Related papers: Some Interesting Connections!
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
The Bernoulli numbers are fascinating and ubiquitous numbers, they occur in several domains of Mathematics like Number theory (FLT), Group theory, Calculus and even in Physics. Since Bernoulli's work, they are yet studied to understand…
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…
A closer look (with hindsight) at Newtonian and relativistic kinematics reveals two things. Not surprisingly, Newtonian time remains the empty and artificial - albeit useful - figment it is known to be. Quite unexpectedly however it turns…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
The binary radix expansion of a real number can be used to code the outcome of any series of coin tosses, a fact that provides an intriguing link between number theory, measure theory and statistical physics. Inspired by this fact, a…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
A unified, consistent and simple view of the Faraday law of induction is presented, which consists of two points: discriminating the lab- from the rest-frame electric field and understanding it is the impossibility for both fields to vanish…
Some highly speculative and serendipitous ideas that might relate thermodynamics, spacetime, shape and symmetry are brought together. A hypothetical spacetime comprising a pointwise lattice with a fixed metric is considered. If there were…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.