blow up of solutions to 1 d euler equations with time dependent damping abstract we study the 1 d isentropic euler equations with time dependent damping t x u 0 t u x u 2 x p 1 t u t 0 1 e 0 x u t 0 e u 0 x in a previous paper 8 we have proven that when 1 2 the 1 d euler equations have global existence of small data solutions however in this paper we will show that when the damping with respect to time decays faster or equal to 2 1 t the c 1 solution of the above system will blow up in finite time more precisely when 1 0 2 or 1 0 we will give a finite upper bound for the lifespan combining the results in this paper and 8 we see that when the damping decays with time like 1 t the critical exponents for to separate the global existence and finite time blow up of small data solutions are 1 2

technical communique a modified extended kalman filter for linear discrete time systems with unknown parameters this technical communique presents a modified extended kalman filter for estimating the states and unknown parameters in discrete time multi input multi output linear systems the hyperstability of the filter is guaranteed by introducing a compensator into the estimation mechanism it is proved that the estimates for the states and unknown parameters converge to the exact values if some conditions are assumed to the estimation mechanism a numerical example shows that the proposed filter is much more effective than the extended kalman filter in the estimation of unknown parameters

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

projective techniques and functional integration for gauge theories a general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact hausdorff spaces the procedure is then applied to gauge theories to carry out integration over the non linear infinite dimensional spaces of connections modulo gauge transformations this method of evaluating functional integrals can be used either in the euclidean path integral approach or the lorentzian canonical approach a number of measures discussed are diffeomorphism invariant and therefore of interest to the connection dynamics version of quantum general relativity the account is pedagogical in particular prior knowledge of projective techniques is not assumed

an interlaced extended kalman filter an estimation algorithm for a class of discrete time nonlinear systems is proposed the system structure we deal with is partitionable into in subsystems each affine w r t the corresponding part of the state vector the algorithm consists of a bank of m interlaced kalman filters and each of them estimates a part of the state considering the remaining parts as known time varying parameters whose values are evaluated by the other filters at the previous step the procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably increasing the noise covariance matrices comparisons through numerical simulations with the extended kalman filter and its modified versions proposed in the literature illustrate the good trade off provided by the algorithm between the reduction of the computational load and the estimation accuracy

the status of diffeomorphism superselection in euclidean 2 1 gravity this work addresses a specific technical question of relevance to canonical quantization of gravity using the so called new variables and loop based techniques of ashtekar rovelli and smolin in particular certain superselection laws that arise in current applications of these techniques to solving the diffeomorphism constraint are considered their status is elucidated by studying an analogous system 2 1 euclidean gravity for that system these superselection laws are shown to be spurious this however is only a technical difficulty the usual quantum theory may still be obtained from a loop representation and the technique known as refined algebraic quantization

convergence to nonlinear diffusion waves for solutions of euler equations with time depending damping abstract in this paper we are concerned with the asymptotic behavior of solutions to the system of euler equations with time depending damping in particular include the constant coefficient damping we rigorously prove that the solutions time asymptotically converge to the diffusion wave whose profile is self similar solution to the corresponding parabolic equation which justifies darcy s law compared with previous results about euler equations with constant coefficient damping obtained by hsiao and liu 1992 2 and nishihara 1996 9 we obtain a general result when the initial perturbation belongs to the same space i e h 3 r h 2 r our proof is based on the classical energy method

convergence to nonlinear diffusion waves for solutions of p system with time dependent damping abstract in this paper we study the cauchy problem for the hyperbolic p system with time gradually degenerate damping term 1 1 t u for 0 1 and show that the damped p system has a couple of global solutions uniquely and such solutions tend time asymptotically to the shifted nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation governed by the darcy s law we further derive the convergence rates when the initial perturbations are in l 2 the approach adopted is the technical time weighted energy method

wave equations with time dependent dissipation ii effective dissipation abstract this article is intended to present a construction of structural representations of solutions to the cauchy problem for wave equations with time dependent dissipation above scaling these representations are used to give estimates of the solution and its derivatives based on l q r n q 2 the article represents the second part within a series in jens wirth wave equations with time dependent dissipation i non effective dissipation j differential equations 222 2 2006 487 514 weak dissipations below scaling were discussed

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

quantization of diffeomorphism invariant theories of connections with local degrees of freedom quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions this provides in particular a quantization of the husain kucha model the main results also pave the way to quantization of other diffeomorphism invariant theories such as general relativity in the riemannian case i e signature the approach appears to contain all the necessary ingredients already in the lorentzian case it will have to be combined in an appropriate fashion with a coherent state transform to incorporate complex connections

extension of friedland s separate bias estimation to randomly time varying bias of nonlinear systems by extending b friedland s 1969 separate bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended kalman filter proposed by d h zhou 1990 and by d h zhou et al a pseudo separate bias estimation algorithm for randomly time varying bias of a class of nonlinear time varying stochastic systems is obtained a simulation example is presented to illustrate the effectiveness of the algorithm

modified extended kalman filtering in this paper we compare the performance of the extended kalman filter ekf with that of a proposed filter called modified extended kalman filter mekf in terms of the actual state and the estimated state as a function of time and the integral squared error as a function of noise intensity both for dynamics and measurement noise all the simulation results indicate that the performance of the mekf is better than ekf for illustration numerical examples are presented using both ekf and mekf

singularity formation for the 1d compressible euler equations with variable damping coefficient abstract in this paper we consider some blow up problems for the 1d euler equations with time and space dependent damping we investigate sufficient conditions on initial data and the rate of spatial or time like decay of the coefficient of damping for the occurrence of the finite time blow up in particular our sufficient conditions ensure that the derivative blow up occurs in finite time with the solution itself and the pressure bounded our method is based on simple estimates with riemann invariant furthermore we give sharp lower and upper estimates of the lifespan of solutions when initial data are small perturbations of constant states

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

modified extended kalman filtering and a real time parallel algorithm for system parameter identification a modification of the extended kalman filter ekf algorithm which is called mekf for short it introduced the modification is achieved by an improved linearization procedure for this purpose a parallel computational scheme is recommended and it has immediate applications to identifying unknown system parameters of time varying linear stochastic state space models in real time it should be noted that just like the ekf the mekf is also ad hoc in the sense that it is a real time approximation method numerical examples with computer simulation are included to demonstrate the effectiveness of this procedure as compared to the ekf algorithm

a reduced order extended kalman filter for sequential images containing a moving object the extended kalman filter ekf is applied to the reduction of noise in sequential images containing a moving object and to the estimation of the object s velocity a computationally tractable approximation of the ekf called the parallel extended kalman filter pekf is generated the pekf consists of a parallel bank of third order ekfs operating on the fourier coefficients of the image followed by a finite impulse response filter the pekf is shown to converge to the optimal in the mean square sense algorithm in the limit as the velocity estimation errors approach zero the performance of the pekf is demonstrated for very low signal to noise ratio snr images the pekf also provides a natural setting for tracking slow changes in the object real or apparent and its velocity since these variations are included in the model the relation of the pekf to another frequency domain algorithm for velocity estimation is discussed the algorithm is illustrated by application to an example and its performance is demonstrated in the presence of velocity estimation errors

a stochastic analysis of a modified gain extended kalman filter with applications to estimation with bearings only measurements a new globally convergent nonlinear observer called the modified gain extended kalman observer mgeko is developed for a special class of systems this observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended kalman filter mgekf a sufficient condition for the estimation errors of the mgekf to be exponentially bounded in the mean square is obtained finally the mgeko and the mgekf are applied to the three dimensional bearings only measurement problem where the extended kalman filter often shows erratic behavior

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

linearized reduced order filtering a reduced order version of extended kalman filtering is presented in which both the filtering equation and the associated riccati equation have been reduced in dimension to allow for real time processing the procedure for designing the reduced order filter is similar to that for designing the extended kalman filter the same approximations being applied one technique useful for limiting the computational burden in a linearized filter design problems is presented and illustrated by an example the primary limitation of the result is that the nonlinearity must be in terms of the vector to be estimated

reduction of the einstein equations in 2 1 dimensions to a hamiltonian system over teichmuller space in this paper the adm arnowitt deser and misner reduction of einstein s equations for three dimensional space times defined on manifolds of the form r where is a compact orientable surface is discussed when the genus g of is greater than unity it is shown how the einstein constraint equations can be solved and certain coordinate conditions imposed so as to reduce the dynamics to that of a time dependent hamiltonian system defined on the 12g 12 dimensional cotangent bundle t t of the teichmuller space t of the hamiltonian is only implicitly defined in terms of the solution of an associated lichnerowicz equation but its existence uniqueness and smoothness are established by standard analytical methods similar results are obtained for the case of genus g 1 where in fact the hamiltonian can be computed explicitly and hamilton s equations integrated exactly as was found previously by martinec the results are relevant to the problem of the reduction of the 3 1 dimensional einstein equations formulated on circle bundles over r and with a spacelike killing field tangent to the fibers of the chosen bundle and to the recent discussion by witten of the possible exact solvability of the topological dynamics associated with einstein s equations in 2 1 dimensions

global existence of solutions to 1 d euler equations with time dependent damping abstract in this paper we study the 1 d isentropic euler equations with time dependent damping our damping decays at a speed of order 1 with respect to time which is a little weaker than the linear one under our assumption we will prove the global existence of solutions to the euler system and obtain l 2 and l estimates for the solutions our approach is based on some detailed energy estimates

asymptotic behavior of solutions to bipolar euler poisson equations with time dependent damping abstract in this paper we study the one dimensional euler poisson equations of bipolar hydrodynamic model for semiconductor device with time dependent damping effect j 1 t for 1 1 where the damping effect is time gradually degenerate for 0 and time gradually enhancing for 0 such a damping effect makes the hydrodynamic system possess the nonlinear diffusion phenomena time asymptotic weakly or strongly based on technical observation and by using the time weighted energy method where the weights are artfully chosen we prove that the system admits a unique global smooth solution which time asymptotically converges to the corresponding diffusion wave when the initial perturbation around the diffusion wave is small enough the convergence rates are specified in the algebraic forms o t 3 4 1 and o t 1 according to different values of in 1 1 7 and 1 7 1 respectively where 1 7 is the critical point and the convergence rate at the critical point is o t 6 7 ln t all these convergence rates obtained in different cases are optimal in the sense when the initial perturbations are l 2 integrable particularly when 1 7 the convergence rate is the fastest namely the asymptotic profile of the original system at the critical point is the best

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

global and blow up solutions for compressible euler equations with time dependent damping abstract this paper deals with the cauchy problem for the compressible euler equations with time dependent damping where the time vanishing damping in the form of 1 t makes some fantastic variety of the dynamic system for 0 1 and 0 or 1 but 2 the solutions are proved to exist globally in time when the derivatives of the initial data are small but the initial data themselves can be arbitrarily large this is the so called challenging case of global solutions with large initial data while when the initial riemann invariants are monotonic and their derivatives with absolute value are large at least at one point then the solutions are still bounded but their derivatives will blow up at finite time somewhat like the singularity formed by shock waves for 1 and 0 or 1 but 0 1 the derivatives of solutions will blow up even for all initial data including the interesting case of blow up solutions with small initial data here the initial riemann invariants are monotonic in fact such a blow up phenomenon is determined by the mechanism of the dynamic system itself in order to prove the global existence of solutions with large initial data we introduce a new energy functional related to the riemann invariants which crucially enables us to build up the maximum principle for the corresponding riemann invariants and the uniform boundedness for the local solutions finally numerical simulations in different cases are carried out which further confirm our theoretical results