tyz expansion for the kepler manifold the main goal of the paper is to address the issue of the existence of kempf s distortion function and the tian yau zelditch tyz asymptotic expansion for the kepler manifold an important example of non compact manifold motivated by the recent results for compact manifolds we construct kempf s distortion function and derive a precise tyz asymptotic expansion for the kepler manifold we get an exact formula finite asymptotic expansion of n 1 terms and exponentially small error terms uniformly with respect to the discrete quantization parameter m rightarrow infty hbar m 1 rightarrow 0 standing for planck s constant and x rightarrow infty x in mathbb c n moreover the coefficients are calculated explicitly and they turned out to be homogeneous functions with respect to the polar radius in the kepler manifold we show that our estimates are sharp by analyzing the nonharmonic behaviour of tm for m rightarrow infty the arguments of the proofs combine geometrical methods quantization tools and functional analytic techniques for investigating asymptotic expansions in the framework of analytic gevrey spaces

structure of the sets of mutually unbiased bases with cyclic symmetry mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest for they can be readily implemented in practice we show that for a system of qubits finding such a generator can be cast as the problem of finding a symmetric matrix over the field 2 equipped with an irreducible characteristic polynomial of a given fibonacci index the entanglement structure of the resulting complete sets is determined by two additive matrices of the same size

the complex monge ampere equation zoll metrics and algebraization let m be a real analytic riemannian manifold an adapted complex structure on tm is a complex structure on a neighborhood of the zero section such that the leaves of the riemann foliation are complex submanifolds this structure is called entire if it may be extended to the whole of tm we prove here that the only real analytic zoll metric on the n sphere with an entire adapted complex structure on tm is the round sphere using similar ideas we answer a special case of an algebraization question raised by the first author characterizing some stein manifolds as affine algebraic in terms of plurisubharmonic exhaustion functions satisfying the homogeneous complex monge ampere equation the result presented here is an extension to higher dimensions of an observation attributed to w stoll for the case of riemann surfaces

nash social and centralized solutions to consensus problems via mean field control theory the purpose of this paper is to synthesize initial mean consensus behavior of a set of agents from the fundamental optimization principles of i stochastic dynamic games and ii optimal control in the stochastic dynamic game model each agent seeks to minimize its individual quadratic discounted cost function involving the mean of the states of all other agents in this formulation we derive the limiting infinite population mean field equation system and explicitly compute its unique solution the resulting mean field mf control strategies drive each agent to track the overall population s initial state distribution mean and by applying these decentralized strategies any finite population system reaches mean consensus asymptotically as time goes to infinity furthermore these control laws possess an en nash equilibrium property where en goes to zero as the population size n goes to infinity finally the analysis is extended to the case of random mean field couplings in the social cooperative formulation the basic objective is to minimize a social cost as the sum of the individual cost functions containing mean field coupling in this formulation we show that for any individual agent the decentralized mean field social mf social control strategy is the same as the mean field nash mf nash equilibrium strategy hence mf nash controls unashn mf social controls usocn on the other hand the solution to the centralized lqr optimal control formulation yields the standard consensus sc algorithm whenever the graph representing the corresponding topology of the network is completely connected cc hence cent lqr controls ucentn sc cc controls uscn moreover a system with centralized control laws reaches consensus on the initial state distribution mean as time and population size n go to infinity hence asymptotically in time mf nash controls unashn mf social controls usocn cent lqr controls ucent sc cc controls usc finally the analysis is extended to the long time average lta cost functions case

the asymptotic estimates of solutions of difference equations abstract the asymptotic estimate of the solution y t of linear difference equations with almost constant coefficients and the condition of asymptotic equivalence between y t and y 0 t are given where y 0 t is the corresponding solution of linear equations with constant coefficients a brief and elementary proof of the results is presented the method of proof carries over to differential equations in which some similar results are stated

o n3 noniterative heuristic algorithm for linear programs with error free implementation we present an o n 3 noniterative heuristic algorithm and describe an implementation of p adic arithmetic to solve the linear programming problems error free an optimality test as well as numerical examples depict the scope of such an algorithm in the few cases where it did not lead to the optimal solution it did provide a nonnegative solution of the system ax b which could be used as the basic feasible solution for any one of the widely used simplex methods say the revised simplex algorithm without the need to include artificial variables in ax b for consistency check thus the algorithm could be at least a pre processor for any simplex algorithm and avoids the enhancement of dimensions of the constraint matrix a and consequent additional space computational complexities and errors

singular monge ampere foliations this paper generalizes results of lempert and szoke on the structure of the singular set of a solution of the homogeneous monge ampere equation on a stein manifold their a priori assumption that the singular set has maximum dimension is shown to be a consequence of regularity of the solution in addition their requirement that the square of the solution be c 3 everywhere is replaced by a smoothness condition on the blowup of the singular set under these conditions the singular set is shown to inherit a finsler metric which in the real analytic case uniquely determines the solution of the monge ampere equation these results are proved using techniques from contact geometry

linear quadratic risk sensitive and robust mean field games this paper considers two classes of large population stochastic differential games connected to optimal and robust decentralized control of large scale multiagent systems the first problem p1 is one where each agent minimizes an exponentiated cost function capturing risk sensitive behavior whereas in the second problem p2 each agent minimizes a worst case risk neutral cost function where the worst case stems from the presence of an adversary entering each agent s dynamics characterized by a stochastic differential equation in both problems the individual agents are coupled through the mean field term included in each agent s cost function which captures the average or mass behavior of the agents we solve both p1 and p2 via mean field game theory specifically we first solve a generic risk sensitive optimal control problem and a generic stochastic zero sum differential game where the corresponding optimal controllers are applied by each agent to construct the mean field systems of p1 and p2 we then characterize an approximated mass behavior effect on an individual agent via a fixed point analysis of the mean field system for each problem p1 and p2 we show that the approximated mass behavior is in fact the best estimate of the actual mass behavior in various senses as the population size n goes to infinity moreover we show that for finite n there exist epsilon nash equilibria for both p1 and p2 where the corresponding individual nash strategies are decentralized in terms of local state information and the approximated mass behavior we also show that epsilon can be taken to be arbitrarily small when n is sufficiently large we show that the epsilon nash equilibria of p1 and p2 are partially equivalent in the sense that the individual nash strategies share identical control laws but the approximated mass behaviors for p1 and p2 are different since in p2 the mass behavior is also affected by the associated worst case disturbance finally we prove that the nash equilibria for p1 and p2 both feature robustness and as the parameter characterizing this robustness becomes infinite the two nash equilibria become identical and equivalent to that of the risk neutral case as in the one agent risk sensitive and robust control theory

linear quadratic n person and mean field games with ergodic cost we consider stochastic differential games with n players linear gaussian dynamics in arbitrary state space dimension and long time average cost with quadratic running cost admissible controls

on predicting the response of non conservative linear vibrating systems by using dynamical matrix solutions abstract formulae are obtained for determining the response of non conservative linear systems without any particular assumption about the nature of the matrix coefficients multiplicity of eigenvalues or external forcing the results apply equally to passive or active systems this is accomplished in terms of the dynamical matrix solution of the given system this solution corresponds to a zero initial matrix displacement and a unit matrix impulse when in standard form moreover it is directly related to the receptance or transfer matrix of the system

sensitivities of frequency response functions of linear dynamic systems to variations in design parameter values abstract expressions for the sensitivities of the frequency response functions of linear constant coefficient systems with distinct eigenvalues to perturbations in the values of their design parameters are derived the expressions are of each of two forms the one involving complex number phasor representation of the responses and the sensitivities the other involving separate amplitude and phase representations the relations derived contain eigenvalue eigenvector and adjoint eigenvector sensitivities engineering applications of the theory are suggested

canonical complex structures associated to connections and complexifications of lie groups the notion of adapted complex structure is extended from riemannian manifolds to general koszul connections the case of the canonical connection of a lie group and the levi civita connection of a pseudo riemannian manifold is studied

gravitational instantons with faster than quadratic curvature decay iii this is our third paper in a series on the gravitational instantons in this paper we classify alg and alh gravitational instantons in alg case we extend tian yau hein s construction slightly and show that it is the only alg gravitational instanton in alh case we prove a torelli type theorem

linear asymptotic equilibrium and uniform exponential and strict stability of linear difference systems following an idea originated by conti for continuous matrix functions an equivalence relation called summable similarity is defined on pairs of n n matrix functions a and b special cases of the results show that if a and b are summably similar and the system a xm amxm m 0 1 2 is uniformly exponentially or strictly stable or has linear asymptotic equilibrium then the system b ym bmym m 0 1 2 has the same property more generally the same conclusion is obtained under weaker conditions relating a and b

indefinite mean field stochastic linear quadratic optimal control from finite horizon to infinite horizon in this paper the finite horizon and the infinite horizon indefinite mean field stochastic linear quadratic optimal control problems are studied firstly the open loop optimal control and the closed loop optimal strategy for the finite horizon problem are introduced and their characterizations difference and relationship are thoroughly investigated the open loop optimal control can be defined for a fixed initial state whose existence is characterized via the solvability of a linear mean field forward backward stochastic difference equation with stationary conditions and a convexity condition on the other hand the existence of a closed loop optimal strategy is shown to be equivalent to any one of the following conditions the solvability of a couple of generalized difference riccati equations the finiteness of the value function for all the initial pairs and the existence of the open loop optimal control for all the initial pairs it is then proved that the solution of the generalized difference riccati equations converges to a solution of a couple of generalized algebraic riccati equations by studying another generalized algebraic riccati equation the existence of the maximal solution of the original ones is obtained together with the fact that the stabilizing solution is the maximal solution finally we show that the maximal solution is employed to express the optimal value of the infinite horizon indefinite mean field linear quadratic optimal control furthermore for the question whether the maximal solution is the stabilizing solution the necessary and the sufficient conditions are presented for several cases

nonlinear panel flutter using high order triangular finite elements a 54 degree of freedom high order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems the finite element formulation is based on kirchhoffs theory of thin plates the quasisteady aerodynamic theory is used numerical solution procedures are presented the limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped respectively the effects of in plane compressive force mass ratio and in plane edge stress free condition are considered stress distributions for the limit cycle oscillation of a two dimensional panel are plotted for the case of panels under static pressure differential the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels respectively the effect of biaxial in plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region dynamically stable buckled region and the limit cycle oscillation region are found alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement

the pluricomplex poisson kernel for strongly convex domains let d be a bounded strongly convex domain in the complex space of dimension n for a fixed point p epsilon partial derivative d we consider the solution of a homogeneous complex monge ampere equation with a simple pole at p we prove that such a solution enjoys many properties of the classical poisson kernel in the unit disc and thus deserves to be called the pluricomplex poisson kernel of d with pole at p in particular we discuss extremality properties such as a generalization of the classical phragmen lindelof theorem relations with the pluricomplex green function of d uniqueness in terms of the associated foliation and boundary behaviors finally using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

computing a matrix symmetrizer exactly using modified multiple modulus residue arithmetic a symmetric solution x satisfying the matrix equation xa atx is called a symmetrizer of the matrix a a general algorithm to compute a matrix symmetrizer is obtained a new multiple modulus residue arithmetic called floating point modular arithmetic is described and implemented on the algorithm to compute an error free matrix symmetrizer

on asymptotic equivalence of perturbed linear systems of differential and difference equations abstract standard results on asymptotic integration of systems of linear differential equations give sufficient conditions which imply that a system is strongly asymptotically equivalent to its principal diagonal part these involve certain dichotomy conditions on the diagonal part as well as growth conditions on the off diagonal perturbation terms here we study perturbations with a triangularly induced structure and see that growth conditions can be substantially weakened in addition we give results for not necessarily triangular perturbations which in some sense interpolate between the classical theorems of levinson and hartman wintner some analogous results for systems of linear difference equations are also given

characterization of strictly convex domains biholomorphic to a circular domain recently parabolic exhaustions have been used successfully to classify complex spaces stoll 6 and 7 burns 2 p wong 9 here we define parabolic exhaustions for strictly convex domains in c and give necessary and sufficient conditions for such a domain to be biholomorphically equivalent to a circular domain or even to the ball the results presented in this note are part of the ph d thesis the author is completing under the direction of professor w stoll details and more implications will appear at a later date a strictly convex domain d c c is a domain for which there exists a defining function whose real hessian is strictly positive on tx dd for all x g dd let a be the open unit disk in c and let s be the unit sphere in c let d c c be a strictly convex domain and p e d be any point for b g s lempert 4 constructs an extremal map f d b a d which is holomorphic with f 0 6 v and f 0 6 x where 1 x 0 is the length of b in the infinitesimal kobayashi metric of d at p these conditions determine f d b uniquely and the map extends smoothly to an embedding f u b s d also f a x s d is of class c and surjective one and only one function r d r exists such that r f z b z for z b g a x s then r is a continuous exhaustion of d positive and of class c on d p also r 1 on 3d we refer to r as the lempert exhaustion of d at p

convergence of calabi yau manifolds abstract in this paper we study the convergence of calabi yau manifolds under kahler degeneration to orbifold singularities and complex degeneration to canonical singularities including the conifold singularities and the collapsing of a family of calabi yau manifolds

mean field games numerical methods mean field type models describing the limiting behavior as the number of players tends to infty of stochastic differential game problems have been recently introduced by j m lasry and p l lions c r math acad sci paris 343 2006 pp 619 625 c r math acad sci paris 343 2006 pp 679 684 jpn j math 2 2007 pp 229 260 numerical methods for the approximation of the stationary and evolutive versions of such models are proposed here in particular existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated numerical experiments are carried out

asymptotic behavior results for solutions to some nonlinear difference equations abstract we give asymptotic results for convergent solutions x n of real or complex difference equations x n 1 j x n f n x n where x n is an m vector j is a constant m m matrix and f n y is a vector valued function which is continuous in y for fixed n and where f n y is small in a sense in addition we obtain asymptotic results for solutions x n of the poincare difference equation x n 1 a b n x n where b n satisfies b n o n with 0 1 an application illustrates the results

an iterative algorithm for solving a finite dimensional linear operator equation t x f with applications abstract this paper proposes an iterative algorithm for solving a general finite dimensional linear operator equation t x f and demonstrates that it will get the exact solution within a finite number of iteration steps this algorithm unifies all the iterative methods in huang 2008 3 peng 2005 7 and peng and peng 2006 8 and provides an iterative method for solving an inverse problem related to hermitian generalized hamiltonian matrices 2 12

dynamic response of some dissipative systems by means of functions of matrices abstract a certain class of linear viscously damped dynamical systems the matrix coefficients of which satisfy a certain commutativity condition are known to exhibit the same normal modes as the ones that exist in the absence of damping these systems are said to have classical normal modes in the present study such systems are shown to be particular cases of dynamical systems that possess a zero commutator which form a subset of separable systems the response of the latter is investigated by means of functions of matrices and its connection with the classical eigenfunction expansion approach is established the paper continues the author s previous work where functions of matrices were used to a develop an algorithm for the numerical integration of the equations of motion for such systems and b to establish their conservation laws

computing matrix symmetrizers part 2 new methods using eigendata and linear means a comparison abstract over any field f every square matrix a can be factored into the product of two symmetric matrices as a s 1 s 2 with s i s i t f n n and either factor can be chosen nonsingular as was discovered by frobenius in 1910 frobenius symmetric matrix factorization has been lying almost dormant for a century the first successful method for computing matrix symmetrizers i e symmetric matrices s such that sa is symmetric was inspired by an iterative linear systems algorithm of huang and nong 2010 in 2013 29 30 the resulting iterative algorithm has solved this computational problem over r and c but at high computational cost this paper develops and tests another linear equations solver as well as eigen and principal vector or schur normal form based algorithms for solving the matrix symmetrizer problem numerically four new eigendata based algorithms use respectively svd based principal vector chain constructions gram schmidt orthogonalization techniques the arnoldi method or the schur normal form of a in their formulations they are helped by datta s 1973 method that symmetrizes unreduced hessenberg matrices directly the eigendata based methods work well and quickly for generic matrices a and create well conditioned matrix symmetrizers through eigenvector dyad accumulation but all of the eigen based methods have differing deficiencies with matrices a that have ill conditioned or complicated eigen structures with nontrivial jordan normal forms our symmetrizer studies for matrices with ill conditioned eigensystems lead to two open problems of matrix optimization

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

on eigenproblem solution of damped vibrations associated with gyroscopic moments a new efficient approach is presented for solving the quadratic eigenvalue problem of weakly nonproportionally damped vibration systems in the analysis of these systems gyroscopic moments and external damping are both considered traditional restriction of symmetry of inertia damping and stiffness matrices is slightly relaxed a second order perturbation theory is developed such that the perturbed solution is based on the eigensolution of an unperturbed subproblem this subproblem considers the unperturbed system in two different forms i a conservative gyroscopic part of an original problem or ii a nonconservative gyroscopic part of an original problem that is proportionally damped to cope with asymmetry of the system matrices a duncan s like state formulation is used to bring these matrices into a suitable form for perturbations two numerical examples are introduced for explaining the detailed implementation of the presented approach additionally a practical problem of rotor supported by two tilting pad bearings is investigated the eigensolutions obtained by the current approach match to a great extent other solutions obtained by time consuming exact methods the investigation procedure given here gives a framework to handle vibration problems of weakly nonproportional damping and or weakly asymmetric inertia damping and stiffness matrices

maximal complexifications of certain riemannian homogeneous manifolds let m g k be a homogeneous riemannian manifold with dim c g c dim r g where g c denotes the universal complexification of g under certain extensibility assumptions on the geodesic flow of m we give a characterization of the maximal domain of definition in tm for the adapted complex structure and show that it is unique for instance this can be done for generalized heisenberg groups and naturally reductive homogeneous riemannian spaces as an application it is shown that the case of generalized heisenberg groups yields examples of maximal domains of definition for the adapted complex structure which are neither holomorphically separable nor holomorphically convex

taussky s theorem symmetrizability and modal analysis revisited this paper is concerned with symmetrization and diagonalization of real matrices and their implications for the dynamics of linear second order systems governed by equations of motion having asymmetric coefficient matrices results in the light of taussky s theorem are presented the connection of the symmetrizers with the eigenvalue problem is brought out an alternative proof of taussky s theorem for real matrices is presented diagonalization of two real symmetric but not necessarily positive definite matrices is discussed in the context of undamped non gyroscopic systems a commutator of two matrices with respect to a given third matrix is defined this commutator is found to play an interesting role in deciding simultaneous diagonalizability of two or three matrices errors in a few previously known results are brought out pseudo conservative systems are studied and their connection with the so called symmetrizable systems is critically examined results for modal analysis of general non conservative systems are presented illustrative examples are given

maximal complexifications of certain homogeneous riemannian manifolds let m g k be a homogeneous riemannian manifold with dim c g c dim r g where g c denotes the universal complexification of g under certain extensibility assumptions on the geodesic flow of m we give a characterization of the maximal domain of definition in tm for the adapted complex structure and show that it is unique for instance this can be done for generalized heisenberg groups and naturally reductive homogeneous riemannian spaces as an application it is shown that the case of generalized heisenberg groups yields examples of maximal domains of definition for the adapted complex structure which are neither holomorphically separable nor holomorphically convex

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

on asymptotic summation of potentially oscillatory difference systems a new technique for the asymptotic summation of linear systems of difference equations y t 1 d t r t y t is derived a fundamental solution y t t i p t is constructed in terms of a product of two matrix functions the first function t is a product of the diagonal part d t the second matrix i p t is a perturbation of the identity matrix i conditions are given on the matrix d t r t that allow us to represent i p t as an absolutely convergent resolvent series without imposing stringent conditions on r t our method could be applied to discretized version of singularly perturbed differential equations y t a t y t that fit the setting of quantum mechanics

the eigenproblem for damped linear vibrating systems with multiple eigenvalues abstract vibration systems with damping are analyzed with the equations written in second order form as well as first order state space form the existence of eigenpairs is studied for vibrating systems with null eigenvalues a detailed study is carried out of the effect of velocity constraints on rigid body motion and on the number of associated linearly independent eigenvectors the results are useful for complex modal synthesis in which subsystems include rigid body motion the analysis is extended to multiple non null eigenvalues by using an eigenvalue shifting technique for the double non null eigenvalue problem a necessary condition is derived for the associated eigenvector in terms of a convenient orthogonality relation

the asymptotic expansion of a cr invariant and grauert tubes cr manifolds the abstract models of real hypersurfaces in complex manifolds are 2n 1 dimensional manifolds m with a codimension one subbundle h of the tangent bundle which carries a complex structure the cr refers to cauchy riemann because for m c c n l the subbundle h consists of induced cauchy riemann operators there is a wealth of geometry and analysis associated with these structures especially when the cr manifolds are strictly pseudoconvex for example two strictly pseudoconvex domains are biholomorphically equivalent if and only if their boundaries are cr equivalent a fundamental problem in cr geometry is to find computable invariants associated with the cr structures the global cr invariant we will consider in this paper is the chem simons type invariant discovered by bums and epstein b e 1 it is a real valued global cr invariant of a compact 3dimensional strictly pseudo convex cr manifold whose holomorphic tangent bundle is trivial cheng and lee independently found this invariant and extend the definition of b e invariant to a relative invariant on an arbitrary compact 3 dimensional cr manifold cf c l we will evaluate this g asymptotically on the boundary of small grauert tubes before posing the question in a more precise form we will first say a few workds about grauert tubes let x be a real analytic manifold then every coordinate patch u c r n can be thickened to obtain an open set r c c n since the coordinate changes of x are real analytic maps by taking power series expansions and by shrinking c u to get convergence they can be extended holomorphically to such enlarged domains and thus they can be used as holomorphic transition

complex monge ampere equations and totally real submanifolds abstract we study the dirichlet problem for complex monge ampere equations in hermitian manifolds with general non pseudoconvex boundary our main result theorem 1 1 extends the classical theorem of caffarelli kohn nirenberg and spruck in c n we also consider the equation on compact manifolds without boundary attempting to generalize yau s theorems in the kahler case as applications of the main result we study some connections between the homogeneous complex monge ampere hcma equation and totally real submanifolds and a special dirichlet problem for the hcma equation related to donaldson s conjecture on geodesics in the space of kahler metrics

asymptotic behavior of solutions of perturbed linear difference systems abstract this paper is concerned with asymptotic behavior of solutions of perturbed linear difference systems several asymptotic results are obtained some of which can be regarded as discrete analogs of the famous asymptotic results for differential systems including the hartman wintner theorem the harris lutz theorem and the eastham theorem in addition the conditions of a result established by z benzaid and d a lutz are weakened

kahler non collapsing eigenvalues and the calabi flow abstract we first prove a new compactness theorem of kahler metrics which confirms a prediction in 17 then we establish several eigenvalue estimates along the calabi flow combining the compactness theorem and these eigenvalue estimates we generalize the method developed for the kahler ricci flow in 22 to obtain several new small energy theorems of the calabi flow

modular data and regularity of monge ampere exhaustions and of kobayashi distance regularity properties of intrinsic objects for a large class of stein manifolds namely of monge ampere exhaustions and kobayashi distance is interpreted in terms of modular data the results lead to a construction of an infinite dimensional family of convex domains with squared kobayashi distance of prescribed regularity properties a new sharp refinement of stoll s characterization of mathbb c n is also given

on asymptotic summations of almost diagonal difference systems and their applications in this paper we derive some new results of asymptotic summations of left and right almost diagonal difference systems in particular we study a special case where the diagonal elements are constants with magnitude 1 conditions on the perturbation matrices are given under which the system is left and right almost diagonal an application of this result in a discrete adiabatic oscillator equation is discussed we also introduce a result for the case when the diagonal matrix is approaching the identity matrix i an example is given to illustrate that the new result can be applied to some cases that do not satisfy the growth condition

symmetric state space method for a class of nonviscously damped systems multiple degree of freedom linear nonviscously damped systems are considered it is assumed that the nonviscousdampingforcesdependonthepasthistoryofvelocitiesviaconvolutionintegralsoverexponentiallydecaying kernel functions the traditional state space approach well known for viscously damped systems is extended to such nonviscously damped systems using a set of internal variables suitable numerical examples are provided to illustrate the proposed approach i introduction v iscousdampingisthemostcommonmodelforthemodeling of vibration damping in linear systems this model e rst introduced by rayleigh 1 assumes that the instantaneous generalized velocities are the only relevant variables that determine damping viscous damping models are used widely for their simplicity and mathematical convenience even though the behavior of real structural materials is at best poorly mimicked by simple viscous models forthisreason itiswellrecognizedthat ingeneral aphysically realistic model of damping will not be viscous damping models in whichthedissipativeforcesdependonanyquantityotherthantheinstantaneous generalized velocities are nonviscous damping models mathematically any causal model that makes the energy dissipation functional nonnegative is a possible candidate for a nonviscous damping model clearly a wide range of choice is possible either based on the physics of the problem or by selecting a model a priori and e tting its parameters from experiments here we will use a particular type of damping model that is not viscous and throughout the paper the terminology nonviscous damping will refer to this specie c model only possiblythemostgeneralwaytomodeldampingwithinthelinear range is to use nonviscous damping models that depend on the past history of motion via convolution integrals over kernel functions 2 the equations of motion of an n degree of freedom linear system with such damping can be expressed by

differential geometry of real monge ampere foliations on etudie les feuilletages qui proviennent de la condition de monge ampere recquerant le hessien d une fonction definie sur une variete affine d avoir un rang inferieur au maximal

asymptotic solutions and error estimates for linear systems of difference and differential equations abstract classical results concerning the asymptotic behavior solutions of systems of linear differential or difference equations lead to formulas containing factors that are asymptotically constant i e k o 1 as t tends to infinity here we are interested in more precise information about the o 1 terms specifically how they depend precisely on certain perturbation terms in the equation results along these lines were given by gel fond and kubenskaya for scalar difference equations and we will both extend and generalize one of them as well as provide some corresponding results for differential equations

epsilon nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents this paper studies large population dynamic games involving nonlinear stochastic dynamical systems with agents of the following mixed types i a major agent and ii a population of n minor agents where n is very large the major and minor agents are coupled via both i their individual nonlinear stochastic dynamics and ii their individual finite time horizon nonlinear cost functions this problem is analyzed by the so called epsilon nash mean field game theory a distinct feature of the mixed agent mean field game problem is that even asymptotically as the population size n approaches infinity the noise process of the major agent causes random fluctuation of the mean field behavior of the minor agents to deal with this the overall asymptotic n rightarrow infty mean field game problem is decomposed into i two nonstandard stochastic optimal control problems with random coefficient processes which yield forward adapted stochastic best response control processes determined from the

complex zeros of real ergodic eigenfunctions we determine the limit distribution as of complex zeros for holomorphic continuations to grauert tubes of real eigenfunctions of the laplacian on a real analytic compact riemannian manifold m g with ergodic geodesic flow if phi j k is an ergodic sequence of eigenfunctions we prove the weak limit formula frac 1 lambda j z phi j k mathbb c to frac i pi partial bar partial xi g where z phi j k mathbb c is the current of integration over the complex zeros and where overline partial is with respect to the adapted complex structure of lempert szoke and guillemin stenzel

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

ergodic bellman systems for stochastic games in arbitrary dimension stochastic games with cost functionals j i x v e 0 e t l i y v d t i 1 2 with controls v v 1 v 2 and state y t with y 0 x are considered each player wants to minimize his her cost functional e denotes the expected value and the state variables y are coupled with the controls v via a stochastic differential equation with initial value x the corresponding bellman system which is used for the calculation of feedback controls v v y and the solvability of the game leads to a class of diagonal second order nonlinear elliptic systems which also occur in other branches of analysis their behaviour concerning existence and regularity of solutions is despite many positive results not yet well understood even in the case where the l i are simple quadratic functions the objective of this paper is to give new insight to these questions for fixed 0 and primarily to analyse the limiting behaviour as the discount 0 we find that the modified solutions of the stochastic games converge for subsequences to the solution of the so called ergodic bellman equation and that the average cost converges a former restriction of the space dimension has been removed a reasonable class of quadratic integrands may be treated more specifically we consider the bellman systems of equations z h x dz where the space variable x belongs to a periodic cube for the sake of simplifying the presentation they are shown to have smooth solutions if u is the solution of u u h x du then the convergence of u to z as tends to 0 is established the conditions on h are such that some quadratic growth in du is allowed

boundedness of solutions for singular hamiltonian differential systems with applications to deficiency indices abstract the paper gives boundedness estimation of solutions for singular hamiltonian differential systems as corollaries limit circle criteria are given and improve some previous results

a canonical form of the equation of motion of linear dynamical systems the equation of motion of a discrete linear system has the form of a second order ordinary differential equation with three real and square coefficient matrices it is shown that for almost all linear systems such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement this canonical form of the equation of motion is unique up to an equivalence class for non defective systems as an important by product a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system

monge ampere foliations with singularities at the boundary of strongly convex domains let d c n be a bounded strongly convex domain with smooth boundary we consider a monge ampere type equation in d with a simple pole at the boundary using the lempert foliation of d in extremal discs we construct a solution u whose level sets are bound aries of horospheres among other things we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques

solving linear programming problems exactly a linear programming problem in an inequality form having a bounded solution is solved error free using an algorithm that sorts the inequalities removes the redundant ones and uses the p adic arithmetic c elsevier science inc 1997

on the modal analysis of non conservative linear systems this paper applies the results of classical eigenvalue theory to the analysis of a non conservative vibratory system general results are obtained for the response of a multiple degree of freedom system which is represented by a set of linear second order differential equations with constant coefficients for the case when the eigenvalues of the system are distinct these results confirm those obtained by 1 fawzy and bishop by a different method the latter results are restricted to distinct eigenvalues but the more general analysis presented here allows the case of multiple eigenvalues to be included the physical interpretation of complex normal co ordinate vectors is discussed and some simple numerical examples illustrate the results the approach described here lends itself to numerical computation using computer library programs for eigenvalue determination