an all frequency weakly singular surface integral equation for electromagnetism in dielectric media reformulation and well posedness analysis abstract we develop and analyze a surface integral equation sie whose solution pertains to numerical simulations of propagating time harmonic electromagnetic waves in three dimensional dielectric media the formulae to evaluate the far field pattern and propagation of the electric and magnetic fields in the interior and exterior of a dielectric body through surface integrals require the solution of a 2 2 system of weakly singular sies for the two unknown electric and magnetic fields at the interface surface of the dielectric body the sie is governed by an operator that is of the classical identity plus compact form the tangential surface currents and normal surface charges of the dielectric model can be easily computed from the surface electric and magnetic fields a novel feature of that second kind sie is that when augmented with two stabilization scalar equations the corresponding reformulation does not suffer from spurious resonances or low frequency breakdown we analyze this novel feature of the sie in both the sobolev and continuous function space settings without any tangential constraints by proving the uniqueness of the stabilized solution of the sie for all positive incident wave frequencies and physically appropriate real complex dielectric media constants using numerical examples we also demonstrate that without our stabilization constraints the 2 2 second kind sie suffers from some spurious resonances and incorporating the two additional scalar equations removes these spurious resonances at the zero frequency limit the two stabilization scalar equations are automatically satisfied and the 2 2 formulation nicely decouples to a well posed system at the zero frequency limit our analysis to establish the equivalence of the classical dielectric model governed by the maxwell equations and the all frequency sie based representation provides a natural decomposition of the surface unknowns into their tangential currents and normal charges the salient features of the representation and well posedness analysis provide a tool to develop a new class of efficient and high order algorithms with numerical analysis for simulation of the three dimensional dielectric media model from low to high frequencies

a d optimality based sensitivity test sensitivity tests are often used to estimate the parameters associated with latent continuous variables that cannot be measured for example each explosive specimen has a threshold the specimen will detonate if and only if an applied shock exceeds this value since there is no way to determine the threshold of an individual specimens are tested at various levels to determine parameters of the population a new test described here produces efficient estimates of the parameters of the distribution even with limited prior knowledge this test efficiently characterizes the entire distribution and desired percentiles of any population

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

strongly elliptic boundary integral equations for electromagnetic transmission problems we study a boundary integral equation method for transmission problems for strongly elliptic differential operators which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with galerkin s procedure the method is shown to work for the vector helmholtz equation in 3 with electromagnetic transmission conditions we propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over h 1 we analyse the boundary integral equations using the calculus of pseudodifferential operators here the concept of the principal symbol is used to derive existence and regularity results for the solution

permanents of doubly stochastic trees abstract for a tree t of order n let t x n x a t i n where n denotes the set of all doubly stochastic matrices of order n and a t denotes the adjacency matrix of t and let t denote the minimum permanent of matrices in t let p n denote the path of length n 1 and k 1 n 1 the complete bipartite graph on 1 n 1 vertices in this paper it is shown that p n and k 1 n 1 are the only trees with minimal and maximal values respectively among all trees of order n

a note on the existence of maximum likelihood estimates in linear regression models using interval censored data summary for a class of linear regression models with interval censored data including the exponential regression model as a special case a necessary and sufficient condition is given for the existence of the maximum likelihood estimator mle the condition is especially simple to check for simple linear regression this result is useful for comparing the small sample properties of mles from different special cases of interval censored data

discrete boundary finite element schemes for an exterior problem for the time harmonic maxwell s equation abstract a general boundary integral formulation using galerkin procedure is applied to compute the scattering electric field produced by the diffraction of an incident electromagnetic wave by a perfectly conducting obstacle this electric field satisfies the three dimensional time harmonic maxwell s equations for which the skin currents and charges are to be approximated using boundary finite element method with the help of linear and quadratic finite elements of lagrange type we introduce an approximate surface on which the discrete formulation is defined and construct approximate surface currents and charges in addition we study the existence and the uniqueness of the solution of the discrete problem and develop some error estimates for the currents and charges numerical results are also presented in order to validate our numerical approach

on the influence of the geometry on skin effect in electromagnetism we consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large assuming smoothness for the dielectric conductor interface relying on recent works we prove that the solution of the maxwell equations admits a multiscale asymptotic expansion with profile terms rapidly decaying inside the conductor this skin effect is measured by introducing a skin depth function that turns out to depend on the mean curvature of the boundary of the conductor we then confirm these asymptotic results by numerical experiments in various axisymmetric configurations we also investigate numerically the case of a nonsmooth interface namely a cylindrical conductor

integral equation procedures for eddy current problems abstract two methods are presented for the solution of a class of two dimensional eddy current problems the specific problem considered is that of a wire carrying a periodic current parallel to a uniform conducting cylinder both methods yield integral equations over the boundary of the conductor the first method is exact while the second is an asymptotic procedure valid for a certain parameter range and reflecting the skin effect numerical implementation procedures are given for both methods and some numerical results are presented

dose finding using the biased coin up and down design and isotonic regression we are interested in finding a dose that has a prespecified toxicity rate in the target population in this article we investigate five estimators of the target dose to be used with the up and down biased coin design bcd introduced by durham and flournoy 1994 statistical decision theory and related topics these estimators are derived using maximum likelihood weighted least squares sample averages and isotonic regression a linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied

algebraic connectivity and doubly stochastic tree matrices abstract in this paper we investigate the relations between the smallest entry of a doubly stochastic tree matrix associated with a tree and the diameter of the tree which are used to deal with merris s conjecture on the algebraic connectivity and the smallest entries further we present a new upper bound for algebraic connectivity in terms of the smallest entry which improves merris result

solution procedures for three dimensional eddy current problems abstract the problem under consideration is that of the scattering of time periodic electromagnetic fields by metallic obstacles a common approximation here is that in which the metal is assumed to have infinite conductivity the resulting problem called the perfect conductor problem involves solving maxwell s equations in the region exterior to the obstacle with the tangential component of the electric field zero on the obstacle surface in the interface problem different sets of maxwell equations must be solved in the obstacle and outside while the tangential components of both electric and magnetic fields are continuous across the obstacle surface solution procedures for this problem are given there is an exact integral equation procedure for the interface problem and an asymptotic procedure for large conductivity both are based on a new integral equation procedure for the perfect conductor problem the asymptotic procedure gives an approximate solution by solving a sequence of problems analogous to the one for perfect conductors

probits of mixtures the tolerances of individuals insects parasites in a population have a frequency or probability distribution called a tolerance distribution many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions a probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions in this article the existence and determination of the maximum likelihood estimates are investigated an expectation maximization em algorithm for probits of mixtures is developed and it is shown that by application of the em algorithm the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

fastest mixing reversible markov chains on graphs with degree proportional stationary distributions in this technical note we study two semi definite programming sdp methods of assigning transition probabilities to a markov chain in order to optimize its mixing rate in the first sdp formulation there is a single transition probability parameter to be optimized the holding probability of vertices which leads to easier and faster computation as opposed to the more general reversible markov chain formulation corresponding to a stationary distribution that is proportional to the degree of vertices by deriving exact analytical results it is shown that both the single parameter and the degree proportional reversible fmmc formulations tend to yield better results than the symmetric sdp formulation for some well known graphs

boundary integral equations for magnetic screens in ℝ 3 on developpe une methode d integrale limite pour la diffusion d ondes electromagnetiques sur des objets minces le probleme aux limites exterieur pour l equation de helmholtz vectorielle avec donnees de neumann sur un morceau de surface ouvert est converti en un systeme d equations integrales pour les sauts de la composante tangentielle du champ et sa divergence a travers l ecran une legere modification des donnees de cauchy donne un systeme fortement elliptique d equations pseudodifferentielles sur s

spanning tree invariants loop systems and doubly stochastic matrices abstract the spanning tree invariant of lind and tuncel 12 is observed in the context of loop systems of markov chains for n 1 2 3 the spanning tree invariants of the loop systems of a markov chain determined by an irreducible stochastic n n matrix p coincide if and only if p is doubly stochastic and in this case the common value of the spanning tree invariants of the loop systems is n

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

inequalities for the spectra of symmetric doubly stochastic matrices we prove majorization relations for symmetric doubly stochastic matrices whose nonzero off diagonal entries lie in an edge transitive graph these results are then used to solve the fastest mixing markov chain problem on edge transitive graphs

gram matrices of reproducing kernel hilbert spaces over graphs in this paper we introduce the notion of reproducing kernel hilbert spaces for graphs and the gram matrices associated with them our aim is to investigate the gram matrices of reproducing kernel hilbert spaces we provide several bounds on the entries of the gram matrices of reproducing kernel hilbert spaces and characterize the graphs which attain our bounds

tridiagonal doubly stochastic matrices abstract we study the facial structure of the polytope t n in r n n consisting of the tridiagonal doubly stochastic matrices of order n we also discuss some subclasses of t n with focus on spectral properties and rank formulas finally we discuss a connection to majorization

existence of maximum likelihood estimates in regression models for grouped and ungrouped data summary in general concavity of the log likelihood alone does not imply that the mle exists always for a class of linear regression models for grouped and ungrouped data a necessary and sufficient condition is obtained for the existence of the maximum likelihood estimator this condition has an intuitively simple interpretation further it turns out that there are similar necessary and sufficient conditions for the existence of maximum likelihood estimates for a number of other non linear models such as cox s regression model for a given set of data these conditions may be verified by linear programming methods

a note on doubly stochastic graph matrices abstract a sharp lower bound for the smallest entries among those corresponding to edges of doubly stochastic matrices of trees is obtained and the trees that attain this bound are characterized this result is used to provide a negative answer to merris question in r merris doubly stochastic graph matrices ii linear multilin algebra 45 1998 275 285

uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism in this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains with a special emphasis for the case when the ratio between these coefficients is large in the most part of the work the interface between the two subdomains is supposed to be lipschitz we first study a scalar transmission problem which is handled through a converging asymptotic series then we derive uniform a priori estimates for maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material the technique is based on an appropriate decomposition of the electric field whose gradient part is estimated thanks to the first part as an application we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity

the inverse eigenvalue problem for symmetric doubly stochastic matrices abstract for a positive integer n and for a real number s let ns denote the set of all n n real matrices whose rows and columns have sum s in this note by an explicit constructive method we prove the following i given any real n tuple 1 2 n t there exists a symmetric matrix in n 1 whose spectrum is ii for a real n tuple 1 2 n t with 1 2 n if 1 n 2 n n 1 3 n n 2 n 2 1 0 then there exists a symmetric doubly stochastic matrix whose spectrum is the second assertion enables us to show that for any 2 n 1 n 1 1 there is a symmetric doubly stochastic matrix whose spectrum is 1 2 n t and also that any number 1 1 is an eigenvalue of a symmetric positive doubly stochastic matrix of any order

a random walk rule for phase i clinical trials we describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose response study or phase i clinical trial patients are sequentially assigned the next higher same or next lower dose level according to some probability distribution which may be determined by ethical considerations as well as the patient s response it is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest estimation of the quantile is discussed the maximum likelihood estimator and its variance are derived under a two parameter logistic distribution and the maximum likelihood estimator is compared with other nonparametric estimators random walk rules have clear advantages they are simple to implement and finite and asymptotic distribution theory is completely worked out for a specific random walk rule we compute finite and asymptotic properties and give examples of its use in planning studies having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design the small sample properties of our rule as determined by exact theory compare favorably to those of the continual reassessment method determined by simulation

a note on maximum likelihood estimation for regression models using grouped data summary the estimation of parameters for a class of regression models using grouped or censored data is considered it is shown that with a simple reparameterization some commonly used distributions such as the normal and extreme value result in a log likelihood which is concave with respect to the transformed parameters apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data two simple examples are given

adaptive multilevel bem for acoustic scattering we study the h and p versions of the galerkin boundary element method for integral equations of the first kind in 2d and 3d which result from the scattering of time harmonic acoustic waves at hard or soft scatterers we derive an abstract a posteriori error estimate for indefinite problems which is based on stable multilevel decompositions of our test and trial spaces the galerkin error is estimated by easily computable local error indicators and an adaptive algorithm for h or p adaptivity is formulated the theoretical results are illustrated by numerical examples for hard and soft scatterers in 2d and 3d