stochastic control for linear systems with additive cauchy noises an optimal predictive controller for linear vector state dynamic systems driven by cauchy measurement and process noises is developed for the vector state system only the characteristic function of the conditional probability density function pdf and not the pdf itself can be expressed analytically in a closed form consequently the conditional performance index formulated for the controller design can also be evaluated only in the spectral domain in particular by taking the conditional expectation of an objective function that is a product of functions resembling cauchy pdfs the conditional performance index is obtained in closed form by using parseval s identity and integrating over the spectral vector this forms a deterministic non convex function of the control signal and the measurement history that must be optimized numerically at each time step a two state example is used to expose the interesting robustness characteristics of the proposed controller

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

subalgebras with converging star products in deformation quantization an algebraic construction for cpn based on a closed formula for a star product of wick type on cpn which has been discovered in an earlier article of the authors we explicitly construct a subalgebra of the formal star algebra with coefficients contained in the uniformly dense subspace of representative functions with respect to the canonical action of the unitary group that consists of converging power series in the formal parameter thereby giving an elementary algebraic proof of a convergence result already obtained by cahen gutt and rawnsley in this subalgebra the formal parameter can be substituted by a real number the resulting associative algebras are infinite dimensional except for the case 1 k k a positive integer where they turn out to be isomorphic to the finite dimensional algebra of linear operators in the kth energy eigen space of an isotropic harmonic oscillator with n 1 degrees of freedom other examples like the 2n torus and the poincare disk are discussed

sdiff s2 and the orbit method the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics

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

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

an efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors based on the works of ruze and vu a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors in this model both nonuniform root mean square rms surface errors and nonuniform illumination functions are employed in addition the model incorporates the dependence on f d in the construction of the solution the mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna the geometrical rms surface value is known it is shown that closed form expressions can then be derived which result in a very efficient computational method for the average power pattern detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels the results clearly demonstrate that as sidelobe levels decrease their dependence on the surface rms lambda becomes much stronger and for a specified tolerance level a considerably smaller rms lambda is required to maintain the low sidelobes within the required bounds

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

local well posedness for membranes in the light cone gauge in this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge a hamiltonian reduction gives a system with one constraint the area preserving constraint the hamiltonian evolution equations corresponding to this system however fail to be hyperbolic making use of the area preserving constraint an equivalent system of evolution equations is found which is hyperbolic and has a well posed initial value problem we are thus able to solve the initial value problem for the hamiltonian evolution equations by means of this equivalent system we furthermore obtain a blowup criterion for the membrane evolution equations and show making use of the constraint that one may achieve improved regularity estimates

deformed noncommutative tori we recall a construction of non commutative algebras related to a one parameter family of deformed spheres and tori and show that in the case of tori the algebras can be completed into c algebras isomorphic to the standard non commutative torus as the former was constructed in the context of matrix or fuzzy geometries it provides an important link to the framework of non commutative geometry and opens up for a concrete way to study deformations of non commutative tori furthermore we show how the well known fuzzy sphere and fuzzy torus can be obtained as formal scaling limits of finite dimensional representations of the deformed algebras and their projective modules are described together with connections of constant curvature

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

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

area preserving diffeomorphisms and supermembrane lorentz invariance the lie algebra of area preserving diffeomorphisms on closed membranes of arbitrary topology is investigated on the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane lorentz generators we derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bysu n one of the additional tensors can then be identified with the invariant symmetric three index tensor ofsu n while the second has no obvious analog we prove that the lorentz generators are classically conserved in the light cone gauge for arbitrary membrane topology as a consequence of these tensor identities this formulation allows a systematic study of the violations of lorentz invariance in thesu n approximation

characters of the bms group in three dimensions using the frobenius formula we evaluate characters associated with certain induced representations of the centrally extended bms3 group this computation involves a functional integral over a coadjoint orbit of the virasoro group a delta function localizes the integral to a single point allowing us to obtain an exact result the latter is independent of the specific form of the functional measure and holds for all values of the bms3 central charges and all values of the chosen mass and spin it can also be recovered as a flat limit of virasoro characters

state estimation for linear scalar dynamic systems with additive cauchy noises characteristic function approach uncertainties in many practical systems such as radar glint and sonar noise have impulsive character and are better described by heavy tailed non gaussian densities for example the cauchy probability density function pdf the cauchy pdf does not have a well defined mean and its second moment is infinite nonetheless the conditional density of a cauchy random variable given a scalar linear measurement with an additive cauchy noise has a conditional mean and a finite conditional variance in particular for scalar discrete linear systems with additive process and measurement noises described by cauchy pdfs the unnormalized characteristic function of the conditional pdf is considered it is expressed as a growing sum of terms that at each measurement update increases by one term constructed from four new measurement dependant parameters the dynamics of these parameters is linear these parameters are shown to decay allowing an approximate finite dimensional recursion from the first two differen

gl and geometric quantization an axiomatic approach to the approximation of infinite dimensional algebras is presented examples illustrating the need for a rigorous treatment of this subject geometric quantization is employed to construct systematicallysu n approximations of diffeomorphism algebras which first appeared in the theory of relativistic membranes

noncommutative riemann surfaces by embeddings in mathbb r 3 we introduce c algebras of compact riemann surfaces sigma as non commutative analogues of the poisson algebra of smooth functions on sigma representations of these algebras give rise to sequences of matrix algebras for which matrix commutators converge to poisson brackets as n for a particular class of surfaces interpolating between spheres and tori we completely characterize even for the intermediate singular surface all finite dimensional representations of the corresponding c algebras

a pattern approximation method for distorted reflector antennas using piecewise linear fitting of the exponential error term integrated structural electromagnetic em optimization design is of great importance in the area of antenna design the quick and exact calculation of patterns for distorted reflectors is an important research topic in this communication based on the previous works a novel pattern approximation method using piecewise linear fitting is presented the exponential error term in the physical optics po formulation is first approximated by a series of straight lines through the piecewise linear fitting by least square algorithm then the radiation integral on each structural element is expressed as the summation of the ideal term and perturbation term which are both weighted by the combinations of coefficients of the corresponding straight lines finally the far field is derived as a simple linear function of structural nodal displacements in a matrix form by assembling the radiation integrals on all the structural elements simulation results show that the proposed method pm could save the storage space because there is no second order term of the nodal displacements facilitate rapid calculation by recalling the prestored data and has high calculation accuracy even for large size of surface error profiles

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

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

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

generalized bergman kernels and geometric quantization in geometric quantization it is well known that if f is an observable and f a polarization on a symplectic manifold m then the condition xf leaves f invariant where xf denotes the hamiltonian vector field associated to f is sufficient to guarantee that one does not have to compute the bks kernel explicitly in order to know the corresponding quantum operator it is shown in this paper that this condition on f can be weakened to xf leaves f f invariant and the corresponding quantum operator is then given implicitly by formula 4 8 in particular when f is a positive kahler polarization all observables can be quantized directly and moreover an explicit formula for the corresponding quantum operator is derived theorem 5 8 applying this to the phase space r2n one obtains a quantization prescription which ressembles the normal ordering of operators in quantum field theory when we translate this prescription to the usual position representation of quantum mechanics the result i

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

multivariate cauchy estimator with scalar measurement and process noises the conditional mean estimator for a n state linear system with additive cauchy measurement and process noises is developed it is shown that although the cauchy densities which model the initial state the process noise and the measurement noise have undefined first moments and an infinite second moment the probability density function conditioned on the measurement history does have a finite conditional mean and conditional variance for the multivariable system state the characteristic function of the unnormalized conditional probability density function is sequentially propagated through measurement updates and dynamic state propagation while expressing the resulting characteristic function in a closed analytical form once the characteristic function of the unnormalized conditional probability density function is obtained the probability density function of the measurement history the conditional mean and conditional variance are easily computed from the characteristic function and its conti

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

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

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

toeplitz quantization of kahler manifolds ang gl n n limits for general compact kahler manifolds it is shown that both toeplitz quantization and geometric quantization lead to a well defined by operator norm estimates classical limit this generalizes earlier results of teh authors and klimek and lesniewski obtained for the tours and higher genus riemann surfaces respectively we thereby arrive at an approximation of the poisson algebra by a sequence of finitedimensional matrix algebrasgl n n

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

categorical perspective on quantization of poisson algebra we propose a generalization of quantization using a categorical approach for a fixed poisson algebra quantization categories are defined as subcategories of the r module category equipped with the structure of classical limits we then construct the generalized quantization categories including matrix regularization strict deformation quantization prequantization and poisson enveloping algebra it is shown that the categories of strict deformation quantization prequantization and matrix regularization with certain conditions are equivalent categories on the other hand the categories of poisson enveloping algebra are not equivalent to the other categories

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

an approximation of the radiation integral for distorted reflector antennas using surface error decomposition the physical optics aperture integration po ai formulation is often used to analyze the radiation patterns of reflector antennas in this study the po ai radiation integrals for distorted reflector antennas are addressed the surface error of the antennas is approximated by a series of surface expansion functions the radiation integral is decomposed into a series of radiation type integrals each of which corresponds to one of the surface expansion functions each of these radiation type integrals is then weighted by amplitude coefficients the advantage of performing the decomposition is that each of the radiation type integrals can be computed and the pattern data stored the computation of the pattern for a distorted reflector antenna with a changing error profile is performed by recalling the pattern data for each perturbation term and weighting it with the amplitude coefficient this facilitates rapid evaluation of the radiation integral in cases where the error profile is changing for example time varying errors the superposition of integrals presented in this paper was shown to be valid for surface error profiles up to 0 1 spl lambda rms amplitude

quantization towards a comparison between methods in this paper it is shown that the procedure of geometric quantiztion applied to kahler manifolds gives the following result the hilbert space h consists roughly speaking of holomorphic functions on the phase space m and to each classical observable f i e a real function on m is associated an operator f on h as follows first multiply by f 1 4 drf dr being the laplace de rham operator on the kahler manifold m and then take the holomorphic part see g m tuynman j math phys 27 573 1987 this result is correct on compact kahler manifolds and correct modulo a boundary term md on noncompact kahler manifolds in this way these results can be compared with the quantization procedure of berezin math ussr izv 8 1109 1974 9 341 1975 commun math phys 40 153 1975 which is strongly related to quantization by products e g see c moreno and p ortega navarro amn inst h poincare sec a 38 215 1983 lett math phys 7 181 1983 c moreno lett math phys 11 3

stochastic estimation for two state linear dynamic systems with additive cauchy noises an efficient recursive state estimator is developed for two state linear systems driven by cauchy distributed process and measurement noises for a general vector state system the estimator is based on recursively propagating the characteristic function of the conditional probability density function cpdf where the number of terms in the sum that expresses this characteristic function grows with each measurement update both the conditional mean and the conditional error variance are functions of the measurement history for systems with two states the proposed estimator reduces substantially the number of terms needed to express the characteristic function of the cpdf by taking advantage of relationships not yet developed in the general vector state case further by using a fixed sliding window of the most recent measurements the improved efficiency of the proposed two state estimator allows an accurate approximation for real time computation in this way the computational complexity of each measurement update eventually becomes constant and an arbitrary number of measurements can be processed the numerical performance of the cauchy estimator in both cauchy and gaussian simulations was demonstrated and compared to the kalman filter

an estimation approach for linear stochastic systems based on characteristic functions abstract this paper presents an alternative characteristic function based approach for the bayesian design of estimators for dynamic linear systems and linear detection problems for a measurement update the a posteriori characteristic function of the unnormalized conditional probability density function ucpdf of the state given the measurement history is obtained as a convolution of the a priori characteristic function of the ucpdf with the characteristic function of the measurement noise it is shown that this convolution holds for a general measurement structure time propagation involves the product of the updated characteristic function of the ucpdf and the characteristic function of the process noise some estimation problems are found to be naturally tractable using only characteristic functions such as the multivariable linear system with additive cauchy measurement and process noise it is shown that even the derivation of the kalman filter algorithm has advantages when formulated using the characteristic function approach finally in some instances the estimation problem can only be formulated in terms of characteristic functions this is illustrated by a one update scalar example for symmetric stable distributions

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

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

chirality and dirac operator on noncommutative sphere we give a derivation of the dirac operator on the noncommutative 2 sphere within the framework of the bosonic fuzzy sphere and define connes triple it turns out that there are two different types of spectra of the dirac operator and correspondingly there are two classes of quantized algebras as a result we obtain a new restriction on the planck constant in berezin s quantization the map to the local frame in noncommutative geometry is also discussed

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

effects of nonuniform surface errors along the radius on reflector s radiation characteristic and its quality evaluation based on the works of yahya rahmat samii a multiobjective optimization model is developed to analyze the effects of surface errors nonuniformity along the radius on the reflector s radiation characteristic through the optimization model pareto front for trading off the peak gain loss pgl and the first sidelobe level increase slli is obtained simulations clearly show that for the same root mean square rms error for the whole reflector different distributions along the radius result in different pgls and first sllis then the weighting function of the rms errors is considered and the evaluation formula of pgl is successfully applied to nonuniform errors it is concluded that besides the radius the amplitude aperture distribution and the ratio of focal length to diameter f d errors nonuniformity is also an important factor that should be considered in the procedure of the quality evaluation of the reflector surface

an approximation of pattern analysis for distorted reflector antennas using structural electromagnetic coupling model based on the concept of structural electromagnetic field coupling an approximation method is developed to analyze the radiation pattern for distorted reflectors in this method the integration point deformation is obtained by a local interpolation scheme which utilizes the same shape functions as that in the structural analysis for the radiation calculation the phase error caused by the distortion is added to the far field integral which is computed on the structural element similar to the assembly of element stiffness matrices in finite element method fem the far field electrical vector is derived as a function of structural nodal displacements in a matrix form by collecting the integrals on structural elements simulation is performed with good results the method can benefit the computation for a given reflector in the integrated structural electromagnetic optimization design procedure

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

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

central charges in the canonical realization of asymptotic symmetries an example from three dimensional gravity it is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level this is done by studying three dimensional gravity with a negative cosmological constant the asymptotic symmetry group in that case is eitherr so 2 or the pseudo conformal group in two dimensions depending on the boundary conditions adopted at spatial infinity in the latter situation a nontrivial central charge appears in the algebra of the canonical generators which turns out to be just the virasoro central charge

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

sensitivity analysis of reflector antennas and its application on shaped geo truss unfurlable antennas this paper presents the sensitivity of far field radiation performance with respect to reflector surface nodal displacements the reflector surface is divided into a series of triangular elements and in any deformation state the surface can be determined by the element nodal displacements the radiation integrals over each small element are summed to obtain the whole electromagnetic performance with the aid of shape functions in triangular elements the integration points inside each element are expressed as functions of element nodal displacements then the partial derivatives of electric far field and directivity with respect to each nodal displacement are derived the sensitivity contour plots of maximum directivity with respect to surface nodal displacements for axis symmetrical and offset parabolic reflectors are numerical simulated the sensitivity is applied to a shaped geo truss unfurlable antenna with accepted results