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

universal finite size scaling amplitudes on a torus for the triangular ising lattice gas recently the author suggested studying the scaling properties of complex two dimensional phase transitions by calculating the universal amplitudes of interfacial free energies on a torus geometry employing monte carlo simulations he tests this method at the 3 3 phase transition in the ising lattice gas on a triangular lattice belonging to the chiral three state potts universality class the interfacial free energies for this lattice gas model can be written in terms of free energy differences between systems with different sizes the algorithm to calculate these free energy differences is presented using lattice sizes up to 18 18 and modest computing effort he finds that the universal amplitude a 1 220 02 in accordance with the exact analytical value for the non chiral three state potts model a 1 203291 which he determined earlier

generalized sphere packing bound kulkarni and kiyavash recently introduced a new method to establish upper bounds on the size of deletion correcting codes this method is based upon tools from hypergraph theory the deletion channel is represented by a hypergraph whose edges are the deletion balls or spheres so that a deletion correcting code becomes a matching in this hypergraph consequently a bound on the size of such a code can be obtained from bounds on the matching number of a hypergraph classical results in hypergraph theory are then invoked to compute an upper bound on the matching number as a solution to a linear programming problem the problem of finding fractional transversals the method by kulkarni and kiyavash can be applied not only for the deletion channel but also for other error channels this paper studies this method in its most general setup first it is shown that if the error channel is regular and symmetric then the upper bound by this method coincides with the well known sphere packing bound and thus is called here the generalized sphere packing bound even though this bound is explicitly given by a linear programming problem finding its exact value may still be a challenging task the art of finding the exact upper bound or slightly weaker ones is the assignment of weights to the hypergraph s vertices in a way that they satisfy the constraints in the linear programming problem in order to simplify the complexity of the linear programming we present a technique based upon graph automorphisms that in many cases significantly reduces the number of variables and constraints in the problem we then apply this method on specific examples of error channels we start with the z channel and show how to exactly find the generalized sphere packing bound for this setup next studied is the nonbinary limited magnitude channel both for symmetric and asymmetric errors where we focus on the single error case we follow up on the deletion channel which was the original motivation of the work by kulkarni and kiyavash and show how to improve upon their upper bounds for single deletion correcting codes since the deletion and grain error channels have a similar structure for a single error we also improve upon the existing upper bounds on single grain error correcting codes finally we apply this method for projective spaces and find its generalized sphere packing bound for the single error case

geometry of the limit sets of linear switched systems this paper is concerned with asymptotic stability properties of linear switched systems under the hypothesis that all the subsystems share a nonstrict quadratic lyapunov function we provide a large class of switching signals for which a large class of switched systems are asymptotically stable for this purpose we define what we call nonchaotic inputs which generalize the different notions of inputs with dwell time next we turn our attention to the behavior for possibly chaotic inputs finally we give a sufficient condition for a system composed of a pair of hurwitz matrices to be asymptotically stable for all inputs

c 1 conformal field theories on riemann surfaces we study the theory ofc 1 torus and 2 orbifold models on general riemann surfaces the operator content and occurrence of multi critical points in this class of theories is discussed the partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered riemann surfaces it is shown that orbifold partition functions are sensitive to the torelli group we give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces modular transformations are naturally incorporated as canonical transformations in the hilbert space

an extension of lasalle s invariance principle for switched systems in this paper we address invariance principles for a certain class of switched nonlinear systems we provide an extension of lasalle s invariance principle for these systems and state asymptotic stability criteria we also present some related results on the compactness of the trajectories of these switched systems

a refinement of matrosov s theorem for differential inclusions this note presents a refinement of matrosov s theorem for a class of differential inclusions whose set valued map is defined as a closed convex hull of finitely many vector fields this class of systems may arise in the analysis of switched nonlinear systems when stability with arbitrary switching between the given vector fields is considered assuming uniform global stability of a compact set it is shown that uniform global attractivity of the set can be verified by tailoring matrosov functions to individual vector fields this refinement of matrosov s theorem is an extension of the existing matrosov results which may be easier to apply to certain differential inclusions than existing results as demonstrated by an example

pasquier models at c 1 cylinder partition functions and the role of the affine coxeter element we calculate the partition functions of the affine pasquier models on the cylinder in the continuum limit we show that the partition function of any affine model may be expressed in terms of the orbit structure of an affine coxeter element of the weyl group associated with the defining graph of the model some of the consequences of this geometric relationship are explored

on the convergence of linear switched systems this paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems we provide a collection of results that use weak dwell time dwell time strong dwell time permanent and persistent activation hypothesis the obtained results are shown to be tight by counterexample finally we apply our result to the three cell converter

phase diagram in the generalized chiral clock models abstract using the results of the integrable chiral potts model we speculate about the possible phase diagram of the generalized chiral clock model in the integrable model it is found that the chiral fields are almost proportional to one another here we consider a chiral model with all the chiral fields exactly proportional to one another with fixed proportionality constants given by the integrable case this reduces the chiral field variables to just one denoted by the model thus defined includes the generalized clock model or z n model at 0 or 1 2 and the chiral clock models as special cases using the results of many authors on the z n model in the so called symmetric case with vertical and horizontal interactions equal and the behavior of the system at t 0 we can get a pretty good picture of the phase diagram of this chiral model the exact results show that the commonly held belief that the massless phase in the z n model for n 5 is in the same universality class as the classical xy model and the belief that the commensurate incommensurate phase transition is of the pokrovskii talapov type and the incommensurate fluid transition is of kosterlitz thouless type may not be correct as universality may not even hold on these phase boundaries

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

symmetries of perturbed conformal field theories the symmetries of perturbed conformal field theories are analysed we explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field we also study the behaviour of d branes under current current bulk deformations we find that the branes always continue to preserve as much symmetry as they possibly can i e as much as is preserved in the bulk we illustrate these findings with several examples including permutation branes in wzw models and b type d branes in gepner models

operator content of n state quantum chains in the c 1 region the authors conjecture the operator content for n state quantum chains n or 5 in the domains of the coupling constants where the central charge of the virasoro algebra is equal to one free boundary conditions as well as boundary conditions compatible with the torus are considered the conjectured operator content is compared with finite size scaling estimates

invariance principles for switched systems with restrictions in this paper we consider switched nonlinear systems with otherwise arbitrary compact index sets and subjected to different switching constraints we present invariance principles for these systems and derive by using observability like notions some convergence and asymptotic stability criteria these results enable us to analyze the stability of solutions of switched systems with restrictions originating from the timing of the switchings state dependent constrained switching and switching whose logic has memory i e the active subsystem can only switch to a prescribed subset of subsystems

partition functions of the two dimensional ashkin teller model on the critical line by mapping the ashkin teller model onto a scalar free field theory the author derives the continuum limit of the partition functions in various finite geometries he justifies expressions which have been conjectured recently explaining in particular why the free field lives on an orbifold and why the spin should be described by a twist operator

operator content of the multicritical magnetic hard square model the transfer matrix spectra of the magnetic hard squares along the multicritical line are analysed using the data for the strip width n up to 12 the operator content of the model is exactly the same as that of the ashkin teller model when n is odd the spectrum is accounted for by the continuum theory in which the antiperiodic boundary condition is imposed to one of the ising variables of the ashkin teller model

new bounds and constructions for granular media coding improved lower and upper bounds on the size and the rate of grain correcting codes are presented the lower bound is gilbert varshamov like combined with a construction by gabrys et al and it improves on the previously best known lower bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval 0 0 0668 one of the two newly presented upper bounds improves on the best known upper bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval tau in 0 1 8 and meets the lower bound of 1 2 for tau geq 1 8 moreover in a nonasymptotic regime both upper bounds improve on the previously best known results on the largest size of t grain correcting codes of length n for certain values of n and t constructions of 1 grain correcting codes based on a partitioning technique are presented for lengths up to 18 finally a lower bound of 1 2 log 2 n on the minimum redundancy of infty grain detecting codes of length n is presented

brief paper on the algebraic characterization of invariant sets of switched linear systems in this paper a suitable lasalle principle for continuous time linear switched systems is used to characterize invariant sets and their associated switching laws an algorithm to determine algebraically these invariants is proposed the main novelty of our approach is that we require no dwell time conditions on the switching laws by not focusing on restricted control classes we are able to describe the asymptotic properties of the considered switched systems observability analysis of a flying capacitor converter is proposed as an illustration

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

global stability results for switched systems based on weak lyapunov functions in this paper we study the stability of nonlinear and time varying switched systems under restricted switching we approach the problem by decomposing the system dynamics into a nominal like part and a perturbation like one most stability results for perturbed systems are based on the use of strong lyapunov functions i e functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state however switched systems under restricted switching may not admit strong lyapunov functions even when asymptotic stability is uniform over the set of switching signals considered the main contribution of the current paper consists in providing stability results that are based on the stability of the nominal like part of the system and require only a weak lyapunov function these results may have wider applicability than results based on strong lyapunov functions the results provided follow two lines first we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal like and the perturbation like parts of the system second we provide input to state stability iss results for the case when the nominal like part is switched linear time varying we provide two types of iss results standard iss that involves the essential supremum norm of the input and a modified iss that involves a power type norm

an extension of lasalle s invariance principle for a class of switched linear systems in this paper lasalle s invariance principle for switched linear systems is studied unlike most existing results in which each switching mode in the system needs to be asymptotically stable in this paper the switching modes are allowed to be only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability of switched linear systems is proposed provided that the kernels of derivatives of a common quadratic lyapunov function with respect to the switching modes are disjoint except the origin

the c 2 3 minimal n 1 superconformal system and its realisation in the critical o 2 gaussian model the structure of the 2 3 minimal n 1 superconformal system is analysed in detail the primary operators are constructed as operators in the critical o 2 gaussian model at some specific fixed radius the operator algebra is verified explicitly operator product coefficients and some superspace correlation functions are calculated exactly

analyzing the stability of switched systems using common zeroing output systems this paper introduces the notion of common zeroing output systems czos to analyze the stability of switched systems the concept of czos allows one to verify weak zero state detectability it characterizes a common behavior of any individual subsystem when the output signal for each subsystem is approaching zero heuristically speaking it removes the effect of switching behavior and thus enables one to analyze stability properties in systems with complex switching signals with the help of czos the krasovskii lasalle theorem can be extended to switched nonlinear time varying systems with both arbitrary switching and more general restricted switching cases for switched nonlinear time invariant systems the needed detectability condition is further simplified leading to several new stability results particularly when a switched linear time invariant system is considered it is possible to generate a recursive method which combines a krasovskii lasalle result and a nested matrosov result to find a czos if it exists the power of the proposed czos is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions

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

operator content of the ashkin teller quantum chain superconformal and zamolodchikov fateev invariance ii boundary conditions compatible with the torus for pt i see ibid vol 20 no 8 p l479 85 1987 the authors present the operator content of the ashkin teller quantum chain with eight boundary conditions corresponding to the eight elements of the group d4 which gives the global symmetry of the system this operator content is a conjecture based on an extensive numerical study and was proven to be correct at the ising decoupling point for the values of the coupling constant where n 2 superconformal invariance was seen for free boundary conditions the situation is now more complex one finds sectors which have n 2 and n 1 superconformal invariance and sectors which have no superconformal invariance at all if however they combine the wrong sectors of the spectra which correspond to two different values of the coupling constant a new symmetry shows up they also analyse the operator content at the fateev zamolodchikov points here the wrong sectors can be described by a few new primary fields

magnetization at corners in two dimensional ising models we investigate the corner spin magnetization of two dimensional ferromagnetic ising models in various wedge geometries results are obtained for triangular and square lattices by numerical studies on finite wedges using the star triangle transformation as well as analytic calculations using corner transfer matrices and a fermionic representation of the row to row transfer matrix the corner magnetizations vanish at the bulk critical temperature tc with an exponent c differing from the bulk exponent for isotropic systems with free edges we find that c is given simply by c 2 where is the angle at the corner for apex magnetizations of conical lattices we obtain the strikingly similar result a 4 these formulas apply equally well to anisotropic lattices if the angle is interpreted as an effective angle eff determined by the relative strengths of the interactions

operator content of the cyclic solid on solid models the operator content of the cyclic solid on solid models is derived under general boundary conditions by mapping the row to row transfer matrix onto the six vertex model and xxz heisenberg chain for the shift boundary conditions the dimensions and spins of the primary operators are derived analytically from finite size corrections to the scaling spectra the full operator content agrees with results for a quantum chain model having the same local symmetry

operator content of the ising model with three spin coupling the ising quantum chain with staggered three spin coupling is studied for free and toroidal boundary conditions the operator content of the finite size limit of the spectra is conjectured it is found to be related to the operator content of the ashkin teller model 1943

operator content of the four state potts quantum chain with z3 boundary conditions the four state potts quantum chain with a toroidal boundary condition leaving a global z3 symmetry of the hamiltonian is investigated at the critical point the infinite system shows su 2 kac moody symmetry the conjectured operator content is confirmed by numerical finite size calculations

boundary conditions and inversion indentities for solvable lattice models with a sublattice symmetry the transfer matrices of solvable lattice spin models are considered under general boundary conditions associated with the symmetry of the models it is shown how the full symmetry can be exploited for systems having a sublattice symmetry by considering an extended model where the states distinguish the sublattices in this extended scheme the parity of the number of sites is tied to the boundary conditions the inversion identities can be extended and be used to obtain the full operator content of the critical models as an application the complete spectra of the transfer matrices for the eight vertex model at the decoupling point are calculated

conformal invariance in incommensurate phases we study finite size corrections to the free energy of free fermion models on a torus with periodic twisted and fixed boundary conditions inside the critical striped incommensurate phase the free energy densityf n m on ann m square lattice with periodic or twisted boundary conditions scales asf n m f a s nm we derive exactly the finite size scaling fss amplitudesa s as a function of the aspect ratios m n these amplitudes are universal because they do not depend on details of the free fermion hamiltonian we establish an equivalence between the fss amplitudes of the free fermion model and the coulomb gas system with electric and magnetic defect lines the twist angle generates magnetic defect lines while electric defect lines are generated by competition between domain wall separation and system size the fss behavior of the free fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec l for instance the fss amplitude on an infinite cylinder with fixed boundary conditions is found to be one quarter of that with periodic boundary conditions finally we conjecture the exact form of the fss amplitudes for an interacting fermion model on a torus numerical calculations employing the bethe ansatz confirm our conjecture in the infinite cylinder limit

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

uniform asymptotic stability of switched nonlinear time varying systems and detectability of reduced limiting control systems this paper is concerned with the study of both local and global uniform asymptotic stability for switched nonlinear time varying nltv systems through the detectability of output maps with this aim the notion of reduced limiting control systems for switched nltv systems whose switchings verify time state dependent constraints and the concept of weak zero state detectability for those reduced limiting systems are introduced necessary and sufficient conditions for the global uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property these sufficient conditions in conjunction with the existence of multiple weak lyapunov functions yield a criterion for the global uniform asymptotic stability of families of trajectories of the switched system this criterion can be seen as an extension of the classical krasovskii lasalle theorem an interesting feature of the results is that no dwell time assumptions are made moreover they can be used for establishing the global uniform asymptotic stability of the switched nltv system under arbitrary switchings the effectiveness of the proposed results is illustrated by means of various interesting examples including the stability analysis of a semiquasi z source inverter

invariance principles for switching systems via hybrid systems techniques invariance principles and sufficient conditions for asymptotic stability for switching systems are given multiple lyapunov like functions are used and dwell time persistent dwell time and weak dwell time switching signals are considered the invariance principles are derived from general invariance principles for hybrid systems asymptotic stability is concluded under observability assumptions or common bounds on the lyapunov like functions

symmetry respecting real space renormalization for the quantum ashkin teller model we use a simple real space renormalization group approach to investigate the critical behavior of the quantum ashkin teller model a one dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously this approach which is based on exploiting the on site symmetry of the model has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse field ising model our investigation explores this approach in more generality in a model in which the critical behavior has a richer structure but which reduces to the simpler ising case at a special point we demonstrate that the correlation length critical exponent as predicted from this real space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality near the ising special point the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods although the accuracy decreases away from the decoupled ising model point

logarithmic singularity in the surface free energy near commensurate incommensurate transitions the authors study finite size scaling behaviour of a two dimensional random tiling model this model exhibits commensurate incommensurate phase transitions of the pokrovsky talapov type where anisotropic scaling appears a simple scaling argument near this transition suggests an integral surface critical exponent which in turn implies a logarithmic singularity with a universal coefficient in the surface free energy they confirm the existence of this singularity numerically employing the transfer matrix method in the case of free boundary conditions

correlation functions of the critical ashkin teller model on a torus the correlation functions of the critical ashkin teller model on a torus are calculated using a free bosonic field formulation in the continuum limit the results include in particular correlators of electromagnetic or twist operators various applications are discussed

operator content of c 1 conformal zn field theories it is shown that the operator content of frustrated sectors of c 1 zn invariant conformal field theories including the n to oi limit the xxy model can be obtained from the field theory of a free massless boson with appropriate boundary conditions it is also shown that for frustrated boundary conditions the requirement of modular invariance is substituted by definite transformation properties of the partition function under the modular group which are satisfied by the partition function constructed

finite size scaling and conformal invariance in a self dual quantum z 5 model considers the critical behaviour of a particular set of onedimensional self dual models with z n symmetry n or 5 the critical indices are evaluated using standard finite size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance the results strongly suggest that the recently introduced z n quantum field theory is the underlying field theory for these statistical mechanics models

linear programming based converses for finite blocklength lossy joint source channel coding a linear programming lp based framework is presented for obtaining converses for finite blocklength lossy joint source channel coding problems the framework applies for any loss criterion generalizes certain previously known converses and also extends to multi terminal settings the finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift and project like method a close but tractable lp relaxation of this problem is derived lower bounds on the original problem are obtained by the construction of feasible points for the dual of the lp relaxation a particular application of this approach leads to new converses which recover and improve on the converses of kostina and verdu for finite blocklength lossy joint source channel coding and lossy source coding for finite blocklength channel coding the lp relaxation recovers the converse of polyanskiy poor and verdu and leads to a new improvement on the converse of wolfowitz showing thereby that our lp relaxation is asymptotically tight with increasing blocklengths for channel coding lossless source coding and joint source channel coding with the excess distortion probability as the loss criterion using a duality based argument a new converse is derived for finite blocklength joint source channel coding for a class of source channel pairs employing this converse the lp relaxation is also shown to be tight for all blocklengths for the minimization of the expected average symbolwise hamming distortion of a q ary uniform source over a q ary symmetric memoryless channel for any q in mathbb n the optimization formulation and the lift and project method are extended to networked settings and demonstrated by obtaining an improvement on a converse of zhou et al for the successive refinement problem for successively refinable source distortion measure triplets

toroidal boundary conditions in n state quantum chains the author considers one dimensional n state quantum chains having as symmetry an abelian group a of order n generalised ising chain these hamiltonians depend on 2 n 1 coupling constants for special values of the coupling constants the symmetry of the quantum chains is larger than a corresponding to a in general non abelian group g with m elements m n for each element of g he finds explicitly a boundary condition which leaves the hamiltonian translationally invariant this problem is relevant in finite size scaling studies at the critical point of a second order phase transition

on weak invariance principles for nonlinear switched systems in this technical note we develop two weak invariance principles for nonlinear switched systems we first present a union weak invariance principle for switched systems which includes as a special case the integral invariance principle it is shown that the switched solution approaches the largest weakly invariant set of the combined zero loci of the output functions then we extend the union weak invariance principle to an intersection weak invariance principle which greatly reduces the convergence region unlike the existing results in which the constructions of lyapunov functions are inevitable our principles do not require the existence of lyapunov functions numerical examples are presented to demonstrate the feasibility of our principles as well as applications to multi agent consensus problems

uniform asymptotic stability of nonlinear switched systems with an application to mobile robots this paper is concerned with the study of both local and global uniform asymptotic stability for general nonlinear and time varying switched systems two concepts of lyapunov functions are introduced and used to establish uniform lyapunov stability and uniform global stability with the help of output functions an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability based on this result a generalized version of krasovskii lasalle theorem in time varying switched systems is proposed for switched systems with persistent dwell time the output persistent excitation condition is guaranteed to hold under a zero state observability condition it is shown that several existing results in past literature can be covered as special cases using the proposed criteria interestingly as opposed to previous work the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin the robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria a novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots

nonasymptotic upper bounds for deletion correcting codes explicit nonasymptotic upper bounds on the sizes of multiple deletion correcting codes are presented in particular the largest single deletion correcting code for q ary alphabet and string length is shown to be of size at most qn q q 1 n 1 an improved bound on the asymptotic rate function is obtained as a corollary upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length and this idea is demonstrated by application to sets of run length limited strings the problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph this problem is formulated as an integer linear program the upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program the nonasymptotic bounds derived imply the known asymptotic bounds of levenshtein and tenengolts and improve on known nonasymptotic bounds numerical results support the conjecture that in the binary case the varshamov tenengolts codes are the largest single deletion correcting codes

hunting for the central charge of the virasoro algebra six and eight state spin models in two dimensions conformal invariance has important implications for the finite size scaling properties of the spectra of transfer matrices and quantum chains at the critical point some relations between the finite size scaling amplitudes are obtained which can be used as a test of conformal invariance and implicitly to distinguished between second order and first order phase transitions the numerical values of the scaling amplitudes give the scale dimensions of various operators six and eight state self dual quantum chains with cubic symmetries are considered at the critical point for three values of the coupling constant the systems are found to be conformal invariant and estimates for several critical exponents are obtained based on the approximate values of the critical exponent one tries to find the values of the corresponding central charges of the virasoro algebras

a generalization of krasovskii lasalle theorem for nonlinear time varying systems converse results and applications this paper presents a practically applicable characterization of uniform global asymptotic stability uas and ugas for general nonlinear time varying systems under certain output dependent conditions in the spirit of the krasovskii lasalle theorem the celebrated krasovskii lasalle theorem is extended from two directions one is using the weak zero state detectability property associated with reduced limiting systems of the system in question to generalize the condition that the maximal invariance set contained in the zero locus of the time derivative of the lyapunov function is the zero set another one is using an almost bounded output energy condition to relax the assumption that the time derivative of the lyapunov function is negative semi definite then the uas and ugas properties of the origin can be guaranteed by employing these two improved conditions related to certain output function for uniformly lyapunov stable systems the proposed conditions turn out to be also necessary under some mild assumptions and thus give a new characterization of ugas and uas through an equivalence relation the proposed detectability condition can also be verified in terms of usual pe condition to validate the proposed results the obtained stability criteria are applied to a class of time varying passive systems and to revisit a tracking control problem of nonholonomic chained systems for the latter under certain persistency of excitation conditions the k exponential stability is achieved based on our approach

finite size scaling amplitudes in a random tiling model we study finite size corrections to the free energy in a two dimensional random tiling model this model is equivalent to an asymmetric six vertex model and exhibits commensurate incommensurate phase transitions of the pokrovsky talapov type we calculate finite size scaling amplitudes of the free energy inside the incommensurate phase analytically and numerically by employing a transfer matrix method both periodic and free boundary conditions are considered these amplitudes are consistent with predictions of the theory of conformal invariance with the conformal charge c 1

stability and persistent excitation in signal sets persistent excitation pe conditions have been widely used to analyze stability properties of various parameter identification algorithms and to establish uniform global asymptotic stability ugas for a large class of nonlinear time varying systems in order to generalize such conditions to a more general setting a new pe condition is proposed with three basic ingredients a signal set to represent a family of time functions e g trajectories a pseudo distance measure to describe the convergence and some binary relations e g state to output relations closely related to detectability this pe condition is a necessary condition to guarantee ugas under uniform global stability and an integral inequality it becomes a sufficient condition of ugas a novel concept m pair which aims at simplifying the checking of the pe condition is introduced by using m pair it is possible to simplify the structure of the referred signal set in the spirit of the classic krasovskii lasalle theorem and to extend the dimension of the reference signal set similar to the matrosov theorem thus the framework of m pair not only unifies these well known results but also generates more flexibility in checking the pe conditions when applied to nonlinear switched systems three new tools to verify the pe condition are obtained finally an example illustrates that a nonlinear time varying switched system with arbitrary switching can be shown to be ugas without using a common lyapunov function

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

relations between the coulomb gas picture and conformal invariance of two dimensional critical models partition functions of critical 2d models on a torus can be derived from their microscopic formulation and their free field representation in the continuum limit this is worked out explicitly for theo n andq state potts model forn orq integer we recover results obtained from conformal invariance but our procedure also extends to nonintegral values in the latter case the expansion on characters of the virasoro algebra involves real coefficients of either sign the operator content of both models is discussed in detail

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

off critical integrable vertex models and conformal theories in finite geometries the author calculates the order parameters local height probabilities in the ordered phase of integrable su n vertex models the author shows that they have formally the same expression as the partition functions of the associated critical theory in a finite box with appropriate boundary conditions once the distance to criticality in the former case is properly identified with the modular parameter in the latter this points out a relation between off critical integrable models and conformal theories in a finite geometry

conformal invariance studies of the baxter wu model and a related site colouring problem the partition function of the baxter wu model is exactly related to the generating function of a site colouring problem on a hexagonal lattice we extend the original bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions the operator content of these models is studied by solving numerically the bethe ansatz equations and by exploring conformal invariance since the eigenspectra are calculated for large lattices the corrections to finite size scaling are also calculated

the off critical integrable ashkin teller model the exact solution of an ashkin teller model with layer and spatial anisotropy and z2 z2 symmetry is presented the model is related to the eight vertex model by a sublattice or orbifold duality and it has the same free energy and magnetisation the exact solution manifold is a three dimensional submanifold of the full six dimensional thermodynamic space it admits a z3 symmetry relating three regimes each exhibiting different partial order in the spatially isotropic case these regimes are separated by three lines of continuously varying critical behaviour which coalesce at the four state potts critical point the magnetisations and polarisation are derived using corner transfer matrices giving rise to the appearance of chiral and virasoro characters the associated critical exponents confirm the known values in particular one obtains the value xsigma 1 8 for the magnetic scaling dimension and identify the next to leading thermal field

conformal invariance and line defects in the two dimensional ising model the quantum ising chain with p equidistant defects is studied the exact form of the hamiltonian is found for an infinite number of sites using conformal invariance generalised corner exponents are computed and found to depend continuously on the defect strengths realisations of extended conformal algebras in the hamiltonian spectrum are obtained