Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular rostricted 3-body problem in R^3 or R^2 are also planar equilateral triangle circular solutions.

中高职“3+2”衔接教育及存在的问题、原因与对策

通过对湖北省及全国部分地区中高职“3+2”衔接技能人才分段培养的调研,梳理人才培养过程中存在的问题及主要原因。一是高职阶段学生学习动力不足,学生管理难度大;原因有中职段管理不严,学习无压力,及教学设计存在问题;二是课程设置存在脱节与重叠现象;问题原因是标准未严格执行,并且中高职校缺乏沟通;三是存在衔接口径不匹配现象;原因在于缺乏专业设置标准及监督。针对问题提出了相应的对策建议。一是要建立统一的专业衔接标准、专业教学标准,加强标准执行情况的检查力度;二是要改革“3+2”转段考核的方式,加强中职学生平时成绩的要求与管理;三是加强中高职的沟通与交流;四是延伸中高职衔接为中高本衔接。

Variational minimizing parabolic and hyperbolic orbits for the restricted 3-body problems Dedicated to my Teacher Professor Yang Wannian on the Occasion of his 75th Birthday

Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.

Geometric characterizations for variational minimizing solutions of charged 3-body problems

We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the τ/2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.

Geometric characterizations for variational minimization solutions of the 3-body problem

For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.

随机正则3-可满足性问题的解簇结构分析

正则3-可满足性(3-SAT)问题是一个NP难问题,研究正则3-SAT问题解簇结构变化,旨在深入理解该问题的判定难度和可满足性解的分布情况。然而,现有分析模型只研究了接近簇集相变点的几个离散值,在不同约束密度下,缺乏统一的分析模型来描述解簇的结构演变。为了解决这一问题,提出解簇结构相变分析模型(PMSS)。该模型主要思想是采用WalkSAT算法和信息传播算法求得正则3-SAT问题可满足的初始解,再利用随机游走构造该初始解的解簇,并对解簇进行分析。用模块度和社区度量解簇社区结构,用结构熵度量解簇结构复杂性。实验结果表明,PMSS能够准确分析解簇结构演变过程,并且正则3-SAT问题实例的可满足相变点位于13~14,与使用Zchaff求解器得到的相变点一致,进一步验证了PMSS的有效性。

三孩政策下0—3岁婴幼儿托育服务存在的问题与对策

2021年三孩政策在全国范围内正式实施,使得托育服务成为民生刚性需求。随着托育服务事业的迅速发展,其面临的一系列困境值得关注。从托育服务的四大主体政府、社会、教师和家庭四方面分析当前0—3岁婴幼儿托育服务存在的问题。在此基础上,提出相应的优化对策,即完善政策体系与托育制度,持续加大政府扶持力度,重点发展普惠性托育服务,提高托育服务质量,加强托育人员队伍建设,发展特色早教课程,创新社区托育模式等,以期促进0—3岁婴幼儿健康成长。

基于高质量发展的“3+2”人才培养问题分析

通过中高职衔接培养方式,拓宽职业教育学生发展通道,是新时代职业教育高质量发展的核心方向之一。本文首先概述了中高职衔接“3+2”人才培养模式的提出及发展历程;其次结合经济社会高质量发展对职业教育提出的新要求、新作为进行了梳理分析;再次针对中高职衔接试点项目,从宏观设计和北京、沈阳两市具体实施现状进行概述;最后指出中高职衔接培养中存在的问题,进而为促进中高职协调发展、提升衔接培养人才质量提出相关对策,奠定基础。

Why is the Danger Cylinder Dangerous in the P3P Problem?

The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.

Key Problems of Cold Power Spinning of Ti-15-3 Alloy

The key problems of cold power spinning of Ti-15-3 alloy are studied. Reasonable billet preparation methods are presented to improve crystal structure and avoid crack of billet. Influences of original wall thickness, reduction rate and feed rate on expanding in diameter are analyzed and some methods to prevent expanding in diameter are given.

An adiabatic quantum optimization for exact cover 3 problem

A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.

On the Solution to the Separated Equation in the 3-Particle Calogero-Moser Problem

We propose the exact solution of the equation in separated variable which appears in the process of constructing solutions to the quantum Calogero-Moser three-particle problem with elliptic two-particle potential . This solution is found for special values of coupling constants . It can be used for solving three-particle Calogero-Moser problem under the appropriate boundary conditions.

Approximation Schemes for the 3-Partitioning Problems

The 3-partitioning problem is to decide whether a given multiset of nonnegative integers can be partitioned into triples that all have the same sum. It is considerably used to prove the strong NP-hardness of many scheduling problems. In this paper, we consider four optimization versions of the 3-partitioning problem, and then present four polynomial time approximation schemes for these problems.

Structure Formation and Non Linear Electrodynamics with Attendant Changes in Gravitational Potential and Its Relationship to the 3 Body Problem

We find that having the scale factor close to zero due to a given magnetic field value, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction of the universe”. We extend such arguments, and refer to the possibility of modified gravity. We hope that some of the issues raised by Kobayashi and Seto as to allowed inflation models may be addressed, once further refinement of these preliminary results commences. We close with statements as to the value of α in a gravitational potential proportional to r?α and how this adjustment affects the 3 body problem.

The Analysis of Convergence for the 3<i>X</i>+ 1 Problem and Crandall Conjecture for the a<i>X</i>+ 1 Problem

The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3X + 1 problem. It is worth noting that, both conjectures are infamous for their simplicity in stating but intractability in solving. In this paper, I aim to provide a clear explanation about the reason why these two problems are difficult to handle and have very different characteristics on convergence of the series via creatively applying the probability theory and global expectancy value E(n) of energy contraction index. The corresponding convergence analysis explicitly shows that a = 3 leads to a difficult problem, while a > 3 leads to a divergent series. To the best of my knowledge, this is the first work to point out the difference between these cases. The corresponding results not only propose a new angle to analyze the 3X + 1 problem, but also shed some light on the future research.

GENERALIZED UPWIND SCHEME WITH FRACTIONAL STEPS FOR 3-D PROBLEM OF CONVECTION DOMINATING GROUNDWATER TRANSPORT

A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.

On the Change Rule of 3x + 1 Problem

This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3n – 1| n ∈ Z+};3) Then this 3n - 1 will change to a smaller 3n – 1 and gradually decrease to 8 (that is 32 - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2n (it might even explain 2n). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.

Numerical Solution of Some Diffusion Problems in 3-Layered 3D Domain

In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.

The Simplest Possible Fully Correct Solution of the Clay Millennium Problem about P vs. NP. A Simple Proof That P ≠ NP = EXPTIME

In the current paper, I present probably the simplest possible abstract formal proof that P ≠ NP, and NP = EXPTIME, in the context of the standard mathematical set theory of computational complexity and deterministic Turing machines. My previous publications about the solution of the P vs. NP with the same result NP = EXPTIME, to be fully correct and understandable need the Lemma 4.1 and its proof of the current paper. The arguments of the current paper in order to prove NP = EXPTME are even simpler than in my previous publications. The strategy to solve the P vs. NP problem in the current paper (and in my previous publications) is by starting with an EXPTIME-complete language (problem) and proving that it has a re-formulation as an NP-class language, thus NP = EXPTIME. The main reason that the scientific community has missed so far such a simple proof, is because of two factors 1) It has been tried extensively but in vain to simplify the solutions of NP-complete problems from exponential time algorithms to polynomial time algorithms (which would be a good strategy only if P = NP) 2) It is believed that the complexity class NP is strictly a subclass to the complexity class EXPTIME (in spite the fact that any known solution to any of the NP-complete problems is not less than exponential). The simplicity of the current solution would have been missed if 2) was to be believed true. So far the majority of the relevant scientific community has considered this famous problem not yet solved. The present results definitely solve the 3rd Clay Millennium Problem about P versus NP in a simple, abstract and transparent way that the general scientific community, but also the experts of the area, can follow, understand and therefore become able to accept.

Enhancing Numeracy Skills of Grade 3 Students Through Authentic Performance Tasks

Numeracy is the capacity to use mathematical ideas in all facets of life.It involves activities such as adding and subtracting numbers,counting,number recognition,solving number problems involving various operations,sorting,observing,identifying,and establishing patterns.It is one of the fundamental skills that students should have mastered by the end of their primary schooling.With the notable importance of mastery of numeracy skills,low achievement and performance of the learners were observed in this aspect.This study aimed in enhancing the numeracy skills of Grade 3 learners through authentic performance tasks.The variable in numeracy skills includes the four fundamental operations and problem solving.The quasi-experimental design was utilized wherein purposive sampling or non-randomized sampling was used.In this study,33 Grade 3 learners of Rizal Elementary School were selected to participate in the tests.Pre-test and post-test crafted by the teacher were the main instrument in the study.The result revealed that in the pre-test the learners obtained a mean percentage score(MPS)of 38.20%in four fundamental operations,which implied a non-numerate level.While in terms of problem solving,the learners obtained a MPS of 20.60%which is also in the non-numerate level.It has a grand mean of 29.40%with an interpretation of non-numerate level.In the post-test,it was observed that four fundamental operations have a MPS of 81.10%which is in average numerate level,while problem solving has a MPS of 76.30%with a grand mean of 78.70%with an interpretation of average numerate level.This implied that there is a significant difference between the pre-test and post-test in the four fundamental operations and problem solving.Thus,it can be concluded that the application of authentic performance tasks was effective to bridge the gap on numeracy skills.