on the spreading of characteristics for non convex conservation laws we study the spreading of characteristics for a class of one dimensional scalar conservation laws for which the ux function has one point of in ection it is well known that in the convex case the characteristic speed satises a one sided lipschitz estimate using dafermos theory of generalized characteristics we show that the characteristic speed in the non convex case satises an holder estimate in addition we give a one sided lipschitz estimate with an error term given by the decrease of the total variation of the solution

a regularity theorem for a nonconvex scalar conservation law abstract in this paper we study the regularity properties of solutions of a single conservation law we prove that if the flux function f is smooth and totally nonlinear in the sense that f vanishes at isolated points only and if the initial data u0 are bounded and measurable then f u t is in the class of functions of locally bounded variation for all t 0

diagonal preconditioners for the efie using a wavelet basis the electric field integral equation efie has found widespread use and in practice has been accepted as a stable method however mathematically the solution of the efie is an ill posed problem in practical terms as one uses more and more expansion and testing functions per wavelength the condition number of the resulting moment method matrix increases without bound this means that for high sampling densities iterative methods such as conjugate gradients converge more slowly however there is a way to change all this the efie is considered using a wavelet basis for expansion and for testing functions then the resulting matrix is multiplied on both sides by a diagonal matrix this results in a well conditioned matrix which behaves much like the matrix for the magnetic field integral equation mfie consequences for the stability and convergence rate of iterative methods are described

optimal results on tv bounds for scalar conservation laws with discontinuous flux abstract this paper is concerned with the total variation of the solution of scalar conservation law with discontinuous flux in one space dimension one of the main unsettled questions concerning conservation law with discontinuous flux was the boundedness of the total variation of the solution near interface in 1 it has been shown by a counter example at t 1 that the total variation of the solution blows up near interface but in that example the solution become of bounded variation after time t 1 so the natural question is what happens to the bv ness of the solution for large time here we give a complete picture of the bounded variation of the solution for all time for a uniform convex flux with only l data we obtain a natural smoothing effect in bv for all time t t 0 also we give a counter example even for a bv data to show that the assumptions which have been made are optimal

regularity and large time behaviour of solutions of a conservation law without convexity a l aide de la methode des caracteristiques generalisees on etudie la regularite et le comportement a grand des solutions faibles admissibles d une seule loi de conservation a 1 variable d espace avec un point d inflexion

on the maximal smoothing effect for multidimensional scalar conservation laws abstract in 1994 lions perthame and tadmor conjectured an optimal smoothing effect for entropy solutions of multidimensional scalar conservation laws this effect estimated in fractional sobolev spaces is linked to the flux nonlinearity we use a new definition of a nonlinear smooth flux in order to show that the conjectured smoothing effect cannot be exceeded first one dimensional solutions are considered in fractional b v spaces then the multidimensional case is handled with a monophase solution

smoothing effect in bvφ for entropy solutions of scalar conservation laws abstract this paper deals with a sharp smoothing effect for entropy solutions of one dimensional scalar conservation laws with a degenerate convex flux we briefly explain why degenerate fluxes are related with the optimal smoothing effect conjectured by lions perthame tadmor for entropy solutions of multidimensional conservation laws it turns out that generalized spaces of bounded variation b v are particularly suitable better than sobolev spaces to quantify the regularizing effect and to obtain traces as in bv the function in question is linked to the degeneracy of the flux up to the present the lax ole nik formula has provided optimal results for a uniformly convex flux this formula is validated in this paper for the more general class of c 1 strictly convex fluxes which contains degenerate convex fluxes and enables the b v smoothing effect in this class we give a complete proof that for a c 1 strictly convex flux the lax ole nik formula provides the unique entropy solution namely the kruzhkov solution

block size optimization of cbfm for scattering problems the characteristic basis function method cbfm was developed as an algorithm to accelerate the analysis based on direct matrix solver in cbfm the optimum block size greatly influences the overall analysis time in this paper we propose a guideline for setting the optimal block size that can be applied to every algorithm based on cbfm rough estimation of the optimal block size is l b rough approx 0 05 n 6 29 and the exact optimal block size can be determined through preprocessing based on rough estimation numerical results of electromagnetic scattering problems are shown to demonstrate the performance of the proposed method

spectral properties of the efie mom matrix for dense meshes with different types of bases the relationship between the properties of the basis functions employed to discretize the electric field integral equation efie and the eigenvalue spectrum of the resulting method of moments mom matrix is studied we concentrate on dense meshes i e on complex geometries with large number of unknowns per wavelength and or disparate mesh cells sizes and or low frequency these are typical occurrences in antennas packaging and microwave circuits we show that if the basis functions have separated fourier spectra the diagonal mom matrix entries are close to the eigenvalues and explain it in terms of the fourier spectrum of the green s function for such a basis diagonal preconditioning drastically reduces the condition number this does not happen with sub domain basis functions like the rao wilton glisson rwg or with their linear combination into loop tree or loop star bases that are employed to solve low frequency problems finally we analyze the properties of a multiresolution mr basis formed by linear combinations of rwg but whose functions possess some degree of fourier spectral resolution we show that there is still correspondence between matrix diagonal green s function fourier spectrum and matrix eigenvalues diagonal preconditioning of the mr mom matrix causes the eigenvalues to cluster around 1 as it happens with the mom matrix for the magnetic field integral equation this strongly impacts on the efie matrix condition number and the speed of convergence of iterative solvers

quickest detection of parameter changes in stochastic regression nonparametric cusum we consider the problem of detecting abrupt parameter changes in a stochastic regression with unknown noise distribution the process changes at some unknown point of time under general conditions on the regression function and unknown distributions of observations before and after the disruption the paper develops a nonparametric cumulative sum procedure cusum unlike likelihood based cusum algorithms constructed mostly on log likelihood ratio statistics we use a special system of basic statistics in page s procedure by applying a sequential sampling scheme which measures time in terms of accumulated kullback leibler k l divergence we come to a system of statistics with the martingale properties close to those of the log likelihood ratios the proposed approach suggests also an alternative performance criterion in the analysis of the procedure by replacing the expected detection delay by the corresponding k l divergence we show that under the false alarm probability constraint the nonparametric cusum rule is optimal in the sense that it ensures the logarithmic asymptotic for the detection delay

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

structure of entropy solutions for multi dimensional scalar conservation laws an entropy solution u of a multi dimensional scalar conservation law is not necessarily in bv even if the conservation law is genuinely nonlinear we show that u nevertheless has the structure of a bv function in the sense that the shock location is codimension one rectifiable this result highlights the regularizing effect of genuine nonlinearity in a qualitative way it is based on the locally finite rate of entropy dissipation the proof relies on the geometric classification of blow ups in the framework of the kinetic formulation

eigenvalues of the moment method matrix and their effect on the convergence of the conjugate gradient algorithm em scattering a theory that relates eigenvalues of a continuous operator to those of the moment method matrix operator is discussed and confirmed by examples this theory suggests reasons for ill conditioning when certain types of basis and testing functions are used in addition the effect of eigenvalue location on the convergence of the conjugate gradient cg method is studied the convergence rate of the cg method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors of the iteration matrix needed to represent the right side of the equation these findings explain the previously reported convergence behavior of the cg method when applied to electromagnetic scattering problems

existence and nonexistence of tv bounds for scalar conservation laws with discontinuous flux for the scalar conservation laws with discontinuous flux an infinite family of a b interface entropies are introduced and each one of them is shown to form an l1 contraction semigroup see 2 one of the main unsettled questions concerning conservation law with discontinuous flux is boundedness of total variation of the solution away from the interface boundedness of total variation of the solution has been proved in a recent paper 6 in this paper we discuss this particular issue in detail and produce a counterexample to show that the solution in general has unbounded total variation near the interface in fact this example illustrates that smallness of the bv norm of the initial data is immaterial we hereby settle the question of determining for which of the aforementioned a b pairs the solution will have bounded total variation in the case of strictly convex fluxes 2010 wiley periodicals inc

regularization of the moment matrix solution by a nonquadratic conjugate gradient method inspired by tikhonov regularization a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation the procedure is based on a nonquadratic conjugate gradient algorithm with exact line search restart and rescale applied to the problem of tm scattering by perfectly conducting rectangular cylinders the method is shown to exhibit a fast convergence rate

efie modeling of high definition multiscale structures we propose a method to significantly improve the spectral properties of the efie mom matrix for broad band analysis of structures with fine details non uniform meshes and large overall sizes a multilevel approach allows to overlay fine meshes and quasi nyquist sampled meshes the fine mesh conditioning is solved via hierarchical basis functions and the quasi nyquist sampled part is treated by an algebraic incomplete lu preconditioner numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten twenty wavelengths and levels of detail from very moderate to extending over the whole structure

nonparametric estimation of the slope of a truncated regression a nonparametric estimate b is presented for the slope of a regression line y 83ox v subject to the truncation y c yo this model is relevant to a cosmological controversy which concerns hubble s law in astronomy the estimate 3 corresponds to the zero crossing of a random function s 3 which for each 8 is a mann whitney type of statistic designed to measure heterogeneity among the calculated residuals y 3x the asymptotic distribution of p is derived making extensive use of u statistics to show that sn 3o is asymptotically normal and then showing that s 3 behaves like sn 3o plus a deterministic term which is locally linear results on asymptotic efficiency are compared with finite sample size results by simulation

validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws nonlinear geometric optics with various frequencies for entropy so lutions only in l 1 of multidimensional scalar conservation laws is analyzed a new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling compactness homogenization and l 1 stability new multidimensional features are recognized especially including nonlinear propagations of oscillations with high frequencies the validity of nonlinear geometric optics for entropy solutions in l 1 of multidimensional scalar con servation laws is justified

a nonparametric control chart for detecting small disorders we consider sequential observation of independent random variables x 1 cdots x n whose distribution changes from f to g after the first lbrack n theta rbrack variables the object is to detect the unknown change point quickly without too many false alarms a nonparametric control chart based on partial weighted sums of sequential ranks is proposed it is shown that if the change from f to g is small then as n rightarrow infty the appropriately scaled and linearly interpolated graph of partial rank sums converges to a brownian motion on which a drift sets in at time theta using this the asymptotic performance of the one sided control chart is compared with one based on partial sums of the x s location change scale change and contamination are considered it is found that for distributions with heavy tails the control chart based on ranks stops more frequently and faster than the one based on the x s performance of the two procedures are also tested on simulated data and the outcomes are compatible with the theoretical results

initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws we consider initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws through the scalar case the entropy solutions we address assume their initial data only in the sense of weak star in l as t 0 and satisfy the entropy inequality in the sense of distributions for t 0 we prove that if the flux function has weakly genuine nonlinearity then the entropy solutions are always unique and the initial layers do not appear we also discuss applications to the zero relaxation limit for hyperbolic systems of conservation laws with relaxation

convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems an iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems in an attempt to characterize the typical rate of convergence of that method it is found that this rate depends on the cell density per wavelength used in the discretization the presence of symmetries in the solution and the degree to which mixed cell sizes are used in the models assuming cell densities used in the discretization are in the range of ten per linear wavelength the iterative algorithm typically requires n 4 to n 2 steps to converge to necessary accuracy where n is the order of the matrix under consideration

on strong uniform consistency of the lynden bell estimator for truncated data in this paper we prove that the lynden bell estimator of a distribution function in the random truncation model is uniformly strong consistent over the whole half line a problem left open by woodroofe

explicit hopf lax type formulas for hamilton jacobi equations and conservation laws with discontinuous coefficients we deal with a hamilton jacobi equation with a hamiltonian that is discontinuous in the space variable this is closely related to a conservation law with discontinuous flux recently an entropy framework for single conservation laws with discontinuous flux has been developed which is based on the existence of infinitely many stable semigroups of entropy solutions based on an interface connection in this paper we characterize these infinite classes of solutions in terms of explicit hopf lax type formulas which are obtained from the viscosity solutions of the corresponding hamilton jacobi equation with discontinuous hamiltonian this also allows us to extend the framework of infinitely many classes of solutions to the hamilton jacobi equation and obtain an alternative representation of the entropy solutions for the conservation law we have considered the case where both the hamiltonians are convex concave furthermore we also deal with the less explored case of sign changing coefficients in which one of the hamiltonians is convex and the other concave in fact in convex concave case we cannot expect always an existence of a solution satisfying rankine hugoniot condition across the interface therefore the concept of generalised rankine hugoniot condition is introduced and prove existence and uniqueness

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

erratum to existence and strong pre compactness properties for entropy solutions of a first order quasilinear equation with discontinuous flux sequences of entropy solutions of a non degenerate first order quasilinear equation are shown to be strongly pre compact in the general case of a caratheodory flux vector existence of the weak and entropy solution to the cauchy problem for such an evolutionary equation is also established the proofs are based on the general localization principle for h measures corresponding to sequences of measure valued functions

an efficient sequential nonparametric scheme for detecting a change of distribution ble and remarkably efficient the method is based on the sequential vectors of signs and ranks of the observations the methodology is one of likelihood ratio a sequence of likelihood ratios for these vectors is computed and the shiryayev roberts approach to changepoint detection is then applied to yield a class of statistics and associated stopping rules inequalities and asymptotic approximations for the operating characteristics of these rules are developed these are found to be valid also for small average run lengths and early changepoints as well the relative efficiency of these schemes with respect to a normal parametric shift detection policy is very high making them a robust alternative to parametric methof s