duality relations and equilibrium crystal shapes of potts models on triangular and honeycomb lattices abstract we consider the q state potts models on triangular and honeycomb lattices for each lattice it is shown that the anisotropic interfacial tension is related to the anisotropic correlation length on the dual lattice using the star triangle transformation we also find that the anisotropic correlation length on the triangular lattice is the same as that of the honeycomb lattice for q 4 at the first order transition point the anisotropic correlation length is exactly calculated at the first order transition point by a method which introduces auxiliary edges into the models from the calculated anisotropic correlation length the equilibrium droplet shape of one ordered phase embedded inside another is derived via the wulff construction the equilibrium shape is written as a simple algebraic curve which corresponds to the dispersion relation of bound states in the terminology of spin chains

two dimensional alternating turing machines abstract this paper introduces a two dimensional alternating turing machine 2 atm which can be considered as a natural extension of a one dimensional alternating turing machine to two dimensions this paper also introduces a three way two dimensional alternating turing machine tr2 atm which is an alternating version of a three way two dimensional turing machine we first investigate a relationship between the accepting powers of space bounded 2 atm s or tr2 atm s and ordinary space bounded two dimensional turing machines or three way two dimensional turing machines we then introduce a simple natural new complexity measure for 2 atm s or tr2 atm s called leaf size and provide a spectrum of complexity classes based on leaf size bounded computations we finally investigate recognizability of connected patterns by 2 atm s or tr2 atm s

a note on three way two dimensional alternating turing machines abstract we investigate the properties of three way two dimensional alternating turing machines tr2 atms which are restricted versions of ordinary four way two dimensional alternating turing machines 2 atms we first show that 2 atms are more powerful than tr2 atms with spaces below log m then we investigate the closure properties of tr2 atms on square and general rectangular input tapes finally we show that o log m space bounded tr2 atms cannot accept the set of all square connected pictures

tracking control for nonaffine systems a self organizing approximation approach this paper considers tracking control for single input single output nonaffine dynamic systems a performance dependent self organizing approximation based approach is proposed the designer specifies a positive tracking error criterion the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification even though the system is not affine the approach is defined such that the approximated function is independent of the control variable u stability is proved and the self organization is derived in a lyapunov based methodology to illustrate certain novel aspects of the proposed controller a numerical example is included

anisotropic correlation length in the eight vertex model we investigate the directional dependence or anisotropy of the correlation length of the eight vertex model by a method which introduces the shift operator into the usual transfer matrix argument for a given x 0 x 1 there are two cases with respect to a parameter q in the case 0 q x3 the anisotropic correlation length acl is independent of q noting that the eight vertex model factors into two ising lattices in the q x4 limit we can directly relate the acl to that of the square lattice ising model when x3 q x2 the acl depends on q using an algebraic curve we show that the acl in this case is connected with that of the ising model on a 4 8 or union jack lattice we suggest that a wide class of models have essentially the same acl as the eight vertex model has

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

self organizing cmac control for a class of mimo uncertain nonlinear systems this paper presents a self organizing control system based on cerebellar model articulation controller cmac for a class of multiple input multiple output mimo uncertain nonlinear systems the proposed control system merges a cmac and sliding mode control smc so the input space dimension of cmac can be simplified the structure of cmac will be self organized that is the layers of cmac will grow or prune systematically and their receptive functions can be automatically adjusted the control system consists of a self organizing cmac socm and a robust controller socm containing a cmac uncertainty observer is used as the principal controller and the robust controller is designed to dispel the effect of approximation error the gradient descent method is used to online tune the parameters of cmac and the lyapunov function is applied to guarantee the stability of the system a simulation study of inverted double pendulums system and an experimental result of linear ultrasonic motor motion control show that favorable tracking performance can be achieved by using the proposed control system

anisotropic interfacial tension and the equilibrium crystal shape of kagome lattice eight vertex model we exactly calculate the anisotropic interfacial tension of the kagome lattice eight vertex model with the help of two types of square lattice models each square lattice model is inhomogeneous but still possesses a one parameter family of commuting transfer matrices from the anisotropic interfacial tension the equilibrium shape of an inclusion of one ordered phase in an environment of another is obtained by applying the wulff construction calculations are expressed by the use of differential forms on a riemann surface of genus 1 and the equilibrium shape is written as an elliptic curve we suggest the possibility of interpreting critical phenomena in terms of the moduli space of riemann surfaces of genus 1

equilibrium crystal shape of the potts model at the first order transition point we investigate the q state two dimensional potts model the anisotropic interfacial tension is related by duality to the anisotropic correlation length for q 4 we calculate exactly the anisotropic correlation length at the first order transition point from the calculated anisotropic correlation length the equilibrium crystal shape ecs is derived via the wulff construction the ecs is expressed by means of a simple algebraic curve regarding q as a temperature scale we show that the potts model has the same ecs as the eight vertex model we discuss a connection between the ecs and the q deformed pseudo euclidian algebra

inversion identities for the self dual potts and ashkin teller models the commuting diagonal to diagonal transfer matrices of the self dual potts and ashkin teller models on the square lattice are shown to satisfy special functional equations called inversion identities these identities generalise the known local inversion or unitarity relations for interaction round a face or irf models satisfying yang baxter or star triangle equations

a space hierarchy result on two dimensional alternating turing machines with only universal states abstract this paper investigates a space hierarchy of the classes of sets accepted by alternating space bounded two dimensional turing machines which have only universal states and whose input tapes are restricted to square ones and shows that there exists a dense hierarchy for the classes of sets accepted by these turing machines with spaces of size less than or equal to log m

a leaf size hierarchy of two dimensional alternating turing machines abstract this paper introduces a simple natural complexity measure for space bounded two dimensional alternating turing machines called leaf size and provides a hierarchy of complexity classes based on leaf size bounded computations specifically we show that for any positive integer k 1 and for any two functions l n n and l n n such that 1 l is a two dimensionally space constructible function such that l m k 1 m m 1 2 lim m l m l m k log m 0 and 3 lim m l m l m 0 l m space bounded and l m k leaf size bounded two dimensional alternating turing machines are more powerful than l m space bounded and l m k leaf size bounded two dimensional alternating turing machines

six vertex model with rotated boundary conditions we investigate the six vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes a model recently introduced by litvin and priezzhev auxiliary vertices are used to define an inhomogeneous system which leads to a one parameter family of commuting transfer matrices a product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system using an equation for commuting transfer matrices we calculate their eigenvalues finite size properties of the model are discussed from the viewpoint of the conformal field theory

three dimensional alternating turing machines with only universal states abstract we investigate several properties of three dimensional alternating turing machines whose input tapes are restricted to cubic ones we first investigate the relationship between the classes of sets accepted by space bounded and finitely leaf size bounded five way three dimensional alternating turing machines and the classes of sets which are finite intersections of sets accepted by space bounded five way three dimensional nondeterministic turing machines then we investigate the accepting powers of three dimensional alternating turing machines with only universal states

the correlation length of the potts model at the first order transition point the authors consider the q state two dimensional potts model for q g i e in the first order phase transition regime following a scheme given by p martin 1991 the authors prove an identity between the spectra of the transfer matrices of the potts model and the transfer matrices connecting the diagonals of a 6 vertex model by using a bethe ansatz for the latter they obtain an exact expression for the correlation length of the potts model at the transition point

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

robust self organizing neural fuzzy control with uncertainty observer for mimo nonlinear systems this paper proposes a robust self organizing neural fuzzy control rsonfc scheme for a class of uncertain nonlinear multiple input multiple output mimo systems we first develop a self organizing neural fuzzy network sonfn with concurrent structure and parameter learning the fuzzy rules of sonfn are generated or pruned systematically the proposed rsonfc scheme comprises an sonfn identifier an uncertainty observer and a supervisory controller the sonfn identifier functions as the principal controller and the uncertainty observer is designed to oversee uncertainties within the compound system the supervisory controller combines sliding mode control smc and an adaptive bound estimation scheme with various weights to achieve h tracking performance with a desired level of attenuation projection type adaptation laws of network parameters developed using the lyapunov s synthesis approach guarantee the stability of the overall control system simulation studies on a single link flexible joint manipulator and a two link robot demonstrate the effectiveness of the proposed control scheme

auxiliary vertices method for kagome lattice eight vertex model we investigate a class of eight vertex models on a kagome lattice with the help of auxiliary vertices the kagome lattice eight vertex model kevm is related to an inhomogeneous system which leads to a one parameter family of commuting transfer matrices using an equation for commuting transfer matrices we determine their eigenvalues from calculated eigenvalues the correlation length of the kevm is derived with its full anisotropy there are two cases in the first case the anisotropic correlation length acl is the same as that of the triangular honeycomb lattice ising model by the use of an algebraic curve it is shown that the kagome lattice ising model the diced lattice ising model and the hard hexagon model also have essentially the same acl as the kevm in the second case we find that the acl displays 12fold rotational symmetry

a hierarchy result for 2 dimensional tm s operating in small space abstract a two dimensional turing machine 2 tm is a tm with a two dimensional input tape whose input head can move in all four directions we show that if s n is a two dimensionally space constructible function such that s n log n and t n is a function satisfying t n o s n then there is a language i e set of square patterns over some finite alphabet that is accepted by a strongly s n space bounded 2 dtm but not by any strongly t n space bounded 2 atm this partially answers a question posed by inoue and takanami since functions such as log n loglog n logloglog n are all two dimensionally space constructible this result implies a rich space hierarchy for strongly o log n space bounded 2 atm s

deterministic two dimensional on line tessellation acceptors are equivalent to two way two dimensional alternating finite automata through 180 rotation abstract a two way two dimensional alternating finite automaton tw2 afa is a two dimensional alternating finite automation whose input head can move right and down or may not move but cannot move left or up let 2 dota denote a two dimensional deterministic on line tesselation acceptor in this paper we show that 2 dota s are equivalent to tw2 afa s through 180 rotation

eight vertex model anisotropic interfacial tension and equilibrium crystal shape the anisotropic interfacial tension of the eight vertex model is found by a new method which introduces two inhomogeneous systems as the width of the system becomes large a doublet of the largest eigenvalues of the row row transfer matrix is asymptotically degenerate the anisotropic interfacial tension is calculated from their finite size correction terms in this limit by the use of the anisotropic interfacial tension the equilibrium crystal shape of the eight vertex model is derived via wulff s construction the equilibrium crystal shape is represented as a simple algebraic curve we discuss the close relation between the algebraic curve and the form of an elliptic function appearing in the expression of the interfacial tension

spatial anisotropy and rotational invariance of critical hard squares we develop a new method to analyse solvable models defined on a square lattice rotated through an arbitrary angle phi with respect to the coordinate axes in the method we introduce auxiliary faces into a rotated system to relate it with an inhomogeneous one in the natural orientation phi 0 the inhomogeneous system is investigated by commuting a transfer matrix argument as an application of the method we consider interacting hard squares at the critical point we discuss relations between spatial anisotropy and rotational or conformal invariance of the model in calculations of finite size properties

equilibrium crystal shape of hard squares with diagonal attractions the author exactly calculates the anisotropic interfacial tension of a square lattice gas model with nearest neighbour exclusion and next nearest neighbour attractions this is achieved by a method which introduces the shift operator into the standard transfer matrix argument from the calculated anisotropic interfacial tension the equilibrium crystal shape ecs is derived by the use of the wulff construction the ecs is a closed curve in the x y plane represented as cosh lambda x y kbt a3cosh lambda x y kbt a4 2 0 with a scale factor lambda and constants a3 a4 he argues that this shape is a universal one which appears as the ecss of a wide class of models