classical states and the brst charge the role played by the brst charge in isolating the physical states in a classical first class constrained system is analysed contrary to popular belief the cohomological argument used to characterize the physical observables in such a system does not extend to the classical states it is shown that in order to recover the physical states the brst charge must be augmented with a new charge of ghost number minus one constructed out of a set of gauge fixing conditions for the original constraints the relevance of this construction to the quantum theory is discussed

optimal error estimate for energy preserving splitting schemes for maxwell s equations abstract two efficient splitting schemes are developed for 3d maxwell s equations the schemes are energy preserving and unconditionally stable while being implemented explicitly rigorous optimal error estimates are established for the proposed schemes and especially the constant in the error estimates is only o t numerical results confirm the theoretical analysis and numerical comparison with some existing methods shows the good performance of the present schemes

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

geometric quantization of the brst charge in the first half of this paper sects 1 4 we generalise the standard geometric quantization procedure to symplectic supermanifolds in the second half sects 5 6 we apply this to two examples that exhibit classical brst symmetry i e we quantize the brst charge and the ghost number more precisely in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with ad equivariant moment map in the second example we consider a foliated configuration space whose cotangent bundle admits the construction of a brst charge associated to this foliation we show that the classical brst symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space and that geometric quantization gives us a super unitary representation of this supergroup finally we point out how these results are related to reduction at the quantum level as compared with the reduction at the classical level

the batalin fradkin and vilkovisky formalism for higher order theories the generalized batalin fradkin and vilkovisky bfv formalism was developed as a method for determining the ghost structure for theories such as gravity and supergravity whose hamiltonian formalism has constraints not related to a lie algebra action previously the classical dynamical content of the bfv description of yang mills theory was investigated there it was found that this approach had a homological interpretation derived from the lie algebra cohomology of the gauge group which allowed one to understand the construction in terms of the dirac approach to constrained systems in this paper the dynamical consequences of the generalized bfv formalism are investigated it is found that even though one no longer has a lie algebra structure associated with the constraints one can still develop a homology theory that reproduces the dirac analysis and from which the generalized bfv formalism can be derived some of the consequences of this approach are discussed

modelling and robust stability of networked control systems with packet reordering and long delay in this article modelling and robust stability of networked control systems ncs are discussed considering the existence of packet reordering and network induced delay a new mathematical model of ncs whose network induced delay is longer than one sampling period is obtained which can fully describe packet reordering and effectively eliminate the impact of packet reordering on the performance of ncs such that the newest control input can be executed by the actuator based on this model the time varying ncs is converted into an uncertain discrete linear system with multi step delay in terms of matrix theory furthermore a sufficient condition for robust stability of ncs is presented linear matrix inequality approach has been employed to solve the controller design problems numerical examples are compared with previous schemes to demonstrate the effectiveness of the proposed method

robust h control for uncertain discrete stochastic time delay systems this paper deals with the problems of robust stabilization and robust h control for discrete stochastic systems with time varying delays and time varying norm bounded parameter uncertainties for the robust stabilization problem attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed loop system for all admissible uncertainties while for the robust h control problem a state feedback controller is designed such that in addition to the requirement of the robust stochastic stability a prescribed h performance level is also required to be satisfied a linear matrix inequality lmi approach is developed to solve these problems and delay dependent conditions for the solvability are obtained it is shown that the desired state feedback controller can be constructed by solving certain lmis an example is provided to demonstrate the effectiveness of the proposed approach

symplectic and multisymplectic numerical methods for maxwell s equations in this paper we compare the behaviour of one symplectic and three multisymplectic methods for maxwell s equations in a simple medium this is a system of pdes with symplectic and multisymplectic structures we give a theoretical discussion of how some numerical methods preserve the discrete versions of the local and global conservation laws and verify this behaviour in numerical experiments we also show that these numerical methods preserve the divergence furthermore we extend the discussion on dispersion for multi symplectic methods applied to pdes with one spatial dimension to include anisotropy when applying multi symplectic methods to maxwell s equations in two spatial dimensions lastly we demonstrate how varying the courant friedrichs lewy cfl number can cause the multi symplectic methods in our comparison to behave differently which can be explained by the study of backward error analysis for pdes

energy conserved splitting finite difference time domain methods for maxwell s equations in three dimensions in this paper we develop and analyze efficient energy conserved splitting finite difference time domain fdtd schemes for solving three dimensional maxwell s equations in electromagnetic computations all proposed energy conserved splitting finite difference time domain ec s fdtd algorithms are strictly proved to be energy conserved and unconditionally stable and they can be computed efficiently rigorous convergence results are obtained for the schemes the ec s fdtdii schemes are proved to have second order in both time step and spatial steps while the ec s fdtdi schemes have second order in spatial steps and first order in time step the error estimates are optimal and especially the constant in the error estimates is proved to be only o t numerical experiments confirm the theoretical analysis results

becchi rouet stora tyutin structure of polynomial poisson algebras the becchi rouet stora tyutin brst structure of polynomial poisson algebras is investigated it is shown that poisson algebras provide nontrivial models where the full brst recursive procedure is needed quadratic poisson algebras may already be of arbitrarily high rank explicit examples are provided for which the first terms of the brst generator are given the calculations are cumbersome but purely algorithmic and have been treated by means of the computer algebra system reduce our analysis is classical nonquantum throughout

the brs method and geometric quantization some examples we recall the method of quantization of constraints as outlined by kostant and sternberg we discuss various examples to test compatibility between geometric quantization and this procedure in almost all cases reduction and quantization commute

new multisymplectic self adjoint scheme and its composition scheme for the time domain maxwell s equations in this paper we investigate euler box scheme for bridges multisymplectic form of maxwell s equations a new multisymplectic scheme is derived for maxwell s equations we prove that it is also a self adjoint scheme in time direction the multisymplecticity of composition schemes based on the new scheme is also discussed two numerical examples are proposed to indicate that the derived multisymplectic schemes are effective when used to integrate the 2 1 dimensional maxwell s equations

the spatial fourth order energy conserved s fdtd scheme for maxwell s equations abstract in this paper we develop a new spatial fourth order energy conserved splitting finite difference time domain method for maxwell s equations based on the staggered grids the splitting technique is applied to lead to a three stage energy conserved splitting scheme at each stage using the spatial fourth order difference operators on the strict interior nodes by a linear combination of two central differences one with a spatial step and the other with three spatial steps we first propose the spatial high order near boundary differences on the near boundary nodes which ensure the scheme to preserve energy conservations and to have fourth order accuracy in space step the proposed scheme has the important properties energy conserved unconditionally stable non dissipative high order accurate and computationally efficient we first prove that the scheme satisfies energy conversations and is in unconditional stability we then prove the optimal error estimates of fourth order in spatial step and second order in time step for the electric and magnetic fields and obtain the convergence and error estimate of divergence free as well numerical dispersion analysis and numerical experiments are presented to confirm our theoretical results

brief paper stabilization of markovian jump linear system over networks with random communication delay this paper is concerned with the stabilization problem for a networked control system with markovian characterization we consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a markov chain the resulting closed loop system is modeled as a markovian jump linear system with two jumping parameters and a necessary and sufficient condition on the existence of stabilizing controllers is established an iterative linear matrix inequality lmi approach is employed to calculate a mode dependent solution finally a numerical example is given to illustrate the effectiveness of the proposed design method

the hamiltonian structure of the maxwell vlasov equations morrison 25 has observed that the maxwell vlasov and poisson vlasov equations for a collisionless plasma can be written in hamiltonian form relative to a certain poisson bracket we derive another poisson structure for these equations by using general methods of symplectic geometry the main ingredients in our construction are the symplectic structure on the co adjoint orbits for the group of canonical transformations and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory our poisson bracket satisfies the jacobi identity whereas morrison s does not 37 our construction also shows where canonical variables can be found and can be applied to the yang mills vlasov equations and to electromagnetic fluid dynamics

reliable finite time h filtering for discrete time delay systems with markovian jump and randomly occurring nonlinearities this paper is concerned with the problem of reliable finite time h filtering for discrete time varying delay systems with markovian jump and randomly occurring nonlinearities rons rons are introduced to model a class of sector like nonlinearities that occur in a probabilistic way according to a two dimensional discrete random variables joint distribution the failures of sensors are quantified by a variable varying in a given interval the time varying delay is unknown with given lower and upper bounds firstly the filtering errr dynamic system is constructed based on an h filter sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite time boundedness and stochastic finite time h filtering in both normal and fault cases the gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter respectively finally numerical examples are given to demonstrate the effectiveness of the proposed design approach

robust static output feedback h control design for linear systems with polytopic uncertainties abstract this paper investigates the problem of robust static output feedback h control for linear systems with polytopic uncertainties a new method is proposed for robust static output feedback h controller design the proposed design method is applicable for general uncertain systems without the need to impose any constraints on system matrices the corresponding design conditions are presented in the form of linear matrix inequalities lmis one of the advantages of the new method lies in its less conservatism the proposed design method is also applicable to both continuous time and discrete time systems the performance of the method is compared with other methods based on several examples

existence theorem for gauge algebra a general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory the structure of the general gauge algebra is derived from these postulates the proof of existence of the structure functions lacking in previous works is given the question of uniqueness is also completely cleared up some unsolved problems are discussed in connection with the covariant quantization conjecture

geometric and algebraic reduction for singular momentum maps this paper concerns the reduction of singular constraint sets of symplectic manifolds it develops a geometric reduction procedure as well as continues the work of sniatycki and patrick on reduction a la dirac the relationships among the dirac geometric and sniatycki weinstein algebraic reduction procedures are studied primary emphasis is placed on the case where the constraints are given by the vanishing of a singular momentum map associated to the hamiltonian action of a compact lie group specifically an explicit local normal form is given for the momentum map which is used to show that these various reductions are all well defined and a necessary and sufficient condition for them to agree is derived related conditions are investigated and shown to be sufficient in the case of torus actions numerous examples are computed illustrating the results some discussion and examples are given for the noncompact case

existence uniqueness and cohomology of the classical brst charge with ghosts of ghosts a complete canonical formulation of the brst theory of systems with redundant gauge symmetries is presented these systems includep form gauge fields the superparticle and the superstring we first define the koszul tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic the global existence of the brst generator is then demonstrated and the brst charge is proved to be unique up to canonical transformations in the extended phase space which includes the ghosts finally the brst cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits as in the irreducible case this is done by re expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree which are identified with the ghosts of ghosts the quantum cohomology is not dealt with

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

from atiyah classes to homotopy leibniz algebras a celebrated theorem of kapranov states that the atiyah class of the tangent bundle of a complex manifold x makes t x 1 into a lie algebra object in d x the bounded below derived category of coherent sheaves on x furthermore kapranov proved that for a kahler manifold x the dolbeault resolution omega bullet 1 t x 1 0 of t x 1 is an l algebra in this paper we prove that kapranov s theorem holds in much wider generality for vector bundles over lie pairs given a lie pair l a i e a lie algebroid l together with a lie subalgebroid a we define the atiyah class e of an a module e as the obstruction to the existence of an a compatible l connection on e we prove that the atiyah classes l a and e respectively make l a 1 and e 1 into a lie algebra and a lie algebra module in the bounded below derived category d mathcal a where mathcal a is the abelian category of left mathcal u a modules and mathcal u a is the universal enveloping algebra of a moreover we produce a homotopy leibniz algebra and a homotopy leibniz module stemming from the atiyah classes of l a and e and inducing the aforesaid lie structures in d mathcal a

new stability criteria for linear discrete time systems with interval like time varying delays this technical note is concerned with stability of linear discrete time systems with interval like time varying delays two new stability criteria are derived by constructing a new lyapunov functional and utilizing two novel techniques for estimating the forward difference of the lyapunov functional the relationship between these stability criteria and some existing ones is established through the relationship it is clear that these stability criteria are less conservative than some existing ones which is confirmed by a numerical example

quantum dynamics on super groups constraints and the brst supergroup the smallest supergroup b k containing among its generators those of a constraint group k the brst charge and the corresponding ghost and antighost operators is constructed the supergroup b k can be enlarged to include the ordinary dynamical variables of the unconstrained physical system in a group approach to quantization b k generalizes the ordinary u 1 phase invariance of wave functions in particular this mechanism reproduces the essential features of the brst quantization when k is diff s1 the critical values of string theory are those for which the space of polarized functions on the enlarged brst supergroup is not irreducible

string field theory inspired algebraic structures in gauge theories we consider gauge theories in a string field theory inspired formalism the constructed algebraic operations lead in particular to homotopy algebras of the related batalin vilkovisky theories we discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields

new results on output feedback h_ infty control for linear discrete time systems this note investigates the problem of output feedback h control for linear discrete time systems three types of h controllers are considered namely static output feedback controllers dynamic output feedback controllers and observer based output feedback controllers new design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality lmi representations which guarantee the prescribed h performances of the closed loop systems in contrast to the existing lmi conditions for designing the output feedback h controllers the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example

splitting multisymplectic integrators for maxwell s equations in the paper we describe a novel kind of multisymplectic method for three dimensional 3 d maxwell s equations splitting the 3 d maxwell s equations into three local one dimensional lod equations then applying a pair of symplectic runge kutta methods to discretize each resulting lod equation it leads to splitting multisymplectic integrators we say this kind of schemes to be lod multisymplectic scheme lod ms the discrete conservation laws convergence dispersive relation dissipation and stability are investigated for the schemes theoretical analysis shows that the schemes are unconditionally stable non dissipative and of first order accuracy in time and second order accuracy in space as a reduction we also consider the application of lod ms to 2 d maxwell s equations numerical experiments match the theoretical results well they illustrate that lod ms is not only efficient and simple in coding but also has almost all the nature of multisymplectic integrators

generalized classical brst cohomology and reduction of poisson manifolds in this paper we formulate a generalization of the classical brst construction which applies to the case of the reduction of a poisson manifold by a submanifold in the case of symplectic reduction our procedure generalizes the usual classical brst construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold i e the case of reducible first class constraints in particular our procedure yields a method to deal with second class constraints we construct the brst complex and compute its cohomology brst cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension we then show that in the general case of reduction of poisson manifolds brst cohomology cannot be identified with the cohomology of vertical differential forms

algebraic structure of the brst symmetry an explicit construction of the brst symmetry is presented in the hamiltonian approach the construction is based on the splitting homotopy and the transference problem

energy dissipation splitting finite difference time domain method for maxwell equations with perfectly matched layers abstract in this paper we develop a novel kind of energy dissipation splitting finite difference time domain scheme for solving two dimensional maxwell equations with perfectly matched layers the discrete energy dissipation law convergence dispersion relation and stability are investigated for the scheme theoretical analysis shows that the scheme is unconditionally stable and of second order accuracy both in time and space numerical experiments confirm the theoretical results

positivity of continuous time descriptor systems with time delays this technical note is concerned with positivity characteristic of continuous time descriptor systems with time delays first a set of necessary and sufficient conditions is presented to check the property then considering a descriptor time delay system with two assumptions a new time delay system is established whose positivity is equivalent to that of the original system furthermore a set of necessary and sufficient conditions is provided to check the positivity of the new system finally a numerical example is given to illustrate the validity of the results obtained

energy conserved splitting spectral methods for two dimensional maxwell s equations in this paper the energy conserved splitting legendre galerkin method and energy conserved splitting legendre collocation method for maxwell s equations in two dimensions are proposed the schemes are energy conserved unconditionally stable and can be implemented efficiently the both methods are of second order convergence in time the high order error estimates in space for the two methods are also obtained for the ec s lc method an identity of the discrete divergence of electric fields is also obtained numerical examples are provided to confirm the theoretical analysis

homotopy algebras inspired by classical open closed string field theory we define a homotopy algebra associated to classical open closed strings we call it an open closed homotopy algebra ocha it is inspired by zwiebach s open closed string field theory and also is related to the situation of kontsevich s deformation quantization we show that it is actually a homotopy invariant notion for instance the minimal model theorem holds also we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

equivariant brst quantization and reducible symmetries working from first principles quantization of a class of hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the brst cohomology the constraints of this system correspond to a first class set for a group g and a second class set for a subgroup h the brst operator constructed is equivariant with respect to h using algebraic techniques analogous to those of equivariant de rham theory the brst operator is shown to correspond to that obtained by bv quantization of a class of systems with reducible symmetry the ghosts for ghosts correspond to the even degree two generators in the cartan model of equivariant cohomology as an example of the methods developed a topological model is described whose brst quantization relates to the equivariant cohomology of a manifold under a circle action

dissipativity analysis and design for uncertain markovian jump systems with time varying delays this paper deals with the problems of dissipativity analysis and dissipativity based controller design for markovian jump systems with both time varying delays and norm bounded parametric uncertainties improved delay dependent conditions for the system concerned to be strictly dissipative are established by using a mode dependent lyapunov krasovskii functional and introducing some slack variables these conditions are expressed by means of linear matrix inequalities lmis which are easy to check it is also shown that these conditions are less conservative than those obtained by using the existing methods the dissipativity synthesis problem is considered and on the basis of the obtained dissipativity conditions both the state feedback and dynamic output feedback controllers are designed to guarantee the strict dissipativity of the closed loop systems numerical examples are provided to demonstrate the utility of the developed methods

a new h_ bm infty stabilization criterion for networked control systems this note is concerned with robust hinfin control of linear networked control systems with time varying network induced delay and data packet dropout a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the time varying network induced delay is proposed to drive a new delay dependent hinfin stabilization criterion the criterion is formulated in the form of a non convex matrix inequality of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequalities in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no slack variable is introduced finally two numerical examples are given to show the effectiveness of the proposed design method

geometric brst quantization i prequantization this is the first part of a two part paper dedicated to the definition of brst quantization in the framework of geometric quantization after recognizing prequantization as a manifestation of the poisson module structure of the sections of the prequantum line bundle we define brst prequantization and show that it is the homological analog of the symplectic reduction of prequantum data we define a prequantum brst cohomology theory and interpret it in terms of geometric objects we then show that all poisson structures correspond under homological reduction this allows to prove in the brst context that prequantization and reduction commute

further results on variable output feedback controllers zak and hui 1993 proposed a sliding mode controller for linear multiple input multiple output mimo systems using static output feedback the author s previous paper 1996 provides an improvement of the output feedback controller of zak hui for a class of linear single input single output siso systems that eliminated two important limitations 1 system uncertainties must be bounded by the system output and 2 a requirement of a matrix inequality the controller developed previously can guarantee global closed loop stability this paper extends the previous results to linear mimo systems it is emphasized that the proposed mimo controller yields global closed loop stability whereas the one in zak hui can only guarantee local stability an application of the proposed mimo controller to an aircraft model is included to show the effectiveness of the method

stabilization of stochastic delay systems via a disordered controller abstract in this paper the stabilization for stochastic delay systems is achieved by a disordered controller different from the traditionally stabilizing controllers the controller designed here experiences a disorder between control gains and system states by exploiting the robust method the above disorder is described as a controller having special uncertainties moreover the probability distribution of such uncertainties is embodied by a bernoulli variable a sufficient condition for the existence of such a disordered controller is given with lmis where the probability is considered in its design procedure based on this description a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied whose lmi conditions are presented too finally a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods

the splitting finite difference time domain methods for maxwell s equations in two dimensions in this paper we consider splitting methods for maxwell s equations in two dimensions a new kind of splitting finite difference time domain methods on a staggered grid is developed the corresponding schemes consist of only two stages for each time step which are very simple in computation the rigorous analysis of the schemes is given by the energy method it is proved that the scheme is unconditionally stable and convergent for the problems with perfectly conducting boundary conditions numerical dispersion analysis and numerical experiments are presented to show the efficient performance of the proposed methods furthermore the methods are also applied to solve a scattering problem successfully