antifield antibracket formulation of the anti brst transformation the antifield antibracket implementation of the anti brst transformation is given for an arbitrary irreducible gauge invariant action as in the hamiltonian case this is done by duplicating the gauge symmetries and by constructing directly the sum of the brst and anti brst transformations the gauge fixing process is then derived along the lines of the standard antifield antibracket formalism this establishes the equivalence of both formulations in a straightforward way a brief discussion of the reducible case is also reported

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

invex equilibrium problems in this paper we introduce a new class of equilibrium problems known as invex equilibrium problems in the setting of invexity this class of equilibrium problems includes equilibrium problems variational inequalities and variational like inequalities as special cases we use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions we also consider the concept of well posedness for invex equilibrium problems our results represent significant and important refinements of the previously known results

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

birkhoff formula for conformal compressions of symmetric cones in this paper we derive the birkhoff formula for conformal compressions on symmetric cones let v be a euclidean jordan algebra and let be the associated symmetric cone then admits a natural finsler metric contracted by any conformal compressions of we show that the lipschitz constant of a conformal compression of is equal to the hyperbolic tangent of one fourth of the diameter of the image this is the same relation which was obtained by birkhoff on positive reals and by liverani and wojtkowski on the space of positive definite real matrices

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

extended brst quantization of gauge theories in the generalized canonical formalism the rules of canonical quantization of gauge theories are formulated on the basis of the extended brst symmetry principle the existence of solutions of the generating equations of the gauge algebra is proved equivalence between the extended brst quantization and the standard method of generalized canonical quantization is established ward identities corresponding to invariance of a theory under the extended brst symmetry are obtained

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

asymptotics for parametric garch in mean models abstract in this paper we develop an asymptotic theory for the quasi maximum likelihood estimator qmle of the parametric garch in mean model the asymptotics is based on a study of the volatility as a process of the model parameters the proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model nevertheless our theory does not yet treat all standard specifications of the mean function

popov type criterion for stability of nonlinear sampled data systems this paper studies input output stability of nonlinear sampled data systems with a sector nonlinearity a stability condition of circle criterion type was derived recently for the case where the sector nonlinearity is possibly time varying and dynamical in contrast this paper deals with the case where it is time invariant and memoryless and gives a less conservative stability criterion for such a case it is derived by applying the multiplier technique and corresponds to the popov criterion in the continuous time setting the arguments make use of the frequency domain theory of sampled data systems and a sort of convexity in the frequency domain plays an important role a method with the cutting plane algorithm is provided for finding a multiplier that proves stability an illustrative example is also given

the positive definite solution of the nonlinear matrix equation xp a m b x1 1m we consider the nonlinear matrix equation xp a m b x1 1m where p1 is a positive integer m is an arbitrary nn matrix and a and b are hermitian positive semidefinite matrices an elegant estimate of the hermitian positive definite hpd solution is derived a fixed point iteration and an inversion free variant iteration for obtaining the hpd solution are proposed some numerical examples are presented to show the efficiency of the proposed two iterative methods

generalized invex monotonicity abstract in this paper the generalized invex monotone functions are defined as an extension of monotone functions a series of sufficient and necessary conditions are also given that relate the generalized invexity of the function with the generalized invex monotonicity of its gradient function this new class of functions will be important in order to characterize the solutions of the variational like inequality problem and mathematical programming problem

basic properties and characterizations of incremental stability prioritizing flow time for a class of hybrid systems abstract this paper introduces incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints the specific class of hybrid systems considered are those that do not have consecutive jumps nor zeno behavior the notion of incremental asymptotic stability is used to describe the behavior of the distance between every pair of solutions to the system having stable behavior incremental stability and approaching zero asymptotically incremental attractivity a version of this notion that is uniform in hybrid time with respect to initial conditions is also introduced these notions prioritize flow time and are illustrated in examples basic properties of the class of systems are considered and those implied by the new notions are revealed an equivalence characterization of the uniform notion is provided in terms of a k l function moreover sufficient and necessary conditions under which asymptotic stability implies the new incremental notions are provided we consider the case when the original hybrid system has an asymptotically stable compact set and also the case when an auxiliary hybrid system which has twice the dimension of the original system has a diagonal like set asymptotically stable

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

kalman filtering with intermittent observations convergence for semi markov chains and an intrinsic performance measure this technical note shows that the stationary distribution for the covariance of kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models semi markov chain these results are proved using the geometric properties of riccati recursions with respect to a particular riemannian distance moreover the riemannian mean induced by that distance is always bounded therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist other interesting properties of that mean include the symmetry between covariance and information matrices averaging covariances or their inverse gives the same result and its interpretation in information geometry as the natural mean for the manifold of gaussian distributions

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

the generalized quasi variational inequality problem over non compact sets abstract in this note we shall prove new existence results for the generalized quasi variational inequality problem which includes as particular cases all the existing generalizations of the classical variational inequality problem

distortion outage analysis for joint space time coding and kalman filtering in this paper we consider the scenario of transmitting a first order gauss markov vector signal over a multi input multi output mimo rayleigh nonfrequency selective fading channel the signal is reconstructed at the receiver side with the help of a kalman filter in order to minimize the mean squared error orthogonal space time codes are utilized in order to increase the quality of estimation and mitigate the destructing effects of the fading channel as a criterion for estimation quality assessment we use the distortion outage probability we first obtain upper and lower bounds for the outage probability as a function of system parameters we then perform high snr analysis of the bounds through which we prove the achievability of the maximum diversity order for a n times k mimo fading channel in addition we obtain upper and lower bounds for the coding gain of the distortion outage probability in the high snr regime and outline the relation between system parameters and the coding gain

gaussian distributions on riemannian symmetric spaces statistical learning with structured covariance matrices the riemannian geometry of covariance matrices has been essential to several successful applications in computer vision biomedical signal and image processing and radar data processing for these applications an important ongoing challenge is to develop riemannian geometric tools which are adapted to structured covariance matrices this paper proposes to meet this challenge by introducing a new class of probability distributions gaussian distributions of structured covariance matrices these are riemannian analogs of gaussian distributions which only sample from covariance matrices having a preassigned structure such as complex toeplitz or block toeplitz the usefulness of these distributions stems from three features 1 they are completely tractable analytically or numerically when dealing with large covariance matrices 2 they provide a statistical foundation to the concept of structured riemannian barycentre i e frechet or geometric mean and 3 they lead to efficient statistical learning algorithms which realise among others density estimation and classification of structured covariance matrices this paper starts from the observation that several spaces of structured covariance matrices considered from a geometric point of view are riemannian symmetric spaces accordingly it develops an original theory of gaussian distributions on riemannian symmetric spaces of their statistical inference and of their relationship to the concept of riemannian barycentre then it uses this original theory to give a detailed description of gaussian distributions of three kinds of structured covariance matrices complex toeplitz and block toeplitz finally it describes algorithms for density estimation and classification of structured covariance matrices based on gaussian distribution mixture models

on vector quasivariational inequalities in this paper we consider the vector quasivariational inequalities and the vector quasivariational like inequalities for multifunctions with vector values and prove some existence theorems of solutions for our inequalities also we give the relationship between a kind of the vector variational inequality for multifunctions and a vector optimization problem involving nondifferentiable lipschitz functions

iterative algorithm for completely generalized set valued strongly nonlinear mixed variational like inequalities a class of completely generalized set valued strongly nonlinear mixed variational likeinequalities is introduced the auxiliary principle technique is extended to study this new class of mixed variational like inequalities the existence of a solution of the auxiliary problem for this new class of mixed variational like inequalities is shown the iterative algorithm for this new class of mixed variational like inequalities is given by virtue of this existence result moreover the existence of a solution of this new class of mixed variational like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown the convergence criteria are different from some early and recent ones presented in the literature

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

on the solution of the nonlinear matrix equation xn f x abstract we consider a class of nonlinear matrix equations x n f x 0 where f is a self map on the convex cone p k of k k positive definite real matrices it is shown that for n 2 the matrix equation has a unique positive definite solution depending continuously on the function f if f belongs to the semigroup of nonexpansive mappings with respect to the gl k r invariant riemannian metric distance on p k which contains congruence transformations translations the matrix inversion and in particular symplectic hamiltonians appearing in kalman filtering we show that the sequence of positive definite solutions varying over n 2 converges always to the identity matrix

state estimation of linear systems in the presence of sporadic measurements this paper deals with the state estimation of linear time invariant systems for which measurements of the output are available sporadically to solve the considered problem we provide an observer with jumps triggered by incoming measurements which is studied in a hybrid systems framework specifically the resulting system is written in estimation error coordinates and augmented with a timer variable that triggers the event of new measurements arriving then the observer design is performed to achieve global exponential stability ges of a closed set including the points for which the state of the plant and its estimate coincide furthermore a computationally tractable design procedure for the proposed observer is presented finally the effectiveness of the proposed methods is demonstrated in two numerical examples

an sp 2 covariant quantization of gauge theories with linearly dependent generators the sp 2 symmetric version of covariant quantization is formulated for the general case of any stage reducible gauge theories

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

characterizations of global transversal exponential stability we study the relationship between the global exponential stability of an invariant manifold and the existence of a positive semi definite riemannian metric which is contracted by the flow in particular we investigate how the following properties are related to each other in the global case i a manifold is globally transversally exponentially stable ii the corresponding variational system c f 7 in section ii admits the same property iii there exists a degenerate riemannian metric which is contracted by the flow and can be used to construct a lyapunov function we show that the transverse contraction rate being larger than the expansion of the shadow on the manifold is a sufficient condition for the existence of such a lyapunov function an illustration of these tools is given in the context of global full order observer design

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

abstract variational inequality problems and a basic theorem of complementarity abstract in this paper a basic theorem of complementarity is established for an abstract variational inequality problem in particular we obtain a basic theorem of complementarity for a class of generalized variational inequality problems studied by parida and sen 1 we also obtain some sufficient conditions for the existence of a solution of this class of problems

convergence of nonlinear observers on bbr n with a riemannian metric part i we study how convergence of an observer whose state lives in a copy of the given system s space can be established using a riemannian metric we show that the existence of an observer guaranteeing the property that a riemannian distance between system and observer solutions is nonincreasing implies that the lie derivative of the riemannian metric along the system vector field is conditionally negative moreover we establish that the existence of this metric is related to the observability of the system s linearization along its solutions moreover if the observer has an infinite gain margin then the level sets of the output function are geodesically convex conversely we establish that if a complete riemannian metric has a lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property then there exists an observer with an infinite gain margin

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

generalized quasi variational like inequality problem this paper gives some very general results on the generalized quasi variational like inequality problem since the problem includes all the existing extensions of the classical variational inequality problem as special cases our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional the approach adopted in this paper is based on continuous selection type arguments and thus is quite different from the berge maximum theorem or hahn banach theorem approach used in the literature

some existence results for multivalued complementarity problems this paper presents some new results for the existence of a solution to a multivalued complementary problem these results are derived under a upper limiting homogeneity ulh property on the multifunction defining the complementarity problem and on a certain closedness interiority condition the closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem we show that this closedness condition is satisfied by the class of polyhedral multifunctions

a simple intrinsic reduced observer for geodesic flow aghannan and rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements the position and velocity observer is based on the riemannian structure of the configuration manifold endowed with the kinetic energy metric and is intrinsic they proved local convergence when the system is conservative we propose an intrinsic reduced order velocity observer based on the jacobi metric which can be initialized such that it converges exponentially for any initial true velocity for non conservative systems the observer can be used as a complement to the one of aghannan and rouchon more generally the reduced observer provides velocity estimation for geodesic flow with position measurements thus it can be formally used as a fluid flow soft sensor in the case of a perfect incompressible fluid when the curvature is negative in all planes the geodesic flow is sensitive to initial conditions surprisingly in this case we have global exponential convergence and the more unstable the flow is faster is the convergence

hamiltonian brst anti brst theory the hamiltonian brst anti brst theory is developed in the general case of arbitrary reducible first class systems this is done by extending the methods of homological perturbation theory originally based on the use of a single resolution to the case of a biresolution the brst and the anti brst generators are shown to exist the respective links with the ordinary brst formulation and with thesp 2 covariant formalism are also established

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

on the generalized quasi variational inequality problems the purpose of this paper is to study the existence problem of solutions for some kinds of abstract generalized quasi variational inequality problems by using a new kind of fixed point approach

a further generalization of yannelis prabhakar s continuous selection theorem and its applications abstract in this article we first prove one improved version of the yannelis prabhakar continuous selection theorem and next as its applications a fixed point theorem in noncompact product spaces a nonempty intersection theorem some existence theorems of solutions for the generalized quasi variational inequalities and some equilibrium existence theorems for the abstract economies are given

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

nonexpansiveness of the resolvent average abstract we show that the resolvent average for positive definite matrices which interpolates between the harmonic and the arithmetic means contracts the thompson metric on the convex cone of positive definite matrices classical results depending on the nonexpansive property of the arithmetic average are considered in the context of the resolvent average in particular resolvent power mean approximation to the karcher mean and ferrante and levy like matrix equations are investigated

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

mutual information of wireless channels and block jacobi ergodic operators shannon s mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver from this viewpoint the channel can also be represented by an ergodic self adjoint block jacobi operator which is close in many aspects to a block version of a random schrodinger operator the mutual information is then related to the so called density of states of this operator in this paper it is shown that under the weakest assumptions on the channel the mutual information can be expressed in terms of a matrix valued stochastic process coupled with the channel process this allows numerical approximations of the mutual information in this general setting moreover assuming further that the channel coefficient process is a markov process a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related markov process this generalizes previous results from levy et al it is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime

a general theorem of complementarity for the implicit gqvi problem abstract in this paper we prove a basic theory of complementarity for the implicit generalized quasi variational inequality problem our result widely extends many known results established in the literature an application to the quasi equilibrium problem is also given

discontinuous quasivariational like inequalities in this note we deal with the following problem given x rn a multification gg x 2x two single valued maps f x rn x x rn find a point x x such that x x and f x x x 0 for all x x we prove an existence theorem in which in particular the function f is not supposed to be continuous

a survey of the s lemma in this survey we review the many faces of the s lemma a result about the correctness of the s procedure the basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization convex geometry and linear algebra as well these were all active research areas but as there was little interaction between researchers in these different areas their results remained mainly isolated here we give a unified analysis of the theory by providing three different proofs for the s lemma and revealing hidden connections with various areas of mathematics we prove some new duality results and present applications from control theory error estimation and computational geometry

irreducible hamiltonian brst anti brst symmetry for reducible systems an irreducible hamiltonian brst anti brst treatment of reducible first class systems based on homological arguments is proposed the general formalism is exemplified on the freedman townsend model

performance of ensemble kalman filters in large dimensions contemporary data assimilation often involves more than a million prediction variables ensemble kalman filters enkf have been developed by geoscientists they are successful indispensable tools in science and engineering because they allow for computationally cheap low ensemble state approximation for extremely large dimensional turbulent dynamical systems the practical finite ensemble filters like enkf necessarily involve modifications such as covariance inflation and localization and it is a genuine mystery why they perform so well with small ensemble sizes in large dimensions this paper provides the first rigorous stochastic analysis of the accuracy and covariance fidelity of enkf in the practical regime where the ensemble size is much smaller than the large ambient dimension for enkfs with random coefficients a challenging issue overcome here is that enkf in huge dimensions introduces unavoidable bias and model errors that need to be controlled and estimated 2017 the authors communications on pure and applied mathematics is published by the courant institute of mathematics and wiley periodicals inc

generalized quasi variational like hemivariational inequalities abstract in this paper we introduce and study a new class of generalized quasi variational like hemivariational inequalities with multi valued pseudomonotone operators in banach spaces some new existence theorems of solutions for this class of generalized quasi variational like hemivariational inequalities are proved the results presented in this paper generalize and extend some known results

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

a cohomological approach to the batalin lavrov tyutin covariant quantization of irreducible gauge theory the anti brst transformation for an arbitrary irreducible gauge invariant action is implemented in the usual batalin vilkovisky bv approach this is done without duplicating the gauge symmetries but rather by duplicating all fields and antifields of the theory in this way the sp 2 covariant quantization can be accomplished in the standard bv approach and its equivalence with the batalin lavrov tyutin blt approach is proved by a special gauge fixing procedure

transverse exponential stability and applications we investigate how the following properties are related to each other i a manifold is transversally exponentially stable ii the transverse linearization along any solution in the manifold is exponentially stable and iii there exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow we illustrate their relevance with the study of exponential incremental stability finally we apply these results to two control design problems nonlinear observer design and synchronization in particular we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

a basic theorem of complementarity for the generalized variational like inequality problem abstract in this paper a basic theorem of complementarity is established for generalized variational like inequality problems introduced by parida and sen some existence results for both generalized variational inequality and complementarity problems are established by employing this basic theorem of complementarity in particular some sets of conditions that are normally satisfied by a nonsolvable generalized complementarity problem are investigated

a bundle type auxiliary problem method for solving generalized variational like inequalities for generalized variational like inequalities by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization we present an implementable iterative method to make the subproblem easier to solve even though the preinvex function may not be convex we still consider using the model similar to the one in r mifflin a modification and extension of lemarechal s algorithm for nonsmooth minimization mathematical programming 17 1982 77 90 which may not be under the preinvex function to approximate locally the involved preinvex function and prove that this local approximation is well defined at each iteration of the algorithm i e the construction of this local approximation can terminate in finite steps at each iteration of the proposed algorithm we not only explain how to construct the approximation but also prove the weak convergence of the sequence generated by the corresponding algorithm under some conditions the proposed algorithm is a generalization of the existing algorithm for generalized variational inequalities to generalized variational like inequalities in some sense see t t hue j j strodiot v h nguyen convergence of the approximate auxiliary problem method for solving generalized variational inequalities journal of optimization theory and applications 121 2004 119 145

covariant quantization of gauge theories in the framework of extended brst symmetry the quantization rules for gauge theories in the lagrangian formalism are formulated on the basis of the requirement of an extended brst symmetry the independence of the s matrix to the choice of a gauge is proved the ward identities are derived and the existence theorem for the solutions of the generating equations within the given formalism is proved rank 1 gauge theories are considered as an example

gossip and distributed kalman filtering weak consensus under weak detectability the paper presents the gossip interactive kalman filter gikf for distributed kalman filtering for networked systems and sensor networks where intersensor communication and observations occur at the same time scale the communication among sensors is random each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link we show that under a weak distributed detectability condition 1 the gikf error process remains stochastically bounded irrespective of the instability of the random process dynamics and 2 the network achieves weak consensus i e the conditional estimation error covariance at a uniformly randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semidefinite matrices independent of the initial state to prove these results we interpret the filtering states estimates and error covariances at each node in the gikf as stochastic particles with local interactions we analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched random riccati equation the switching being dictated by a nonstationary markov chain on the network graph

the contraction rate in thompson s part metric of order preserving flows on a cone application to generalized riccati equations abstract we give a formula for the lipschitz constant in thompson s part metric of any order preserving flow on the interior of a possibly infinite dimensional closed convex pointed cone this shows that in the special case of order preserving flows a general characterization of the contraction rate in thompson s part metric given by nussbaum leads to an explicit formula as an application we show that the flow of the generalized riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its lipschitz constant by a matrix inequality we also show that the same flow is no longer a contraction in other invariant finsler metrics on this cone including the standard invariant riemannian metric this is motivated by a series of contraction properties concerning the standard riccati equation established by bougerol liverani wojtkowski lawson lee and lim we show that some of these properties do and that some other do not carry over to the generalized riccati equation

a differential lyapunov framework for contraction analysis lyapunov s second theorem is an essential tool for stability analysis of differential equations the paper provides an analog theorem for incremental stability analysis by lifting the lyapunov function to the tangent bundle the lyapunov function endows the state space with a finsler structure incremental stability is inferred from infinitesimal contraction of the finsler metrics through integration along solutions curves

the osp 1 2 covariant lagrangian quantization of reducible massive gauge theories the osp 1 2 covariant lagrangian quantization of irreducible gauge theories is generalized to l stage reducible theories the dependence of the generating functional of green s functions on the choice of gauge in the massive case is discussed and ward identities related to osp 1 2 symmetry are given massive first stage theories with closed gauge algebra are studied in detail the generalization of the chapline manton model and topological yang mills theory to the case of massive fields are considered as examples

remarks on the sp 2 covariant lagrangian quantization of gauge theories the existence of a solution of the exact generating equations with 0 for the sp 2 covariant lagrangian quantization scheme is established the characteristic arbitrariness of this solution is also studied the equivalence between the sp 2 covariant quantization and the standard one is proven

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator

local superfield lagrangian brst quantization a local formulation of superfield lagrangian quantization in non abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a grassmann parameter we solve the problem of describing the quantum action and the gauge algebra of an l stage reducible superfield model in terms of a brst charge for a formal dynamical system with first class constraints of l 1 stage reducibility starting from local functions of the quantum and gauge fixing actions with an essential use of darboux coordinates on the antisymplectic manifold we construct a superfield generating functionals of green s functions including the effective action we present two superfield forms of brst transformations considered as shifts along vector fields defined by hamiltonian like systems constructed in terms of the quantum and gauge fixing actions and an arbitrary local boson function as well as in terms of corresponding fermion functionals through poisson b