replica treatment of non hermitian disordered hamiltonians we employ the fermionic and bosonic replicated nonlinear models to treat ginibre unitary symplectic and orthogonal ensembles of non hermitian random matrix hamiltonians using the saddle point approach combined with the borel resummation procedure we derive the exact large n results for microscopic density of states in all three ensembles we also obtain tails of the density of states as well as the two point function for the unitary ensemble

inference in dynamic models containing surprise variables abstract some new results on calculating moving average representation mar coefficients and their limiting distribution from estimated vector arma processes are presented the technique is applied to the problem of estimating the coefficients of unanticipated or surprise variables in a single equation for a multi period expectations horizon the method naturally conditions the expectations on all past values of the process and avoids the necessity of using two step regression procedures and adjusting the resulting standard errors

equivariance brst symmetry and superspace the structure of equivariant cohomology in non abelian localization formulas and topological field theories is discussed equivariance is formulated in terms of a nilpotent becchi rouet stora tyutin brst symmetry and another nilpotent operator which restricts the brst cohomology onto the equivariant or basic sector a superfield formulation is presented and connections to reducible batalin fradkin vilkovisky bfv quantization of topological yang mills theory are discussed

localization and diagonalization a review of functional integral techniques for low dimensional gauge theories and topological field theories localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low dimensional gauge theories are reviewed these are the functional integral counterparts of the mathai quillen formalism the duistermaat heckman theorem and the weyl integral formula respectively in each case the necessary mathematical background euler classes of vector bundles equivariant cohomology topology of lie groups is introduced and the finite dimensional integration formulae described then some applications to path integrals are discussed and an overview of the relevant literature is given the applications include supersymmetric quantum mechanics cohomological field theories phase space path integrals and two dimensional yang mills theory

consistent estimation of equations with composite moving average disturbance terms abstract the paper examines the circumstances under which an equation with a composite ma disturbance term can be consistently estimated by single equation non linear least squares the composite disturbance may arise as a result of the dependent or an explanatory variable being unobservable either because it is subject to measurement error or because it is a desired or expected variable it may also arise as a result of substituting out an explanatory variable from an equation or because a vector ma process is specified for the structural form of a linear simultaneous equation model the argument of the paper relies on some results relating to the sum of finite ma processes presented in nelson 1975a and darroch and mcdonald 1981

a fuzzy lyapunov krasovskii functional approach to sampled data output feedback stabilization of polynomial fuzzy systems this paper presents an output feedback exponential stabilization condition of sampled data polynomial fuzzy control systems under variable sampling rates compared with previous work the proposed method is less conservative because of the newly developed time dependent fuzzy lyapunov krasovskii functional that is based on the conventional fuzzy lyapunov function moreover the controller is allowed to contain polynomial gain matrices thereby improving the control performance and design flexibility this is realized by assuming the difference between the continuous and discrete time state vectors as time varying norm bounded uncertainties which are manipulated using a robust control technique a new sufficient condition is introduced to cast the stability condition containing the integral term as the sum of square conditions finally the effectiveness of the proposed method is validated by simulations

symplectic surgery and the spinc dirac operator abstract letgbe a compact connected lie group and m a compact hamiltoniang space with moment mapj m g under the assumption that these data are pre quantizable one can construct an associated spinc dirac operator formula whose equivariant index yields a virtual representation ofg we prove a conjecture of guillemin and sternberg that if 0 is a regular value ofj the multiplicityn 0 of the trivial representation in the index space formula is equal to the index of the spinc dirac operator for the symplectic quotientm0 j 1 0 g this generalizes previous results for the case thatg tis abelian i e a torus

abcd of instantons we solve open image in new window 2 supersymmetric yang mills theories for an arbitrary classical gauge group i e su n so n sp n in particular we derive the prepotential of the low energy effective theory and the corresponding seiberg witten curves we manage to do this without resolving singularities of the compactified instanton moduli spaces

robust sampled data stabilization of uncertain fuzzy systems via input delay approach this paper is concerned with robust sampled data stabilization for uncertain fuzzy systems the system is modeled as a continuous time fuzzy system while the control input is a zero order sampled data signal when a zero order control input is considered the closed loop system can be seen as an input delay system hence an input delay system approach is introduced for sampled data control design sufficient stability conditions for the closed loop system are given in terms of linear matrix inequalities lmis under the assumption that sampling interval is not greater than some prescribed number stability conditions for fuzzy time delay systems are given by using jensen s inequality which simplifies conditions with less matrix variables a design method of robust sampled data state feedback controller for uncertain fuzzy systems is then proposed numerical examples are given to illustrate our robust sampled data state feedback control design and to show the effectiveness over other existing results

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

nonfragile retarded sampled data switched control of t s fuzzy systems and its applications this article investigates the nonfragile retarded fuzzy sampled data control design of takagi sugeno t s fuzzy system when compared to the traditional sampled data control scheme a constant signal transmission delay is involved with uncertainties in control gain parameters which exploited for the first time to tackle the stabilization analysis of the closed loop t s fuzzy systems based on the switched control idea by constructing a fuzzy membership function fmf dependent lyapunov krasovskii functional lkf and utilizing the time derivative information of the fmf the sufficient conditions are carried out in terms of linear matrix inequalities lmis such that the resultant t s fuzzy systems can achieve the globally asymptotically stable under the designed control then the desired control gain is determined by solving the obtained lmis finally the numerical simulations are demonstrated to show the advantage and applicability of the derived sufficient conditions

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

the spectrum of coupled random matrices the study of the spectrum of coupled random matrices has received rather little attention to the best of our knowledge coupled random matrices have been studied to some extent by mehta in this work we explain how the integrable technology can be brought to bear to gain insight into the nature of the distribution of the spectrum of coupled hermitean random matrices and the equations the associated probabilities satisfy in particular the two toda lattice its algebra of symmetries and its vertex operators will play a prominent role in this interaction namely the method is to introduce time parameters in an artificial way and to dress up a certain matrix integral with a vertex integral operator for which we find virasoro like differential equations these methods lead to very simple nonlinear third order partial differential equations for the joint statistics of the spectra of two coupled gaussian random matrices comment 56 pages published version abstract added in migration

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

the infinitesimal lefschetz formulas a heat equation proof abstract in this paper the lefschetz formulas of atiyah and bott ann of math 86 1967 374 407 88 1968 451 491 and atiyah and singer ann of math 87 1968 546 604 93 1971 119 138 are proved by heat equation methods in infinitesimal form i e without using the usual localization on the fixed point set the proof is obtained by a homotopic deformation of the dirac operator and uses probabilistic methods the main applications are potentially in noncompact situations where fixed point formulas do not always hold while their infinitesimal analogues are still valid

gauged vortices in a background we discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism at critical self coupling and for low temperatures it has been argued that the configuration space for vortex dynamics in each topological class of the abelian higgs model approximately truncates to a finite dimensional moduli space with a kahler structure for the case where the vortices live on a 2 sphere we explain how localization formulae on the moduli spaces can be used to compute exactly the partition function of the vortex gas interacting with a background potential the coefficients of this analytic function provide geometrical data about the kahler structures the simplest of which being their symplectic volume computed previously by manton using an alternative argument we use the partition function to deduce simple results on the thermodynamics of the vortex system in particular the average height on the sphere is computed and provides an interesting effective picture of the ground state

supersymmetry for systems with unitary disorder circular ensembles a generalized hubbard stratonovitch transformation relating an integral over random unitary matrices to an integral over efetov s unitary model manifold is introduced this transformation adapts the supersymmetry method to disordered and chaotic systems that are modelled not by a hamiltonian but by their scattering matrix or time evolution operator in contrast to the standard method no saddle point approximation is made and no massive modes have to be eliminated this first paper on the subject applies the generalized hubbard stratonovitch transformation to dyson s circular unitary ensemble it is shown how a supersymmetric variant of the harish chandra itzykson zuber formula can be used to compute in the large n limit the n level correlation function for any n non trivial applications to random network models quantum chaotic maps and lattice gauge theory are expected

homogeneous quantization and multiplicities of group representations let b be a compact manifold a cone over b is a principal r bundle x with base b let a x a x be the mapping associated with the action of a r on x x is called a symplectic cone if it possesses a symplectic form such that a a a compact lie group g is said to act in a homogeneous fashion on x if it acts on x in such a way that both and the principal bundle structure are preserved it is known that to such an action one can associate in a fairly canonical way a representation of g on a hilbert space h see 3 in this paper we propose a symplectic recipe for the multiplicities with which h decomposes into g irreducibles and show that this recipe is correct generically

spatially piecewise fuzzy control design for sampled data exponential stabilization of semilinear parabolic pde systems this paper employs a takagi sugeno t s fuzzy partial differential equation pde model to solve the problem of sampled data exponential stabilization in the sense of spatial l infty norm vert cdot vert infty for a class of nonlinear parabolic distributed parameter systems dpss where only a few actuators and sensors are discretely distributed in space initially a t s fuzzy pde model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear dpss subsequently a static sampled data fuzzy local state feedback controller is constructed based on the t s fuzzy pde model by constructing an appropriate lyapunov krasovskii functional candidate and employing vector valued wirtinger s inequalities a variation of vector valued poincare wirtinger inequality in one dimensional spatial domain as well as a vector valued agmon s inequality it is shown that the suggested sampled data fuzzy controller exponentially stabilizes the nonlinear dpss in the sense of vert cdot vert infty if sufficient conditions presented in term of standard linear matrix inequalities lmis are fulfilled moreover an lmi relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled data fuzzy controller finally the satisfactory and better performance of the suggested sampled data fuzzy controller are demonstrated by numerical simulation results of two examples

heckman kostant and steinberg formulas for symplectic manifolds abstract let m be a compact symplectic manifold on which a compact connected lie group k acts in a hamiltonian fashion in part i we derive a formula for j m which generalizes the heckman formula for co adjoint orbits here j is the moment map associated with the action of k on m and m the liouville measure on m in part ii we derive a quantum analogue of this formula which extends to the symplectic setting classical multiplicity formulas of kostant and steinberg

quotient spaces and critical points of invariant functions for c actions consider a linear action of the group c on x c n 1 we study the fundamental algebraic properties of the sheaves of invariant and basic differential forms for such an action and use these to define an algebraic notion of multiplicity for critical points of functions which are invariant under the c action we also prove a theorem relating the cohomology of the milnor fibre of the critical point on the quotient space with this algebraic multiplicity we also include an appendix showing how to use cech complexes to compute local cohomology

12 24 and beyond abstract we generalize the well known 12 and 24 theorems for reflexive polytopes of dimension 2 and 3 to any smooth reflexive polytope our methods apply to a wider category of objects here called reflexive gkm graphs that are associated with certain monotone symplectic manifolds which do not necessarily admit a toric action as an application we provide bounds on the betti numbers for certain monotone hamiltonian spaces which depend on the minimal chern number of the manifold

sampled data fuzzy control of chaotic systems based on a t s fuzzy model in this paper a sampled data fuzzy controller is designed to stabilize a class of chaotic systems a takagi sugeno t s fuzzy model is employed to represent the chaotic systems based on this general model the exponential stability issue of the closed loop systems with an input constraint is first investigated by a novel time dependent lyapunov functional which is positive definite at sampling times but not necessary between the sampling times then two sufficient conditions are developed for sampled data fuzzy controller synthesis of the underlying t s fuzzy model with or without input constraint all the proposed results in this paper depend on both the upper and lower bounds on a sampling interval and the available information about the actual sampling pattern is fully utilized the proposed sampled data fuzzy control scheme is successfully applied to the chaotic lorenz system which is shown to be effective and less conservative compared with existing results

correlation functions of the bc calogero sutherland model the bc type calogero sutherland model csm is an integrable extension of the ordinary a type csm that possesses a reflection symmetry point the bc cs mi sr elated to the chiral classes of random matrix ensembles rmes in exactly the same way as the a csm is related to the dyson classes we first develo pt he fermionic replica model formalism suitable to treat all chiral rmes by exploiting generalized colour flavour transformation we then extend the method to find the exact asymptotics of the bc csm density profile consistency of our result with the c 1g aussian conformal field theory description is verified the emerging friedel oscillations structure and sum rules are discussed in details we also compute the distribution of the particle nearest to the reflection point

adaptive fuzzy control with guaranteed convergence of optimal approximation error with no a priori knowledge of plant boundary functions a novel direct adaptive fuzzy controller afc for a class of single input single output siso uncertain affine nonlinear systems is developed in this paper based on the theory of fuzzy logic systems flss with variable universes of discourse uds sufficient conditions that guarantee that the optimal fuzzy approximation error fae is locally convergent are given by the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters a variable ud fls with an optimal fae local convergence is constructed and its parameter adaptive law is derived by virtue of the lyapunov stability theorem under the assumption that the optimal fae is bounded it is proved that the closed loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero the proposed approach eliminates the influence of the fae on the tracking errors by means of the inherent mechanism of the variable ud fls thus it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules simulation studies demonstrate the superiority of the proposed afc in terms of the settling time tracking accuracy smoothness of the control input and robustness against external disturbances and parameter variations

the genus and a regularization of an s1 equivariant euler class we show that a new multiplicative genus in the sense of hirzebruch can be obtained by generalizing a calculation due to atiyah and witten we introduce this as the genus compute its value for some examples and highlight some of its interesting properties we also indicate a connection with the study of multiple zeta values which gives an algebraic interpretation for our proposed regularization procedure

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a riemann surface let n and d be coprime positive integers and define m n d to be the moduli space of semi stable holomorphic vector bundles of rank n degree d and fixed determinant on a compact riemann surface e this moduli space is a compact kifhler manifold which has been studied from many different points of view for more than three decades see for instance narasimhan and seshadri 41 the subject of this article is the characterization of the intersection pairings in the cohomology ring1 h m n d a set of generators of this ring was described by atiyah and bott in their seminal 1982 paper 2 on the yangmills equations on riemann surfaces where in addition inductive formulas for the betti numbers of m n d obtained earlier using number theoretic methods 13 25 were rederived by poincare duality knowledge of the intersection pairings between products of these generators or equivalently knowledge of the evaluation on the fundamental class of products of the generators completely determines the structure of the cohomology ring in 1991 donaldson 15 and thaddeus 47 gave formulas for the intersection pairings between products of these generators in h m 2 1 in terms of bernoulli numbers then using physical methods witten 50 found formulas for generating functions from which could be extracted the intersection pairings between products of these generators in h m n d for general rank n these generalized his rigorously proved formulas 49 for the symplectic volume of m n d for instance the symplectic volume of m 2 1 is given by

large sample estimation and testing procedures for dynamic equation systems abstract joint two step estimation procedures which have the same asymptotic properties as the maximum likelihood ml estimator are developed for the final equation transfer function and structural form of a multivariate dynamic model with normally distributed vector moving average errors the ml estimator under fixed and known initial values is obtained by iterating the procedure until convergence the asymptotic distribution of the two step estimators is used to construct large sample testing procedures for the different forms of the model

replica field theories painleve transcendents and exact correlation functions exact solvability is claimed for nonlinear replica ensuremath sigma models derived in the context of random matrix theories contrary to other approaches reported in the literature the framework outlined does not rely on traditional replica symmetry breaking but rests on a previously unnoticed exact relation between replica partition functions and painlev e transcendents while expected to be applicable to matrix models of arbitrary symmetries the method is used to treat fermionic replicas for the gaussian unitary ensemble gue chiral gue symmetry classes a and aiii in cartan classification and ginibre s ensemble of complex non hermitian random matrices further applications are briefly discussed

bohr sommerfeld conditions for integrable systems with critical manifolds of focus focus type we present a detailed study in the semi classical regime h of microlocal properties of systems of two commuting h pseudo dierential operators ph ph such that the joint principal symbol p p p has a special kind of singularity called a focusfocus singularity typical examples include the quantum spherical pendulum or the quantum champagne bottle in the spirit of colin de verdiere and parisse we show that such systems have a universal behavior described by singular quantization conditions of bohr sommerfeld type these conditions are used to give a precise description of the joint spectrum of such systems including the phenomenon of quantum monodromy and dierent formulations of the counting function for the joint eigenvalues close to the singularity in which a logarithm of the semi classical constant h appears thanks to numerical computations done by ms child for the case of the champagne bottle we are able to accurately illustrate our statements

critique of the replica trick it is shown that the replica trick fails to give the correct non perturbative result for the two point function s2 of the gaussian unitary ensemble of n n random matrices the failure arises from an incorrect description of the symmetries of the random matrix system in the limit n to infinity the correct description which involves integration over both non compact and compact degrees of freedom is obtained by using the method of superfields some implications for the localisation transition in disordered electronic systems and the theory of the quantised hall effect are suggested

non hamiltonian actions with isolated fixed points we construct a non hamiltonian symplectic circle action on a closed connected six dimensional symplectic manifold with exactly 32 fixed points

random matrices close to hermitian or unitary overview of methods and results the paper discusses recent progress in understanding statistical properties of eigenvalues of weakly non hermitian and non unitary random matrices the first type of ensembles is of the form i with being a large random n n hermitian matrix with independent entries deformed by a certain anti hermitian n n matrix i satisfying in the limit of large dimension n the condition tr 2 n tr 2 here can be either a random or just a fixed given hermitian matrix ensembles of such a type with 0 emerge naturally when describing quantum scattering in systems with chaotic dynamics and serve to describe resonance statistics related models are used to mimic complex spectra of the dirac operator with chemical potential in the context of quantum chromodynamics ensembles of the second type arising naturally in scattering theory of discrete time systems are formed by n n matrices with complex entries such that i for 0 this coincides with the circular unitary ensemble and 0 i describes deviation from unitarity our result amounts to answering statistically the following old question given the singular values of a matrix describe the locus of its eigenvalues we systematically show that the obtained expressions for the correlation functions of complex eigenvalues describe a non trivial crossover from wigner dyson statistics of real unimodular eigenvalues typical of hermitian unitary matrices to ginibre statistics in the complex plane typical of ensembles with strong non hermiticity tr 2 tr 2 when n finally we discuss scarce results available on eigenvector statistics for weakly non hermitian random matrices

stochastic equivariant cohomologies and cyclic cohomology we give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the chen souriau sense and to establish a link with cyclic cohomology with the second one we can establish a stochastic fixed point theorem

the fixed point theorem in equivariant cohomology in this paper we study the s equivariant de rham cohomology of infinite dimensional s manifolds our main example is the free loop space lx where x is a finite dimensional manifold with the circle acting by rotating loops we construct a new form of equivariant cohomology h which agrees with the usual periodic equivariant cohomology in finite dimensions and we prove a suitable analogue of the classical fixed point theorem which is valid for loop spaces lx this gives a cohomological framework for studying differential forms on loop spaces and we apply these methods to various questions which arise from the work of witten 16 atiyah 2 and bismut 5 in particular we show following atiyah in 2 that the a polynomial of x arises as an equivariant characteristic class in the theory h of the normal bundle to x considered as the space of constant loops in lx

eigenvalue correlations in non hermitean symplectic random matrices a correlation function of complex eigenvalues of n n random matrices drawn from non hermitean random matrix ensembles of symplectic symmetry is given in terms of a quaternion determinant spectral properties of gaussian ensembles are studied in detail in the regimes of weak and strong non hermiticity

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

estimation principal components and hamiltonian systems in this paper we show how symplectic geometry can be used to analyse a fundamental problem in estimation theory the fitting of lines and planes to a data set in n dimensions symplectic methods yield information not only on the critical point structure of the maximum likelihood estimation mle function see byrnes and willems 7 but also on the asymmetries in the distribution of the data points in n space

eigenvalue distribution in the self dual non hermitian ensemble we consider an ensemble of self dual matrices with arbitrary complex entries this ensemble is closely related to a previously defined ensemble of anti symmetric matrices with arbitrary complex entries we study the two level correlation functions numerically although no evidence of non monotonicity is found in the real space correlation function a definite shoulder is found on the analytical side we discuss the relationship between this ensemble and the 4 two dimensional one component plasma and also argue that this ensemble combined with other ensembles exhausts the possible universality classes in non hermitian random matrix theory this argument is based on combining the method of hermitization of feinberg and zee with zirnbauer s classification of ensembles in terms of symmetric spaces

an improved result on exponential stabilization of sampled data fuzzy systems this brief paper studies the exponential stabilization problem for the takagi sugeno fuzzy systems with a variable sampling different from previous results the gains of fuzzy state feedback controller adopted in this paper are time varying during two consecutive sampling instants which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter to reduce the design conservativeness a novel fuzzy time dependent lyapunov functional ftdlf is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions moreover a more relaxed constraint condition is presented to ensure the positive definiteness of the ftdlf on sampling intervals by resorting to the novel ftdlf and the relaxed constraint condition new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established by which a larger sampling interval can be achieved one example is offered to demonstrate the validity and superiorities of the obtained new results

large sample estimation and testing procedures for dynamic equation systems abstract in 1980 palm and zellner presented a number of joint or system estimation and testing procedures for the final equations transfer functions and structural equations of a multivariate dynamic model with normally distributed vector moving average errors in this paper we show that there is a flaw in their argument which renders most of the procedures invalid possible alternative procedures are described

integrability of zero dimensional replica field theories at β 1 building on insights from the theory of integrable lattices the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrices specifically the fermionic and the bosonic replica partition functions are proven to form a single supersymmetric pfaff kp hierarchy whose replica limit is shown to reproduce the celebrated nonperturbative formula for the density density eigenvalue correlation function in the infinite dimensional gaussian orthogonal ensemble implications of the formalism outlined are briefly discussed

finite time synchronization of sampled data t s fuzzy complex dynamical networks subject to average dwell time approach abstract the problem of finite time synchronization for takagi sugeno t s fuzzy complex dynamical networks with coupling delays via sampled data control is presented in this paper to change the sampled data control system into a continuous time delayed system an input delay approach is applied based on the lyapunov stability theory a suitable lyapunov krasovskii functional lkf is constructed with the kronecker products furthermore by applying the average dwell time approach a novel sufficient condition is established to ascertain the finite time stabilization of fuzzy complex dynamical networks cdns with switching signals the proposed method is less conservative than conventional approaches since the newly developed time dependent fuzzy lkf is used the proposed sufficient condition can be represented in the form of linear matrix inequalities lmis finally the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples

group valued equivariant localization we prove a localization formula for group valued equivariant de rham cohomology of a compact g manifold this formula is a non trivial generalization of the localization formula of berline vergne and atiyah bott for the usual equivariant de rham cohomology we derive from this result a duistermaat heckman formula for group valued moment maps as an application we prove part of witten s conjectures about intersection pairings on moduli spaces of flat connections on 2 manifolds

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

integrable structure of ginibre s ensemble of real random matrices and a pfaffian integration theorem in the recent publication e kanzieper and g akemann in phys rev lett 95 230201 2005 an exact solution was reported for the probability pn k to find exactly k real eigenvalues in the spectrum of an n n real asymmetric matrix drawn at random from ginibre s orthogonal ensemble ginoe in the present paper we offer a detailed derivation of the above result by concentrating on the proof of the pfaffian integration theorem the key ingredient of our analysis of the statistics of real eigenvalues in the ginoe we also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a ginoe matrix restricted to have exactly k real eigenvalues in the particular case of k 0 all correlation functions of complex eigenvalues are determined

on the construction of certain 6 dimensional symplectic manifolds with hamiltonian circle actions let m w be a connected compact 6 dimensional symplectic manifold equipped with a semi free hamiltonian s 1 action such that the fixed point set consists of isolated points or surfaces assume dim h 2 m 3 in an earlier paper we defined a certain invariant of such spaces which consists of fixed point data and twist type and we divided the possible values of these invariants into six types in this paper we construct such manifolds with these types as a consequence we have a precise list of the values of these invariants

when is a pure state of three qubits determined by its single particle reduced density matrices using techniques from symplectic geometry we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one particle reduced density matrices exactly when their ordered spectra belong to the boundary of the so called kirwan polytope otherwise the states with given reduced density matrices are parameterized up to local unitary equivalence by two real variables given inevitable experimental imprecision this means that already for three qubits a pure quantum state can never be reconstructed from single particle tomography we moreover show that the knowledge of the reduced density matrices is always sufficient if one is given the additional promise that the quantum state is not convertible to the greenberger horne zeilinger state by stochastic local operations and classical communication and discuss generalizations of our results to an arbitrary number of qubits

wigner dyson statistics from the replica method we compute the correlation functions of the eigenvalues in the gaussian unitary ensemble using the fermionic replica method we show that non trivial saddle points which break replica symmetry must be included in the calculation in order to correctly reproduce the exact asymptotic behaviour of the correlation functions at a large distance

dissipativity based sampled data fuzzy control design and its application to truck trailer system this paper is concerned with the problem of dissipative control for takagi sugeno fuzzy systems under time varying sampling with a known upper bound on the sampling intervals based on the time dependent lyapunov krasovskii functional approach which makes full use of the available information about the actual sampling pattern a sufficient condition is established to guarantee the sampled data systems to be exponentially stable and strictly mathcal q mathcal s mathcal r gamma dissipative based on the criterion a design algorithm for the desired sampled data controller is proposed the effectiveness and benefits of the results developed in this paper is demonstrated by a controller design for a truck trailer system

correlation functions of harish chandra integrals over the orthogonal and the symplectic groups the harish chandra correlation functions i e integrals over compact groups of invariant monomials prod operatorname tr x p 1 varomega y q 1 varomega dagger x p 2 cdots with the weight exp tr x y are computed for the orthogonal and symplectic groups we proceed in two steps first the integral over the compact group is recast into a gaussian integral over strictly upper triangular complex matrices with some additional symmetries supplemented by a summation over the weyl group this result follows from the study of loop equations in an associated two matrix integral and may be viewed as the adequate version of duistermaat heckman s theorem for our correlation function integrals secondly the gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions

localization formulas superconnections and the index theorem for families in this paper we give a new proof of the localization formulas of berline and vergne 9 and duistermaat and heckman 18 when interpreted in the framework of atiyah 2 the probabilistic heat equation proof of the index theorem given in our paper 12 appears as the rigorous infinite dimensional version of this new proof of the localization formulas in finite dimensions the results of quillen 25 on superconnections are briefly presented the heat equation proofs 15 of the index theorem for families are described it is shown that in this framework the superconnections formalism is the operator theoretic description of integration along the fiber in the loop space

bordism of semi free s1 actions we calculate geometric and homotopical bordism rings associated to semi free s1 actions on complex manifolds giving explicit generators for the geometric theory the classification of semi free actions with isolated fixed points up to cobordism complements similar results from symplectic geometry

multiplicities formula for geometric quantization part ii 1 introduction let p be a compact manifold let h be a compact lie group acting on the right on p we assume that the stabilizer of each element y e p is a finite subgroup of h the space m p h is an orbifold and every orbifold can be presented this way if h acts freely then m is a manifold if ae graded space of h invariant solutions of the h horizontal dirac operator on p twisted by the line bundle let m o 9 be the moment map for the g action assume 0 is a regular value of let mred be the reduced orbifold of m that is mred o g consider the reduced orbifold line bundle rd lu lto g on m oa in the ease where both g andh are torus we prove here the formula

ginzburg weinstein via gelfand zeitlin let u n be the unitary group and u n the dual of its lie al gebra equipped with the kirillov poisson structure in their 1983 paper guillemin sternberg introduced a densely defined hamil tonian action of a torus of dimension n 1 n 2 on u n with mo ment map given by the gelfand zeitlin coordinates a few years later flaschka ratiu described a similar multiplicative gelfand zeitlin system for the poisson lie group u n by the ginzburg weinstein theorem u n is isomorphic to u n as a poisson manifold flaschka ratiu conjectured that one can choose the ginzburg weinstein diffeomorphism in such a way that it intertwines the linear and nonlinear gelfand zeitlin systems our main result gives a proof of this conjecture and produces a canonical ginzburg weinstein diffeomorphism

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller