Related papers: Some Remarkable Concurrences in the Quadrilateral
In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…
The paper investigates the properties of a nonlinear recursive sequence which includes several ones studied formerly in the literature.
By focusing on the X-matrix part of a density matrix of two qubits we provide an algebraic lower bound for the concurrence. The lower bound is generalized for cases beyond two qubits and can serve as a sufficient condition for…
If there exists a cyclic quadrilateral whose sides go through the given four collinear points, then there are infinitely many such quadrilaterals inscribed in the same circle. We give two proofs of this porism; one based on cross-ratios,…
A simple field theory approach is developed to model the properties of charged, dielectric bodies and their associated counterions. This predictive theory is able to accurately describe the properties of systems (as compared to computer…
In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been…
We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
We study algebras and varieties where every non-trivial congruence has some class being a non-trivial subuniverse of the algebra in question. Then we focus on algebras where this non-trivial class is a unique non-singleton class of the…
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…
We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain…
Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a…
For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
In this article we obtain a complete description of the congruences of lines in $\p^4$ of order one provided that the fundamental surface $F$ is non-reduced (and possibly reducible) at one of its generic points, and their classification…
The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…
This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.
As an extension of positive and almost positive diagrams and links, we study two classes of links we call successively almost positive and weakly successively almost positive links. We prove various properties of polynomial invariants and…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
The main properties of hypercomplex generalization of quaternion system as antiquaternion are presented in this article. Definitions and studied of antiquaternions conjugation are introduced, their norm and zero divisor, and how to perform…