geometric quantisation of the mic kepler problem the geometric quantisation scheme is applied to the compact kaehler orbit manifolds of the modified kepler problem thus the authors obtain the quantisation of the magnetic charge and energy spectrum of the corresponding quantum problem a new regularisation of the standard kepler problem is presented

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

an algorithm using the finite volume element method and its splitting extrapolation this paper is to present a new efficient algorithm by using the finite volume element method and its splitting extrapolation this method combines the local conservation property of the finite volume element method and the advantages of splitting extrapolation such as a high order of accuracy a high degree of parallelism less computational complexity and more flexibility than a richardson extrapolation because the splitting extrapolation formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid a large scale multidimensional problem is turned into a set of smaller discrete subproblems additionally this method is efficient for solving interface problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition

extrapolation for finite volume approximations in this paper the extrapolation technique is applied to a finite volume method based on some asymptotic error expansions of finite volume solutions established in this paper several extrapolation schemes are proposed for finite volume approximations to elliptic problems

coherent states on horospheric three dimensional lobachevsky space in the paper it is shown that due to separation of variables in the laplace beltrami operator hamiltonian of a free quantum particle in horospheric and quasi cartesian coordinates of three dimensional lobachevsky space it is possible to introduce standard conventional according to perelomov generalized coherent states and their applications springer verlag 1986 p 320 coherent states some problems oscillator on horosphere charged particle in analogy of constant uniform magnetic field where coherent states are suitable for treating were considered

indecomposable representations of the nonlinear lie algebras on the two state heisenberg weyl basis the indecomposable representations of the nonlinear lie algebras of vector type r 0 1 one of which is generated by two angular momentum operators j0 j2 and any component of an irreducible tensor operator of rank 1 t 1 0 1 of an so 3 group are studied in detail we give the explicit expressions for the infinite dimensional indecomposable representations of r which further subduce the infinite dimensional indecomposable representations on the invariant subspaces and induce the finite dimensional or infinite dimensional indecomposable irreducible representations on the quotient spaces as special cases the standard angular momentum representations of r are given also

an hybrid finite volume finite element method for variable density incompressible flows this paper is devoted to the numerical simulation of variable density incompressible flows modeled by the navier stokes system we introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint the breakthrough relies on the definition of a suitable footbridge between the two methods through the design of compatibility condition in turn the method is very flexible and allows to deal with unstructured meshes several numerical tests are performed to show the scheme capabilities in particular the viscous rayleigh taylor instability evolution is carefully investigated

path integral treatment of the hydrogen atom in a curved space of constant curvature ii hyperbolic space for pt i see ibid vol 20 p 6271 the path integral treatment of the hydrogen atom in a hyperbolic space is discussed the authors show by mapping the radial path integral into the su 1 1 group manifold that the system has a dynamical su 1 1 symmetry the energy spectrum and normalised energy eigenfunctions are calculated in the flat space limit the standard hydrogen spectrum and corresponding normalised wavefunctions are regained

exact and quasiexact solvability of second order superintegrable quantum systems i euclidean space preliminaries we show that second order superintegrable systems in two dimensional and three dimensional euclidean space generate both exactly solvable es and quasiexactly solvable qes problems in quantum mechanics via separation of variables and demonstrate the increased insight into the structure of such problems provided by superintegrability a principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable most past separation of variables treatments of qes problems via partial differential equations have only incorporated separability not multiseparability also we propose another definition of es and qes the quantum mechanical problem is called es if the solution of schrodinger equation can be expressed in terms of hypergeometric functions fnm and is qes if the schrodinger equation admits polynomial solutions with coefficients necessarily satisfying a three term or higher order of recurrence relations in three dimensions we give an example of a system tha

reduction of the two body problem with central interaction on simply connected spaces of constant sectional curvature the problem of two particles with central interaction on simply connected spaces of a constant curvature was considered due to the absence of the galilei transformation in this case the reduction to the dynamic problem in four dimensional phase space was carried out using the marsden weinstein method canonically conjugate coordinates were found the classification of reduced dynamic systems was given for some of them conditions of the existence global solutions for dynamic equations with attractive potentials were found the comparison of the structure of obtained hamiltonians with integrals of the one particle problem with bertrand s potentials was carried out

exact evolution equations for su 2 quasidistribution functions we derive an exact differential evolution equation for a class of su 2 quasiprobability distribution functions linear and quadratic cases are considered as well as the quasiclassical limit of the large dimension of representation s 1

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

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

bounded error parameter estimation a sequential analytic center approach a sequential analytic center approach for bounded error parameter estimation is proposed the authors show that the analytic center minimizes the logarithmic average output error among all the estimates within the membership set and is a maximum likelihood estimator for a class of noise density functions which include parabolic densities and approximations of truncated gaussian they also show that the analytic center is easily computable for both offline and online problems with a sequential algorithm the convergence proof of this sequential algorithm is obtained and moreover it is shown that the complexity in terms of the maximum number of newton iterations is linear in the number of observed data points

robust target localization in the absence of signal propagation models this paper considers a problem of target or source localization based on the measurements from a mobile sensor or a network of sensors the assumption is that the received signal strength is strictly monotonic with the distance between the target and the sensor no explicit signal propagation model neither the structure nor the mathematical description is assumed or used in localization the contribution of the paper is to show that this mere knowledge of monotonicity suffices in locating the unknown target in the absence of noise further in the presence of noise robust localization algorithms are developed and analyzed by exploiting various forms of angular temporal and spatial averages the asymptotic convergence results have been established in the presence of noise and further the finite step performance results are developed

a non iterative algorithm based on richardson s extrapolation application to groundwater flow modelling in this report a promising third order algorithm based on richardson s extrapolation and crank nicholson s method is studied the algorithm having a wide scope for applications was initially intended to be used for time integration on non linear advection diffusion problems then stability low oscillations and low additional diffusion become important numerical properties it is shown that this method using three single steps for extrapolation is very close to be unconditionally stable under the previous requirements it behaves essentially as well as crank nicholson s scheme but with a better performance at least in relation to spurious oscillations and perhaps not so good for dispersion properties in addition the method is third order accurate and provides useful information related to time integration error to be used for time step control these features indicate that the algorithm is a good candidate to efficiently solve problems with significant variations in time additionally its non iterative version saves important amounts of cpu time specially for applied 3d modelling to illustrate the good performance of the algorithm we include several tests comparing it with crank nicholson s scheme and a 2d application to variably saturated groundwater flow modelling

canonical structure in so 4 q and relations to e 3 q and so 3 1 q starting with the su 2 q su 2 q basis and using q cg coefficients the closest possible q deformation of the classical canonical gelfand zetlin formalism is constructed explicitly for so 4 q simple introduction of q brackets for each factor of the classical matrix elements valid for su n q is shown to need significant and unexpected modifications for so n q even when n 4 contraction to e 3 q and continuation to so 3 1 q are studied making explicit the possibilities and the problems that arise periodic representations for q a root of unity are commented upon briefly

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

conformal regularization of the kepler problem the manifoldm of null rays through the origin of 2 n 1 is diffeomorphic tos1 s n and it is a homogeneous space of so 2 n 1 this group therefore acts ont m which we show to be the generating manifold of the extended phase space of the regularized kepler problem a local canonical chart int m is found such that the restriction to the subbundle of the null nonvanishing covectors is given byp0 h q p 0 whereh q p is the hamiltonian of the kepler problem by means of this construction we get some results that clarify and complete the previous approaches to the problem

stabilized finite element method based on the crank nicolson extrapolation scheme for the time dependent navier stokes equations this paper provides an error analysis for the crank nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two dimensional time dependent navier stokes problem where the finite element space pair x h m h for the approximation u n h p n h of the velocity u and the pressure p is constructed by the low order finite element the q 1 p 0 quadrilateral element or the p 1 p 0 triangle element with mesh size h error estimates of the numerical solution u n h p n h to the exact solution u t n p t n with t n 0 t are derived

the three dimensional euclidean quantum group e 3 q and its r matrix a contraction procedure starting from so 4 q is used to determine the quantum analog e 3 q of the three dimensional euclidean group and the structure of its representations a detailed analysis of the contraction of the r matrix is then performed and its explicit expression has been found the classical limit of r is shown to produce an integrable dynamical system by means of the r matrix the pseudogroup of the noncommutative representative functions is considered it will finally be shown that a further contraction made on e 3 q produces the two dimensional galilei quantum group and this in turn can be used to give a new realization of e 3 q and e 2 1 q

nonlinear lie algebra and ladder operators for orbital angular momentum based on the nonlinear lie algebra a new framework is put forward to treat the problem of angular momentum from this framework the ladder operators for the orbital angular momentum can be solved as simultaneous eigenvectors of the lie derivations ad l2 and ad l2 in an operator space the ladder operators for solvable central potentials can also be found in a united way

optimization with few violated constraints for linear bounded error parameter estimation in the context of linear constrained optimization we study the problem of finding an optimal solution satisfying all but k of the given n constraints a solution is obtained by means of an algorithm of the complexity min o n spl middot k sup d o n spl middot d sup k 1 where d is the dimension of the problem we then use these results to solve the problem of robust identification in the presence of outliers in the setting of bounded error parameter identification finally we show that the estimate obtained converges to the true but unknown parameter in the presence of outliers

separation of variables in path integrals and path integral solution of two potentials on the poincare upper half plane the author discusses how to separate variables in path integrals it is assumed that a one dimensional problem with potential v x has an exact solution with energy levels elambda and wavefunctions psi lambda in order to perform the separation of variables a time transformation is performed back and forth in the path integral which allows one to insert the path integral solution corresponding to the potential v x the author illustrates the method by discussing some specific potential problems on the poincare upper half plane

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

variables separation and superintegrability of the nine dimensional micz kepler problem the nine dimensional micz kepler problem is of recent interest this is a system describing a charged particle moving in the coulomb field plus the field of a so 8 monopole in a nine dimensional space interestingly this problem is equivalent to a 16 dimensional harmonic oscillator via the hurwitz transformation in the present paper we report on the multiseparability a common property of superintegrable systems and the superintegrability of the problem first we show the solvability of the schrodinger equation of the problem by the variables separation method in different coordinates second based on the so 10 symmetry algebra of the system we construct explicitly a set of seventeen invariant operators which are all in the second order of the momentum components satisfying the condition of superintegrability the found number 17 coincides with the prediction of 2n 1 law of maximal superintegrability order in the case n 9 until now this law is accepted to apply only to scalar hamiltonian eigenvalue equations in n dimensional space therefore our results can be treated as evidence that this definition of superintegrability may also apply to some vector equations such as the schrodinger equation for the nine dimensional micz kepler problem the nine dimensional micz kepler problem is of recent interest this is a system describing a charged particle moving in the coulomb field plus the field of a so 8 monopole in a nine dimensional space interestingly this problem is equivalent to a 16 dimensional harmonic oscillator via the hurwitz transformation in the present paper we report on the multiseparability a common property of superintegrable systems and the superintegrability of the problem first we show the solvability of the schrodinger equation of the problem by the variables separation method in different coordinates second based on the so 10 symmetry algebra of the system we construct explicitly a set of seventeen invariant operators which are all in the second order of the momentum components satisfying the condition of superintegrability the found number 17 coincides with the prediction of 2n 1 law of maximal superintegrability order in the case n 9 until now this law is accepted to apply only to scalar hamiltonia

on the regularization of the kepler problem an intimate relationship between moser s regularization 1 and the ks regularization 3 of the 3 dimensional kepler problem is established explicit formulae linking moser s and the ks transformation are obtained in the case of negative as well as in the case of positive energies as a side result it is shown that the ks transformation owes its existence to the local isomorphism of so 2 4 and su 2 2

nonlinear symmetry algebra of the mic kepler problem on the sphere s3 the quantum mechanical problem of motion in the dual charged coulomb field modified by a centrifugal term mic kepler problem is considered in the three dimensional space of constant positive curvature s3 conserved operators in this problem form a cubic algebra similar to that of the kepler problem on s3 the explicit form of invariants of this algebra shows that its representation associated with the mic kepler problem on s3 is a nondegenerate one the cubic symmetry algebra is used to obtain the energy spectrum of the problem

mechanical quadrature methods and their extrapolation for solving first kind abel integral equations this paper presents high accuracy mechanical quadrature methods for solving first kind abel integral equations to avoid the ill posedness of problem the first kind abel integral equation is transformed to the second kind volterra integral equation with a continuous kernel and a smooth right hand side term expressed by weakly singular integrals by using periodization method and modified trapezoidal integration rule not only high accuracy approximation of the kernel and the right hand side term can be easily computed but also two quadrature algorithms for solving first kind abel integral equations are proposed which have the high accuracy o h 2 and asymptotic expansion of the errors then by means of richardson extrapolation an approximation with higher accuracy order o h 3 is obtained moreover an a posteriori error estimate for the algorithms is derived some numerical results show the efficiency of our methods

implicit extrapolation methods for variable coefficient problems implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly multigrid tau extrapolation is a special case of this idea in the context of multilevel finite element methods an algorithm of this type can be used to raise the approximation order even when the meshes are nonuniform or locally refined the implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system this is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm the algorithm requires only a small change of a basic low order multigrid method

probabilistic optimal estimation with uniformly distributed noise the classical approach to system identification is based on stochastic assumptions about the measurement error and provides estimates that have random nature worst case identification on the other hand only assumes the knowledge of deterministic error bounds and establishes guaranteed estimates thus being in principle better suited for the use in control design however a main limitation of such deterministic bounds lies in their potential conservatism thus leading to estimates of restricted use in this paper we propose a rapprochement between the stochastic and worst case system identification viewpoints which is based on the probabilistic setting of information based complexity the main idea in this line of research is to discard sets of measure at most where is a probabilistic accuracy from the set of deterministic estimates therefore we are decreasing the so called worst case radius of information at the expense of a given probabilistic risk in the case of uniformly distributed noise we derive new computational results and in particular we compute a trade off curve called violation function which shows how the radius of information decreases as a function of the accuracy to this end we construct randomized and deterministic algorithms which provide approximations of this function we report extensive simulations showing numerical comparisons between the stochastic worst case and probabilistic approaches thus demonstrating the efficacy of the methods proposed in this paper

on the path integral in imaginary lobachevsky space the path integral on the single sheeted hyperboloid i e in d dimensional imaginary lobachevsky space is evaluated a potential problem which we call the kepler problem and the case of a constant magnetic field are also discussed

algebraic treatment of second poschl teller morse rosen and eckart equations the method of an earlier paper see ibid vol 20 p 4075 1987 is applied to the non compact case to solve a family of second poschl teller morse rosen and eckart equations with quantised coupling constants both discrete and continuous spectra bound state and scattering wavefunctions transmission coefficients are found from the matrix elements of group representations

the generalized mic kepler system this paper deals with the dynamical system that generalizes the mic kepler system it is shown that the schrodinger equation for this generalized mic kepler system can be separated in spherical and parabolic coordinates the spectral problem in spherical and parabolic coordinates is solved

generalized kaluza klein monopole quadratic algebras and ladder operators we present a generalized kaluza klein monopole system we solve this quantum superintegrable system on a euclidean taub nut manifold using the separation of variables of the corresponding schr odinger equation in spherical and parabolic coordinates we present the integrals of motion of this system the quadratic algebra generated by these integrals the realization in terms of a deformed oscillator algebra using the daskaloyannis construction and the energy spectrum the structure constants and thecasimir operator are functions not only of the hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an abelian subalgebra we present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators

on some nonlinear extensions of the angular momentum algebra deformations of the lie algebras so 4 so 3 1 and e 3 that leave their so 3 subalgebra undeformed and preserve their coset structure are considered it is shown that such deformed algebras are associative for any choice of the deformation parameters their casimir operators are obtained and some of their unitary irreducible representations are constructed for vanishing deformation the unitary irreducible representations of the deformed algebras transform into those of the corresponding lie algebras that contain each of the so 3 unitary irreducible representations at most once it is also proved that similar deformations of the lie algebras su 3 sl 3 r and of the semidirect sum of an abelian algebra t 5 and so 3 do not lead to associative algebras

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

reduction in stages and complete quantization of the mic kepler problem the one parameter deformation family of the standard kepler problem known as the mic kepler problem is completely quantized using the explicit momentum mapping of the torus actions on some toric manifolds and some equivariant cohomology theory these manifolds appear as symplectic faces of the system during reduction process

convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing in this article we design the semiimplicit finite volume scheme for coherence enhancing diffusion in image processing and prove its convergence to the weak solution of the problem the finite volume methods are natural tools for image processing applications since they use piecewise constant representation of approximate solutions similarly to the structure of digital images they have been successfully applied in image processing e g for solving the perona malik equation or curvature driven level set equations where the nonlinearities are represented by a scalar function dependent on a solution gradient design of suitable finite volume schemes for tensor diffusion is a nontrivial task here we present the first such scheme with a convergence proof for the practical nonlinear model used in coherence enhancing image smoothing we provide basic information about this type of nonlinear diffusion including a construction of its diffusion tensor and we derive a semiimplicit finite volume scheme for this nonlinear model with the help of covolume mesh this method is well known as the diamond cell method owing to the choice of covolume as a diamond shaped polygon further we prove a convergence of a discrete solution given by our scheme to the weak solution of the problem the proof is based on kolmogorov s compactness theorem and a bounding of a gradient in the tangential direction by using a gradient in the normal direction finally computational results illustrated in figures are discussed

boson and differential realizations of polynomial angular momentum algebra the inhomogeneous multiboson and multivariable differential realizations of the polynomial angular momentum algebra of quadratic type l2 which may be seen as the nonlinear extension of an ordinary angular momentum algebra su 2 or its noncompact form su 1 1 are obtained from fock representations of l2 which are related to master representation of l2 on the space of its universal enveloping algebra u l2 or to induced representations on their respective quotient spaces u l2 ii with different left ideals ii

the quantised mic kepler problem and its symmetry group for negative energies the author discusses the quantised mic kepler problem and it s symmetry group for negative energies at the lie algebraic level on the basis of complex line bundles

system identification in the presence of outliers and random noises in this paper we consider robust system identification of fir systems when both sparse outliers and random noises are present we reduce this problem of system identification to a sparse error correcting problem using a toeplitz structured real numbered coding matrix and prove the performance guarantee thresholds on the percentage of correctable errors for toeplitz structured matrices are established when both outliers and observation noise are present we have shown that the estimation error goes to 0 asymptotically as long as the probability density function for observation noise is not vanishing around origin no probabilistic assumptions are imposed on the outliers

path integration over compact and noncompact rotation groups applications of group theoretical methods in the path integral formalism of nonrelativistic quantum theory are considered analysis of the symmetry of the lagrangian leads to the expansion of the short time propagator in matrix elements of unitary irreducible representations of the symmetry group identification of the coordinates with the group parameters transforms the path integral to integrals over the group manifold the integration is performed using the orthogonality of the representations compact and noncompact rotation groups are considered where the corresponding path integral is embedded in euclidean and pseudo euclidean spaces respectively the unit sphere and unit hyperboloid may either be viewed as the group manifold itself or at least as a group quotient in the first case fourier analysis leads to an expansion in group characters in the second case an expansion in zonal spherical functions is obtained as examples the groups so n su 2 so n 1 1 and su 1 1 are explicitly discussed the path integral on so n m and so n m in bispherical coordinates is also treated

superconvergence of finite volume methods for the second order elliptic problem abstract this paper derives a superconvergence result for finite volume approximations of the second order elliptic problem by using a l2 projection post processing technique the superconvergence result is applicable to different kind of finite volume methods and to general quasi uniform meshes

error estimates for a finite volume element method for elliptic pdes in nonconvex polygonal domains we consider standard finite volume piecewise linear approximations for second order elliptic boundary value problems on a nonconvex polygonal domain based on sharp shift estimates we derive error estimations in h1 l2 and l infty norms taking into consideration the regularity of the data numerical experiments and counterexamples illustrate the theoretical results

interval predictor models identification and reliability this paper addresses the problem of constructing reliable interval predictors directly from observed data differently from standard predictor models interval predictors return a prediction interval as opposed to a single prediction value we show that in a stationary and independent observations framework the reliability of the model that is the probability that the future system output falls in the predicted interval is guaranteed a priori by an explicit and non asymptotic formula with no further assumptions on the structure of the unknown mechanism that generates the data this fact stems from a key result derived in this paper which relates at a fundamental level the reliability of the model to its complexity and to the amount of available information number of observed data

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

klauder s coherent states for the radial coulomb problem in a uniformly curved space and their flat space limits first a set of coherent states a la klauder is formally constructed for the coulomb problem in a curved space of constant positive curvature then the flat space limit is taken to reduce the set for the radial coulomb problem to a set of hydrogen atom coherent states corresponding to both the discrete and the continuous portions of the spectrum for a fixed l sector

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

path integral on s2 the rosen morse oscillator guided by the group chain so 3 contains implies o 2 the authors construct an angular path integral for the symmetric rosen morse oscillator on s2 by explicit path integration they obtain the normalised energy eigenfunction as well as the exact energy spectrum

brief paper convergence properties of the membership set in this paper we study the convergence properties of the membership set for system identification in the presence of unknown but bounded noise besides the classical pointwise noise model we also analyze the so called window and average models two different scenarios are considered 1 the bound tight or overestimated is known 2 the bound is unknown and has to be estimated from measurement data under some probabilistic assumptions on the noise sequence and with the persistent excitation regressor in the first case we prove that the diameter of the associated membership sets converges to zero with probability one if the noise bound is tight if the bound is overestimated we compute upper bounds for the diameter which are stated in terms of the difference between the true and the over estimated bound in the second case we show that the estimates of the bound converge to the true but unknown noise bound

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

on certain quantum deformations of gl n r in this article all deformations of the general linear group subject to certain restrictions which in particular ensure a smooth passage to the lie group limit are obtained representations are given in terms of certains sets of creation and annihilation operators these creation and annihilation operators may belong to a generalization of the q quark type or q hadronic type with q boson or q fermion behavior this leads to a natural definition of q direct sums of q algebras

quantum brst charge for quadratically nonlinear lie algebras we consider the construction of a nilpotent brst charge for extensions of the virasoro algebra of the form ta tb fabctc vabcdtctd classical algebras in terms of poisson brackets and ta tb habi fabctc vabcd tctd quantum algebras in terms of commutator brackets normal ordering of the product tctd is understood in both cases we assume that the set of generators ta splits into a set hi generating an ordinary lie algebra and remaining generators s such that only thevij are nonvanishing in the classical case a nilpotent brst charge can always be constructed for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent brst charge non trivial examples are the spin 3 algebra with central chargec 100 and theso n extended superconformal algebras with levels 2 n 3

a new realisation of dynamical groups and factorisation method a new method of algebraisation of quantum mechanical eigenvalue equations is presented in this method the dynamical algebra is represented on the space of group matrix elements the ladder operators of the dynamical algebra are obtained from infeld hull miller factorisations the method is used to study the first poschl teller equation even in the non symmetric case the energy spectrum and the exact normalised solutions are obtained in agreement with the results of non algebraic methods

randomized methods for design of uncertain systems in this paper we study randomized methods for feedback design of uncertain systems the first contribution is to derive the sample complexity of various constrained control problems in particular we show the key role played by the binomial distribution and related tail inequalities and compute the sample complexity this contribution significantly improves the existing results by reducing the number of required samples in the randomized algorithm these results are then applied to the analysis of worst case performance and design with robust optimization the second contribution of the paper is to introduce a general class of sequential algorithms denoted as sequential probabilistic validation spv in these sequential algorithms at each iteration a candidate solution is probabilistically validated and corrected if necessary to meet the required specifications the results we derive provide the sample complexity which guarantees that the solutions obtained with spv algorithms meet some pre specified probabilistic accuracy and confidence the performance of these algorithms is illustrated and compared with other existing methods using a numerical example dealing with robust system identification

path integral treatment of the hydrogen atom in a curved space of constant curvature the path integral treatment of the hydrogen atom in a spherical space is discussed the dynamical group su 1 1 of the system is used for path integration by mapping the radial path integral onto the su 1 1 manifold the energy spectrum and the normalised wavefunctions are obtained in the flat space limit the standard hydrogen spectrum and the corresponding normalised energy eigenfunctions are recovered the scattering states are also found in the limit

random convex programs random convex programs rcps are convex optimization problems subject to a finite number n of random constraints the optimal objective value j of an rcp is thus a random variable we study the probability with which j is no longer optimal if a further random constraint is added to the problem violation probability v it turns out that this probability rapidly concentrates near zero as n increases we first develop a theory for rcps leading to explicit bounds on the upper tail probability of v then we extend the setup to the case of rcps with r a posteriori violated constraints rcpvs a paradigm that permits us to improve the optimal objective value while maintaining the violation probability under control explicit and nonasymptotic bounds are derived also in this case the upper tail probability of v is upper bounded by a multiple of a beta distribution irrespective of the distribution on the random constraints all results are derived under no feasibility assumptions on the problem further the relation between rcpvs and chance constrained problems ccp is explored showing that the optimal objective j of an rcpv with the generic constraint removal rule provides with arbitrarily high probability an upper bound on the optimal objective of a corresponding ccp moreover whenever an optimal constraint removal rule is used in the rcpvs then appropriate choices of n and r exist such that j approximates arbitrarily well the objective of the ccp

asymptotic expansions and richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods in this paper asymptotic error expansions for mixed finite element approximations of general second order elliptic problems are derived under rectangular meshes and the richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation postprocessing technique the results of this paper provide new asymptotic expansions and new approximate solutions which are one order and a half order higher in accuracy than those obtained in j wang math comp 56 1991 pp 477 503 and h chen r e ewing and r lazarov asymptotic error expansion for the lowest order raviart thomas rectangular mixed finite elements technical report isc 97 01 1997 respectively as a by product we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators for the mixed finite element method

constraints reduction and quantization theorems are proved that establish the unitary equivalence of the extended and reduced phase space quantizations of a constrained classical system with symmetry several examples are presented

quantization and representation theory of finite w algebras in this paper we study the finitely generated algebras underlyingw algebras these so called finitew algebras are constructed as poisson reductions of kirillov poisson structures on simple lie algebras the inequivalent reductions are labeled by the inequivalent embeddings ofsl 2 into the simple lie algebra in question for arbitrary embeddings a coordinate free formula for the reduced poisson structure is derived we also prove that any finitew algebra can be embedded into the kirillov poisson algebra of a semi simple lie algebra generalized miura map furthermore it is shown that generalized finite toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finitew symmetry in the second part we brst quantize the finitew algebras the brst cohomology is calculated using a spectral sequence which is different from the one used by feigin and frenkel this allows us to quantize all finitew algebras in one stroke examples are given in the last part of the paper we study the representation theory of finitew algebras it is shown using a quantum version of the generalized miura transformation that the representations of finitew algebras can be constructed from the representations of a certain lie subalgebra of the original simple lie algebra as a byproduct of this we are able to construct the fock realizations of arbitrary finitew algebras

the relation between polynomial deformations of sl 2 r and quasi exact solvability a general method based on the polynomial deformations of the lie algebra sl 2 r is proposed in order to exhibit the quasi exact solvability of specific hamiltonians implied by quantum physical models this method using the finite dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on second harmonic generation

generalized micz kepler system duality polynomial and deformed oscillator algebras we present the quadratic algebra of the generalized micz kepler system in three dimensional euclidean space e3 and its dual the four dimensional singular oscillator in four dimensional euclidean space e4 we present their realization in terms of a deformed oscillator algebra using the daskaloyannis construction the structure constants are in these cases functions not only of the hamiltonian but also of other integrals commuting with all generators of the quadratic algebra we also present a new algebraic derivation of the energy spectrum of the micz kepler system on the three sphere s3 using a quadratic algebra these results point out also that results and explicit formula for structure functions obtained for quadratic cubic and higher order polynomial algebras in the context of two dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles

two grid finite volume element method for linear and nonlinear elliptic problems two grid finite volume element discretization techniques based on two linear conforming finite element spaces on one coarse and one fine grid are presented for the two dimensional second order non selfadjoint and indefinite linear elliptic problems and the two dimensional second order nonlinear elliptic problems with the proposed techniques solving the non selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non selfadjoint and indefinite elliptic problem on a much smaller space solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space convergence estimates are derived to justify the efficiency of the proposed two grid algorithms a set of numerical examples are presented to confirm the estimates

addendum to on the variation in the cohomology of the symplectic form of the reduced phase space here we have used the notation rlx for the inner product of the vector field x with the form a and ix m x j m for the x component of a in an earlier paper 4 it was shown that the push forward j dm of the liouville measure dm on m under the momentum mapping j is a piecewise polynomial measure on moreover in case x has isolated isolated zeros on m an explicit formula for the integral

a splitting extrapolation for solving nonlinear elliptic equations with d quadratic finite elements nonlinear elliptic partial differential equations are important to many large scale engineering and science problems for this kind of equations this article discusses a splitting extrapolation which possesses a high order of accuracy a high degree of parallelism less computational complexity and more flexibility than richardson extrapolation according to the problems some domain decompositions are constructed and some independent mesh parameters are designed multi parameter asymptotic expansions are proved for the errors of approximations based on the expansions splitting extrapolation formulas are developed to compute approximations with high order of accuracy on a globally fine grid because these formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid a large scale multidimensional problem is turned into a set of smaller discrete subproblems additionally this method is efficient for solving interface problems

path integrals for potential problems with δ function perturbation the author presents several examples of potential problems with a function perturbation by means of path integrals the idea is to sum a perturbation series expansion resulting in an energy dependent green function g e the energy levels en of the perturbed problem are determined by the equation one dimensional case ig v a a en gamma where g v is the green function of the unperturbed problem gamma is the strength of the potential and a its location in r in d dimensional radial problems with a spherically shaped delta function located at r a this equation changes into ig v l a a en ad 1 where l denotes the angular momentum number

an adaptive ghost fluid finite volume method for compressible gas water simulations an adaptive ghost fluid finite volume method is developed for one and two dimensional compressible multi medium flows in this work it couples the real ghost fluid method gfm c w wang t g liu b c khoo a real ghost fluid method for the simulation of multi medium compressible flow siam j sci comput 28 2006 278 302 and the adaptive moving mesh method h z tang t tang moving mesh methods for one and two dimensional hyperbolic conservation laws siam j numer anal 41 2003 487 515 h z tang t tang p w zhang an adaptive mesh redistribution method for non linear hamilton jacobi equations in two and three dimensions j comput phys 188 2003 543 572 and thus combines their advantages this work shows that the local mesh clustering in the vicinity of the material interface can effectively reduce both numerical and conservative errors caused by the gfm around the material interface and other discontinuities besides the improvement of flow field resolution the adaptive gfm also largely increases the computational efficiency several numerical experiments are conducted to demonstrate robustness and efficiency of the current method they include several 1d and 2d gas water flow problems involving a large density gradient at the material interface and strong shock interface interactions the results show that our algorithm can capture the shock waves and the material interface accurately and is stable and robust even for solutions with large density and pressure gradients