solutions of the yang baxter equation for isotropic quantum spin chains the author considers solutions of the yang baxter equation such that the logarithmic derivative of the transfer matrix yields a quantum spin hamiltonian which is isotropic in spin space i e su 2 invariant four such solutions are known for each value of the spin s for s 1 2 they degenerate into the same solution and for s 1 they only give three different solutions for s or 6 he shows that these are the only solutions which are su 2 invariant except for s 3 when there is a fifth solution

a jacobi davidson method for solving complex symmetric eigenvalue problems we discuss variants of the jacobi davidson method for solving the generalized complex symmetric eigenvalue problem the jacobi davidson algorithm can be considered as an accelerated inexact rayleigh quotient iteration we show that it is appropriate to replace the euclidean inner product in mathbb c n with an indefinite inner product the rayleigh quotient based on this indefinite inner product leads to an asymptotically cubically convergent rayleigh quotient iteration advantages of the method are illustrated by numerical examples we deal with problems from electromagnetics that require the computation of interior eigenvalues the main drawback that we experience in these particular examples is the lack of efficient preconditioners

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

infinite conservation laws in the one dimensional hubbard model we show that the hamiltonian of the 1d hubbard model commutes with a one parameter family of transfer matrices of a new 2d classical model corresponding to two coupled six vertex models central to this result is a new local algebraic relation a generalization of the infinitesimal startriangle relation

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

quantum r matrix for g2 and a solvable 175 vertex model the quantum r matrix for cartan s exceptional simple lie algebra g2 in its seven dimensional minimal representation is presented the r matrix is determined through the irreducible decomposition of the tensor modules over the quantised universal enveloping algebra uq g2 this defines a new solvable seven state 175 vertex model on the planar square lattice whose boltzmann weights satisfy the yang baxter equation for the equivalent face model the local state probability is obtained in terms of a relative of a level 1 string function related to the affine lie algebra pair b3 1 contains implies g2 1

from frequency dependent mass and stiffness matrices to the dynamic response of elastic systems abstract more than three decades ago przemieniecki introduced a formulation for the free vibration analysis of bar and beam elements based on a power series of frequencies in the present paper the authors generalize this formulation for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements based on the mode superposition method a set of coupled higher order differential equations of motion is transformed into a set of uncoupled second order differential equations which may be integrated by means of standard procedures motivation for this theoretical achievement is the hybrid boundary element method which has been developed by the authors for time dependent as well as frequency dependent problems this formulation as a generalization of pian s previous achievements for finite elements yields a stiffness matrix for which only boundary integrals are required for arbitrary domain shapes and any number of degrees of freedom the use of higher order frequency terms drastically improves numerical accuracy the introduced modal assessment of the dynamic problem is applicable to any kind of finite element for which a generalized stiffness matrix is available some academic examples illustrate the theory

diagonalization of the transfer matrix of a nonintersecting string model abstract in this paper we obtain the eigenvectors of the transfer matrix of a nonintersecting string model using the bethe ansatz the result is in agreement with baxter s conjecture of weak equivalence of the present model with the six vertex model

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

numerical treatment of acoustic problems with the hybrid boundary element method abstract the symmetric hybrid boundary element method in the frequency and time domain is introduced for the computation of acoustic radiation and scattering in closed and infinite domains the hybrid stress boundary element method in a frequency domain formulation is based on the dynamical hellinger reissner potential and leads to a hermitian frequency dependent stiffness equation as compared to previous results published by the authors new considerations concerning the interpretation of singular contributions in the stiffness matrix are communicated on the other hand the hybrid displacement boundary element method for time domain starts out from hamilton s principle formulated with the velocity potential the field variables in both formulations are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of singular fundamental solutions generated by dirac distributions and generalized loads that are time dependent in the transient case the domain is modified such that small spheres centered at the nodes are subtracted then the property of the dirac distribution now acting outside the domain cancels the remaining domain integral in the hybrid principle and leads to a boundary integral formulation incorporating singular integrals in the time domain formulation an analytical transformation is employed to transform the remaining domain integral into a boundary one this approach results in a linear system of equations with a symmetric stiffness and mass matrix earlier 2d results are generalized in the present paper by a 3d implementation numerical results of transient pressure wave propagation in a closed domain are presented

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

complex variable boundary element method for potential flow with thin objects a complex variable boundary element method cvbem is developed for potential flow in the presence of thin objects singularities caused by such objects are expressed analytically through the conformal mapping technique and the resultant singular solution is coupled with the cvbem by the principle of superposition this can be done by virtue of the semi analytic nature of the cvbem the numerical results for example problems including flow barriers and high conductivity fractures confirm that the proposed model yields accurate solutions of the velocity potential and the stream function within the flow domain

solvable spin 1 models in one dimension we look for solvable spin 1 su 3 models in the seven parameter manifold of translation and reflection invariant hamiltonians with nearest neighbour couplings we prove that only discrete solutions of the reshetikhin criterion exist therefore the situation here differs greatly from the corresponding spin 1 2 su 2 case where reshetikhin s criterion is satisfied for any model of the xyz type

decorated star triangle relations and exact integrability of the one dimensional hubbard model the exact integrability of the one dimensional hubbard model is demonstrated with the help of a novel set of triangle relations the decorated star triangle relations the covering two dimensional statistical mechanical model obeys the star triangle or yang baxter relation a conjecture is presented for the eigenvalues of the transfer matrix

representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang baxter equation quantum doubles of finite group algebras form a class of quasitriangular hopf algebras that algebraically solve the yang baxter equation each representation of the quantum double then gives a matrix solution of the yang baxter equation such solutions do not depend on a spectral parameter and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups dn these results may be used to determine constant solutions of the yang baxter equation we then discuss baxterization ansatze to obtain solutions of the yang baxter equation with a spectral parameter and give several examples including a new 21 vertex model we also describe this approach in terms of minimal dimensional representations of the quantum doubles of the alternating group a4 and the symmetric group s4

integrability test for spin chains we examine a simple heuristic test of integrability for quantum chains this test is applied to a variety of systems including isotropic spin 1 models with nearest neighbour interaction potts type inhomogeneous spin 1 2 chains and a multiparameter family of spin 1 2 models generalizing the xyz chain with next to nearest neighbour interactions and bond alternation within the latter family we determine all the integrable models with an o 2 symmetry

exact integrability of the one dimensional hubbard model the 1d hubbard model is shown to be an exactly integrable system a covering model of 2d statistical mechanics which i proposed recently was shown to provide a one parameter family of transfer matrices commuting with the hamiltonian of the hubbard model i show in this work that any two transfer matrices of a family commute mutually at the root of the commutation relation is the ubiquitous yang baxter factorization condition the form of the r operator is displayed explicitly

comment on solutions of the yang baxter equation for isotropic quantum spin chains we comment on a recent paper by kennedy j phys a math gen 25 1992 2809 in which a systematic search for integrable spin s su 2 invariant quantum chains for s or 6 revealed four spin s families of integrable chains along with an additional integrable chain at s 3 we identify these su 2 invariant chains with known g invariant r matrices where g is a simple lie algebra and give arguments that kennedy s results may well constitute the complete classification of integrable spin s su 2 invariant chains

spin s quantum chains and temperley lieb algebras the authors construct a family of isotropic spin s quantum chains consisting of sums of operators satisfying a temperley lieb algebra exact values for the infinite lattice limit of the ground state energy per site and for the non zero gap to the lowest energy excited state follow from the temperley lieb equivalence with a bethe ansatz soluble xxz model the family of spin chains includes the biquadratic spin 1 model

on the inverse of generalized λ matrices with singular leading term an algorithm is introduced for the inverse of a matrix given as the truncated series a0 i a1 2a2 i 3a3 4a4 o n 1 with square coefficient matrices and singular leading term a0 moreover a1 may be conditionally singular and no restrictions are made for the remaining terms the result is a matrix given as a unique truncated series of the same error order motivation for this problem is the evaluation of the frequency dependent stiffness matrix of general boundary or macro finite elements in the frame of a hybrid variational formulation that is based on a flexibility matrix f expressed as a truncated power series of the circular frequency copyright 2005 john wiley sons ltd

variations on the drygas equation and its stability abstract we study the stability of the drygas functional equation g x y g x y 1 2 g x g y g y 1 mixing the direct method of the proof with the method of the invariant means dropping the assumption about the domain to be an abelian group we assume that the function we are dealing with is central i e g x y g y x is approximatively central i e g x y g y x satisfies the kannappan condition i e g x y z g x z y or that the group is amenable