splitting comodules over hopf algebras and application to representation theory of quantum groups of type a0 0 abstract in this work we study some properties of comodules over hopf algebras possessing integrals co frobenius hopf algebras in particular we give a necessary and sufficient condition for a simple comodule to be injective we apply the result obtained to the classification of representations of quantum groups of type a 0 0

co frobenius coalgebras abstract we investigate left and right co frobenius coalgebras and give equivalent characterizations which prove statements dual to the characterizations of frobenius algebras we prove that a coalgebra is left and right co frobenius if and only if c rat c c as right c modules and also that this is equivalent to the fact that the functors hom k k and hom c c from m c to m c are isomorphic this allows a definition of a left right symmetric concept of co frobenius coalgebras that is perfectly dual to the one of frobenius algebras and coincides to the existing notion left and right co frobenius coalgebra

solutions and perturbation estimates for the matrix equation xs a x ta q abstract in this paper the nonlinear matrix equation x s a x t a q is investigated necessary conditions and sufficient conditions for the existence of hermitian positive definite solutions are derived an effective iterative method to obtain the special solution x l we proved that if there is a maximal hermitian positive definite solution then it must be x l is established moreover some new perturbation estimates for x l are obtained several numerical examples are given to illustrate the effectiveness of the algorithm and the perturbation estimates

newton s method for solving a class of nonlinear matrix equations in this paper a class of nonlinear matrix equations x q a h i x c 1a is considered an equivalent form of this equation is derived and the properties of the solutions are studied then newton s iterative method is applied to solve this equivalent one finally two numerical examples are given to illustrate the efficiency of newton s method

on the dimension of the space of integrals on coalgebras abstract we study the injective envelopes of the simple right c comodules and their duals where c is a coalgebra this is used to give a short proof and to extend a result of iovanov on the dimension of the space of integrals on coalgebras we show that if c is right co frobenius then the dimension of the space of left m integrals on c is dim m for any left c comodule m of finite support and the dimension of the space of right n integrals on c is dim n for any right c comodule n of finite support some examples of integrals are computed for incidence coalgebras

a fast near to far field transformation in body of revolution finite difference time domain method we present an efficient near to far field transformation technique to be used in conjunction with the body of revolution finite difference time domain bor fdtd algorithm the efficiency is gained by factoring out the azimuthal angle spl phi from the two dimensional 2d far field integration using an analytical approach thereby reducing the 2d integral on the surface of the huygens box to a 1d version in the process to illustrate the application of the proposed algorithm the potter horn is analyzed the numerical results show good agreement with those obtained by using either analytical where possible or 2d integration schemes

perturbation analysis of the matrix equation x a x pa q abstract consider the nonlinear matrix equation x a x p a q with 0 p 1 this paper shows that there exists a unique positive definite solution to the equation a perturbation bound and the backward error of an approximate solution to this solution is evaluated we also obtain explicit expressions of the condition number for the unique positive definite solution the theoretical results are illustrated by numerical examples

improved perturbation estimates for the matrix equations x a x 1a q abstract we give new and improved perturbation estimates for the solution of the matrix quadratic equations x a x 1 a q some of the estimates depend and some do not depend on knowledge of the exact solution x these bounds are compared numerically against other known bounds from the literature

finiteness conditions co frobenius hopf algebras and quantum groups abstract some finiteness conditions for infinite dimensional coalgebras particularly right or left semiperfect coalgebras or co frobenius hopf algebras are studied as well examples of co frobenius hopf algebras are constructed via a hopf algebra structure on an ore extension of a group algebra and it is shown that bicrossproducts of co frobenius hopf algebras are themselves co frobenius

on two conjectures of faith abstract we prove that a profinite algebra whose left right cyclic modules are torsionless is finite dimensional and qf we give a relative version of the notion of left right pf ring for pseudocompact algebras and prove it is left right symmetric and dual to the notion of quasi co frobenius coalgebras we also prove two ring theoretic conjectures of faith in the setting and supplementary hypothesis of profinite algebras any profinite semiartinian selfinjective algebra is finite dimensional and qf and any fgf profinite algebra is finite dimensional qf

on positive definite solutions of the nonlinear matrix equations x a x q a q in this paper we investigate the nonlinear matrix equations x a x q a q 0 q 1 and x a x q a q q 1 necessary and sufficient conditions for the unique existence of hermitian positive definite solutions of these equations are derived effective iterative algorithms are also provided to obtain the unique solution of x a x q a q 0 q 1 and the minimal and maximal hermitian positive definite solutions of x a x q a q q 1 numerical examples are included to illustrate the efficiency of the presented iteration algorithms

on the solution of a class of large body problems with full or partial circular symmetry by using the finite difference time domain fdtd method this paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry the method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem it does so by dividing the problem into two parts a larger 3 d region with circular symmetry and a smaller 2 d region without circular symmetry an finite difference time domain fdtd algorithm is used to analyze the circularly symmetric 3 d case while a method of moments mom code is employed for the nonsymmetric part of the structure the results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system the advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2 d as opposed to a full 3 d fdtd simulation in addition to enhancing computational efficiency the fdtd algorithm used in this paper also features one improvement over conventional fdtd methods a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces the accuracy of the method is validated via a comparison of simulated and measured results

on two perturbation estimates of the extreme solutions to the equations x a x 1a q abstract two perturbation estimates for maximal positive definite solutions of equations x a x 1 a q and x a x 1 a q are considered these estimates are proved in hasanov et al improved perturbation estimates for the matrix equations x a x 1 a q linear algebra appl 379 2004 113 135 we derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations the theoretical results are illustrated by numerical examples

hermitian solutions of the equation x q nx 1n we consider the matrix equation x q nx 1n its hermitian solutions are parametrized in terms of the generalized lagrangian eigenspaces of a certain matrix pencil we show that the equation admits both a largest and a smallest solution the largest solution corresponds to the unique positive definite solution the smallest solution is the unique negative definite solution if and only if n is nonsingular if n is singular no negative definite solution exists an interesting relation between the given equation and a standard algebraic riccati equation of kalman filtering theory is also obtained finally we present an algorithm which converges to the positive definite solution for a wide range of initial conditions

solutions and perturbation analysis for the nonlinear matrix equation x i 1mai x 1ai i abstract in this paper we study the nonlinear matrix equation x i 1 m a i x 1 a i i arising in some physical calculations some new necessary and sufficient conditions for the existence of positive definite solutions are given based on the matrix differentiation a precise perturbation bound for the maximal positive definite solution is derived and the new result is illustrated by a numerical example in the end

co frobenius hopf algebras integrals doi koppinen modules and injective objects abstract we investigate hopf algebras with non zero integral from a coalgebraic point of view categories of doi koppinen modules are studied in the special case where the defining coalgebra is left and right semiperfect and several pairs of adjoint functors are constructed as applications we give a very short proof for the uniqueness of the integrals and provide information about injective objects in the category of doi koppinen modules

iterative solution of two matrix equations we study iterative methods for finding the maximal hermitian positive definite solutions of the matrix equations x a x 1 a q and x a x 1 a q where q is hermitian positive definite general convergence results are given for the basic fixed point iteration for both equations newton s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation numerical results are reported to illustrate the convergence behaviour of various algorithms

improved methods and starting values to solve the matrix equations x a x 1a i iteratively the two matrix iterations x k 1 i a x 1 k a are known to converge linearly to a positive definite solution of the matrix equations x a x 1 a i respectively for known choices of x 0 and under certain restrictions on a the convergence for previously suggested starting matrices x 0 is generally very slow this paper explores different initial choices of x 0 in both iterations that depend on the extreme singular values of a and lead to much more rapid convergence further the paper offers a new algorithm for solving the minus sign equation and explores mixed algorithms that use newton s method in part

frobenius structural matrix algebras abstract we discuss when the incidence coalgebra of a locally finite preordered set is right co frobenius as a consequence we obtain that a structural matrix algebra over a field k is frobenius if and only if it consists up to a permutation of rows and columns of diagonal blocks which are full matrix algebras over k

notes on two perturbation estimates of the extreme solutions to the equations x a x 1 a q two perturbation estimates of the maximal positive definite solutions to the matrix equations x a x 1a q and x a x 1a q are considered these estimates are like to the estimates discussed by hasanov and ivanov 8 the conditions x l 1a 2 1 and x 1a 2 1 in 8 are not always satisfied we replace this conditions by px l 1ap 1 2 1 and px 1ap email protected 2 1 respective where p is positive definite matrix the theoretical results are illustrated by numerical examples

necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation x a x 1a q abstract we consider the problem of when the matrix equation x a x 1 a q has a positive definite solution here q is positive definite we study both the real and the complex case this equation plays a crucial role in solving a special case of the discrete time riccati equation we present both necessary and sufficient conditions for its solvability this result is obtained by using an analytic factorization approach moreover we present algebraic recursive algorithms to compute the largest and smallest the solution of the equation respectively finally we discuss the number of solutions

perturbation analysis of the maximal solution of the matrix equation x a x 1a p consider the nonlinear matrix equation x a x 1 a p where a p are n x n complex matrices with p hermitian positive definite and a denotes the conjugate transpose of a matrix a in this pape

co frobenius hopf algebras and the coradical filtration we prove that a hopf algebra with a finite coradical filtration is co frobenius we also characterize co frobenius hopf algebras with coradical a hopf subalgebra let h be a hopf algebra whose coradical is a hopf algebra let gr h be the associated graded coalgebra and let r be the diagram of h c f 2 then the following are equivalent 1 h is co frobenius 2 gr h is co frobenius 3 r is finite dimensional 4 the coradical filtration of h is finite this theorem allows us to give systematically examples of co frobenius hopf algebras and opens the way to the classification of ample classes of such hopf algebras

near to far field transformation by a time domain spherical multipole analysis the contribution deals with a new time domain near to far field nff transformation which is particularly suited for the finite difference time domain fdtd method the far field is derived from the tangential field components on a surface enclosing the scatterer by employing a time domain spherical multipole representation the necessary time domain convolution is performed as on the fly in parallel with the fdtd time stepping algorithm the efficiency of the method is improved by incorporating a temporal linear interpolation of the near field data with the once obtained multipole amplitudes an analytic series representation of the time domain far field is achieved which allows a physical interpretability of the result moreover this expansion serves as an ideal basis for a systematic and efficient post processing the proposed technique may also be useful for other numerical and for asymptotic methods

positive definite solutions of the matrix equations x a x q a q q 1 in this paper we investigate nonlinear matrix equations x a x qa q where q 1 we derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations we provide a sufficient condition for the equation x a x qa q to have two different positive definite solutions and several sufficient conditions for the equation x a x qa q to have a unique positive definite solution we also propose iterative methods for obtaining positive definite solutions of these equations numerical examples are given to illustrate the effectiveness of the methods

on positive definite solutions of nonlinear matrix equation xs a x ta qxs a x ta q in this paper the nonlinear matrix equation xs a x ta qxs a x ta q is investigated based on the fixed point theory the existence and the uniqueness of the positive definite solution are studied an effective iterative method to obtain the unique positive definite solution is established given a q 1 s ts st in addition some computable estimates of the unique positive definite solution are derived finally numerical examples are given to illustrate the effectiveness of the algorithm and the perturbation estimates

positive definite solutions of the nonlinear matrix equation x a xqa q q 0 abstract in this paper the nonlinear matrix equation x a x q a q q 0 is investigated some necessary and sufficient conditions for existence of hermitian positive definite solutions of the nonlinear matrix equations are derived an effective iterative method to obtain the positive definite solution is presented some numerical results are given to illustrate the effectiveness of the iterative methods