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The Generalization and Proof of “Square Root of 2 Is Not a rational number” on the Integral Domain

Advances in Pure Mathematics 2021年第7期11卷 665-669页

作者： Tongchao Liu Math Teaching and Research Office in Chengdu College of Arts and Sciences Chengdu China

In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if n is not a square, square root of n is not a rational number”. And then some conceptions of ring, integral domain, ideal, quotient ring in Advanced algebra, have been introduced. Integers can be regarded as an integral domain, the rational numbers can be regard as a fractional domain. Evens and odds are principal ideals in integral domain. The operations on evens and odds are operations on quotient ring. After introducing “the minimalist form” in fraction ring. The paper proves the main conclusion: in a integral domain, multiplicative subset S produces a fraction ring S−1R, and n is not a square element in R, then to every element a∈R, a2≠n.

关键词： rational number Integral Domain Ideal Fraction Ring Generalize

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Efficient Protocols for the General Millionaires' Problem

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Chinese Journal of Electronics 2017年第4期26卷 696-702页

作者： LI Shundong GUO Yimin ZHOU Sufang DOU Jiawei WANG Daoshun School of Computer Science Shaanxi Normal University School of Mathematics and Information Science Shaanxi Normal University Department of Computer Science and Technology Tsinghua University

Secure multiparty computation(SMC) is a research focusing in the international cryptographic community. The protocols used to address the millionaires’ problem are the basic building blocks of most SMC protocols and their efficiency dominates that of many other SMC protocols. To the best of our knowledge, almost all protocols used to address the millionaires’ problem are based on integers, which means that their applications are limited. In this study, we propose precise and efficient protocols for rational numbers based on additively homomorphic encryptions. One of our protocols is inspired by computational geometry and it reduces the millionaires’ problem to computing the area of a triangle formed by three private points. This approach can determine whether the relationship between two private inputs is greater than, equal to or less than, and it has a much lower computational complexity compared with existing methods. We proved that these protocols are secure using simulation paradigm. Our approaches can be used in many SMC protocols that involve rational numbers and integers, and they can also be used directly to solve some secure multiparty computational geometry problem in rational number field.

关键词： General millionaires’ problem Secure multiparty computation rational number Computational geometry Homomorphic encryption

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Periodic Orbits Around Kerr Sen Black Holes

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Communications in Theoretical Physics 2019年第12期71卷 1461-1468页

作者： Chang-Qing Liu Chi-Kun Ding Ji-Liang Jing Department of Physics Hunan University of Humanities Science and TechnologyLoudi 417000China Department of Physics and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of EducationHunan Normal UniversityChangsha 410081China

We investigate periodic orbits and zoom-whirl behaviors around a Kerr Sen black hole with a rational number q in terms of three integers(z,w,v),from which one can immediately read off the number of leaves(or zooms),the ordering of the leaves,and the number of *** characteristic of zoom-whirl periodic orbits is the precession of multi-leaf orbits in the strong-field *** feature is analogous to the counterpart in the Kerr ***,we analyze the impact of the charge parameter b on the zoom-whirl periodic *** to the periodic orbits around the Kerr black hole,it is found that typically lower energies are required for the same orbits in the Kerr Sen black hole.

关键词： periodic orbits Kerr Sen black hole zoom-whirl rational number

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