic expansions the methods are applied both to the full becker doring equations and to a coarse grained or contracted system comparison of the results show good qualitative agreement all the phenomena present in the full model are reproduced in the contracted system and no anomalous effects are introduced however the quantitative agreement depends strongly on the choice of parameter values in the contracted system