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On Solutions of cubic equations with Prime Variables in Arithmetic Progressions

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Chinese Quarterly Journal of Mathematics 2006年第3期21卷 317-321页

作者： ZHOU Hai-gang WANG Tian-ze Department of Mathematics Tongji University Shanghai 200092 China College of Mathematics and Information Sciences Henan University Kaifeng 475001 China

In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.

关键词： cubic equation prime variable prime solution

cubic Diophantine Inequalities

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Acta Mathematica Sinica,English Series 2001年第1期17卷 153-160页

作者： Hong Ze LI Department of Mathematics Shandong University

Let λ1, λ2,...,λ7 be real numbers satisfying λi≥1. In this paper, we prove there are integers x1,...,x7 such that the inequalities |λ1x13+λ2x23+...+λ7x73|i|xi]3 （λ1λ2…λ7）89814) hold simultaneously.

关键词： Diophantine inequality cubic equation Non-trivial solution

A New General equation of State

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Chinese Journal of Chemical Engineering 1999年第2期7卷 161-165页

作者：云志秦金平史美仁时钧南京化工大学化工系江苏南京

A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous ... 详细信息

关键词： equation of state general equation cubic equation quartic equation

The Possibility of Angle Trisection （A Compass-Straightedge Construction） Kimuya M Alex

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Journal of Mathematics and System Science 2017年第1期7卷 25-42页

作者： Kimuya M Alex Department of Mathematics Faculty of Physics Meru University of Science and Technology Kenya.

The objective of this paper is to provide a provable solution of the ancient Greek problem of trisecting an arbitrary angle employing only compass and straightedge （ruler）. （Pierre Laurent Wantzel, 1837） obscurely presented a proof based on ideas from Galois field showing that, the solution of angle trisection corresponds to solution of the cubic equation; x3 - 3x - 1 = 0, which is geometrically irreducible [1]. The focus of this work is to show the possibility to solve the trisection of an angle by correcting some flawed methods meant for general construction of angles, and exemplify why the stated trisection impossible proof is not geometrically valid. The revealed proof is based on a concept from the Archimedes proposition of straightedge construction [2, 3].

关键词： Angle trisection Compass Ruler (Straightedge) Classical Construction GeoGebra Software Greek's geometry cubic equation Plane geometry Solid geometry