cloaking via change of variables for the helmholtz equation the transformation optics approach to cloaking uses a singular change of coordinates which blows up a point to the region being cloaked this paper examines a natural regularization obtained by 1 blowing up a ball of radius rather than a point and 2 including a well chosen lossy layer at the inner edge of the cloak we assess the performance of the resulting near cloak as the regularization parameter tends to 0 in the context of dirichlet and neumann boundary measurements for the time harmonic helmholtz equation since the goal is to achieve cloaking regardless of the content of the cloaked region we focus on estimates that are uniform with respect to the physical properties of this region in three space dimensions our regularized construction performs relatively well the deviation from perfect cloaking is of order in two space dimensions it does much worse the deviation is of order 1 log in addition to proving these estimates we give numerical examples demonstrating their sharpness some authors have argued that perfect cloaking can be achieved without losses by using the singular change of variable based construction in our regularized setting the analogous statement is false without the lossy layer there are certain resonant inclusions depending in general on that have a huge effect on the boundary measurements 2010 wiley periodicals inc

on approximate electromagnetic cloaking by transformation media we give a comprehensive study on regularized approximate electromagnetic cloaking in the spherical geometry via the transformation optics approach the following aspects are investigated i near invisibility cloaking of passive media as well as active radiating sources ii the existence of cloak busting inclusions without lossy medium lining iii overcoming the cloaking busts by employing a lossy layer outside the cloaked region and iv the frequency dependence of the cloaking performances we address these issues and connect the obtained asymptotic results to singular ideal cloaking numerical verifications and demonstrations are provided to show the sharpness of our analytical study

nearly cloaking the electromagnetic fields the approximate cloaking is investigated for time harmonic maxwell s equations via the approach of transformation optics the problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an asymptotically small support but an arbitrary content enclosed by a thin high conducting layer sharp estimates are established in terms of the asymptotic parameter which are independent of the material tensors of the small electromagnetic inclusion the result implies that the blow up a small region construction via the transformation optics approach yields a near cloak for the electromagnetic waves a novelty lies in the fact that the geometry of the cloaking construction of this work can be very general moreover by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region arbitrary electromagnetic contents can be nearly cloaked our mathematical technique extends the general one developed in h y

path integral approach to multiple scattering multiple scattering of a wave in a system of scatterers with random uncorrelated positions is studied with path integrals the edwards gulyaev expression for the position averaged green s function is used to find the density expansion of the complex optical potential the expansion is in terms of exact medium propagators and scattering matrices in the medium the first term is the coherent potential approximation a source dependent generalization of the path integral is used to derive a functional equation for the optical potential this leads to a hierarchy for correlation functions that involves exact medium propagators and scattering matrices the simplest truncations yield new integral equations that are generalizations of the coherent potential approximation and are compatible with the density expansion

developing a time domain finite element method for modeling of electromagnetic cylindrical cloaks in this paper we propose a time domain finite element method for modeling of electromagnetic cloaks the permittivity and permeability of the cloak model are described by the drude dispersion model the model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in different regions our method is based on a mixed finite element method using edge elements with different types of meshes in different regions numerical results demonstrate that our algorithm is quite effective for simulating cloaks in time domain to our knowledge this is the first cloak simulation carried out by the time domain finite element method

constructing the exact significance level for a person fit statistic this paper uses an extension of the network algorithm originally introduced by mehta and patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the rasch model by assuming that item difficulties are known the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score a simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less

long time asymptotics of diffusion in random media and related problems for n dimensional diffusion in gaussian random fields with continuous and singular covariances the leading long time behaviour of the averaged population is derived by estimating brownian motion expectations it is shown how these results are related to the leading low energy behaviour of the density of states for a particle in a corresponding random potential and to the strong coupling limit of the free energy of the pekar frolich polaron

well posedness study for a time domain spherical cloaking model in this paper we study a time domain spherical cloaking model recently introduced by zhao and hao 2009 this model is quite complicated and is composed of four coupled differential equations here we first prove the existence and uniqueness of a solution for this model then we obtain a stability result which analysis is quite involved due to the coupling between the four variables to our best knowledge this is the first well posedness study carried out for the time domain cloaking model with metamaterials

partition function of a particle subject to gaussian noise we study the averaged partition function for a quantum particle subjected to gaussian noise using the path integral representation the noise is characterized by a covariance function with a strength and a range it falls off rapidly with distance but the analytic form at short distances and the dimensionality are important the remaining parameter is the thermal length of the particle for a finite range we study the behavior of the partition function over the entire domain of strengths and thermal lengths the techniques used are successively more accurate upper and lower bounds that include contributions from configurations involving traps particular attention is paid to a self consistent field analysis lower bound and to a nonlocal quadratic action bound we also study the white noise limit i e vanishing range with finite values of the other parameters in one dimension the white noise limit leads to convergent results in three or higher dimensions the divergent terms can be isolated and computed in two dimensions the degree of divergences changes at a finite value of the product of the strength and thermal length squared

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

the many null distributions of person fit indices this paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of rasch contrary to the standard analysis of the rasch model where all persons are kept in the analysis and badly fittingitems may be removed this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the rasch model such persons are called anomalous or aberrant from the response vectors consisting ofk symbols each equal to 0 or 1 it is desired to classify each respondent as either anomalous or as conforming to the model as this model is probabilistic such a classification will possibly involve false positives and false negatives both for the rasch model and for other item response models the literature contains several proposals for a person fit index which expresses for each individual the plausibility that his her behavior follows the model the present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model this distribution however turns out to be rather different for different values of the person s latent trait value this value will be called ability parameter although our results are equally valid for rasch scales measuring other attributes

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

numerical design of fshl based approximate cloaks with arbitrary shapes this paper considers numerical design of finite sound hard lining fshl based approximate cloaks with arbitrary shapes regarding the complexity of the shape two new approaches are proposed to design the transformation map from the virtual space to the physical space via transformation optics for star shaped geometry we propose an explicit global transformation map which can be easily differentiated and inverted for more general shapes an initialize untangle extend iue approach is initiated to build locally piecewise differentiable deformations which can be locally inverted with the help of an approximate triangulation with the locally piecewise constructed transformation the parameters of acoustic scattering models in physical space can be determined in both approaches based on the transformation invariance of the helmholtz system then the cloaking effects for an arbitrary shape fshl based cloak can be realized following li et al 2012 5 extensive numerical experiments are presented to illustrate both the effectiveness of cloak design and the efficiency of the proposed fshl based cloaks with arbitrary shapes

the ump exact test and the confidence interval for person parameters in irt models in educational and psychological measurement when short test forms are used the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold as a result hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic inferences based on the exact distribution on the other hand do not suffer from this limitation however the computation involved for the exact distribution approach is often prohibitively expensive in this paper we propose a general framework for constructing hypothesis tests and confidence intervals for irt models within the exponential family based on exact distribution in addition an efficient branch and bound algorithm for calculating the exact p value is introduced the type i error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation we also demonstrate its practical use by analyzing three real data sets

upper bounds for density matrices using path integrals we discuss upper bounds for density matrices for a particle that occur in potential theory and as a result of averaging over other degrees of freedom the weiner path integral representation is used a basic technique of symanzik is generalized in a variety of ways to a series of sharper upper bounds there are distinct ways of applying the technique to the two parameter integrals that describe averaged density matrices a single parameter application of the symanzik technique leads to a temperature dependent potential problem the nature of the bounds is illustrated for two parameter integrals by studying a soluble quadratic action a one dimensional delta correlation function action and shell correlation functions the dependence on dimension is studied in the latter case

electromagnetic inverse problems and generalized sommerfeld potentials in this article we study the inverse boundary value problem for maxwell s equation that is we determine the scalar permeability permissibility and conductivity of a body from electromagnetic field measurements outside the body in this paper the problem is approached by using certain generalized sommerfeld potentials that are shown to satisfy a vector valued schrodinger equation by using these potentials the inverse boundary value problem is reduced to the problem of determining the potential of this second order operator further it is shown that the electromagnetic material parameters can be determined by using electric or magnetic dipole point sources only

optimal and most exact confidence intervals for person parameters in item response theory models the common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter is normally distributed however this approximation is often inadequate for short and medium test lengths as a result the coverage probabilities fall below the given level of significance in many cases and therefore the corresponding intervals are no longer confidence intervals in terms of the actual definition in the present work confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach

unbiased estimators of ability parameters of their variance and of their parallel forms reliability given known item parameters unbiased estimators are derived i for an examinee s ability parameter and for his proportion correct true score ii for the variances of and across examinees in the group tested and iii for the parallel forms reliability of the maximum likelihood estimator hat theta

power divergence family of statistics for person parameters in irt models we generalize the power divergence pd family of statistics to the two parameter logistic irt model for the purpose of constructing hypothesis tests and confidence intervals of the person parameter the well known score test statistic is a special case of the proposed pd family we also prove the proposed pd statistics are asymptotically equivalent and converge in distribution to chi 1 2 in addition a moment matching method is introduced to compare statistics and choose the optimal one within the pd family simulation results suggest that the coverage rate of the associated confidence interval is well controlled even under small sample sizes for some pd statistics compared to some other approaches the associated confidence intervals exhibit smaller lengths while maintaining adequate coverage rates the utilities of the proposed method are demonstrated by analyzing a real data set

exact and best confidence intervals for the ability parameter of the rasch model a commonly used method to evaluate the accuracy of a measurement is to provide a confidence interval that contains the parameter of interest with a given high probability smallest exact confidence intervals for the ability parameter of the rasch model are derived and compared to the traditional asymptotically valid intervals based on the fisher information tables of the exact confidence intervals termed clopper pearson intervals can be routinely drawn up by applying a computer program designed by and obtainable from the author these tables are particularly useful for tests of only moderate lengths where the asymptotic method does not provide valid confidence intervals

an adaptive edge finite element method for electromagnetic cloaking simulation in this paper we develop an adaptive edge finite element method based on a reliable and efficient recovery type a posteriori error estimator for time harmonic maxwell equations the asymptotically exact a posteriori error estimator is based on the superconvergence result proved for the lowest order edge element on triangular grids where most pairs of triangles sharing a common edge form approximate parallelograms the efficiency and robustness of the proposed method is demonstrated by extensive numerical experiments for electromagnetic cloaking problems with highly anisotropic permittivity and permeability

cloaking via change of variables for the helmholtz equation in the whole space this paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics i e a change of variables that blows up a small ball to the cloaked region and a fixed lossy layer for the helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity we establish a degree of near invisibility which is independent of the content inside the cloaked region for this device we also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed 2010 wiley periodicals inc