characteristic of left invertible semigroups and admissibility of observation operators in this paper we discuss the characteristic property of the left invertible semigroups on general banach spaces and admissibility of the observation operators for such semigroups we obtain a sufficient and necessary condition about their generators further for the left invertible and exponentially stable semigroup in hilbert space we show that there is an equivalent norm under which it is contractive based on these results we prove that for any observation operator satisfying the resolvent condition is admissible for the left invertible semigroup if its range is finite dimensional in addition we prove that any observation operator satisfying the resolvent condition can be approximated by the admissible observation operators finally we give a sufficient condition of exact observability of the left invertible semigroup

infinite time exact observability of volterra systems in hilbert spaces abstract we study infinite time exact observability of volterra systems in hilbert spaces sufficient conditions are established under which infinite time exact observability of a volterra system follows from that of the corresponding cauchy system without convolution term this is done by combining the composition operator method with a result about bounded below composition operators on the hardy space

application of analytical retarded time potential expressions to the solution of time domain integral equations recently exact closed form expressions of the electric and magnetic fields and potentials due to impulsively excited rao wilton glisson basis functions have been presented in this work the application of these expressions in the solution of the combined field integral equation cfie is presented solutions via analytical expressions of the electric and magnetic fields are verified and compared with the conventional marching on in time mot algorithm solutions that employ numerical basis integrations it is shown that the accuracy and stability of the solutions obtained with the proposed analytical approach are better when compared to those obtained with the conventional numerical method in addition a discussion section about the effect of the proposed approach in solving the electric field integral equation efie is added in this section it is demonstrated that the dependency of the solution via analytical expressions of the fields are less sensitive to the time step size in comparison to the conventional solution and that the increase in accuracy is a necessary but not sufficient condition for stability

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

on probabilistic φ contractions on menger spaces abstract recently ciric lj b ciric solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces nonlinear anal 72 2010 2009 2018 obtained a fixed point theorem with the intention to get a probabilistic version of the boyd wong theorem d w boyd j s w wong on nonlinear contractions proc amer math soc 20 1969 458 464 we give a counterexample to the key lemma of ciric and we establish a corrected version of his main theorem we also discuss the relations between our result and fixed point theorems of browder f e browder on the convergence of successive approximations for nonlinear functional equations nederl akad wetensch proc ser a 71 indag math 30 1968 27 35 and matkowski j matkowski integrable solutions of functional equations dissertationes math rozprawy mat 127 1975 68 pp

a novel scheme for the solution of the time domain integral equations of electromagnetics a new method to numerically solve time domain integral equations pertinent to electromagnetic surface scattering phenomena is presented the method uses approximate prolate spheroidal wave functions and standard rao wilton glisson basis functions to effect the temporal and spatial discretization of the integral equations respectively because the temporal basis functions are noncausal an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time domain solver

on analytical evaluation of retarded time potentials for swg bases the radon transform interpretation of impulsively excited time domain integrals is recently shown to provide the time samples of these integrals in closed analytical form here the derivation of such formulas for the time samples of the retarded time scalar and vector potentials due to an impulsively excited schaubert wilton glisson swg basis function is accomplished it was proven conceptually before that the aforementioned potentials are related to the geometrical quantities of the surface of intersection between the tetrahedral supports of the swg basis and the hyper cone centered at the observation point with radius ct where c is the speed of light analytical evaluation of these quantities involves proper introduction of the corresponding solid angle and its gradient rigorously obtained formulas and numerical results are presented for them

controllability and observability for non autonomous evolution equations the averaged hautus test abstract we consider the observability problem for non autonomous evolution systems i e the operators governing the system depend on time we introduce an averaged hautus condition and prove that for skew adjoint operators it characterizes exact observability next we extend this to more general class of operators under a growth condition on the associated evolution family we give an application to the schrodinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient

polar integration for exact space time quadrature in time domain integral equations a space time polar quadrature technique for numerical integration of green s function interactions in time domain integral equations is presented the method transforms 2 d surface space time integrals associated with vector and scalar potentials to a 1 d integral that is performed using gauss legendre integration the advantage of the presented technique compared to standard 2 d gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner this ensures highly accurate temporal behavior of the green s function interactions thereby contributing to the stability of the overall time domain integral equations

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

equivalent conditions for stabilizability of infinite dimensional systems with admissible control operators in this paper we study the optimizability of infinite dimensional systems with admissible control operators we show that under a weak condition such a system is optimizable if and only if the system can be split into an exponentially stable subsystem and an unstable subsystem that is exactly controllable in finite time the state space of the unstable subsystem equals the span of all unstable generalized eigenvectors of the original system this subsystem can be infinite dimensional furthermore the unstable poles satisfy a summability condition the state space of the exponentially stable subsystem is given by all vectors for which the action of the original c0 semigroup is stable

how to get a conservative well posed linear system out of thin air part ii controllability and stability let a0 be a possibly unbounded positive operator on the hilbert space h which is boundedly invertible let c0 be a bounded operator from cal d a 0 1 2 with the norm z 1 2 2 langle

a class of contractions in fuzzy metric spaces using the notion of geometrically convergent t norms a fixed point theorem in fuzzy metric spaces in the sense of kramosil and michalek for a class of contractions larger than the class of e l contraction mappings has been proved

a note on fixed point theorems of hadzci c abstract in this paper we give a fixed point theorem for multi valued probabilistic contraction mappings on a menger space as a special case a fixed point theorem for multi valued contraction mappings on a fuzzy metric space is obtained the results presented improve and generalize in a sense some recent fixed point theorems proved by had ic

on invariance of p admissibility of control and observation operators to q type of perturbations of generator of c0 semigroup abstract in this paper it is proved in general setting that p admissibilities of control operators and observation operators are invariant to any q type of perturbations of generator of c 0 semigroups on banach space moreover some relations between the extensions of observation operators with respect to the original generator and the perturbed generator are also characterized so that the output can be expressed in the mild sense as an application the admissibility as well as the mild expressibility of output of a class of observation systems with time delay in state is deduced

admissibility of control operators for solution families to volterra integral equations we reduce the admissibility of finite dimensional control operators for an evolution system satisfying certain mild regularity conditions to that for a semigroup control system for which there are plenty of results available in the literature one such necessary and sufficient condition is the carleson measure criterion we prove this condition explicitly for evolution systems without the regularity assumption mentioned above we also look at some examples which show that our respective hypotheses are necessary

fixed point theorems for nonlinear contractions in kaleva seikkala s type fuzzy metric spaces in this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces in the sense of kaleva and seikkala is discussed nonlinear contractions of the boyd wong s type alber guerre delabriere s type and kannan reich s type are considered and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented respectively also some error estimates are given for iterations to approximate fixed point previous work with respect to fixed point in fuzzy metric spaces is based on the t conorm max the presented work does away with this restriction by proposing weaker conditions defining a generic class of suitable binary operations as applications the corresponding fixed point theorems for menger probabilistic metric spaces are obtained

interpolation by vector valued analytic functions with applications to controllability in this paper norm estimates are obtained for the problem of minimal norm tangential interpolation by vector valued analytic functions expressed in terms of the carleson constants of related scalar measures applications are given to the controllability properties of linear semigroup systems with a riesz basis of eigenvectors

on laplace carleson embedding theorems this paper gives embedding theorems for a very general class of weighted bergman spaces the results include a number of classical carleson embedding theorems as special cases the little hankel operators on these bergman spaces are also considered next a study is made of carleson embeddings in the right half plane induced by taking the laplace transform of functions defined on the positive half line these embeddings have applications in control theory particular attention is given to the case of a sectorial measure or a measure supported on a strip and complete necessary and sufficient conditions for a bounded embedding are given in many cases c 2012 elsevier inc all rights reserved

marching on in time solution of the time domain magnetic field integral equation using a predictor corrector scheme an explicit marching on in time mot scheme for solving the time domain magnetic field integral equation td mfie is presented the proposed mot td mfie solver uses rao wilton glisson basis functions for spatial discretization and a pe ce m type linear multistep method for time marching unlike previous explicit mot td mfie solvers the time step size can be chosen as large as that of the implicit mot td mfie solvers without adversely affecting accuracy or stability an algebraic stability analysis demonstrates the stability of the proposed explicit solver its accuracy and efficiency are established via numerical examples

carleson measures for hilbert spaces of analytic functions on the complex half plane the notion of a carleson measure was introduced by lennart carleson in his proof of the corona theorem for h d in this paper we will define it for certain type of reproducing kernel hilbert spaces of analytic functions of the complex half plane c which will include hardy bergman and dirichlet spaces we will obtain several necessary or sufficient conditions for a positive borel measure to be carleson by preforming tests on reproducing kernels weighted bergman kernels and studying the tree model obtained from a decomposition of the complex half plane the dirichlet space will be investigated in detail as a special case finally we will present a control theory application of carleson measures in determining admissibility of controls in well posed linear evolution equations

riesz bases and exact controllability of c0 groups with one dimensional input operators abstract this paper considers linear infinite dimensional systems with c 0 group generators and one dimensional admissible input operators the exact controllability and riesz basis generation property are discussed the corresponding results of jacob and zwart advances in mathematical systems theory birkhauser boston ma 2000 under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the eigenvalues are allowed to be algebraically multiple but with a uniform bound on the multiplicity

new blow up rates for fast controls of schrodinger and heat equations abstract we consider the null controllability problem for the schrodinger and heat equations with boundary control we concentrate on short time or fast controls we improve recent estimates see l miller geometric bounds on the growth rate of null controllability cost for the heat equation in small time j differential equations 204 2004 202 226 l miller how violent are fast controls for schrodinger and plate vibrations arch ration mech anal 172 2004 429 456 l miller controllability cost of conservative systems resolvent condition and transmutation j funct anal 218 2005 425 444 l miller the control transmutation method and the cost of fast controls siam j control optim 45 2006 762 772 on the norm of the operator associating to any initial state the minimal norm control driving the system to zero our main results concern the schrodinger and heat equations in one space dimension they yield new estimates concerning window problems for series of exponentials as described in t i seidman the coefficient map for certain exponential sums nederl akad wetensch indag math 48 1986 463 478 and in t i seidman s a avdonin s a ivanov the window problem for series of complex exponentials j fourier anal appl 6 2000 233 254 these results are used following l miller the control transmutation method and the cost of fast controls siam j control optim 45 2006 762 772 to deal with the case of several space dimensions

an alternative characterization of probabilistic menger spaces with h type triangular norms abstract the class of h type triangular norms was introduced for the first time by had ic in 1978 in this paper a new characteristic property of the h type triangular norm is presented by virtue of this alternative characterization the continuity of quasi metrics and quasi norms is studied and some properties of the probabilistic menger spaces with this triangular norm are considered as applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given

admissible input elements for systems in hilbert space and a carleson measure criterion we study the control system dot x ax bu quad x in x quad u text scalar where a generates a semigroup on the hilbert space x but in general the control input element b notin x many boundary value control systems point control force situations etc can be studied in this context we define and analyze admissible input elements b and develop sufficient conditions for b to be admissible in terms of the carleson measure theorem of h p theory

the regularity of the wave equation with partial dirichlet control and colocated observation in this paper we analyze a multidimensional controlled wave equation on a bounded domain subject to partial dirichlet control and colocated observation by means of a partial fourier transform it is shown that the system is well posed and regular in the sense of d salamon and g weiss the corresponding feedthrough operator is found to be the identity operator on the input space

simultaneous extrapolation in time and frequency domains using hermite expansions the time domain response of a three dimensional 3 d conducting object is modeled as an associate hermite ah series expansion using the isomorphism of the ah function and its fourier transform the frequency domain response can be expressed as a scaled version of the time domain expansion using early time and low frequency data we demonstrate simultaneous expansion in both domains this approach is attractive because expansions with only 10 20 terms give good extrapolation in both time and frequency domains the computation involved is minimal with this method in this paper we have applied this technique to the problem of extrapolating the current on a scatterer being excited by a uniform plane wave five scatterers were considered a plate disk sphere cube and cone

on the singularity of the closed form expression of the magnetic field in time domain the singularity of the time domain magnetic field is derived in terms of the closed form expression of the magnetic field due to an impulsively excited rao wilton glisson basis function it is shown that the singular contribution depends on the location of the observer on the support of the basis function the derivation of the singularity is performed completely in the time domain without any approximations

on probabilistic φ contractions in menger spaces abstract in this note we show that the fixed point theorems given for menger spaces by j jachymski 2010 5 theorem 1 and j x fang 2015 2 theorem 3 1 are equivalent

admissibility in input elements for diagonal semigroups on l 2 abstract we characterize the admissible unbounded input elements for diagonal semigroups on l 2 the result verifies the necessity of a condition whose sufficience was previously established by l f ho and d l russell

nonlinear contraction theorems in probabilistic spaces abstract in this paper first we prove a common fixed point theorem in menger probabilistic metric spaces then we present a nonlinear contraction case of jungck s common fixed point theorem in menger probabilistic metric spaces finally we prove a common fixed point theorem for six self maps in a menger probabilistic metric space

semigroup generation and stabilization by a r bounded feedback perturbations abstract let a be a generator of a strongly continuous semigroup of operators and assume that c and h are operators such that a ch generates a strongly continuous semigroup sh t on x let 0 be a real number in the resolvent set of a and let 1 1 then there are some fairly unrestrictive conditions under which a 0 a ch 0 a also generates a strongly continuous semigroup sk t on x which has the same exponential growth rate as sh t given an input operator b we can use this to identify a class of feedback perturbations k such that a bk generates a strongly continuous semigroup we can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system for example we show that if the control on a cantilever beam in the state space h02 0 1 l2 0 1 is a moment force on the free end then we cannot stabilize the beam with an a 1 2 bounded feedback but we can find an a e 1 4 bounded feedback for any e 0 which does stabilize the beam

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

exact evaluation of retarded time potential integrals for the rwg bases a new analytical approach for obtaining the time samples of the retarded time scalar and vector potentials due to an impulsively excited rao wilton glisson rwg basis function is presented the approach is formulated directly in the time domain without any assumptions regarding the temporal behavior of the currents represented by the rwg bases to the best knowledge of the authors analytical evaluation of the potential integrals due to the rwg bases have not been formulated prior to the present work either in the time domain or the frequency domain it is shown that the aforementioned potentials are related to the arc segments formed by the intersection of the triangular supports of the rwg basis and the sphere that is centered at the observation point and that has a radius r ct where c is the speed of light in particular the scalar potential is directly proportional to the total arc length and the vector potential is a function of the bisectors of these arc segments a simple algorithm to evaluate these quantities is also presented the validity of the obtained time domain formulae is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

a stabilized marching on in degree scheme for the transient solution of the electric field integral equation time domain electric integral equation methods td efie suffer from the numerical stability problem numerous schemes have been proposed over the years for the purpose of taking care of this instability among them the marching on in degree mod method is one of the newly proposed algorithms for calculating the various transient responses the mod solver employs a set of associated laguerre functions and incorporates exact temporal galerkin testing although the mod scheme is assumed to be more stable when compared with marching on in time mot there are few numerical or theoretical investigations on the stability of the various numerical recursive operations for the mod methodology it has been shown that the time domain magnetic field integral equation td mfie using the mod method can be stabilized by using a filon type quadrature formula to accurately integrate the highly oscillatory laguerre functions which has caused instability for the mod solvers using a higher degree of approximation on the other hand the analytical expression of temporal derivatives used in the mod scheme is strongly affected by an unbounded initial value of the transient current in this paper a novel filon type radial integration method and a sequential constraint term for td efie mod are proposed which make the stabilized mod solver accurate and stable for the arbitrary degree of the laguerre polynomials some numerical results are presented to illustrate the validity of the stabilized mod solution of td efie for transient scattering problems

a note on probabilistic φ contractions in menger spaces abstract in this note we prove that each probabilistic e contraction in a complete menger space x f with of h type is a picard mapping where 0 0 be a function with the properties i 0 1 0 1 ii for each t 0 there exists r t such that lim n n r 0 as a consequence we answer an open question raised by mihet and zaharia affirmatively

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

weak admissibility does not imply admissibility for analytic semigroups two conjectures on admissible control operators by george weiss are disproved in this paper one conjecture says that an operator b defined on an infinite dimensional hilbert space u is an admissible control operator if for every element u in u the vector bu defines an admissible control operator the other conjecture says that b is an admissible control operator if a certain resolvent estimate is satisfied the examples given in this paper show that even for analytic semigroups the conjectures do not hold in the last section we construct a semigroup example showing that the first estimate in the hille yosida theorem is not sufficient to conclude boundedness of the semigroup

efficient evaluation of double surface integrals in time domain integral equation formulations a new integration approach is presented for accurately calculating time domain efie mfie and cfie matrix elements over triangular domains it mainly consists of a radial integration scheme for handling weakly singular and near hypersingular inner integrals and some new smoothing techniques for treating outer two dimensional 2 d integrals the proposed approach has sufficient generality and efficiency for solving time domain integral equations tdie with arbitrary types of temporal basis functions and temporal discretization schemes such as marching on in time mot marching on in degree mod and finite difference delay modeling convolution quadrature fddm cq etc the numerical results for calculating some typical integrals are given to demonstrate its capability with high accuracy and rapid convergence rate achieved

necessary conditions for exact controllability with a finite dimensional input space we derive necessary conditions for exact controllability of infinite dimensional systems described by x ax bu where the generator a has a riesz basis of eigenvectors and the input space is finite dimensional these conditions are in terms of the eigenvalues of a and the degree of unboundedness of b but no further information about b is needed our results easily imply lack of exact controllability for a wide range of distributed parameter systems it is known from partial differential equation pde examples that the addition of damping into an exactly controllable second order system can destroy exact controllability we discuss the effect of damping on such systems using our general conditions we also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension

the operator carleson measure criterion for admissibility of control operators for diagonal semigroups on 1 2 abstract suppose a control system is described by a diagonal semigroup on the state space l 2 and by an unbounded control operator b defined on the input space l 2 we formulate a condition called the operator carleson measure criterion and show that this condition is necessary for the admissibility of b if the semigroup is analytic or invertible then the condition is sufficient as well our results extend the ones of ho russell and weiss concerning the case where the input space is one dimensional

on the stability of time domain magnetic field integral equation using laguerre functions the marching on in degree mod method has been proposed for solving time domain integral equations tdies and it uses the associated laguerre functions as temporal basis and testing functions although the mod scheme is assumed to be stable and accurate there exists little investigation into the accuracy of the integral operations involving the associated laguerre functions of high degree it is shown in this paper that the numerical quadrature for integrating the highly oscillatory laguerre functions may not be accurate and this may result in instability for the mod solvers in this paper the highly oscillatory nature of the high degree associated laguerre functions is investigated first based on that the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order laguerre functions this can produce instability for the mod solvers when a solution requires a high degree of the laguerre functions hence a novel filon type quadrature method and a stabilized mod technique for time domain magnetic field integral equations td mfie smod are presented in this paper some numerical results are presented to illustrate the validity of the proposed filon type quadrature rule resulting in stable solution of the td mfie for transient scattering problems

on linearly topological structure and property of fuzzy normed linear space in this paper the simplified definition of fuzzy normed linear space is introduced the different structure of fuzzy normed linear space with variable right norm r is discussed in terms of topological vector space and its properties such as compactness completeness and density are studied under more general left norm l and right norm r as application the linearly topological structure of menger pn space is obtained

boundary control of a linear thermoelastic beam abstract we show in this paper that the motions of a linear thermoelastic beam may be controlled exactly to zero in a finite time by a single boundary control that acts on one end of the beam the optimal time of controllability depends upon the moment of inertia parameter of the beam and becomes arbitrarily small if this parameter is omitted as in the euler bernoulli beam theory

a note on φ contractions in probabilistic and fuzzy metric spaces abstract in a recent paper fang 2015 1 j x fang generalized a crucial fixed point theorem for probabilistic contractions on complete menger spaces due to jachymski 2010 3 in this note we show that actually fang s theorem is an easy consequence of jachymski s theorem we also observe that the proof of a fixed point theorem for complete metric spaces deduced by fang from his main result is not correct and present a new proof of it

p admissible control elements for diagonal semigroups on l r spaces for linear systems described by dot x t a x t bu t where a is a diagonal operator on the state space l r for some 1 leq r infty we develop necessary and sufficient conditions for b to be p admissible this extends results by ho russell and weiss to the case r neq 2

necessary conditions for the exact observability of systems on hilbert spaces abstract in this paper we introduce the zero class of admissible observation operators for which the norm of the output map tends to zero as the time tends to zero we show that for such an observation operator exact observability implies that the semigroup of the system is bounded from below in addition if the semigroup generator has no residual spectrum then the semigroup can be extended to a c 0 group

exact observability of diagonal systems with a finite dimensional output operator in this paper equivalent conditions for exact observability of diagonal systems with a finite dimensional output operator are given one of these equivalent conditions is the conjecture of russell and weiss siam j control opt 32 1 1994 1 23 the other conditions are in terms of the eigenvalues and the lyapunov solutions of finite dimensional subsystems

on the cost of fast controls for some families of dispersive or parabolic equations in one space dimension in this paper we consider the cost of fast controls for a large class of linear equations of parabolic or dispersive type in one space dimension in small time by extending the work of tenenbaum and tucsnak j differential equations 243 2007 pp 70 100 we are able to give precise upper bounds on the time dependance of the cost of fast controls when the time of control t tends to 0 we also give a lower bound of the cost of fast controls for the same class of equations which proves the optimality of the power of t involved in the cost of the control these general results are then applied to treat notably the case of linear kdv equations and fractional heat or schrodinger equations

zero class admissibility of observation operators abstract an admissible observation operator is zero class admissible if the norm of the output map tends to zero as the time tends to zero sufficient and necessary conditions for zero class admissibility of observation operators are developed and a modified weiss condition is studied it is shown that the modified weiss condition is in general necessary but not sufficient for zero class admissibility for several important classes of c 0 semigroups it is proved that the modified weiss condition is indeed equivalent to zero class admissibility the methods are illustrated by certain pde examples

explicit solution of the time domain volume integral equation using a stable predictor corrector scheme an explicit marching on in time mot scheme for solving the time domain volume integral equation is presented the proposed method achieves its stability by employing at each time step a corrector scheme which updates corrects fields computed by the explicit predictor scheme the proposed method is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit mot schemes numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements

on some classes of nonlinear contractions in probabilistic metric spaces motivated by a question in j x fang 2015 6 we investigate the existence of fixed points for several classes of probabilistic contractions under fang type conditions

observability of polynomially stable systems abstract for finite dimensional systems the hautus test is a well known and easily checkable condition for observability russell and weiss a general necessary condition for exact observability siam j control optim 32 1994 1 23 suggested an infinite dimensional version of the hautus test which is necessary for exact infinite time observability and sufficient for approximate infinite time observability of exponentially stable systems in this paper the notion of observability is studied for polynomially stable systems several known results for exponentially stable systems are extended to the setting of polynomially stable systems by means of an example the obtained results are illustrated

common fixed point theorems of compatible and weakly compatible maps in menger spaces abstract in this paper we prove some new common fixed point theorems for compatible and weakly compatible self maps on menger space under contractive conditions our results improve and generalize the results of singh and jain b singh s jain a fixed point theorem in menger space through weak compatibility j math anal appl 301 2005 439 448 razani and shirdaryazdi a razani m shirdaryazdi a common fixed point theorem of compatible maps in menger space chaos solitons fractals 32 2007 26 34 and others

on probabilistic ψ contractions in menger probabilistic metric spaces abstract in this paper we prove some equivalence for probabilistic contractions in menger probabilistic metric spaces by which we answer open question 3 in mihet and zaharia 2016 11 affirmatively

counterexamples concerning observation operators for c0 semigroups this paper concerns systems of the form dot x t ax t y t cx t where a generates a c 0 semigroup two conjectures which were posed in 1991 and 1994 are shown not to hold the first conjecture by g weiss states that if the range of c is one dimensional then c is admissible if and only if a certain resolvent estimate holds the second conjecture by d russell and g weiss states that a system is exactly observable if and only if a test similar to the hautus test for finite dimensional systems holds the c 0 semigroup in both counterexamples is analytic and possesses a basis of eigenfunctions using the a c pair from the second counterexample we construct a generator a e on a hilbert space such that si a e is uniformly left invertible but its semigroup does not have this property

on controllability of diagonal systems with one dimensional input space abstract this paper deals with diagonal systems on a hilbert state space with a one dimensional input space and a possibly unbounded control operator a priori it is not assumed that the input operator is admissible necessary and sufficient conditions for different notions of controllability such as null controllability exact controllability and approximate controllability are presented these conditions which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator are linked with the theory of interpolation in hardy spaces

necessary condition of linear distributed parameter systems with exact controllability abstract in this paper we studied the necessary condition of distributed parameter system with exact controllability let 0 t be the control mapping we introduce new a class of control operators that is called the i class control which satisfy r 0 t r t t is closed set for t 0 if the system is exactly controllable in finite time then the semigroup t t must have closed range in particular if the generator of t t has compact resolvent its spectra distribute in a strip parallel to imaginary axis as an application we assert that the systems associated with the immediately norm continuous semigroups are never exact controllable for zero class or i class controls

analytical evaluation of transient magnetic fields due to rwg current bases a new analytical approach for obtaining the time samples of the magnetic field intensity due to an impulsively excited rao wilton glisson rwg basis function is presented the approach is formulated directly in the time domain it is shown that the magnetic field is related to the arc segments formed by the intersection of the triangular patch of the rwg basis with the sphere that is centered at the observation point and that has a radius of where is the speed of light in particular the magnetic field can be expressed as the variations of two quantities with respect to the first quantity is the arc segment length and the second quantity is the bisecting vector of the arc segment analytical representations of these quantities are presented contrary to previous studies these representations do not require the calculation of the intersection points of the sphere with the boundaries of the bases the validity of the obtained time domain formulae is demonstrated through comparison of the results with those obtained in the frequency domain by using numerical quadrature finally it is demonstrated that the derived formulae yield closed form expressions when convolved with piecewise polynomial temporal basis functions

a stable marching on in time scheme for solving the time domain electric field volume integral equation on high contrast scatterers a time domain electric field volume integral equation td efvie solver is proposed for characterizing transient electromagnetic wave interactions on high contrast dielectric scatterers the td efvie is discretized using the schaubert wilton glisson swg and approximate prolate spherical wave apsw functions in space and time respectively the resulting system of equations cannot be solved by a straightforward application of the marching on in time mot scheme since the two sided apsw interpolation functions require the knowledge of unknown future field samples during time marching causality of the mot scheme is restored using an extrapolation technique that predicts the future samples from known past ones unlike the extrapolation techniques developed for mot schemes that are used in solving time domain surface integral equations this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane this increases the stability of the mot td efvie solver significantly since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme numerical results demonstrate that the proposed mot solver maintains its stability even when applied to analyzing wave interactions on high contrast scatterers

approximate and approximate null controllability of a class of piecewise linear markov switch systems abstract we propose an explicit easily computable algebraic criterion for approximate null controllability of a class of general piecewise linear switch systems with multiplicative noise this gives an answer to the general problem left open in goreac and martinez 2015 the proof relies on recent results in confortola et al 2015 allowing to reduce the dual stochastic backward system to a family of ordinary differential equations second we prove by examples that the notion of approximate controllability is strictly stronger than approximate null controllability a sufficient criterion for this stronger notion is also provided the results are illustrated on a model derived from repressed bacterium operon given in krishna et al 2005 and reduced in crudu et al 2009

generalized sampled data stabilization of well posed linear infinite dimensional systems we consider well posed linear infinite dimensional systems the outputs of which are sampled in a generalized sense using a suitable weighting function under certain natural assump tions on the system the weighting function and the sampling period we show that there exists a generalized hold function such that unity sampled data feedback renders the closed loop system exponentially stable in the state space sense as well as l 2 stable in the input output sense to illustrate our main result we describe an application to a structurally damped euler bernoulli beam

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

exponential stabilization of well posed systems by colocated feedback we consider well posed linear systems whose state trajectories satisfy dot x ax bu where u is the input and a is an essentially skew adjoint and dissipative operator on the hilbert space x this means that the domains of a and a are equal and a a q where q geq 0 is bounded on x the control operator b is possibly unbounded but admissible and the observation operator of the system is b such a description fits many wave and beam equations with colocated sensors and actuators and it has been shown for many particular cases that the feedback u ka y v with ka 0 stabilizes the system strongly or even exponentially here y is the output of the system and v is the new input we show by means of a counterexample that if b is sufficiently unbounded then such a feedback may be unsuitable the closed loop semigroup may even grow exponentially our counterexample is a simple regular system with feedthrough operator zero however we prove that if the original system is exactly controllable and observable and if ka is sufficiently small then the closed loop system is exponentially stable

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

applications of laplace carleson embeddings to admissibility and controllability it is shown how results on carleson embeddings induced by the laplace transform can be used to derive new and more general results concerning the weighted infinite time admissibility of control and observation operators for linear semigroup systems with q riesz bases of eigenvectors as an example the heat equation is considered next a new carleson embedding result is proved which gives further results on weighted admissibility for analytic semigroups finally controllability by smoother inputs is characterized by means of a new result about weighted interpolation

common coupled fixed point results for probabilistic φ contractions in menger spaces abstract several hybrid probabilistic contractions with a gauge function are considered using the properties of the pseudo metric and the triangular norm some common coupled fixed point theorems are obtained in complete menger probabilistic metric spaces the main results are general because they do not assume any continuity or monotonicity conditions for