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Full-wave Analyses of Scattering of Electromagnetic Wave from the Weakly Ionized Plasma in plane geometry

Plasma Science and Technology 2005年第2期7卷 2713-2715页

作者：宋法伦曹金祥王舸 Department of Modern Physics University of Science and Technology of China Hefei 230027China

The purpose of the present work is to present a full-wave analysis of scattering from the weakly ionized plasma in the plane geometry. We have yielded an approximate solution in an analytic form to the electromagnetic wave scattering from the weakly ionized plasma. In the normal and oblique incidence, the analytic solution works well, as compared with the exact solution and the solution based on the Wenzell-Kramers-Brillouin-Jeffreys (WKBJ) approximation to the uniform density profile.

关键词： full-wave analyses electromagnetic wave weakly ionized plasma plane geometry

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Construction of Regular Heptagon by Rhombic Bicompasses and Ruler

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Applied Mathematics 2014年第15期5卷 2370-2380页

作者： A.Wünsche Humboldt-Universitat Berlin Institut für PhysikBerlinGermany

We discuss a new possible construction of the regular heptagon by rhombic bicompasses explained in the text as a new geometric mean of constructions in the spirit of classical constructions in connection with an unmarked ruler (straightedge). It avoids the disadvantages of the neusis construction which requires the trisection of an angle and which is not possible in classical way by compasses and ruler. The rhombic bicompasses allow to draw at once two circles around two fixed points in such correlated way that the position of one of the rotating points (arms) on one circle determines the position of the points on the other circle. This means that the positions of all points (arms) on both circles are determined in unique way.

关键词： plane geometry Algebra Geometric Constructions Heptagon Cyclotomic Equations Neusis

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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

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