Related papers: Another look at e
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
This note presents an interesting counterexample to a basic covering problem.
This note is devoted to the construction of a graded Lie algebra, whose grading is not given by a semigroup.
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
This note presents a rather intuitive approach to extreme value theory. This approach was devised mostly for pedagogical reason.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
We obtain simple proofs of certain inequalites for bivariate means.
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
We propose a criterion of equidistribution by the differentiability of certain arithmetic invariants. Combined with the slope method and the asymptotic measures, this criterion gives a new "conceptual" proof to equidistribution results…
The main purpose of this Note is to provide a non-trivial bound on certain Kloosterman sums as considered in the recent paper of E. Fouvry [F], leading to a small improvement of his result on the Pell equation.
In this paper, we prove that two different observers don't equally measure the distance between two points A and B. For this, we introduce some postulates and obtain a new formula to show distance between A and B. In this formula, radius of…
We give evaluations in closed form of certain non linear differential equations
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
The notions of potential infinity (understood as expressing a direction) and actual infinity (expressing a quantity) are investigated. It is shown that the notion of actual infinity is inconsistent, because the set of all (finite) natural…
This note comprises a negative resolution of the Efficient Market Hypothesis.
These notes are concerned with the existence and the basic properties of the set-theoretic universes for nonstandard analysis, compiled by a beginner in the subject. It assumes a basic background in first-order logic, though the necessary…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
This technical note provides a high-level overview of the present state of basic field electron emission (FE) theory, as suitable for use in the context of technological applications of FE theory. At present there is much theoretical…