canonical orthonormal wigner supermultiplet basis the explicit construction of an orthonormal basis for states of good spin isospin and su 4 wigner supermultiplet symmetry is given in a bargmann representation space a complete set of quantum labels is provided by a sp 3 r contains implies u 3 complementary symmetry

an analytic formula for u 3 boson matrix elements the u 3 boson lie algebra is the liquid limit of the symplectic algebra sp 3 r an analytic formula is given for the u 3 boson matrix elements in irreducible unitary representations corresponding to the sp 3 r discrete series the formula also applies to the generators of the mathematically isomorphic but physically different interacting boson algebra

schur function analysis of the unitary discrete series representations of the non compact symplectic group the authors develop and analyse certain character reductions for the infinite dimensional unitary discrete series representations of the non compact symplectic group sp 2n r the group reductions considered are sp 2k r contains implies sp 2 r o k and the more general sp 2nk r contains implies sp 2n r o k they use schur function techniques to derive succinct formulae involving certain infinite series of schur functions the results are relevant to the study of many body systems with interactions of bilinear form and to the description of various quantum phenomena including collective behaviour

simulation of the three dimensional ising model on the creutz cellular automaton abstract the three dimensional ising model is simulated on the creutz cellular automaton the values computed for the critical temperature and the static critical exponents within the framework of the finite size scaling theory are in agreement with their values obtained by different methods

perturbation series for the mass gap of the 1 1 dimensional o 2 model the strong coupling mass gap series to 10th order in the dimensionless coupling is presented for the 1 1 dimensional o 2 model the second logarithmic derivative of the euler transformed series is examined using pade techniques to yield the critical parameter estimates lambda c approximately 0 89 0 02 and sigma approximately 0 50 or 0 08 these results are consistent with the model exhibiting a kosterlitz thouless transition

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

representations of the groups sp n r and sp n in a u n basis the explicit expressions for the infinitesimal operators and the finite matrix elements with respect to a u n basis are obtained for the representations of the most degenerate series of sp n r and for the irreducible unitary representations of sp n with the highest weights m 0 0

analytic expressions for the matrix elements of generators of sp 6 in an sp 6 u 3 basis work done by many authors indicates that important tools for calculations in microscopic collective models are the matrix elements of the generators of the symplectic group sp 6 in an sp 6 u 3 basis rosensteel has derived recursion relations for these matrix elements while filippov has determined them using generating function technique but it would also be convenient to have explicit and analytic formulas for them this is what we do in this paper for the case of closed shells i e when the irreducible representation irrep of sp 6 is characterized by equal values for the three weight generators in the lowest weight state we also indicate how our results can be extended to the case of arbitrary irreps of sp 6 i e when we have open shells

the 2 1 d ising model on a triangular lattice the 2 1 d ising model on a triangular lattice is explored for lattices of up to 5 5 sites finite size scaling techniques are used to estimate the critical parameters xc 0 2096 2 nu 0 627 4 beta 0 322 6 gamma 1 236 8 these agree with previous estimates within errors and with the hypotheses of universality and hyperscaling the behaviour at low temperatures is also studied and theoretical predictions of finite size scaling at a first order transition are confirmed

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

accurate estimates of 3d ising critical exponents using the coherent anomaly method abstract an analysis of the critical behavior of the three dimensional ising model using the coherent anomaly method cam is presented various sources of errors in cam estimates of critical exponents are discussed and an improved scheme for the cam data analysis is tested using a set of mean field type approximations based on the variational series expansion approach accuracy comparable to the most precise conventional methods has been achieved our results for the critical exponents are given by 0 108 5 0 327 4 1 237 4 and 4 77 5

approximation in normal linear spaces abstract a historical account is given of the development of methods for solving approximation problems set in normed linear spaces approximation of both real functions and real data is considered with particular reference to lp or lp and chebyshev norms as well as coverage of methods for the usual linear problems an account is given of the development of methods for approximation by functions which are nonlinear in the free parameters and special attention is paid to some particular nonlinear approximating families

coherent state theory of the noncompact symplectic group an extended coherent state theory is presented for the noncompact sp 3 r group which reveals a simple relationship between the sp 3 r algebra and its contracted u 3 boson limit the relationship is used to derive a remarkably accurate analytic expression for sp 3 r matrix elements for the generic lowest weight representations the expression is shown to be exact whenever the states involved are multiplicity free with respect to the u 3 subalgebra it is further shown how exact matrix elements are easily calculated in general dyson and holstein primakoff type u 3 boson expansions are given

boson realization of sp 4 i the matrix formulation holstein and primakoff derived long ago the boson realization of a su 2 lie algebra for an arbitrary irreducible representation irrep of the su 2 group the corresponding result for su 1 1 sp 2 is also well known this raises the question of whether it is possible to obtain in an explicit analytic and closed form and for any integer d the boson realization of a sp 2d lie algebra for an arbitrary irrep of the sp 2d group which is a problem of considerable physical interest the case d 2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp 4 the dyson realization is well known and the passage to bosons satisfying the appropriate hermiticity conditions can be done by a similarity transformation through an operator k what we want though is an explicit boson realization for sp 2d similar to the one that exists for sp 2 in sec vi we show how we can get it for sp 4 if the operator k is known unfortunately while the matrix form of k2 can be ex

series studies of the potts model i the simple cubic ising model the finite lattice method of series expansion is generalized to the q state potts model on the simple cubic lattice it is found that the computational effort grows exponentially with the square of the number of series terms obtained unlike two dimensional lattices where the computational requirements grow exponentially with the number of terms for the ising q 2 case the authors have extended the low temperature series for the partition functions magnetization and zero field susceptibility to u26 from u20 the high temperature series for the zero field partition function is extended from nu 18 to nu 22 subsequent analysis gives critical exponents in agreement with those from field theory

the high temperature susceptibility and spin spin correlation function of the three dimensional ising model the series analysis protocol developed in a preceding paper ibid vol 20 p 1839 1987 is applied to the susceptibility and correlation function of the three dimensional ising model for the spin 1 2 ising data the author argues that the protocol needs modification to take account of trends in the data which trends arise from the nature of the series in this way the author obtains gamma 1 239 or 0 003 for all cubic lattices and for a variety of spin values the diamond lattice data lies outside this range and it is argued that this series is effectively far shorter than the others the author also estimates nu 0 632 0 002 0 003 for the bcc lattice and obtains critical point estimates for all lattice and spin models studied

on the convergence of interior reflective newton methods for nonlinear minimization subject to bounds we consider a new algorithm an interior reflective newton approach for the problem of minimizing a smooth nonlinear function of many variables subject to upper and or lower bounds on some of the variables this approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths reflection paths the interior reflective approach does not require identification of an activity set in this paper we establish that the interior reflective newton approach is globally and quadratically convergent moreover we develop a specific example of interior reflective newton methods which can be used for large scale and sparse problems

finite size scaling and universality in the 2 1 d ising model the energy and magnetisation density of the 2 1 d ising model are investigated for the thermal exponent the author finds xepsilon 1 42 or 0 02 in agreement with hyperscaling the privman fisher universality hypothesis is confirmed by two methods first the author presents at the critical point numerical data for the finite size scaling amplitudes of the singular free energy magnetisation susceptibility and surface tension and checks them for universality second using the explicitly computed eigenvectors of the hamiltonian it is shown that the ratios of matrix elements of the energy and magnetisation density are universal

the gap exponent δ for the spin s ising model on the fcc lattice high temperature series expansions are presented for the magnetisation m k h of the spin s ising model on the face centred cubic lattice series coefficients are derived to order 13 and 5 respectively in the variables k j kt and h mh kt for 1 2 or s or 9 2 the data are analysed for 2 delta gamma where delta and gamma denote the gap exponent and the susceptibility exponent respectively the estimate 2 delta gamma 1 890 or 0 003 satisfies the data for all s

high temperature series for scalar field lattice models generation and analysis an implementation of the free embedding scheme for high temperature series generation on the body centered cubic family of lattices in arbitrary dimensiond is described series to order 21 in inverse temperature are tabulated for several scalar field models both for the magnetic susceptibility and for the second moment of the spin correlation function the critical behavior of a family of 3 dimensional double gaussian models which interpolate continuously between the spin 1 2 ising model and the gaussian model is analyzed in detail away from the gaussian model limit using confluent inhomogeneous secondorder differential approximants with our best estimate of the correction to scaling exponent 0 52 0 03 the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by 1 237 0 002 and 0 630 0 0015 respectively and 2 0 0359 0 0007

on the critical behaviour of self avoiding walks for pt i see ibid vol 22 p 1839 1989 for the self avoiding walk problem the coefficients of the chain generating function and of the generating function for the sum of square end to end distances have been extended to 20 terms for the triangular lattice to 27 terms for the diamond lattice to 21 terms for the simple cubic lattice and to 16 terms for the bcc lattice precise estimates of the critical points are obtained and for the exponents we find that gamma 1 161 or 0 002 and nu 0 592 or 0 003 encompasses all the three dimensional lattice data

large scale robust beamforming via ell _ infty minimization in this paper linearly constrained and robust ell infty norm beamforming techniques are proposed for non gaussian signals a conventional approach for ell infty minimization needs to solve a linear programming lp or second order cone programming socp however this strategy is computationally prohibitive for big data because the existing algorithms for lp or socp such as simplex method or interior point method can only solve small or medium scale problems in this paper the alternating direction method of multipliers admm is devised for large scale ell infty beamforming problems where the core subproblems can be formulated concisely as a linearly or second order cone constrained least squares and the proximity operator of the ell infty norm in each iteration remarkably a linear time complexity algorithm is devised that efficiently computes the ell infty norm proximity operator simulation results verify the high efficiency of the admm and the superiority of the ell infty norm beamforming techniques over several representative beamformers indicating that its performance can approach the optimal upper bound

stochastic truncation for the 2 1 d ising model the method of symmetrized stochastic truncation is applied to the 2 1 dimensional ising model to calculate the ground state energy mass gap magnetization and susceptibility on lattices of sizes up to 6 6 sites the method is shown to be a powerful and accurate monte carlo technique provided the lattice size is not too large and the model is suitably convergent finite size scaling estimates of the critical indices are nu 0 627 2 alpha 0 12 2 beta 0 324 3 and delta 1 23 1 an estimate of the combination gamma nu 2 beta nu 3 000 1 is obtained in outstanding agreement with the expected hyperscaling relation

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

magnetisations from finite size scaling a method of obtaining the spontaneous magnetisation from finite lattice matrix elements of the magnetic field operator due to yang 1952 and uzelac 1980 is discussed the method is demonstrated for the case of the ising model in 1 1 dimensions and is shown to provide smooth and rapidly convergent finite lattice sequences applied to the case of the three state potts z3 model in 1 1 dimensions the method yields an estimate beta 0 111 09 or 0 000 05 for the critical exponent this confirms alexander s conjecture of universality with the hard hexagonal model

spin wave expansion for the o 2 heisenberg spin model in d 1 dimensions spin wave expansions are carried out for the hamiltonian version of the o 2 heisenberg spin model and evaluated for the cases of the 1 1 dimensional linear chain and the 2 1 dimensional square and triangular lattices expressions are obtained for the bulk limits and finite size corrections to the ground state energy the one boson excitation energy the magnetization and susceptibility at low temperatures results are derived for the critical parameters in the 1 1 dimensional model and the goldstone mode parameters in the 2 1 dimensional models comparison is made with the finite size scaling predictions of fisher and privman 1985

a globally and superlinearly convergent algorithm for convex quadratic programs with simple bbounds a globally and superlinearly convergent algorithm for solving convex quadratic programs with simple bounds is presented the algorithm is developed using a new formulation of the problem the minimization of an unconstrained piecewise quadratic function that has the same optimality conditions as the original problem the major work at each iteration is the cholesky factorization of a positive definite matrix with the size and structure of the hessian of the quadratic hence the algorithm is suitable for solving large sparse problems and for implementation on parallel computers the numerical results indicate that the new approach has promise

canonical orthonormal basis for su 3 so 3 i construction of the basis a canonical orthonormal basis is given for generic representations of the group chain su 3 contains implies so 3

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

finite lattice methods in quantum hamiltonian field theory i o 2 and o 3 heisenberg models for pt i see ibid vol 14 p 241 57 1981 two efficient methods for finding the low lying states of hamiltonians on finite lattices are described the first involves constructing a finite representation of the hamiltonian using strong coupling eigenstates while the second is based on the lanczos recursion method the methods are used to determine the mass gap of the o 2 and o 3 heisenberg hamiltonians in 1 1 dimensions for a sequence of finite chains the critical behaviour of the infinite chain is then analysed by extrapolating the finite lattice estimates using finite size scaling a remarkably sensitive test is developed for the presence of a phase transition for the o 2 model data this test yields strong evidence for a phase transition with the weak coupling phase massless while in the o 3 case the test supports although more weakly the absence of any transition

unitary representations branching rules and matrix elements for the non compact symplectic groups the complementarity of the symplectic and orthogonal groups is used to infer properties of the infinite dimensional unirreps of the former from the character theory of the latter the complete set of d series metaplectic unirreps of sp n r is identified and branching rules are given for their restrictions to the maximal compact subgroup u n developed in terms of the properties of schur functions a known algorithm for the evaluation of matrix elements of the sp 3 r lie algebra is extended to any sp n r and analytic expressions are given for important classes of unirreps and multiplicity free states

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

cluster expansions for the ising and heisenberg spin models in hamiltonian lattice field theory cluster expansion methods are applied to calculate high temperature series for the vacuum energy the susceptibility and the mass gap for the ising model and the o 2 and o 3 heisenberg models in 1 1 dimensions and 2 1 dimensions critical points and critical indices are estimated for the line the square and the triangular lattices the results demonstrate universality with the normal euclidean versions of these models within errors

series expansions for the zero temperature transverse ising model series expansions are presented for the magnetisation susceptibility magnetic field derivatives of the susceptibility and specific heat of the zero temperature transverse ising model coefficients in these series have been calculated to tenth order in lambda 2 where lambda is the transverse field for the linear chain to eighth order for the square lattice and to seventh order for the triangular lattice these series yield estimates of the low temperature critical exponents alpha beta gamma and delta of the two and three dimensional ising models they provide good evidence for the symmetry of exponents above and below the critical point e g gamma gamma

asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces relation to surface stiffness and step free energy two and three dimensional ising type systems are considered in the finite cross section cylindrical geometry an interface is forced along the cylinder strip in 2d by the antiperiodic or boundary conditions detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues for rough interfaces i e for 0 t tc in 2d tr t tc in 3d the eigenvalues are split algebraically and the spectral gaps are governed by thesurface stiffness coefficient for rigid interfaces i e 0 t tr in 3d the eigenvalues are split exponentially with the gaps determined by thestep free energy

generating set search methods for piecewise smooth problems we consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra a generating set search method is proposed which is named structured because the structure of the set of nondifferentiability near the current iterate is exploited to define the search directions at each iteration some numerical results are presented to validate the approach

finite size scaling in the 2 1 d ising model hamiltonian eigenvalues are calculated for the 2 1 d ising model on lattices up to 5 5 sites finite size scaling techniques are used to estimate the critical coupling xc 0 329 or 0 001 and index v 0 635 or 0 005 the prospects are discussed for further applications of these methods in three and four dimensions

primal methods are better than dual methods for solving overdetermined linear systems in the l sense it is generally believed that methods based upon solving the dual of the linear programming formulation of the linear l infty problem are superior to methods based upon the primal formulation a primal approach is presented along with evidence that for random problems primal methods are to be preferred it is then shown that the method generally considered to be the best algorithm for discrete linear approximation in the l infty norm actually owes much of its efficiency to effective choice of a starting point this phenomenon is explained with the aid of results from classical minimax theory which are then used to determine a suitable initial point for a primal method with this enhancement it would appear that the primal approach is also preferable for problems arising from function approximations

cluster expansions in the 2 1 d ising model the cluster expansion methods of nickel are applied to calculate high temperature series for the vacuum energy and specific heat the susceptibility and the mass gap in the 2 1 d ising model critical points and critical exponents are estimated for the square and triangular lattices the results demonstrate universality with the 3d ising model within errors exact linked cluster expansions are formulated for the quantities above and their convergence and scaling properties are investigated

on the method of weighting for equality constrained least squares problems the generalized singular value decomposition is used to analyze the problem of minimizing ax b 2 subject to the constraint bx d a byproduct of the analysis is a new iterative procedure that can be used to improve an approximate solution obtained via the method of weights all that is required to implement the procedure is a single qr factorization these developments turn out to be of interest when a and b are sparse and for the case when systolic architectures are used to carry out the computations

accurate monte carlo critical exponents for ising lattices abstract a careful monte carlo investigation of the phase transition very close to the critical point t t c h 0 in relatively large d 3 s 1 2 ising lattices did produce critical exponents 3 d 0 3126 4 5 16 3 d 1 0 1997 4 1 5 and 3 d 1 253 4 5 4 our results indicate that within experimental error they are given by simple fractions corresponding to the linear interpolations between the respective two dimensional onsager and four dimensional mean field critical exponents an analysis of our inverse susceptibility data 1 t vs t t c shows that these data lead to a value of 3 d compatible with and t c 4 51152 12 while values obtained recently by high and low temperature series expansions and renormalization group methods are not

models for su 3 in terms of so n 2 and so 2n algebras mathematical and physical models for su 3 are given in terms of unirreps of the so n 2 and so 2n algebras vector coherent state representations are given for all the discrete series unirreps of so n 2 and so 2n traceless bosons are shown to arise naturally in these representations a new and elegant realisation of the so 8 approximately so 6 2 model for su 3 is given and it is shown how to perform calculations in the so 8 model using the powerful vector coherent state representations formalism

series expansions for the 3d transverse ising model at t 0 both weak coupling and strong coupling series expansions are calculated for the ising model in a transverse field at zero temperature in three dimensions series are obtained for the ground state energy the magnetization the susceptibility and the energy gaps on the simple cubic the body centred cubic and the face centred cubic lattices the analysis of the critical behaviour is consistent with the behaviour predicted by renormalization group theory for the four dimensional simple ising model there is a remarkable degree of universality between all three lattices

heisenberg weyl algebras of symmetric and antisymmetric bosons all the polynomials in symmetric 2 and antisymmetric 11 u n bosons are constructed in u n bases and u n reduced matrix elements for the bosons between polynomial basis states are computed applications to representation theory of lie groups paired fermion and boson physics are briefly discussed

boson realisation of symplectic algebras the boson realisation of the two dimensional symplectic lie algebra sp 2 for a given irreducible representation irrep of the sp 2 group has been known for a long time more recently the boson realisation of the 2d dimensional symplectic lie algebras sp 2d have been derived for particular irreps of the sp 2d group the author outlines the corresponding result for an arbitrary irrep of sp 2d

cam approach to the ground state phase transition in the two dimensional transverse ising model the double cluster approximation dca and the multi effective field approximation mefa are formulated for the two dimensional s 1 2 transverse ising model on a square lattice in the ground state these two cluster effective field approximations expand the sizes of clusters effectively combining some suitable series of these approximations with the coherent anomaly method cam the authors have analysed the critical phenomenon of this model they have obtained g c 1 528 or 0 016 and gamma 1 25 or 0 08 using the dca and gamma 1 26 or 0 10 using the mefa these estimates are consistent with the other results g c approximately 1 52 and gamma approximately 1 24 their scheme is expected to be useful in the study of frustrated systems because various shapes of clusters can be used in their calculations

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

strong coupling expansion analysis of the false vacuum decay rate of the lattice phi4 model in 1 1 dimensions strong coupling expansion is performed for the lattice 4 model in 1 1 dimensions because the strong coupling limit itself is not solvable we employed numerical calculations so as to set up unperturbed eigensystems restricting the number of hilbert space bases we performed linked cluster expansion up to 11th order we carried out an alternative simulation by means of the density matrix renormalization group thereby we confirmed that our series expansion data with a convergence acceleration trick are in good agreement with the simulation result through the analytic continuation to the domain of negative biquadratic interaction we obtain the false vacuum decay rate contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments our series expansion reproduces the instanton theory behaviour for a high potential barrier for a shallow barrier in contrast our result tells us that the relaxation is no longer described by an instanton but the decay rate acquires notable enhancement

vector coherent state theory and its application to the orthogonal groups vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple lie groups and their lie algebras it is shown that in a suitable basis the vector coherent state inner product can be inferred algebraically by k matrix theory and changed to a simpler bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of lie algebras applications are made to the even and odd orthogonal lie algebras

high temperature series expansions for the 2 1 dimensional ising model using efficient cluster expansion methods the known high temperature series for the vacuum energy specific heat susceptibility and mass gap of the 2 1 dimensional ising model on the square and triangular lattices have been extended by several terms estimates of the critical indices demonstrate very convincing universality with the euclidean version of the model

finite size scaling in the transverse ising model on a square lattice energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse ising model on square lattices of up to 6 6 sites finite size scaling is used to estimate the critical parameters of the model confirming universality with the three dimensional classical ising model critical amplitudes are also estimated for both the energy gap and the ground state energy

a global and quadratically convergent method for linear l problems a new globally and quadratically convergent algorithm is proposed for the linear l infty problem this method works on the piecewise linear l infty problem directly by generating descent directions via a sequence of weighted least squares problems and using a piecewise linear line search to ensure a decrease in the l infty function at every step it is proven that ultimately full newton like steps are taken where the newton step is based on the complementary slackness condition holding at the solution numerical results suggest a very promising method the number of iterations required to achieve high accuracy is relatively insensitive to problem size

high accuracy estimates of the critical parameters for the xy model on the square and the triangular lattices using the high temperature expansions abstract the high temperature expansions of the spin spin correlation function of the two dimensional classical x y planar rotator model are extended by two terms from order 24 through order 26 in the case of the square lattice and by five terms from order 15 through order 20 in the case of the triangular lattice the data are analyzed to improve the current estimates of the critical parameters of the models we determine c 0 5599 7 and 0 499 5 in the case of the square lattice for the triangular lattice case we estimate c 0 3412 4 and 0 500 5

componentwise perturbation theory for linear systems with multiple right hand sides existing definitions of componentwise backward error and componentwise condition number for linear systems are extended to systems with multiple right hand sides and to a general class of componentwise measure of perturbations involving holder p norms it is shown that for a system of order n with r right hand sides the componentwise backward error can be computed by finding the minimum p norm solutions to n underdetermined linear systems and an explicit expression is obtained in the case r 1 a perturbation bound is derived and from this the componentwise condition number is obtained to within a multiplicative constant applications of the results are discussed to invariant subspace computations quasi newton methods based on multiple secant equations and an inverse ode problem

analytical expressions for the matrix elements of the non compact symplectic algebra analytic matrix elements are derived for all the lowest weight representations of the noncompact symplectic algebra sp 3 r it is shown that the expressions are exact for representations of the type sigma 1 sigma 2 sigma 3 and for all states of an arbitrary representation that are multiplicity free with respect to the u 3 subalgebra furthermore they are remarkably accurate in general

the 1 1 do 2 model a finite lattice analysis finite size methods and the theory of conformal invariance are applied to the 1 1 do 2 or x y planar model the critical point is found to be xc approximately 2 0 the value sigma 0 501 or 0 005 is obtained for the index governing the critical divergence of the correlation length and the conformal anomaly is confirmed to be c 1 the kosterlitz thouless features of a low temperature phase with zero spontaneous magnetisation but algebraic decay of correlations together with a standard high temperature phase are observed the critical exponent eta is determined as a function of coupling constant and compared with theoretical expectations

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v