Related papers: Some new theorems on Pentagon and Pentagram
We discuss eight new(?) configuration theorems of classical projective geometry in the spirit of the Pappus and Pascal theorems.
A conjecture regarding the structure of expander graphs is discussed.
In this study, various rotationally symmetric tilings that can be formed using pentagons that are related to rhombus are discussed. The pentagons can be convex or concave and can be degenerated into a trapezoid. If the pentagons are convex,…
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
The new form of pentagon equations suggested by Volkov for the $ q $-exponential on the basis of formal series is derived within the Hilbert space framework for the modular version of the quantum dilogarithm.
We present an overview of recent experimental and theoretical advances in our understanding of the spin structure of protons and neutrons.
We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be determined by the angle information only. We also investigate…
We review recent developments in the theory of Thompson group representations related to knot theory.
The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. $O$-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra,…
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We survey recent developments on the Restriction conjecture.
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.
We give a new simpler proof of a theorem of Jayne and Rogers.
New cases of the multiplicity conjecture are considered.