| viXra.org > Functions and Analysis > 2206 |
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| viXra.org > Functions and Analysis > 2206 |
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[5] viXra:2206.0134 [pdf] submitted on 2022-06-25 19:20:38
Authors: Yulia Meshkova
Comments: 2 Pages. (Corrections made by viXra Admin to conform with scholarly norm)
A very brief explanation what are the operator error estimates in periodic homogenization.
Category: Functions and Analysis
[4] viXra:2206.0091 [pdf] submitted on 2022-06-18 18:36:46
Authors: Theophilus Agama
Comments: 5 Pages.
In this note we, we prove the inequality \r\n\\begin{align}\r\n\\int \\limits_{|a_n|}^{|b_n|} \\int \\limits_{|a_{n-1}|}^{|b_{n-1}|}\\cdots \\int \\limits_{|a_1|}^{|b_1|}\\frac{1}{\\sqrt[4s+3]{\\sum \\limits_{j=1}^{n}x^{4s+3}_j}}dx_1dx_2\\cdots dx_n \\geq \\frac{2\\pi \\times |\\log (\\langle a,b \\rangle)|\\bigg|\\prod_{j=1}^{n}|b_j|-|a_j|\\bigg|}{||\\vec{a}||^{4s+4}+||\\vec{b}||^{4s+4}}\\nonumber\r\n\\end{align}under some special conditions.
Category: Functions and Analysis
[3] viXra:2206.0076 [pdf] submitted on 2022-06-15 21:33:02
Authors: Theophilus Agama
Comments: 4 Pages.
In this note we introduce the notion of the local product on a sheet and associated space. As an application, we prove that for $\langle a,b \rangle>e^e$ then \begin{align} \int \limits_{|a_n|}^{|b_n|} \int \limits_{|a_{n-1}|}^{|b_{n-1}|}\cdots \ints_{|a_1|}^{|b_1|}\bigg|\log \bigg(i\frac{\sqrt[4s]{\sum \limits_{j=1}^{n}x^{4s}_j}}{||\vec{a}||^{4s+1}+||\vec{b}||^{4s+1}}\bigg)\bigg| dx_1dx_2\cdots dx_n\nonumber \\ \geq \frac{\bigg| prod_{j=1}^{n}|b_j|-|a_j|\bigg|}{\log \log (\langle a,b\rangle)}\nonumber \end{align}for all $s\in \mathbb{N}$, where $\langle,\rangle$ denotes the inner product and $i^2=-1$.
Category: Functions and Analysis
[2] viXra:2206.0012 [pdf] replaced on 2023-09-25 08:08:59
Authors: Dmitrii V. Guryanov
Comments: 36 Pages.
The purpose of this article as a continuation of development of the Multiplical concept is to give an answer to the earlier raised question of why the place of the operator in the function y = e↗x is taken by the operator - a power tower with left associativity, and not with the generally accepted right associativity (the Tetration). Answering on this question required to conduct an hyperoperator analyze. The hyperoperator nature is considered, definition is made and an alternative way of its development is proposed in the present analysis.
Category: Functions and Analysis
[1] viXra:2206.0003 [pdf] replaced on 2022-08-02 15:41:48
Authors: Dmitrii V. Guryanov
Comments: 59 Pages.
The purpose of this article as a continuation of development of the multiplical topic is to find a solution for operation of differentiation and factorization of a function with points of interruption, points where function turns to zero. The solution which allows restoring the original function as result of reverse operation of integration and factorial-multiplication of previously obtained derivative and factor-derivative respectively and with an appropriate selection of an arbitrary multiplier B or addend C, respectively. As the result of the work madenew classes of function properties are introduced as function point properties.
Category: Functions and Analysis
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