Related papers: A note on Gurzadyan theorem
In cosmology, the Gurzadyan's theorem identifies the most general force law consistent with the finding of Newton's first shell theorem -- that a spherical symmetric mass exerts the same gravitational force as a point mass at its center.…
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
This is a series of lectures on M Theory for cosmologists. After summarizing some of the main properties of M Theory and its dualities I show how it can be used to address various fundamental and phenomenological issues in cosmology.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its…
Some discussion of physical and geometrical interpretation of Einsteins theory of gravitation which is on basic of cosmology.
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
Cosmology is becoming an important tool to test particle physics models. We provide an overview of the standard model of cosmology with an emphasis on the observations relevant for testing fundamental physics.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
This paper continues the development of a discrete space-time concept that is recently used in the explanation of the cosmological constant. Instead of order estimation, a more theoretical treatment of the theory is introduced. Based on the…
A slight modification to one of Tarski's axioms of plane Euclidean geometry is proposed. This modification allows another of the axioms to be omitted from the set of axioms and proven as a theorem. This change to the system of axioms…
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
The issue of the cosmological constant is discussed in details and a solution to the problem is suggested.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.