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| viXra.org > Functions and Analysis > 2205 |
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[6] viXra:2205.0150 [pdf] replaced on 2022-07-31 18:09:57
Authors: Dmitrii V. Guryanov
Comments: 48 Pages.
The purpose of this article is to introduce and to describe a concept of math calculus"Multiplical". To my total surprise I have found that currently such a concept does not existamong set of math definitions in its direct and explicit form. Nevertheless there are number ofareas of its practical use, where this concept would be suitable and potentially would benaturally used in its direct and explicit form, especially, in statistics, finance and economyresearches and analysis and many other areas. Moreover from my perspective this conceptperfectly fits into the coherent system of standard mathematical concepts and operators andshould take its rightful place there. In this article also other topics are considered and someinteresting conclusions are made.
Category: Functions and Analysis
[5] viXra:2205.0117 [pdf] replaced on 2023-08-14 06:40:15
Authors: Johan Aspegren
Comments: 5 Pages.
In this paper we will prove the Kakeya maximal function conjecture in a special case when tube intersections behave like points. We achieve this by showing there exist large essentially disjoint tube-subsets.
Category: Functions and Analysis
[4] viXra:2205.0090 [pdf] replaced on 2022-06-08 01:20:01
Authors: Robert Lloyd Jackson
Comments: 8 Pages. contact at rljacksonmd@gmail.com
In the past, theorems have shown that individuals can implement a (formal) power series method to derive solutions to algebraic ordinary differential equations, or AODEs. First, this paper will give a quick synopsis of these “bottom-up” approaches while further elaborating on a recent theorem that established the (modified) generating function technique, or [m]GFT, as a powerful method for solving differentials equations. Instead of building a (formal) power series, the latter method uses a predefined set of (truncated) Laurent series comprised of polynomial linear, exponential, hypergeometric, or hybrid rings to produce an analytic solution. Next, this study will utilize the [m]GFT to create several analytic solutions to a few example AODEs. Ultimately, one will find [m]GFT may serve as a powerful "top-down" method for solving linear and nonlinear AODEs.
Category: Functions and Analysis
[3] viXra:2205.0083 [pdf] submitted on 2022-05-16 20:54:25
Authors: Saburou Saitoh
Comments: 5 Pages.
We introduce a mysterious property in conformal mappings and division by zero calculus with some elementary linear mapping.
Category: Functions and Analysis
[2] viXra:2205.0016 [pdf] submitted on 2022-05-03 02:56:33
Authors: Yang Liu
Comments: 19 Pages.
The first part of the article mainly gives some concepts and lemmas, such as the definition of some function spaces, Radon integral and its basic properties, $L^1-$seminorm, the definition of Lebesgue integral and so on. These basic concepts and lemmas are very helpful in proving the main theorem later. The proof of the main theorem is divided into two parts. The main idea is to locally approximate the transformation $\phi:U\to V$ around a point $a\in U$ by an affine map. In order to be able to use this local approximation meaningfully, we decompose the given function $\psi\in C_c\left(V\right)$ into a sum of functions with very small support, so that the
approximation of $\phi:U\to V$ by the local affine approximation is very good. This is done with the help of the $\zeta-$function introduced below, which provides a practical partition of the one on $\mathbb{R}^n$. In the second part, the proof will be performed on suitable approximations of any integrable function.
Category: Functions and Analysis
[1] viXra:2205.0006 [pdf] submitted on 2022-05-02 16:45:11
Authors: Saburou Saitoh
Comments: 6 Pages.
We examined many examples of the relation between general solutions with singular points in ordinary differential equations and division by zero calculus, however, here we will introduce a new type example that was appeared from some general solution of an ordinary differential equation.
Category: Functions and Analysis
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