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[8] viXra:2211.0165 [pdf] submitted on 2022-11-27 11:07:03
Authors: Viktor Strohm
Comments: 10 Pages.
On the ruler of the ellipsograph, we set point C. We set the movement of the ruler: uniform, uniformly accelerated, elliptical. We calculate the angle of rotation of point C relative to the center of the ellipse, the sectoral velocity and the velocity and acceleration vectors. We compare the sectoral velocity with Kepler's second law.
Category: General Mathematics
[7] viXra:2211.0160 [pdf] submitted on 2022-11-27 17:00:43
Authors: Dongjun Wu
Comments: 1 Page.
A technical mistake of the paper [Wu2021] is pointed out and corrected.
Category: General Mathematics
[6] viXra:2211.0149 [pdf] replaced on 2024-10-02 21:06:31
Authors: Mohamed E. Hassani
Comments: 18 Pages.
The main motivation behind this paper is the question ‘What is the factorization of(��^�� + ��^��) when n is an even positive integer?’ which was and is frequently asked on theInternet by many high school and university students and, to our knowledge, even thespecialized textbooks and research articles have not yet answered it, and over time the questionitself is not only transformed into a problem that needs to be solved but also became aninteresting subject of investigation. In the present paper, the question is positively answered and the problem is solved through the detailed study of the factorizations that leads directly to the concept of algebraic factorization with fractional degree and positive integral order, and an apparently new type of indefinite irrational and rational integrals.
Category: General Mathematics
[5] viXra:2211.0105 [pdf] submitted on 2022-11-18 20:17:28
Authors: Edgar Valdebenito
Comments: 9 Pages.
In this note we give some representations of pi^3 involving infinite sums and the golden ratio.
Category: General Mathematics
[4] viXra:2211.0062 [pdf] submitted on 2022-11-11 01:49:51
Authors: Murad Abdullah, Wai Ho Mow
Comments: 5 Pages.
In this paper, we present some new constructions of the binary linear block codes (BLBCs) that achieve the largest possible minimum Hamming distance and the lowest possible number of codewords of this Hamming weight (also known as error coefficient), and they are said to be [d, A d ]-optimal (n, k) linear codes. These (n, k) BLBCs give the best possible frame error rate (FER) in the asymptotic regime under maximum-likelihood decoding over the additive white Gaussian noise channel. Specifically, for all positive integers k and m, and 0 ≤ l ≤ k − 1, we give the constructions of ((2 k − 1)m + l, k), ((2 k − 1) + k, k + 1), (15m + 4, 4), (15m + 6, 4), (12, 5), and (33, 5) BLBCs. Many of these BLBCs have A d = 1, and some achieve the lower bound on A d, which asserts their optimality. Our constructions show the asymptotic E b /N o gain of up to 1.24 dB over their d-optimal counterpart at a FER of 10 −7 .
Category: General Mathematics
[3] viXra:2211.0024 [pdf] submitted on 2022-11-03 10:40:52
Authors: Timothy W. Jones
Comments: 8 Pages.
Simple craps, a Vegas casino game, is easily modeled using a TI-83's programming, list, and statistics features. Roll two dice. If the coming out roll, as it is called is 2, 3, or 12, the player immediately loses. If a 7 or 11 is rolled, they immediately win. If any of the remaining totals are rolled, if the player rolls that number before rolling a 7, they win, not they lose. A program can be initialized with a bank roll and a standard, non-changing bet. Using the list feature 999 rolls, the maximum size of a list, can be stored in a built-in list. A bar chart for the distribution of numbers is easily generated and confirms the calculated probabilities. The code to mimic the game is straight-forward. The user repeatedly plays the game until the stake is 0, an inevitability given say a stake of $100 and a bet of $5. This certainty instills the truth: it's a loser's game.
Category: General Mathematics
[2] viXra:2211.0012 [pdf] submitted on 2022-11-01 06:41:21
Authors: Kai Cheung
Comments: 6 Pages.
This paper introduces a simpler method to compute sums of powers and polynomials, which can be done by hand, and efficiently implemented in software.
Category: General Mathematics
[1] viXra:2211.0004 [pdf] replaced on 2023-02-22 23:12:23
Authors: Abdelkrim ben Mohamed
Comments: 09 Pages.
In this working paper I try to prove the Riemann hypothesis
Category: General Mathematics
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