asymptotic expansion of solutions to the drift diffusion equation with large initial data abstract we consider the large time behavior of the solution to the initial value problem for the nernst planck type drift diffusion equation in whole spaces in the l p framework the global existence and the decay of the solution were shown moreover the second order asymptotic expansion of the solution as t was derived we also deduce the higher order asymptotic expansion of the solution especially we discuss the contrast between the odd dimensional case and the even dimensional case

the richer representation the better registration in this paper the registration problem is formulated as a point to model distance minimization unlike most of the existing works which are based on minimizing a point wise correspondence term this formulation avoids the correspondence search that is time consuming in the first stage the target set is described through an implicit function by employing a linear least squares fitting this function can be either an implicit polynomial or an implicit b spline from a coarse to fine representation in the second stage we show how the obtained implicit representation is used as an interface to convert point to point registration into point to implicit problem furthermore we show that this registration distance is smooth and can be minimized through the levengberg marquardt algorithm all the formulations presented for both stages are compact and easy to implement in addition we show that our registration method can be handled using any implicit representation though some are coarse and others provide finer representations hence a tradeoff between speed and accuracy can be set by employing the right implicit function experimental results and comparisons in 2d and 3d show the robustness and the speed of convergence of the proposed approach

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

surface from gradients without discrete integrability enforcement a gaussian kernel approach representative surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint in a discrete manner while enforcing integrability allows the subsequent integration to produce surface heights existing algorithms have one or more of the following disadvantages they can only handle dense per pixel gradient fields smooth out sharp features in a partially integrable field or produce severe surface distortion in the results in this paper we present a method which does not enforce discrete integrability and reconstructs a 3d continuous surface from a gradient or a height field or a combination of both which can be dense or sparse the key to our approach is the use of kernel basis functions which transfer the continuous surface reconstruction problem into high dimensional space where a closed form solution exists by using the gaussian kernel we can derive a straightforward implementation which is able to produce results better than traditional techniques in general an important advantage of our kernel based method is that the method does not suffer discretization and finite approximation both of which lead to surface distortion which is typical of fourier or wavelet bases widely adopted by previous representative approaches we perform comparisons with classical and recent methods on benchmark as well as challenging data sets to demonstrate that our method produces accurate surface reconstruction that preserves salient and sharp features the source code and executable of the system are available for downloading

large time behavior of bounded solutions to a parabolic system of chemotaxis in the whole space abstract we consider the cauchy problem for a parabolic system of chemotaxis in r n n 1 and give the decay rates and asymptotic profiles of bounded solutions

remarks on the local existence of solutions to the debye system abstract in this paper we study the cauchy problem of the debye system for initial data in the lorentz space l n 1 r n and the besov space b l n 1 r n for 0 1 some local existence theorems are proved

fitting curves and surfaces with constrained implicit polynomials a problem which often arises while fitting implicit polynomials to 2d and 3d data sets is the following although the data set is simple the fit exhibits undesired phenomena such as loops holes extraneous components etc previous work tackled these problems by optimizing heuristic cost functions which penalize some of these topological problems in the fit the paper suggests a different approach to design parameterized families of polynomials whose zero sets are guaranteed to satisfy certain topological properties namely we construct families of polynomials with star shaped zero sets as well as polynomials whose zero sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse this is more rigorous than using heuristics which may fail and result in pathological zero sets the ability to parameterize these families depends heavily on the ability to parameterize positive polynomials to achieve this we use some powerful results from real algebraic geometry

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

stability of viscous scalar shock fronts in several dimensions we prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions the proof uses the integrated equation and an effective equation for the motion of the front itself we derive energy estimates that balance terms from the integrated equation with terms from the front motion equation in this paper we prove that viscous shock profiles for scalar conservation laws are stable in two or more space dimensions these multidimensional stability questions are separate from their one dimensional analogues because of the possibility of transverse instabilities such as those that occur in combustion fronts lu and in shock waves with phase changes the proof here is a rigorous version of arguments that are used to derive effective equations such as the kuramoto sivashinsky equation to describe the behavior of fronts the one dimensional stability for scalar conservation laws was proven by ii in and oleinik io using the integrated equation see below and a max imum principle another proof based on weighted norms and spectral theory for the linearized problem was given by sattinger s the multidimensional stability proof below has more in common with the stability proofs for systems of conservation laws in one space dimension begun by kawashima and mat sumura km and goodman go and completed by liu li these proofs use l2 energy estimates for the integrated equation we consider equations of the form ut f u x g u y uxx uyy where f u is a strictly convex function of u

appearance cloning photo consistent scene recovery from multi view images this paper introduces the novel volumetric methodology appearance cloning as a viable solution for achieving a more improved photo consistent scene recovery including a greatly enhanced geometric recovery performance from a set of photographs taken at arbitrarily distributed multiple camera viewpoints we do so while solving many of the problems associated with previous stereo based and volumetric methodologies we redesign the photo consistency decision problem of individual voxel in volumetric space as the photo consistent shape search problem in image space by generalizing the concept of the point correspondence search between two images in stereo based approach within a volumetric framework in detail we introduce a self constrained greedy style optimization methodology which iteratively searches a more photo consistent shape based on the probabilistic shape photo consistency measure by using the probabilistic competition between candidate shapes our new measure is designed to bring back the probabilistic photo consistency of a shape by comparing the appearances captured from multiple cameras with those rendered from that shape using the per pixel maxwell model in image space through various scene recoveries experiments including specular and dynamic scenes we demonstrate that if sufficient appearances are given enough to reflect scene characteristics our appearance cloning approach can successfully recover both the geometry and photometry information of a scene without any kind of scene dependent algorithm tuning

generalized burgers equations and euler painleve transcendents ii initial value problems for the generalized burgers equation gbe ut u betaux lambdaualpha delta 2 uxx are discussed for the single hump type of initial data both continuous and discontinuous the numerical solution is carried to the self similar intermediate asymptotic regime when the solution is given analytically by the self similar form the nonlinear transformed ordinary differential equations ode s describing the self similar form are generalizations of a class discussed by euler and painleva and quoted by kamke these ode s are new and it is postulated that they characterize gbe s in the same manner as the painlev equations categorize the kortweg de vries kdv type a connection problem for some related ode s satisfying proper asymptotic conditions at x infinity is solved the range of amplitude parameter is found for which the solution of the connection problem exists the other solutions of the above gbe which display several interesting features such as peaking breaking and a long shelf on the left for negative values of the damping coefficient lambda are also discussed the results are compared with those holding for the modified kdv equation with damping journal of mathematical physics is copyrighted by the american institute of physics

large time behavior of the vorticity of two dimensional viscous flow and its application to vortex formation we consider the cauchy problem for the two dimensional vorticity equation we show that the solution behaves like a constant multiple of the gauss kernel having the same total vorticity as time tends to infinity no particular structure of initial data 0 x 0 is assumed except the restriction that the reynolds numberr 0 dx v is small wherev is the kinematic viscosity applying a time dependent scale transformation we show a stability of burgers vortex which physically implies formation of a concentrated vortex

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

pointwise estimates for solutions of fractal burgers equation abstract in this paper we provide two sided estimates and uniform asymptotics for the solution of d dimensional critical fractal burgers equation u t 2 u b u u q 0 1 2 b r d for q 1 d and u 0 l 1 r d we consider also q 1 d under additional condition u 0 l r d in both cases we assume u 0 0 which implies that the solution is non negative the estimates are given in the terms of the function p t u 0 where p t denotes the semigroup for the operator t 2

the arrival time distribution the extended probability approaches we present a calculation of the arrival time probability distribution based on the extended probability as proposed by hartle 2008 phys rev a 78 012108 we show that two cases of the arrival time probability distribution can be used first we use the path decomposition expansion to discuss a fine grained history for which a particle has a first crossing x 0 at time the arrival time probability related to the probability current is obtained second we consider that the arrival time distribution is modeled by the first photon emitted from a two level atom the basic atom laser model the partition dynamic of this system is discussed each history is in the form of a coarse grained history we confirm that the arrival time probability distribution computed by this method agrees with that computed via the probability of no photon detection crucially the resulting arrival time distributions can be obtained without the restriction of the consistency condition

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

asymptotic behaviour in a one dimensional model of interacting particles abstract we consider the equation u t e u x x u k u x for x r t 0 and with e 0 supplemented with a nonnegative integrable initial datum we present a class of interaction kernels k such that the large time behaviour of solutions to this initial value problem is described by a compactly supported self similar profile

invariant manifolds for parabolic partial differential equations on unbounded domains in this paper finite dimensional invariant manifolds for nonlinear parabolic partial differential equations of the form

a theory of shape by space carving in this paper we consider the problem of computing the 3d shape of an unknown arbitrarily shaped scene from multiple photographs taken at known but arbitrarily distributed viewpoints by studying the equivalence class of all 3d shapes that reproduce the input photographs we prove the existence of a special member of this class the photo hull that 1 can be computed directly from photographs of the scene and 2 subsumes all other members of this class we then give a provably correct algorithm called space carving for computing this shape and present experimental results on complex real world scenes the approach is designed to 1 capture photorealistic shapes that accurately model scene appearance from a wide range of viewpoints and 2 account for the complex interactions between occlusion parallax shading and their view dependent effects on scene appearance

on asymptotic behaviors of solutions to parabolic systems modelling chemotaxis abstract this paper deals with large time behaviors of solutions to a keller segel system which possesses self similar solutions by taking into account the invariant properties of the equation with respect to a scaling and translations we show that suitably shifted self similar solutions give more precise asymptotic profiles of general solutions at large time the convergence rate is also computed in details

left ventricular motion reconstruction based on elastic vector splines in medical imaging it is common to reconstruct dense motion estimates from sparse measurements of that motion using some form of elastic spline thin plate spline snakes and other deformable models etc usually the elastic spline uses only bending energy second order smoothness constraint or stretching energy first order smoothness constraint or a combination of the two these elastic splines belong to a family of elastic vector splines called the laplacian splines this spline family is derived from an energy minimization functional which is composed of multiple order smoothness constraints these splines can be explicitly tuned to vary the smoothness of the solution according to the deformation in the modeled material tissue in this context it is natural to question which members of the family will reconstruct the motion more accurately the authors compare different members of this spline family to assess how well these splines reconstruct human cardiac motion they find that the commonly used splines containing first order and or second order smoothness terms only are not the most accurate for modeling human cardiac motion

self similar solutions to a parabolic system modeling chemotaxis we study the forward self similar solutions to a parabolic system modeling chemotaxisut u u v vt v u in the whole space r2 where is a positive constant using the liouville type result and the method of moving planes it is proved that self similar solutions u v must be radially symmetric about the origin then the structure of the set of self similar solutions is investigated as a consequence it is shown that there exists a threshold in r2u for the existence of self similar solutions in particular for 0 1 2 there exists a self similar solution u v if and only if r2u 8

uniform decay rated for parabolic conservations laws on etablit des taux de decroissance uniformes optimaux pour des solutions du probleme de cauchy avec donnees grandes pour des lois de conservation paraboliques scalaires a plusieurs dimensions d espace

convergence to diffusion waves of solutions for viscous conservation laws we study the large time behavior of solutions of viscous conservation laws it is shown that solutions tend to diffusion waves which are constructed based on the heat equation and burgers equation the convergence is in thelp 1 p sense and is obtained as a consequence of thel2 decay of the difference between the solution and its asymptotic state of diffusion waves

linearly positive histories probabilities for a robust family of sequences of quantum events non negative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories the resulting linearly positive histories avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply thus linearly positive histories are a broad extension of decohering histories moreover the resulting theory is manifestly time reversal invariant

inference of integrated surface curve and junction descriptions from sparse 3d data we address the problem of inferring integrated high level descriptions such as surfaces 3d curves and junctions from a sparse point set for precise localization we propose a noniterative cooperative algorithm in which surfaces curves and junctions work together initial estimates are computed based on the work by guy and medioni 1997 where each point in the given sparse and possibly noisy point set is convolved with a predefined vector mask to produce dense saliency maps these maps serve as input to our novel extremal surface and curve algorithms for initial surface and curve extraction these initial features are refined and integrated by using excitatory and inhibitory fields consequently intersecting surfaces resp curves are fused precisely at their intersection curves resp junctions results on several synthetic as well as real data sets are presented

large time behaviour of the solutions of a semilinear parabolic equation in rn abstract the asymptotic behaviour as t tends to of the solution of u t u u u p 1 0 in r n r p 1 was studied it was proved that the behaviour depends strongly on the sign of n 2 n p and also on the rate of decay of the admissible initial data u 0 x as x tends to

asymptotic expansion of solutions to the nonlinear dissipative equation with the anomalous diffusion abstract the initial value problem for the dissipative equation with the extra force term is considered the dissipative effect on this equation is given by the fractional laplacian which describes the anomalous diffusion the main goal of this paper is to give an estimate on the difference between solutions and their asymptotic expansion as the space and the time variables tend to infinity furthermore as an application the large time behavior of solutions to some concrete problems are discussed

on the relationship between complex potentials and strings of projection operators it is of interest in a variety of contexts and in particular in the arrival time problem to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the positive x axis pulsed measurements echanobe del campo and muga have given a compelling but heuristic argument that the state thus obtained is approximately equivalent to the state obtained by evolving in the presence of a certain complex potential of step function form in this paper with the help of the path decomposition expansion of the associated propagators we give a detailed derivation of this approximate equivalence the propagator for the complex potential is known so the bulk of the derivation consists of an approximate evaluation of the propagator for the free particle interspersed with periodic position projections this approximate equivalence may be used to show that to produce significant reflection the projections must act at time spacing less than e where e is the energy scale of the initial state

asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance abstract there are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations if a solution is invariant under the scaling then it is called a self similar solution which is a candidate for the asymptotic profile of general solutions at large time in this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self similar solutions suitably

almost global solutions of semilinear wave equations with the critical exponent in high dimensions abstract we are interested in the almost global in time existence of classical solutions in the general theory for nonlinear wave equations all the three such cases are known to be sharp due to blow up results in the critical case for model equations however it is known that we have a possibility to get the global in time existence for two of them in low space dimensions if the nonlinear term is of derivatives of the unknown function and satisfies the so called null condition or non positive condition but another one for the quadratic term in four space dimensions is out of the case as the nonlinear term should include a square of the unknown function itself in this paper we get one more example guaranteeing the sharpness of the almost global in time existence in four space dimensions it is also the first example of the blow up of classical solutions for non single and indefinitely signed term in high dimensions such a term arises from the neglect of derivative loss factors in duhamel s formula for positive and single nonlinear term this fact may help us to describe a criterion to get the global in time existence in this critical situation

implicit b spline surface reconstruction this paper presents a fast and flexible curve and surface reconstruction technique based on implicit b spline this representation does not require any parameterization and it is locally supported this fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations this method is further accelerated to reduce the dimension to the active control lattice moreover the surface smoothness and user interaction are allowed for controlling the surface finally a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions the whole framework is very fast and efficient and can handle large cloud of points with very low computational cost the experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data

source solutions and asymptotic behavior in conservation laws abstract we study the uniqueness of the solutions to the scalar conservation law u t u x 0 when the initial datum is a finite measure the case of a dirac mass is particularly emphasized it is shown how it provides a description of the asymptotic behavior of the solutions initiated by an arbitrary integrable function this behavior is proved to depend on one parameter in the case when is odd while it depends on two when is convex

a new approach to quantum backflow we derive some rigorous results concerning the backflow operator introduced by bracken and melloy we show that it is linear bounded self adjoint and non compact thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator from the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant finally detailed position probability flow properties of a numerical approximation to the perhaps improper wavefunction of maximal backflow are displayed

well posedness for a model derived from an attraction repulsion chemotaxis system abstract in this paper we are interested in a model derived from an attraction repulsion chemotaxis system in high dimensions t u u 1 u v 2 u w x r n t 0 1 v v u x r n t 0 2 w w u x r n t 0 u x 0 u 0 x x r n with the parameters 1 0 2 0 1 0 2 0 and nonnegative initial data u 0 x l 1 r n l r n we prove that a global bounded solution exists when the repulsion prevails over the attraction in the sense of 1 1 moreover we give the smoothness of the solution and obtain its decay rates in w s p r n which coincide with the ones of the classical heat equation conversely when n 2 1 2 we prove that the finite time blow up may occur

an orientation inference framework for surface reconstruction from unorganized point clouds in this paper we present an orientation inference framework for reconstructing implicit surfaces from unoriented point clouds the proposed method starts from building a surface approximation hierarchy comprising of a set of unoriented local surfaces which are represented as a weighted combination of radial basis functions we formulate the determination of the globally consistent orientation as a graph optimization problem by treating the local implicit patches as nodes an energy function is defined to penalize inconsistent orientation changes by checking the sign consistency between neighboring local surfaces an optimal labeling of the graph nodes indicating the orientation of each local surface can thus be obtained by minimizing the total energy defined on the graph the local inference results are propagated over the model in a front propagation fashion to obtain the global solution the reconstructed surfaces are consolidated by a simple and effective inspection procedure to locate the erroneously fitted local surfaces a progressive reconstruction algorithm that iteratively includes more oriented points to improve the fitting accuracy and efficiently updates the rbf coefficients is proposed we demonstrate the performance of the proposed method by showing the surface reconstruction results on some real world 3 d data sets with comparison to those by using the previous methods

reconstructing surfaces by volumetric regularization using radial basis functions we present a new method of surface reconstruction that generates smooth and seamless models from sparse noisy nonuniform and low resolution range data data acquisition techniques from computer vision such as stereo range images and space carving produce 3d point sets that are imprecise and nonuniform when compared to laser or optical range scanners traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to vision based data sets our method constructs a 3d implicit surface formulated as a sum of weighted radial basis functions we achieve three primary advantages over existing algorithms 1 the implicit functions we construct estimate the surface well in regions where there is little data 2 the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate rather than exactly interpolate the data and 3 the reconstructed surface is locally detailed yet globally smooth because we use radial basis functions that achieve multiple orders of smoothness

matching 3 d anatomical surfaces with non rigid deformations using octree splines presents a new method for determining the minimal nonrigid deformation between two 3d surfaces such as those which describe anatomical structures in 3d medical images although the authors match surfaces they represent the deformation as a volumetric transformation their method performs a least squares minimization of the distance between the two surfaces of interest to quickly and accurately compute distances between points on the two surfaces the authors use a precomputed distance map represented using an octree spline whose resolution increases near the surface to quickly and robustly compute the deformation the authors use a second octree spline to model the deformation function the coarsest level of the deformation encodes the global e g affine transformation between the two surfaces while finer levels encode smooth local displacements which bring the two surfaces into closer registration the authors present experimental results on both synthetic and real 3d surfaces

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

a general surface approach to the integration of a set of range views this paper presents a new and general solution to the problem of range view integration the integration problem consists in computing a connected surface model from a set of registered range images acquired from different viewpoints the proposed method does not impose constraints on the topology of the observed surfaces the position of the viewpoints or the number of views that can be merged the integrated surface model is piecewise estimated by a set of triangulations modeling each canonical subset of the venn diagram of the set of range views the connection of these local models by constrained delaunay triangulations yields g non redundant surface triangulation describing all surface elements sampled by the set of range views experimental results show that the integration technique can be used to build connected surface models of free form objects no integrated models built from objects of such complexity have yet been reported in the literature it is assumed that accurate range views are available and that frame transformations between all pairs of views can be reliably computed

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

uc hierarchy and monodromy preserving deformation the uc hierarchy is an extension of the kp hierarchy which possesses not only an infinite set of positive time evolutions but also that of negative ones through a similarity reduction we derive from the uc hierarchy a class of the schlesinger systems including the garnier sys

the 3l algorithm for fitting implicit polynomial curves and surfaces to data we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials the power of these models is in their ability to represent nonstar complex shapes in two 2d and three dimensional 3d data to permit fast repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps to permit position invariant shape recognition based on new complete sets of euclidean and affine invariants and to permit fast stable single computation pose estimation the algorithm represents a significant advancement of implicit polynomial technology for four important reasons first it is orders of magnitude taster than existing fitting methods for implicit polynomial 2d curves and 3d surfaces and the algorithms for 2d and 3d are essentially the same second it has significantly better repeatability numerical stability and robustness than current methods in dealing with noisy deformed or missing data third it can easily fit polynomials of high such as 14th or 16th degree fourth additional linear constraints can be easily incorporated into the fitting process and general linear vector space concepts apply

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

asymptotic expansion of solutions to the drift diffusion equation with fractional dissipation abstract the initial value problem for the drift diffusion equation arising from the model of semiconductor device simulations is studied the dissipation on this equation is given by the fractional laplacian 2 large time behavior of solutions to the drift diffusion equation with 0 1 is discussed when 1 large time behavior of solutions is known however when 0 1 the perturbation methods used in the preceding works would not work in this paper the asymptotic expansion of solutions with high order is derived