local channels preserving the states without measurement induced nonlocality measurement induced nonlocality is a measure of nonlocality introduced recently by luo and fu we present here sufficient and necessary conditions for a quantum state for which this quantity is equal to zero furthermore it is shown that for such a state ab with any local channel acting on ha cannot create measurement induced nonlocality if and only if either it is a completely contractive channel or it is a nontrivial isotropic channel for the qubit case this property is an additional characteristic of the completely contractive channel or the commutativity preserving unital channel

a new domain decomposition method for an hjb equation in this paper we propose a new domain decompostion method for solving a hamilton jacobi bellman equation of second order the basic idea is to solve an equivalent quasivariational inequality instead of the original discretized hjb equation

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

discord and nonclassicality in probabilistic theories quantum discord quantifies nonclassical correlations in quantum states we introduce discord for states in causal probabilistic theories inspired by the original definition proposed by h ollivier and w h zurek phys rev lett 88 017901 2001 we show that the only probabilistic theory in which all states have null discord is classical probability theory non null discord is then not just a quantum feature but a generic signature of nonclassicality

a two level additive schwarz method for a kind of tensor complementarity problem abstract in this paper we present a two level additive schwarz method for a kind of tensor complementarity problem tcp the method is proved to be convergent monotonically and can reach the solution within finite steps we report some preliminary numerical results to test the efficiency of the proposed method

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

a domain decomposition method for a kind of optimization problems in this paper we are concerned with the monotone convergence of a multiplicative method for solving a kind of optimization problems we show that the iterate sequence produced by the method converges to the solution of the problem monotonically

a fuzzy approach for robust reference tracking control design of nonlinear distributed parameter time delayed systems and its application this paper addresses the robust reference tracking control problem for nonlinear distributed parameter systems ndpss with time delays external disturbances and measurement noises the ndps is measured at several sensor locations for output feedback tracking control a fuzzy spatial state space model derived via finite difference approach is introduced to represent the nonlinear distributed parameter time delayed system thus we use a fuzzy interpolation method with several local linear systems to approximate the nonlinear system and employ the finite difference method to approximate the partial differential operators in fuzzy spatial state space model based on this model a robust fuzzy observer based reference tracking controller is proposed to control the ndps to track a desired reference trajectory first a 2 d tracking performance in a spatiotemporal domain is proposed for robust tracking design of nonlinear distributed parameter time delayed systems then an equivalent 1 d reference tracking design is developed to simplify the design procedure and the linear matrix inequality lmi technique is applied to solve the control gains and observer gains for the robust tracking design problem via a systematic control design procedure finally a tracking control design example for the nervous system is given to confirm the proposed reference tracking control scheme of nonlinear distributed parameter time delayed systems

additive schwarz algorithm for the nonlinear complementarity problem with m function in this paper an additive schwarz algorithm is considered for solving the finite dimensional nonlinear complementarity problem with m function the monotone convergence of the algorithm is obtained with special choices of initial values moreover the weighted max norm bound is obtained for the iterative errors

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

rate of convergence for some constraint decomposition methods for nonlinear variational inequalities some general subspace correction algorithms are proposed for a convex optimization problem over a convex constraint subset one of the nontrivial applications of the algorithms is the solving of some obstacle problems by multilevel domain decomposition and multigrid methods for domain decomposition and multigrid methods the rate of convergence for the algorithms for obstacle problems is of the same order as the rate of convergence for jump coefficient linear elliptic problems in order to analyse the convergence rate we need to decompose a finite element function into a sum of functions from the subspaces and also satisfying some constraints a special nonlinear interpolation operator is introduced for decomposing the functions

weighted max norm estimate of additive schwarz iteration scheme for solving linear complementarity problems in this paper we consider an algebraic additive schwarz iteration scheme for solving the finite dimensional linear complementarity problem that involves an m matrix the scheme contains some existing algorithms as special cases we establish monotone convergence of the iteration scheme under appropriate conditions moreover using the concept of weak regular splitting we estimate weighted max norm bounds for iteration errors thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point

vanishing quantum discord is necessary and sufficient for completely positive maps two long standing open problems in quantum theory are to characterize the class of initial system bath states for which quantum dynamics is equivalent to i a map between the initial and final system states and ii a completely positive cp map the cp map problem is especially important due to the widespread use of such maps in quantum information processing and open quantum systems theory here we settle both these questions by showing that the answer to the first is all with the resulting map being hermitian and that the answer to the second is that cp maps arise exclusively from the class of separable states with vanishing quantum discord

channel optimized quantum error correction we develop a theory for finding quantum error correction qec procedures which are optimized for given noise channels our theory accounts for uncertainties in the noise channel against which our qec procedures are robust we demonstrate via numerical examples that our optimized qec procedures always achieve a higher channel fidelity than the standard error correction method which is agnostic about the specifics of the channel this demonstrates the importance of channel characterization before qec procedures are applied our main novel finding is that in the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction we show this using a general rank minimization heuristic and supporting numerical calculations therefore one can further improve the fidelity by utilizing all the available ancillas in the encoding block

convergence analysis ofgeneralized schwarz algorithms for solving obstacle problems with t monotone operator this paper proves the convergence of some generalized schwarz algorithms for solvingthe obstacle problems with a t monotone operator numerical results show that the generalized schwarz algorithms converge faster than the classical schwarz algorithms

on monotone and geometric convergence of schwarz methods for two sided obstacle problems convergence of schwarz methods is discussed for certain discretizations of two sided obstacle problems monotone and especially geometrical convergence are established if the stiffness matrix is a kind of m matrix and an h independent convergence rate is proved for uniformly overlapping decomposition

domain decomposition method for a parabolic variational inequality abstract in this paper we propose a domain decomposition method for the euler galerkin approximation of a parabolic variational inequality it is proved that the convergence rate of the algorithm is independent of the space meshsize h and the time stepsize

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

monotonic iterative algorithms for an implicit two sided obstacle problem abstract in this paper we present some iterative algorithms mainly schwarz algorithms for an implicit two sided obstacle problem the monotonic convergence of the algorithms is proved

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

two sided estimates of minimum error distinguishability of mixed quantum states via generalized holevo curlander bounds we prove a concise factor of 2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states generalizing work of holevo theor probab appl 23 411 1978 and curlander ph d thesis mit 1979 a modification to the minimal principle of cocha and poor proceedings of the 6th international conference on quantum communication measurement and computing rinton princeton nj 2003 is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction this measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by je ek et al phys rev a 65 060301 2002 unlike the so called pretty good measurement it coincides with holevo s asymptotically optimal measurement in the case of nonequiprobable pure states a quadratically weighted version of the measurement bound by barnum and knill j math phys 43 2097 2002 is proven bounds on the distingu

output tracking control for fuzzy systems via output feedback design fuzzy observer based control design is proposed to deal with the output tracking problem for nonlinear systems for the purpose of tracking design the new concept of virtual desired variables and in turn the so called generalized kinematics are introduced to simplify the design procedure in light of this concept the design procedure is split into two steps i determine the virtual desired variables from the generalized kinematics and ii determine the control gains just like solving linear matrix inequalities for stabilization problem for immeasurable state variables output feedback design is proposed here we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a lipschitz like property based on this setting control gains and observer gains can be designed separately moreover zero tracking error and estimation error are concluded three different types of systems including nonlinear mass spring systems dc dc converters and induction motors are considered to demonstrate the design procedure their satisfactory simulation results verify the proposed approach

electrical stimulation tracking control for paraplegic patients using t s fuzzy models abstract this paper presents the design and simulation results considering the use of functional electrical stimulation to control the leg position of paraplegic patients the plant is described by a nonlinear system using takagi sugeno fuzzy models and a closed loop control is presented a transfer function represents the mathematical model related to the muscle torque and the electrical stimulation pulse width considering that during the operation the leg position is between 0 and 60 then two fuzzy regulators were designed assuming that the state vector is available or using an observer when only the output is available this design was based on the lyapunov stability theory and linear matrix inequalities lmis the simulation results show that the proposed procedures are efficient and offer good results for this control problem finally new conditions regarding the design of the output tracking control using a suitable nonlinear transformation for the description of the plant in an adequate form is presented

a cone programming approach to the bilinear matrix inequality problem and its geometry we discuss an approach for solving the bilinear matrix inequality bmi based on its connections with certain problems defined over matrix cones these problems are among others the cone generalization of the linear programming lp and the linear complementarity problem lcp referred to as the cone lp and the cone lcp respectively specifically we show that solving a given bmi is equivalent to examining the solution set of a suitably constructed cone lp or cone lcp this approach facilitates our understanding of the geometry of the bmi and opens up new avenues for the development of the computational procedures for its solution

some remarks on assignment maps we study the properties of general linear assignment maps showing that positivity axiom can be suitably relaxed and propose a new class of dynamical maps generalized dynamics a puzzling result arising in such a context in quantum information theory is also discussed

two sided bounds on minimum error quantum measurement on the reversibility of quantum dynamics and on maximum overlap using directional iterates in a unified framework we estimate the following quantities of interest in quantum information theory 1 the minimum error distinguishability of arbitrary ensembles of mixed quantum states 2 the approximate reversibility of quantum dynamics in terms of entanglement fidelity this is referred to as channel adapted quantum error recovery when applied to the composition of an encoding operation and a noise channel 3 the maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state and 4 the conditional min entropy of bipartite quantum states a refined version of the author s techniques j tyson j math phys 50 032016 2009 for bounding the first quantity is employed to give two sided estimates of the remaining three quantities we obtain a closed form approximate reversal channel using a state dependent kraus decomposition our reversal may be interpreted as a quadratically

generalizations of quantum discord the original definition of quantum discord of bipartite states was defined over projective measurements in this paper we discuss some generalizations of it these generalizations are defined over general measurements rank 1 general measurements or neumark extension measurements we investigate the non negativity zero discord sets of all these quantum discords and some properties of them

an iterative algorithm for a quasivariational inequality system related to hjb equation this paper presents a new iterative algorithm for a quasivariational inequality system related to hjb equation a domain decomposition method based on this algorithm is proposed the convergence theorems have been established

robust quantum error correction via convex optimization we present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel our approach allows us to optimize the encoding recovery or both and is amenable to approximations that significantly improve computational cost while retaining fidelity we illustrate our theory numerically for optimized 5 qubit codes using the standard 5 1 3 code as a benchmark our optimized encoding and recovery yields fidelities that are uniformly higher by 1 2 orders of magnitude against random unitary weight 2 errors compared to the 5 1 3 code with standard recovery

on switched regulator design of uncertain nonlinear systems using takagi sugeno fuzzy models this paper is concerned with the design of state feedback switched controllers for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models the proposed methodology eliminates the need to find the membership function expressions to implement the control law which is relevant in cases where the membership function depends on uncertain parameters the design of the switched controllers is based on a minimum type lyapunov function and the minimization of the time derivative of this lyapunov function the conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities bmis that has been solved by the path following method a numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure

asynchronous domain decomposition methods for continuous casting problem two asynchronous domain decomposition methods which appear to be a two stage schwarz alternating algorithms to solve the finite difference schemes approximating dynamic continuous casting problem are theoretically and numerically studied fully implicit and semi implicit implicit for the diffusion operator while explicit for the nonlinear convective term finite difference schemes are considered unique solvability of the finite difference schemes as well as a monotone dependence of the solution on the right hand side the so called comparison theorem are proved geometric rate of convergence for the iterative methods is investigated the comparison theorem being the main tool of this study numerical results are included and analyzed

on the schwarz alternating method with more than two subdomains for nonlinear monotone problems in a hilbert space an iterative process is defined which generalizes the schwarz alternating method for nonlinear monotone problems to more than two subdomains and the convergence of this process is proved in the case of the problems with the solution in a convex of h 0 1 omega it is proved that the method converges geometrically numerical results are given concerning the problem of elastic plastic torsion of prismatic bars and the problem of seepage of fluids through porous media

a multiplicative schwarz iteration scheme for solving the linear complementarity problem with an h matrix in this paper we consider an algebraic multiplicative schwarz iteration scheme for solving the linear complementarity problem that involves an h matrix we show that the sequence generated by the multiplicative schwarz iteration scheme converges to the unique solution of the problem without any restriction on the initial point for different overlapping sizes the convergence rate of the proposed method is analyzed in an algebraic setting moreover we establish monotone convergence of the proposed method under appropriate conditions numerical results show that efficiency can be achieved by the multiplicative schwarz iteration scheme

convergence rate analysis of an asynchronous space decomposition method for convex minimization we analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive banach space this method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations in particular the method generalizes the additive schwarz domain decomposition methods to allow for asynchronous updates it also generalizes the bpx multigrid method to allow for use as solvers instead of as preconditioners possibly with asynchronous updates and is applicable to nonlinear problems applications to an overlapping domain decomposition for obstacle problems are also studied the method of this work is also closely related to relaxation methods for nonlinear network flow accordingly we specialize our convergence rate results to the above methods the asynchronous method is implementable in a multiprocessor system allowing for communication and computation delays among the processors

generalized schwarz algorithm for obstacle problems abstract in this paper we present so called generalized additive and multiplicative schwarz algorithms for solving the discretization problems of obstacle problems with a self adjoint elliptic operator we establish convergence theorems for the proposed algorithms numerical tests show that a faster convergence rate can be obtained by choosing suitable parameters in the algorithms

convergence analysis of p1 finite element method for free boundary problems on non overlapping subdomains abstract the paper applies a conforming p1 finite element method to general variational inequalities derived from free boundary problems the domain of the free boundary problem can be properly split into two non overlapping subdomains where the free boundary is located in only one subdomain the variational inequality is reduced to a partial differential equation in the subdomain which does not contain the free boundary but still keeps its original form in the other subdomain therefore the original variational inequality can be discretized separately with p1 finite element in different subdomains a non overlapping domain decomposition method is introduced to solve these two discretized sub problems by p1 finite element method iteratively while a robin type boundary condition is utilized for the data transfer on the common boundary we show that the sequence of such finite element solutions converges to the discretized solution of the original problem application to a free seepage problem verifies the theory

reference state for arbitrary u consistent subspace the reduced dynamics of the system s interacting with the environment e is not given by a linear map in general however if it is given by a linear map then this map is also hermitian in order that the reduced dynamics of the system is given by a linear hermitian map there must be some restrictions on the set of possible initial states of the system environment or on the possible unitary evolutions of the whole se in this paper adding an ancillary reference space r we assign to each convex set of possible initial states of the system environment for which the reduced dynamics is hermitian a tripartite state which we call the reference state such that the set is given as the steered states from the reference state the set of possible initial states of the system is also given as the steered set from a bipartite reference state the relation between these two reference states is as where is the identity map on r and is a hermitian assignment map from s to se as an important consequence of introducing the reference state we generalize the result of buscemi 2014 phys rev lett 113 140502 we show that for a u consistent subspace the reduced dynamics of the system is completely positive for arbitrary unitary evolution of the whole system environment u if and only if the reference state is a markov state in addition we show that the evolution of the set of system environment system states is determined by the evolution of the reference state

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

an additive schwarz method for variational inequalities this paper proposes an additive schwarz method for variational inequalities and their approximations by finite element methods the schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain the result is based on an framework of convergence analysis established for general variational inequalities in hilbert spaces

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

on the rank minimization problem over a positive semidefinite linear matrix inequality we consider the problem of minimizing the rank of a positive semidefinite matrix subject to the constraint that an affine transformation of it is also positive semidefinite our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice this problem is of importance in many contexts for example in feedback synthesis problems and such an example is also provided