newton method for stationary and quasi stationary problems for smoluchowski type equations abstract an efficient implementation of the newton krylov iterative method finding numerical solutions of aggregation fragmentation equations without spontaneous fragmentation is reported it is based on application of fast numerical schemes for evaluation of the smoluchowski operator associated with these equations and structure of jacobi matrix allowing implementation of fast multiplication by a vector we also propose an efficient preconditioner based on lower triangular band matrix extracted from a jacobi matrix resulting in a dramatic speedup of internal gmres based iterations between the newton steps we compare the efficiency of the novel method with the existing ones and demonstrate a noticeable superiority of our approach moreover we show that the new method may be utilized for modeling of a wider class of aggregation fragmentation phenomena and derive a new class of quasi stationary solutions for aggregation fragmentation equations source of monomers

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

the asymptotic distributions of the size of the largest length of a reversible markov process of polymerization in this paper the subcritical near critical and supercritical asymptotic behaviour of a reversible markov process as a chemical model for polymerization was studied we establish the existence of three distinct stages subcritical near critical and supercritical stages of polymerization in the thermodynamic limit as n depending on the value of strength of the fragmentation reaction these three stages correspond to the size of the largest length of polymers of size n to be itself of order log n na 1 2 a 1 and n respectively especially a 2 2 1 when the coagulation reaction rate constant rij of the polymers satisfies rij i j with 1 2 3 2

two direct methods in linear programming abstract in this paper we introduce two direct methods for solving some classes of linear programming problems the first method produces the extreme vertex or a neighboring vertex with respect to the extreme point the second method is based on the game theory both these methods can be used in the preparation of the starting point for the simplex method the efficiency of the improved simplex method whose starting point is constructed by these introduced methods is compared with the original simplex method and the interior point methods and illustrated by examples also we investigate the elimination of excessive constraints

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

two species coagulation approach to consensus by group level interactions we explore the self organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole to this end we employ the widespread example of coagulation kinetics and characterize which interaction types lead to consensus formation and which do not as well as the corresponding different macroscopic patterns the crucial technical point is extending the usual one species coagulation dynamics to the two species one this is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning the corresponding solutions are calculated in the long time limit in which consensus may or may not be reached the lack of consensus is characterized by means of scaling limits of the solutions the possible applications of our results to some topics in which consensus reaching is fundamental such as collective animal motion and opinion spreading dynamics are also outlined

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

some analytical and numerical solutions for colloidal aggregation with fragmentation we study the kinetic equation which describes the evolution of cluster size distribution of the aggregation fragmentation problem the so called generalized smoluchowski equation for several dynamics of cluster growth by using the method of the generating function we find analytical solutions for some cases besides numerical solutions are found for the time evolution of clusters where the aggregation and fragmentation kernels do not allow a complete analytical solution

the smoluchowski coagulation equations with continuous injection we study a system of equations which models the formation of clusters by coagulation with particles of unit size being injected at a time dependent rate we observe that the criteria under which gelation occurs are the same as for the constant mass and constant monomer cases which have been studied previously we identify a variety of types of behaviour in the large time limit depending on the coagulation kernel and on the rate at which monomer is introduced into the system the results are obtained by means of exact generating function techniques matched asymptotic expansions and numerical simulations

strongly differentiable solutions of the discrete coagulation fragmentation equation we examine an infinite system of ordinary differential equations that models the binary coagulation and multiple fragmentation of clusters in contrast to previous investigations our analysis does not involve finite dimensional truncations of the system instead we treat the problem as an infinite dimensional differential equation posed in an appropriate banach space and apply perturbation results from the theory of strongly continuous semigroups of operators the existence and uniqueness of physically meaningful solutions are established for uniformly bounded coagulation rates but with no growth restrictions imposed on the fragmentation rates

convergence to equilibrium for the discrete coagulation fragmentation equations with detailed balance under the condition of detailed balance and some additional restrictions on the size of the coefficients we identify the equilibrium distribution to which solutions of the discrete coagulation fragmentation system of equations converge for large times thus showing that there is a critical mass which marks a change in the behavior of the solutions this was previously known only for particular cases as the generalized becker doring equations our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

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

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

numerical simulation of the smoluchowski coagulation equation in this paper we develop a numerical scheme for the smoluchowski coagulation equation which relies on a conservative formulation and a finite volume approach several numerical simulations are performed to test the validity of the scheme and the expected behavior of the model in particular the gelation phenomenon and the long time behavior of the solution are numerically studied

the discrete diffusive coagulation fragmentation equations with scattering we consider the discrete coagulation fragmentation equations with diffusion presupposing a maximal cluster size such a feature requires a new interaction mechanism in order to prevent occurrence of too large clusters being produced by coagulation existence of a unique solution for this model is proven and long time behaviour is studied in situations where equilibria are explicitly known

similarity solution of coagulation equation with an inverse kernel abstract we analyse a model for the aggregation of polystyrene particles which arises in an electrorheology system in which linear clusters grow upon the application of an alternating electromagnetic field we consider a coagulation kernel involving negative powers of cluster sizes and investigate the reduction of the governing equations to a similarity solution in the large time limit comparison between the experimental results and the theory presented here shows a good collapse of the data onto a single curve which matches the theoretical results particularly well at the larger cluster sizes

gelation time in the discrete coagulation fragmentation equations with a bilinear coagulation kernel the discrete coagulation fragmentation equations with a bilinear coagulation kernel describing the evolution of clusters of particles undergoing binary reactions are studied we compute the gelation time and post gelation mass for the pure coagulation equation a method of characteristics is developed to solve numerically the partial differential equation satisfied by a moment generating function for a product coagulation kernel and a constant fragmentation rate the accuracy of the numerical method is verified by comparison of the numerical results with an exact solution for the number density of monomers for a given coagulation rate a critical value of the fragmentation rate values greater than which lead to mass conservation is identified

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

existence and uniqueness of steady state solution to a singular coagulation fragmentation equation abstract in this article we prove the existence of an equilibrium solution to the coagulation fragmentation equation with i a singular coagulation kernel in the form k x y 1 x y x y where 0 1 2 and 0 1 and ii a fragmentation kernel in the form f x y b 0 b x y m where b 0 0 and b m 0 importantly in the entire study the detailed balance condition is not assumed it is shown that the equilibrium solution of the problem under consideration is unique in the space of all continuous functions on 0 the proposed results are demonstrated by a numerical illustration

critical behavior of the heterogeneous random coagulation fragmentation processes in this paper we study the asymptotic distributions of the heterogeneous random coagulation fragmentation processes hcfp which model the coagulation fragmentation and diffusion of clusters of particles on a lattice based on a closed form of the stationary distribution for the hcfp we prove that the mutually dependent clusters with a finite size finite particles in the sub critical stage will become independent in the critical and super critical stages and the asymptotic distributions of the number of clusters may converge to gaussian or poisson distribution according to its size to be small or large in the critical and super critical stages

on the existence of moments of solutions to fragmentation equations abstract we consider the multiple fragmentation equations with polynomially bounded fragmentation rates both in the discrete and continuous cases the theory of semigroups of operators on frechet spaces is used to produce a simple proof that if moments of all non negative orders of solutions are initially finite then they remain finite for all future times moreover a class of fragmentation processes is identified in which the existence of the first moment of the initial distribution suffices for the existence of all other moments for positive times

asymptotic behaviour of solutions to the diffusive fragmentation coagulation system abstract we study the time asymptotics of solutions to the diffusive fragmentationdashcoagulation system which we derived in a previous work j f collet f poupaud transp theory and stat phys 25 3 5 1996 503 513 in the case where a detailed balance equilibrium exists we derive convergence to such a state by using a careful analysis of the free energy dissipation rate of the system in the case where no detailed balance equilibrium exists we show the existence of an attractor by using classical energy inequalities and some estimates on higher moments of the solution

the homotopy perturbation method applied for solving complex valued differential equations with strong cubic nonlinearity abstract in this paper the homotopy perturbation method is adopted for solving a complex valued second order strongly nonlinear differential equation homotopy with an imbedding parameter p 0 1 is constructed the perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex valued differential equations whose solutions give the approximate solution of the initial differential equation to illustrate the effectiveness and convenience of the suggested procedure a duffing equation with strong cubic nonlinearity is considered the periodic solution in the first approximation is obtained the solution is compared with the exact one and shows good agreement

linearized perturbation method for stochastic analysis of a rill erosion model the linearization and correction method lcm proposed by he is a simple and effective perturbation technique to solve nonlinear equations to analyze the random properties of rill erosion model a new stochastic perturbation technique called linearized perturbation method is developed by combining the traditional stochastic perturbation method with the lcm comparisons between the numerical results obtained by the linearized perturbation method and those obtained by monte carlo method indicated an excellent agreement however the calculation efficiency of the linearized perturbation method is higher

self attracting poisson clouds in an expanding universe we consider the following elementary model for clustering by ballistic aggregation in an expanding universe at the initial time there is a doubly infinite sequence of particles lying in a one dimensional universe that is expanding at constant rate we suppose that each particle p attracts points at a certain rate a p 2 depending only on p and when two particles say p and q collide by the effect of attraction they merge as a single particle p q the main purpose of this work is to point at the following remarkable property of poisson clouds in these dynamics under certain technical conditions if at the initial time the system is distributed according to a spatially stationary poisson cloud with intensity 0 then at any time t 0 the system will again have a poissonian distribution now with intensity t where the family solves a generalization of smoluchowski s coagulation equation

an analytical solution of coagulation processes with collision induced fragmentation we propose a single species coagulation model with collision induced fragmentation in which a pair of clusters can coagulate into a larger one if their encounter is a complete inelastic collision otherwise one of them will fragment into two smaller clusters due to a destructive collision consider a simple system with the constant coagulation kernel i i j i and the size dependent fragmentation kernel j l i j 2jlu we then investigate analytically the kinetic behavior of such a system by means of the rate equation approach it is indicated that the results are crucially dependent on the value of index u in the case of u 1 and i 2j u here x is the riemann zeta function the cluster size distribution ak t approaches the conventional scaling form and the system will evolve permanently in time while in other cases ak t always takes the modified scaling form moreover a balance can be established between coagulation and collision induced breakage processes and thus the system can eventually evolve to a steady state

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition the coagulation fragmentation equation describes the concentration f i t of particles of size i in nn 0 at time t geq 0 in a spatially homogeneous infinite system of particles subjected to coalescence and break up we show that when the rate of fragmentation is sufficiently stronger than that of coalescence f i t i in nn 0 tends to an unique equilibrium as t tends to infinity although we suppose that the initial datum is sufficiently small we do not assume a detailed balance or reversibility condition the rate of convergence we obtain is furthermore exponential

from the discrete to the continuous coagulation fragmentation equations the connection between the discrete and the continuous coagulation fragmentation models is investigated a weak stability principle relying on a priori estimates and weak compactness in l 1 is developed for the continuous model we approximate the continuous model by a sequence of discrete models and writing the discrete models as modified continuous ones we prove the convergence of the latter towards the former with the help of the above mentioned stability principle another application of this stability principle is the convergence of an explicit time and size discretization of the continuous coagulation fragmentation model

numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations this paper presents a finite volume scheme fvs for solving general breakage population balance equations bpbes in particular the number density based bpbe is transformed to the form of a mass conservation law then it becomes easy to apply the well known fvss that have an important property of mass conservation following kumar and warnecke for fixed pivot fp method 16 and cell average technique cat 15 the stability and the convergence analysis of the semi discretized fvs are studied unlike the cat and the fp method the fvs is second order consistent independently of the type of meshes we also observe that fvs gives second order convergence rate on four different types of uniform and non uniform meshes with non decreasing behavior of mesh width nevertheless one order better accuracy than the fp method is achieved on locally uniform meshes it is also noticed that on non uniform random meshes the fvs shows one order and two orders higher accuracy than the cat and the fp method respectively the mathematical results of convergence analysis are validated numerically by taking three test problems the numerical simulations are also compared with the results obtained by the cat and the fp method

deformations of super kms functionals we investigate the stability of the super kms property under deformations we show that a family of continuous deformations of the super derivation in the quantum algebra yields a continuous family of deformed super kms functionals these functionals define a family of cohomologous entire cocycles in this paper we investigate the super kms skms property of functionals co on a quantum algebra our interest in skms functionals was inspired by work of kastler and by conversations with alain connes ci k jlo2 the skms construction relies on the existence of a super derivation d acting on a dense subalgebra of a c algebra d the square of d is the infinitesimal generator of a continuous one parameter automorphism group c of the quantum algebra the usual kms property relates the cyclicity of a state co to the analytic continuation of a group et of automorphisms the skms property also involves invariance under the super derivation d whose square generates the automorphism group er it is known that an skms functional on a quantum algebra defines an entire cyclic cocycle z this is just the chern character which jaffe lesniewski and osterwalder defined in the context ofsupertrace functionals on a quantum algebra jlo 1 the skms property ensures that the functional co and the cocycle z which is derived from it are invariant under this group action in this paper we study the stability of this structure under perturbations of d we study only bounded perturbations which arise from the graded super commutator with an odd element q of the algebra d we show that such perturbations dq of d can be used to define a deformation coq of co which satisfies the skms property furthermore the corresponding family of cocycles z are cohomologous of course more singular unbounded perturbations can lead to

algebraic simplex initialization combined with the nonfeasible basis method we propose in this paper a new method to initialize the simplex algorithm this approach does not involve any artificial variables it can detect also the redundant constraints or infeasibility if any generally the basis found by this approach is not feasible to achieve feasibility this algorithm appeals to the nonfeasible basis method nfb furthermore we propose a new pivoting rule for nfb method which shows to be beneficial in both numerical and time complexity when solving a linear program we develop an efficient criterion to decide in advance which algorithm between nfb and formal nonfeasible basis method seems to be more rapid comparative analysis is carried out with a set of standard test problems from netlib our computational results indicate that the proposed algorithm is more advantageous than two phase and perturbation algorithm in terms of number of iterations number of involved variables and also computational time

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

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

asymptotic behaviour of solutions to the generalized becker doring equations for general initial data we prove the following asymptotic behaviour for solutions to the generalized becker doring system for general initial data under a detailed balance assumption and in situations where density is conserved in time there is a critical density s such that solutions with an initial density s converge strongly to the equilibrium with density and solutions with initial density s converge in a weak sense to the equilibrium with density s this extends the previous knowledge that this behaviour happens under more restrictive conditions on the initial data the main tool is a new estimate on the tail of solutions with density below the critical density

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

a pure jump markov process associated with smoluchowski s coagulation equation the aim of the present paper is to construct a stochastic process whose law is the solution of the smoluchowski s coagulation equation we introduce first a modified equation dealing with the evolution of the distribu tion q t dx of the mass in the system the advantage we take on this is that we can perform an unified study for both continuous and discrete models the integro partial differential equation satisfied by q t t 0 can be interpreted as the evolution equation of the time marginals of a markov pure jump process at this end we introduce a nonlinear poisson driven stochastic differential equation related to the smoluchowski equation in the following way if x t satisfies this stochastic equation then the law of x t satisfies the modified smoluchowski equation the nonlinear process is richer than the smoluchowski equation since it provides historical information on the particles existence uniqueness and pathwise behavior for the solution of this sde are studied finally we prove that the nonlinear process x can be obtained as the limit of a marcus lushnikov procedure 1 introduction the coagulation model governs various phenomena as for example polymerization aggregation of colloidal particles formation of stars and planets behavior of fuel mixtures in engines etc smoluchowski s coagulation equation models the dynamic of such phenomena and describes the evolution of a system of clusters which coalesce in order to form bigger clusters each cluster is identified by its size the only mechanism taken into account is the coalescence of two clusters other effects as multiple coagulation are neglected we assume also that the rate of these reactions depends on the sizes of clusters involved in the coagulation denoting by n k t the nonnegative concentration of clusters of size k at time t the discrete

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

renormalization theoretic analysis of non equilibrium phase transitions i the becker doring equations with power law rate coefficients we study in detail the application of renormalization theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes we investigate the becker d oring equations originally formulated to describe and analyse non equilibrium phase transitions and more recently generalized to describe a wide range of physicochemical problems in this paper we analyse how the systematic coarse graining renormalization of the becker d oring system of equations affects the aggregation and fragmentation rate coefficients we consider the case of power law size dependent cluster rate coefficients which we show lead to only three classes of system that require analysis coagulation dominated systems fragmentation dominated systems and those where coagulation and fragmentation are exactly balanced we analyse the late time asymptotics associated with each class

the nonlinear fragmentation equation we study the kinetics of nonlinear irreversible fragmentation here fragmentation is induced by interactions collisions between pairs of particles and modelled by general classes of interaction kernels for several types of breakage models we construct initial value and scaling solutions of the fragmentation equations and apply the non vanishing mass flux criterion for the occurrence of shattering transitions these properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters

self similarity in a coarsening model in one dimension motivated from asymptotic laws of motion for transition layers in the equation u t 2 u xx u u 2 we consider the following model for coarsening of a fine partition of an interval find the shortest subinterval of the partition and joint it with its neighbours combining three into one making a random order assumption we develop and study an unusual coagulation equation for the distribution of interval lengths we establish the existence of a self similar solution of this equation by using laplace transform techniques simulation data indicate that random order does persist if present initially and the distribution approaches similarity form

hydrodynamic limit of coagulation fragmentation type models of k nary interacting particles hydrodynamic limit of general k nary mass exchange processes with discrete mass distribution is described by a system of kinetic equations that generalize classical smoluchovski s coagulation equations and many other models that are intensively studied in the current mathematical and physical literature existence and uniqueness theorems for these equations are proved at last for k nary mass exchange processes with k 2 an alternative nondeterministic measure valued limit diffusion approximation is discussed

the s monotone index selection rules for pivot algorithms of linear programming abstract in this paper we introduce the concept of s monotone index selection rule for linear programming problems we show that several known anti cycling pivot rules like the minimal index last in first out and the most often selected variable pivot rules are s monotone index selection rules furthermore we show a possible way to define new s monotone pivot rules we prove that several known algorithms like the primal dual simplex mbu simplex algorithms and criss cross algorithm with s monotone pivot rules are finite methods we implemented primal simplex and primal mbu simplex algorithms in matlab using three s monotone index selection rules the minimal index the last in first out lifo and the most often selected variable mosv index selection rule numerical results demonstrate the viability of the above listed s monotone index selection rules in the framework of pivot algorithms

global strict solutions to continuous coagulation fragmentation equations with strong fragmentation in this paper we give an elementary proof of the unique global in time solvability of the coagulation multiple fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate the proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument

a global weak solution via transport projection scheme to a thin film growth kinetic model with nonlocal boundary conditions we examine the existence of a global weak solution associated with a numerical scheme for kinetic models of nuclei growth and coagulation of liquid droplet formation on a solid surface a nonlinear transport equation of the density with a bilinear operator and with a nonlocal boundary condition is coupled to an ode which gives the supersaturation the numerical scheme constructed is a transport projection method that is a combination of an s t operator semigroup associated with the continuous problem and a p delta projection operator on the discrete space three estimates 1 l infty bound 2 a uniform total variation bound and 3 l1 continuity in time of the approximate solution are established with a self contained treatment of the stability and convergence properties numerical calculations of thin film growth kinetics are reported and some related mathematical issues are examined

an overview on the simplex algorithm in this paper the simplex algorithm and its variants are investigated first we define a new concept called formal tableau which leads to derive easily the dual solution from the latest primal table without any distinction between the original variables and the slack ones second we propose a new method for initializing the simplex algorithm unlike the two phase and the big m methods our technique does not involve artificial variables the computational results reveal that this new method is very favorable especially when the number of artificial variables is significant finally this method will be combined with the notion of formal tableau leading naturally to a second new approach

the many facets of linear programming we examine the history of linear programming from computational geometric and complexity points of view looking at simplex ellipsoid interior point and other methods

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

asymptotic behaviour of solutions to the becker doring equations for arbitrary initial data on determine le comportement asymptotique des solutions des equations d amas de becker doring sous certaines hypotheses de decroissances sur les donnees initiales faites dans un article anterieur