finite element solution of the fundamental equations of semiconductor devices in part i of the paper see zlamal 13 finite element solutions of the nonstationary semiconductor equations were constructed two fully discrete schemes were proposed one was nonlinear the other partly linear in this part of the paper we justify the nonlinear scheme we consider the case of basic boundary conditions and of constant mobilities and prove that the scheme is unconditionally stable further we show that the approximate solution extended to the whole time interval as a piecewise linear function converges in a strong norm to the weak solution of the semiconductor equations these results represent an extended and corrected version of results announced without proof in zlamal 14

sieve empirical likelihood ratio tests for nonparametric functions generalized likelihood ratio statistics have been proposed in fan zhang and zhang ann statist 29 2001 153 193 as a generally applicable method for testing norparametic hypotheses about nonparametric functions the likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family we extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio selr tests the approach is also applied to test conditional estimating equations on the distributions of stochastic errors it is shown that the proposed selr statistics follow asymptotically resealed chi 2 distributions with the scale constants and the degrees of freedom being independent of the nuisance parameters this demonstrates that the wilks phenomenon observed in fan zhang and zhang ann statist 29 2001 153 193 continues to hold under more relaxed models and a larger class of techniques the asymptotic power of the proposed test is also derived which achieves the optimal rate for nonparametric hypothesis testing the proposed approach has two advantages over the generalized likelihood ratio method it requires one only to specify some conditional estimating equations rather than the entire distribution of the stochastic error and the procedure adapts automatically to the unknown error distribution including heteroscedasticity a simulation study is conducted to evaluate our proposed procedure empirically

a note on maximizing a special concave function subject to simultaneous loewner order constraints maximization of functions with multivariate arguments can be computationally difficult we show that for a special function which is proportional to the density of a wishart distribution reparametrization can lead to maximization of a concave function we use this fact to produce an algorithm which maximizes the function over a restricted parameter space of the form 0 l u where l u means that u l is a nonnegative definite matrix and l u means that u l is positive definite this restriction is often referred to as the loewner ordering

arbitrary order numerical methods conserving integrals for solving dynamic equations abstract a number of problems in celestial mechanics some hamiltonian systems and non hamiltonian ones may be solved numerically by a modification of polynomial extrapolation which conserves integrals it means that it is possible to get numerical solutions of dynamic equations which possess the same properties that follow from the theoretical study this paper is a survey of problems for which this modification may be applied

deconvolution density estimation on so n this paper develops nonparametric deconvolution density estimation over so n the group of n x n orthogonal matrices of determinant 1 the methodology is to use the group and manifold structures to adapt the euclidean deconvolution techniques to this lie group environment this is achieved by employing the theory of group representations explicit to so n general consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions application to empirical bayes prior estimation and inference is also discussed

conservative numerical methods for x f x abstract two distinctly different numerical methods are developed for solving the conservative initial value problem x f x x o dot x o both methods conserve exactly the same total energy as does the given differential equation computer examples are described and

a mixed method for the mixed initial boundary value problems of equations of semiconductor devices in this article the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered the approximate procedure of this system using a galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite element method for the concentration equations is presented due to the poor regularity properties of the solutions to the semiconductor equations caused by mixed boundary conditions a nonstandard analysis for the semidiscrete galerkin procedure is used existence and uniqueness of the approximate solution is proved a convergence analysis is also given for the method

a poisson nernst planck model for biological ion channels an asymptotic analysis in a three dimensional narrow funnel we wish to predict ionic currents that flow through narrow protein channels of biological membranes in response to applied potential and concentration differences across the channel when some features of channel structure are known we propose to apply singular perturbation analysis to the coupled poisson nernst planck equations which are the basic continuum model of ionic permeation and semiconductor physics in semiconductor physics the problem is a singular perturbation because the ratio of the debye length to the width of the channel is a very small parameter that multiplies the laplacian term in the poisson equation in contrast to semiconductors the atomic scale geometry of narrow ion channels sometimes makes this ratio a large parameter which surprisingly renders the problem a singular perturbation in a different sense we construct boundary layers and match them asymptotically across the different regions of the channel to derive good approximations for fick s and ohm s laws our aim is to e

on strongly reverse biased semiconductor diodes a singular perturbation analysis of the drift diffusion model for stationary flow of charge carriers in a semiconductor device is given an extension of earlier results provides deeper insight into the structure of the solution and the possibility of computing approximations for leakage currents the solvability of the approximating problem is proved

finite element approximation to initial boundary value problems of the semiconductor device equations with magnetic influence we shall consider zlamal s approach to the nonstationary equations of the semiconductor device theory under magnetic fields with mixed boundary conditions owing to the reduced smoothness of the electric potential v and carrier densities n and p caused by considering the mixed boundary conditions we must use a nonstandard analysis for this procedure existence as well as uniqueness of the approximate solution is proved the convergence rates obtained in this paper are slower than those previously obtained for pure dirichlet or neumann boundary conditions

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions abstract in this paper the limit of vanishing debye length in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions is studied in one dimensional case the quasi neutral limit zero debye length limit is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods our results imply that one kind of the new and interesting phenomena in semiconductor physics occurs

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

conservation properties of a time fe method part iii mechanical systems with holonomic constraints a galerkin based discretization method for index 3 differential algebraic equations pertaining to finite dimensional mechanical systems with holonomic constraints is proposed in particular the mixed galerkin mg methodis introduced which leads in a natural way to time stepping schemes that inherit major conservation properties of the underlying constrained hamiltonian system namely total energy and angular momentum in addition to that the constraints on the configuration level and on the velocity momentum level are fulfilled exactly the application of the mg method to specific mechanical systems such as the pendulum rigid body dynamics and the coupled motion of rigid and flexible bodies is presented related numerical examples are investigated to evaluate the numerical performance of the mg 1 and mg 2 method

a singularly perturbed boundary value problem modelling a semiconductor device this paper is concerned with the static one dimensional modelling of a semiconductor device namely the pn junction when a bias is applied the governing equations are the well known equations describing carrier transport in a semiconductor which consist of a system of ordinary differential equations subject to boundary conditions imposed at the contacts because of the different orders of magnitude of the solution components at the boundaries we scale the components individually and obtain a singular perturbation problem we analyse the equilibrium case zero bias applied and set up approximate models posed as singularly perturbed second order equations by neglecting the hole and electron current densities this makes sense for small forward bias and for moderate reverse bias for the full problem we prove an a priori estimate on the number of electron hole carrier pairs and derive asymptotic expansions as the perturbation parameter tends to zero by setting up the reduced system and the boundary

arbitrary order hamiltonian conserving numerical solutions of calogero and toda systems abstract for calogero and toda dynamical equations two numerical methods of arbitrary high order conserving the hamiltonian are developed the methods consist of modifications of conventional polynomial extrapolation with the gragg method used as a basic method the theoretical study is confirmed by a number of numerical examples

continuous finite element methods which preserve energy properties for nonlinear problems abstract continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations schemes are constructed that give high orders of accuracy time discretization algorithms for the cahn hilliard klein gordon korteweg de vries and schrodinger equations are presented comparisons are made with existing schemes

differentiable transformations preserving a cone preordering abstract a necessary and sufficient condition for a differentiable transformation to be isotone w r t cone preorderings on a convex set is given the result is applied to characterize monotone matrix functions a a p with integer p 2 and isotone differentiable transformations w r t g majorizations

admissibility as a touchstone on considere le probleme de l estimation simultanee de moyennes i de variables aleatoires normales independantes x i de variance unite on etudie le concept d admissibilite

electrical structures of interfaces a painleve ii model a painleve ii model derived out of the classical nernst planck system is applied in the context of boundary value problems that describe the electric field distribution in a region x 0 occupied by an electrolyte for privileged flux ratios of the ion concentrations the auto backlund transformation admitted by the painleve ii equation may be applied iteratively to construct exact solutions to classes of physically relevant boundary value problems these representations involve in turn either yablonskii vorob ev polynomials or classical airy functions the requirement that the electric field distribution and ion concentrations in these representations be non singular imposes constraints on the physical parameters these are investigated in detail along with asymptotic properties

conservative difference formulations of calogero and toda hamiltonian systems abstract calogero and toda hamiltonian systems are reformulated using only differences the formulations prove to have the same fundamental invariants as the continuous systems and in addition are readily implementable on modern digital computers

posterior propriety and admissibility of hyperpriors in normal hierarchical models hierarchical modeling is wonderful and here to stay but hyperparameter priors are often chosen in a casual fashion unfortunately as the number of hyperparameters grows the effects of casual choices can multiply leading to considerably inferior performance as an extreme but not uncommon example use of the wrong hyperparameter priors can even lead to impropriety of the posterior for exchangeable hierarchical multivariate normal models we first determine when a standard class of hierarchical priors results in proper or improper posteriors we next determine which elements of this class lead to admissible estimators of the mean under quadratic loss such considerations provide one useful guideline for choice among hierarchical priors finally computational issues with the resulting posterior distributions are addressed

inequalities theory of majorization and its applications by albert w marshall and ingram olkin abstract in the years since the appearance of marshall and olkin s masterful survey the influence of this work has been so great that some comments however incomplete and idiosyncratic on subsequent developments will be of value figure 1 an appendix lists minor errata to the first printing of the book

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions and the general sign changing doping profile abstract the quasi neutral limit in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions the general sign changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one dimensional case the dynamic structure stability of the solution with respect to the scaled debye length is proven by the asymptotic analysis of singular perturbation and the entropy energy method the key point of the proof is to use sufficiently the fact that the length of the boundary layer is very small in a short time period

a singular perturbation analysis of the fundamental semiconductor device equations in this paper we present a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed neumann dirichlet boundary conditions the system consists of poisson s equation and the continuity equations and describes potential and carrier distributions in an arbitrary emiconductor device the singular perturbation parameter is the minimal normed debye length of the device under consideration using matched asymptotic expansions we demonstrate the occurrence of internal layers at surfaces across which the impurity distribution appearing as an inhomogeneity of poisson s equation has a jump discontinuity these surfaces are called junctions and the occurrence of boundary layers at semiconductor oxide interfaces we derive the layer equations and the reduced problem charge neutral approximation and give existence proofs for these problems the layer solutions which characterize the solutions of the s

uniform asymptotic error estimates for semiconductor device and electrochemistry equations abstract the paper is organized as follows section 1 sets up the problem our purpose and results and the existing results in the literature section 2 gives the notations used in the paper sections 3 and 4 set up the problem in the case of a symmetric piecewise constant junction and recall the associated asymptotic expansion in section 5 our method is introduced and uniform asymptotic error estimates for a symmetric piecewise constant junction are derived section 6 is an application of our technique for the case of a biological membrane with a constant concentration of fixed charges uniform asymptotic error estimates are also proved to hold in that case a brief summary and conclusion are given in the appendix we give the proofs of the lemmas which are used in sections 5 and 6

an exact decomposition theorem and a unified view of some related distributions for a class of exponential transformation models on symmetric cones a class of exponential transformation models is defined on symmetric cones q with the group of automorphisms on q as the acting group we show that these models are reproductive and the exponent of their joint distribution for a given sample of size q can be split into q independent components introducing one sample point at a time the automorphism group can be factorized into the group of positive dilation and another group accordingly the symmetric cone q can be seen as the direct product of r and a unit orbit and every x in q can be identified by its orbital decomposition we derive the distributions of the independent components of the exponent of the length of x the direction of x the conditional distribution of the direction given the length and other distributions for a given sample the wishart distribution and the hyperboloid distribution are two special cases in the class we define we also give a unified view of several distributions which are usually treated separately