a deconvolution problem related to a singular system we present a recursive deconvolution algorithm for a volterra integral equation which corresponds to a singular differential equation in a hilbert space the algorithm is robust with respect to errors in the sampling of the output and to the sampling times

schwarz and gruss type inequalities for c seminorms and positive linear functionals on banach modules abstract let a be a unital banach algebra a c seminorm or a positive linear functional on a and x be a semi inner product a module we define a real function on x by x x x 1 2 and show that the schwarz inequality holds therefore x is a semi hilbert a module we also obtain some gruss type inequalities for c seminorms and positive linear functionals on a

the deconvolution problem fast algorithms including the preconditioned conjugate gradient to compute a map estimator different aspects of the deconvolution problem are discussed and a solution by the map estimator using the a priori knowledge of smoothness and nonnegativity of the unknown signal is proposed several fast algorithms are examined and the conjugate gradient cg method is show to have several advantages it allows computation of a constrained solution and when used with a preconditioning technique it can be faster than other algorithms for general near to toeplitz systems in particular for toeplitz block toeplitz systems

a recursive deconvolution approach to disturbance reduction active noise control anc uses an estimate of the noise affecting a system in order to remove its effect from the output in some applications it is possible to directly measure the noise and a feedforward compensator can be used other applications require instead that the noise be estimated from its effect on the system this results in an adaptive feedback anc see a previous paper by gan and kuo the identification of the disturbance from the output of the linear system is a deconvolution problem in this paper we study a deconvolution technique for the active reduction of the influence of the disturbance on the output of a linear control system the regulator that we present does not affect the behavior of the system in the absence of disturbances

some remarks on the chebyshev functional identities are provided for the chebyshev functional defined on a real linear space equipped with a bilinear form in addition some inequalities for the functional are discussed

a singular perturbation approach to a recursive deconvolution problem following the approach described by a v kryazhimskii and yu s osipov we present a recursive algorithm which can be applied to solve the deconvolution problem of linear finite dimensional input output systems the method gives an on line approximation of the unknown input based on approximate samples of the output key features of this approach are the introduction of an associated singularly perturbed system and the use of a quasi canonical form due to morse

eulerian multi fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays in this paper we present a new eulerian multi fluid modeling for dense sprays of evaporating liquid droplets which is able to describe droplet coalescence and size polydispersion as well as the associated size conditioned dynamics it is an uncommon feature of eulerian spray models which are required in a number of non stationary simulations because of the optimization capability of a solver coupling a eulerian description for both phases the chosen framework is the one of laminar flows or the one of direct numerical simulations since no turbulence models are included in the present study the model is based on a rigorous derivation from the kinetic level of description p d f equation and can be considered as a major extension of the original sectional method introduced by tambour et al we obtain a set of conservation equations for each fluid a statistical average of all the droplets in given size intervals associated to a discretization of the size phase space the coalescence phenomenon appears as quadratic source terms the coefficients of which the collisional integrals can be pre calculated from a given droplet size discretization and do not depend on space nor time we validate this eulerian model by performing several comparisons for both stationary and non stationary cases to a classical lagrangian model which involves a stochastic algorithm in order to treat the coalescence phenomenon the chosen configuration is a self similar 2d axisymmetrical decelerating nozzle with evaporating sprays having various size distributions ranging from smooth ones up to dirac delta functions through discontinuous ones we show that the eulerian model if the discretization in the size phase space is fine enough the problem is then 3d unstationary 2d in space and 1d in size is able to reproduce very accurately the non stationary coupling of evaporation dynamics and coalescence moreover it can still reproduce the global features of the behavior of the spray with a coarse size discretization which is a nice feature compared to lagrangian approaches the computational efficiency of both approaches are then compared and the eulerian model is provided to be a good candidate for more complex and realistic configurations

commutators and accretive operators abstract in this paper singular values of commutators of hilbert space operators are estimated to this aim the accretivity of a transform of the operators is applied some recent results of kittaneh f kittaneh singular value inequalities for commutators of hilbert space operators linear algebra appl 430 2009 2362 2367 are extended

input identification to a class of nonlinear input output causal systems in this paper we adapt lavrent ev method so to obtain a reconstruction procedure for the input u to a nonlinear input output system described by a volterra integral equation the proof is based on a monotonicity assumption which does not imply the monotonicity of the operators appearing in the volterra equation

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

gruss type inequalities in normed spaces abstract generalizations of the classic gruss inequality in normed spaces are given the results are illustrated with some specific examples

a generalization of gruss s inequality in inner product spaces and applications a generalization of the classical gruss s integral inequality in inner product spaces is given some applications for positive linear functionals and integrals are also pointed out

adaptive recursive deconvolution and adaptive noise cancellation in this paper we apply a recursive deconvolution method to active noise cancellation anc in a linear system the observation of the output of a linear system of relative degree one read at discrete time instants is fed to a deconvolution algorithm which identifies the disturbance with the delay of one step this information is used in order to reduce the effect of the disturbance itself deconvolution being an ill posed problem a regularization parameter is to be introduced the choice of the value of the parameter is a delicate issue we show that when studying anc the discrepancy principle applied recursively is a feasible method for the choice of the parameter

a survey on some inequalities for expectation and variance inequalities for continuous random variables having the probability density function defined on a finite interval obtained recently by the authors are surveyed

nonparametric input estimation in physiological systems problems methods and case studies input estimation from output data is an important problem in the analysis of physiological systems because many signals of interest are not directly accessible to measurement when the system is time invariant this problem is often referred to as deconvolution three representative physiological problems regarding hormone secretion insulin dynamics and hepatic glucose production are used to illustrate the major challenges ill conditioning confidence intervals assessment infrequent and nonuniform sampling nonnegativity constraints and computational efficiency the paper provides a critical overview of the existing techniques focusing on regularization theory and bayesian estimation in order to overcome some inadequacies of the existing methods some new results are derived in particular the connection between the maximum likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied moreover a fast svd based numerical algorithm is developed that includes the optimization of the regularization parameter and the computation of confidence intervals the proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

translation invariant maps and applications in this paper we study translation invariant maps on a linear space a method for estimating quantities induced by such maps is presented applications for differences of operators commutators g contractive maps and gruss type inequalities are also given

gruss type inequalities abstract a connection between gruss inequality and the error of best approximation is revealed a gruss type inequality that unifies the continuous and discrete versions of the classical gruss inequalities is established

new inequalities of the kantorovich type for bounded linear operators in hilbert spaces some new inequalities of the kantorovich type are established they hold for larger classes of operators and subsets of complex numbers than considered before in the literature and provide refinements of the classical results in the case when the involved operator satisfies the usual conditions several new reverse inequalities for the numerical radius of a bounded linear operator are obtained as well

numerical approximations of pressureless and isothermal gas dynamics we study several schemes of first or second order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations the pressureless gas system is weakly hyperbolic giving rise to the formation of density concentrations known as delta shocks for the isothermal gas system the infinite speed of expansion into vacuum leads to zero timestep in the godunov method based on exact riemann solver the schemes we consider are able to bypass these difficulties they are proved to satisfy positiveness of density and discrete entropy inequalities to capture the delta shocks and to treat data with vacuum

a gruss type discrete inequality in inner product spaces and applications a gruss type inequality in inner product spaces and applications for the discrete fourier transform mellin transform of sequences polynomials with coefficients in hilbert spaces and lipschitzian vector valued mappings are given

on generalized gruss type inequalities for k fractional integrals the aim of the present paper is to investigate some new integral inequalities of gruss type for k riemann liouville fractional integrals from our results new weighted or classical gruss type inequalities have been established for some special cases moreover special cases of the integral inequalities in this paper have been obtained by dahmani and tabharit 2010 in 5

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities