the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

perturbation methods for the matrix eigenproblem some computational experiments are reported on the solution of the eigenproblem for a matrix h by using an iterative sequence of transformations of type h to s 1hs where s is trivially invertible and is usually calculated from a first order perturbation formula simple improved methods of constructing s are reported these methods greatly improve the convergence properties of the eigenvalue calculations

pixelwise adaptive blind optical flow assuming nonstationary statistics we address some of the major issues in optical flow within a new framework assuming nonstationary statistics for the motion field and for the errors problems addressed include the preservation of discontinuities model data errors outliers confidence measures and performance evaluation in solving these problems we assume that the statistics of the motion field and the errors are not only spatially varying but also unknown we thus derive a blind adaptive technique based on generalized cross validation for estimating an independent regularization parameter for each pixel our formulation is pixelwise and combines existing first and second order constraints with a new second order temporal constraint we derive a new confidence measure for an adaptive rejection of erroneous and outlying motion vectors and compare our results to other techniques in the literature a new performance measure is also derived for estimating the signal to noise ratio for real sequences when the ground truth is unknown

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

a non archimedean ohsawa takegoshi extension theorem we prove an ohsawa takegoshi type extension theorem on the berkovich closed unit disc over certain non archimedean fields as an application we establish a non archimedean analogue of demailly s regularization theorem for quasisubharmonic functions on the berkovich unit disc

similarity solutions for unsteady free convection flow from a continuous moving vertical surface the transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid the thermal boundary layer induced within a vertical semi infinite layer of boussinseq fluid by a constant heated bounding plate the application of two parameter groups reduces the number of independent variables by two and consequently the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions the obtained ordinary differential equations are solved analytically for the temperature and numerically for the velocity using the shooting method effect of prandtl number on the thermal boundary layer and velocity boundary layer are studied and plotted in curves

equidistribution quantitative des points de petite hauteur sur la droite projective we introduce a new class of adelic heights on the projective line we estimate their essential minimum and prove a result of equidistribution at every place for points of small height with estimates on the speed of convergence to each rational function r in one variable and defined over a number field k is associated a normalized height on the algebraic closure of k we show that these dynamically defined heights are adelic in our sense and deduce from this equidistribution results for preimages of points under r at every place of k our approach follows that of bilu and relies on potential theory in the complex plane as well as in the berkovich space associated to the projective line over open image in new window for each prime p

extrapolation methods for vector sequences this is an expository paper that describes and compares five methods for extrapolating to the limit or anti limit of a vector sequence without explicit knowledge of the sequence generator the methods are the minimal polynomial extrapolation mpe studied by cabay and jackson mesina and skelboe the reduced rank extrapolation rre of eddy which we show to be equivalent to mesina s version of mpe the vector and scalar versions of the epsilon algorithm vea sea introduced by wynn and extended by brezinski and gekeler and the topological epsilon algorithm tea of brezinski we cover the derivation and error analysis of iterated versions of the algorithms as applied to both linear and nonlinear problems and we show why these versions tend to converge quadratically we also present samples from extensive numerical testing that has led us to the following conclusions a tea in spite of its role as a theoretical link between the polynomial type and the epsilon type methods has no practical appl

analysis of 3 1 dimensional boitileonmannapempinelli equation via lax pair investigation and group transformation method singular manifolds method smm is utilized to detect the lax pair and bcklund transformation of 3 1 dimensional boitileonmannapempinelli blmp equation an extension of group transformation method with three parameters is exploited in transforming the lax pair directly to a system of ordinary differential equations odes two cases of similarity variables are considered resulting in solvable systems of odes new analytical solutions are attained and graphed containing some soliton waves some of these solutions are applicable of plasma explosions and fluid dynamics both of investigation of lax pair of 3 1 dimensional evolution equations and three parameters group method are seldom utilized in this kind of evolution equations

differentiation of discrete multidimensional signals we describe the design of finite size linear phase separable kernels for differentiation of discrete multidimensional signals the problem is formulated as an optimization of the rotation invariance of the gradient operator which results in a simultaneous constraint on a set of one dimensional low pass prefilter and differentiator filters up to the desired order we also develop extensions of this formulation to both higher dimensions and higher order directional derivatives we develop a numerical procedure for optimizing the constraint and demonstrate its use in constructing a set of example filters the resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature

boolean functions and finite difference eigenvalues finite difference calculations involving the expectation values of boolean functions are shown to yield detailed information about the properties of the energy levels and eigenfunctions for double well potentials

on the adiabatic theorem for nonself adjoint hamiltonians the authors consider the evolution of a two level system driven by a nonself adjoint hamiltonian h in t and treat the adiabatic limit in to 0 while adiabatic theorem like results do not hold true in general for this case they prove that they are still valid for the subspace corresponding to the eigenvalue having the largest imaginary part least dissipative eigenvalue the theory gives the full asymptotic expansion of the evolution restricted to this subspace the first correction beyond berry s phase is to their best knowledge given explicitly for the first time

effective characteristic polynomials and two point pade approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators pad e approximants are able to sum effectively the rayleigh schr odinger perturbation series for the ground state energy of the quartic anharmonic oscillator as well as the corresponding renormalized perturbation expansion e j weniger j ifmmode check c else v c fi i ifmmode check z else v z fi ek and f vinette j math phys 34 571 1993 in the sextic case pad e approximants are still able to sum these perturbation series but convergence is so slow that they are computationally useless in the octic case pad e approximants are not powerful enough and fail on the other hand the inclusion of only a few additional data from the strong coupling domain e j weniger ann phys ny to be published greatly enhances the power of summation methods the summation techniques which we consider are two point pad e approximants and effective characteristic polynomials it is shown that these summation methods give good results for the quartic and sextic anharmonic oscillators and even in the case of the octic anharmonic oscillator which represents an extremely challenging summation problem two point pad e approximants give relatively good results textcopyright 1996 the american physical society

group method analysis of steady free convective laminar boundary layer flow on a nonisothermal vertical circular cylinder the transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder the application of two parameter group reduces the number of independent variables by two and consequently the system of the governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions the ordinary differential equations are solved numerically using a fourth order runge kutta scheme and the gradient method numerical results are obtained for the study of the boundary layer characteristics the general analysis developed in this study corresponds to the case of surface temperature that varies exponentially with time and uniform with respect to the axial coordinate i e in the formt w ae bt wherea andb are constants the effect of prandtl number pr andb on the boundary layer characteristics and the maximum value of the vertical component of the velocity are studied

recursive filters for optical flow working toward efficient real time implementations of optical flow methods the authors have applied simple recursive filters to achieve temporal smoothing and differentiation of image intensity and to compute 2d flow from component velocity constraints using spatiotemporal least squares minimization accuracy in simulation is similar to that obtained in the study by barren et al 1994 while requiring much less storage less computation and shorter delays

the bloch wave operator generalizations and applications part i the time independent case this is part 1 of a two part review on wave operator theory and methods the basic theory of the time independent wave operator is presented in terms of partitioned matrix theory for the benefit of general readers with a discussion of the links between the matrix and projection operator approaches the matrix approach is shown to lead to simple derivations of the wave operators and effective hamiltonians of lowdin bloch des cloizeaux and kato as well as to some associated variational forms the principal approach used throughout stresses the solution of the nonlinear equation for the reduced wave operator leading to the construction of the effective hamiltonians of bloch and of des cloizeaux several mathematical techniques which are useful in implementing this approach are explained some of them being relatively little known in the area of wave operator calculations the theoretical discussion is accompanied by several specimen numerical calculations which apply the described techniques to a selection of test matrices taken from the previous literature on wave operator methods the main emphasis throughout is on the use of numerical methods which use iterative or perturbation algorithms with simple pade approximant methods being found sufficient to deal with most of the cases of divergence which are encountered the use of damping factors and relaxation parameters is found to be effective in stabilizing calculations which use the energy dependent effective hamiltonian of lowdin in general the computations suggest that the numerical applications of the nonlinear equation for the reduced wave operator are best carried out with the equation split into a pair of equations in which the bloch effective hamiltonian appears as a separate entity the presentation of the theoretical and computational details throughout is accompanied by references to and discussion of many works which have used wave operator methods in physics chemistry and engineering some of the techniques described in this part 1 will be further extended and applied in part 2 of the review which deals with the changes which are required to extend wave operator theory to the case of a time dependent hamiltonian such as that which describes the interaction of a laser pulse with an atom or molecule

numerical solution of burgers equation by quadratic b spline finite elements in this paper a galerkin quadratic b spline finite element method is used to solve numerically the one dimensional burgers equation reduced by the hopf cole transformation the performance of the method is tested on two model problems involving moderately reynolds numbers with known exact solutions the obtained numerical results show that the method is efficient robust and reliable for solving burgers equation accurately even involving high reynolds numbers for which the exact solution fails computed results are compared with other numerical results in the literature a stability analysis of the method is also investigated

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

solution of counter diffusion problem with position dependent diffusion coefficent by using variational methods unsteady state counter diffusion problem with position dependent diffusion coefficient can be modeled using fick s second law a mathematical model was constructed and solved to quantitatively describe the dynamic behavior of solute diffusion through non homogeneous materials where diffusion coefficient is a function of position the eigenfunction expansion approach was utilized to solve the model the eigenvalues and eigenfunction of the system were obtained using a variational method it has been shown that position dependency of the material can be neglected if the thickness of the material is relatively small mathematical models were solved for different thicknesses and different diffusion coefficient functions

on geometric phases and dynamical invariants a formalism is developed for calculating berry phases for nonadiabatic time periodic quantum systems when a dynamical invariant is known it is found that when the invariant is periodic and has a nondegenerate spectrum this method allows a convenient way to obtain generalized berry phases and the proper cyclic initial states the method is applied to the generalized harmonic oscillator and the two level system where the invariant operators are explicitly constructed formulae for the conventional berry s phases are readily obtained by taking the adiabatic limit of the exact results

invariance of plurigenera in this paper we give a proof of the following long conjectured result on the invariance of the plurigenera main theorem let p x d be a smooth projective family of compact complex manifolds parametrized by the open unit 1 disk d assume that the bers xt py1 t t 2 d are of general type then for every positive integer m the plurigenus dimc c xt mkxt is independent of t 2 d where kxt is the canonical line bundle of xt

a direct variational methods applied to burgers equation in this study a compact approximate method in limiting form for calculating the solution of burgers equation with appropriate boundary conditions is presented the results obtained by present method are found to be in good agreement with those due to earlier authors and offers appreciable advantages for burgers like nonlinear problems

contour tracking with a spatio temporal intensity moment standard edge detection operators such as the laplacian of gaussian and the gradient of gaussian can be used to track contours in image sequences when using edge operators a contour which is determined on a frame of the sequence is simply used as a starting contour to locate the nearest contour on the subsequent frame however the strategy used to look for the nearest edge points may not work when tracking contours of non isolated gray level discontinuities in these cases strategies derived from the optical flow equation which look for similar gray level distributions appear to be more appropriate since these can work with a lower frame rate than that needed for strategies based on pure edge detection operators however an optical flow strategy tends to propagate the localization errors through the sequence and an additional edge detection procedure is essential to compensate for such a drawback in this paper a spatio temporal intensity moment is proposed which integrates the two basic functions of edge detection and tracking

matrix spectroscopy computation of interior eigenstates of large matrices using layered iteration the computation of a small group of interior eigenstates of a large matrix h is an important problem in chemical physics this general problem is approached in this study through the application of a two layer iteration scheme the design of the outer loop is based upon the strategy developed by ericsson and ruhe math comput 35 1251 1980 starting with a variable input energy e this loop uses the lanczos algorithm with no reorthogonalization to develop a reduced tridiagonal representation of the total green function g e diagonalization of this small matrix denoted t yields through a simple mapping excellent approximations to the eigenvalues of h that lie near energy e the inner iteration loop of the algorithm computes the matrix vector product g e mathbf q mathit j where mathbf q mathit j is one of the lanczos vectors both direct and indirect methods may be used for this operation the direct method uses a perturbative expansion of the green function while the indirect method is based upon the iterative solution of a linear algebraic system the indirect method yields a parametrized polynomial representation of the green function with the coefficients chosen variationally the method is adaptive in the sense that these coefficients change during the course of the lanczos iteration convergence of these iterative methods is improved significantly by developing the green function in the partial adiabatic representation conversion to this representation involves diagonalization of the diagonal block of h involving those states whose zeroth order energies surround the energy of interest the two layer scheme is applied to a model hamiltonian matrix that has a variable coupling strength within and between a number of dense bands of states with this scheme it is possible to accurately compute a group of eigenstates near energy e in just a few lanczos iteration steps 10

multi frame estimation of planar motion traditional plane alignment techniques are typically performed between pairs of frames we present a method for extending existing two frame planar motion estimation techniques into a simultaneous multi frame estimation by exploiting multi frame subspace constraints of planar surfaces the paper has three main contributions 1 we show that when the camera calibration does not change the collection of all parametric image motions of a planar surface in the scene across multiple frames is embedded in a low dimensional linear subspace 2 we show that the relative image motion of multiple planar surfaces across multiple frames is embedded in a yet lower dimensional linear subspace even with varying camera calibration and 3 we show how these multi frame constraints can be incorporated into simultaneous multi frame estimation of planar motion without explicitly recovering any 3d information or camera calibration the resulting multi frame estimation process is more constrained than the individual two frame estimations leading to more accurate alignment even when applied to small image regions

valuative analysis of planar plurisubharmonic functions we show that valuations on the ring r of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions giving rise to generalized lelong numbers in the sense of demailly any plurisubharmonic function thus defines a real valued function on the set mathcal v of valuations on r and by way of a natural laplace operator defined in terms of the tree structure on mathcal v a positive measure on mathcal v this measure contains a great deal of information on the singularity at the origin under mild regularity assumptions it yields an exact formula for the mixed monge ampere mass of two plurisubharmonic functions as a consequence any generalized lelong number can be interpreted as an average of valuations using our machinery we also show that the singularity of any positive closed 1 1 current t can be attenuated in the following sense there exists a finite composition of blowups such that the pull back of t decomposes into two parts the first associated to a divisor with normal crossing support the second having small lelong numbers

group solution of a time dependent chemical convective process the time dependent progress of a chemical reaction over a flat vertical plate is here considered the problem is solved using the two parameter group method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation the behavior of the process is numerically investigated for the chemical reaction order n 1 and different schmidt numbers as the problem shows a singularity at n 1 the nonlinear system of ordinary differential equation resulting from the transformation of the problem are analytically solved through the perturbation method the velocity and concentration of chemicals based on the analytical and numerical solutions are presented compared and discussed

potential method applied to boussinesq equation in this paper a solution of the nonlinear boussinesq equation is presented using the potential similarity transformation method the equation is first written in a conserved form a potential function is then assumed reducing it to a system of equations which is further solved through the group transformation method new transformations are found

histories of adiabatic quantum transitions the way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation for a 2 state quantum system by transforming to a series of superadiabatic bases clinging ever closer to the exact evolving state it is shown that transition histories renormalize onto a universal one in which the amplitude grows to its final value as an error function rather than via large oscillations as in the ordinary adiabatic basis the time for the universal transition is of order surd hslash delta where delta is the small adiabatic slowness parameter in perturbation theory the pre exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value textstyle frac 1 3 pi for the ordinary adiabatic basis to the correct value unity the various histories could be observed in spin experiments

numerical solutions of the burgers equation by the least squares quadratic b spline finite element method in this study a least squares quadratic b spline finite element method for calculating the numerical solutions of the one dimensional burgers like equations with appropriate boundary and initial conditions is presented three test problems have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each problem and are found to be in good agreement with each other a fourier stability analysis of the method is also investigated

symmetries of differential equations from sophus lie to computer algebra the topic of this article is the symmetry analysis of differential equations and the applications of computer algebra to the extensive analytical calculations which are usually involved in it the whole area naturally decomposes into two parts depending on whether ordinary or partial differential equations are considered we show how a symmetry may be applied to lower the order of an ordinary differential equation or to obtain similarity solutions of partial differential equations the computer algebra packages sods and spde respectively which have been developed to perform almost all algebraic manipulations necessary to determine the symmetry group of a given differential equation are presented furthermore it is argued that the application of computer algebra systems has qualitatively changed this area of applied mathematics

high order transverse schemes for the numerical solution of pdes many existing numerical schemes for the solution of initial boundary value problems for partial differential equations can be derived by the method of lines the pdes are converted into a system of ordinary differential equations either with initial conditions longitudinal scheme or with boundary conditions transverse scheme in particular this paper studies the performance of the transverse scheme in combination with boundary value methods moreover we do not restrict the semi discretization by the usual first or second order finite difference approximations to replace the derivative with respect to time but we use high order formulae

solution to a non archimedean monge ampere equation let x be a smooth projective berkovich space over a complete discrete valuation field k of residue characteristic zero and assume that x is defined over a function field admitting k as a completion let further m be a positive measure on x and l be an ample line bundle such that the mass of m is equal to the degree of l then we show the existence a continuous semipositive metric whose associated measure is equal to m in the sense of zhang and chambert loir this we do under a technical assumption on the support of m which is for instance fulfilled if the support is a finite set of divisorial points our method draws on analogues of the variational approach developed to solve complex monge ampere equations on compact kahler manifolds by berman guedj zeriahi and the first named author and of ko l odziej s continuity estimates it relies in a crucial way on the compactness properties of singular semipositive metrics as defined and studied in a companion article

a model and tracking algorithm for a class of video targets algorithms are developed for a real time automatic system capable of tracking two dimensional 2 d targets in complex scenes a mathematical model of 2 d image spatial and temporal evolution applicable to certain classes of targets and target perturbations is developed it is shown that for small target perturbations the 2 d tracking problem may be approximated as a 1 d time varying parameter estimation problem a ccd implementable solution is developed which is particularly useful when considering target rotation and dilation and target background separation results of system simulation and suggestions for future research are presented

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

suita conjecture and the ohsawa takegoshi extension theorem we prove a conjecture of n suita which says that for any bounded domain d in one has c d 2 leq pi k d where cd z is the logarithmic capacity of d with respect to z d and kd the bergman kernel on the diagonal we also obtain optimal constant in the ohsawa takegoshi extension theorem

group theoretic methods applied to burgers equation abstract in this study the group theoretic methods for calculating the solution of burgers equation with appropriate boundary and initial conditions is presented the application of a one parameter group reduces the number of independent variables by one and consequently the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with the appropriate corresponding conditions the obtained differential equation is solved analytically and the solution obtained in closed form for a specific choice of boundary condition

group solution for unsteady free convection flow from a vertical moving plate subjected to constant heat flux the problem of heat and mass transfer in an unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method the nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions the obtained ordinary differential equations are solved numerically using the shooting method the effect of prandlt number on the velocity and temperature of the boundary layer is plotted in curves a comparison with previous work is presented

an exponentially fitted method for solving burgers equation in this paper an exponentially fitted method is used to numerically solve the one dimensional burgers equation the performance of the method is tested on the model involving moderately large reynolds numbers the obtained numerical results show that the method is efficient stable and reliable for solving burgers equation accurately even involving high reynolds numbers for which the exact solution fails copyright 2009 john wiley sons ltd

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

super potentials of positive closed currents intersection theory and dynamics we introduce a notion of super potential for positive closed currents of bidegree p p on projective spaces this gives a calculus on positive closed currents of arbitrary bidegree we define in particular the intersection of such currents and the pull back operator by meromorphic maps one of the main tools is the introduction of structural discs in the space of positive closed currents which gives a geometry on that space we apply the theory of super potentials to construct green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms

numerical solution of the burgers equation by automatic differentiation abstract we compute the solution of the one dimensional burgers equation by marching the solution in time using a taylor series expansion our approach does not require symbolic manipulation and does not involve the solution of a system of linear or non linear algebraic equations instead we use recursive formulas obtained from the differential equation to calculate exact values of the derivatives needed in the taylor series we illustrate the effectiveness of our method by solving four test problems with known exact solutions the numerical solutions we obtain are in excellent agreement with the exact solutions while being superior to other previously reported numerical solutions

group analysis for natural convection from a vertical plate the steady laminar natural convection of a fluid having chemical reaction of order n past a semi infinite vertical plate is considered the solution of the problem by means of one parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations two different similarity transformations are found in each case the set of differential equations are solved numerically using runge kutta and the shooting method for each transformation different schmidt numbers and chemical reaction orders are tested

a version of thirring s approach to the kolmogorov arnold moser theorem for quadratic hamiltonians with degenerate twist we give a proof of the kolmogorov arnold moser kam theorem on the existence of invariant tori for weakly perturbed hamiltonian systems based on thirring s approach for hamiltonians that are quadratic in the action variables the main point of this approach is that the iteration of canonical transformations on which the proof is based stays within the space of quadratic hamiltonians we show that thirring s proof for nondegenerate hamiltonians can be adapted to hamiltonians with degenerate twist this case in fact drastically simplifies thirring s proof

comparison between fixed and gaussian steplength in monte carlo simulations for diffusion processes we analyze the different degrees of accuracy of two monte carlo methods for the simulation of one dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation the methods analyzed correspond to fixed and gaussian steplengths for a homogeneous diffusion coefficient it is known that the gaussian steplength generates exact results at fixed time steps dt for spatial dependent diffusion coefficients the symmetric character of the gaussian distribution introduces an error that increases with time as an example we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities

group theoretic approach for solving the problem of diffusion of a drug through a thin membrane the transformation group theoretic approach is applied to study the diffusion process of a drug through a skinlike membrane which tends to partially absorb the drug two cases are considered for the diffusion coefficient the application of one parameter group reduces the number of independent variables by one and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions the obtained differential equation is solved numerically using the shooting method and the results are illustrated graphically and in tables

analysis of some vector extrapolation methods for solving systems of linear equations in this paper we consider some vector extrapolation methods for solving nonsymmetric systems of linear equations when applied to sequences generated linearly these methods namely the minimal polynomial extrapolation mpe and the reduced rank extrapolation rre are krylov subspaces methods and are respectively equivalent to the method of arnoldi and to the gcr and gmres by considering the geometrical aspect of these methods we derive new expressions for their residual norms and give a relationship between them this allows us to compare the two methods using this new approach we will show that for nonsingular skew symmetric matrices the gmres stagnates every two iterations and the restarted version gmres m m ge 2 is always convergent finally the incomplete forms are considered and some convergence results are given