sl2 gaudin model with jordanian twist sl2 gaudin model with jordanian twist is studied this system can be obtained as the semiclassical limit of the xxx spin chain deformed by the jordanian twist the appropriate creation operators that yield the bethe states of the gaudin model and consequently its spectrum are defined their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given the inner products and norms of bethe states and the relation to the solutions of the knizhnik zamolodchikov equations are discussed

supersymmetric t j gaudin models and kz equations supersymmetric t j gaudin models with open boundary conditions are investigated by means of the algebraic bethe ansatz method off shell bethe ansatz equations of the boundary gaudin systems are derived and used to construct and solve the kz equations associated with sl 2 1 1 superalgebra

jordanian deformation of sl 2 as a contraction of its drinfeld jimbo deformation we introduce a contraction procedure for obtaining the jordanian deformation of sl 2 from its drinfeld jimbo deformation to be specific we obtain slh 2 its differential geometry and its star product from their q deformed counterparts we also present a transformation of the generators of uq sl 2 which in a limit yield the generators of uh sl 2

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

adaptive fuzzy control of nonlinear systems in pure feedback form based on input to state stability using mean value theorem and backstepping technique a robust adaptive fuzzy control scheme is proposed for a class of pure feedback nonlinear systems with unknown dead zone and disturbances via input to state stability takagi sugeno t s type fuzzy logic systems are used to approximate the uncertain nonlinear functions and fewer learning parameters need to be adjusted online based on small gain theorem the closed loop control system is proven to be semiglobally uniformly ultimately bounded and the tracking error converges to a neighborhood of zero by choosing appropriate parameters simulation results demonstrate the effectiveness of the control scheme

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

universal r matrices for non standard 1 1 quantum groups a universal quasi triangular r matrix for the non standard quantum 1 1 poincare algebra uziso 1 1 is deduced by imposing analyticity in the deformation parameter z a family uwgmu of quantum graded contractions of the algebra uziso 1 1 u ziso 1 1 is obtained quantum analogues of the two dimensional euclidean poincare and galilei algebras enlarged with dilations are contained in uwgmu as hopf subalgebras with two primitive translations universal r matrices for these quantum weyl similitude algebras and their associated quantum groups are constructed

creation operators and bethe vectors of the osp 1 2 gaudin model a gaudin model based on the orthosymplectic lie superalgebra osp 1 2 is studied the eigenvectors of the osp 1 2 invariant gaudin hamiltonians are constructed by algebraic bethe ansatz corresponding creation operators are defined by a recurrence relation furthermore explicit solution to this recurrence relation is found the action of the creation operators on the lowest spin vector yields bethe vectors of the model the relation between the bethe vectors and solutions to the knizhnik zamolodchikov equation of the corresponding super conformal field theory is established

adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead zone inputs this paper considers the problem of adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with mismatched external disturbances parameter uncertainties and nonsymmetric dead zone inputs without the help of the dead zone inverse function and by incorporating the implicit function theorem both the adaptive state feedback tracking controller and the adaptive output feedback tracking controller based on high gain observer are designed by utilizing fuzzy logic systems fls to approximate the appropriate nonlinear control input functions a compounded disturbance is defined in terms of the external disturbance parameter uncertainty nonsymmetric dead zone input and approximation error of fls under the condition that the upper bound of the compounded disturbance is unknown novel adaptive laws are introduced to estimate and tune the unknown controller parameters on line furthermore on the basis of lyapunov stability analysis it is also proved that the presented control methods can guarantee that all the closed loop system error signals are uniformly ultimately bounded finally two simulation examples are provided to demonstrate efficiency of the proposed adaptive fuzzy tracking control approaches

adaptive neural network tracking control of mimo nonlinear systems with unknown dead zones and control directions in this paper adaptive neural network nn tracking control is investigated for a class of uncertain multiple input multiple output mimo nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions it is shown that the dead zone output can be represented as a simple linear system with a static time varying gain and bounded disturbance by introducing characteristic function by utilizing the integral type lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead zone disturbance the closed loop control system is proved to be semiglobally uniformly ultimately bounded with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal simulation results demonstrate the effectiveness of the approach

the general uq sl 2 invariant xxz integrable quantum spin chain the boundary conditions are constructed for the general xxz quantum integrable spin chain such that the resulting system is invariant under the quantum algebra uq sl 2 action the result generalizes that due to pasquier and saleur 1990 obtained for spin 1 2 and spin 1

on integrable models related to the osp 1 2 gaudin algebra the osp 1 2 gaudin algebra is defined and integrable models described by it are considered the models include the osp 1 2 gaudin magnet and the dicke model related to it detailed discussion of the simplest cases of these models is presented the effect of the presence of fermions on the separation of variables is indicated

logarithmic voltage anomalies in random resistor networks the authors investigate the behaviour of the maximum voltage drop across the bonds in a random resistor network above the percolation threshold on the basis of numerical simulations on randomly diluted l l square lattice networks we find that the average value of the maximum voltage vmax p l exhibits a peak as a function of the bond concentration p which is located above the percolation threshold this peak value appears to grow logarithmically with l while the location of the peak appears to approach the percolation threshold very slowly as l increases to help understand these results they introduce the bubble model a quasi one dimensional structure in which the system length varies exponentially in the system width this model is exactly soluble and a rather good description of percolation in systems of greater than one dimension can be obtained moreover within the bubble model the peak value of the maximum voltage increases as in l while the peak location approaches the percolation threshold as in in l in l in good agreement with our numerical results

twisting cocycle for null plane quantized poincare algebra the twisting cocycle for a quantized poincare algebra introduced by ballesteros et al is evaluated the solution is obtained as a specific case of a formulated multidimensional generalization of the non standard jordanian quantization of sl 2

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

non standard quantum 1 1 poincare group a t matrix approach the hopf algebra dual form for the non standard uniparametric deformation of the 1 1 poincare algebra iso 1 1 is deduced in this framework the quantum coordinates that generate funw iso 1 1 define an infinite dimensional lie algebra the t matrix formalism is used to derive a universal r matrix for both uwiso 1 1 and funw iso 1 1 it is also shown how these results can be generalized for the triangular deformations of 1 1 poincare and galilei algebras that include a spacetime dilation generator

trigonometric osp 1 2 gaudin model the problems connected with gaudin models are reviewed by analyzing model related to the trigonometric osp 1 2 classical r matrix the eigenvectors of the trigonometric osp 1 2 gaudin hamiltonians are found using explicitly constructed creation operators the commutation relations between the creation operators and the generators of the trigonometric loop superalgebra are calculated the coordinate representation of the bethe states is presented the relation between the bethe vectors and solutions to the knizhnik zamolodchikov equation yields the norm of the eigenvectors the generalized knizhnik zamolodchikov system is discussed both in the rational and in the trigonometric case

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

brief paper adaptive output control of uncertain nonlinear systems with non symmetric dead zone input this paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non symmetric dead zone nonlinearity the nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states an adaptive control scheme is developed without constructing the dead zone inverse the proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead zone nonlinearity the novelty of this paper is that a universal type adaptive output feedback controller is numerically constructed by using a sum of squares sos optimization algorithm which ensures the boundedness of all the signals in the adaptive closed loop without knowing the growth rate of the uncertainties an example is presented to show the effectiveness of the proposed approach

adaptive output neural network control for a class of stochastic nonlinear systems with dead zone nonlinearities this paper investigates the problem of adaptive output neural network nn control for a class of stochastic nonaffine and nonlinear systems with actuator dead zone inputs first based on the intermediate value theorem a novel design scheme that converts the nonaffine system into the corresponding affine system is developed in particular the priori knowledge of the bound of the derivative of the nonaffine and nonlinear functions is removed then by employing nns to approximate the appropriate nonlinear functions the corresponding adaptive nn tracking controller with the adjustable parameter updated laws is designed through a backstepping technique furthermore it is shown that all the closed loop signals are bounded in probability and the system output tracking error can converge to a small neighborhood in the sense of a mean quartic value finally experimental simulations are provided to demonstrate the efficiency of the proposed adaptive nn tracking control method

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

structure of clusters generated by random walks the authors study the cluster structure resulting from a nearest neighbour random walk embedded in a d dimensional space each bond visited by the random walks is regarded as belonging to the cluster the diffusion exponent and the fracton dimensional of the fractal cluster in d 3 is found to be dw 3 5 or 0 1 and d 0 57 or 0 02 using a method of exact enumeration of random walks on these fractals

extended jordanian twists for lie algebras jordanian quantizations of lie algebras are studied using the factorizable twists for a restricted borel subalgebra b of sl n the explicit expressions are obtained for the twist element f universal r matrix and the corresponding canonical element t it is shown that the twisted hopf algebra uf b is self dual the cohomological properties of the involved lie bialgebras are studied to justify the existence of a contraction from the dinfeld jimbo quantization to the jordanian one the construction of the twist is generalized to a certain type of inhomogenious lie algebras

quantum heisenberg weyl algebras all lie bialgebra structures on the heisenberg weyl algebra are classified and explicitly quantized the complete list of quantum heisenberg weyl algebras so obtained includes new multiparameter deformations most of them being of the non coboundary type

generalized knizhnik zamolodchikov equations and isomonodromy quantization of the equations integrable via the inverse scattering transform maxwell bloch system with pumping canonical quantization of the isomonodromy solutions of equations integrable via the inverse scattering transform leads to generalized knizhnik zamolodchikov equations one can solve these equations by the off shell bethe ansatz method provided the knizhnik zamolodchikov equations are related with the highest weight representations of the corresponding lie algebras these solutions can be written in terms of multi variable generalizations of special functions of the hypergeometric type in this work we consider a realization of the above scheme for the maxwell bloch system with pumping quantum states for this system are found in terms of the multi variable confluent hypergeometric function

colored quantum universal enveloping algebras we define some new algebraic structures termed colored hopf algebras by combining the coalgebra structures and antipodes of a standard hopf algebra set h corresponding to some parameter set q with the transformations of an algebra isomorphism group g herein called color group such transformations are labeled by some color parameters taking values in a color set c we show that various classes of hopf algebras such as almost cocommutative coboundary quasitriangular and triangular ones can be extended into corresponding colored algebraic structures and that colored quasitriangular hopf algebras in particular are characterized by the existence of a colored universal r matrix satisfying the colored yang baxter equation the present definitions extend those previously introduced by ohtsuki which correspond to some substructures in those cases where the color group is abelian we apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple lie algebras considering several examples with fixed or varying parameters as a by product some of the matrix representations of colored universal r matrices derived in the present paper provide new solutions of the colored yang baxter equation which might be of interest in the context of integrable models

sliding mode control for a class of non affine nonlinear systems abstract the objective of this paper is to present a sliding mode control smc technique for a class of nonlinear and control non affine systems a rotor supported by a pair of magnetic bearings is introduced as a nonlinear system which is designed as a sequence of linear time varying ltv systems and iterated for each time the sliding surface is designed for each iterated ltv system by using the time response of the previous iteration the surface parameters are selected so that the poles of reduced order ltv system remain on the left hand side of the complex plane it is shown that the response of ltv approximations converges to the nonlinear system s response which is validated by using the non affine nonlinear dynamical equations of rotor active magnetic bearing system

stable adaptive control for nonlinear multivariable systems with a triangular control structure a stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators by utilizing the system triangular property integral type lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the decoupling matrix of the multivariable nonlinear system it is shown that stability of the adaptive closed loop system is guaranteed and transient performance is analytically quantized by mean square and l sub spl infin tracking error bound criteria

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

the group with grassmann structure uosp 1 2 the finite dimensional representations of the lie superalgebraosp 1 2 and the group with grassmann structureosp 1 2 have been studied the explicit expression of the projection operator of the superalgebraosp 1 2 has been found the operator permits an arbitrary finite dimensional representation to be expanded in the components multiple to the irreducible ones the clebsch gordan coefficients for the tensor product of two arbitrary irreducible representations have been obtained the matrix elements of the irreducible representations of the groupuosp 1 2 the analoque of the compact form of the grouposp 1 2 are studied the explicit form of these matrix elements the differential equations satisfied by them and the integral of their product have been found

new time type and space type non standard quantum algebras and discrete symmetries starting from the classical r matrix of the non standard or jordanian quantum deformation of the sl 2 algebra new triangular quantum deformations for the real lie algebras so 2 2 so 3 1 and iso 2 1 are simultaneously constructed by using a graded contraction scheme these are realized as deformations of conformal algebras of 1 1 dimensional spacetimes time and space type quantum algebras are considered according to the generator that remains primitive after deformation either the time or the space translation respectively furthermore by introducing differential difference conformal realizations these families of quantum algebras are shown to be the symmetry algebras of either a time or a space discretization of 1 1 dimensional wave and laplace equations on uniform lattices the relationship with the known lie symmetry approach to these discrete equations is established by means of twist maps

1 1 schrodinger lie bialgebras and their poisson lie groups all lie bialgebra structures for the 1 1 dimensional centrally extended schrodinger algebra are explicitly derived and proved to be of coboundary type therefore since all of them come from a classical r matrix the complete family of schrodinger poisson lie groups can be deduced by means of the sklyanin bracket all possible embeddings of the harmonic oscillator extended galilei and gl 2 lie bialgebras within the schrodinger classification are studied as an application new quantum hopf algebra deformations of the schrodinger algebra including their corresponding quantum universal r matrices are constructed

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

contraction of the gr s quantum group to its nonstandard analog and corresponding colored quantum groups the quantum group gr s provides a realization of the two parameter quantum glp q 2 which is known to be related to the two parameter nonstandard glh h 2 group via the contraction method we apply the contraction procedure to gr s and obtain a new jordanian quantum group gm k furthermore we provide a realization of glh h 2 in terms of gm k the contraction procedure is then extended to the colored quantum group glr 2 to yield a new jordanian quantum group glm 2 both gr s and gm k are then generalized to their colored versions which in turn provide similar realizations of glr 2 and glm 2

finite size electrical resistivity and resistance in fractals it is shown that from an ansatz recently proposed by dekeyser et al 1987 for anomalous diffusion and electrical resistance in fractals one can derive predictions for the relation between intensive resistivity and extensive resistance quantities in these structures which differ from the usually assumed forms numerical predictions for the ratio of finite size resistance to resistivity in percolation clusters in space dimensions 2 or d or 6 are made which are amenable to testing via e g monte carlo simulations

the quantum group glh 2 among all quantum group structures on the space mat 2 of 2 by 2 matrices how many have a central quantum determinant so that one can define quantum sl 2 out of quantum gl 2 up to isomorphism there are two such structures glq 2 and glh 2 the former is well known the latter is described in this letter

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

non standard quantum so 2 2 and beyond a new non standard quantization of the universal enveloping algebra of the split natural real form so 2 2 of d2 is presented some classical graded contractions of so 2 2 associated to a z2 z2 grading are studied and the automorphisms defining this grading are generalized to the quantum case thus providing quantum contractions of this algebra this produces a new family of non standard quantum algebras some of these algebras can be realized as 2 1 kinematical algebras we explicitly introduce a new deformation of poincare algebra which is naturally linked to the null plane basis another realization of these quantum algebras as deformations of the conformal algebras for the two dimensional euclidean galilei and minkowski spaces is given and its new properties are emphasized

fusion rules of the lowest weight representations of rm osp _q 1 2 at roots of unity polynomial realization the degeneracy of the lowest weight representations of the quantum superalgebra and their tensor products at exceptional values of q is studied the main features of the structures of the finite dimensional lowest weight representations and their fusion rules are illustrated using realization of group generators as finite difference operators acting in the space of the polynomials the complete fusion rules for the decompositions of the tensor products at roots of unity are presented the appearance of indecomposable representations in the fusions is described using clebsh gordan coefficients derived for general values of q and at roots of unity

the a 2 2 gaudin model and its associated knizhnik zamolodchikov equation the semiclassical limit of the algebraic bethe ansatz for the izergin korepin 19 vertex model is used to solve the theory of gaudin models associated with the twisted a 2 2 r matrix we find the spectra and eigenvectors of the n 1 independents gaudin hamiltonians we also use the off shell bethe ansatz method to show how the off shell gaudin equation solves the associated trigonometric system of knizhnik zamolodchikov equations

cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time varying actuator faults in this paper the cooperative adaptive fault tolerant fuzzy tracking control caftftc problem of networked high order multiagent with time varying actuator faults is studied and a novel caftftc scheme is proposed to guarantee that all follower nodes asymptotically synchronize a leader node with tracking errors converging to a small adjustable neighborhood of the origin in spite of actuator faults the leader node is modeled as a higher order nonautonomous nonlinear system it acts as a command generator giving commands only to a small portion of the networked group each follower is assumed to have nonidentical unknown nonlinear dynamics and the communication network is also assumed to be a weighted directed graph with a fixed topology a distributed robust adaptive fuzzy controller is designed for each follower node such that the tracking errors are cooperative uniform ultimate boundedness cuub moreover these controllers are distributed in the sense that the controller designed for each follower node only requires relative state information between itself and its neighbors the adaptive compensation term of the optimal approximation errors and external disturbances is adopted to reduce the effects of the errors and disturbances which removes the assumption that the upper bounds of unknown function approximation errors and disturbances should be known analysis of stability and parameter convergence of the proposed algorithm are conducted that are based on algebraic graph theory and lyapunov theory comparing with results in the literature the caftftc scheme can minimize the time delay between fault occurrence and accommodation and reduce its adverse effect on system performance in addition the ftc scheme requires no additional fault isolation model which is necessary in the traditional active ftc scheme finally an example is provided to validate the theoretical results

the gervais neveu felder equation for the jordanian quasi hopf uh y sl 2 algebra using a contraction procedure we construct a twist operator that satisfies a shifted cocycle condition and leads to the jordanian quasi hopf uh y sl 2 algebra the corresponding universal h y matrix obeys a gervais neveu felder equation associated with the uh y sl 2 algebra for a class of representations the dynamical yang baxter equation may be expressed as a compatibility condition for the algebra of the lax operators

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non symmetric dead zone nonlinearities this paper is concerned with the problem of robust adaptive fuzzy tracking controller design for a class of uncertain nonaffine nonlinear systems with external disturbances and non symmetric dead zone nonlinearities with the help of fuzzy logic systems flss to approximate the desired nonlinear functions a novel direct adaptive tracking control scheme is established first the implicit function theorem and the mean value theorem are used to deal with the nonaffine term with unknown dead zone input then based on the estimation information for the unknown upper bound of the compounded disturbance an adaptive fuzzy tracking controller with the corresponding parameter updating laws is designed to eliminate the effect of the compounded disturbance furthermore it is proved that all the resulting closed loop system signals are uniformly bounded and the tracking error can asymptotically converge to zero via the lyapunov stability analysis finally a numerical example is provided to verify the effectiveness of the proposed adaptive fuzzy asymptotic tracking design method

representations and clebsch gordan coefficients for the jordanian quantum algebra representation theory for the jordanian quantum algebra is developed closed form expressions are given for the action of the generators of on the basis vectors of finite dimensional irreducible representations it is shown how representation theory of has a close connection to the combinatorial identities involving summation formulae a general formula is obtained for the clebsch gordan coefficients of these clebsch gordan coefficients are shown to coincide with those of su 2 for but for they are in general a non zero monomial in

boson representations non standard quantum algebras and contractions a gelfan d dyson mapping is used to generate a one boson realization for the non standard quantum deformation of which directly provides its infinite and finite dimensional irreducible representations tensor product decompositions are worked out for some examples relations between contraction methods and boson realizations are also explored in several contexts so a class of two boson representations for the non standard deformation of is introduced and contracted to the non standard quantum 1 1 poincar representations likewise a quantum extended hopf algebra is constructed and non standard quantum oscillator algebra representations are obtained from it by means of another contraction procedure

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

algebraic bethe ansatz for deformed gaudin model the gaudin model based on the sl2 invariant r matrix with an extra jordanian term depending on the spectral parameters is considered the appropriate creation operators defining the bethe states of the system are constructed through a recurrence relation the commutation relations between the generating function t of the integrals of motion and the creation operators are calculated and therefore the algebraic bethe ansatz is fully implemented the energy spectrum as well as the corresponding bethe equations of the system coincide with the ones of the sl2 invariant gaudin model as opposed to the sl2 invariant case the operator t and the gaudin hamiltonians are not hermitian finally the inner products and norms of the bethe states are studied

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

command filter based adaptive fuzzy backstepping control for a class of switched nonlinear systems abstract this paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems the considered switched nonlinear systems contain unknown nonlinearities the switching signals with average dwell time and without requiring that state variables are available for measurement fuzzy logic systems are used to approximate the unknown nonlinearities and a fuzzy switched state observer is designed to estimate the immeasurable states in the framework of observer based output feedback control design technique and by introducing a command filter into the backstepping design algorithm a command filter based adaptive fuzzy backstepping output feedback control scheme is developed the stability of the closed loop system and the convergence of the tracking error are proved via average dwell time and multiple lyapunov function a numerical example is provided to illustrate the effectiveness of the proposed approach

self avoiding walk model for proteins a real space renormalisation group treatment diffusion on the model for proteins introduced by helman coniglio and tsallis 1984 hct is discussed using real space renormalisation group ideas the authors perform cell to cell transformations in two dimensions for both the hct model and the self avoiding walk the latter system is quasi linear and so they expect trivial diffusive behaviour given by dw 2df 8 3 diffusion on the hct model however is complicated by the possibility of jumps across nearest neighbour hydrogen bond bridges the authors results are not consistent with the prediction that dw 2 for the hct model rather they support the assertion that dwhct is close to but slightly greater than dwsaw

dynamical weyl groups and applications abstract following a preceding paper of tarasov and the second author we define and study a new structure which may be regarded as the dynamical analog of the weyl group for lie algebras and of the quantum weyl group for quantized enveloping algebras we give some applications of this new structure

jordanian quantum algebra h sl n via contraction method and mapping using a contraction procedure developed earlier we construct in the first part of the present paper the jordanian quantum hopf algebra h sl 3 which has a remarkably simple coalgebraic structure and contains the jordanian algebra h sl 2 obtained by ohn as a hopf subalgebra a nonlinear map between the quantum h sl 3 and the classical sl 3 algebras is then established and the universal h matrix of the h sl 3 algebra is given in the second part we give the higher dimensional jordanian algebras h sl n for all n the universal h matrix of the h sl n algebra is also given

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

a jordanian quantum two photon schrodinger algebra a non standard quantum deformation of the two photon algebra is constructed and its quantum universal r matrix is given representations of this new quantum algebra are studied on the fock space and translated into fock bargmann realizations that provide a direct formalism for the definition of deformed states of light finally the isomorphism between and the 1 1 schrodinger algebra is used to introduce a new non standard hopf algebra deformation of this latter symmetry algebra

irreducible decomposition for tensor product representations of jordanian quantum algebras tensor products of irreducible representations of the jordanian quantum algebras and are considered for both the highest weight finite dimensional representations of and the lowest weight infinite dimensional ones of it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding lie algebras

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

duality for the jordanian matrix quantum group we find the hopf algebra dual to the jordanian matrix quantum group as an algebra it depends only on the sum of the two parameters and is split into two subalgebras with three generators and with one generator the subalgebra is a central hopf subalgebra of the subalgebra is not a hopf subalgebra and its co algebra structure depends on both parameters we discuss also two one parameter special cases g h and g h the subalgebra is a hopf algebra and coincides with the algebra introduced by ohn as the dual of the subalgebra is isomorphic to u sl 2 as an algebra but has a nontrivial co algebra structure and again is not a hopf subalgebra of

quantum jordanian twist the quantum deformation of the jordanian twist q for the standard quantum borel algebra uq b is constructed it gives the family uq b of quantum algebras depending on parameters and h in a generic point these algebras represent the hybrid standard nonstandard quantization the quantum jordanian twist can be applied to the standard quantization of any kac moody algebra the corresponding classical r matrix is a linear combination of the drinfeld jimbo and the jordanian ones the two parametric families of hopf algebras obtained here are smooth and for the limit values of the parameters the standard and nonstandard quantizations are recovered the twisting element q also has correlated limits in particular when q tends to unity it acquires the canonical form of the jordanian twist to illustrate the properties of the quantum jordanian twist we construct the hybrid quantizations for u sl 2 and for the corresponding affine algebra the universal quantum matrix and its defining representation are presented

separation of variables in the elliptic gaudin model for the elliptic gaudin model a degenerate case of the xyz integrable spin chain a separation of variables is constructed in the classical case the corresponding separated coordinates are obtained as the poles of a suitably normalized baker akhiezer function the classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed the simplest one degree of freedom case is studied in detail

universal r matrix for non standard quantum a universal r matrix for the non standard jordanian quantum deformation of is presented a family of solutions of the quantum yang baxter equation is obtained from some finite dimensional representations of this lie bialgebra quantization of