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Physical Sciences and Mathematics Commons™
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- Curvature (1)
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- Dehn function (1)
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- Discrete Swarm Particle Optimization (1)
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- Distribution of Primes (1)
- Elliptic Curve (1)
- Elliptic Group of points. (1)
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- Prime Values of Polynomial (1)
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- Primitive Point (1)
- Primitive Root Producing Polynomial (1)
- Primitive Root; Irreducible Polynomials (1)
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Asymptotics For Primitive Roots Producing Polynomials And Primitive Points On Elliptic Curves, Nelson Carella
Asymptotics For Primitive Roots Producing Polynomials And Primitive Points On Elliptic Curves, Nelson Carella
Publications and Research
Let $x \geq 1$ be a large number, let $f(n) \in \mathbb{Z}[x]$ be a prime producing polynomial of degree $\deg(f)=m$, and let \(u\neq \pm 1,v^2\) be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes $p=f(n) \leq x$ with a fixed primitive root $u$ is derived in this note. This asymptotic result has the form $$\pi_f(x)=\# \{ p=f(n)\leq x:\ord_p(u)=p-1 \}=\left (c(u,f)+ O\left (1/\log x )\right ) \right )x^{1/m}/\log x$$, where $c(u,f)$ is a constant depending on the polynomial and the fixed integer. Furthermore, new results for the asymptotic order of elliptic primes with …
Algorithmically Complex Residually Finite Groups, Olga Kharlampovich, Alexei Myanikov, Mark Sapir
Algorithmically Complex Residually Finite Groups, Olga Kharlampovich, Alexei Myanikov, Mark Sapir
Publications and Research
We construct the first examples of algorithmically complex finitely presented residually finite groups and the first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn functions, and arbitrarily large depth functions. The groups are solvable of class 3.
Case Study Of Undergraduate Research Projects In Vector Analysis, Alexander Vaninsky, Willy Baez Lara, Madieng Diao, Analilia Mendez
Case Study Of Undergraduate Research Projects In Vector Analysis, Alexander Vaninsky, Willy Baez Lara, Madieng Diao, Analilia Mendez
Publications and Research
This paper presents two examples of the undergraduate research projects in vector analysis conducted under the first author’s supervision at one of the community colleges that is an integral part of a large city university. The projects were accomplished by the students pursuing associated degrees in engineering, during their sophomore year. One project was to obtain an explicit formula for the curvature of a curve in plane defined implicitly in rectangular or polar coordinates. Another project was aimed to develop an alternative procedure for finding potential function for a vector field in space based on simultaneous integration. Participation in these …
A Novel Approach For Library Materials Acquisition Using Discrete Particle Swarm Optimization, Daniel A. Sabol
A Novel Approach For Library Materials Acquisition Using Discrete Particle Swarm Optimization, Daniel A. Sabol
Publications and Research
The academic library materials acquisition problem is a challenge for librarian, since library cannot get enough funding from universities and the price of materials inflates greatly. In this paper, we analyze an integer mathematical model by considering the selection of acquired materials to maximize the average preference value as well as the budget execution rate under practical restrictions. The objective is to improve the Discrete Particle Swarm Optimization (DPSO) algorithm by adding a Simulate Annealing algorithm to reduce premature convergence. Furthermore, the algorithm is implemented in multiple threaded environment. The experimental results show the efficiency of this approach.