flexibly imposing periodicity in kernel independent fmm a multipole to local operator approach abstract an important but missing component in the application of the kernel independent fast multipole method kifmm is the capability for flexibly and efficiently imposing singly doubly and triply periodic boundary conditions in most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes which may give an incorrect answer due to the conditional convergence of some kernel sums here we present an efficient method to properly impose periodic boundary conditions using a near far splitting scheme the near field contribution is directly calculated with the kifmm method while the far field contribution is calculated with a multipole to local m2l operator which is independent of the source and target point distribution the m2l operator is constructed with the far field portion of the kernel function to generate the far field contribution with the downward equivalent source points in kifmm this method guarantees the sum of the near field far field converge pointwise to results satisfying periodicity and compatibility conditions the computational cost of the far field calculation observes the same o n complexity as fmm and is designed to be small by reusing the data computed by kifmm for the near field the far field calculations require no additional control parameters and observes the same theoretical error bound as kifmm we present accuracy and timing test results for the laplace kernel in singly periodic domains and the stokes velocity kernel in doubly and triply periodic domains

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

stability analysis and design for a class of continuous time fuzzy control systems this paper presents a design method for a class of fuzzy control systems the class of fuzzy systems considered can be represented by the takagi sugeno fuzzy model which is a type of dynamic fuzzy model a constructive algorithm is developed to obtain the stabilizing feedback control law for the system the main contribution of this paper is the development of an equivalent principle that is the design of a fuzzy control system is equivalent to the design of a set of linear time invariant extreme systems thus any design method in linear control system theory can be used to design a fuzzy control system an example is given to illustrate the application of the method

a tensor train accelerated solver for integral equations in complex geometries abstract we present a framework using the quantized tensor train qtt decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions we describe how the qtt decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations for a broad range of problems computational and storage costs of the inversion scheme are extremely modest o log n and once the inverse is computed it can be applied in o n log n we analyze the qtt ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as fmm and hss we prove that the qtt ranks are bounded for translation invariant systems and argue that this behavior extends to non translation invariant volume and boundary integrals for volume integrals the qtt decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers we present results demonstrating the remarkable performance of the qtt based solver when applied to both translation and non translation invariant volume integrals in 3d for boundary integral equations we demonstrate that using a qtt decomposition to construct preconditioners for a krylov subspace method leads to an efficient and robust solver with a small memory footprint we test the qtt preconditioners in the iterative solution of an exterior elliptic boundary value problem laplace formulated as a boundary integral equation in complex multiply connected geometries

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

concentration phenomena of a semilinear elliptic equation with large advection in an ecological model abstract we consider a reaction diffusion advection equation arising from a biological model of migrating species the qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined in particular a conjecture of cantrell cosner and lou on concentration phenomena is resolved under mild conditions applications to a related parabolic competition system are also discussed

entropy energy stable schemes for evolutionary dispersal models in this paper we propose some entropy energy stable finite difference schemes for the reaction diffusion advection equation arising in the evolution of biased dispersal of population dynamics the peculiar feature of these active dispersal models is that the transient solution converges to the stable steady state when time goes to infinity for the numerical method to capture the long time pattern of persistence or extinction we use the relative entropy when the resource potential is logarithmic and explore the usual energy for other resource potentials the present schemes are shown to satisfy three important properties of the continuous model for the population density i positivity preserving ii equilibrium preserving and iii entropy or energy satisfying these ensure that our schemes provide a satisfying long time behavior thus revealing the desired dispersal pattern moreover we present several numerical results which confirm the second order accuracy for various resource potentials and underline the efficiency to preserve the large time asymptotic

positive steady states of reaction diffusion advection competition models in periodic environment abstract in this paper we consider the positive steady states for reaction diffusion advection competition models in the whole space with a spatially periodic structure under the spatially periodic setting we establish sufficient conditions for the existence of positive steady states of this model respectively by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems as an application a lotka volterra reaction diffusion advection model for two competing species in a spatially periodic environment is considered finally some numerical simulations are presented to seek dynamical behaviors

global dynamics of a classical lotka volterra competition diffusion advection system abstract in this paper we study a classical two species lotka volterra competition diffusion advection system where the diffusion and advection rates of two competitors are supposed to be proportional by employing the principal spectral theory we first establish a key a priori estimate on the co existence positive steady state which is a powerful tool to link the local and global dynamics we then further present a complete classification on all possible long time dynamical behaviors by appealing to the theory of monotone dynamical systems lastly we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics this work gives a positive answer to the conjecture proposed by lou et al in 34 by considering a more general model under certain conditions and also can be seen as a further development of he and ni 19 for competition diffusion system where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection

acrobatic control of a pendubot this paper presents acrobatic control of an underactuated two link robot called the pendubot to achieve acrobatic control for the pendubot we design a fuzzy controller for keeping first link swinging periodically while the second link maintains standing vertically to facilitate the controller design we represent the pendubot dynamics with a takagi sugeno fuzzy model we derive a linear matrix inequality lmi design condition to realize the acrobatic behavior to accomplish the numerical feasibility design we need to select carefully reference fuzzy model dynamics by taking into account some constraints after selecting reference fuzzy model dynamics an acrobatic controller is designed by solving the lmi condition simulation results show the utility of the proposed acrobatic control

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

limiting structure of steady states to the lotka volterra competition model with large diffusion and advection abstract this paper is concerned with the neumann problem of a stationary lotka volterra competition model with diffusion and advection first we obtain some sufficient conditions of the existence of nonconstant solutions by the leray schauder degree theory next we derive a limiting system as diffusion and advection of one of the species tend to infinity the limiting system can be reduced to a semilinear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system can be classified depending on the coefficients for example this structure involves a global bifurcation curve which connects two different singularly perturbed states boundary layer solutions and internal layer solutions our proof employs a levelset analysis for the associate integral mapping

random dispersal versus fitness dependent dispersal abstract this work extends previous work cantrell et al 2008 9 on fitness dependent dispersal for a single species to a two species competition model both species have the same population dynamics but one species adopts a combination of random and fitness dependent dispersal and the other adopts random dispersal global existence of smooth solutions to the time dependent quasilinear parabolic system is studied when a single species has a strong tendency to move up its fitness gradient it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution cantrell et al 2008 9 for the two species competition model if one species has strong tendency to move up its fitness gradient such approximately ideal free dispersal is advantageous relative to random dispersal bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate

the inverse fast multipole method using a fast approximate direct solver as a preconditioner for dense linear systems although some preconditioners are available for solving dense linear systems there are still many matrices for which preconditioners are lacking particularly in cases where the size of the matrix n becomes very large examples of preconditioners include incomplete lu ilu preconditioners that sparsify the matrix based on some threshold algebraic multigrid preconditioners and specialized preconditioners e g calderon and other analytical approximation methods when available despite these methods there remains a great need to develop general purpose preconditioners whose cost scales well with the matrix size n in this paper we propose a preconditioner with broad applicability and with cost mathcal o n for dense matrices when the matrix is given by a smooth as opposed to a highly oscillatory kernel extending the method using the same framework as general mathcal h 2 matrices i e algebraic instead of defined in terms of an analytical kernel is relatively straightforward but

the role of protection zone on species spreading governed by a reaction diffusion model with strong allee effect abstract it is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity such a phenomenon which is termed as the strong allee effect is well supported by numerous evidence from ecosystems mainly due to the environmental pollution as well as unregulated harvesting and hunting to save an endangered species in this paper we introduce a protection zone that is governed by a fisher kpp nonlinearity and examine the dynamics of a reaction diffusion model with strong allee effect and protection zone we show the existence of two critical values 0 l l and prove that a vanishing transition spreading trichotomy result holds when the length of protection zone is smaller than l a transition spreading dichotomy result holds when the length of protection zone is between l and l only spreading happens when the length of protection zone is larger than l this suggests that the protection zone works when its length is larger than the critical value l furthermore we compare two types of protection zone with the same length a connected one and a separate one and our results reveal that the former is better for species spreading than the latter

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

advection mediated competition in general environments abstract we consider a reaction diffusion advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient while the other species by random diffusion only it has been shown that under some non degeneracy conditions on the environment function the two species always coexist when the advection is strong in this paper we show that for general smooth environment function in contrast to what is known there can be competitive exclusion when the advection is strong and we give a sharp criterion for coexistence that includes all previously considered cases moreover when the domain is one dimensional we derive in the strong advection limit a system of two equations defined on different domains uniqueness of steady states of this non standard system is obtained when one of the diffusion rates is large

concentration through large advection abstract in this paper we extend the elegant results of chen lam and lou 6 section 2 where a concentration phenomenon was established as the advection blows up to a general class of adventive diffusive generalized logistic equations of degenerate type our improvements are really sharp as we allow the carrying capacity of the species to vanish in some subdomain with non empty interior the main technical devices used in the derivation of the concentration phenomenon are proposition 3 2 of cano casanova and lopez gomez 5 theorem 2 4 of amann and lopez gomez 1 and the classical harnack inequality by the relevance of these results in spatial ecology complete technical details seem imperative because the proof of theorem 2 2 of 6 contains some gaps originated by an optimistic use of proposition 3 2 of 5 some of the general assumptions of 6 are substantially relaxed

isogeometric collocation method for the fractional laplacian in the 2d bounded domain abstract we consider the isogeometric analysis for fractional pdes involving the fractional laplacian in two dimensions an isogeometric collocation method is developed to discretize the fractional laplacian and applied to the fractional poisson problem and the time dependent fractional porous media equation numerical studies exhibit monotonous convergence with a rate of o n 1 where n is the degrees of freedom a comparison with finite element analysis shows that the method enjoys higher accuracy per degree of freedom and has better convergence rate we demonstrate that isogeometric analysis offers a novel and promising computational tool for nonlocal problems

does movement toward better environments always benefit a population abstract we study the effects of advection along environmental gradients on logistic reaction diffusion models for population growth the local population growth rate is assumed to be spatially inhomogeneous and the advection is taken to be a multiple of the gradient of the local population growth rate it is also assumed that the boundary acts as a reflecting barrier to the population we show that the effects of such advection depend crucially on the shape of the habitat of the population if the habitat is convex the movement in the direction of the gradient of the growth rate is always beneficial to the population while such advection could be harmful for certain non convex habitats

an o nlogn hierarchical random compression method for kernel matrices by sampling partial matrix entries abstract in this paper we propose an o n log n hierarchical random compression method hrcm for kernel matrix compressing which only requires sampling o n log n entries of a matrix the hrcm combines the hierarchical framework of the h matrix and a randomized sampling technique of column and row spaces for far field interaction kernel matrix we show that a uniform column row sampling of a far field kernel matrix thus without the need and associated cost to pre compute a costly sampling distribution will give a low rank compression of such low rank matrix independent of the matrix size and only dependent on the separation of the source and target locations this far field random compression technique is then implemented at each level of the hierarchical decomposition for general kernel matrices resulting in an o n log n random compression method error and complexity analysis for the hrcm are included numerical results for electrostatic and low frequency helmholtz wave kernels have validated the efficiency and accuracy of the proposed method in comparison of direct o n 2 summations