new numerical algorithms for the nonlinear diffusion model of image denoising and segmentation abstract in this paper for the nonlinear diffusion model of image denoising and segmentation we present two high order explicit algorithms and a semi implicit algorithm using algebraic multi grid method the unconditional stability of the semi implicit approximation is given the numerical results of the above three algorithms are demonstrated with comparison to general explicit algorithm in y chen b c vemuri l wang image denoising and segmentation via nonlinear diffusion comput math appl 39 2000 131 149 for real noised images the numerical results show that the implicit algorithm is quicker and sharper than all explicit algorithms

eventual practical stability of impulsive differential equations with time delay in terms of two measurements in this paper we introduce a new stability eventual practical stability for impulsive differential equations with time delay by using lyapunov functions and comparison principle we will get some criteria of eventual practical stability eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements

practical stability of impulsive hybrid differential systems in terms of two measures on time scales abstract in this paper we establish a new comparison theorem on time scales and give some new stability criteria for impulsive hybrid differential systems

image denoising and segmentation via nonlinear diffusion abstract image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications in this paper we present a nonlinear pde based model for image denoising and segmentation which unifies the popular model of alvarez lions and morel alm for image denoising and the caselles kimmel and sapiro model of geodesic snakes our model includes nonlinear diffusive as well as reactive terms and leads to quality denoising and segmentation results as depicted in the experiments presented here we present a proof for the existence uniqueness and stability of the viscosity solution of this pde based model the proof is in spirit similar to the proof of the alm model however there are several differences which arise due to the presence of the reactive terms that require careful treatment consideration a fast implementation of our model is realized by embedding the model in a scale space and then achieving the solution via a dynamic system governed by a coupled system of first order differential equations the dynamic system finds the solution at a coarse scale and tracks it continuously to a desired fine scale we demonstrate the smoothing and segmentation results on several real images

stability of moving invariant sets and uncertain dynamic systems on time scales abstract in this paper we study the stability of moving invariant sets and uncertain dynamic systems on time scale a control application is considered

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

evaluation of abramowitz functions in the right half of the complex plane a numerical scheme is developed for the evaluation of abramowitz functions jn in the right half of the complex plane for n 1 2 the scheme utilizes series expansions for z r with r determined by the required precision and least squares laurent polynomial approximations on each sub region in the intermediate region 1 z r for n 2 jn is evaluated via a forward recurrence relation the scheme achieves nearly machine precision for n 1 2 at a cost that is competitive as compared with software packages for the evaluation of other special functions in the complex domain

on the practical stability of the solutions of impulsive systems of differential difference equations with variable impulsive perturbations in the present paper the question of the practical stability of the solutions of impulsive systems of differential difference equations with variable impulsive perturbations is discussed in the investigations piecewise continuous functions are used which are analogues of lyapunov s functions and a technique such that certain minimal subsets of a suitable space of piecewise continuous functions are chosen by the elements of which the derivatives of lyapunov s functions are estimated

linearized fe approximations to a nonlinear gradient flow we study fully discrete linearized galerkin finite element approximations to a nonlinear gradient flow applications of which can be found in many areas due to the strong nonlinearity of the equation existing analyses for implicit schemes require certain restrictions on the time step and no analysis has been explored for linearized schemes this paper focuses on the unconditionally optimal l 2 error estimate of a linearized scheme the key to our analysis is an iterated sequence of time discrete elliptic equations and a rigorous analysis of its solution we prove the w 1 infty boundedness of the solution of the time discrete system and the corresponding finite element solution based on a more precise estimate of elliptic pdes in w 2 2 epsilon 1 and h 2 epsilon 2 and a physical feature of the gradient dependent diffusion coefficient numerical examples are provided to support our theoretical analysis

stability criteria of impulsive differential systems the notion of eventual stability has been recently discussed we extend this notion to impulsive systems of differential equations our technique depends on liapunov s direct method

impulsive control of a nuclear spin generator in this paper several new theorems on the stability of impulsive control systems are presented these theorems are then used to find the conditions under which the nuclear spin generator can be asymptotically controlled to the equilibrium point by using impulsive control given the parameters of the nuclear spin generator and the impulsive control law we also present a theory of impulsive synchronization of two nuclear spin generators moreover a larger upper bound of impulsive intervals for the stabilization and synchronization can be obtained

stability and instability for dynamic equations on time scales in this paper we examine the stability and instability of the equilibrium solution x 0 to the first order system of dynamic equations x d f t x t t 0 x d r n where t is from a so called time scale t with t 0 tand d is a compact set our methods involve the existence of a positive definite liapunov function v such that its delta derivative v d satisfies certain integral definite or semidefinite sign properties finally we use liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation

analysis and accurate numerical solutions of the integral equation derived from the linearized bgkw equation for the steady couette flow the integral equation for the flow velocity u x k in the steady couette flow derived from the linearized bhatnagar gross krook welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the knudsen number k between 0 003 and 100 0 first it is shown that the integral equation is a fredholm equation of the second kind in which the norm of the compact integral operator is less than 1 on l p for any 1 p and thus there exists a unique solution to the integral equation via the neumann series second it is shown that the solution is logarithmically singular at the endpoints more precisely if x 0 is an endpoint then the solution can be expanded as a double power series of the form n 0 m 0 c n m x n x ln x m about x 0 on a small interval x 0 a for some a 0 and third a high order adaptive numerical algorithm is designed to compute the solution numerically to high precision the solutions for the flow velocity u x k the stress p x y k and the half channel mass flow rate q k are obtained in a wide range of the knudsen number 0 003 k 100 0 and these solutions are accurate for at least twelve significant digits or better thus they can be used as benchmark solutions

derivation of slip boundary conditions for the navier stokes system from the boltzmann equation rarefied gas flow behavior is usually described by the boltzmann equation the navier stokes system being valid when the gas is less rarefied slip boundary conditions for the navier stokes equations are derived in a rigorous and systematic way from the boundary condition at the kinetic level boltzmann equation these slip conditions are explicitly written in terms of asymptotic behavior of some linear half space problems the validity of this analysis is established in the simple case of the couette flow for which it is proved that the right boundary conditions are obtained

a new comparison principle for impulsive differential systems with variable impulsive perturbations and stability theory in this paper the stability properties in terms of two measures for impulsive differential systems with variable impulses are investigated a new comparison principlem which allows trajectories strike the same hypersurface finite times is established and then be applied to obtain a stability criterion finally one example is worked out to show the advantage of our results

uniform eventual lipschitz stability of impulsive systems on time scales in this paper we discuss the uniform eventual lipschitz stability of impulsive system on time scales by using comparison method lyapunov function and analysis technology some criteria of such stability for system with impulses on time scales are obtained an example is presented to illustrate the efficiency of proposed results

nonlinear multigrid method for solving the llt model our goal in this paper is to study a nonlinear multigrid method for solving the llt model in order to improve the convergence rate of the proposed multigrid method an improved dual iteration is proposed as its smoother furthermore we give the local fourier analysis lfas of the chambolle s dual iterations and a modified smoother for solving the llt model respectively numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large sized images

hybrid systems on time scales in this paper we study hybrid dynamic systems on time scales using lyapunov like functions we obtain sufficient conditions for the practical stability of hybrid dynamic systems on time scales

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

lattice boltzmann modeling of microchannel flow in slip flow regime we present the lattice boltzmann equation lbe with multiple relaxation times mrt to simulate pressure driven gaseous flow in a long microchannel we obtain analytic solutions of the mrt lbe with various boundary conditions for the incompressible poiseuille flow with its walls aligned with a lattice axis the analytical solutions are used to realize the dirichlet boundary conditions in the lbe we use the first order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel we validate the lbe results using the compressible navier stokes ns equations with a first order slip velocity the information preservation direct simulation monte carlo ip dsmc and dsmc methods as expected the lbe results agree very well with ip dsmc and dsmc results in the slip velocity regime but deviate significantly from ip dsmc and dsmc results in the transition flow regime in part due to the inadequacy of the slip velocity model while still agreeing very well with the slip ns results possible extensions of the lbe for transition flows are discussed

an unconditionally stable numerical method for bimodal image segmentation in this paper we propose a new level set based model and an unconditionally stable numerical method for bimodal image segmentation our model is based on the lee seo active contour model the numerical scheme is semi implicit and solved by an analytical method the unconditional stability of the proposed numerical method is proved analytically we demonstrate performance of the proposed image segmentation algorithm on several synthetic and real images to confirm the efficiency and stability of the proposed method

a fast direct solver for the integral equations of scattering theory on planar curves with corners we describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners it is rather comprehensive in that it applies to a wide variety of boundary value problems here we treat the neumann and dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids it achieves high accuracy is applicable to large scale problems and perhaps most importantly does not require asymptotic estimates for solutions instead the singularities of solutions are resolved numerically the approach is efficient however only in the low and mid frequency regimes once the scatterer becomes more than several hundred wavelengths in size the performance of the algorithm of this paper deteriorates significantly we illustrate our method with several numerical experiments including the solution of a neumann problem for the helmholtz equation given on a domain with nearly 10000 corner points

boundedness of the solutions of impulsive differential systems with time varying delay in this paper we investigate boundedness of the solutions of impulsive functional differential equations with time varying delay by using lyapunov functions and razumikhin techniques we will see that impulses do contribute to the solutions boundedness property

new razumikhin type theorems for impulsive functional differential equations in this paper we investigate stability and boundedness for a class of impulsive functional differential equations by using liapunov functions and razumikhin technique some new razumikhin type theorems on stability and boundedness are obtained the corresponding results obtained recently in j shen j yan nonlinear anal 33 1998 519 531 x liu j shen to appear are improved

on the algebraic multigrid method new formulations for the algebraic multigrid amg method are presented a new interpolation operator is developed in which the weighting could be negative numerical experiments demonstrate that the use of negative interpolation weights is necessary in some applications new approaches to construct the restriction operator and the coarse grid equations are discussed two new amg methods are proposed theoretical study and convergence analysis of the amg methods are presented the main contributions of this paper are to improve the convergence rate and to extend the range of applications of an amg method numerical experiments are reported for matrix computations that resulted from partial differential equations signal processing and queueing network problems the success of the proposed new amg algorithms is clearly demonstrated by applications to non diagonally dominant matrix problems for which the standard amg method fails to converge

on cone perturbing liapunov function for impulsive differential systems the concept of f 0 stability and f 0 boundedness recently were introduced for systems of ordinary differential equations odes perturbing liapunov function method was discussed for systems of odes and extend to systems of functional differential equations fdes in this paper we extend these notions to impulsive systems of differential equations via cone perturbing liapunov function method

instability results for slowly time varying linear dynamic systems on time scales abstract we develop eigenvalue criteria under which the solutions of a slowly time varying linear dynamic system of the form x t a t x t are unstable

a nonlinear optimization procedure for generalized gaussian quadratures we present a new nonlinear optimization procedure for the computation of generalized gaussian quadratures for a broad class of square integrable functions on intervals while some of the components of this algorithm have been previously published we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works the new algorithm successfully computes generalized gaussian quadratures in a number of instances in which the previous algorithms fail four applications of our scheme to computational physics are presented the construction of discrete plane wave expansions for the helmholtz green s function the design of linear array antennae the computation of a quadrature for the discretization of laplace boundary integral equations on certain domains with corners and the construction of quadratures for the discretization of laplace and helmholtz boundary integral equations on smooth surfaces

stability for impulsive delay differential equations abstract in this paper the stability for the scalar impulsive delay differential equation y t a t y t f t y 0 t 0 t k y k y k i k y k k 1 2 lim k k where delay arguments may be bounded or unbounded is investigated some new stability theorems are established which improve and extend several known results in the literature

a new approach to practical stability of impulsive functional differential equations in terms of two measures in this work we consider a new approach to the practical stability theory of impulsive functional differential equations with lyapunov functionals and razumikhin technique we use a new technique in the division of lyapunov functions given by shunian zhang and obtain conditions sufficient for the uniform practical asymptotical stability of impulsive delay differential equations an example is also discussed to illustrate the advantage of the proposed results

generalized gaussian quadrature rules for systems of arbitrary functions a numerical algorithm is presented for the construction of generalized gaussian quadrature rules originally introduced by s karlin and w studden over three decades ago the quadrature rules to be discussed possess most of the desirable properties of the classical gaussian integration formulae such as positivity of the weights rapid convergence mathematical elegance etc the algorithm is applicable to a wide class of functions including smooth functions not necessarily polynomials as well as functions with end point singularities such as those encountered in the solution of integral equations complex analysis potential theory and several other areas the performance of the algorithm is illustrated with several numerical examples

stability criteria of impulsive differential systems this paper discusses the uniform eventual lipschitz stability and uniform eventual asymptotic stability of impulsive differential system some criteria of such stability for impulsive differential system are given compared with the existing result the condition is less conservative our technique depends on lyapunov s direct method and comparison principle