Related papers: Some new theorems on Pentagon and Pentagram
In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two…
A brief review of the latest developments in the spectroscopy of heavy quarks is presented. The current status of the recently `discovered' pentaquarks is also discussed.
New results on comparison of distributions of Gaussian quadratic forms are presented
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
We introduce and study a new kind of congruent number problem on the right trapezoid.
This note comments on parts of "New 5-designs." We cite Chebotarev's theorem; we correct some minor errors and we clarify our proof of the Gleason-Prange theorem.
Determinism and indeterminism in physical theories are reviewed and some broader implications of determinism are discussed.
We survey some results on toric topology.
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
We prove a new and unified GAGA theorem. This recovers all analytic and formal GAGA results in the literature, and is also valid in the non-noetherian setting. Our method can also be used to establish various Lefschetz theorems and…
We review the idea of leptonic unitary triangles and extend the concept of the recently proposed unitary boomerangs to the lepton sector. Using a convenient parameterization of the lepton mixing, we provide approximate expressions for the…
A new mechanism for the parity doublers in hadrons is suggested.
Alternating sign triangles have been introduced by Ayyer, Behrend and Fischer in 2016 and it was proven that there is the same number of alternating sign triangles with $n$ rows as there is of $n\times n$ alternating sign matrices. Later on…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
We isolate several classes of stationary sets of kappa^omega and investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.
Comments are made on some recently published papers on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We define a new family of valuations on polyhedral cones valued in the space of bounded polyhedra.