differential stackel matrices we show that additive separation of variables for linear homogeneous equations of all orders is characterized by differential stackel matrices generalizations of the classical stackel matrices used for multiplicative separation of second order schrodinger equations and additive separation of hamilton jacobi equations we work out the principal properties of these matrices and demonstrate that even for second order laplace equations additive separation may occur when multiplicative separation does not

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

new variable separation approach application to nonlinear diffusion equations the concept of the derivative dependent functional separable solution ddfss as a generalization to the functional separable solution is proposed as an application it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach as a consequence a complete list of canonical forms for such equations which admit the ddfss is obtained and some exact solutions to the resulting equations are described

robustness bound for receding horizon finite memory control lyapunov krasovskii approach this article presents a robustness bound rb of receding horizon finite memory control rhfmc kwon w h and han s 2004 receding horizon finite memory controls of output feedback controls for state space systems ieee transactions on automatic control 49 1905 1915 for continuous time state space systems with norm bounded uncertainties the proposed rb is easily obtained by solving a convex problem in terms of a linear matrix inequality we show through a numerical example that the rhfmc can guarantee the robust stabilisation for a larger class of uncertain systems than linear quadratic gaussian controls when some poles of closed loop systems are close to an imaginary axis in the complex plane

group properties of generalized quasi linear wave equations abstract in this paper complete group classification of a class of 1 1 dimensional generalized quasi linear wave equations is performed by using the lie ovsiannikov method additional equivalent transformation and furcate split method lie reductions of some truly variable coefficient wave equations which are singled out from the classification results are investigated some classes of exact solutions of these variable coefficient wave equations are constructed by means of both the reductions and the additional equivalent transformations the nonclassical symmetries to the generalized quasi linear wave equation are also studied this enabled to obtain some exact solutions of the wave equations which are invariant under certain conditional symmetries

robust deadbeat continuous time observer design based on modulation integrals abstract in this paper the state estimation problem of linear continuous time systems is dealt with by a non asymptotic state observer which allows the state estimation error to decay within an arbitrarily small finite time without resorting to high gain injection by processing the measured input and output signals through modulation integrals a number of auxiliary signals not affected by the initial conditions are obtained from which the system state can be computed by simple algebra the problem of internal instability of modulation integrals is addressed by resorting to a periodic rescaling mechanism that prevents error accumulation and singularities we show that the combination of modulation integrals with periodic rescaling can be implemented as a jump linear system the robustness of the devised method with respect to additive measurement perturbations on the system s input output is characterized by input to state stability arguments

optimal state estimation without the requirement of a priori statistics information of the initial state the result given by the kalman filter is the best linear unbiased estimate blue provided that the mean and variance of the initial state are known the same state estimation problem is reconsidered for multi input multi output mimo stochastic time varying discrete systems when the statistics knowledge about the initial state is not known the algorithm presented in this paper gives the blue of system states without the requirement of any a priori knowledge about the initial state the concept of complete reconstructibility of stochastic systems is established and the necessary and sufficient condition for complete reconstructibility is given when applied to a completely reconstructible deterministic system the proposed algorithms give the deadbeat state estimates even if the system is not observable

receding horizon unbiased fir filters for continuous time state space models without a priori initial state information a receding horizon unbiased finite impulse response filter rhuff is proposed for continuous time state space models linearity unbiasedness finite impulse response fir structure and independence of the initial state information will be required in advance in addition to a performance index of minimum variance the proposed rhuff is obtained by directly minimizing the performance index with the unbiasedness constraint the proposed rhuff is represented first in a standard fir form and then in an iterative form it is shown that the rhuff is equivalent to the existing receding horizon rh kalman fir filter the former is more systematic and logical while the latter is heuristic due to the handling of infinite covariance of the initial state information

unique isoperimetric foliations of asymptotically flat manifolds in all dimensions the question of isoperimetry what is the largest amount of volume that can be enclosed by a given amount of area can be traced back to antiquity 1 the first mathematically rigorous results are as recent as the nineteenth century the question of isoperimetry and its close relative the analysis of minimal surfaces are two of the model problems of the geometric calculus of variations the list of geometries where an explicit answer to the question of isoperimetry is available is short we provide an overview of available results in appendix h in this paper and 22 we extend this list by a class of riemannian manifolds m g for which we describe all large isoperimetric regions completely we refer the reader to sect 2 for the precise definitions of all terms in the statement of our first main theorem

fir filters and recursive forms for continuous time invariant state space models an fir finite impulse response filter and an fir smoother are introduced for continuous time invariant state space models it is shown in this note that finite impulse responses of the fir filter and smoother can be easily determined by solving a simple riccati type matrix differential equation on a finite interval especially for systems with stationary processes finite impulse responses of the fir filter and smoother become time invariant and can be computed from simpler equations for fast computational purposes recursive forms of the fir filter and smoother are derived by using adjoint variables in this case all gains for recursive forms are shown to be constant

generalized stackel matrices stackel and differential stackel matrices are generalized so that the matrix elements may be functions of the derivatives of the dependent variable as well as the independent variable the inverses of these matrices are characterized and it is shown that for significant classes of linear and nonlinear partial differential equations variable separation is accomplished via this generalized stackel mechanism

optimal memory for discrete time fir filters in state space in this correspondence we propose an efficient estimator of optimal memory averaging interval for discrete time finite impulse response fir filters in state space its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics testing by the two state polynomial model has shown a very good correspondence with predicted values even in the worst case of the harmonic model the estimator demonstrates practical applicability

observer matrix gain optimization for stochastic continuous time nonlinear systems it is shown that for a class of stationary stochastic nonlinear systems satisfying a global lipschitz condition the high gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation the nonlinearity is assumed to be a priory known the main contribution of this paper consists in designing of a numerical procedure for the optimal gain matrix minimizing this upper bound the convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability it is shown that within a neighborhood of the optimal matrix gain the others provide lower estimation performance

positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature in this paper we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary using a general version of positive mass theorem of schoen yau and witten we prove the following theorem for any compact manifold with boundary and nonnegative scalar curvature if it is spin and its boundary can be isometrically embedded into euclidean space as a strictly convex hypersurface then the integral of mean curvature of the boundary of the manifold cannot be greater than the integral of mean curvature of the embedded image as a hypersurface in euclidean space moreover equality holds if and only if the manifold is isometric with a domain in the euclidean space conversely under the assumption that the theorem is true then one can prove the adm mass of an asymptotically flat manifold is nonnegative which is part of the positive mass theorem

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

recursive solutions to deadbeat observers for time varying multivariable systems this paper describes a new construction of the deadbeat observer for the state estimation of linear time varying multivariable systems the proposed design methods are computationally attractive because of their simplicity and recursive nature and are recommendable even for time invariant multivariable systems

brief paper minimax fir smoothers for deterministic continuous time state space models in order to design a smoother for a deterministic continuous time state space model a new performance criterion is proposed which is given by a ratio of the current estimation error to the weighted energy of the deterministic disturbance applied during the recent finite horizon among smoothers with the deadbeat property and finite impulse response fir structure a minimax fir smoother mfs is obtained to optimize the proposed performance criterion to begin with the functional optimization problem is formulated with respect to kernel functions of the mfs and then its solution is explicitly presented the mfs depends only on inputs and outputs on the finite recent horizon and is independent of any a priori state information the mfs is first represented in an integral form for simple representation and then a differential form is introduced for efficient numerical computation as in h iir smoothing and h 2 iir filtering it is shown that the proposed mfs for a deterministic system can be interpreted as the minimum variance unbiased fir smoother for a stochastic system

design of rls fir filter using covariance information in linear continuous time stochastic systems this paper addresses a new design method of recursive least squares rls and finite impulse response fir filter using covariance information in linear continuous time stochastic systems the signal process is observed with additive white noise it is assumed that the white observation noise is independent of the signal process the auto covariance function of the signal is expressed in the semi degenerate kernel form the rls fir filter uses the following information 1 the auto covariance function of the signal expressed in the semi degenerate kernel form 2 the variance of the white observation noise process 3 the observed values

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

a family of nonlinear klein gordon equations and their solutions various forms of the nonlinear klein gordon equation are seen to have exact solitonlike solutions when separation of variables is postulated the family for which these exact solutions are found includes the sine gordon equation as a special case an interesting conclusion obtained is that both the soliton antisoliton and breather solutions hitherto known for the sine gordon equations result from a broader class of klein gordon equations the method can be extended to other equations

h_2 output feedback control with finite multiple measurement information this paper proposes a new h 2 output feedback control with finite multiple measurement information for discrete time systems with disturbances this control is called an h 2 finite multiple measurement output feedback control h2fmmofc the new control ascertains the h 2 performance for disturbances and the equivalence to the h 2 state feedback control without disturbances on a finite measurement horizon the boundedness and exponential stability of the proposed h2fmmofc are also investigated the gain matrices of the h2fmmofc are obtained by solving a convex problem utilizing the linear matrix inequality tool via a numerical example the h2fmmofc is shown to ensure the h 2 performance as well as the excellent robustness property against unexpected temporary model uncertainty although the uncertainty is not considered in its design

short time fourier analysis via optimal harmonic fir filters the fourier coefficients fcs of quasiperiodic signals are assumed to be in random walk motion in order to represent a broader class a state model for such quasiperiodic signals is derived the optimal short time estimate of the fourier coefficients is obtained via the suggested optimal harmonic fir filter ohff based on this state space signal model the optimal harmonic fir filter can be considered to be a generalization of the discrete fourier transform dft in the sense that it becomes the same as the dft when the state model is for periodic signals and the filter length is equal to the order of the state model the optimal harmonic fir filter derived from the model even with nonzero state noise and measurement noise gives an exact harmonic estimate when an incoming signal is periodic and noiseless it is shown by examples that the ability to suppress noise and the ability to resolve changes of the fourier coefficients can be adjusted by the filter length and the noise covariance of the state model finally the suggested scheme is compared with existing short time fourier analysis methods in a test signal that has time varying fourier coefficients

2 1 dimensional m n component akns system painleve integrability infinitely many symmetries similarity reductions and exact solutions the 2 1 dimensional m n component akns system that is derived from the inner parameter dependent symmetry constraint of the kp equation is studied in detail first the painleve integrability of the model is proved by using the standard wtc and kruskal approach using the formal series symmetry approach the generalized kmv symmetry algebra and the related symmetry group are found the two dimensional similarity partial differential equation reductions and the ordinary differential equation reductions are obtained from the generalized kmv symmetry algebra and the direct method abundant localized coherent structures are revealed by the variable separation approach some special types of the localized excitations like the multiple solitoffs dromions lumps ring solitons breathers and instantons are plotted also

separation of variables in the nonlinear wave equation we develop a technique making it possible to handle the problem of separation of variables in nonlinear differential equations using it we obtain a number of new two dimensional nonlinear wave equations admitting separation of variables and construct their exact solutions

functionally separable solutions to nonlinear wave equations by group foliation method abstract we apply functional separation of variables within the approach of the group foliation method to the nonlinear wave equation with variable speed and external force u t t a x d u u x x b x q u a x 0 a classification of these equations admitting functionally separable solutions is performed and the resulting solutions are obtained in explicit form in many cases

separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source abstract a solution of a partial differential equation with two real variables t and x is functionally separable in these variables if q u x t for some single variable functions q and in this paper the generalized conditional symmetry approach is used to study the separation of variables of quasilinear diffusion equations with nonlinear source we obtain a complete list of canonical forms for such equations which admit the functionally separable solutions as a result we get broad families of exact solutions to some quasilinear diffusion equations with nonlinear source the behavior and blow up properties of some solutions are described

foliations by stable spheres with constant mean curvature for isolated systems with general asymptotics we prove the existence and uniqueness of constant mean curvature foliations for initial data sets which are asymptotically flat satisfying the regge teitelboim condition near infinity it is known that the hamiltonian center of mass is well defined for manifolds satisfying this condition we also show that the foliation is asymptotically concentric and its geometric center is the center of mass the construction of the foliation generalizes the results of huisken yau ye and metzger where strongly asymptotically flat manifolds and their small perturbations were studied

evolution equations invariant surface conditions and functional separation of variables abstract this paper is devoted to a discussion of the reduction methods for evolution equations based on invariant surface conditions related to functional separation of variables the relationship of these methods with nonclassical and weak point symmetries is stressed applications to diffusion equations with an inhomogeneous reaction term or with saturating dissipation are provided

differential invariants and group foliation for the complex monge ampere equation we apply the method of group foliation to the complex monge ampere equation cma 2 with the goal of establishing a regular framework for finding its non invariant solutions we employ the infinite symmetry subgroup of the equation the group of unimodular biholomorphisms to produce a foliation of the solution space into leaves which are orbits of solutions with respect to the symmetry group accordingly cma 2 is split into an automorphic system and a resolvent system which we derive in this paper this is an intricate system and here we make no attempt to solve it in order to obtain non invariant solutions we obtain all differential invariants up to third order for the group of unimodular biholomorphisms and in particular all the basis differential invariants we construct the operators of invariant differentiation from which all higher differential invariants can be obtained consequently we are able to write down all independent partial differential equations with one real unknown and two complex independent variables which keep the same infinite symmetry subgroup as cma 2 we prove explicitly that applying operators of invariant differentiation to third order invariants we obtain all fourth order invariants at this level we have all the information which is necessary and sufficient for group foliation we propose a new approach in the method of group foliation which is based on the commutator algebra of operators of invariant differentiation the resolving equations are obtained by applying this algebra to differential invariants with the status of independent variables furthermore this algebra together with jacobi identities provides the commutator representation of the resolvent system this proves to be the simplest and most natural way of arriving at the resolving equations

foliations of asymptotically flat 3 manifolds by 2 surfaces of prescribed mean curvature we construct 2 surfaces of prescribed mean curvature in 3manifolds carrying asymptotically flat initial data for an isolated gravitating system with rather general decay conditions the surfaces in question form a regular foliation of the asymptotic region of such a manifold we recover physically relevant data especially the adm momentum from the geometry of the foliation for a given set of data m g k with a three dimensional manifold m its riemannian metric g and the second fundamental form k in the surrounding four dimensional lorentz space time manifold the equation we solve is h p const or h p const here h is the mean curvature and p trk is the 2 trace of k along the solution surface this is a degenerate elliptic equation for the position of the surface it prescribes the mean curvature anisotropically since p depends on the direction of the normal

separation of variables for scalar evolution equations in one space dimension the flow of an autonomous kth order evolution equation in one space dimension is generated by a kth order ordinary differential operator on the space of fields the characteristic fields are the solutions of the characteristic equation of the operator a solution of the evolution equation is separable if and only if it is a curve in the k c 1 parameter space of characteristic fields the non stationary characteristic fields with separable evolution are those which remain characteristic under small dilation every characteristic field has local separable evolution if and only if the characteristic equation is infinitesimally dilation invariant this is the case when the evolutionary generator is an infinitesimal symmetry of the characteristic equation so that its flow stabilizes the space of characteristic fields the evolution equation is then locally homogeneous if and only if the characteristic value is an invariant of the restricted flow which is a non generic property the separable kth order evolution equations are parametrized by the kth order invariants of the locally homogeneous k c 1 th order ordinary differential equations

receding horizon recursive state estimation describes a receding horizon discrete time state observer using the deterministic least squares framework the state estimation horizon which determines the number of past measurement samples used to reconstruct the state vector is introduced as a tuning parameter for the proposed state observer a stability result concerning the choice of the state estimation horizon is established it is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

separation of variables of a generalized porous medium equation with nonlinear source this paper considers a general form of the porous medium equation with nonlinear source term ut d u u n x f u n 1 the functional separation of variables of this equation is studied by using the generalized conditional symmetry approach we obtain a complete list of canonical forms for such equations which admit the functional separable solutions as a consequence some exact solutions to the resulting equations are constructed and their behavior are also investigated 2002 elsevier science usa all rights reserved

brief a receding horizon unbiased fir filter for discrete time state space models this paper concerns with a new linear finite impulse response fir filter called the receding horizon unbiased fir rhuf filter for the state estimation in discrete time state space models to obtain the rhuf filter linearity unbiasedness and fir structure will be required beforehand in addition to a performance criteria of minimum variance the rhuf filter is obtained by directly solving an optimization problem with the unbiasedness constraint the rhuf filter has time invariance and deadbeat properties the rhuf filter is represented in both a batch form and an iterative form it is shown that the rhuf filter is equivalent to the existing receding horizon kalman fir rhkf filter whose optimality is not clear to understand the former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state information

least squares finite impulse response fixed lag smoother and filter in linear discrete time stochastic systems abstract this paper proposes the least squares ls finite impulse response fir fixed lag smoother and filter in linear discrete time wide sense stationary stochastic systems the fir fixed lag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values it is assumed that the signal is observed with additional white noise which is uncorrelated with the signal process by solving the simultaneous linear equations transformed from the wiener hopf equation the optimal impulse response function is obtained the necessary information of the ls fir fixed lag smoothing algorithm is the auto covariance function of the signal process and the variance of the observation noise process in particular this paper proposes the levinson durbin algorithm which needs less amount of arithmetic operations than the gauss jordan elimination method in the inverse of the toeplitz matrix for the optimal impulse response function from the numerical simulation example the proposed ls fir fixed lag smoother and filter are superior in estimation accuracy to the rls wiener fir estimators

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

the ricci flow on the 2 sphere the classical uniformization theorem interpreted differential geomet rically states that any riemannian metric on a 2 dimensional surface ispointwise conformal to a constant curvature metric thus one can con sider the question of whether there is a natural evolution equation whichconformally deforms any metric on a surface to a constant curvature met ric the primary interest in this question is not so much to give a newproof of the uniformization theorem but rather to understand nonlinearparabolic equations better especially those arising in differential geome try a sufficiently deep understanding of parabolic equations should yieldimportant new results in riemannian geometry the question in the preceding paragraph has been studied by richardhamilton 3 and brad osgood ralph phillips and peter sarnak 6 in 3 hamilton studied the following equation which we refer to as

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

a continuous time recursive fixed lag smoother converging in finite time in this technical note we propose a new fixed lag smoother that estimates the fixed delayed state for a stochastic continuous time system the estimation error variance of the proposed smoother is minimized under the constraint that the estimated state converges to the real state exactly in finite time after noises or uncertainties disappear for numerical computing the proposed smoother is represented in a recursive form unlike other approaches any additional processes such as batch processing and sampling data through discrete time techniques are not required to achieve the finite time convergence a numerical example is presented to illustrate the finite time convergence of the proposed smoother in comparison with the asymptotic convergence of an optimal smoother

directional sensitivity of continuous least squares state estimators abstract least squares state estimators present an alternative to luenberger observers and yield an exact deadbeat estimate of the state vector of a dynamic system as the optimal solution to a least squares problem in some vector or functional space for instance the conventional l 2 optimal finite memory observer is shown to be a special case of the continuous least squares state estimator sensitivity of these estimators to structured uncertainty in the system matrix of the plant is studied using the frechet derivative it is shown that the state estimation error caused by the plant model s mismatch is proportional to the frechet derivative of the symbol of the parameterization operator used for the estimator implementation evaluated for the nominal value of the system matrix for the special case of state estimation in a single tone continuous oscillator the crucial impact of the parameterization operator choice on the state estimator sensitivity to the plant model s uncertainty is investigated in detail

linear optimal fir estimation of discrete time invariant state space models this paper addresses a general p shift linear optimal finite impulse response fir estimator intended for solving universally the problems of filtering p 0 smoothing p 0 of discrete time invariant models in state space an optimal solution is found in the batch form with the initial mean square state function self determined by solving the discrete algebraic riccati equation an unbiased solution represented both in the batch and recursive forms does not involve any knowledge about noise and initial state the mean square errors in both the optimal and unbiased estimates are found via the noise power gain npg and a recursive algorithm for fast computation of the npg is supplied applications are given for fir filtering with fixed receding and full averaging horizons

symmetry groups and separation of variables of a class of nonlinear diffusion convection equations in this paper a class of nonlinear diffusion convection equations ut d u uxn x p u ux which has quite a large number of physical applications is analysed by using symmetry group methods which include the classical method the potential symmetry method and the generalized conditional symmetry method a complete classification of the functional forms of the diffusion and convection coefficients is presented when the equation admits lie s point symmetry groups and potential symmetry groups the separation of variables for the equation is investigated using the generalized conditional symmetry approach for some interesting cases exact solutions using the method of separation of variables are discussed in detail

exact solutions of semilinear radial wave equations in n dimensions abstract exact solutions are derived for an n dimensional radial wave equation with a general power nonlinearity the method which is applicable more generally to other nonlinear pdes involves an ansatz technique to solve a first order pde system of group invariant variables given by group foliations of the wave equation using the one dimensional admitted point symmetry groups these groups comprise scalings and time translations admitted for any nonlinearity power in addition to space time inversions admitted for a particular conformal nonlinearity power this is shown to yield not only group invariant solutions as derived by standard symmetry reduction but also other exact solutions of a more general form in particular solutions with interesting analytical behavior connected with blow ups as well as static monopoles are obtained

fir filters and recursive forms for discrete time state space models abstract an fir finite impulse response filter and an fir smoother are introduced for discrete time state space models with system noise the fir structure not only guarantees both the bibo stability and the robustness to some parameter changes but also improves the filter divergence problem it is shown in this paper that impulse responses of both the fir filter and the fir smoother are easily obtained from riccati type difference equations especially for time invariant state space models they are also to be time invariant and finally determined by simple equations on a finite interval for the purpose of implementation recursive forms of the fir filter and smoother are derived using each other as adjoint variables improved characteristics of the fir filter in the divergence problem are demonstrated via a simulation

recursive limited memory filtering and scattering theory corresp redheffer scattering theory is reviewed in a generalized setting as a method to derive recursive solutions of linear two point boundary value problems tpbvp over arbitrarily varying intervals the results can be used to derive a complete solution for the problem of limited memory or sliding window estimation when a usual state space model for the signal is available recursive limited memory filters are derived for both continuous and discrete time signals

fast design of 2 d linear phase complex fir digital filters by analytical least squares method two dimensional full plane and half plane filters are more general and much better frequency responses can be obtained than the quarter plane filters in this correspondence the analytical least squares method is generalized and extended for designing 2 d full plane and half plane linear phase complex fir digital filters the 2 d filter s coefficients can be effectively determined by use of a closed form transformation matrix and some simple element functions the unique advantage of this technique is that it is very fast without employing iterative optimization procedures and matrix inversions design examples are presented to illustrate the simplicity and efficiency of the proposed method

suboptimal fir filtering of nonlinear models in additive white gaussian noise the first and second order extended finite impulse response efir1 and efir2 respectively filters are addressed for suboptimal estimation of nonlinear discrete time state space models with additive white gaussian noise it is shown that unlike the extended kalman filter ekf and efir2 filter the efir1 one does not require noise statistics and initial errors only within a narrow region around actual noise covariances efir filters fall a bit short of ekf and they demonstrate better performance otherwise it is shown that the optimal averaging interval for efir filters can be determined via measurement without a reference model in a learning cycle we also notice that the second order approximation can improve the local performance but it can also deteriorate it we thus have no recommendations about its use at least for tracking considered as an example of applications

a receding horizon kalman fir filter for discrete time invariant systems a receding horizon kalman fir filter is presented that combines the kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown the suggested filter is a fir filter form which has many good inherent properties it can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state the suggested filter can be represented in either an iterative form or a standard fir form it is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition the validity of the suggested filter is illustrated by numerical examples

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

on the new approach to variable separation in the time dependent schrodinger equation with two space dimensions we suggest an effective approach to separation of variables in the schrodinger equation with two space variables using it we classify inequivalent potentials v x1 x2 such that the corresponding schrodinger equations admit separation of variables besides that we carry out separation of variables in the schrodinger equation with the anisotropic harmonic oscillator potential v k1x21 k2x22 and obtain a complete list of coordinate systems providing its separability most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free schrodinger equation v 0

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

a receding horizon kalman fir filter for linear continuous time systems a receding horizon kalman finite impulse response fir filter is suggested for continuous time systems combining the kalman filter with the receding horizon strategy in the suggested filter the horizon initial state is assumed to be unknown it can always be obtained irrespective of unknown information on the horizon initial state the filter may be the first stochastic fir form for continuous time systems that may have many good inherent properties the suggested filter can be represented in an iterative form and also in a standard fir form the suggested filter turns out to be a remarkable deadbeat observer the validity of the suggested filter is illustrated by numerical examples

separation of variables in 1 2 dimensional schrodinger equations using our classification of separable schrodinger equations with two space dimensions published in j math phys 36 5506 1995 we give an exhaustive description of the coordinate systems providing their separability furthermore we apply these results to separate variables in the heat hamilton jacobi and fokker planck equations

a note on sampling and parameter estimation in linear stochastic systems numerical differentiation formulas that yield consistent least squares parameter estimates from sampled observations of linear time invariant higher order systems have been introduced previously by duncan et al 1994 the formulas given by duncan et al have the same limiting system of equations as in the continuous time case the formula presented in this note can be characterized as preserving asymptotically a partial integration rule it leads to limiting equations for the parameter estimates that are different from the continuous case but they again imply consistency the numerical differentiation formulas given here can be used for an arbitrary linear system which is not the case in the previous paper by duncan et al

a new solution to the induced l finite impulse response filtering problem based on two matrix inequalities in this paper we use an induced l approach to create a new filter with a finite impulse response fir structure for state space models with external disturbances this filter is called an induced l fir filter iliff the proposed iliff s gain matrix can be determined by solving a linear matrix inequality problem for a fixed positive scalar variable an illustrative example is given to demonstrate the effectiveness of the iliff

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose