an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

exponential stabilization for 1 d linear ito type state dependent stochastic parabolic pde systems via static output feedback abstract this paper deals with the problem of exponential stabilization for 1 d linear stochastic parabolic partial differential equation pde systems with state multiplicative noise in the form of ito type a static output feedback sof control scheme is proposed to stabilize the stochastic pde system in a stochastic framework via locally collocated piecewise uniform actuators and sensors the closed loop well posedness analysis is provided by virtue of the semi group theory based on the infinite dimensional infinitesimal operator and lyapunov technique the sof controller design is developed to guarantee the exponential stability of the resulting closed loop system in the mean square sense finally simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method

block truncation coding with entropy coding block truncation coding btc is a simple and fast image compression algorithm which achieves a constant bit rate of 2 0 bits per pixel the method is however suboptimal we propose a modification of btc in which the compression ratio is improved by coding the quantization data and the bit plane by arithmetic coding with an adaptive modelling scheme the results compare favorable with other btc variants the bit rate for test image lena is 1 53 bits per pixel with a mean square error of 16 51

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

deformed systems at finite temperature abstract we apply the formalism of thermo field dynamics to two kinds of deformed hamiltonians these hamiltonians are made up of operators which satisfy deformed heisenberg algebras the entropy and the specific heat are computed for small q 1 where q is the deformation parameter

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

d type anticipatory iterative learning control for a class of inhomogeneous heat equations in this paper a d type anticipatory iterative learning control ilc scheme is applied to the boundary control of a class of inhomogeneous heat equations where the heat flux at one side is the control input while the temperature measurement at the other side is the control output by transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded jacobi theta functions the learning convergence of ilc is guaranteed through rigorous analysis without any simplification or discretization of the 3d dynamics in the time space as well as iteration domains the adopted ilc scheme makes full use of the process repetition and deals with state independent or state dependent uncertainties meanwhile due to the feedforward characteristic of ilc the proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking but also eliminates the gain margin limitation encountered in feedback control in the end an illustrative example is presented to demonstrate the performance of the proposed ilc scheme

q deformed classical lie algebras and their anyonic realization all classical lie algebras can be realized a la schwinger 1965 in terms of fermionic oscillators we show that the same can be done for their q deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice the deformation parameter q is a phase related to the anyonic statistical parameter a crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones the entire procedure works even on one dimensional chains in such a case q can also be real

stability analysis of linear partial differential equations with generalized energy functions we present a method for the stability analysis of a large class of linear partial differential equations pdes in one spatial dimension we rely on lyapunov analysis to establish the exponential stability of the systems under consideration the proposed test for the verification of the underlying lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations we illustrate the application of this method using a pde actuated by a backstepping computed feedback law furthermore for the case of pdes defined by polynomial data we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically we show the effectiveness of the proposed numerical methodology using examples of different types of pdes

exponential stabilization of the uncertain wave equation via distributed dynamic input extension the wave equation is studied under the effect of a persistent external perturbation a dynamical distributed controller is suggested based on an infinite dimensional generalization of second order sliding mode control techniques that provides the exponential attainment of a sufficiently smooth arbitrary reference of the state trajectory the control system comprises of both feedforward and feedback parts the latter being a discontinuous term directly connected to the plant input through a dynamical filter that augments the system state smoothing out the discontinuity of the feedback control loop as a result a continuous input is applied to the plant a constructive lyapunov based proof of convergence of the proposed control algorithm is carried out and supporting numerical results are presented

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

pointwise exponential stabilization of a linear parabolic pde system using non collocated pointwise observation this paper deals with the problem of exponential stabilization for a linear distributed parameter system dps using pointwise control and non collocated pointwise observation where the system is modeled by a parabolic partial differential equation pde the main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic pde system using the non collocated pointwise observation the observer based output feedback control technique is utilized to overcome the design difficulty caused by the non collocation pointwise observation we construct a luenberger type pde state observer to exponentially track the state of the pde system a collocated pointwise feedback controller is proposed based on the estimated state a variation of poincare wirtinger inequality is derived and the spatial domain is decomposed into multiple sub domains according to the number of the actuators and sensors by using lyapunov s direct method integration by parts and the variation of poincare wirtinger inequality at each sub domain sufficient conditions for the existence of the observer based out feedback controller are developed such that the resulting closed loop system is exponentially stable and presented in terms of standard linear matrix inequalities lmis furthermore the closed loop well posedness analysis is also provided by the semigroup approach extensive numerical simulation results are presented to show the performance of the proposed output feedback controller

planck distribution for a q boson gas the energy density distributions for bosons obeying the q deformation of the harmonic oscillator algebra have been studied in order to obtain some physical insight into the parameter q the action of this parameter on the energy distributions resembles the action of the temperature parameter in the classical planck law q 1

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

on the class of possible non local anyon like operators and quantum groups we find a class of non local operators constructed by attaching a disorder operator to fermionic degrees of freedom which can be used to generate q deformed algebras following the schwinger approach this class includes anyonic operators defined on a lattice

event based control of linear hyperbolic systems of conservation laws in this article we introduce event based boundary controls for 1 dimensional linear hyperbolic systems of conservation laws inspired by event triggered controls developed for finite dimensional systems an extension to the infinite dimensional case by means of lyapunov techniques is studied the main contribution of the paper lies in the definition of two event triggering conditions by which global exponential stability and well posedness of the system under investigation is achieved some numerical simulations are performed for the control of a system describing traffic flow on a roundabout

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

a two parametric quantization of sl 2 a two parametric solution of the constant yang baxter equation is used for the construction of structures corresponding to quantized groups the corresponding hopf algebra is generated by five generators

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity