Results 1  10
of
45
Mahler's Measure and Special Values of Lfunctions
, 1998
"... this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula, ..."
Abstract

Cited by 63 (1 self)
 Add to MetaCart
this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula,
Differential Invariants for Color Images
, 1998
"... We present in this paper a new method for matching points in stereoscopic color images, based on color differential invariants involving only first order derivatives of images. Our method is able to match robustly the images even if they present important transformations like rotation, range of v ..."
Abstract

Cited by 27 (5 self)
 Add to MetaCart
We present in this paper a new method for matching points in stereoscopic color images, based on color differential invariants involving only first order derivatives of images. Our method is able to match robustly the images even if they present important transformations like rotation, range of viewpoint and change of intensity between each other. We present here a generalization of a gray level corner detector to the case of color images. This detector is robust and allows us to extract point primitives in stereoscopic images to be matched together, only with first order derivatives. We then describe these points with our set of local color invariants, and we propose a simple and efficient scheme for matching them. The robustness of the matching against local deformations is shown using deformations of single color images, then our stereo matching scheme is evaluated using true stereo color images with viewpoint variations. The results obtained on complex scenes clearly show...
Symmetries of Polynomials
 J. Symb. Comp
"... New algorithms for determining discrete and continuous symmetries of polynomials  also known as binary forms in classical invariant theory  are presented. Implementations in Mathematica and Maple are discussed and compared. The results are based on a new, comprehensive theory of moving frames ..."
Abstract

Cited by 21 (15 self)
 Add to MetaCart
New algorithms for determining discrete and continuous symmetries of polynomials  also known as binary forms in classical invariant theory  are presented. Implementations in Mathematica and Maple are discussed and compared. The results are based on a new, comprehensive theory of moving frames that completely characterizes the equivalence and symmetry properties of submanifolds under general Lie group actions. This work was partially supported by NSF Grant DMS 9803154. 1 Introduction. The purpose of this paper is to explain the detailed implementation of a new algorithm for determining the symmetries of polynomials (binary forms). The method was first described in the second author's new book [24], and the present paper adds details and refinements. We shall demonstrate that the symmetry group of both real and complex binary forms can be completely determined by solving two simultaneous bivariate polynomial equations, which are based on two fundamental covariants of the for...
Classical Invariants and 2descent on Elliptic Curves
 JOURNAL OF SYMBOLIC COMPUTATION
, 1996
"... ..."
Reduction Of Binary Cubic And Quartic Forms
, 1999
"... A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four with integer coefficients. The resulting coefficient bounds simplify and improve on those in the literature, particularly in the case of negative discriminant. Applications include systematic enumera ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four with integer coefficients. The resulting coefficient bounds simplify and improve on those in the literature, particularly in the case of negative discriminant. Applications include systematic enumeration of cubic number fields, and 2descent on elliptic curves defined over Q. Remarks are given concerning the extension of these results to forms defined over number fields. This paper has now appeared in the LMS Journal of Computation and Mathematics, Volume 2, pages 6292, and the full published version, with hyperlinks etc., is available online (to subscribers) at http://www.lms.ac.uk/jcm/2/lms98007/. This version contains the complete text of the published version in a very similar format. 1. Introduction Reduction theory for polynomials has a long history and numerous applications, some of which have grown considerably in importance in recent years with the growth of algorithmic an...
Graph method for generating affine moment invariants
 IN PROC. INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION
, 2004
"... A general method of systematic derivation of affine moment invariants of any weights and orders is introduced. Each invariant is expressed by its generating graph. Techniques for elimination of reducible invariants and dependent invariants are discussed. This approach is illustrated on the set of al ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
A general method of systematic derivation of affine moment invariants of any weights and orders is introduced. Each invariant is expressed by its generating graph. Techniques for elimination of reducible invariants and dependent invariants are discussed. This approach is illustrated on the set of all affine moment invariants up to the weight ten.
Symmetric Powers of Modular Representations, Hilbert Series and Degree Bounds
, 1999
"... Let G = Zp be a cyclic group of prime order p with a representation G ! GL(V ) over a field K of characteristic p. In 1976, Almkvist and Fossum gave formulas for the decomposition of the symmetric powers of V in the case that V is indecomposable. From these they derived formulas for the Hilbert seri ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
Let G = Zp be a cyclic group of prime order p with a representation G ! GL(V ) over a field K of characteristic p. In 1976, Almkvist and Fossum gave formulas for the decomposition of the symmetric powers of V in the case that V is indecomposable. From these they derived formulas for the Hilbert series of the invariant ring K[V ] G . Following Almkvist and Fossum in broad outline, we start by giving a shorter, selfcontained proof of their results. We extend their work to modules which are not necessarily indecomposable. We also obtain formulas which give generating functions encoding the decompositions of all symmetric powers of V into indecomposables. Our results generalize to groups of the type Zp \Theta H with jHj coprime to p. Moreover, we prove that for any finite group G whose order is divisible by p but not by p 2 , the invariant ring K[V ] G is generated by homogeneous invariants of degrees at most dim(V ) \Delta (jGj \Gamma 1). Contents Introduction 1 1 Symmetrization ...
On the Combinatorics of Cumulants
, 2000
"... this paper, we shall employ the full freedom of Umbral Calculus to study cumulants. Umbral Calculus leads to various formulae for the cumulant sequence, each of which reveals one portion of the secret encoded in cumulants. Through these formulae, cumulants are connected to familiar combinatorial obj ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
this paper, we shall employ the full freedom of Umbral Calculus to study cumulants. Umbral Calculus leads to various formulae for the cumulant sequence, each of which reveals one portion of the secret encoded in cumulants. Through these formulae, cumulants are connected to familiar combinatorial objects such as binomial sequences and symmetric functions. In return, the study of cumulants has stimulated new extension of the existing theory of Umbral Calculus. For instance, for the first time in this paper, we discuss umbral derivatives (or the star algebra)