parameter estimator based on a minimum discrepancy criterion a bayesian approach a new estimation criterion based on the discrepancy between the estimator s error covariance and its information lower bound is proposed this discrepancy measure criterion tries to take the information content of the observed data into account a minimum discrepancy estimator mde is then obtained under a linearity assumption this estimator is shown to be equivalent to the maximum likelihood estimator mle if one assumes that a linear efficient estimator exists and the prior distribution of parameters is uniform moreover it is equivalent to the minimum variance unbiased estimator mvue if the mde is required to be unbiased illustrative examples of mde and its comparisons with other estimators are given

eventual practical stability of impulsive differential equations with time delay in terms of two measurements in this paper we introduce a new stability eventual practical stability for impulsive differential equations with time delay by using lyapunov functions and comparison principle we will get some criteria of eventual practical stability eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements

some additional results on principal components analysis of three mode data by means of alternating least squares algorithms kroonenberg and de leeuw 1980 have developed an alternating least squares method tuckals 3 as a solution for tucker s three way principal components model the present paper offers some additional features of their method starting from a reanalysis of tucker s problem in terms of a rank constrained regression problem it is shown that the fitted sum of squares in tuckals 3 can be partitioned according to elements of each mode of the three way data matrix an upper bound to the total fitted sum of squares is derived finally a special case of tuckals 3 is related to the carroll harshman candecomp parafac model

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

stability of impulsive functional differential equations abstract in this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied by using lyapunov functions and razumikhin techniques some criteria of stability asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided some examples are also presented to illustrate the efficiency of the results obtained

about some new integral inequalities of wendroff type for discontinuous functions abstract in this article we obtain some new nonlinear integral inequalities for discontinuous functions of two independent variables wendroff type by including also inequalities with delay we deduce new generalizations of earlier results given by r p agarwal r bellman i bihari b k bondge v lakshmikantham s leela b g pachpatte for continuous and discrete functions furthermore generalizations of some results for integro sum inequalities are obtained as well

persistent impulsive effects on stability of functional differential equations with finite or infinite delay abstract in this paper the stability problem of impulsive functional differential equations ifdes is considered several criteria ensuring the uniform stability of ifdes with finite or infinite delay are derived by establishing some new razumikhin conditions different with the current existing ones our development results can be applied to delay systems with persistent impulsive effects finally an example and its computer simulation is given to show the effectiveness and advantages of the proposed method

an online parameter estimator for quick convergence and time varying linear systems a recursive algorithm called 3 om is presented to estimate parameters and noise variances for discrete time linear stochastic systems the unprojected version of 3 om is globally convergent with probability 1 to minima of the asymptotic negative log likelihood function 3 om approximates the quick convergence attained by the optimal nonlinear filter used as a parameter estimator the state space form of 3 om permits application to time varying linear systems and to online tuning of a kalman filter

oblique rotaton in canonical correlation analysis reformulated as maximizing the generalized coefficient of determination to facilitate the interpretation of canonical correlation analysis cca solutions procedures have been proposed in which cca solutions are orthogonally rotated to a simple structure in this paper we consider oblique rotation for cca to provide solutions that are much easier to interpret though only orthogonal rotation is allowed in the existing formulations of cca our task is thus to reformulate cca so that its solutions have the freedom of oblique rotation such a task can be achieved using yanai s jpn j behaviormetrics 1 46 54 1974 j jpn stat soc 11 43 53 1981 generalized coefficient of determination for the objective function to be maximized in cca the resulting solutions are proved to include the existing orthogonal ones as special cases and to be rotated obliquely without affecting the objective function value where ten berge s psychometrika 48 519 523 1983 theorems on suborthonormal matrices are used a real data example demonstrates that the proposed oblique rotation can provide simple easily interpreted cca solutions

investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces abstract in this work sufficiently conditions boundedness stability asymptotical stability exponential stability attraction practical stability nondisturbed motion systems with impulse perturbations on some hypersurfaces are obtained we formulate the conditions which guarantee that no beating motion of hypersurfaces will be present estimates of cauchy matrix system of variation for approximated system are obtained for different kinds of right side shorted system these estimates are used as one parametric scale increasing functions moreover we also consider two parametric scale such as proposed by demidovich

a convergent approximation of the continuous time optimal parameter estimator continuous time linear stochastic systems that are bilinear in the state and parameters are considered a specific approximation to the optimal nonlinear filter used as a recursive parameter estimator is derived by retaining third order moments and using a gaussian approximation for higher order moments with probability one the specific approximation is proved to converge to a minimum of the likelihood function the proof uses the ordinary differential equation technique and requires that the trajectories of the slow system be bounded on finite time intervals and that the fixed parameter fast system by asymptotically stable the fixed parameter fast system is proved to be asymptotically stable if the parameter update gain is small enough essentially the specific approximation is asympotically equivalent to the recursive prediction error method thus inheriting its asymptotic rate of convergence a numerical simulation for a simple example indicates that the specific approximation has better transient response than other commonly used convergent parameter estimators

razumikhin type theorems for time delay systems with persistent impulses abstract the main results of the paper are generalizations of the razumikhin classical theorems for stability analysis of impulsive time delay systems by employing lyapunov razumikhin method and impulsive control theory several razumikhin type theorems for uniform stability and global exponential stability are obtained the significance and novelty of the results lie in that the criteria for stability of impulsive time delay systems admit the existence of persistent impulses and unbounded time varying delays two examples are provided to show the effectiveness of the proposed results

maximization of sums of quotients of quadratic forms and some generalizations monotonically convergent algorithms are described for maximizing six constrained functions of vectors x or matrices x with columns x 1 x r these functions are h 1 x sigma k x a k x x c k x 1 h 1 x sigma k tr x a k x x c k x 1 h over tilde 1 x sigma k sigma l x l a k x l x l c k x l 1 with x constrained to be columnwise orthonormal h 2 x sigma k x a k x 2 x c k x 1 subject to x x 1 h 2 x sigma k tr x a k x x a k x x c k x 1 subject to x x i and h over tilde 2 x sigma k sigma l x l a k x l 2 x l c k x l 1 subject to x x i in these functions the matrices c k are assumed to be positive definite the matrices a k can be arbitrary square matrices the general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis several applications of the general algorithms are given specifically algorithms are given for reciprocal principal components analysis binormamin rotation generalized discriminant analysis variants of generalized principal components analysis simple structure rotation for one of the latter variants and set component analysis for most of these methods the algorithms appear to be new for the others the existing algorithms turn out to be special cases of the newly derived general algorithms

some clarifications of the tuckals2 algorithm applied to the idioscal problem kroonenberg and de leeuw have suggested fitting the idioscal model by the tuckals2 algorithm for three way components analysis in theory this is problematic because tuckals2 produces two possibly different coordinate matrices that are useless for idioscal unless they are equal kroonenberg has claimed that when idioscal is fitted by tuckals2 the resulting coordinate matrices will be identical in the present paper this claim is proven valid when the data matrices are semidefinite however counterexamples for indefinite matrices are also constructed by examining the global minimum in the case where the data matrices have the same eigenvectors similar counterexamples have been considered by ten berge and kiers in the related context of candecomp parafac to fit the indscal model

simple structure in component analysis techniques for mixtures of qualitative and quantitative variables several methods have been developed for the analysis of a mixture of qualitative and quantitative variables and one called pcamix includes ordinary principal component analysis pca and multiple correspondence analysis mca as special cases the present paper proposes several techniques for simple structure rotation of a pcamix solution based on the rotation of component scores and indicates how these can be viewed as generalizations of the simple structure methods for pca in addition a recently developed technique for the analysis of mixtures of qualitative and quantitative variables called indomix is shown to construct component scores without rotational freedom maximizing the quartimax criterion over all possible sets of component scores a numerical example is used to illustrate the implication that when used for qualitative variables indomix provides axes that discriminate between the observation units better than do those generated from mca

uniform stability of delayed impulsive reaction diffusion systems abstract in this article the stability problem of impulsive reaction diffusion functional differential equations irfdes is discussed applying lyapunov functional method and the comparison principle of irfdes some useful criteria are acquired to assure uniform stability and uniformly asymptotical stability of the equilibrium point of irfdes respectively finally a numerical example is provided to show the validity of our findings

letter to the editor stationary oscillation for high order hopfield neural networks with time delays and impulses we investigate stationary oscillation for high order hopfield neural networks with time delays and impulses in a recent paper j zhang z j gui existence and stability of periodic solutions of high order hopfield neural networks with impulses and delays journal of computational and applied mathematics 224 2008 602 613 the authors claim that they obtain a criterion of existence uniqueness and global exponential stability of periodic solution i e stationary oscillation for high order hopfield neural networks with time delays and impulses in this paper we point out that the main result of the recent paper is unture and present a new sufficient condition of stationary oscillation for the neural networks a numerical example is given to illustrate the effectiveness of the obtained result

bayesian system identification in bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to describe mathematically the uncertain relation between the statistician and the external world the statistical inference is understood as a correction of prior subjective probability distribution by objective data the paper shows that on this bayesian basis it is possible to build a consistent theory of system identification the following problems are considered one shot and real time identification estimation and prediction in closed control loop redundant and unidentifiable parameters time varying parameters and adaptivity

singular dirichlet second order bvps with impulses abstract the paper deals with the existence of solutions to singular second order differential equations with impulse effects and with the dirichlet boundary conditions the right hand side of the differential equation can be singular in its phase variable

on the stability of invariant sets of functional differential equations abstract a system of functional differential equations with delay dz dt z t zt where z x y x rn y rm and z is the vector valued functional is considered it is supposed that this system has a positive invariant set x 0 definitions of its stability asymptotic stability and uniform asymptotic stability are given theorems on the uniform asymptotic stability are formulated and proved

periodic solutions to impulsive differential inclusions with constraints abstract the existence of a periodic solution to an impulsive differential inclusion being invariant with respect to a non convex set of state constraints is established by the use a lefschetz type fixed point theorem for set valued maps

about a generalization of bellman bihari type inequalities for discontinuous functions and their applications abstract in the present paper we introduce the conditions of solvability for chaplygin s problem with discontinuous functions in two independent variables satisfying integro sum inequalities the new type of nonlinear integral and wendroff s inequality for discontinuous functions are investigated as applications the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces j r 2 are obtained some historical aspects of the theory of integro sum inequalities are presented

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

on green best linear composites with a specified structure and oblique estimates of factor scores green solved the problem of least squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix in the present paper an omission in green s proof is discussed and resolved furthermore it is shown that some recently published solutions for estimating oblique factor scores are special cases of green s solution for the case of fixed covariance matrices

optimality conditions for the trace of certain matrix products abstract kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form x 1 x k k where the matrices j are diagonal and fixed and the x j vary unrestrictedly and independently over the set of orthonormal matrices in the present paper necessary and sufficient conditions for maximality and minimality of this trace are formulated the proof for necessity and sufficiency of these conditions is given only for the case k 1 and for the case k 2 with 1 and 2 nonnegative ten berge has generalized kristof s theorem to handle the case where the x j are submatrices of orthonormal matrices necessary and sufficient conditions for optimality in the generalized theorem are formulated

a generalization of takane s algorithm for dedicom an algorithm is described for fitting the dedicom model for the analysis of asymmetric data matrices this algorithm generalizes an algorithm suggested by takane in that it uses a damping parameter in the iterative process takane s algorithm does not always converge monotonically based on the generalized algorithm a modification of takane s algorithm is suggested such that this modified algorithm converges monotonically it is suggested to choose as starting configurations for the algorithm those configurations that yield closed form solutions in some special cases finally a sufficient condition is described for monotonic convergence of takane s original algorithm

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

uniform stability of impulsive infinite delay differential equations with applications to systems with integral impulsive conditions in this paper a class of impulsive infinite delay differential equations is considered by employing lyapunov razumikhin method and analysis techniques several new sufficient conditions ensuring the uniform stability are obtained from impulsive perturbation and impulsive control point of view respectively the main advantage of those results is that they can be applied to the delay systems with integral impulsive conditions as an application we study a class of delayed neural networks with integral impulsive conditions and derive some results ensuring the uniform stability finally two examples are given to show the effectiveness of the presented criteria

a nondegenerate maximum principle for the impulse control problem with state constraints in this article a free time impulsive control problem with state constraints and equality and inequality constraints on the trajectory endpoints is considered a weakened maximum principle is obtained for problems with data measurable in the time variable being the time transversality conditions deduced with the help of some extra convexity assumption on the state constraints in the case of smooth problems a nondegenerate maximum principle is derived by using a penalty function method

state feedback impulse elimination for singular systems over a hermite domain we reduce the problem of impulse elimination via state feedback in singular differential equations to algebra our results are developed for systems over an arbitrary hermite domain we show that the established theories for the time invariant and the real analytic time varying settings can be unified in this way besides the constant and real analytic functions several other function rings are considered our algebraic theory is applied to these cases providing solutions to the impulse elimination problem for classes of systems not previously studied in particular our work allows the restriction of the feedback matrix to certain function rings

matrices with special reference to applications in psychometrics multidimensional scaling item response theory and factor analysis may be considered three major contributions of psychometricians to statistics matrix theory played an important role in early developments of these techniques unfortunately nonlinear models are currently very prevalent in these areas still one can identify several areas of psychometrics where matrix algebra plays a prominent role they include analysis of asymmetric square tables multiway data analysis reduced rank regression analysis and multiple set t set canonical correlation analysis among others in this article we review some of the important matrix results in these areas and suggest future studies

a generalization of kristofs theorem on the trace of certain matrix products kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form x 1 hat gamma 1 x 2 hat gamma 2 cdots x n hat gamma n where the matrices hat gamma i are diagonal and fixed and thex i vary unrestrictedly and independently over the set of orthonormal matrices the theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints the present paper contains a generalization of kristof s theorem to the case where thex i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank the generalized theorem contains the schwarz inequality as a special case various examples from the psychometric literature illustrating the practical use of the generalized theorem are discussed

clustered common factor exploration in factor analysis the factor analysis fa model does not permit unique estimation of the common and unique factor scores this weakness is notorious as the factor indeterminacy in fa luckily some part of the factor scores can be uniquely determined thus as a whole they can be viewed as a sum of determined and undetermined parts the paper proposes to select the undetermined part such that the resulting common factor scores have the following feature the rows i e individuals of the common factor score matrix are as well classified as possible into few clusters the clear benefit is that we can easily interpret the factor scores simply by focusing on the clusters the procedure is called clustered common factor exploration ccfe an alternating least squares algorithm is developed for ccfe it is illustrated with real data examples the proposed approach can be viewed as a parallel to the rotation techniques in fa they exploit another fa indeterminacy the rotation indeterminacy which is resolved by choosing the rotation that transforms the loading matrix into the most interpretable one according to a pre specified criterion in contrast to the rotational indeterminacy the factor indeterminacy is utilized to achieve well clustered factor scores by ccfe to the best of our knowledge such an approach to the fa interpretation has not been studied yet

bayesian parameter estimation taking the bayesian approach in solving the discrete time parameter estimation problem has two major results the unknown parameters are legitimately included as additional system states and the computational objective becomes calculation of the entire posterior density instead of just its first few moments this viewpoint facilitates intuitive analysis allowing increased qualitative understanding of the system behavior with the actual posterior density in hand the true optimal estimate for any given loss function can be calculated although the computational burden of doing so might preclude online use it does not provide a clearly justified baseline for comparative studies these points are demonstrated by analyzing a scalar problem with a single unknown and by comparing an established point estimator s performance to the true optimal estimate

bifurcations of periodic solutions of delay differential equations abstract in this paper we develop kaplan yorke s method and consider the existence of periodic solutions for some delay differential equations we especially study hopf and saddle node bifurcations of periodic solutions with certain periods for these equations with parameters and give conditions under which the bifurcations occur we also give application examples and find that hopf and saddle node bifurcations often occur infinitely many times

new razumikhin type theorems for impulsive functional differential equations in this paper we investigate stability and boundedness for a class of impulsive functional differential equations by using liapunov functions and razumikhin technique some new razumikhin type theorems on stability and boundedness are obtained the corresponding results obtained recently in j shen j yan nonlinear anal 33 1998 519 531 x liu j shen to appear are improved

integro sum inequalities and motion stability of systems with impulse perturbations abstract this article is devoted to the investigation of the properties of motion represented by essential nonlinear system of differential equations with impulse effect the results based on the solvability problem by s a chaplygin for discontinuous functions satisfy integro sum inequalities the conditions of boundedness stability asymptotical stability practical stability attraction motion for different kinds of nonlinearities of systems are obtained

some new results on correlation preserving factor scores prediction methods anderson and rubin and mcdonald have proposed a correlation preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables green has proposed a correlation preserving method which minimizes the trace of a residual covariance matrix for factors krijnen wansbeek and ten berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix and offered an iterative procedure to that effect in the present paper it is shown that the iterative procedure can be replaced by a closed form solution when all unique variances are strictly positive this solution is the same as mcdonald s the solution coincides with green s solution in certain special cases for instance when the factors are orthogonal

existence of optimal controls for a general class of impulsive systems on banach spaces this paper presents some results on the question of existence of optimal controls for a large class of semilinear impulsive systems in infinite dimensional spaces with admissible controls from the space of vector measures this also includes as a special case the class of purely impulsive controls two physical examples are presented for illustration

string submodular functions with curvature constraints consider the problem of choosing a string of actions to optimize an objective function that is string submodular it was shown in previous papers that the greedy strategy consisting of a string of actions that only locally maximizes the step wise gain in the objective function achieves at least a 1 e 1 approximation to the optimal strategy this paper improves this approximation by introducing additional constraints on curvature namely total backward curvature total forward curvature and elemental forward curvature we show that if the objective function has total backward curvature sigma then the greedy strategy achieves at least a 1 sigma 1 e sigma approximation of the optimal strategy if the objective function has total forward curvature epsilon then the greedy strategy achieves at least a 1 epsilon approximation of the optimal strategy moreover we consider a generalization of the diminishing return property by defining the elemental forward curvature we also introduce the notion of string matroid and consider the problem of maximizing the objective function subject to a string matroid constraint we investigate two applications of string submodular functions with curvature constraints 1 choosing a string of actions to maximize the expected fraction of accomplished tasks and 2 designing a string of measurement matrices such that the information gain is maximized

an impulsive delay differential inequality and applications an impulsive delay differential inequality is formulated in this paper an estimate of the rate of decay of solutions to this inequality is obtained it can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view as an application we consider a class of impulsive control systems with time varying delays and establish a sufficient condition to guarantee the global exponential stability it is shown that via proper impulsive control law a linear delay differential system can be exponentially stabilized even if it is initially unstable a numerical example is given to demonstrate the effectiveness of the development method

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

general impulsive control of chaotic systems based on a ts fuzzy model in this paper a time delayed impulsive controller is constructed and the uniformly asymptotic stability of chaotic systems based on a takagi sugeno ts fuzzy model is investigated and some new and useful criteria are derived in addition the uniformly asymptotic synchronization of chaotic systems based on the ts fuzzy model is discussed using similar techniques finally some numerical simulations are presented to illustrate the effectiveness and feasibility of the derived results

impulsive differential systems the problem of stability and practical stability abstract this article is devoted to the analysis properties of the solutions of nonlinear impulsive differential systems with perturbations on some hypersurfaces t i x the conditions of boundedness practical stability uniformly attractive stability uniformly asymptotical attraction of the solutions perturbed system by using linear approximation are obtained

stability criteria for impulsive differential equations in terms of two measures in general the stability notions of a given solution d t of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables this is because of the fact that moments of impulse effects of 4 t need not be the same as that of a different solution x t and therefore demanding that the difference lx t d t 1 be small for all future time seems unnatural see 4 73 as a result the definitions of stability require suitable changes in the general situations and the corresponding theory has not yet been developed however in the case of impulsive differential systems with fixed moments of impulse effects such a problem does not arise and hence the standard definitions of stability will suffice employing suitable discontinuous lyapunov functions stability theory has recently been developed for such systems 1 2 3 51 in this paper we shall discuss stabiliy theory of impulsive differential systems with fixed moments of impulse effects in terms of two measures since such a theory enables us to unify a variety of stability results found in the literature we shall employ theory of impulsive differential inequalities as well as a direct approach to bring out the advantages of each approach

some mathematical properties of the matrix decomposition solution in factor analysis a new factor analysis fa procedure has recently been proposed which can be called matrix decomposition fa mdfa all fa model parameters common and unique factors loadings and unique variances are treated as fixed unknown matrices then the mdfa model simply becomes a specific data matrix decomposition the mdfa parameters are found by minimizing the discrepancy between the data and the mdfa model several algorithms have been developed and some properties have been discussed in the literature notably by stegeman in comput stat data anal 99 189 203 2016 but as a whole mdfa has not been studied fully yet a number of new properties are discovered in this paper and some existing ones are derived more explicitly the properties provided concern the uniqueness of results covariances among common factors unique factors and residuals and assessment of the degree of indeterminacy of common and unique factor scores the properties are illustrated using a real data example

some new integral inequalities of bellman bihari type with delay for discontinuous functions abstract in this article we investigate some integral functional inequalities of bellman bihari type for piecewise continuous functions with some fixed points of discontinuity we also prove a new analogy and generalization of results which were obtained by bellman and bihari to integro sum inequalities with delay and discontinuities that do not belong to lipschitz s type

practical and asymptotic stabilization of chained systems by the transverse function control approach a control approach for the practical and asymptotic stabilization of nonlinear driftless systems subjected to additive perturbations is proposed such perturbations arise naturally for instance in the modeling of trajectory stabilization problems for controllable driftless systems on lie groups the objective of the approach is to provide practical stability of an arbitrary given point in the state space whatever the perturbations and asymptotic stability resp convergence to the point when the perturbations are absent resp tend to zero a general framework is presented in this paper and a control solution is proposed for the class of the chained systems