conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

finite size scaling and universality in the spectrum of the quantum ising chain i periodic and antiperiodic boundary condition the spectrum of the quantum ising chain is studied in the finite size scaling limit for periodic and antiperiodic boundary conditions the finite size corrections are computed for all energy gaps the results of the model are used to test the privman fisher universality hypothesis and conformal theory at the critical point it is shown how to build the spectrum from the irreducible representations of the virasoro algebra in addition the author finds evidence for an unsuspected symmetry for systems both non critical and of finite size

proof of a conjecture of wohltmann on target path controllability we prove that a sufficient condition for target path controllability as defined by h w wohltmann is also necessary

on finite generation of symbolic rees rings of space monomial curves and existence of negative curves abstract in this paper we shall study finite generation of symbolic rees rings of the defining ideal of the space monomial curves t a t b t c for pairwise coprime integers a b c such that a b c 1 1 1 if such a ring is not finitely generated over a base field then it is a counterexample to the hilbert s fourteenth problem finite generation of such rings is deeply related to existence of negative curves on certain normal projective surfaces we study a sufficient condition definition 3 6 for existence of a negative curve using it we prove that in the case of a b c 2 a b c a negative curve exists using a computer we shall show that there exist examples in which this sufficient condition is not satisfied

finite size corrections to matrix elements in a conformal theory applications to the magnetisation of the three state potts model using conformal invariance the authors calculate the leading corrections in 1 n to the magnetisation of the three state potts quantum chain the results are in good agreement with the numerical finite size results

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

m 0 n is not a mori dream space building on the work of goto nishida and watanabe on symbolic rees algebras of monomial primes we prove that the moduli space of stable rational curves with n punctures is not a mori dream space for n 133 this answers a question posed by hu and keel

irrelevant operators in the two dimensional ising model by using conformal field theory we classify the possible irrelevant operators for the ising model with nearest neighbour interactions on the square and triangular lattices we analyse the existing results for the free energy and its derivatives and for the correlation length showing that they are in agreement with the conformal field theory predictions moreover these results imply that the nonlinear scaling field of the t operator where t is the energy momentum tensor vanishes at the critical point several other peculiar cancellations are explained in terms of a number of general conjectures we show that all existing results on the square and triangular lattices are consistent with the assumption that only nonzero spin operators are present

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

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 spectra of quantum chains with free boundary conditions and virasoro algebras at the critical point the spectra of quantum chains with periodic and twisted boundary conditions are described by irreducible representations of two virasoro algebras with the same central charge the authors show that in the case of free boundary conditions the spectra can be understood in terms of irreducible representations of a single virasoro algebra for the ising and the three state potts models the corresponding irreducible representations are identified

control aspects of linear discrete time varying systems results for time invariant linear systems concerning controllability reachability output controllability stabilizability and target path controllability are extended to time varying systems for the extensions which are already known in the literature elementary proofs are given moreover necessary and sufficient conditions are given for the strong admissibility of a target path

operator content of the three state potts quantum chain the authors compute the lowest excitations of the spectra of the three state potts quantum chain with periodic and twisted boundary conditions these spectra can be understood in terms of eighteen irreducible representations of the virasoro algebra with c 4 5

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

target path controllability of linear time varying dynamical systems the purpose of this paper is to derive necessary and sufficient conditions for target path controllability tpc of time varying dynamical systems and to relate the results to those of brockett and mesarovic in 1965 it is shown that conditions for tpc in w p 1 by means of lp controls are easy to verify but are very strong tpc implies that the number of target variables is less than or equal to the number of control variables

reproducibility of linear and nonlinear input output systems a control system may be viewed as effecting a transformation under fixed initial conditions of the input the control to the output the controls are to be chosen from a given family of functions and consequently the outputs are members of a set of functions this viewpoint may be extended in various ways for example the initial conditions may be allowed to vary within a given set alternatively one may start with a set of possible outputs and try to find one or more allowed controls and permissible initial conditions which will yield the set of outputs put concretely one can ask when a spacecraft starting at one of a set of initial conditions and steered by one of a set of prescribed controls can be made to follow any one of a family of curves with preassigned velocity this roughly is what is meant by reproducibility reproducibility has been studied extensively by a number of investigators 1 5 10 111 here we obtain necessary and sufficient conditions for the reproducibility of linear time varying as well as time invariant input output systems and

conformal invariance and correction to finite size scaling applications to the three state potts model corrections to finite size scaling are determined numerically for several levels of the three state potts quantum chain with various boundary conditions it is found that the leading correction term behaves like wo in the case of periodic and twisted boundary conditions the coefficients of the n o term are determined by the three point correlation functions of the conformal theory

constructing non mori dream spaces from negative curves abstract we study blowups of weighted projective planes at a general point and more generally blowups of toric surfaces of picard number one based on the positive characteristic methods of kurano and nishida we give a general method for constructing examples of mori dream spaces and non mori dream spaces among such blowups compared to previous constructions this method uses the geometric properties of the varieties and applies to a number of cases we use it to fully classify the examples coming from two families of negative curves

analytical and non analytical corrections to finite size scaling using conformal invariance the author calculates finite size corrections to the scaled spectra of one dimensional quantum chains at the critical point an explicit application to the ising and three state potts model gives good agreement with analytical and numerical results respectively

on blowing up the weighted projective plane we investigate the blow up of a weighted projective plane at a general point we provide criteria and algorithms for testing if the result is a mori dream surface and we compute the cox ring in several cases moreover applications to the study of overline m 0 n are discussed

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

path controllability of linear input output systems the varied definitions used in four studies of path controllability of linear input output systems are given their similarities and differences examined and some of their corresponding results compared and discussed

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified