equality conditions for matrix kantorovich type inequalities abstract following a recent paper of 7 we present sufficient and necessary conditions snecs under which equalities occur in those corresponding matrix kantorovich type inequalities we also present several relevant inequalities

on classification of n 2 supersymmetric theories we find a relation between the spectrum of solitons of massiven 2 quantum field theories ind 2 and the scaling dimensions of chiral fields at the conformal point the condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricn 2 conformal theories and their massive deformations in terms of a suitable generalization of dynkin diagrams which coincides with the a d e dynkin diagrams for minimal models the landau ginzburg theories are a proper subset of this classification in the particular case of lg theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of picard lefschetz theory

a brief biography and appreciation of calyampudi radhakrishna rao with a bibliography of his books and papers we present a brief biography and appreciation of calyampudi radhakrishna rao to whom this fifth special issue on linear algebra and statistics of linear algebra and its applications is dedicated in celebration of his 75th birthday a bibliography of his books and papers is also included

kink manifolds in 1 1 dimensional scalar field theory the general structure of kink manifolds in 1 1 dimensional complex scalar field theory is described by analysing three special models new solitary waves are reported kink energy sum rules arise between different types of solitary waves

generalized mstb models structure and kink varieties abstract in this paper we describe the structure of a class of two component scalar field models in a 1 1 minkowskian space time which generalize the well known montonen sarker trullinger bishop hence mstb model this class includes all the field models whose static field equations are equivalent to the newton equations of two dimensional type i liouville mechanical systems with a discrete set of instability points we offer a systematic procedure to characterize these models and to identify the solitary wave or kink solutions as homoclinic or heteroclinic trajectories in the analogous mechanical system this procedure is applied to a one parametric family of generalized mstb models with a degree eight polynomial as potential energy density

an implicit explicit runge kutta chebyshev scheme for diffusion reaction equations an implicit explicit imex extension of the explicit runge kutta chebyshev rkc scheme designed for parabolic pdes is proposed for diffusion reaction problems with severely stiff reaction terms the imex scheme treats these reaction terms implicitly and diffusion terms explicitly within the setting of linear stability theory the new imex scheme is unconditionally stable for reaction terms having a jacobian matrix with a real spectrum for diffusion terms the stability characteristics remain unchanged a numerical comparison for a stiff nonlinear radiation diffusion problem between an rkc solver an imex rkc solver and the popular implicit bdf solver vodpk using the krylov solver gmres illustrates the excellent performance of the new scheme

several matrix kantorovich type inequalities 1994 217 221 7 h neudecker the hessian matrix for image factor analysis in psychometric methodol ogy r steyer k f wender and k f widaman eds pp 361 365 gustav fischer stuttgart 1993 8 h neudecker w polasek and s liu the heteroskedastic linear regression model andthe hadamard product a note

kink manifolds in a three component scalar field theory in this work we identify the manifold of solitary waves arising in a three component scalar field model using the bogomol nyi arrangement of the energy functional a rich structure of topological and non topological kinks exists in the different sub models contained in the theory

starting algorithms for irk methods in this paper some classes of starting algorithms for the iterations of irk methods are studied they are of three types according to their additional cost by means of b series the order conditions for them are obtained the maximum order attained by these algorithms and their construction are derived too

some further matrix extensions of the cauchy schwarz and kantorovich inequalities with some statistical applications abstract the well known cauchy schwarz and kantorovich inequalities may be expressed in terms of vectors and a positive definite matrix we consider what happens to these inequalities when the vectors are replaced by matrices the positive definite matrix is allowed to be positive semidefinite singular and the usual inequalities are replaced by lowner partial orderings some examples in the context of linear statistical models are presented

the inefficiency of least squares extensions of the kantorovich inequality abstract four different measures of inefficiency of the simple least squares estimator in the general gauss markoff model are considered previous work on the bounds to some of these measures is briefly reviewed and new bounds are obtained for a particular measure

bounds for the trace of the difference of the covariance matrices of the olse and blue in the linear model y x v the inefficiency of the ordinary least squares estimator of x can be measured as the difference of the covariance matrices of the ordinary least squares estimator and the best linear unbiased estimator of x rao 1985 gave an upper bound for the trace of this difference assuming that the covariance matrix v is positive definite in this paper we generalize this result to the situation when v is allowed to be singular

design and implementation of predictors for additive semi implicit runge kutta methods space discretization of some time dependent partial differential equations gives rise to stiff systems of ordinary differential equations in this case implicit methods should be used and therefore in general nonlinear systems must be solved the solutions to these systems are approximated by iterative schemes and in order to obtain an efficient code good initializers should be used recently a parallel code based on some runge kutta and additive runge kutta methods has been constructed focusing especially on additive semi implicit runge kutta asirk methods the aim of the present paper is to develop efficient initializers for these methods

additive semi implicit runge kutta methods for computing high speed nonequilibrium reactive flows this paper is concerned with time stepping numerical methods for computing stiff semi discrete systems of ordinary differential equations for transient hypersonic flows with thermo chemical nonequilibrium the stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite rate thermo chemical processes implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations this paper studies three different semi implicit runge kutta methods for additively split differential equations in the form ofu f u g u wherefis treated by explicit runge kutta methods andgis simultaneously treated by three implicit runge kutta methods a diagonally implicit runge kutta method and two linearized implicit runge kutta methods the coefficients of up to third order accurate additive semi implicit runge kutta methods have been derived such that the methods are both high order accurate and strongly a stable for the implicit terms the results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper

extending some results and proofs for the singular linear model abstract this note gives some new forms and shortened proofs for results on the linear model with singular dispersion matrix

inefficiency and correlation summary various extremal results have been proved concerning the efficiency of least squares estimates relative to gauss markov estimates and concerning the canonical correlations between two sets of random variables in this paper we show how these two types of result are related and derive a new result from which many previous inequalities can be derived some key word8 canonical correlation inefficiency least squares the inequality for the generalized efficiency of least squares estimates relative to best linear unbiased estimates bloomfield watson 1975 knott 1975 has found applications in other areas a consequence was used by venables 1976 in testing for sphericity of a gaussian distribution and by khatri 1978 in proving extremal results for canonical correlations we shall prove a slightly more general result concerning canonical

soliton stability in systems of two real scalar fields in this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime the main motivation being the study of the classical or linear stability of soliton solutions first we present the class of systems and comment on the topological profile of soliton solutions one can find from the first order equations that solve the equations of motion we then follow the standard approach to classical stability to introduce the main steps one needs to obtain the spectra of schrodinger operators that appear in this class of systems we consider a specific system from which we illustrate the general calculations and present some analytical results we also consider another more general system and present an investigation that introduces new results and offers a comparison with former investigations

central schemes for balance laws of relaxation type several models in mathematical physics are described by quasi linear hyperbolic systems with source term and in several cases the production term can become stiff here suitable central numerical schemes for such problems are developed and applications to the broadwell model and extended thermodynamics are presented the numerical methods are a generalization of the nessyahu tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations a second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed numerical tests confirm the accuracy and robustness of the scheme

irk methods for dae starting algorithms abstract when semi explicit differential algebraic equations are solved with implicit runge kutta methods the computational effort is dominated by the cost of solving the nonlinear systems that is why it is important to have good starting values to begin the iterations in this paper we study a type of starting algorithms without additional computational cost in the case of index 1 dae the order of the starting values is defined and by using da series and rooted trees we obtain their general order conditions if the rk satisfies some simplified assumptions then the maximum order can be obtained

new inequalities of the kantorovich type for bounded linear operators in hilbert spaces some new inequalities of the kantorovich type are established they hold for larger classes of operators and subsets of complex numbers than considered before in the literature and provide refinements of the classical results in the case when the involved operator satisfies the usual conditions several new reverse inequalities for the numerical radius of a bounded linear operator are obtained as well

the canonical correlations of a 2 2 block matrix with given eigenvalues abstract let 1 k n 2 and a a 11 a 12 1pt a 21 a 22 be an n n positive definite matrix so that a11 is k k suppose that a has given eigenvalues 1 n 0 the singular values j a11 1 2a12a22 1 2 j 1 k are known as the canonical correlations of the partitioned matrix a and have been extensively studied with regard to the inefficiency of the ordinary least squares method in statistics the object of this paper is to provide proofs of some new inequalities for the canonical correlations in terms of 1 n

application of implicit explicit high order runge kutta methods to discontinuous galerkin schemes despite the popularity of high order explicit runge kutta erk methods for integrating semi discrete systems of equations erk methods suffer from severe stability based time step restrictions for very stiff problems we implement a discontinuous galerkin finite element method dgfem along with recently introduced high order implicit explicit runge kutta imex rk schemes to overcome geometry induced stiffness in fluid flow problems the imex algorithms solve the non stiff portions of the domain using explicit methods and isolate and solve the more expensive stiff portions using an l stable stiffly accurate explicit singly diagonally implicit runge kutta method esdirk furthermore we apply adaptive time step controllers based on the embedded temporal error predictors we demonstrate in a number of numerical test problems that imex methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid induced stiffness

kantorovich and cauchy schwarz inequalities involving positive semidefinite matrices and efficiency comparisons for a singular linear model abstract matrix kantorovich inequalities involving two positive semidefinite matrices are presented corresponding cauchy schwarz inequalities are discussed some of these are used to compare several efficient and inefficient estimators for a singular linear model

nonoscillatory interpolation methods applied to vlasov based models we demonstrate the ability of nonoscillatory interpolation strategies for solving efficiently the transport phase in kinetic systems with applications to charged particle transport in plasmas and semiconductors pointwise weighted essentially nonoscillatory pweno interpolation is applied to obtain semi lagrangian and flux balance methods that together with splitting techniques form the building blocks of our numerical approach these methods do not present the restrictive cfl condition typical of finite difference methods with explicit time solvers and moreover they provide reliable results controlling parasite oscillations from classical polynomial interpolation while giving highly accurate approximations of smooth parts of the solutions we perform and compare these methods in different benchmark problems for vlasov or collisional models for charged particle transport