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The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem
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作者 Bijay Kumar Sharma 《International Journal of Astronomy and Astrophysics》 2024年第1期1-19,共19页
Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubatio... Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study. 展开更多
关键词 Hill’s Radius Two-Body problem Fixed-Point solution Lagrange Points Earth-Moon-Test Particle CRTBP
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矩阵秩的Sylvester与Frobenius等式问题 被引量:2
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作者 吕登峰 刘琼 胡付高 《孝感学院学报》 2006年第6期62-65,共4页
本文通过线性空间的线性变换讨论了Sylvester与Frobenius不等式取等号的条件,并将它们推广到矩阵多项式中,建立了一类广泛的秩恒等式。
关键词 sylvester不等式Frobenius不等式 线性变换 矩阵的秩
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求解Sylvester方程的正交迭代算法
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作者 殷霞 章里程 廖祖华 《江南大学学报(自然科学版)》 CAS 2014年第6期731-735,共5页
对于任意初始矩阵,运用求解Sylvester矩阵方程的正交迭代算法可以在有限步内得到方程的最小二乘解,而且通过选择初始矩阵还可以得到方程的极小范数最小二乘解,这种算法还能用于解决最佳逼近问题,数值例子表明了所提出算法的有效性。
关键词 sylvester矩阵方程 正交迭代算法 最小二乘解 极小范数解 最佳逼近问题
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S-T-S混合式循环互助教学模式用于少学时“化工原理”课程
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作者 吕玲 《教育教学论坛》 2024年第31期157-160,共4页
“化工原理”课程是化工及相关专业的专业基础课程,相关专业的学时少,课程难,需重点解决的问题是“三多”“三不愿”“三不明”。针对痛点问题,提出了线上线下混合式循环互助的创新设计思路,包括:教师帮助学生自制课前、课中、课后习题... “化工原理”课程是化工及相关专业的专业基础课程,相关专业的学时少,课程难,需重点解决的问题是“三多”“三不愿”“三不明”。针对痛点问题,提出了线上线下混合式循环互助的创新设计思路,包括:教师帮助学生自制课前、课中、课后习题,学生帮助教师反馈真实学习情况,学生帮助学生组团互助学习。问卷调查和评教结果显示,在一定程度上解决了“三多”“三不愿”的问题;通过建立“助教团队”反馈不同层次学生的学习情况,较好地解决了“三不明”的问题。学生的成绩与教改前相比有明显提高。 展开更多
关键词 线上线下 s-T-s教学模式 化工原理 痛点问题
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求解Sylvester问题的梯度镜面下降算法 被引量:1
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作者 董榕恩 杨娅 胡清洁 《桂林电子科技大学学报》 2018年第6期500-504,共5页
针对Sylvester问题,基于对数指数光滑方法,提出了一种求解Sylvester问题的梯度镜面下降算法,并给出了该算法的收敛速度分析。数值结果表明,梯度镜面下降算法求解Sylvester问题是有效的。
关键词 sylvester问题 对数指数光滑方法 梯度镜面下降算法
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The Gleason's problem on normal weight general function spaces in the unit ball of C^(n)
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作者 GUO Yu-ting ZHANG Xue-jun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第4期604-613,共10页
In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the G... In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s). 展开更多
关键词 Gleason's problem sOLVABILITY F(p μ s)space integral operator
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Hilbert’s First Problem and the New Progress of Infinity Theory
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作者 Xijia Wang 《Journal of Applied Mathematics and Physics》 2023年第4期891-904,共14页
In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it th... In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory. 展开更多
关键词 Hilbert’s First problem Cardinal Numbers Method Grossone Method Continuum Paradox Infinity Theory
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A Key to Solving the Angle Trisection Problem
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作者 Lyndon O. Barton 《Advances in Pure Mathematics》 2023年第9期625-634,共10页
This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach ... This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem. 展开更多
关键词 Archimedes Construction College Geometry College Mathematics Angle Trisection Trisector Famous problems in Mathematics History of Mathematics Mechanism Analysis Kinematics Geometer’s sketch Pad
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Relationship between Authoritative Parenting Style and Preschool Children’s Emotion Regulation:A Moderated Mediation Model
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作者 Yan Jin Wei Chen 《International Journal of Mental Health Promotion》 2024年第3期189-198,共10页
An authoritative parenting style has been shown to promote children’s emotion regulation in European-American family studies.However,little is known about how sleep problems and the child’s sibling status in Chinese... An authoritative parenting style has been shown to promote children’s emotion regulation in European-American family studies.However,little is known about how sleep problems and the child’s sibling status in Chinese families affect this relationship.Based on family system theory,this study attempts to better understand the relationship between authoritative parenting style and emotion regulation.Mothers of preschool children in Chinese kindergartens completed questionnaires about their children’s sleep habits,their authoritative parenting styles,and children’s emotion regulation.A total of 531 children participated in this study.Results showed that authoritative parenting was positively associated with emotional regulation.Sleep problems mediated the effects of authoritative parenting style on emotion regulation.The child’s sibling status moderated the mediating effects of sleep problems in authoritative parenting and emotion regulation relationships.Specifically,the relationship between the authoritative parenting style and sleep problems was significant for only children,while birth order had no significant influence on the authoritative parenting style and sleep problems in two-child families.These findings suggest that a lowauthoritative parenting style predicts low emotion regulation through sleep problems,and this depends on the child’s sibling status,indicating that children without siblings may impair emotion regulation due to increased sleep problems. 展开更多
关键词 sleep problem emotional regulation authoritative parenting child’s sibling status preschool children
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A Poisson Solver Based on Iterations on a Sylvester System
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作者 Michael B. Franklin Ali Nadim 《Applied Mathematics》 2018年第6期749-763,共15页
We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations oc... We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur on this Sylvester system directly after introducing a deflation-type parameter that enables optimized convergence. Analytical bounds are obtained on the spectral radii of the iteration matrices. Our method is comparable to Successive Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework with considerable improvement in performance as shown herein. 展开更多
关键词 Poisson’s EQUATION sylvester sYsTEM MULTIGRID
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列正交约束下广义Sylvester方程极小化问题的有效算法
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作者 刘月园 王凯 +1 位作者 秦树娟 李姣芬 《数学物理学报(A辑)》 CSCD 北大核心 2021年第2期479-495,共17页
研究列正交约束下广义Sylvester方程极小化问题的有效算法.基于Stiefel流形的几何性质和欧氏空间中的MPRP共轭梯度法,构造一类黎曼MPRP共轭梯度迭代求解算法,给出算法全局收敛性.该迭代格式得到的搜索方向总能保证该目标函数下降.数值... 研究列正交约束下广义Sylvester方程极小化问题的有效算法.基于Stiefel流形的几何性质和欧氏空间中的MPRP共轭梯度法,构造一类黎曼MPRP共轭梯度迭代求解算法,给出算法全局收敛性.该迭代格式得到的搜索方向总能保证该目标函数下降.数值实验和数值比较验证所提出算法对于问题模型是高效可行的. 展开更多
关键词 广义sylvester方程 极小化问题 列正交约束 黎曼共轭梯度法
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A Procedure for Trisecting an Acute Angle (Method 2)
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作者 Lyndon O. Barton 《Advances in Pure Mathematics》 2024年第4期204-213,共10页
This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”.... This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others. 展开更多
关键词 Archimedes Construction College Geometry College Mathematics Angle Trisection Famous problems in Mathematics Mechanism Analysis Geometer’s sketch Pad
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value problem sign-Changing Green’s Function Fixed Point Index Iterative Technique Monotone Positive solution EXIsTENCE
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Manual Order Picking Route Optimization in Distribution Warehouse of Chain Furniture Retail Enterprise
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作者 Yongzhen Zeng Junkun Wang +1 位作者 Ching-Kuei Kao King-Zoo Tang 《American Journal of Operations Research》 2024年第3期105-136,共32页
Due to the effects of the COVID-19 pandemic and the rise of online shopping, the offline sales of IKEA Fuzhou have been declining since 2020. Because the cost of distribution warehouse is a major expense for offline c... Due to the effects of the COVID-19 pandemic and the rise of online shopping, the offline sales of IKEA Fuzhou have been declining since 2020. Because the cost of distribution warehouse is a major expense for offline chain furniture retailers, and the picking process is a key activity in distribution warehouse operations. To reduce the cost of distribution warehouse and alleviate the survival pressure of the offline chain furniture retailers, this paper focuses on optimizing the picking route of the IKEA Fuzhou distribution warehouse. It starts by creating a two-dimensional coordinate system for the storage location of the distribution warehouse using the traditional S-type picking strategy to calculate the distance and time of the sorting route. Then, the problem of optimizing the picking route is then transformed into the travelling salesman problem (TSP), and picking route optimization model is developed using a genetic algorithm to analyze the sorting efficiency and picking route optimization. Results show that the order-picking route using the genetic algorithm strategy is significantly better than the traditional S-type picking strategy, which can improve overall sorting efficiency and operations, reduce costs, and increase efficiency. Thus, this establishes an implementation process for the order-picking path based on genetic algorithm optimization to improve overall sorting efficiency and operations, reduce costs, increase efficiency, and alleviate the survival pressure of pandemic-affected enterprises. 展开更多
关键词 s-shaped Picking strategy Picking Route Traveling salesman problem Genetic Algorithm
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(S,T)-WEAK TRACTABILITY OF MULTIVARIATE LINEAR PROBLEMS IN THE AVERAGE CASE SETTING 被引量:1
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作者 Yongping LIU Guiqiao XU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期1033-1052,共20页
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function... The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem. 展开更多
关键词 (s t)-weak TRACTABILITY LINEAR problem LINEAR tensor product problem HILBERT space AVERAGE case setting
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EXISTENCE OF SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION 被引量:10
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作者 Su Xinwei Liu Landong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第3期291-298,共8页
This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
关键词 fractional differential equation boundary value problem Caputo's fractional derivative schauder fixed-point theorem.
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(r, s)-STABILITY OF UNFOLDING OF г-EQUIVARIANT BIFURCATION PROBLEM 被引量:1
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作者 刘恒兴 张敦穆 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期408-418,共11页
In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally ... In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability. 展开更多
关键词 г-equivariant bifurcation problem UNFOLDING TRANsVERsALITY г-equivariant infinitesimally (r s)-stability г-equivariant (r s)-equivalence.
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A Solution to the Famous “Twin’s Problem” 被引量:2
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作者 Prodromos Char. Papadopoulos 《Advances in Pure Mathematics》 2019年第9期794-826,共33页
In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introductio... In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introduction of special intervals between square of prime numbers that I call silver intervals . And I make introduction of another also new mathematic phenomenon of logical proposition “In mathematics nothing happens without reason” for which I use the ancient Greek term “catholic information”. From the theorem of prime numbers we know that the expected multitude of prime numbers in an interval is given by formula ?considering that interval as a continuous distribution of real numbers that represents an elementary natural numbers interval. From that we find that in the elementary interval around of a natural number ν we easily get by dx=1 the probability that has the ν to be a prime number. From the last formula one can see that the second part of formula (4.18) is absolutely in agreement with the above theorem of prime numbers. But the benefit of the (4.18) is that this formula enables correct calculations in set N on finding the multitude of twin prime numbers, in contrary of the above logarithmic relation which is an approximation and must tend to be correct as ν tends to infinity. Using the relationship (4.18) we calculate here the multitude of twins in N, concluding that this multitude tends to infinite. But for the validity of the computation, the distribution of the primes in a random silver interval is examined, proving on the basis of catholic information that the density of primes in the same random silver interval is statistically constant. Below, in introduction, we will define this concept of “catholic information” stems of “information theory” [1] and it is defined to use only general forms in set N, because these represent the set N and not finite parts of it. This concept must be correlated to Riemann Hypothesis. 展开更多
关键词 Twin problem Twin’s problem Unsolved Mathematical problems Prime NUMBER problems Millennium problems Riemann HYPOTHEsIs Rie-mann’s HYPOTHEsIs NUMBER THEORY Information THEORY Probabilities statistics
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EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS 被引量:2
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作者 龚循华 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1179-1192,共14页
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we der... In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set. 展开更多
关键词 Ekeland's principle set-valued vector equilibrium problems weakly efficient solution c-approximate solution EXIsTENCE
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Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part III. An Original Solution of Hilbert’s Fourth Problem 被引量:3
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作者 Alexey Stakhov Samuil Aranson 《Applied Mathematics》 2011年第3期283-293,共11页
This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geom... This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements. 展开更多
关键词 Euclid’s Fifth Postulate Lobachevski’s GEOMETRY HYPERBOLIC GEOMETRY Phyllotaxis Bodnar’s GEOMETRY Hilbert’s FOURTH problem the “Golden” and “Metallic” Means Binet Formulas HYPERBOLIC FIBONACCI and Lucas Functions Gazale Formulas “Golden” FIBONACCI -Goniometry
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