colored solutions of the yang baxter equation from representations of uqgl 2 we study the hopf algebra structure and the highest weight representation of a multiparameter version of uqgl 2 the hopf algebra maps of this algebra are explicitly given we show that the multiparameter universal r matrix can be constructed directly as a quantum double intertwiner without using reshetikhin s twisting transformation we find there are two types highest weight representations for this algebra type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity when applying the representation theory to the multi parameter universal r matrix both standard and nonstandard colored solutions of the yang baxter equation are obtained

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

on some quantum r matrices associated with representations of uq sl 2 c when q is a root of unity the author constructs quantum r matrices associated with certain non cyclic irreducible representations of uq sl 2 c at roots of unity which are parametrized by one continuous parameter the author finds solutions for the two and three dimensional representations via baxterization the two dimensional case corresponds to the free fermion model of fan and wu 1970

q deformation of the lorentz group we describe a q deformation of the lorentz group in terms of a q deformation of the van der waerden spinor algebra

a quantum analog of the z algebra we define a natural quantum analog for the z algebra and which we refer to as the zq algebra by modding out the heisenberg algebra from the quantum affine algebra uq sl 2 with level k we discuss the representation theory of this zq algebra in particular we exhibit its reduction to a group algebra and to a tensor product of a group algebra with a quantum clifford algebra when k 1 and k 2 and thus we recover the explicit constructions of uq sl 2 standard modules as achieved by frenkel jing and bernard respectively moreover for arbitrary nonzero level k we show that the explicit basis for the simplest z generalized verma module as constructed by lepowsky and primc is also a basis for its corresponding zq module i e it is invariant under the q deformation for generic q we expect this zq algebra associated with uq sl 2 at level k to play the role of a dynamical symmetry in the off critical zk statistical models

roe matrices for ideal mhd and systematic construction of roe matrices for systems of conservation laws in this paper the construction of a roe s scheme for the conservative system of ideal magnetohydrodynamics mhd is presented as this method relies on the computation of a roe matrix the problem is to find a matrixa ul ur which satisfies the following properties it is required to be consistent with the jacobian of the fluxf to have real eigenvalues a complete set of eigenvectors and to satisfy the relation f a ul ur u whereulandurare two admissible states and utheir difference for the ideal mhd system using eulerian coordinates a roe matrix is obtained without any hypothesis on the specific heat ratio especially its construction relies on an original expression of the magnetic pressure jump moreover a roe matrix is computed for lagrangian ideal mhd by extending the results of munz who obtained such a matrix for the system of lagrangian gas dynamics so this second matrix involves arithmetic averages unlike the eulerian one which contains classical roe averages like in eulerian gas dynamics in this paper a systematic construction of lagrangian roe matrices in terms of eulerian roe matrices for a general system of conservation laws is also presented this result applied to the above eulerian and lagrangian matrices for ideal mhd gives two new matrices for this system in the same way by applying this construction to the gas dynamics equations new roe matrices are also obtained all these matrices allow the construction of roe type schemes some numerical examples on the shock tube problem show the applicability of this method

on positive definite solutions to the algebraic riccati equation abstract complete necessary and sufficient conditions for the existence of a positive definite solution to the algebraic riccati equation are given it is also shown that when a positive definite solution exists it is either unique or else there are uncountably many such solutions

existence condition of positive definite solutions for algebraic matrix riccati equations abstract algebraic matrix riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time invariant systems a necessary and sufficient condition is established for the existence of unique positive definite solutions and the asymptotically stable closed loop system the condition is stated in terms of the detectability and stabilizability of certain matrix pairs as was the case for the non negative definite solution simple examples are included to illustrate the new results against the existing ones

singular vectors of representations of quantum groups the author gives explicit formulae for singular vectors of verma modules over uq g they give the general formula for g an for some cases when g dn and for some rank two subalgebras of g not an dn for this he uses a special basis of uq g where g is the negative root subalgebra of g which was introduced in his earlier work on the case q 1 this basis seems more economical than the poincare birkhoff witt type of basis used by malikov feigin and fuchs 1986 for the construction of singular vectors of verma modules in the case q 1 furthermore this basis turns out to be part of a general basis introduced recently for other reasons by lusztig 1988 for uq b where b is a borel subalgebra of g

periodic solutions of riccati equations applied to multirate sampling from some basic relations in estimation theory a comprehensive set of formulae are obtained for the periodic solution of riccati equations to obtain numerically stable algorithms square root formulations are introduced both the discrete time and continuous time cases are considered closed loop properties for periodic systems are also investigated the results are applied to multirate measurement sampling the control of a continuous stirred tank reactor serves as an illustrative example the temperature measurements are then complemented by concentration analysis available at a slower rate than the basic sampling and control rate the results give some guidelines about the benefits of multirate sampling

differential operators on quantized flag manifolds at roots of unity abstract the quantized flag manifold which is a q analogue of the ordinary flag manifold is realized as a non commutative scheme and we can define the category of d modules on it using the framework of non commutative algebraic geometry however when the parameter q is a root of unity lusztig s frobenius morphism allows us to handle d modules on the quantized flag manifold through modules over a certain sheaf of rings on the ordinary flag manifold in this paper we will show that this sheaf of rings on the ordinary flag manifold is an azumaya algebra over its center we also show that its restriction to certain subsets are split azumaya algebras these are analogues of some results of bezrukavnikov mirkovic rumynin on d modules on flag manifolds in positive characteristics

new solutions of yang baxter equations birman wenzl algebra and quantum group structures new braid group representations associated with the fundamental representations of bn cn and dn are derived they are shown to satisfy birman wenzl algebra by yang baxterization the authors obtain new solutions of yang baxter equations including the twisted extensions quantum group structures related to these new solutions are explicitly given

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

new braid group representations of the b2 b3 and b4 types their associated link polynomials and quantum r matrices new braid group representations of the b2 b3 and b4 types are obtained by solving the defining relations of artin s braid group bn directly they give their associated link polynomials the authors discuss a procedure baxterization which allows them to construct their corresponding quantum r matrices

a finite element method for magnetohydrodynamics abstract this paper presents a finite element method for the solution of 3d incompressible magnetohydrodynamic mhd flows two important issues are thoroughly addressed first appropriate formulations for the magnetic governing equations and the corresponding weak variational forms are discussed the selected b q formulation is conservative in the sense that the local divergence free condition of the magnetic field is accounted for in the variational sense a galerkin least squares variational formulation is used allowing equal order approximations for all unknowns in the second issue a solution algorithm is developed for the solution of the coupled problem which is valid for both high and low magnetic reynolds numbers several numerical benchmark tests are carried out to assess the stability and accuracy of the finite element method and to test the behavior of the solution algorithm

extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics an extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper the multidimensional scheme is constructed from a one dimensional functioning code based on the dimensional splitting method originally suggested by strang the functioning code is built upon a nonlinear riemann solver for ideal mhd equations recently developed by the authors the correctness of the scheme is tested in the steepening of waves in both one and two dimensional situations and in various mhd shock tube problems which involve all the discontinuities in ideal mhd the robust character of the scheme is demonstrated in the shock tube problems and in the interaction between mhd shocks and a cloud the results of these problems show that the scheme keeps the principal advantages of a high order godunov scheme robust operation in the presence of very strong waves thin shock fronts with little attendant noise generation and thin contact discontinuity

accurate and robust pressure weight advection upstream splitting method for magnetohydrodynamics equations this research was supported by national space laboratory nsl s10801000121 08a0100 12110 program through the korea science and engineering foundation funded by the ministry of education science and technology

flux corrected transport techniques for multidimensional compressible magnetohydrodynamics a prescription is given for conservatively integrating generalized hydromagnetic equations using flux corrected transport fct techniques by placing the magnetic field components at the interface locations of the finite difference grid the field is kept divergence free to within machine roundoff error the use of fct techniques allows an integration scheme of high accuracy to be employed while the numerical ripples associated with large dispersion errors are avoided the method is particularly well suited for problems involving magnetohydrodynamic shocks and other discontinuities

a positive conservative method for magnetohydrodynamics based on hll and roe methods the exact riemann problem solutions of the usual equations of ideal magnetohydrodynamics mhd can have negative pressures if the initial data has b 0 this creates a problem for numerical solving because in a first order finite volume conservative godunov type method one cannot avoid jumps in the normal magnetic field component even if the magnetic field was divergenceless in the three dimensional sense we show that by allowing magnetic monopoles in mhd equations and properly taking into account the magnetostatic contribution to the lorentz force an additional source term appears in faraday s law only using the harten lax vanleer hll riemann solver and discretizing the source term in a specific manner we obtain a method which is positive and conservative we show positivity by extensive numerical experimentation this mhd hll method is positive and conservative but rather diffusive thus we show how to hybridize this method with the roe method to obtain a much higher accuracy while still retaining positivity the result is a fully robust positive conservative scheme for ideal mhd whose accuracy and efficiency properties are similar to the first order roe method and which keeps b small in the same sense as powell s method as a special case a method with similar characteristics for accuracy and robustness is obtained for the euler equations as well

comments on existence conditions of positive definite solutions for algebraic matrix riccati equations abstract it is pointed out that the main results in a recent paper by kano 1987 have previously been published in the literature

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

an hllc type approximate riemann solver for ideal magnetohydrodynamics this paper presents a solver based on the hllc harten lax van leer contact wave approximate nonlinear riemann solver for gas dynamics for the ideal magnetohydrodynamics mhd equations written in conservation form it is shown how this solver also can be considered a modification of linde s adequate solver this approximation method is intended to resolve slow alfven and contact waves better than the original hll harten lax van leer solver compared to exact nonlinear solvers and roe s solver this new solver is computationally inexpensive in addition the method will exactly resolve isolated contacts and fast shocks the method also preserves positive density and pressure with two caveats first the numerical signal velocities the eigenvalues of the roe average matrix do not underestimate the physical signal velocities and second in a very few cases it may be required to change the wavespeeds of the riemann fan for the underlying hll method to guarantee positive pressures these conditi

new braid group representations of the d2 and d3 types and their baxterization new braid group bn representations of the d2 and d3 types are obtained by solving the defining relations of bn directly the authors discuss a procedure baxterization which allows one to construct their corresponding quantum r matrices

periodic solutions of matrix riccati equations in discrete time invariant systems the well known matrix riccati equations arising in optimal filtering as well as control problems for discrete time invariant systems are considered in this paper existence conditions are established both for general periodic solutions and for non negative definite periodic solutions it is shown that a pair of complex conjugate eigenvalues or a pair of real eigenvalues in a certain symplectic matrix produce periodic solutions furthermore algorithms are obtained to derive such periodic solutions using the symplectic matrix which require slight additional computations to deriving steady state solutions finally numerical examples which possess periodic solutions are presented

nonlinear magnetohydrodynamics simulation using high order finite elements a conforming representation composed of 2d finite elements and finite fourier series is applied to 3d nonlinear non ideal magnetohydrodynamics using a semi implicit time advance the self adjoint semi implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments growth rates for resistive tearing modes with experimentally relevant lundquist number are computed accurately with time steps that are large with respect to the global alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree p two or larger an error diffusion method controls the generation of magnetic divergence error convergence studies show that this approach is effective for continuous basis functions with p 2 where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity is computed accurately with p 3 without mesh alignment a simulation of tearingmode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3d magnetic topologies

irregular uq sl 3 representations at roots of unity via gel fand weyl zetlin basis the gel fand weyl zetlin gwz description of the uq sl 3 irregular irreps at roots of unity is explicitly given those are irreps fixed by the same parameters as the unitary irreducible representations uirs of su 3 yet having dimensions smaller than their classical counterparts the reason being that to obtain an irregular irrep one has to make factorization of an additional submodule this description is made geometrically transparent by an arrangement of the standard su 3 gwz basis in a hexagonal pyramid which is valid for any q and seems new even for q 1 the pyramid has as a base the standard hexagon which gives the weight space of the uirs of su 3 in the plane of third component of isospin iz and hypercharge y while third dimension of this pyramid is related to the isospin i algebraically this arrangement is related to a one to one correspondence between the abstract gwz states and monomials in the algebra of raising generators uq g however those monomials are not in the standard poi

two parametric solution to graded yang baxter equation and two parametric uuvgl 1 mod 1 algebra as a hopf algebra the authors discuss a two parametric solution of the graded yang baxter equation ybe and perform the yang baxterization to obtain the solution to the quantum ybe in the formalism developed previously they present the two parametric quantized superalgebra uuvgl 1 mod 1 and prove that this algebra is a hopf algebra with the hopf operations explicitly provided