Related papers: Some new theorems on Pentagon and Pentagram
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
I first give a brief overview of the status of exotic hadron search so far. Then I review the recent theoretical development on pentaquarks. Finally I emphasize that none of theoretical formalisms predicts the existence of $\Theta$…
We give improved lower bounds on the minimum number of $k$-holes (empty convex $k$-gons) in a set of $n$ points in general position in the plane, for $k=5,6$.
Compton scattering offers in principle an intriguing new window on nucleon structure. Existing experiments and future programs are discussed and the state of theoretical understanding of such measurements is explored.
In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an $n$-triangular net by solving the corresponding recursive formulaes.
We introduce a novel notion of pasting shapes for iterated Segal spaces which classify particular arrangements of composing cells in d-uple Segal spaces. Using this formalism, we then continue to prove a pasting theorem for these iterated…
We describe the recent experiments which claimed an observation of a tetra-neutron signal. Production reactions like transfer, knockout, fragmentation or photodisintegration have been used at very different experiments and facilities to…
Harborth [{\it Elemente der Mathematik}, Vol. 33 (5), 116--118, 1978] proved that every set of 10 points in the plane, no three on a line, contains an empty convex pentagon. From this it follows that the number of disjoint empty convex…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
In the past decade, more and more charmoniumlike and bottomoniumlike states have been reported in experiments, which have led us to extensive discussions on the underlying structure of these states. In this review paper, we briefly…
I review some of the recent experimental results on the so-called XYZ mesons.
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
In this note, we find a new way to prove several properties of 2-alternating capacities.
We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.
Greig Cowan and Tim Gershon describe new types of matter called tetraquarks and pentaquarks, and discuss the outlook for understanding these particles.
This paper considers a simple geometric construction, called the Pentagram map. The pentagram map, performed on N-gons, gives rise to a birational mapping on the space of all N-gons. This paper finds what conjecturally are all the…