on controllability and near controllability of discrete time inhomogeneous bilinear systems without drift in this paper controllability and near controllability of discrete time inhomogeneous bilinear systems without drift are studied necessary and sufficient conditions for controllability and near controllability of the systems are respectively presented in particular algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided examples are shown to demonstrate the conceptions and results of the paper

controllability of the impulsive functional bbm equation with nonlinear term involving spatial derivative abstract for a broad class of control systems modeling real life problems delays and impulses are natural properties that do not modify their behavior so we conjecture that under certain conditions delays and abrupt changes as perturbations of a system do not modify properties such as controllability in this regard we prove the approximate controllability of the impulsive functional benjamin bona mahony bbm equation with nonlinear term involving spatial derivative this can be achieved using the technique avoiding fixed point theorems employed by a e bashirov et al in this case the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval

on the relationship between the separability measures and the bayes probability of error the information measures as a special class of efficiency measures of muiticategory information systems and their relations to the bayes probability of error p b have been recently defined and investigated another class of efficiency measures called the separability measures is introduced in this paper the relationship between any separability measure and p b is determined for any 2 leq q where q denotes the number of categories in a multicategory information system as before epsilon 0 and epsilon m criteria are proposed as the similarity measures between the separability measures and p b the problems of determination for any 2 leq q of all the separability measures with minimal epsilon 0 and epsilon m criteria called epsilon 0 optimal and epsilon m optimal are defined and completely solved respectively the minimal values of epsilon 0 and epsilon m criteria are evaluated as well it is proved that the information measures are for each 3 leq q more similar to p b than the separability measures with respect to the minimal values of both epsilon 0 and epsilon m criteria it is pointed out that the average conditional quadratic entropy is not only an information measure but also a separability measure which is for each 3 leq q optimal and very close to epsilon m optimal separability measures with respect to the epsilon m criterion

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

on the relationship between the efficiency measures of multicategory information systems the concepts of efficiency measures of multicategory information systems and similarity measures between two efficiency measures are introduced and developed the relationship between two efficiency measures is defined by the corresponding set d and the appropriate marginal functions are introduced an earlier work of ben bassat s dealing with the ranking of features according to feature selection criteria is generalized and refined consequently a general similarity measure between two efficiency measures is established it is analyzed in the case of monotonic marginal functions and especially when the set d is convex some important sufficient conditions for d to be convex are also given finally two other similarity measures are defined and interpreted

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

partial controllability concepts the main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form i e given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract hilbert or banach space and disturbed by a deterministic function or by a white noise process at the same time some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged respectively the ordinary controllability conditions for them are too strong since they assume extended state space it is reasonable to introduce partial controllability concepts which assume original state space in this paper we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases

motives and siegel modular forms for a motive m over q we define the fundamental periods of m using invariant theory our definition generalizes deligne s periods we show that if a motive m is constructed from motives m 1 m 2 m n by a standard algebraic operation then the fundamental periods of m can be expressed as monomials of the fundamental periods of m 1 m 2 m n applying this theory we discuss two hypothetical motives attached to a siegel modular form we show that a siegel modular form of degree m has at most m 1 period invariants

on the relationship between the information measures and the bayes probability of error the concept of efficiency measures of multicategory information systems as well as the concepts of the relationship and the similarity measures between two efficiency measures have been recently introduced and developed in this paper the concave measures as a general class of efficiency measures and the information measures as a special class of concave measures are defined and investigated the relationship between any concave measure information measure in particular and the bayes probability of error p b is determined for any 2 leq q where q denotes the number of categories in a multicategory information system the so called epsilon 0 and epsilon m criteria are proposed as the similarity measures between the information measures and p b the problems of determination for any 2 leq q of all the information measures with minimal epsilon 0 and epsilon m criteria called epsilon 0 optimal and epsilon m optimal are formulated and completely solved respectively additionally the minimal values of epsilon 0 and epsilon m criteria are evaluated as well it is pointed out that the well known average conditional quadratic entropy is for all 2 leq q very close to the epsilon 0 optimal and epsilon m optimal information measures with respect to epsilon 0 and epsilon m criteria respectively

stochastic maximum principle in the pontryagin s form for wide band noise driven systems the control problems for wide band noise driven systems have the following specific feature a wide band noise is given by its autocovariance function at the same time different wide band noises may have the same autocovariance function therefore it is important to obtain the results which are invariant under the change of wide band noises corresponding to the same autocovariance function in this paper one such result is obtained a stochastic maximum principle in the pontryagin s form is proved for a control system driven by a state dependent wide band noise the result is demonstrated on an example of controlled stochastic differential equation of risky asset price

comment on relations between entropy and error probability for original paper see feder and merhav ieee trans inform theory vol 40 p 259 66 1994 january the present authors discuss the upper and lower bounds on the equivocation in terms of the bayes error probability

on special l values attached to metaplectic modular forms in this paper we establish some algebraic properties of special l values attached to siegel modular forms of half integral weight often called metaplectic modular forms these results are motivated by some exercises left by shimura to the reader in his marvellous book arithmeticity in the theory of automorphic forms

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

on partial s controllability of semilinear partially observable systems in this paper the partial s controllability of semilinear partially observable control systems is investigated the essence of study is the presence of partial observations we define a weakened partial s controllability concept for partially observable systems a sufficient condition for this controllability concept is proved the method of proof differs from the traditional proofs by fixed point theorems the obtained result is demonstrated with examples

partial controllability of stochastic linear systems the controllability concepts for linear stochastic differential equations driven by different kinds of noise processes can be reduced to the partial controllability concepts for the same systems driven by correlated white noises based on this fact in this article we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes including correlated white noises as well as coloured wide band and shifted white noises it is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments

on controllability conception for stochastic systems the controllability notions for partially observed stochastic systems are defined their relation with complete and approximate controllabilities is shown in particular it is proven that the approximate controllability condition is necessary and the complete controllability condition is sufficient for the partially observed linear gaussian control system to attain the arbitrarily small neighborhood of each point in the state space with probability arbitrarily closely to one

critical values of l functions on gsp 2 gl 2 this paper deals with deligne s conjecture on the critical values of l functions let z g h s denote the tensor product l function attached to a siegel modular form g of weight k and an elliptic cusp form h of weight l we assume that the first fourier jacobi coefficient of g is not identically zero then deligne s conjecture is fully proven for z g h s when l 2k 2 and partly for the remaining case

an explicit arithmetic formula for the fourier coefficients of siegel eisenstein series of degree two and square free odd levels we give an explicit arithmetic formula for the fourier coefficients of siegel eisenstein series of degree two and square free odd levels