Related papers: The Mystery of the Shape Parameter IV
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
We prove that the dimension of a quartic symmetroid singular along a quadric of codimension 1 is at most 4, if it is not a cone. In the maximal case, the quadric is reducible and consists of rank-3-points. If the quadric is irreducible, it…
We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
The usual concept of shape invariance is discussed and one extension of this concept is suggested.
If the unitary quark- mixing matrix, $V$, is moduli symmetric then it depends on three real parameters. This means that there is a relation between the four parameters needed to parametrize a general $V$. It is shown that there exists a…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
We perform an exploratory study of the allowed parameter range for the CKM-like mixing of hypothetical quarks of a fourth generation. As experimental constraints we use the tree-level determinations of the 3 $\times$ 3 CKM elements and FCNC…
The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…
A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…
Some facts about 4-spinors listed and discussed. None, well perhaps some, of the work is original. However, locating formulas in other places has proved a time-consuming process in which one must always worry that the formulas found in any…
One of the unspoken challenges of tractography is choosing the right parameters for a given dataset or bundle. In order to tackle this challenge, we explore the multi-dimensional parameter space of tractography using streamline-specific…
We compute quaisideterminants and determinants of quaternionic matrices
We show that all four of the nucleon form factors can be very well explained using the manifestly covariant spectator theory. The nucleon is modeled as a spherical state of three constituent quarks with electromagnetic form factors, all…
Parametrization of qutrits on the complex projective plane CP^2 = SU(3)/U(2) is given explicitly. A set of constraints that characterize mixed state density matrices is found.
In this work we deal with parameter estimation in a latent variable model, namely the multiple-hidden i.i.d. model, which is derived from multiple alignment algorithms. We first provide a rigorous formalism for the homology structure of k…