| viXra.org > General Mathematics > 2001 |
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| viXra.org > General Mathematics > 2001 |
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[12] viXra:2001.0629 [pdf] submitted on 2020-01-29 02:12:01
Authors: M.Parimala, R.Jeevitha, Saeid Jafari, F.Smarandache, M.Karthika
Comments: 9 Pages.
In this article we introduce the notation of neutrosophic nano semi closed, neutrosophic nano α
closed, neutrosophic nano pre closed, neutrosophic nano semi preclosed and neutrosophic nano regular closed and investigate some of their properties. Further we study the concept of neutrosophic nano sg closed, neutrosophic nano ψ closed and neutrosophic nano αψ closed and derive some of their properties.
Category: General Mathematics
[11] viXra:2001.0614 [pdf] submitted on 2020-01-28 12:30:57
Authors: Christopher Goddard
Comments: 10 Pages.
The scope of this short note is to outline a research programme for the exploration of 'subtlety theory', which can be thought of as a framework for exploring various classes of structure associated to higher categories. It is hoped that this might form a logical springboard for researchers wishing to explore said ideas and potentially take them further.
Category: General Mathematics
[10] viXra:2001.0533 [pdf] submitted on 2020-01-25 07:16:11
Authors: Saeid Jafari, N. Rajesh
Comments: 6 Pages.
In this paper, we introduce and study the concept of ideal topological vector spaces.
Category: General Mathematics
[9] viXra:2001.0487 [pdf] submitted on 2020-01-22 10:54:42
Authors: Edgar Valdebenito
Comments: 1 Page.
Elementary integral
Category: General Mathematics
[8] viXra:2001.0475 [pdf] replaced on 2020-02-28 12:19:12
Authors: Leszek Mazurek
Comments: 51 Pages; Short Introduction -> https://vixra.org/abs/2002.0070 ; Polish version -> https://vixra.org/abs/2001.0374
This paper solves the problem of division by zero. Starting with a deep analysis of multiplication and division, it is presented that they are one in the same, as an operation. Together with the operation of selection, they are different forms of the transformation operation, that changes one pair of numbers into another pair of numbers. It is presented that the numbers are always in reference to some other numbers. Therefore, the only correct form of the number, is when it is a ratio between the certain value and the base measure, which this value is related to. It is clearly proven that the problem of division by zero is the result of unauthorized simplification, which was done by bringing all the rational numbers (which are represented by the ratio of the value to the measure) to the fractions, with a denominator of 1. This paper shows why we should not make fractions with different numerators and denominators equal, even so they seem to be in the same proportion. Finally, there are two graphs with the functions presented 1/x and tg(x) with their discontinuity points, which are visible only on the real numbers graph. This result is from projecting points of the rational numbers graph onto the real numbers graph with a denominator of 1. These discontinuity points disappear when we present our graphs in rational numbers. This paper fixes one of the foundations of mathematics and shows us how to divide by zero. This is only the first issue that was solved, but based on the proper understanding of numbers in their natural form, still many other things need to be fixed. It is still difficult to predict all the consequences, which this change can bring, to everything that was created based on this wrong foundation.
Keywords: Division by zero, Real numbers, Rational numbers, Ratio, Fraction, Fixing mathematics
Category: General Mathematics
[7] viXra:2001.0460 [pdf] submitted on 2020-01-22 07:54:05
Authors: Theophilus Agama
Comments: 4 Pages.
In this paper we study the Theta splitting function $\Theta(s+1)$, a function defined on the positive integers. We study the distribution of this function for sufficiently large values of the integers. As an application we show that \begin{align}\sum \limits_{m=0}^{s}\prod \limits_{\substack{0\leq j \leq m\\\sigma:[0,m]\rightarrow [0,m]\\\sigma(j)\neq \sigma(i)}}(s-\sigma(j))\sim s^s\sqrt{s}e^{-s}\sum \limits_{m=1}^{\infty}\frac{e^m}{m^{m+\frac{1}{2}}}.\nonumber
\end{align} and that \begin{align}\sum \limits_{j=0}^{s-1}e^{-\gamma j}\prod \limits_{m=1}^{\infty}\bigg(1+\frac{s-j}{m}\bigg)e^{\frac{-(s-j)}{m}}\sim \frac{e^{-\gamma s}}{\sqrt{2\pi}}\sum \limits_{m=1}^{\infty}\frac{e^m}{m^{m+\frac{1}{2}}}.\nonumber
\end{align}
Category: General Mathematics
[6] viXra:2001.0431 [pdf] submitted on 2020-01-21 01:45:01
Authors: Shyamal Dalapati
Comments: 180 Pages.
Thesis
Submitted for the Degree of
Doctor of Philosophy (Science)
of
Indian Institute of Engineering, Science
and Technology, Shibpur
by
Shyamal Dalapati
Department of Mathematics
Indian Institute of Engineering Science and Technology,
Shibpur
P.O. Botanic Garden, Howrah - 711103, India
July, 2018
Category: General Mathematics
[5] viXra:2001.0419 [pdf] submitted on 2020-01-20 11:42:21
Authors: Francisco Moga Moscoso, Marina Moga Lozano
Comments: 5 Pages. email for contact: mmoga@uma.es. Book and copyright: Desdedondetodocomienza
A possible demonstrations of the riemann hypothesis based on every infinite complex solution of zeta function of Riemann ζ(s) with it is conjugated root, can also be used to be the solution of a quadratic equation of real coefficients which admits it as zeros, using the root theorem of Viete.
Category: General Mathematics
[4] viXra:2001.0374 [pdf] submitted on 2020-01-19 12:35:05
Authors: Leszek Mazurek
Comments: 49 Pages, English version -> https://vixra.org/abs/2001.0475
This paper solves the problem of division by zero. Starting with a deep analysis of multiplication and division, it is presented that they are one in the same, as an operation. Together with the operation of selection, they are different forms of the transformation operation, that changes one pair of numbers into another pair of numbers. It is presented that the numbers are always in reference to some other numbers. Therefore, the only correct form of the number, is when it is a ratio between the certain value and the base measure, which this value is related to. It is clearly proven that the problem of division by zero is the result of unauthorized simplification, which was done by bringing all the rational numbers (which are represented by the ratio of the value to the measure) to the fractions, with a denominator of 1. This paper shows why we should not make fractions with different numerators and denominators equal, even so they seem to be in the same proportion. Finally, there are two graphs with the functions presented 1/x and tg(x) with their discontinuity points, which are visible only on the real numbers graph. This result is from projecting points of the rational numbers graph onto the real numbers graph with a denominator of 1. These discontinuity points disappear when we present our graphs in rational numbers. This paper fixes one of the foundations of mathematics and shows us how to divide by zero. This is only the first issue that was solved, but based on the proper understanding of numbers in their natural form, still many other things need to be fixed. It is still difficult to predict all the consequences, which this change can bring, to everything that was created based on this wrong foundation. Keywords: Division by zero, Real numbers, Rational numbers, Ratio, Fraction, Fixing mathematics
Category: General Mathematics
[3] viXra:2001.0054 [pdf] submitted on 2020-01-04 13:06:37
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give a formula involving Pi.
Category: General Mathematics
[2] viXra:2001.0053 [pdf] submitted on 2020-01-04 13:08:05
Authors: Edgar Valdebenito
Comments: 4 Pages.
We give some elementary integrals.
Category: General Mathematics
[1] viXra:2001.0036 [pdf] submitted on 2020-01-02 23:38:03
Authors: Shiyou Lian
Comments: 26 Pages.
This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD interpolation. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; n(n>1)-dimensional AD interpolation is firstly separated into n parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the n-dimensional interpolation. If the parallel processing is used, the efficiency of n-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.
Category: General Mathematics
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