The purpose of this note is to give a specific form for Kruppa’s equations in terms of the Fundamental matrix. Kruppa’s equations can be written explicitly in terms of the singular value decomposition (SVD) of the

This paper deals with the problem of characterizing and parametrizing the manifold of trifocal tensors that describe the geometry of three views like the fundamental matrix characterizes the geometry of two. The paper contains two new results. First a new, simpler, set of algebraic constraints that characterizes the set of trifocal tensors is presented. Second, we give a new parametrization of ...

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ(N), with respect to the usual fundamental domain FN , where N is assumed prime. The cycles Q1, . . . , Qn that this algorithm produces are such that the the corresponding paths γ1, . . . , γn in the Riemann surface X0(N)(C) have a nice behaviour around the elliptic points of...

This paper concerns the relation between a proof’s beauty and its explanatory power — that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical...

One of the unique attractions of atomic physics is the possibility of the extremely accurate theoretical predictions and stingiest experimental tests of those predictions. There are numerous observable quantities which can be accurately calculated and measured. The advancements in the experimental technologies and further development of the high-precision atomic theory methodologies lead not on...

In this paper, we consider structure and motion recovery for scenes consisting of static and dynamic features. More particularly, we consider a single moving uncalibrated camera observing a scene consisting of points moving along straight lines converging to a unique point and lying on a motion plane. This scenario may describe a roadway observed by a moving camera whose motion is unknown. We s...

Let W be a compact manifold and let ρ be a representation of its fundamental group into PSL(2,C) Isom(H3). The volume of ρ is defined by taking any ρ-equivariant map from the universal cover W̃ to H and then by integrating the pullback of the hyperbolic volume form on a fundamental domain. This volume does not depend on the choice of the equivariant map because two equivariant maps are always eq...

This paper presents a method for creating a robust system for modeling physical interactions between objects. The system avoids problems such as objects escaping or passing through each other due to undetected collisions caused by excessive velocities or insufficient time resolution.

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X–ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the dynamical state of the cluster. We introduce a new concept of allocation of the fundamental plane of clusters derived from their intrinsic morphological properti...

We propose, in maximum likelihood sense, an optimal method for the affine fundamental matrix estimation in the presence of both Gaussian noise and outliers. It is based on weighting the squared residuals by the iteratively computed, residual posterior probabilities to be relevant. The proposed principle is also used for the covariance matrix estimation of the affine F-matrix where the novelty i...