the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

disturbance decoupled estimation for linear differential algebraic systems we study the disturbance decoupled estimation problem for linear differential algebraic systems which are not necessarily regular we introduce the notion of partial state observers following a rec

a novel td vie based on mot scheme for analysis of dispersive objects a novel time domain volume integral equation td vie is proposed to analyze the transient electromagnetic scattering from inhomogeneous dispersive objects in this td vie method the higher order nystrom method is applied in spatial domain namely the curvilinear tetrahedron elements are utilized to discretize dielectric objects and resulting unknowns are volume electric current density the lagrange interpolation polynomials are used to represent spatial basis functions in temporal domain the marching on in time mot scheme is applied and the shifted lagrange interpolation functions are used to represent temporal basis functions moreover the point matching method is applied both in spatial and temporal domain compared with the traditional spatial schaubert wilton glisson basis based on td vie this novel td vie method is more efficient several numerical examples have demonstrated that the proposed method is accurate stable and also more efficient than the traditional td vie

nonlinear second order elliptic equations v the dirichlet problem for weingarten hypersurfaces on etudie le probleme de dirichlet pour une fonction u dans un domaine borne de r n a frontiere lisse strictement convexe en un point x de les courbures principales k k 1 k n du graphe x u x satisfont une relation f k 1 k n x 0 ou est une fonction positive lisse donnee sur de plus u doit satisfaire la condition aux limites de dirichlet u 0 sur sous certaines conditions on demontre qu il existe une solution u unique admissible lisse dans

on the dirichlet problem for degenerate monge ampere equations we prove global second derivative estimates for the dirichlet problem for degenerate monge ampere equations which yield corresponding existence and regularity results our conditions are essentially optimal and our techniques while drawing on previous investigations are substantially new

full order observer design for linear systems with unknown inputs in this article a full order observer without unknown inputs reconstruction is suggested in order to achieve finite time reconstruction of the state vector for a class of linear systems with unknown inputs the observer is a simple one its derivation being direct and easy it will be shown that the problem of full order observers for linear systems with unknown inputs can be reduced in this case to a standard one the unknown input vector will not interfere in the observer equations the effectiveness of the suggested design algorithm is illustrated by a numerical example aircraft longitudinal motion and for the same aircraft dynamics we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics point of view the superiority of the new designed observer is demonstrated

disturbance decoupled observer design for linear time invariant systems a matrix pencil approach we give a new analysis of the observer design problem for linear time invariant systems with partly unknown inputs we use a matrix pencil approach that is based on a condensed form under orthogonal transformations the solvability conditions that we obtain can be verified and the desired observer can be constructed by a numerically stable method

bounded solutions of a k hessian equation involving a weighted nonlinear source abstract we consider the problem 1 s k d 2 u x 1 u q in b u 0 in b u 0 on b where b denotes the unit ball in r n n 2 k k n 0 q k and 0 we study the existence multiplicity and uniqueness of radially symmetric bounded solutions of 1 the methodology for obtaining our results is based on a dynamical systems approach for this we introduce a new transformation which reduces problem 1 to an autonomous two dimensional generalized lotka volterra system

two dimensional transverse magnetic time domain scattering using the nystro spl uml m method and bandlimited extrapolation a method is presented for the solution of the integral equations that describe the electromagnetic scattering from an infinitely long conducting cylinder in the time domain the method discretizes the integral equations spatially using a high order locally corrected nystro spl uml m method and temporally using a filtered kernel the filtering of the kernel both controls aliasing and reduces the order of its singularity on the other hand filtering also gives rise to a noncausal kernel so the time marching is accomplished with a bandlimited extrapolation scheme numerical results demonstrate the stability and accuracy of the proposed method

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

the exterior dirichlet problem for hessian quotient equations abstract in this paper using a reverse maclaurin inequality we established the existence theorem of the exterior dirichlet problem for hessian quotient equations with a stronger asymptotic behavior at infinity when k n 1 2 we improve the result in l m dai the dirichlet problem for hessian quotient equations in exterior domains j math anal appl 380 2011 87 93 for s k l with k l 3 to the result with any 0 l k

stable electric field tdie solvers via quasi exact evaluation of mot matrix elements prior theoretical studies and experience confirm that the stability of marching on in time mot solvers pertinent to the analysis of scattering from free standing three dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of mot matrix elements resulting from a galerkin discretization of the underlying time domain integral equation tdie unfortunately the accurate evaluation of the four dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means here a method that permits the quasi exact evaluation of mot matrix elements is presented specifically the proposed method permits the analytical evaluation of three out of the four spatial integrations leaving only one integral to be evaluated numerically since the latter has finite range and a piecewise smooth integrand it can be evaluated to very high accuracy using standard quadrature rules as a result the proposed method permits the fast evaluation of mot matrix elements with arbitrary user specified accuracy extensive numerical experiments show that an mot solver for the electric field tdie that uses the proposed quasi exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes

fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm the computational complexity of classical marching on in time mot methods for solving time domain integral equations tdies pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as o n sub t n sub s sup 2 n sub t and n sub s denote the number of temporal and spatial degrees of freedom dof of the electric current on the target this scaling law impedes the application of these schemes to the analysis of large scale scattering phenomena the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based tdie solvers previously we described a two level pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting targets the computational complexity of this algorithm scales as o n sub t n sub s sup 1 5 logn sub s here a multilevel pwtd scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described in addition a multilevel pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting scatterers using o n sub t n sub s log sup 2 n sub s cpu resources is outlined last the accuracy and cpu memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies

analysis of transient electromagnetic scattering phenomena using a two level plane wave time domain algorithm a fast algorithm is presented for solving electric magnetic and combined field time domain integral equations pertinent to the analysis of surface scattering phenomena the proposed two level plane wave time domain pwtd algorithm permits a numerically rigorous reconstruction of transient near fields from their far field expansion and augments classical marching on in time mot based solvers the computational cost of analyzing surface scattering phenomena using pwtd enhanced mot schemes scales as o n sub i n sub s sup 2 3 log n sub s as opposed to spl oscr n sub t n sub s sup 2 for classical mot methods where n sub t and n sub s are the numbers of temporal and spatial basis functions discretizing the scatterer current numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented

time domain adaptive integral method for surface integral equations an efficient marching on in time mot scheme is presented for solving electric magnetic and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium the proposed scheme is the extension of the frequency domain adaptive integral pre corrected fast fourier transform fft method to the time domain fields on the scatterer that are produced by space time sources residing on its surface are computed 1 by locally projecting for each time step all sources onto a uniform auxiliary grid that encases the scatterer 2 by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global multilevel blocked space time ffts 3 by locally interpolating these fields back onto the scatterer surface as this procedure is inaccurate when source and observer points reside close to each other and 4 near fields are computed classically albeit pre corrected for errors introduced through the use of global ffts the proposed scheme has a computational complexity and memory requirement of o n sub t n sub s log sup 2 n sub s and o n sub s sup 3 2 when applied to quasiplanar structures and of o n sub t n sub s sup 3 2 log sup 2 n sub s and o n sub s sup 2 when used to analyze scattering from general surfaces here n sub s and n sub t denote the number of spatial and temporal degrees of freedom of the surface current density these computational cost and memory requirements are contrasted to those of classical mot solvers which scale as o n sub t n sub s sup 2 and o n sub s sup 2 respectively a parallel implementation of the scheme on a distributed memory computer cluster that uses the message passing interface is described simulation results demonstrate the accuracy efficiency and the parallel performance of the implementation

regularity for radial solutions of degenerate fully nonlinear equations abstract in this paper we prove the c 1 regularity of radial solutions for fully nonlinear degenerate elliptic equations

a novel grid robust higher order vector basis function for the method of moments a set of novel grid robust higher order vector basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems these basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the lagrange interpolation polynomials the highlight of these basis functions is that the lagrange interpolation points are chosen to be the same as the nodes of the well developed gaussian quadratures as a result the evaluation of the integrals in the mom is greatly simplified additionally the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch which is a very stringent requirement for traditional vector basis functions the proposed basis functions are implemented with point matching for the mom solution of the electric field integral equation the magnetic field integral equation and the combined field integral equation numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions

on axially symmetric solutions of fully nonlinear elliptic equations we show that in dimension 3 axial symmetric viscosity solutions of uniformly elliptic hessian equations are in fact the classical ones

solution of time domain electric field integral equation using the laguerre polynomials in this paper we propose a numerical method to obtain a solution for the time domain electric field integral equation td efie for arbitrary shaped conducting structures this method does not utilize the customary marching on in time mot solution method often used to solve a hyperbolic partial differential equation instead we solve the wave equation by expressing the transient behaviors in terms of laguerre polynomials by using these causal orthonormal basis functions for the temporal variation the time derivatives can be handled analytically in order to solve the wave equation we introduce two separate testing procedures a spatial and temporal testing by introducing first the galerkin temporal testing procedure the mot procedure is replaced by a recursive relation between the different orders of the weighted laguerre polynomials the other novelty of this approach is that through the use of the entire domain laguerre polynomials for the expansion of the temporal variation of the current the spatial and the temporal variables can be separated and the temporal variables can be integrated out for convenience we use the hertz vector as the unknown variable instead of the electric current density to verify our method we compare the results of a td efie and inverse fourier transform of a frequency domain efie

hessian equations on exterior domain abstract in the paper we consider the hessian equation k d 2 u f x where f is a positive function outside a bounded domain of r n n 3 and f x 1 o x for some 2 at infinity using the perron s method we prove the existence and uniqueness for viscosity solutions of exterior dirichlet problem with prescribed asymptotic behavior at infinity there are examples to show that the result is optimal this is an extension of the theorems given by bao li li in 2 for f 1 and bao li zhang in 3 for k n

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

the obstacle problem for hessian equations on riemannian manifolds abstract in this paper we consider the obstacle problem for a class of fully nonlinear equations on riemannian manifolds the c 1 1 regularity of the greatest viscosity solutions is established

liouville property and regularity of a hessian quotient equation we are concerned with properties of convex solutions to the hessian quotient equation sn c d2 p 1 k n as our first main result we prove some regularity of strong solutions while the second states that for p 1 an entire convex solution with a quadratic growth bound must be a quadratic polynomial

simultaneous observation of linear systems a state space interpretation necessary and sufficient conditions for the existence of a simultaneous functional observer for several linear time invariant lti systems are derived using distinguishability concepts that generalize the detectability concept for a single system they generalize also the known results a structure for common functional observers is proposed and for two systems or for several systems without inputs the problem can be constructively solved a relationship between the simultaneous observation problem and the existence of unknown input observers is established

bifurcation and admissible solutions for the hessian equation abstract we study the following eigenvalue problem of k hessian equation s k d 2 u k f u in b u 0 on b global bifurcation result is established for this problem as applications of the bifurcation result we determine the intervals of for the existence nonexistence uniqueness and multiplicity of radially symmetric k admissible solutions for this problem

disturbance decoupled functional observers if a state observer does not exist it is possible to design a functional observer principally this is also true for systems with unknown inputs termed as disturbances necessary and sufficient conditions for the existence of disturbance decoupled functional observers for linear time invariant systems are provided a method for designing such observers is given the analysis and design are based on a matrix pencil approach the design can also be used to obtain functional observers for descriptor systems with or without unknown inputs

partial state observers for linear systems with unknown inputs we consider the problem of constructing partial state observers for discrete time linear systems with unknown inputs specifically for any given system we develop a design procedure that characterizes the set of all linear functionals of the system state that can be reconstructed through a linear observer with a given delay by treating the delay as a design parameter we allow greater flexibility in estimating state functionals and are able to obtain a procedure that directly produces the corresponding observer parameters our technique is also applicable to continuous time systems by replacing delayed outputs with differentiated outputs

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

some existence results for fully nonlinear elliptic equations of monge ampere type we study the existence and uniqueness of solutions of monge ampere type equations this type of equations has been studied extensively by caffarelli nirenberg spruck and many others see 5 through 8 and the references therein we present some existence and uniqueness results for this type of equations on compact riemannian manifolds with non negative sectional curvature we have also generalized some results in 7

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

solving time domain electric field integral equation without the time variable an improved testing procedure using the marching on in order method to solve the time domain electric field integral equation td efie for conducting objects using the laguerre polynomials is presented exact temporal testing is performed before the spatial testing therefore the retarded terms composed of the spatial and the temporal variables can be analytically separated the uniqueness of this testing procedure is that the time variable can be analytically integrated out and the accuracy can be improved this paper is then an improvement over the earlier marching on in order method in addition this methodology is quite different from the conventional marching on in time algorithm as the present method leads to a set of final equations which need to be numerically solved containing only the spatial variables therefore there is no requirement to have a courant stability condition in this procedure how the singular integrals are treated is also discussed several examples are simulated both for radiation and scattering problem the results are compared with the inverse discrete fourier transform of the frequency domain data and they agree well

time domain integral equation analysis of scattering from composite bodies via exact evaluation of radiation fields a novel marching on in time and poggio miller chang harrington wu tsai pmchwt based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented to render the marching on in time procedure stable observer and source integrals are approximated via multipoint collocation and evaluated in closed form the proposed scheme avoids the costly evaluation of five dimensional integrals required in full space time galerkin schemes and proves to be stable for all targets investigated including coated perfect electrically conducting surfaces and multiregion penetrable volumes

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

brief unknown disturbance inputs estimation based on a state functional observer design we consider the problem of function of state plus unknown input estimation of a linear time invariant system using only the measured outputs two reduced order input estimators built upon a state functional observer are proposed the first is an extension of a state input estimator while the second is based on adaptive observer design technique the proposed estimator can be designed under less restrictive conditions than those of the previous work and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

conformal metrics with prescribed curvature functions on manifolds with boundary we study the dirichlet problem for a class of fully nonlinear elliptic equations related to conformal deformations of metrics on riemannian manifolds with boundary as a consequence we prove the existence of a conformal metric given its value on the boundary as a prescribed metric conformal to the induced background metric with a prescribed curvature function of the schouten tensor

fault detection and isolation observers a design of reduced order observers is proposed for linear time invariant systems with unknown inputs including unknown measurement disturbances based on the unknown input observer design a systematic treatment of designing fault detection and isolation fdi observers is provided the core of the fdi observer design is to find an observable subsystem where the faults of interest show up and the rest of the faults disappear the fdi observer design procedure has a clear physical meaning robust fdi observers for uncertain systems can also be obtained using the fdi observer design provided the uncertainties of the system can be formulated as unknown inputs it is shown that the parity equations of another important fdi method can be generated in an elegant way using a dead beat fdi observer scheme directly in the time domain examples are included to show some concepts and to illustrate the fdi observer design method

geometric inequalities on locally conformally flat manifolds through the study of some elliptic and parabolic fully nonlinear pdes we establish conformal versions of the quermassintegral inequality the sobolev inequality and the moser trudinger inequality for the geometric quantities associated to the schouten tensor on locally conformally flat manifolds

a higher order nystrom scheme for a marching on in time solution of time domain integral equation a marching on in time mot solution of the time domain integral equation tdie using the higher order nystrom scheme is developed to analyze the transient electromagnetic scattering from arbitrarily shaped perfect electrically conducting pec objects in this scheme the curvilinear triangular patches are utilized to discretize the pec objects for their great ability to model geometric configuration moreover we use the lagrange interpolation polynomials to stand for the spatial basis functions and the triangle functions to represent the temporal basis functions furthermore the spatial and temporal point matching is applied numerical examples demonstrate that the proposed scheme is stable accurate and efficient

transverse fully nonlinear equations on sasakian manifolds and applications abstract we prove a priori estimates for a class of transverse fully nonlinear equations on sasakian manifolds and give some geometric applications such as the transversion calabi yau theorem for transverse balanced and strongly gauduchon metrics we also explain that similar results hold on compact oriented taut transverse hermitian foliated manifold of complex co dimension n and give some geometric applications such as the transverse calabi yau theorems for transverse hermitian and strongly gauduchon metrics