subgradient based neural networks for nonsmooth nonconvex optimization problems this paper presents a subgradient based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function a class of affine equality constraints and a class of nonsmooth convex inequality constraints the proposed neural network is modeled with a differential inclusion under a suitable assumption on the constraint set and a proper assumption on the objective function it is proved that for a sufficiently large penalty parameter there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter it is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network and coincides with the set which consists of the critical points of the objective function in the feasible region a condition is given to ensure the convergence to the equilibrium point set in finite time moreover under suitable assumptions the coincidence between the solution to the differential inclusion and the ldquoslow solutionrdquo of it is also proved furthermore three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

functional determinant of the massive laplace operator and the multiplicative anomaly after a brief survey of zeta function regularization issues and of the related multiplicative anomaly illustrated with a couple of basic examples namely the harmonic oscillator and quantum field theory at finite temperature an application of these methods to the computation of functional determinants corresponding to massive laplacians on spheres in arbitrary dimensions is presented explicit formulas are provided for the laplace operator on spheres in dimensions and for vector and tensor laplacians on the unitary sphere s4

functional determinants in quantum field theory functional determinants of differential operators play a prominent role in theoretical and mathematical physics and in particular in quantum field theory they are however difficult to compute in non trivial cases for one dimensional problems a classical result of gel fand and yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues here i report recent progress in extending this approach to higher dimensions i e functional determinants of partial differential operators with applications in quantum field theory

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

functional determinants in higher derivative lagrangian theories motivated by the considerable success of alternative theories of gravity we consider the toy model of a higher derivative lagrangian theory which reduces in the gaussian approximation to the pais uhlenbeck oscillator studied in a recent paper by hawking and hertog phys rev d 65 103515 2002 its euclidean path integral is studied with a certain detail and a pedagogical derivation of the propagator which makes use of a theorem due to forman is consequently proposed

functionals of brownian motion localization and metric graphs we review several results related to the problem of a quantum particle in a random environment in an introductory part we recall how several functionals of brownian motion arise in the study of electronic transport in weakly disordered metals weak localization two aspects of the physics of the one dimensional strong localization are reviewed some properties of the scattering by a random potential time delay distribution and a study of the spectrum of a random potential on a bounded domain the extreme value statistics of the eigenvalues then we mention several results concerning the diffusion on graphs and more generally the spectral properties of the schrodinger operator on graphs the interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated finally we consider a two dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices we recall the connection between spectral properties of this model and winding functionals of planar brownian motion

zeta determinants on manifolds with boundary abstract through a general theory for relative spectral invariants we study the determinant of global boundary problems of aps type in particular we compute the determinant ratio for dirac laplacian boundary problems in terms of a scattering fredholm determinant over the boundary

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

symbol calculus and zeta function regularized determinants in this work we use semigroup integral to evaluate zeta function regularized determinants this is especially powerful for nonpositive operators such as the dirac operator in order to understand fully the quantum effective action one should know not only the potential term but also the leading kinetic term in this purpose we use the weyl type of symbol calculus to evaluate the determinant as a derivative expansion the technique is applied both to a spin 0 bosonic operator and to the dirac operator coupled to a scalar field

eigenvalue boundary problems for the dirac operator on a compact riemannian spin manifold with mean convex boundary we analyse the ellipticity and the symmetry of four boundary conditions for the fundamental dirac operator including the global aps condition and a riemannian version of the local mit bag condition we show that friedrich s inequality for the eigenvalues of the dirac operator on closed spin manifolds holds for the corresponding four eigenvalue boundary problems more precisely we prove that for both the aps and the mit conditions the equality cannot be achieved and for the other two conditions the equality characterizes respectively half spheres and domains bounded by minimal hypersurfaces in manifolds carrying non trivial real killing spinors

meyer vietoris type formula for determinants of elliptic differential operators abstract for a closed codimension one submanifold of a compact manifold m let m be the manifold with boundary obtained by cutting m along let a be an elliptic differential operator on m and b and c be two complementary boundary conditions on if a b is an elliptic boundary valued problem on m then one defines an elliptic pseudodifferential operator r of neumann type on and prove the following factorization formula for the regularized determinants det a det a b k det r with k a local quantity depending only on the jets of the symbols of a b and c along the particular case when m has dimension 2 a is the laplace beltrami operator and b resp c is the dirichlet resp neumann boundary condition is considered

stabilizing receding horizon h sub spl infin controls for linear continuous time varying systems in this note new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time varying systems under these conditions nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed it is proved that the proposed terminal inequality conditions ensure the closed loop stability of the receding horizon h sub spl infin control rhhc the stabilizing rhhc guarantees the h sub spl infin norm bound of the closed loop system the proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed loop stability include most well known existing terminal conditions as special cases the results for time invariant systems are obtained correspondingly from those in the time varying case

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

multirate and composite control of two time scale discrete time systems the design of stabilizing feedback control of singularly perturbed diserete time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control composite control strategies are developed for the case of single rate measurements all variables are measured at the same rate as well as for the case of multirate measurements slow variables are measured at a rate slower than that of fast variables

a general methodology for designing globally convergent optimization neural networks we present a general methodology for designing optimization neural networks we prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets in contrast with the gradient methods whose convergence is not guaranteed we show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases based on the theoretical results of the proposed method we study the convergence and stability of general gradient models in the case of unisolated solutions using the proposed method we derive some new neural network models for a very large class of optimization problems in which the equilibrium points correspond to exact solutions and there is no variable parameter finally some numerical examples show the effectiveness of the method

estimation of a nonlinear panel data model with semiparametric individual effects abstract this paper investigates identification and estimation of a class of nonlinear panel data single index models the model allows for unknown time specific link functions and semiparametric specification of the individual specific effects we develop an estimator for the parameters of interest and propose a powerful new kernel based modified backfitting algorithm to compute the estimator we derive uniform rates of convergence results for the estimators of the link functions and show the estimators of the finite dimensional parameters are root n consistent with a gaussian limiting distribution we study the small sample properties of the estimator via monte carlo techniques

on functional determinants of matrix differential operators with multiple zero modes we generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by mckane and tarlie to differential operators with multiple zero eigenvalues we derive general formulas for such functional determinants of r times r matrix second order differential operators o with 0 n leqslant 2r linearly independent zero modes we separately discuss the cases of the homogeneous dirichlet boundary conditions when the number of zero modes cannot exceed r and the case of twisted boundary conditions including the periodic and anti periodic ones when the number of zero modes is bounded above by 2r in all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r n or 2r n depending on the boundary conditions solutions of the homogeneous equation o h 0 in the spirit of gel fand yaglom approach in instanton calculations the contribution of the zero modes is taken into account by introducing the so called collective coordinates we show that there is a remarkable cancellation of a factor involving scalar products of zero modes between the jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues this cancellation drastically simplifies instanton calculations when one uses our formulas

dirac operator on a disk with global boundary conditions we compute the functional determinant for a dirac operator in the presence of an abelian gauge field on a bidimensional disk under global boundary conditions of the type introduced by atiyah patodi singer we also discuss the connection between our result and the index theorem

a one layer recurrent neural network for pseudoconvex optimization subject to linear equality constraints in this paper a one layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints the global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex the finite time state convergence to the feasible region defined by the equality constraints is also proved in addition global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network

p determinant regularization method for elliptic boundary problems an expression for thep determinant of the quotient of two differential elliptic operators with boundary conditions is given in terms of the boundary values of their solutions applications to physical examples are considered

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks this paper presents a neural network approach to robust model predictive control mpc for constrained discrete time nonlinear systems with unmodeled dynamics affected by bounded uncertainties the exact nonlinear model of underlying process is not precisely known but a partially known nominal model is available this partially known nonlinear model is first decomposed to an affine term plus an unknown high order term via jacobian linearization the linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning the minimax methodology is exploited to deal with bounded uncertainties the minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two layer recurrent neural network the proposed neurodynamic approach to nonlinear mpc improves the computational efficiency and sheds a light for real time implementability of mpc technology simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach

determinants finite difference operators and boundary value problems we relate the determinants of differential and difference operators to the boundary values of solutions of the operators previous proofs of related results have involved considering one parameter families of such operators showing the desired quantities are equal up to a constant and then calculating the constant we take a more direct approach for a fixed operator we prove immediately that the two sides of our formulas are equal by using the following simple observation proposition 1 3 let u su n c write u in block form u left begin array 20 c u 11 u 12 u 21 u 22 end array right where u11and u22are square matrices then det u 11 overline det u 22

a semiparametric maximum likelihood estimator this paper presents a procedure for analyzing a model in which the parameter vector has two parts a finite dimensional component 8 and a nonparametric component a the procedure does not require parametric modeling of but assumes that the true density of the data satisfies an index restriction the idea is to construct a parametric model passing through the true model and to estimate by setting the score for the parametric model to zero the score is estimated nonparametrically and the estimator is shown to be n consistent and asymptotically normal the estimator is then shown to attain the semiparametric efficiency bound characterized in begun et al 1983 for multivariate nonlinear regression simultaneous equations partially specified regression index regression censored regression switching regression and disequilibrium models in which the error densities are unknown

regularization of functional determinants using boundary perturbations the formalism which has been developed to give general expressions for the determinants of differential operators is extended to the physically interesting situation where these operators have a zero mode which has been extracted in the approach adopted here this mode is removed by a novel regularization procedure which allows remarkably simple expressions for these determinants to be derived

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

a projection neural network for constrained quadratic minimax optimization this paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network compared with some of the existing neural networks for quadratic minimax optimization the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems and the designed neural network does not include any parameter moreover the neural network has lower model complexities the number of state variables of which is equal to that of the dimension of the optimization problems the simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

simplified vacuum energy expressions for radial backgrounds and domain walls we extend our previous results of simplified expressions for functional determinants for radial schrodinger operators to the computation of vacuum energy or mass corrections for static but spatially radial backgrounds and for domain wall configurations our method is based on the zeta function approach to the gel fand yaglom theorem suitably extended to higher dimensional systems on separable manifolds we find new expressions that are easy to implement numerically for both zero and non zero temperatures

the number of solutions for a class of nonlocal nonhomogeneous gradient operator equations abstract this paper deals with the number of solutions for a class of nonlocal nonhomogeneous gradient operator equations of the form a i u i u f where i c 1 x r x is a reflexive banach space i 0 0 i is even and strictly convex i u u as u i x x is a bounded homeomorphism but is not necessarily homogeneous a 0 r is continuous f x 0 some properties and examples of such a functional i are given some results on the number of solutions of the nonlocal equation are obtained

determinants of dirac operators with local boundary conditions we study functional determinants for dirac operators on manifolds with boundary we give for local boundary conditions an explicit formula relating these determinants to the corresponding green s functions we finally apply this result to the case of a bidimensional disk under baglike conditions

on the gluing problem for the spectral invariants of dirac operators abstract in this paper we solve the gluing problem for the determinant of a dirac laplacian to do so we develop a new approach to solve such problems which relies heavily on the theory of elliptic boundary problems the analysis of the resolvent of the dirac operator and the introduction of an auxiliary model problem moreover as a byproduct of our approach we obtain a new gluing formula for the eta invariant au gratis

a one layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints this paper presents a one layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints the proposed neural network is designed based on two projection operators linear equality constraints and bound constraints the objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex pseudoconvex on a set defined by the constraints compared with existing recurrent neural networks for nonsmooth optimization the proposed model does not have any design parameter which is more convenient for design and implementation it is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

on the spectrum of the laplace operator of metric graphs attached at a vertex spectral determinant approach we consider a metric graph made of two graphs and attached at one point we derive a formula relating the spectral determinant of the laplace operator in terms of the spectral determinants of the two subgraphs the result is generalized to describe the attachment of n graphs the formulae are also valid for the spectral determinant of the schrodinger operator

fermionic determinants for chiral bag like two dimensional systems this paper evaluates the determinant of a dirac like operator for a system of fermions confined to a region of two dimensional euclidean space and subject to bag like boundary conditions in the framework of the function regularization method use is made of seeley s developments for the resolvent of such operators a relation is derived between the green s function and the finite part of the diagonal element of the kernel of the power z of the operator for z 1 which amounts to having information about the whole seeley s series

moduli spaces of meromorphic functions and determinant of laplacian the hurwitz space is the moduli space of pairs x f where x is a compact riemann surface and f is a meromorphic function on x we study the laplace operator delta df 2 of the flat singular riemannian manifold x df 2 we define a regularized determinant for delta df 2 and study it as a functional on the hurwitz space we prove that this functional is related to a system of pde which admits explicit integration this leads to an explicit expression for the determinant of the laplace operator in terms of the basic objects on the underlying riemann surface the prime form theta functions the canonical meromorphic bidifferential and the divisor of the meromorphic differential df the proof has several parts that can be of independent interest as an important intermediate result we prove a decomposition formula of the type of burghelea friedlander kappeler for the determinant of the laplace operator on flat surfaces with conical singularities and euclidean or conical ends we introduce and study the s matrix s lambda of a surface with conical singularities as a function of the spectral parameter lambda and relate its behavior at lambda 0 with the schiffer projective connection on the riemann surface x we also prove variational formulas for eigenvalues of the laplace operator of a compact surface with conical singularities when the latter move

a neural network for a class of convex quadratic minimax problems with constraints in this paper we propose a neural network for solving a class of convex quadratic minimax problems with constraints four sufficient conditions are provided to ensure the asymptotic stability of the proposed network furthermore the exponential stability of the proposing network is also proved under certain conditions the results obtained here can be further extended to the globally projected dynamical system in addition some new stability conditions for the system are also obtained since our stability conditions can be easily checked in practice these results becomes more attractive in real applications

binary choice panel data models with predetermined variables we present a class of binary choice models for panel data with the following features i the explanatory variables are predetermined but not strictly exogenous this includes lagged dependent variables as well as other forms of unspecified feedback ii individual effects are allowed to be correlated with the explanatory variables dependence is specified through the conditional expectation of the effects which is let to be non parametric we also present a gmm estimator for these models which is consistent and asymptotically normal for fixed t and large n we study its finite sample properties in an autoregressive model by means of monte carlo simulations finally as an empirical illustration we estimate a female labour force participation equation with predetermined children using psid data

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

zeta function on surfaces of revolution in this paper we applied the contour integral method for the zeta function associated with a differential operator to the laplacian on a surface of revolution using the wkb expansion we calculated the residues and values of the zeta function at several important points the results agree with those obtained from the heat kernel expansion we also obtained a closed form formula for the determinant of the laplacian on such a surface

multiplicity results for a p laplacian discrete problems of kirchhoff type this paper is concerned with the existence and multiplicity solutions for a discrete boundary value problem of p kirchhoff type our technical approach is based on variational methods

ζ determinants of laplacians with neumann and dirichlet boundary conditions in this paper we derive a formula for the ratio of the determinants of the laplacian with neumann and dirichlet boundary conditions over a noncompact manifold with an infinite cylindrical end and a compact boundary in terms of the determinant of the dirichlet to neumann map

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

a dynamical model for solving degenerate quadratic minimax problems with constraints this paper presents a new neural network model for solving degenerate quadratic minimax dqm problems on the basis of the saddle point theorem optimization theory convex analysis theory lyapunov stability theory and lasalle invariance principle the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the dqm problems it is also shown that the proposed network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the original problem several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

zeta function of self adjoint operators on surfaces of revolution in this article we analyze the zeta function for the laplace operator on a surface of revolution a variety of boundary conditions separated and unseparated are considered formulas for several residues and values of the zeta function as well as for the determinant of the laplacian are obtained the analysis is based upon contour integration techniques in combination with a wkb analysis of solutions of related initial value problems

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

zeta function determinant of the laplace operator on the d dimensional ball we present a direct approach for the calculation of functional determinants of the laplace operator on balls dirichlet and robin boundary conditions are considered using this approach formulas for any value of the dimension d of the ball can be obtained quite easily explicit results are presented here for dimensionsd 2 3 4 5 and 6

hill type formula for hamiltonian system with lagrangian boundary conditions abstract in this paper we build up hill type formula for linear hamiltonian systems with lagrangian boundary conditions which include standard neumann dirichlet boundary conditions such a kind of boundary conditions comes from the n reversible symmetry periodic orbits in n body problem naturally where n is an anti symplectic orthogonal matrix with n 2 i the hill type formula connects the infinite determinant of the hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions consequently we derive the krein type trace formula and give nontrivial estimation for the eigenvalue problem combined with the maslov type index theory we give some new stability criteria for the n reversible symmetry periodic solutions of hamiltonian systems as an application we study the linear stability of elliptic relative equilibria in planar 3 body problem

cross section and panel data estimators for nonseparable models with endogenous regressors we propose two new methods for estimating models with nonseparable errors and endogenous regressors the first method estimates a local average response one estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning the second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables an external variable is used to impose an equality restriction at two points of support on the conditional distribution of the unobservable random term given the regressor and the external variable our methods apply to cross sections but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group

p determinants and boundary values it is shown that a regularized determinant based on hilbert s approach which we call the p determinant of a quotient of elliptic operators defined on a manifold with boundary is equal to the p determinant of a quotient of pseudodifferential operators the last ones are entirely expressible in terms of boundary values of solutions of the original differential operators it is argued that in the context of quantum field theory these boundary values also determine the subtractions i e the counterterms to which this regularization scheme gives rise

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

a novel neural network for a class of convex quadratic minimax problems based on the inherent properties of convex quadratic minimax problems this article presents a new neural network model for a class of convex quadratic minimax problems we show that the new model is stable in the sense of lyapunov and will converge to an exact saddle point in finite time by defining a proper convex energy function furthermore global exponential stability of the new model is shown under mild conditions compared with the existing neural networks for the convex quadratic minimax problem the proposed neural network has finite time convergence a simpler structure and lower complexity thus the proposed neural network is more suitable for parallel implementation by using simple hardware units the validity and transient behavior of the proposed neural network are illustrated by some simulation results

semiparametric binary choice panel data models without strictly exogeneous regressors previous estimators of binary choice panel data models with fixed effects require strong parametric error asumptions strictly exogeneous regressors or both this is because nonlinearity of the model precludes the use of the moment conditions on differences based estimators that are generally employed for linear models without strictly exogeneous regressors based on the cross section binary choice estimator in lewbel 2000a we show how discrete choice panel data models with fixed effects can be estimated with only predetermined regressors the estimator is semiparametric in that the error distribution is not specified it allows for some general forms of heteroskedasticity and converges at rate root n this abstract was borrowed from another version of this item

profile likelihood and conditionally parametric models in this paper we outline a general approach to estimating the parametric component of a semiparametric model for the case of a scalar parametric component the method is based on the idea of first estimating a one dimensional subproblem of the original problem that is least favorable in the sense of stein the likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem the scalar parameter is then estimated by maximizing this generalized profile likelihood this method of estimation is applied to a particular class of semiparametric models where it is shown that the resulting estimator is asymptotically efficient

functional determinants for ordinary differential operators the authors study the analytic properties of regularized functional determinants for ordinary differential operators to this end a new regularization scheme is introduced relations between different approaches are analysed and the connection between the presence of divergent traces and regularization differences is discussed

functional determinants and geometry in this paper we study the zeta function determinant in the context of elliptic boundary value problems our main technique is to relate the determinant of an operator or a ratio of determinants to the boundary values of the solutions of the operator this has the advantage of restricting attention to the solutions of the operator which do not depend on the boundary conditions and can often be written down explicitly rather than the eigenvalues which are usually difficult to work with in addition the problem is reduced to a calculation over the boundary of the manifold which is a closed manifold of dimension one less than the original manifold this has special significance in the case that the manifold is a finite interval in this case the boundary is a pair of points and the determinant of an ordinary differential operator is expressed in terms of the determinant of a finite matrix

on nonlocal p x laplacian dirichlet problems abstract this paper deals with the nonlocal p x laplacian dirichlet problems with non variational form a u p x u x b u f x u x in u 0 and with variational form a u p x p x d x p x u x b f x u d x f x u x in u 0 where f x t 0 t f x s d s and a is allowed to be singular at zero using s mapping theory and the variational method some results on existence and multiplicity for the problems are obtained under weaker hypotheses our results are also new even for the case when p x p is a constant

recurrent neural network for non smooth convex optimization problems with application to the identification of genetic regulatory networks a recurrent neural network is proposed for solving the non smooth convex optimization problem with the convex inequality and linear equality constraints since the objective function and inequality constraints may not be smooth the clarke s generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network it is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the lagrangian saddle point theorem under weak conditions the proposed neural network is proved to be stable and the state of the neural network is convergent to one of its equilibrium points compared with the existing neural network models for non smooth optimization problems the proposed neural network can deal with a larger class of constraints and is not based on the penalty method finally the proposed neural network is used to solve the identification problem of genetic regulatory networks which can be transformed into a non smooth convex optimization problem the simulation results show the satisfactory identification accuracy which demonstrates the effectiveness and efficiency of the proposed approach

reformulating the schrodinger equation as a shabat zakharov system we reformulate the second order schrodinger equation as a set of two coupled first order differential equations a so called shabat zakharov system sometimes called a zakharov shabat system there is considerable flexibility in this approach and we emphasize the utility of introducing an auxiliary condition or gauge condition that is used to cut down the degrees of freedom using this formalism we derive the explicit but formal general solution to the schrodinger equation the general solution depends on three arbitrarily chosen functions and a path ordered exponential matrix if one considers path ordering to be an elementary process then this represents complete quadrature albeit formal of the second order linear ordinary differential equation

critical metrics for the determinant of the laplacian in odd dimensions let m be a closed compact n dimensional manifold with n odd we calculate the first and second variations of the zeta regularized determinants det a and det l as the metric on m varies where a denotes the laplacian on functions and l denotes the conformal laplacian we see that the behavior of these functionals depends on the dimension indeed every critical metric for 1 n 1 2det a or 1 n 1 21 det l has finite index consequently there are no local maxima if n 4rm 1 and no local minima if n 4m 3 we show that the standard 3 sphere is a local maximum for det a while the standard 4m 3 sphere with m 1 2 is a saddle point by contrast for all odd n the standard n sphere is a local extremal for det l an important tool in our work is the canonical trace on odd class operators in odd dimensions this trace is related to the determinant by the formula det q tr log q and we prove some basic results on how to calculate this trace

zeta determinant for laplace operators on riemann caps the goal of this paper is to compute the zeta function determinant for the massive laplacian on riemann caps or spherical suspensions these manifolds are defined as compact and boundaryless d dimensional manifolds deformed by a singular riemannian structure the deformed spheres considered previously in the literature belong to this class after presenting the geometry and discussing the spectrum of the laplacian we illustrate a method to compute its zeta regularized determinant the special case of the deformed sphere is recovered as a limit of our general formulas

a comment on the gelfand yaglom theorem zeta functions and heat kernels for pt symmetric hamiltonians we propose a numerical method for computing zeta functions for general classes of hamiltonians based on the gelfand yaglom theorem which computes the determinant without needing to compute the eigenvalues we verify that this agrees with known analytic results for certain hermitean hamiltonians and we present numerical evidence that it may extend also to non hermitean pt symmetric hamiltonians

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

effective computation of traces determinants and ζ functions for sturm liouville operators abstract the principal aim in this paper is to develop an effective and unified approach to the computation of traces of resolvents and resolvent differences fredholm determinants functions and function regularized determinants associated with linear operators in a hilbert space in particular we detail the connection between fredholm and function regularized determinants concrete applications of our formalism to general i e three coefficient regular sturm liouville operators on bounded intervals with various separated and coupled boundary conditions and schrodinger operators on a half line are provided and further illustrated with an array of examples

functional determinants for general sturm liouville problems simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest we extend the range of situations for which these hold to cover systems of self adjoint operators of the sturm liouville type with arbitrary linear boundary conditions the results hold whether or not the operators have negative eigenvalues the physically important case of functional determinants of operators with a zero mode but where that mode has been extracted is studied in detail for the same range of situations as when no zero mode exists the method of proof uses the properties of generalized zeta functions the general form of the final results is the same for the entire range of problems considered