Related papers: The Picard Scheme
In this paper, we use the theory of Riordan matrices to introduce the notion of an oriented Riordan graph. The oriented Riordan graphs are a far-reaching generalization of the well known and well studied Toeplitz oriented graphs and…
This paper is partly a historical survey of various approaches and methods in the fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparison with the classical one. The significance and outstanding…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We present a derivation of the structure and dynamics of a ticking clock by showing that for finite systems a single natural principle serves to distinguish what we understand as ticking clocks from time-keeping systems in general. As a…
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
We give some necessary and sufficient conditions for the existence of N\'{e}ron models of jacobians of semistable morphisms of arbitrary relative dimension over base schemes of arbitrary dimension. To do this, we introduce a notion of…
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…
This article is a conceptual exposition on the structure of the tree. It demonstrates an evolutionary design that the tree possesses in the perspective of a structural engineer.
In an earlier work, the author together with Guo [Hermitian adjacency matrix of digraphs and mixed graphs, J. Graph Theory 85 (2017) 217-248] introduced the Hermitian adjacency matrix of directed (and partially directed) graphs. However, it…
An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.
The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we set up an abstract framework in which we can prove theorems…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We give a combinatorial interpretation of a Pieri formula for double Grothendieck polynomials in terms of an interval of the Bruhat order. Another description had been given by Lenart and Postnikov in terms of chain enumerations. We use…
This paper reconstructs the derivations underlying the kinematical part of Einstein's 1905 special relativity paper, emphasizing their operational clarity and minimalist use of mathematics. Einstein employed modest tools-algebraic…
Personal recollections about Alexandre Grothendieck and early days of his theory of motives
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…