fast methods for the eikonal and related hamilton jacobi equations on unstructured meshes the fast marching method is a numerical algorithm for solving the eikonal equation on a rectangular orthogonal mesh in o m log m steps where m is the total number of grid points the scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a dijkstra like programming approach in this paper we discuss several extensions to this technique including higher order versions on unstructured meshes in rn and on manifolds and connections to more general static hamilton jacobi equations

a free boundary problem for the laplacian with a constant bernoulli type boundary condition we study a free boundary problem for the laplace operator where we impose a bernoulli type boundary condition we show that there exists a solution to this problem we use a beurling s technique by defining two classes of sub and supersolutions and a perron argument we try to generalize here a previous work of a henrot and h shahgholian we extend these results in different directions

an autoregressive growth model for longitudinal item analysis a first order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits specifically the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time or the lagged response an initial conditions problem arises because there is no lagged response at the initial time period we handle this problem by adapting solutions proposed for dynamic models in panel data econometrics asymptotic and finite sample power for the autoregressive parameters are investigated the consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first order autoregressive growth model the proposed methods are applied to longitudinal data on korean students self esteem

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

concavity properties for elliptic free boundary problems abstract we prove some concavity properties connected to nonlinear bernoulli type free boundary problems in particular we prove a brunn minkowski inequality and an urysohn s type inequality for the bernoulli constant and we study the behavior of the free boundary with respect to the given boundary data moreover we prove a uniqueness result regarding the interior problem

the conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling consider a boundary integral operator on a bounded d dimensional surface in mbox smallbbb r d 1 suppose that the operator is a pseudodifferential operator of order 2m m in mbox smallbbb r and that the associated bilinear form is symmetric and positive definite the surface may be open or closed and m may be positive or negative let b denote the stiffness matrix arising from a galerkin boundary element method with standard nodal basis functions if local mesh refinement is used then the partition may contain elements of very widely differing sizes and consequently b may be very badly conditioned in fact if the elements are nondegenerate and 2 m d then the ell 2 condition number of b satisfies rm cond mbox bf em b leq c n 2 m d left frac h rm max h rm min right d 2m where hmax and h min are the sizes of the largest and smallest elements in the partition and n is the number of degrees of freedom however if b is preconditioned using a simple diagonal scaling then the condition number is reduced to cal o n 2 m d that is diagonal scaling restores the condition number of the linear system to the same order of growth as that for a uniform partition the growth in the critical case 2 m d is worse by only a logarithmic factor

factor copula models for item response data factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses the factor copula models have interpretations of latent maxima minima in comparison with latent means and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution or multidimensional normal ogive model details on maximum likelihood estimation of parameters for the factor copula model are given as well as analysis of the behavior of the log likelihood our general methodology is illustrated with several item response data sets and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data

geometric solution strategy of laplace problems with free boundary summary this paper introduces a geometric solution strategy for laplace problems our main interest and emphasis is on efficient solution of the inverse problem with a boundary with cauchy condition and with a free boundary this type of problem is known to be sensitive to small errors we start from the standard laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another this results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of laplace s problem interpretation in terms of a geometric flow will provide us with stability considerations the approach is demonstrated with several examples copyright 2015 john wiley sons ltd

nonlinear integral equations for bernoulli s free boundary value problem in three dimensions abstract in this paper we present a numerical solution method for the bernoulli free boundary value problem for the laplace equation in three dimensions we extend a nonlinear integral equation approach for the free boundary reconstruction kress 2016 from the two dimensional to the three dimensional case the idea of the method consists in reformulating bernoulli s problem as a system of boundary integral equations which are nonlinear with respect to the unknown shape of the free boundary and linear with respect to the boundary values the system is linearized simultaneously with respect to both unknowns i e it is solved by newton iterations in each iteration step the linearized system is solved numerically by a spectrally accurate method after expressing the frechet derivatives as a linear combination of single and double layer potentials we obtain a local convergence result on the newton iterations and illustrate the feasibility of the method by numerical examples

some improvements of the fast marching method the fast marching method published by sethian proc natl acad sci usa 93 1996 pp 1591 1595 is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic it has been used in a wide variety of applications such as robotic path planning r kimmel and j sethian fast marching methods for computing distance maps and shortest paths tech report 669 cpam university of california berkeley 1996 crack propagation m stolarska et al modelling crack growth by level sets in the extended finite element method comput methods appl mech engrg to appear internat j numer methods engrg 51 2001 pp 943 960 n sukumar d l chopp and b moran extended finite element method and fast marching method for three dimensional fatigue crack propagation j comput phys submitted seismology j sethian and a popovici geophysics 64 1999 pp 516 523 photolithography j sethian fast marching level set methods for three dimensional photolithography development in proceedings of the spie 1996 international symposium on microlithography santa clara ca 1996 and medical imaging r malladi and j sethian proc natl acad sci usa 93 1996 pp 9389 9392 it has also been a valuable tool for the implementation of modern level set methods where it is used to efficiently compute the distance to the front and or an extended velocity function in this paper we improve upon the second order fast marching method of sethian siam rev 41 1999 pp 199 235 by constructing a second order approximation of the interface generated from local data on the mesh the data is interpolated on a single box of the mesh using a bicubic approximation the distance to the front is then calculated by using a variant of newton s method to solve both the level curve equation and the orthogonality condition for the nearest point to a given node the result is a second order approximation of the distance to the interface which can then be used to produce second order accurate initial conditions for the fast marching method and a third order fast marching method

convexity of solutions and brunn minkowski inequalities for hessian equations in r3 by using minkowski addition of convex functions we prove convexity and rearrangement properties of solutions to some hessian equations in r 3 and brunn minkowski and isoperimetric inequalities for related functionals

a relation between the domain topology and the number of minimal nodal solutions for a quasilinear elliptic problem abstract we consider the quasilinear problem div u p 2 u u p 2 u u q 2 u in u 0 on where r n is a bounded smooth domain 1 p n and p q p np n p we show that if is invariant by a non trivial orthogonal involution then for q close to p the equivariant topology of is related with the number of solutions which change sign exactly once the results complement those of castro and clapp nonlinearity 16 2003 579 590 since we consider subcritical nonlinearities and the quasilinear case without any assumption of symmetry we also extend theorem b in benci and cerami arch rational mech anal 114 1991 79 93 for the quasilinear case and prove that the topology of affects the number of positive solutions

improved trial methods for a class of generalized bernoulli problems the aim of this article is to develop improved trial methods for the solution of a generalized exterior bernoulli free boundary problem at the free boundary we prescribe the neumann boundary condition and update the free boundary with the help of the remaining dirichlet boundary condition appropriate update rules are obtained by expanding the dirichlet data at the actual boundary via a taylor expansion of first and second order the resulting trial methods converge linearly for both cases although the trial method based on the second order taylor expansion is much more robust nevertheless via results of shape sensitivity analysis we are able to modify the update rules such that their convergence is improved the feasibility of the proposed trial methods and their performance is demonstrated by numerical results

stochastic approximation em for large scale exploratory irt factor analysis a stochastic approximation em algorithm saem is described for exploratory factor analysis of dichotomous or ordinal variables the factor structure is obtained from sufficient statistics that are updated during iterations with the robbins monro procedure two large scale simulations are reported that compare accuracy and cpu time of the proposed saem algorithm to the metropolis hasting robbins monro procedure and to a generalized least squares analysis of the polychoric correlation matrix a smaller scale application to real data is also reported including a method for obtaining standard errors of rotated factor loadings a simulation study based on the real data analysis is conducted to study bias and error estimates the saem factor algorithm requires minimal lines of code no derivatives and no large matrix inversion it is programmed entirely in r

velocity extension for the level set method and multiple eigenvalues in shape optimization in the context of structural optimization by the level set method we propose an extension of the velocity of the underlying hamilton jacobi equation the gradient method is endowed with a hilbertian structure based on the h1 sobolev space numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level set method another important application is the optimization of multiple eigenvalues

lord wingersky algorithm version 2 0 for hierarchical item factor models with applications in test scoring scale alignment and model fit testing lord and wingersky s appl psychol meas 8 453 461 1984 recursive algorithm for creating summed score based likelihoods and posteriors has a proven track record in unidimensional item response theory irt applications extending the recursive algorithm to handle multidimensionality is relatively simple especially with fixed quadrature because the recursions can be defined on a grid formed by direct products of quadrature points however the increase in computational burden remains exponential in the number of dimensions making the implementation of the recursive algorithm cumbersome for truly high dimensional models in this paper a dimension reduction method that is specific to the lord wingersky recursions is developed this method can take advantage of the restrictions implied by hierarchical item factor models e g the bifactor model the testlet model or the two tier model such that a version of the lord wingersky recursive algorithm can operate on a dramatically reduced set of quadrature points for instance in a bifactor model the dimension of integration is always equal to 2 regardless of the number of factors the new algorithm not only provides an effective mechanism to produce summed score to irt scaled score translation tables properly adjusted for residual dependence but leads to new applications in test scoring linking and model fit checking as well simulated and empirical examples are used to illustrate the new applications

discrete gradient flows for shape optimization and applications we present a variational framework for shape optimization problems that establishes clear and explicit connections among the continuous formulation its full discretization and the resulting linear algebraic systems our approach hinges on the following essential features shape differential calculus a semi implicit time discretization and a finite element method for space discretization we use shape differential calculus to express variations of bulk and surface energies with respect to domain changes the semi implicit time discretization allows us to track the domain boundary without an explicit parametrization and has the flexibility to choose different descent directions by varying the scalar product used for the computation of normal velocity we propose a schur complement approach to solve the resulting linear systems efficiently we discuss applications of this framework to image segmentation optimal shape design for pde and surface diffusion along with the choice of suitable scalar products in each case we illustrate the method with several numerical experiments some developing pinch off and topological changes in finite time

numerical solution of bernoulli type free boundary value problems by variable domain method the variable domain method for a free surface problem is considered as a weighted residual method this considerably simplifies discretization of the problem and at the same time allows implementation of any standard discretization technique discretization of the problem results in a non linear system of equations for discrete values of a field variable and co ordinates of the nodes on the free boundary variables corresponding to a field variable are eliminated and the resulting non linear system is of considerable smaller size some new update strategies of the jacobian together with discussion of the cost effectiveness and covergence rate are introduced and compared to broyden s method

variational approach to shape derivatives for a class of bernoulli problems the shape derivative of a functional related to a bernoulli problem is derived without using the shape derivative of the state the gradient information is combined with level set ideas in a steepest descent algorithm numerical examples show the feasibility of the approach

on the curvature of free boundaries with a bernoulli type condition abstract in this paper we study the classical external bernoulli problem set in an annular domain of the plane we focus on the curvature of the free boundary outer component of the boundary of our domain and establish a one to one correspondence between positive negative curvature arcs of and of the curve representing the data extending a method put forward by a acker moreover we show that the positive curvature arcs on the free boundary bend less than the corresponding arcs on the inner curve i e the maximum attained by the curvature is greater on than on thus we can draw the following conclusions the geometry of is simpler than that of an already known result the shape of is alleviated with respect to that of

maximum likelihood estimation of multilevel structural equation models with random slopes for latent covariates a maximum likelihood estimation routine for two level structural equation models with random slopes for latent covariates is presented because the likelihood function does not typically have a closed form solution numerical integration over the random effects is required the routine relies upon a method proposed by du toit and cudeck psychometrika 74 1 65 82 2009 for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically reducing the computational burden of high dimensional numerical integration the method is demonstrated and assessed using a small scale simulation study and an empirical example

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

a brunn minkowski inequality for the monge ampere eigenvalue abstract we prove a brunn minkowski type inequality for the eigenvalue of the monge ampere operator 1 2 n is concave in the class of c 2 domains in r n endowed with minkowski addition the equality case is explicitly described too the main device of the proof is a notion of addition for convex functions called infimal convolution which corresponds to the minkowski addition of the graphs of the involved functions

the one phase free boundary problem for the p laplacian with non constant bernoulli boundary condition our objective here is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a bernoulli type boundary gradient condition and with the p laplacian as the governing operator the main theorems of this paper assert that the exterior and the interior free boundary problem with a bernoulli law i e with a prescribed pressure a x on the free streamline of the flow have convex solutions provided the initial domains are convex the continuous function a x is subject to certain convexity properties in our earlier results we have considered the case of constant a x in the lines of the proof of the main results we also prove the semi continuity up to the boundary of the gradient of the p capacitary potentials in convex rings with c 1 boundaries

dealing with reflection invariance in bayesian factor analysis this paper considers the reflection unidentifiability problem in confirmatory factor analysis cfa and the associated implications for bayesian estimation we note a direct analogy between the multimodality in cfa models that is due to all possible column sign changes in the matrix of loadings and the multimodality in finite mixture models that is due to all possible relabelings of the mixture components drawing on this analogy we derive and present a simple approach for dealing with reflection in variance in bayesian factor analysis we recommend fitting bayesian factor analysis models without rotational constraints on the loadings allowing markov chain monte carlo algorithms to explore the full posterior distribution and then using a relabeling algorithm to pick a factor solution that corresponds to one mode we demonstrate our approach on the case of a bifactor model however the relabeling algorithm is straightforward to generalize for handling multimodalities due to sign invariance in the likelihood in other factor analysis models

computational study of fast methods for the eikonal equation a computational study of the fast marching and the fast sweeping methods for the eikonal equation is given it is stressed that both algorithms should be considered as direct as opposed to iterative methods on realistic grids fast sweeping is faster than fast marching for problems with simple geometry for strongly nonuniform problems and or complex geometry the situation may be reversed finally fully second order generalizations of methods of this type for problems with obstacles are proposed and implemented

on the number of solutions of nls equations with magnetics fields in expanding domains abstract in this paper we look for multiple weak solutions u c for the complex equation i a x 2 u u f u 2 u in the set r n is a smooth bounded domain 0 is a parameter a is a regular magnetic field and f is a superlinear function with subcritical growth our main result relates for large values of the number of solutions with the topology of the set in the proof we apply minimax methods and ljusternik schnirelmann theory

a cut finite element method for the bernoulli free boundary value problem we develop a cut finite element method for the bernoulli free boundary problem the free boundary represented by an approximate signed distance function on a fixed background mesh is allowed to i

conformal modulus and its reduction via mean curvatures abstract this note shows that the conformal modulus of a condenser and the reduced conformal modulus of a compact subset in r n 2 are naturally but optimally tied with the corresponding graphic mass and the semi diameter through mean curvatures

existence of classical solutions to a free boundary problem for the p laplace operator i the exterior convex case in this paper we prove under convexity assumptions for the data the existence of classical solutions for a bernoulli type free boundary problem with the p laplacian as the governing operator the method employed here originates from a pioneering work of a beurling where he proves the existence for the harmonic case in the plane though with no geometrical restrictions

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

a person fit test for irt models for polytomous items a person fit test based on the lagrange multiplier test is presented for three item response theory models for polytomous items the generalized partial credit model the sequential model and the graded response model the test can also be used in the framework of multidimensional ability parameters it is shown that the lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account the lagrange multiplier statistic has an asymptotic 2 distribution the type i error rate and power are investigated using simulation studies results show that test statistics that ignore the effects of estimation of the persons ability parameters have decreased type i error rates and power incorporating a correction to account for the effects of the estimation of the persons ability parameters results in acceptable type i error rates and power characteristics incorporating a correction for the estimation of the item parameters has very little additional effect it is investigated to what extent the three models give comparable results both in the simulation studies and in an example using data from the neo personality inventory revised

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

the brunn minkowski inequality for p capacity of convex bodies in this paper we prove the brunn minkowski inequality for the p capacity of convex bodies i e convex compact sets with non empty interior in r n for every p 1 n moreover we prove that the equality holds in such inequality if and only if the involved bodies coincide up to a translation and a dilatation

critical points of solutions to quasilinear elliptic problems abstract we describe the set of critical points points of vanishing gradient associated to solutions of an important class of quasilinear elliptic problems with zero dirichlet condition in planar domains we show that the critical set is made up of finitely many isolated points and finitely many regular analytic jordan curves further we generalize the well known result of makar limanov according to which the solution to the poisson equation u 1 with zero dirichlet condition in a convex domain has a unique critical point

the hadamard variational formula and the minkowski problem for p capacity abstract a hadamard variational formula for p capacity of convex bodies in r n is established when 1 p n the formula is applied to solve the minkowski problem for p capacity which involves a degenerate monge ampere type equation uniqueness for the minkowski problem for p capacity is established when 1 p n and existence and regularity when 1 p 2 these results are non linear extensions of the now classical solution of jerison of the minkowski problem for electrostatic capacity p 2

the brunn minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators abstract we prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a brunn minkowski type inequality on the class of open bounded sets in r n satisfying a uniform exterior sphere condition in particular the result applies to the possibly normalized p laplacian and to the minimal pucci operator the proof is inspired by the approach introduced by colesanti for the principal frequency of the laplacian within the class of convex domains and relies on a generalization of the convex envelope method by alvarez lasry lions we also deal with the existence and log concavity of positive viscosity eigenfunctions

a composite likelihood inference in latent variable models for ordinal longitudinal responses the paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model the model considers time dependent latent variables and item specific random effects to be accountable for the interdependencies of the multivariate ordinal items time dependent latent variables are linked with an autoregressive model simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood model selection criteria developed for composite likelihood estimation are used in the applications furthermore lower order residuals are used as measures of fit for the selected models

a computational framework for the regularization of adjoint analysis in multiscale pde systems this paper examines the regularization opportunities available in the adjoint analysis and optimization of multiscale pde systems regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis typically l2 brackets are used in the definition of the cost functional the adjoint operator and the cost functional gradient if instead we adopt the more general sobolev brackets the various fields involved in the adjoint analysis may be made smoother and therefore easier to resolve numerically the present paper identifies several relationships which illustrate how the different regularization options fit together to form a general framework the regularization strategies proposed are exemplified using a id kuramoto sivashinsky forecasting problem and computational examples are provided which exhibit their utility a multiscale preconditioning algorithm is also proposed that noticeably accelerates convergence of the optimization procedure application of the proposed regularization strategies to more complex optimization problems of physical and engineering relevance is also discussed

numerical solution of the free boundary bernoulli problem using a level set formulation we present a numerical method based on a level set formulation to solve the bernoulli problem the formulation uses time as a parameter of boundary evolution the level set formulation enables to consider nonconnected domains numerical experiments show the efficiency of the method if boundary conditions are handled accurately in particular the case of multiple solutions is treated

hardy spaces of the conjugate beltrami equation we study hardy spaces of solutions to the conjugate beltrami equation with lipschitz coefficient on dini smooth simply connected planar domains in the range of exponents 1 infty we analyse their boundary behaviour and certain density properties of their traces we derive on the way an analog of the fatou theorem for the dirichlet and neumann problems associated with the equation mbox div sigma nabla u 0 with l p boundary data

a computational quasi reversiblility method for cauchy problems for laplace s equation this work concerns the use of the method of quasi reversibility for solving cauchy problems for laplace s equation the paper begins with a derivation of an error estimate for this method using car

some inverse problems around the tokamak tore supra we consider two inverse problems related to the tokamak textsl tore supra through the study of the magnetostatic equation for the poloidal flux the first one deals with the cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary namely the limiter from available overdetermined data on the outer boundary using tools from complex analysis and properties of genereralized hardy spaces we establish stability and existence properties secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization again results about existence and optimality are provided they give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from textsl tore supra

n capacity n harmonic radius and n harmonic transplantation abstract for the n laplacian n on a regular domain the n green s function exists this allows us to define the n robin s function and the n harmonic radius we show their basic properties and extend the method of the harmonic transplantation to that of the n harmonic transplantation the method is used to estimate the first eigenvalue of the n laplacian n we also give another proof of the isoperimetric inequality for the n capacity and give the isoperimetric inequality for the n harmonic radius

on trefftz integral equation for the bernoulli free boundary value problem we propose a new numerical method for the solution of bernoulli s free boundary value problem for a harmonic function w in a doubly connected domain d in mathbb r 2 where an unknown free boundary vargamma 0 is determined by prescribed cauchy data of w on vargamma 0 in addition to a dirichlet condition on the known boundary vargamma 1 our method is based on a two by two system of boundary integral equations for the unknown boundary vargamma 0 and the unknown normal derivative g partial nu w of w on vargamma 1 this system is nonlinear with respect to vargamma 0 and linear with respect to g and we suggest to solve it simultaneously for vargamma 0 and g by newton iterations we establish a local convergence result and exhibit the feasibility of the method by a few numerical examples

multiple minimal nodal solutions for a quasilinear schrodinger equation with symmetric potential abstract we deal with the quasilinear schrodinger equation div u p 2 u a x 1 u p 2 u u q 2 u u w 1 p r n where 2 p n 0 and p q p n p n p the potential a 0 has a potential well and is invariant under an orthogonal involution of r n we apply variational methods to obtain for large existence of solutions which change sign exactly once we study the concentration behavior of these solutions as by taking q close p we also relate the number of solutions which change sign exactly once with the equivariant topology of the set where the potential a vanishes

short note o n implementation of the fast marching algorithm in this note we present an implementation of the fast marching algorithm for solving eikonal equations that in practice reduces the original run time from o nlogn to linear this lower run time cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm this improvement is achieved introducing the straight forward untidy priority queue obtained via a quantization of the priorities in the marching computation we present the underlying framework estimations on the error and examples showing the usefulness of the proposed approach

a boundary mixture approach to violations of conditional independence conditional independence is a fundamental principle in latent variable modeling and item response theory violations of this principle commonly known as local item dependencies are put in a test information perspective and sharp bounds on these violations are defined a modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side in contrast to alternative approaches the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory this has attractive interpretational advantages and may be useful for general test construction purposes

full information item bi factor analysis a plausibles factor solution for many types of psychological and educational tests is one that exhibits a general factor ands 1 group or method related factors the bi factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes 1 group factors this paper derives a bi factor item response model for binary response data in marginal maximum likelihood estimation of item parameters the bi factor restriction leads to a major simplification of likelihood equations and a permits analysis of models with large numbers of group factors b permits conditional dependence within identified subsets of items and c provides more parsimonious factor solutions than an unrestricted full information item factor analysis in some cases

stress concentration for closely located inclusions in nonlinear perfect conductivity problems abstract we study the stress concentration which is the gradient of the solution when two smooth inclusions are closely located in a possibly anisotropic medium r n n 2 the governing equation may be degenerate of p laplace type with 1 p n we prove optimal l estimates for the blow up of the gradient of the solution as the distance between the inclusions tends to zero

boundary element preconditioners for problems defined on slender domains within the framework of two dimensional potential theory we consider problems defined on slender domains the boundary element matrices for such problems are poorly conditioned due to the presence of two disparate length scales a new class of preconditioners is proposed to remedy this problem so that the preconditioned boundary element matrices become insensitive to the domain slenderness the preconditioners are constructed using the spectral properties of the boundary integral operators defined on the elliptical domains

goal oriented error estimation and adaptivity for free boundary problems the domain map linearization approach in free boundary problems the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation we develop duality based a posteriori error estimates for functional outputs of solutions of free boundary problems that include both sources of error the derivation of an appropriate dual problem linearized adjoint is however nonobvious for free boundary problems to derive an appropriate dual problem we present the domain map linearization approach in this approach the free boundary problem is first transformed into an equivalent problem on a fixed reference domain after which the dual problem is obtained by linearization with respect to the domain map we show for a bernoulli type free boundary problem that this dual problem corresponds to a poisson problem with a nonlocal robin type boundary condition furthermore we present numerical experiments that demonstrate the effectivity of the dual based error estimate and its usefulness in goal oriented adaptive mesh refinement

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose

fast numerical methods for bernoulli free boundary problems the numerical solution of the free boundary bernoulli problem is addressed an iterative method based on a level set formulation and boundary element method is proposed issues related to the implementation the accuracy and the generality of the method are discussed the efficiency of the approach is illustrated by numerical results