Related papers: Old and new applications of Katona's circle
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
In his talk "Integral Apollonian disk Packings" Peter Sarnak asked if there is a "proof from the Book" of the Descartes theorem on circles. A candidate for such a proof is presented in this note
This is a series of lecture notes explaining topos theory and its application in physics.
In this article we establish several Ohsawa-Takegoshi type theorems for twisted pluricanonical forms and metrics of adjoint $\bR$-bundles.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
In this paper we prove the WALA conjecture.
In this paper, we find a new recurrence formula fo the Euler zeta functions.
We offer some further applications of some Bailey pairs related to some mock theta functions which were established in a recent study. We discuss and offer some double-sum $q$-series, with new relationships among mock theta functions. We…
The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two types of new relations and five conjectural formulas. This…
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…
We establish some new theorems on pentagon and pentagram.
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…
The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing inductive proof search. In addition, we will show how various…
The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.
Quandle cocycle invariants form a powerful and well developed tool in knot theory. This paper treats their variations - namely, positive and twisted quandle cocycle invariants, and shadow invariants. We interpret the former as particular…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.