edge location to subpixel values in digital imagery a new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented for one dimensional edge patterns an ideal edge is fit to the data by matching moments it is shown that the edge location is related to the so called christoffel numbers also presented is the study of the effect of additive noise on edge location the method is extended to include two dimensional edge patterns where a line equation is derived to locate an edge this in turn is compared with the standard hueckel edge operator an application of the new edge operator as an edge detector is also provided and is compared with sobel and hueckel edge detectors in presence and absence of noise

on mordell weil groups of isotrivial abelian varieties over function fields we show that the mordell weil rank of an isotrivial abelian variety with cyclic holonomy depends only on the fundamental group of the complement to the discriminant provided the discriminant has singularities in cm class introduced here this class of singularities includes all unibranched plane curves singularities as a corollary we describe a family of simple jacobians over the field of rational functions in two variables for which the mordell weil rank is arbitrarily large

new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

generalized multiple riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations in this paper based on symbolic computation and the idea of rational expansion method a generalized multiple riccati equations rational expansion method gmrere is proposed to uniformly construct a series of exact complexiton solutions for nonlinear partial differential equations compared with most existing tanh function methods and rational expansion methods the proposed method not only recovers some known solutions but also finds some new and general complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

jacobians with group actions and rational idempotents abstract the object of this paper is to prove some general results about rational idempotents for a finite group g and deduce from them geometric information about the components that appear in the decomposition of the jacobian variety of a curve with g action we give an algorithm to find explicit primitive rational idempotents for any g as well as for rational projectors invariant under any given subgroup these explicit constructions allow geometric descriptions of the factors appearing in the decomposition of a jacobian with group action from them we deduce the decomposition of any prym or jacobian variety of an intermediate cover in the case of a jacobian with g action in particular we give a necessary and sufficient condition for a prym variety of an intermediate cover to be such a factor

abelian surfaces of type 1 4 pair dl d2 is called the type of l according to riemann r o c h h did2 and l induces a rational map cpl a pn d2 t we want to study this map in the special case dl d2 1 4 let us first recollect what is known in the other cases for d 1 3 tp l is an embedding by a classical theorem of lefschetz see m for da 2 cpl is an embedding if and only if d2 2 and a l is not of the form el x e2 p li with elliptic curves e 1 and e 2 and line bundles l on e i see l n suppose now dl 1 the complete linear system ill has base components if and only if a l et x e2 p li as above we assume that a l is not a product of euiptic curves since it is easy to work out the map q l in the exceptional case for d2 2 ill has exactly 4 base points blowing up we get a morphism pt with general fibre a smooth curve of genus 3 see b if d2 3 ill is base point free and we get a morphism pz a p 1if d2 3 pl a p2 is a 6 1 covering ramified in a curve of degree 18 if de 4 there is a cyclic covering

finite linear groups lattices and products of elliptic curves let v be a finite dimensional complex linear space and g an irreducible finite subgroup of gl v for a g invariant lattice in v of maximal rank we describe the structure of complex torus v

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

stochastic exact solutions of the wick type stochastic nls equation based upon the hermite transformation and the extended sub equation expansion method soliton like solutions of the stochastic schrodinger equation in the white noise environment are obtained via maple

mdpe a very robust estimator for model fitting and range image segmentation in this paper we propose a novel and highly robust estimator called mdpe1 maximum density power estimator this estimator applies nonparametric density estimation and density gradient estimation techniques in parametric estimation model fitting mdpe optimizes an objective function that measures more than just the size of the residuals both the density distribution of data points in residual space and the size of the residual corresponding to the local maximum of the density distribution are considered as important characteristics in our objective function mdpe can tolerate more than 85 outliers compared with several other recently proposed similar estimators mdpe has a higher robustness to outliers and less error variance we also present a new range image segmentation algorithm based on a modified version of the mdpe quick mdpe and its performance is compared to several other segmentation methods segmentation requires more than a simple minded application of an estimator no matter how good that estimator is our segmentation algorithm overcomes several difficulties faced with applying a statistical estimator to this task

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

idempotent relations and the conjecture of birch and swinnerton dyer this is a special case of the main theorem from this 1 follows immediately by using the results of milne 9 a secondary aim of this paper is to introduce twisted idempotent relations which generalize the idempotent relations of kani 5 and kani rosen 6 we show how to use such relations to obtain similar results involving twists of abelian varieties cf main theorem which enable us to give some interesting applications cf theorem 11 and corollaries 12 14

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

singularities of the prym theta divisor for the jacobian of a curve the riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve this paper proves an analogous theorem for prym varieties applications of this theorem to cubic threefolds and prym varieties of dimension five are also considered

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

two dimensional polar harmonic transforms for invariant image representation this paper introduces a set of 2d transforms based on a set of orthogonal projection bases to generate a set of features which are invariant to rotation we call these transforms polar harmonic transforms phts unlike the well known zernike and pseudo zernike moments the kernel computation of phts is extremely simple and has no numerical stability issue whatsoever this implies that phts encompass the orthogonality and invariance advantages of zernike and pseudo zernike moments but are free from their inherent limitations this also means that phts are well suited for application where maximal discriminant information is needed furthermore phts make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application

theta duality on prym varieties and a torelli theorem let c c be an unramified double covering of irreducible smooth curves and let p be the attached prym variety we prove the schemetheoretic theta dual equalities in the prym variety t c v 2 and t v 2 c where v 2 is the brill noether locus of p associated to considered by welters as an application we prove a torelli theorem analogous to the fact that the symmetric product d g of a curve d of genus g determines the curve

approximate solution for system of differential difference equations by means of the homotopy analysis method abstract in this paper the homotopy analysis method is successfully applied to solve approximate solutions of the differential difference system the solution of another relativistic toda lattice system is considered comparisons made between the results of the proposed method and exact solutions reveal that the homotopy analysis method is very effective in solving differential difference system

hyperelliptic curves on 1 4 polarised abelian surfaces we investigate the number and the geometry of smooth hyperelliptic curves on a general complex abelian surface we give a short proof for the known fact the only possibilities of genera of such curves are 2 3 4 and 5 then we focus on the genus five case we prove that up to translation there is a unique hyperelliptic curve in the linear system of a general 1 4 polarised abelian surface moreover the curve is invariant with respect to a subgroup of translations isomorphic to the klein group our proof of the existence of hyperelliptic curves on general 1 4 polarised abelian surfaces is different from that in the recent paper 10 we give the decomposition of the jacobian of such a curve into abelian subvarieties displaying jacobians of quotient curves and prym varieties motivated by the construction we prove the statement every etale klein covering of a hyperelliptic curve is a hyperelliptic curve provided that the group of 2 torsion points defining the covering is non isotropic with respect to the weil pairing and every element of this group can be written as a difference of two weierstrass points

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

fast and accurate method for high order zernike moments computation abstract zernike moments zms which belong to a class of circularly orthogonal rotation invariant moments are very useful image descriptors for various image processing applications they however suffer from various errors such as discretization error geometric error and numerical integration error in this paper we present an approach for their computation which reduces geometric error and numerical integration error geometric error is reduced by performing exact mapping of a square grid domain into a circular grid by using both the square and arc grids numerical integration error is reduced by resorting to gaussian numerical integration over the square and arc grids it is observed that the contribution of numerical integration error to the total error is much more than the geometric error the effect of these two errors is more significant in small images as compared to large images the use of numerical integration however enhances the time complexity this problem is resolved by using recursive algorithms for the computation of radial polynomials 8 way symmetry of radial polynomials and 8 way symmetry anti symmetry of angular part of the kernel function exhaustive experiments on synthetic and real images are performed to demonstrate the effectiveness of the proposed approach

robust optical flow estimation using semi invariant local features this paper presents a robust algorithm for computation of 2 d optical flow using the principle of conservation of a set of invariant local features that are representatives of local gray level properties in an image specifically a set of rotation invariant local orthogonal zernike moments is used as invariant features these are inherently integral based features and therefore are expected to be robust against possible variations of intensity values that may occur over a sequence of images due to sensor noise varying illumination etc the 2 d local optical flow field is obtained using singular value decomposition of an overdetermined set of linear equations of velocity field components resulting from the principle of conservation of invariant features in a small neighborhood the proposed moment based approach is compared with two existing optical flow techniques experimental results with synthetic as well as real sequences are presented to demonstrate the overall robustness of the proposed approach

recovering of curves with involution by extended prym data the classical torelli theorem states that every smooth projective algebraic curve x is determined uniquely up to isomorphism by its principally polarized jacobian j x 0 in this paper we consider curves c with involution without fixed points a c c we let c c tr and denote by n c c the factor map one associates the principally polarized prym variety p where p p c a 1 tr d t and e is algebraically equivalent to 23 the natural question whether the prym variety determines uniquely the pair c tr up to isomorphism has negative answer in general if the genus g of c is 7 for some special loci of curves e g for hyperelliptic c the problem of spotting the pairs c rr which are not determined uniquely by the prym variety is still open some partial results have been obtained in f s k dol do2 del de2 n v in this paper we propose an extension of the prym data p 3 and prove that it determines uniquely up to isomorphism any pair c tr for g 2 our extension originates from the following observation consider the case of c of genus 1 here the involution is a translation t by some point p of order 2 in j c notice that 0 ker nm j c j c the prym variety is equal to 0 there is a classically known data which determines uniquely the pair c tj up to isomorphism see e g m3 c namely one can always represent j c as c z z where z belongs to the upper half plane so that

a new korteweg de vries equation based sub equation method and its application to the 2 1 dimensional korteweg de vries equation with the help of the symbolic computation system maple we present korteweg de vries equation based sub equation method being concise and straightforward it is applied to the 2 1 dimensional korteweg de vries equation it is shown that n soliton solution of the 2 1 dimensional korteweg de vries equation can be found by this new method the method can be applied to other nonlinear partial differential equations in mathematical physics

formal variable separation approach for nonintegrable models using a formal variable separation approach a nonlinear partial differential equation can be solved by solving ordinary different equations or even algebraic equations taking the kdv burgers and modified kdv burgers equations with background interaction as simple examples some explicit solitary wave solutions which are induced by background source and nonlinearity or dispersion are obtained

precision edge contrast and orientation estimation the contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive gaussian noise the test image is an ideal step edge that has been sampled with a square aperture grid the effects of subpixel translations and rotations of the edge on the performance of the operators are studied it is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels methods with improved results are presented for sobel angle estimates and the nevatia babu operator and theoretical noise performance evaluations are also provided an edge operator based on two dimensional spatial moments is presented all methods are compared according to worst case and rms error in an ideal noiseless situation and rms error under various noise levels

on jacobians with group action and coverings let s be a compact riemann surface and let h be a finite group it is known that if h acts on s then there is a h equivariant isogeny decomposition of the jacobian variety js of s called the group algebra decomposition of js with respect to h if s 1 rightarrow s 2 is a regular covering map then it is also known that the group algebra decomposition of js 1 induces an isogeny decomposition of js 2 in this article we deal with the converse situation more precisely we prove that the group algebra decomposition can be lifted under regular covering maps under appropriate conditions

generalized riccati equation rational expansion method and its application by directly extending the riccati equation rational expansion method a new method is developed for constructing a series of exact analytical solutions of an averaged dispersion managed fiber system equation adme including some new rational formal soliton like solutions triangle like solutions and rational solutions

a note on large automorphism groups of compact riemann surfaces abstract belolipetsky and jones classified those compact riemann surfaces of genus g admitting a large group of automorphisms of order g 1 for each 6 under the assumption that g 1 is a prime number in this article we study the remaining large cases namely we classify riemann surfaces admitting 5 g 1 and 6 g 1 automorphisms with g 1 a prime number as a consequence we obtain the classification of riemann surfaces admitting a group of automorphisms of order 3 g 1 with g 1 a prime number we also provide isogeny decompositions of their jacobian varieties

similarity reductions of the kp equation by a direct method basing on a direct method developed by clarkson and kruskal 1989 the kadomtsev petviashvili kp equation has been reduced to three types of 1 1 dimensional partial differential equations which are equivalent to the three types of the similarity reduction equations obtained by the classical lie approach but with different independent variables more arbitrary functions which have been missed by the classical lie approach have been included in the solutions of the kp equation for instance the third type of reduction obtained by the direct method can be divided into three subcases and the third type of solution of the kp equation obtained by the classical lie approach is only a special case of one subcase of the authors results

infinite dimensional symmetry algebras and an infinite number of conserved quantities of the 2 1 dimensional davey stewartson equation an infinite dimensional symmetry algebra of the davey stewartson equation is explicitly presented it is shown that this algebra is a gauge generalization of the symmetry transformation for the schrodinger equation and that the virasoro algebra appears as the subalgebra an infinite number of conserved quantities associated with the transformations are also obtained

subpixel measurements using a moment based edge operator recent results in precision measurements using computer vision are presented an edge operator based on two dimensional spatial moments is given the operator can be implemented for virtually any size of window and has been shown to locate edges in digitized images to a twentieth of a pixel this accuracy is unaffected by additive or multiplicative changes to the data values the precision is achieved by correcting for many of the deterministic errors caused by nonideal edge profiles using a lookup table to correct the original estimates of edge orientation and location this table is generated using a synthesized edge which is located at various subpixel locations and various orientations the operator is extended to accommodate nonideal edge profiles and rectangularly sampled pixels the technique is applied to the measurement of imaged machined metal parts theoretical and experimental noise analyses show that the operator has relatively small bias in the presence of noise

on relations between jacobians of certain modular curves abstract we confirm a conjecture of l merel h darmon and l merel j reine angew math 490 1997 81 100 describing a certain relation between the jacobians of various quotients of x p in terms of specific correspondences the method of proof involves reducing this conjecture to a question about certain z gl 2 f p module homomorphisms which is in turn answered by exhibiting some peculiar relations in a double coset algebra

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

finding edges in noisy scenes edge detection in the presence of noise is a well known problem this paper examines an applications motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets roc curves are used to compare this method with other well known edge detection operators with favorable results a theoretical argument is presented that favors lmmse filtering over median filtering in extremely noisy scenes simulated results of the research are presented

prym map and second gaussian map for prym canonical line bundles abstract we show that the second fundamental form of the prym map lifts the second gaussian map a of the prym canonical bundle we prove by degeneration to binary curves that a is surjective for the general point c a of r g for g 20

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

arithmetic of abelian varieties in artin schreier extensions we study abelian varieties defined over function fields of curves in positive characteristic p focusing on their arithmetic within the system of artin schreier extensions first we prove that the l function of such an abelian variety vanishes to high order at the center point of its functional equation under a parity condition on the conductor second we develop an artin schreier variant of a construction of berger this yields a new class of jacobians over function fields for which the birch and swinnerton dyer con jecture holds third we give a formula for the rank of the mordell weil groups of these jacobians in terms of the geometry of their fibers of bad reduction and homomorphisms between jacobians of auxiliary artin schreier curves we illustrate these theorems by computing the rank for explicit examples of jaco bians of arbitrary dimension g exhibiting jacobians with bounded rank and others with unbounded rank in the tower of artin schreier extensions fi nally we compute the mordell weil lattices of an isotrivial elliptic curve and a family of non isotrivial elliptic curves the latter exhibits an exotic phenom enon whereby the angles between lattice vectors are related to point counts on elliptic curves over finite fields our methods also yield new results about supersingular factors of jacobians of artin schreier curves msc2000 primary 11g10 11g40 14g05 secondary 11g05 11g30 14h25 14j20 14k15

image field categorization and edge corner detection from gradient covariance edges corners and vertices in an image correspond to 1d one dimensional and 2d discontinuities in the intensity surface of the underlying scene ridges and peaks correspond to 1d and 2d extrema in it all of them can be characterized by the distribution of gradients particularly by the dimensionality of it the approach to image field categorization here is to construct a covariance matrix of the gradient vector in each small window and apply the canonical correlation analysis to it schwarz s inequality on the matrix determinant and the related differential equation is the key to this analysis we obtain two operators p sub eg and q sub eg to categorize the image field into a unidirectionally varying region univar an omidirectionally varying region omnivar and a nonvarying region we investigate the conditions under which their absolute maximum response i e p sub eg 1 and q sub eg 1 occurs in the small window and show that they are respectively the desired 1d and 2d discontinuities extrema and omnivar is in many cases a 1d pattern in polar coordinates this leads to an algorithm to obtain further classification and accurate localization of them into edges ridges peaks corners and vertices through detailed analysis in the informative varying axis of them we examined and compared the performance of the operators and the localization algorithm on various types of images and various noise levels the results indicate that the proposed method is superior with respect to stability localization and resolution

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

algebraic cycles on prym varieties this article proposes a generalization of tautological rings introduced by beauville and moonen for jacobians the main result is that under certain hypotheses the special subvarieties of prym varieties are algebraically equivalent and their classes belong to the tautological ring

on a numerical characterization of non simple principally polarized abelian varieties to every abelian subvariety of a principally polarized abelian variety a mathcal l we canonically associate a numerical class in the neron severi group of a we prove that these classes are characterized by their intersection numbers with mathcal l moreover the cycle class induced by an abelian subvariety in the chow ring of a modulo algebraic equivalence can be described in terms of its numerical divisor class over the field of complex numbers this correspondence gives way to an explicit description of the coarse moduli space that parametrizes non simple principally polarized abelian varieties with a fixed numerical class

adaptive pseudo dilation for gestalt edge grouping and contour detection we consider the problem of detecting object contours in natural images in many cases local luminance changes turn out to be stronger in textured areas than on object contours therefore local edge features which only look at a small neighborhood of each pixel cannot be reliable indicators of the presence of a contour and some global analysis is needed we introduce a new morphological operator called adaptive pseudo dilation apd which uses context dependent structuring elements in order to identify long curvilinear structure in the edge map we show that grouping edge pixels as the connected components of the output of apd results in a good agreement with the gestalt law of good continuation the novelty of this operator is that dilation is limited to the voronoi cell of each edge pixel an efficient implementation of apd is presented the grouping algorithm is then embedded in a multithreshold contour detector at each threshold level small groups of edges are removed and contours are completed by means of a generalized reconstruction from markers the use of different thresholds makes the algorithm much less sensitive to the values of the input parameters both qualitative and quantitative comparison with existing approaches prove the superiority of the proposed contour detector in terms of larger amount of suppressed texture and more effective detection of low contrast contours

a family of prym tyurin varieties of exponent 3 abstract we investigate a family of correspondences associated to etale coverings of degree 3 of hyperelliptic curves they lead to prym tyurin varieties of exponent 3 we identify these varieties and derive some consequences

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

construction scheme for discrete miura transformations a direct and elementary scheme for the construction of miura type transformations and discrete differential equations related to them scalar and vector is presented the scheme is illustrated using as examples the volterra and toda models a discrete differential analogue of the calogero degasperis equation is discussed in detail this example is used to show how to construct conservation laws higher symmetries and solutions for an equation obtained with the help of the scheme

detection of composite edges the paper presents a new parametric model based approach to high precision composite edge detection using orthogonal zernike moment based operators it deals with two types of composite edges a generalized step and b pulse staircase edges a 2 d generalized step edge is modeled in terms of five parameters two gradients on two sides of the edge the distance from the center of the candidate pixel the orientation of the edge and the step size at the location of the edge a 2 d pulse staircase edge is modeled in terms of two steps located at two positions within the mask and the edge orientation a pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity two complex and two real zernike moment based masks are designed to determine parameters of both the 2 d edge models for a given edge model estimated parameter values at a point are used to detect the presence or absence of that type of edge extensive noise analysis is performed to demonstrate the robustness of the proposed operators experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment based step edge detection technique and canny s 1986 edge detector

analytical and numerical aspects of certain nonlinear evolution equations 1v numerical modified korteweg de vries equation various numerical methods are used in order to approximate the korteweg de vries equation namely i zabusky kruskal scheme ii hopscotch method iii a scheme due to goda iv a proposed local scheme v a proposed global scheme vi a scheme suggested by kruskal vii split step fourier method by tappert viii an improved split step fourier method and ix pseudospectral method by fornberg and whitham comparisons between our proposed scheme which is developed using notions of the inverse scattering transform and the other utilized schemes are obtained

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave