In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a...In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f（x） whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.展开更多
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...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].展开更多
A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), wh...A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), which can reach 2 orders higher than that of traditional high birefringence fiber, and this equal diameter circular-hole structure reduces the difficulty of the actual drawing process. The effect of different parameters on the birefringence of this PCF is investigated, and the application of the Sagnac interferometer based on fiber filling technology in temperature sensing is studied. The result shows that the high birefringence PCF can be used in both optical communication and optical sensing fields.展开更多
基金Supported by the National Key Basic Research Project of China under Grant No. 2004CB318000
文摘In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f（x） whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.
文摘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].
基金supported by the National Natural Science Foundation of China(Nos.61301124,61471075 and 61671091)the Basic Research Project of Chongqing Science and Technology Commission(Nos.cstc2014gjhz40001,cstc2015jcyj BX0068,cstc2014jcyj A1350,cstc2015jcyj B0360 and KJZH17115)+3 种基金the University Innovation Team Construction Plan of Smart Medical System and Core Technologythe Enhancement Plan of Chongqing Key Laboratory of Photoelectronic Information Sensing and Transmitting Technologythe Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJ1704091)the Funds of Chongqing University of Posts and Telecommunications(No.A2016-72)
文摘A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), which can reach 2 orders higher than that of traditional high birefringence fiber, and this equal diameter circular-hole structure reduces the difficulty of the actual drawing process. The effect of different parameters on the birefringence of this PCF is investigated, and the application of the Sagnac interferometer based on fiber filling technology in temperature sensing is studied. The result shows that the high birefringence PCF can be used in both optical communication and optical sensing fields.
