approximation of the levy feller advection dispersion process by random walk and finite difference method in this paper we present a random walk model for approximating a levy feller advection dispersion process governed by the levy feller advection dispersion differential equation lfade we show that the random walk model converges to lfade by use of a properly scaled transition to vanishing space and time steps we propose an explicit finite difference approximation efda for lfade resulting from the grunwald letnikov discretization of fractional derivatives as a result of the interpretation of the random walk model the stability and convergence of efda for lfade in a bounded domain are discussed finally some numerical examples are presented to show the application of the present technique

finite difference spectral approximations for the fractional cable equation fujian nsf s0750017 national nsf of china 10531080 ministry of education of china 973 high performance scientific computation research program 2005cb321703

fitting parameterized three dimensional models to images model based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3 d model to matching 2 d image features the author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation variable dimensions or surface deformations numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters the levenberg marquardt method is used to always ensure convergence of the solution these techniques allow model based vision to be used for a much wider class of problems than was possible with previous methods their application is demonstrated for tracking the motion of curved parameterized objects

the period function of reversible quadratic centers abstract in this paper we investigate the bifurcation diagram of the period function associated to a family of reversible quadratic centers namely the dehomogenized loud s systems the local bifurcation diagram of the period function at the center is fully understood using the results of chicone and jacobs c chicone m jacobs bifurcation of critical periods for plane vector fields trans amer math soc 312 1989 433 486 most of the present paper deals with the local bifurcation diagram at the polycycle that bounds the period annulus of the center the techniques that we use here are different from the ones in c chicone m jacobs bifurcation of critical periods for plane vector fields trans amer math soc 312 1989 433 486 because while the period function extends analytically at the center it has no smooth extension to the polycycle at best one can hope that it has some asymptotic expansion another major difficulty is that the asymptotic development has to be uniform with respect to the parameters in order to prove that a parameter is not a bifurcation value we study also the bifurcations in the interior of the period annulus and we show that there exist three germs of curves in the parameter space that correspond to this type of bifurcation moreover we determine some regions in the parameter space for which the corresponding period function has at least one or two critical periods finally we propose a complete conjectural bifurcation diagram of the period function of the dehomogenized loud s systems our results can also be viewed as a contribution to the proof of chicone s conjecture c chicone review in mathscinet ref 94h 58072

dulac time of a resonant saddle in the loud family abstract we study the critical periods of the loud family of quadratic centers we give the first terms of the asymptotic expansion of the period function and we conclude that no bifurcation occurs for certain values of the parameters this result contributes to complete the bifurcation diagram of critical periods in the loud family

on the upper bound of the criticality of potential systems at the outer boundary using the roussarie ecalle compensator abstract this paper is concerned with the study of the criticality of families of planar centers more precisely we study sufficient conditions to bound the number of critical periodic orbits that bifurcate from the outer boundary of the period annulus of potential centers in the recent years the new approach of embedding the derivative of the period function into a collection of functions that form a chebyshev system near the outer boundary has shown to be fruitful in this issue in this work we tackle with a remaining case that was not taken into account in the previous studies in which the roussarie ecalle compensator plays an essential role the theoretical results we develop are applied to study the bifurcation diagram of the period function of two different families of centers the power like family x x q x p p q r with p q and the family of dehomogenized loud s centers

an algebraic method for detection and recognition of polyhedral objects from a single image abstract this paper proposes an algorithm to recognize rotated scaled or overlapping polyhedral objects using only one orthographic projection the procedure is not based on the numerical solution of nonlinear equations and does not require any a priori knowledge it is an algebraic method for testing whether a cluster of edges and vertices in a line drawing correspond to an orthographic view of a given 3d model it has the advantage of being based on simple algebraic equations which are easy to solve and do not require time consuming numerical procedures

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

a numerical method for a partial integro differential equation a method is considered for the integration in time of a partial integro differential equation the discretization technique employed is patterned after an idea of ch lubich error bounds are derived for both smooth and nonsmooth initial data

asymptotic expansion of the dulac map and time for unfoldings of hyperbolic saddles local setting abstract in this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle we give a structure theorem for the asymptotic expansion of the local dulac time as well as the local dulac map with the remainder uniformly flat with respect to the unfolding parameters here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used the principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm the so called roussarie ecalle compensator especial attention is paid to the remainder s properties concerning the derivation with respect to the unfolding parameters

on the period function of reversible quadratic centers with their orbits inside quartics abstract this paper is concerned with the monotonicity of the period function for a class of reversible quadratic centers with their orbits inside quartics it is proved that such a system has a period function with at most one critical point

on the return time function around monodromic polycycles abstract in this paper we study the period function of centers of planar polynomial differential systems with a convenient compactification of the phase portrait the boundary of the period annulus of the center has two connected components the center itself and a polycycle we are interested in the behaviour of the period function near the polycycle the desingularization of its critical points gives rise to a new polycycle monodromic as well with hyperbolic saddles or saddle nodes at the vertices in this paper we compute the first terms in the asymptotic development of the time function around any orbitally linearizable saddle that may come from this desingularization process in addition we use these developments to study the bifurcation diagram of the period function of the dehomogenized loud s centers more generally the tools developed here can be used to study the return time function around a monodromic polycycle this work is a continuation of the results in p mardesic d marin j villadelprat on the time function of the dulac map for families of meromorphic vector fields nonlinearity 16 2003 855 881 p mardesic d marin j villadelprat the period function of reversible quadratic centers j differential equations 224 2006 120 171

determination of the attitude of 3d objects from a single perspective view a method for finding analytical solutions to the problem of determining the attitude of a 3d object in space from a single perspective image is presented its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model and on the search for the model attitude consistent with these projections the geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight degree equation in the general case using simple logical rules it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3d objects because few admissible hypotheses are retained from the interpolation of the three line segments line matching by the prediction verification procedure is thus less complex

3d euclidean versus 2d non euclidean two approaches to 3d recovery from images methods of 3d recovery in computer vision for computing the shape and motion of an object from projected images when an object model is available are classified into two types the 3d euclidean approach which is based on geometrical constraints in 3d euclidean space and the 2d non euclidean space implications of these two approaches are discussed and some illustrating examples are presented

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

alternating direction implicit euler method for the two dimensional fractional evolution equation in this paper we present a fast and efficient numerical method to solve a two dimensional fractional evolution equation on a finite domain this numerical method combines the alternating direction implicit adi approach with the second order difference quotient in space the backward euler in time and order one convolution quadrature approximating the integral term by using the discrete energy method we prove that the adi scheme is unconditionally stable and the numerical solution converges to the exact one with order o k h x 2 h y 2 where k is the temporal grid size and h x h y are spatial grid sizes in the x and y directions respectively two numerical examples with known exact solution are also presented and the behavior of the error is analyzed to verify the order of convergence of the adi euler method

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

a remark on the period of the periodic solution in the lotka volterra system abstract an important consideration in the nonlinear predator prey problem of lotka volterra type is the determination of the period this paper gives a general expression for the period in terms of the given parameters in the lotka volterra system we also discuss the qualitative behavior of the period related to the energy level of the lotka volterra system

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

the criticality of centers of potential systems at the outer boundary abstract the number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied we call this number the criticality at the outer boundary our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1 we apply them to study the bifurcation diagram of the period function of x y x x 1 p x 1 q y with q p this family was previously studied for q 1 by y miyamoto and k yagasaki

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

compact alternating direction implicit scheme for the two dimensional fractional diffusion wave equation in this paper we consider the numerical method for solving the two dimensional fractional diffusion wave equation with a time fractional derivative of order alpha 1 alpha 2 a difference scheme combining the compact difference approach for spatial discretization and the alternating direction implicit adi method in the time stepping is proposed and analyzed the unconditional stability and h 1 norm convergence of the scheme are proved rigorously the convergence order is mathcal o tau 3 alpha h 1 4 h 4 2 where tau is the temporal grid size and h 1 h 2 are spatial grid sizes in the x and y directions respectively in addition a crank nicolson adi scheme is presented and the corresponding error estimates are also established numerical results are presented to support our theoretical analysis and indicate that the compact adi scheme reduces the storage requirement and cpu time successfully

a criticality result for polycycles in a family of quadratic reversible centers abstract we consider the family of dehomogenized loud s centers x y x 1 x x d x 2 f y 2 y where d f r 2 and we study the number of critical periodic orbits that emerge or disappear from the polycycle at the boundary of the period annulus this number is defined exactly the same way as the well known notion of cyclicity of a limit periodic set and we call it criticality the previous results on the issue for the family x r 2 distinguish between parameters with criticality equal to zero regular parameters and those with criticality greater than zero bifurcation parameters a challenging problem not tackled so far is the computation of the criticality of the bifurcation parameters which form a set b of codimension 1 in r 2 in the present paper we succeed in proving that a subset of b has criticality equal to one

numerical methods for the variable order fractional advection diffusion equation with a nonlinear source term in this paper we consider a variable order fractional advection diffusion equation with a nonlinear source term on a finite domain explicit and implicit euler approximations for the equation are proposed stability and convergence of the methods are discussed moveover we also present a fractional method of lines a matrix transfer technique and an extrapolation method for the equation some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis

the period in the lotka volterra system is monotonic abstract periodic solutions in a class of hamiltonian systems with one degree of freedom containing the lotka volterra system are considered their period is represented as an integral appropriate for numerical evaluation as well as for theoretical investigations the monotonicity of the period in the lotka volterra system follows as a simple consequence

model based recognition and positioning of polyhedra using intensity guided range sensing and interpretation in 3 d space abstract this paper presents a design of 3 d multi sensory visual and ranging system capable of identifying and locating polyhedral objects in six degrees of spatial freedom due to differences in sensor characteristics e g the fast data acquisition in intensity domain and the abundance of information inherent in range domain sensors should operate in a cooperative manner to increase system efficiency and to yield information otherwise unavailable or hard to obtain from any single sensor the adopted strategy of intensity guided range sensing firstly extracts features e g the line drawing and the control points from intensity images and then uses them as a guide to selectively sense ranges through the interfusion of both types of information 3 d object description in terms of a relational graph structure is thus constructed for recognition and positioning purposes to identify the object interpretation tree search in 3 d space is applied to the matching between the constructed relational graph and those stored in database since high level primitives such as faces derived from intensity and range informations are utilized for interpretation or matching the search space can be significantly reduced finally a non iterative method based on the quaternion technique is adopted to solve the transformation between sensor and model coordinates for further robotic applications

unfoldings of saddle nodes and their dulac time in this paper we study unfoldings of saddle nodes and their dulac time by unfolding a saddle node saddles and nodes appear in the first result theorem a we give a uniform asymptotic expansion of the trajectories arriving at the node uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle node and a parameter belonging to a space of functions in the second part we apply this first result for proving a regularity result theorem b on the dulac time time of dulac map of an unfolding of a saddle node this result is a building block in the study of bifurcations of critical periods in a neighborhood of a polycycle finally we apply theorem a theorem b to the study of critical periods of the loud family of quadratic centers and we prove that no bifurcation occurs for certain values of the parameters theorem c

model matching in robot vision by subgraph isomorphism abstract in this paper we describe a systematic method for three dimensional 3d model matching in robot vision by using subgraph matching techniques 3d objects are modeled as attributed graphs called model graphs where the nodes correspond to object vertices and the branches correspond to object edges the 2d projections of a 3d object are modeled as subgraph isomorphisms of the object s model graph recognition is done by searching whether a 2d projection graph constructed from the 2d projection of a 3d object is a subgraph isomorphism of the object s model graph

centennial history of hilbert s 16th problem the second part of hilbert s 16th problem deals with polynomial differential equations in the plane it remains unsolved even for quadratic polynomials there were several attempts to solve it that failed yet the problem inspired significant progress in the geometric theory of planar differential equations as well as bifurcation theory normal forms foliations and some topics in algebraic geometry the dramatic history of the problem as well as related developments are presented below 1 the problem and its counterparts what may be said about the number and location of limit cycles of a planar polynomial vector field of degree n the limit cycle is an isolated closed orbit of a vector field this second part of hilbert s 16th problem appears to be one of the most persistent in the famous hilbert list h second only to the riemann function conjecture traditionally hilbert s question is split into three each one requiring a stronger answer problem 1 is it true that a planar polynomial vector field has but a finite number of limit cycles problem 2 is it true that the number of limit cycles of a planar polynomial vector field is bounded by a constant depending on the degree of the polynomials only the bound on the number of limit cycles in problem 2 is denoted by h n and known as the hilbert number linear vector fields have no limit cycles hence h 1 0 it is still unknown whether or not h 2 exists problem 3 give an upper bound for h n a solution to any of these problems implies a solution for the previous ones only the first problem is solved now the positive answer was established in e92 i91 there are analytic counterparts of problems 1 and 2 received by the editors december 2001 2000 mathematics subject classification primary 34cxx 34mxx 37f75

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions