Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In this paper, it was shown that the fourth power-free element of the divisibility sequence generated by a non-torsion point on the elliptic curve always has a primitive divisor.
Abstract: Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibility sequence generated by $P$ always has a primitive divisor.
1 citations
Patent•
04 May 2018
TL;DR: In this article, a division function implementation method for a programmable device is described, which is characterized by comprising the following steps that 1, after a divisor X and a dividend Y are received, the divisors X and Y are signed 32-bit binary-system fixed-point numbers with the order magnitude as 16 and decimal as 16, the dividend Y is judged, when Y is zero, a zero result and a normal state code are returned, and when X is zero a maximum expression value and a division-by-zero state code is returned; 2
Abstract: The invention provides a division function implementation method for a programmable device. The method is characterized by comprising the following steps that 1, after a divisor X and a dividend Y arereceived, the divisor X and the dividend Y are signed 32-bit binary-system fixed-point numbers with the order magnitude as 16 and decimal as 16, the dividend Y is judged, when Y is zero, a zero result and a normal state code are returned, and when the divisor X is zero, a maximum expression value and a division-by-zero state code are returned; 2, the divisor X and the dividend Y are subjected topositive-negative judgment, and a result is calculated to be positive or negative; the divisor X and the dividend Y are 32-bit signed numbers, and the maximum bit is a symbol bit; whether the divisorX and the dividend Y are positive numbers or negative numbers are determined by judging the sign bit; when the divisor X and the dividend Y are both positive numbers or negative numbers, the result ispositive, otherwise, the result is negative.
1 citations
TL;DR: In this paper, the authors derived an explicit formula for the number of primitive elements, in quartic extensions of Mersenne prime fields, having absolute trace zero, for a positive integer N whose prime factors divide Q and satisfy the so called semi-primitive condition, and showed that if all the prime factors of q − 1 divide m, then the primitive elements in Fqm, with prescribed nonzero trace, is uniformly distributed.
1 citations
07 Nov 2020
TL;DR: This work aims to provide a new tool to increase the drilling team’s efficiency by recreating drilling visualizations in a virtual environment that enables training, evaluating, and simulating different scenarios in a well drilling and provide realtime insights to the engineers when coupled with other diagnostics tools.
Abstract: Well drilling is one of the most expensive tasks in oilfield exploration and development projects, especially in offshore assets. Thus, this activity is under constant evolution, given that any improvement in equipment or process can result in significant savings for the company operating that field. Meanwhile, virtual reality (VR) is one of the vital industry 4.0 trends to enable simulations and training safely for users. This work aims to provide a new tool to increase the drilling team’s efficiency by recreating drilling visualizations in a virtual environment. This environment enables training, evaluating, and simulating different scenarios in a well drilling and provide realtime insights to the engineers when coupled with other diagnostics tools.
1 citations
TL;DR: In this article, it was shown that the Dirichlet problem for the cone {Q(x) < 0} has polynomial harmonic solutions for polynomials with parameters α, β.
Abstract: Let \(P_{n}^{ ( \alpha,\beta ) } ( x ) \) be the Jacobi polynomial of degree n with parameters α,β. The main result of the paper states the following: If b≠1,3 and c are non-zero relatively prime natural numbers then \(P_{n}^{ ( k+ ( d-3 ) /2,k+ ( d-3 ) /2 ) } ( \sqrt{b/c} )
eq0\) for all natural numbers d,n and \(k\in\mathbb{N}_{0}\). Moreover, under the above assumption, the polynomial \(Q ( x ) = \frac{b}{c} ( x_{1}^{2}+\cdots+x_{d-1}^{2} ) + ( \frac{b}{c}-1 ) x_{d}^{2}\) is not a harmonic divisor, and the Dirichlet problem for the cone {Q(x)<0} has polynomial harmonic solutions for polynomial data functions.
1 citations