Related papers: Disquisitiones 235
In a multigranular framework, the two most important binary predicates are those for subsumption and disjointness. In the first part of this work, a sound and complete inference system for assertions using these predicates is developed. It…
The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…
This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…
Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.
For a pair of quadratic forms with rational coefficients in at least $10$ variables, we prove an asymptotic formula for the number of common zeros under the assumption that the two forms determine a projective variety with exactly two…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can…
We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two…
We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…
We discuss multiplicative properties of the binary quadratic form $a x^2 + b x y + c y^2$ by considering a ring of matrices which is closed under a triple product. We prove that the ring forms a ternary algebra in the sense of Hestenes, and…
We investigate the universal Jacobian of degree n line bundles over the Hurwitz stack of double covers of P^1 by a curve of genus g. Our main results are: the construction of a smooth, irreducible, universally closed (but not separated)…
This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…
Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators…
The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic forms, and found that ideal classes of…