on fully implicit space time discretization for motions of incompressible fluids with shear dependent viscosities the case p le 2 in this paper we deal with a rigorous error analysis for a fully implicit space time discretization of an unsteady non newtonian fluid flow model where the nonlinear operator related to the stress tensor exhibits p structure in a first step a semidiscretization in time using the implicit euler method is discussed due to limitation of regularity of the solution for the case p neq 2 a decrease with respect to convergence rates of the method is stated in general by retaining smoothly first order in appropriate norms for the stokes law i e p 2 the analysis is then extended to a full discretization using stable pairings of finite element spaces in a second step

some convergence estimates for semidiscrete type schemes for time dependent nonselfadjoint parabolic equations l2 norm error estimates are shown for semidiscrete continuous in time galerkin finite element type approximations to solutions of general time dependent nonselfadjoint second order parabolic equations under dirichlet boundary conditions the semidiscrete solutions are defined in terms of given methods for the corresponding elliptic problem such as the standard galerkin method in which the boundary conditions are satisfied exactly but also methods for which this is not necessary the results are proved by energy arguments and include estimates for the homogeneous equation with both smooth and nonsmooth initial data

maximum l 2 convergence rates of the crank nicolson scheme to the stokes initial value problem let a denote the stokes operator and d a alpha the domain of its fractional powers a alpha we consider the homogeneous stokes initial value problem with initial data u 0 u 0 in d a 1 varepsilon varepsilon in 0 1 for stokes like equations the range varepsilon in 0 frac 1 4 is of special interest as any solution derived from varepsilon ge frac 1 4 would necessarily have to satisfy an additional in practice unverifiable compatibility condition at time t 0 approximating any strong solution u in c 0 0 infty d a 1 varepsilon in time direction on a finite time interval 0 t with a crank nicolson scheme we show convergence of order o frac tau 2 t 1 varepsilon which is maximal for the assumed regularity of the data and reflects the loss of regularity as t rightarrow 0 the error estimates are derived by energy and semigroup methods combined with a parabolic duality argument

superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data a semidiscrete mixed finite element approximation to parabolic initial boundary value problems is introduced and analyzed superconvergence estimates for both pressure and velocity are obtained the estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in l 2 and data in h r for r sufficiently large because of the smoothing properties of the parabolic operator these estimates for large time levels essentially coincide with the estimates obtained earlier for smooth solutions however for small time intervals we obtain the correct convergence orders for nonsmooth data

adaptive time stepping for incompressible flow part i scalar advection diffusion even the simplest advection diffusion problems can exhibit multiple time scales this means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally the performance of the second order trapezoid rule using an explicit adams bashforth method for error control is assessed in this work this combination is particularly well suited to long time integration of advection dominated problems herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations specifically diffusion problems with rough initial data and general advection diffusion problems with different physical time scales governing the system evolution

l2 estimates for the finite element method for the dirichlet problem with singular data in this paper we consider the approximation by the finite element method of second order elliptic problems on convex domains and homogeneous dirichlet condition on the boundary in these problems the data are borel measures using a quasiuniform mesh of finite elements and polynomials of degree 1 we prove that in two dimensions the convergence is of orderh inl 2 and in three dimensions of orderh 1 2

adaptive galerkin methods with error control for a dynamical ginzburg landau model in superconductivity the time dependent ginzburg landau model which describes the phase transitions taking place in superconductors is a coupled system of nonlinear parabolic equations it is discretized semi implicitly in time and in space via continuous piecewise linear finite elements a posteriori error estimates are derived for the l infty l 2 norm by studying a dual problem of the linearization of the original system other than the dual of error equations numerical simulations are included which illustrate the reliability of the estimators and the flexibility of the proposed adaptive method

optimal control of mobile sources for heat conductivity processes abstractwe consider a problem of optimal control of the mobile sources for heat conductivity processes described by parabolic equation and systems of ordinary differential equations sufficient conditions for frechet differentiability of the performance criterion and an expression for its gradient were determined the necessary optimality condition was established in the form of the integral principles of maximum the theoretical conclusions are illustrated by the solution of a numerical example

error estimates for semidiscrete galerkin type approximations to semilinear evolution equations with nonsmooth initial data error estimates for the semidiserete galerkin method for abstract semilinear evolution equations with non smooth initial data are given in concrete cases almost optimal order of convergence for linear finite elements results

on computational proofs of the existence of solutions to nonlinear parabolic problems abstract this paper is an extension of the preceding study nakao this journal 1991 in which we described a numerical verification method of the solution for one space dimensional parabolic problems to the several space dimensional case here numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer we reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed point problem of a compact operator on certain function spaces as in the preceding study based upon a simple c 0 finite element approximation and its constructive a priori error estimates a numerical verification procedure is presented with some numerical examples

some optimal error estimates for piecewise linear finite element approximations it is shown that the ritz projection onto spaces of piecewise linear finite elements is bounded in the sobolev space wl for 2 p oc this implies that for functions in wf n w2 the error in approximation behaves like 0 h in wp for 2 p oo and like 0 h2 in lp for 2 p oo in all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur

a note on sargan densities abstract this note reconsiders the general class of sargan densities studied by goldfeld and quandt 1981 and missiakoulis 1983 in the context of approximating normal densities in regression models some errors in these papers are pointed out and the sargan densities are re computed to the contrary of missiakoulis conclusion the first two order densities are not the best choice higher order densities are better approximations though the best choice appears to be the second order density based on the goldfeld quandt criteria

pointwise control of burgers equation a numerical approach abstract we describe a methodology for numerically solving pointwise control problems for the viscous burger s equation in one space dimension the solution methods are based on a combination of finite difference and finite element techniques for the time and space discretizations with iterative algorithms such as quasi newton methods and gmres numerical experiments validate the methods

adaptive finite element method for parabolic equations with dirac measure abstract in this paper we study the adaptive finite element method for parabolic equations with dirac measure two kinds of problems with separate measure data in time and measure data in space are considered it is well known that the solutions of such kind of problems may exhibit lower regularity due to the existence of the dirac measure and thus fit to adaptive fem for space discretization and variable time steps for time discretization for both cases we use piecewise linear and continuous finite elements for the space discretization and backward euler scheme or equivalently piecewise constant discontinuous galerkin method for the time discretization the a posteriori error estimates based on energy and l 2 norms for the fully discrete problems are then derived to guide the adaptive procedure numerical results are provided at the end of the paper to support our theoretical findings

applications of axiomatic fuzzy set clustering method on management strategic analysis abstract in this paper first the axiomatic fuzzy set afs clustering method x d liu w wang t y chai the fuzzy clustering analysis based on afs theory ieee transactions on systems man and cybernetics part b 35 5 2005 1013 1027 is investigated further by improving the algorithm to be more applicable then it is used to analyze the evaluation results of 30 companies which have been studied and analyzed by g s liang et al g s liang t y chou t c han cluster analysis based on fuzzy equivalence relation european journal of operational research 166 2005 160 171 compared with liang s algorithm the proposed method is more transparent understandable and interpretable this method can be applied to the management strategic analysis based on the datasets described by mixed features such as real numbers boolean logical values linguistic descriptions the illustrative examples show that the interpretations of the clustering results of the 30 companies are almost consistent with the expert s intuitions

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

non smooth initial data error estimates with the weight norms for the linear finite element method of parabolic partial differential equations we analyze the galerkin approximation of a parabolic equation for the second order continuous time method with initial data only in l2 we prove an optimal order error estimate with weight norm our analysis uses elementary energy techniques and spectral representations and weight function techniques the same techniques are shown to give an analysis of the galerkin method time discretization

on error estimates for galerkin spectral discretizations for parabolic problems with nonsmooth initial data we analyze the legendre and chebyshev spectral galerkin semi discretizations of a one dimensional homogeneous parabolic problem with non constant coefficients we present error estimates for both smooth and nonsmooth data in the chebyshev case a limit in the order of approximation is established on the contrary in the legendre case we find an arbitrary high order of convegence

a priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control we consider finite element approximations of parabolic control problems with pointwise control the state equation exhibits low regularity due to the control imposed pointwisely this introduces some difficulties for both theoretical and numerical analysis to discretize the optimal control problem we use variational discretization together with piecewise linear and continuous finite elements for the space discretization of the state and we use the backward euler scheme for time discretization we prove a priori error estimates for the control state and adjoint state numerical experiments are provided which support the theoretical results

unsupervised fuzzy clustering with multi center clusters a new unsupervised fuzzy clustering algorithm is provided in this paper to cluster the data patterns without a priori information about the number of clusters the initial guesses of the locations of the cluster centers or the initial guesses of the membership values are not necessary with the minimization of a new objective function cluster centers are generated one by one related centers are defined to belong to the same cluster multi centers are adopted to represent the non spherical shape of clusters thus the clustering algorithm with multi center clusters can handle non traditional curved clusters the proposed algorithm is tested on different data sets with a variety of cluster shapes cluster densities and number of points in each cluster also the results are compared with some other clustering algorithms to show the effectiveness of the algorithm moreover the designed unsupervised fuzzy clustering algorithm is applied to cluster the pixels in a color image to show the efficiency of the algorithm

some new error estimates of a semidiscrete finite volume element method for a parabolic integro differential equation with nonsmooth initial data a semidiscrete finite volume element fve approximation to a parabolic integro differential equation pide is analyzed in a two dimensional convex polygonal domain an optimal order l 2 error estimate for smooth initial data and nearly the same optimal order l 2 error estimate for nonsmooth initial data are obtained more precisely for homogeneous equations an elementary energy technique and a duality argument are used to derive an error estimate of order o left t 1 h 2 ln h right in the l 2 norm for positive time when the given initial function is only in l 2

gaps a clustering method using a new point symmetry based distance measure in this paper an evolutionary clustering technique is described that uses a new point symmetry based distance measure the algorithm is therefore able to detect both convex and non convex clusters kd tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point adaptive mutation and crossover probabilities are used the proposed ga with point symmetry gaps distance based clustering algorithm is able to detect any type of clusters irrespective of their geometrical shape and overlapping nature as long as they possess the characteristic of symmetry gaps is compared with existing symmetry based clustering technique sbkm its modified version and the well known k means algorithm sixteen data sets with widely varying characteristics are used to demonstrate its superiority for real life data sets anova and manova statistical analyses are performed

a priori error estimates for space time finite element discretization of parabolic optimal control problems part i problems without control constraints in this paper we develop a priori error analysis for galerkin finite element discretizations of optimal control problems governed by linear parabolic equations the space discretization of the state variable is done using usual conforming finite elements whereas the time discretization is based on discontinuous galerkin methods for different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters the paper is divided into two parts in the first part we develop some stability and error estimates for space time discretization of the state equation and provide error estimates for optimal control problems without control constraints in the second part of the paper the techniques and results of the first part are used to develop a priori error analysis for optimal control problems with pointwise inequality constraints on the control variable

optimal error estimates for linear parabolic problems with discontinuous coefficients a finite element discretization is proposed and analyzed for a linear parabolic problems with discontinuous coefficients due to low global regularity of the solution it seems difficult to achieve optimal order of convergence with classical finite element methods numer math 79 1998 pp 175 202 in this paper we have used a finite element discretization where interface triangles are assumed to be curved triangles instead of straight triangles as in classical finite element methods optimal order error estimates in l2 and h1 norms are shown to hold even if the regularity of the solution is low on the whole domain while the continuous time galerkin method is discussed for the spatially discrete scheme the discontinuous galerkin method is analyzed for the fully discrete scheme the interfaces and boundaries of the domains are assumed to be smooth for our purpose

fully discrete galerkin approximations of parabolic boundary value problems with nonsmooth boundary data in this paper we study the convergence properties of a fully discrete galerkin approximation with a backwark euler time discretization scheme an approach based on semigroup theory is used to deal with the nonsmooth dirichlet boundary data which cannot be handled by standard techniques this approach gives rise to optimal rates of convergence inl p o t l 2 norms for boundary conditions inl p o t l 2 1 p

a posteriori error estimates for optimal control problems governed by parabolic equations in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation we obtain a posteriori error estimates for both the state and the control approximation such estimates which are apparently not available in the literature are an important step towards developing reliable adaptive finite element approximation schemes for the control problem

discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems the main goal of the paper is to establish time semidiscrete and space time fully discrete maximal parabolic regularity for the lowest order time discontinuous galerkin solution of linear parabolic

a note on sargan densities abstract this note reexamines the general class of sargan densities analyzed by goldfeld and quandt 1981 kafei and schmidt 1985 and others in the context of approximating normal densities in certain econometric models it suggests a third order sargan density which complies with the goldfeld and quandt criteria is unimodal and is the best approximation to the normal for orders less than or equal to 3 some errors in goldfeld and quandt paper are corrected

theoretical and numerical analysis of an optimal control problem related to wastewater treatment in this work we deal with the design and management of wastewater treatment systems mainly the disposal of sea outfalls discharging polluting effluent from a sewerage system this problem is formulated as a pointwise optimal control problem with state and control constraints the main difficulties arise from the lack of regularity of the second member in the state system and from the pointwise constraints on the state variables we develop the theoretical analysis of the problem we propose an algorithm for its numerical resolution and finally we give results for a realistic problem posed in the ria of vigo spain

constructive a priori error estimates for a full discrete approximation of the heat equation in this paper we consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation our method is based on the finite element galerkin method with an interpolation in time that uses the fundamental solution for semidiscretization in space the present estimates play an essential role in the numerical verification method of exact solutions for the nonlinear parabolic equations this implies that by utilizing the present results we could get the guaranteed a posteriori error estimates for various kinds of nonlinear evolutional problems our results can also be considered as an explicit optimal estimate with the limited regularity of solutions which should be unknown up to the present

galerkin approximations of abstract parabolic boundary value problems with rough boundary data l p theory etude des approximations de galerkin d un probleme aux valeurs limites parabolique abstrait avec des donnees aux limites grossieres determination des vitesses de convergence optimales dans les normes lp

optimal pointwise control of semilinear parabolic equations we study optimal control problems for semilinear parabolic equations with pointwise controls in a bounded domain of r when the nonlinear term in the state equation is of the form y y we prove the existence of solutions for such equations when 1 n n 2 we next study a control problem with a terminal observation we prove existence of optimal controls and a pontryagin principle for these problems

econometric modelling with non normal disturbances abstract this paper analyzes a general class of non normal density functions dubbed sargan densities in the context of the ordinary regression model and the simple one market disequilibrium model use of the normal density in disequilibrium models is unwieldy especially for multimarket models since the application of maximum likelihood methods requires numerical evaluation of multiple integrals these difficulties are avoided with the sargan densities and based on both asymptotic results and limited sampling experiments these densities appear to offer a promising alternative to the normal in disequilibrium models

solving nonlinear parabolic problems with result verification part i one space dimensional case abstract we propose some numerical methods for the automatic proof of existence of weak solutions for parabolic initial boundary value problems with one space dimension it also means that one can obtain a posteriori error bounds for the approximate solutions of the problems based upon schauder s fixed point theorem a verification condition is formulated and by the use of finite element approximation and its error estimates for a simple parabolic problem we present a numerical verification algorithm of exact solutions in a computer some numerical examples which are verified by the method are illustrated

on the smoothing property of the galerkin method for parabolic equations we analyze the galerkin approximation of the general second order parabolic initial boundary value problem for the second order continuous time method with initial data only in l 2 we prove an l 2 error estimate of order o h 2 t analogous results are shown to hold for the error in negative sobolev norms and for the time derivative of the error our analysis uses only elementary energy techniques and the same techniques are shown to give a simple analysis of the backward euler time discretization

subdiffusion with time dependent coefficients improved regularity and second order time stepping this article concerns second order time discretization of subdiffusion equations with time dependent diffusion coefficients high order differentiability and regularity estimates are established for subdiffusion equations with time dependent coefficients using these regularity results and a perturbation argument of freezing the diffusion coefficient we prove that the convolution quadrature generated by the second order backward differentiation formula with proper correction at the first time step can achieve second order convergence for both nonsmooth initial data and incompatible source term numerical experiments are consistent with the theoretical results

a priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time in this paper we consider an optimal control problem which is governed by a linear parabolic equation and is subject to state constraints pointwise in time optimal order error estimates are developed for a space time finite element discretization of this problem numerical examples confirm the theoretical results as a by product of our analysis we derive a new regularity result for the optimal control

error estimates for the spectral approximation of the nonstationary stokes problem this paper analyzes a discretization of the nonstationary stokes problem with periodic nonperiodic boundary conditions fourier legendre spectral approximations are considered with respect to the space variables while the time discretization is based on the second order crank nicolson scheme optimal convergence estimates are proved for the velocity field

sargan densities which one abstract goldfeld and quandt 1981 suggest the use of sargan distribution as a viable alternative to normal distribution in econometric models this paper examines the resemblance of a sargan type family of densities to the normal density and concludes that the first two order cases are the best choice

mixed finite element approximations of parabolic integro differential equations with nonsmooth initial data we analyze the semidiscrete mixed finite element methods for parabolic integro differential equations that arise in the modeling of nonlocal reactive flows in porous media a priori l 2 error estimates for pressure and velocity are obtained with both smooth and nonsmooth initial data more precisely a mixed ritz volterra projection introduced earlier by ewing et al in siam j numer anal 40 2002 pp 1538 1560 is used to derive optimal l 2 error estimates for problems with initial data in h 2 cap h 0 1 in addition for homogeneous equations we derive optimal l 2 error estimates for initial data just in l 2 here we use an elementary energy technique and duality argument

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

a priori error estimates for space time finite element discretization of parabolic optimal control problems in this article we summarize recent results on a priori error estimates for space time finite element discretizations of linear quadratic parabolic optimal control problems we consider the following three cases problems without inequality constraints problems with pointwise control constraints and problems with state constraints pointwise in time for all cases error estimates with respect to the temporal and to the spatial discretization parameters are derived the results are illustrated by numerical examples

on the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems we consider the guaranteed a posteriori estimates for the inverse parabolic operators with homogeneous initial boundary conditions our estimation technique uses a full discrete numerical scheme which is based on the galerkin method with an interpolation in time by using the fundamental solution for semidiscretization in space in our technique the constructive a priori error estimates for a full discretization of solutions for the heat equation play an essential role combining these estimates with an argument for the discretized inverse operator and a contraction property of the newton type formulation we derive an a posteriori estimate of the norm for the infinite dimensional operator in numerical examples we show that the proposed method should be more efficient than the existing method moreover as an application we give some prototype results for numerical verification of solutions of nonlinear parabolic problems which confirm the actual usefulness of our technique

error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions semidiscrete finite element error estimates for linear parabolic equations are derived under minimal regularity with the help of l2 projectors then analogous minimal regularity semidiscrete error estimates for semilinear parabolic equations are derived

error estimates for a class of degenerate parabolic equations the degenerate parabolic equation u t delta beta u is considered in the cylinder omega times 0 t where omega subset r n is bounded beta 0 beta 0 0 and beta geq0 e g beta u u u m 1 m 1 a fully discrete scheme is given using c0 piecewise linear finite elements in space and a backward difference scheme in time l2 error estimates for the approximation of u and of beta u are proven for that purpose we employ the fact that the free boundary has a finite speed of propagation

optimal error estimates for a semi implicit euler scheme for incompressible fluids with shear dependent viscosities certain rheological behaviors of fluids in engineering sciences are modeled by power law ansatz with p in 1 2 in the present paper a semi implicit time discretization scheme for such fluids is proposed the main result is the optimal mathcal o k error estimate where k is the time step size our results hold in the range p in 3 2 2 in the three dimensional setting for strong solutions of the continuous problem whose existence is guaranteed under appropriate assumptions on the data the estimates are uniform with respect to the degeneracy parameter delta in 0 delta 0 of the extra stress tensor additional regularity properties of the solution of the discrete problem are proved

optimal order multilevel preconditioners for regularized ill posed problems in this article we design and analyze multilevel preconditioners for linear systems arising from regularized inverse problems using a scale independent distance function that measures spectral equivalence of operators it is shown that these preconditioners approximate the inverse of the operator to optimal order with respect to the spatial discretization parameter h as a consequence the number of preconditioned conjugate gradient iterations needed for solving the system will decrease when increasing the number of levels with the possibility of performing only one fine level residual computation if h is small enough the results are based on the previously known two level preconditioners of rieder 1997 see also hanke and vogel 1999 and on applying newton like methods to the operator equation x 1 a 0 we require that the associated forward problem has certain smoothing properties however only natural stability and approximation properties are assumed for the discrete operators the algorithm is applied to a reverse time parabolic equation that is the problem of finding the initial value leading to a given final state we also present some results on constructing restriction operators with preassigned approximating properties that are of independent interest

error estimates for the semidiscrete finite element approximation of a damped wave equation with a smoothing property error estimates are given for the semidiscrete finite element approximation of an inhomogeneous wave equation damped by a constant times the positive square root of the elliptic operator in the wave equation times the time derivative of the solution the damping term smooths the solution the smoothing property is used to obtain higher order error estimates for positive time even when the initial data are non smooth

min sum clustering with penalties abstract given a complete graph g v e a weight function w e n 0 on its edges and p n 0 a penalty function on its vertices the penalized k min sum problem is the problem of finding a partition of v to k 1 sets s 1 s k 1 minimizing i 1 k w s i p s k 1 where for s v w s e i j s w e and p s i s p i our main result is a randomized approximation scheme for the metric version of the penalized 1 min sum problem when the ratio between the minimal and maximal penalty is bounded for the metric penalized k min sum problem where k is a constant we offer a 2 approximation

measure valued directional sparsity for parabolic optimal control problems a directional sparsity framework allowing for measure valued controls in the spatial direction is proposed for parabolic optimal control problems it allows for controls which are localized in space where the spatial support is independent of time well posedness of the optimal control problems is established and the optimality system is derived it is used to establish structural properties of the minimizer an a priori error analysis for finite element discretization is obtained and numerical results illustrate the effects of the proposed cost functional and the convergence results

the structure of simultaneous equation estimators a generalization towards nonnormal disturbances a general linear simultaneous equation system with a multivariate student t disturbance vector is considered the normal equations of the corresponding maximum likelihood estimator are used as estimator generating equations to introduce a new class of estimators properties of large subclasses of these estimators are determined for disturbance vectors other than the multivariate student t

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

an overlapping cluster algorithm to provide non exhaustive clustering abstract the partitioning clustering is a technique to classify n objects into k disjoint clusters and has been developed for years and widely used in many applications in this paper a new overlapping cluster algorithm is defined it differs from traditional clustering algorithms in three respects first the new clustering is overlapping because clusters are allowed to overlap with one another second the clustering is non exhaustive because an object is permitted to belong to no cluster third the goals considered in this research are the maximization of the average number of objects contained in a cluster and the maximization of the distances among cluster centers while the goals in previous research are the maximization of the similarities of objects in the same clusters and the minimization of the similarities of objects in different clusters furthermore the new clustering is also different from the traditional fuzzy clustering because the object cluster relationship in the new clustering is represented by a crisp value rather than that represented by using a fuzzy membership degree accordingly a new overlapping partitioning cluster opc algorithm is proposed to provide overlapping and non exhaustive clustering of objects finally several simulation and real world data sets are used to evaluate the effectiveness and the efficiency of the opc algorithm and the outcomes indicate that the algorithm can generate satisfactory clustering results

differentiability and convergence rates of approximating semigroups for retarded functional differential equations in this paper the averaging approximations i e semidiscrete finite difference scheme for linear retarded functional differential equations are considered in the context of the semigroups on the hilbert space r n times l 2 it is shown that the approximating semigroups are all differentiable uniformly with respect to the index n determining the mesh size this fact makes it possible to prove the existence of a uniform exponential decay or growth rate for the approximating semigroups which can be made arbitrarily close to the decay respectively growth rate of the original semigroup more importantly the uniform differentiability makes it possible to establish convergence rates that improve with time and to prove the convergence of the approximating semigroups in the uniform operator topology the dependence of the convergence rate on the initial conditions and system parameters is also established

a first order projection based time splitting scheme for computing chemically reacting flows the simulation of chemically reacting flows is a basic tool in natural sciences as well as engineering sciences to understand and predict complex flow phenomena e g concentrations of salt in oceans or crystal growth in semiconductor industries see e g 7 19 the objective of this paper is two fold first a first order time splitting scheme is presented that allows for efficient parallelization of the related quantities in each time step this scheme is based on the decoupled computation of the new velocity field and pressure iterates by means of chorin s projection method second a thorough analysis of this scheme is given that leads to optimal error statements which apply to general flow situations

on a class of fuzzy c numbers clustering procedures for fuzzy data this paper describes a class of fuzzy clustering procedures for fuzzy data most fuzzy clustering techniques are designed for handling crisp data with their class memberships using the idea of fuzzy set theory here we derive new types of fuzzy clustering procedures in dealing with fuzzy data these procedures are called fuzzy c numbers fcn clusterings specially we construct these fcns for u type triangular trapezoidal and normal fuzzy numbers k jwoy s cluster analysis fuzzy clustering fuzzy data analysis fuzzy numbers fuzzy intervals fuzzy c means clustering fuzzy c numbers clustering

almost sure convergence of galerkin approximations for a heat equation with a random initial condition we analyze probabilistic convergences of random galerkin approximations for a heat equation with a random initial condition almost sure l2 convergence results for both continuous time and discrete time galerkin approximations are obtained by the borel cantelli s lemma a criterion for determining the sample size is suggested

finite element solution of diffusion problems with irregular data diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break down of the solution s regularity this may drastically reduce the accuracy of discretization schemes over the whole interval of integration unless certain precautions are taken the diagonal pade schemes of order 2 combined with a standard finite element discretization usually require an unnatural step size restriction in order to achieve even locally optimal accuracy it is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and in the case 1 does not increase the costs

approximate methods for optimal pointwise control of parabolic systems in this paper we study an optimal pointwise control problem for systems governed by a parabolic equation the state equation is first analyzed and a transposed galerkin type method is used for approximating this equation a conditional gradient method is then applied to the control problem convergence proofs are given in both cases

continuous finite elements in space and time for the heat equation on analyse une nouvelle methode variationnelle pour l approximation de l equation de la chaleur a l aide des elements finis continus dans l espace et le temps on presente les estimations d erreurs et les resultats d experiences numeriques

optimal a priori error estimates of parabolic optimal control problems with pointwise control in this paper we consider a parabolic optimal control problem with a pointwise dirac type control in space but variable in time in two space dimensions to approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous galerkin method in time despite low regularity of the state equation we show almost optimal h 2 k convergence rate for the control in l 2 norm this result improves almost twice the previously known estimate in w gong m hinze and z zhou a priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control tech report 2011 07 hamburger beitrage zur angewandten mathematik hamburg germany 2011

a galerkin method for mixed parabolic elliptic partial differential equations in this article boundary value problems for partial differential equations of mixed elliptic parabolic type are considered to ensure that the considered problems possess a unique solution the usual variational existence proof for parabolic problems is extended to the mixed situation further the convergence of approximations computed by a time space galerkin method to the solution of the mixed problem is proven and error estimates are given

conjecturable knowledge discovery a fuzzy clustering approach traditionally clustering is the task of dividing objects into homogeneous clusters based on their degrees of similarity as objects are assigned to clusters users need to manually give descriptions for all clusters characterizing clusters by hand can consume a great deal of time of users in addition users sometimes have no specific idea as to how to explain the clustering results thus they might give inappropriate descriptions a clustering technique is proposed to discover conjecturable rules providing descriptions of clusters with a decision tree classification technique every cluster in a conjecturable tree is depicted by only one conjecturable rule however less utilized rules are not necessarily trivial in some real life circumstances there might be some clusters which can be depicted by two or more rules namely recessive conjecturable rules for example customers usually prefer to buy inexpensive red wines however on certain occasions such for a birthday celebration they will buy expensive wine therefore we know that there are some people who generally belong to a low value cluster but may simultaneously be assigned to a high value one in this study we propose a new discovery model for mining conjecturable rules to reveal this type of knowledge the experimental results show that our proposed model is able to discover conjecturable rules as well as recessive rules the results of sensitivity analysis are also given for practitioners reference

analysis of a robust finite element approximation for a parabolic equation with rough boundary data the approximation of parabolic equations with nonhomogeneous dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward euler time discretization is studied the boundary values are assumed in a least squares sense it is shown that this method achieves an optimal rate of convergence for rough only l2 boundary data and for smooth data as well the results of numerical computations which confirm the robust theoretical error estimates are also presented

a class of partially adaptive one step m estimators for the non linear regression model with dependent observations in this paper we consider a class of partially adaptive one step m estimators for the non linear regression model with dependent observations those estimators adapt themselves with respect to a measure of the tailthickness of the disturbance distribution as well as to a measure of the scale the large sample behavior of those estimators is examined theoretically for general disturbance distributions and numerically for various specific ones the estimators considered are motivated by the student r maximum likelihood estimator given appropriate specifications of the adaptation parameter the estimators are asymptotically efficient on the family of student t distributions including the normal distribution

partially adaptive estimation via a normal mixture abstract this paper proposes a new partially adaptive regression estimator the estimator is derived by modeling the disturbance distribution as a variance mixture of normal distributions yet the true disturbance distribution need not be a variance mixture in order for the proposed estimator to be consistent and asymptotically normal moreover the partially adaptive estimator is shown to be less sensitive to extreme values than the ordinary least squares estimator a point that is illustrated with some monte carlo experiments the paper also provides some easily programmed em algorithms for computing estimates

error estimates for the discontinuous galerkin methods for parabolic equations the classical discontinuous galerkin method for a general parabolic equation is analyzed symmetric error estimates for schemes of arbitrary order are presented the ideas developed below relax many assumptions required in previous work for example different discrete spaces may be used at each time step and the spatial operator need not be self adjoint or independent of time our error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

approximations of elliptic optimal control problems with controls acting on a lower dimensional manifold in this paper we study finite element approximations to some elliptic optimal control problems with controls acting on a lower dimensional manifold which can be a point a curve or a surface we use piecewise linear finite elements to approximate state variables while utilizing the variational discretization to approximate control variables we derive several a priori error estimates for optimal controls from different cases depending on the dimensions of the computational domain and the manifold where controls act we ends up with extensive numerical experiments which confirm our theoretical findings