Related papers: Another look at e
The purpose of this note is to describe a space that is regular but not completely regular, but only barely so: all closed sets are $G_\delta$-sets and every singleton is a zero-set.
In this paper, we consider the concept of limit, one of the basic concepts of mathematical analysis. At a point $a\in{\mathbb{R}}$, the limit of a function $f$ from $A\subset\mathbb{R}$ to $\mathbb{R}$ is $L\in{\mathbb{R}}$ if and only if…
In this note we provide a simple formula of general term of recurrent sequence.
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We demonstrate and discuss the process of gaining information and show an example in which some specific way of gaining information about an object results in the Tsallis form of entropy rather than in the Shannon one.
These informal notes deal with a number of questions related to sums and integrals in analysis.
This note presents a new definition of nonlinear statistics mean and variance to simplify the nonlinear statistics computations. These concepts aim to provide a theoretical explanation of a novel nonlinear weighted residual methodology…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
These notes describe some results on dice comparisons when changing the numbers on the faces while the sum of all the face stay the same.
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
Under some assumptions, an analytic expression for the transmission spectrum can be obtained, which can form the basis of atmospheric retrievals and allows insight on the degeneracies involved. In this Research Note we present an…
The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Contrary to what has been presumed for a long time, we prove that such zeros cannot…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.