Radio Network Planning and Optimization for 5G Telecommunication System Based on Physical Constraints

The paper mainly focuses on the network planning and optimization problem in the 5G telecommunication system based on the numerical investigation.There have been two portions of this work,such as network planning for efficient network models and optimization of power allocation in the 5G network.The radio network planning process has been completed based on a specific area.The data rate requirement can be solved by allowing the densification of the system by deploying small cells.The radio network planning scheme is the indispensable platform in arranging a wireless network that encounters convinced coverage method,capacity,and Quality of Service necessities.In this study,the eighty micro base stations and two-hundred mobile stations are deployed in the-15km×15km wide selected area in the Yangon downtown area.The optimization processes were also analyzed based on the source and destination nodes in the 5G network.The base stations’location is minimized and optimized in a selected geographical area with the linear programming technique and analyzed in this study.

SOME GENERAL THEOREMS AND GENERALIZED AND PIECEWISE GENERALIZED VARIATIONAL PRINCIPLES FOR LINEAR ELASTODYNAMICS

From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variational principles is derived. If the time dimension is not considered, the formulations obtained in the paper will become the corresponding ones for elastostatics.

Dynamic Analysis of Submarine Pipelines on an Elastic / Viscoelastic Foundation

This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation model. Some examples are also presented.

Research on Location-Routing Problem with Empirical Analysis for Regional Logistics Distribution

The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.

Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

A Procedure for Trisecting an Acute Angle (Method 2)

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.

基于Hash算法的DNA序列k-mer index问题的数学建模

针对查找DNA序列的相似序列问题,给出了建立索引和查找索引的数学模型,基于Hash算法,建立了依赖于k值大小的顺序索引模型和散列索引模型,特别对较大k值选用了DJBHash函数,有效的避免了Hash冲突问题。最后在硬件平台CPU为2.6GHz、内存为8G、操作系统为64位Windows 7的条件下,对100万条长度为100的DNA序列进行了测试,给出了不同k值下建立和查询索引的用时和占用内存情况,有效的解决了DNA序列的k-mer index问题。

ON THE NONLINEAR STABILITY OF SYMMETRICALLY LAMINATED CYLINDRICALLY ORTHOTROPIC SHALLOW SPHERICAL SHELLS

In this paper, the large deflection theory of symmetrically laminated cylindrically orthotropic shallow spherical shells is established. Based on this theory, applying the modified iteration method, the analytic solution for critical buckling loads of the shells with rigidly clamped edges under actions of uniform pressure has been obtained.

NONLINEAR BENDING OF SHALLOW SPHERICAL SHELLS ON THE PASTERNAK FOUNDATIONS

Based on Karman's nonlinear fundamental differential equations, the new approach, which combines modified iteration method with Galerkin's one, has been put forward to solve nonlinear bending of shallow spherical shell with concave base and clamped edges on the Pasternak foundation under uniform loads in this paper. Mathematical expression of load-deflection has been given; furthermore, results obtained are in good agreement with existent ones.

A Key to Solving the Angle Trisection Problem

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.

A Simplified Graphical Procedure for Constructing a 10˚or 20˚Angle

This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.

Polymetrical Analysis as Universal System of Formalization the Knowledge

Problem of search of universal system of formalization the knowledge is discussed.Philisophical,mathematical,cybernetic and computing aspects of its problem are analyzed.Foundation of polymetrical analysis as variant of resolution of this problem is represented.We show that this system allowed resolving S.Beer centurial problem in cybernetics.Also it allowed creating the natural(operational)approach in the foundation of mathematics and system concept of computing science.

中学生数学问题解决能力的发展轨迹——基于认知网络分析法的一项研究

培养中学生数学问题解决能力是中学数学课程与教学的重要目标之一。该研究采用认知网络分析法探索中学生数学问题解决能力的发展轨迹,表现为:首先具备问题转化能力与解题方案执行能力,进而具备问题转化能力、解题方案执行能力与问题结构化能力,最终具备解题方案制订能力在内的数学问题解决各维度能力。其中,问题结构化能力是促使中学生数学问题解决能力从低水平到中水平的关键,解题方案制订能力是促使中学生数学问题解决能力从中水平到高水平的关键。

“双减”背景下小学数学大单元教学问题分析及其解决策略

在“双减”政策背景下,大单元教学是落实核心素养、适应教育改革的新型教学模式。通过调查小学数学大单元教学的现状,总结了小学数学大单元教学目前存在的问题(教学方法枯燥呆板,缺乏创新变化;教学内容庞杂抽象,学生兴趣不高;考核方式片面单一,评价结果不全),提出了小学数学大单元教学的可行性策略(加强小学数学教师大单元教学培训;实施小学数学大单元的差异化教学;整合优化小学数学大单元教学内容;改进小学数学大单元教学考核方式)。提出的大单元教学实施策略可为今后开展小学数学的大单元教学提供方法学依据,也可促进教师专业发展和小学数学课堂的有机融合。

中考试题中数学建模问题情境的比较分析——以2020—2023年贵阳市中考卷为例

模型观念是初中阶段核心素养的主要表现形式之一,其在中考数学试题中常以问题情境的形式来考查.研究从“情境类型”“模型层次”“真实性水平”“表征特征”“阅读量”5个维度出发,对2020—2023年贵阳市中考数学建模问题情境的试题进行比较分析.研究发现:4套试题数量变化不大,保持了较高的稳定性;情境类型倾向于对“生活情境”的考查,逐渐增加对“文化情境”的涉及;模型层次水平较低,重视模型理解和应用的考查;真实性水平、表征特征及阅读量上有差异.鉴于此,提出以下教学建议:丰富情境类型,提升数学建模素养;创设真实情境,感悟数学本质;多样表征方式,助力获取问题信息;培养学生快速阅读能力.

利用数学分析的思想方法解决中学数学问题的途径探究

本文通过研究数学分析的相关概念和思想方法,与中学数学相对应的部分进行对比,探究利用数学分析的思想方法解决高中数学问题的途径,有利于丰富目前的高中数学解题方法和技巧,同时可促进数学分析课程的教学改革。

初中生“提出数学问题”的现状与对策

教育观念的偏差、教学方式的单一、教育评价的片面、问题意识的淡薄,造成了我国初中学生提出数学问题能力的欠缺.在数学教学中,应探讨培养初中学生提出数学问题能力的具体对策,比如:营造宽松和谐的问题环境;精心创设问题情境;培养学生的问题意识;开展合作交流学习;教给学生提出数学问题的具体方法.

数学问题解决中的元认知问卷量表的设计

数学问题解决中元认知问卷量表的设计应以数学问题解决中的元认知知识、元认知体验、元认知策略3者为基本因素.施测问卷过程中对数据进行探索性因素分析和验证性因素分析,检验因素假设与数据之间的拟合程度.结果表明:理论假设与数据间有较好的拟合,且“三主因素九次因素”假设与数据间的拟合更佳.

地表水污染源识别方法研究进展

地表水污染源的准确识别对于突发水污染事件中制定补救策略、确定责任方具有重要的指导意义。从污染源识别的基本问题出发,综述了地表水污染源识别的两类方法,一类是数学模拟法,包括直接求解法和间接求解法,直接求解法又包括解析法和正则化方法,间接求解法又包括模拟优化法、概率统计法及耦合算法;另一类是足迹分析法。在此基础上,系统地讨论了污染源识别的不确定性,包括污染源信息、观测数据、地表水模型、水动力条件、污染物性质5个方面。并指出地表水污染源识别的不确定性和时效性是制约其应用价值的关键因素,需要在方法耦合、识别效率提高、不确定性分析及污染物性质等方面做进一步的研究。

天然气需求自适应优化组合预测模型研究

文章用线性回归预测法、人工神经网络预测法、灰色系统预测法等对天然气消费需求量进行预测后,发现各预测值与实际需求量之间存在较大误差。为综合利用各方法提供的信息,避免单一预测模型丢失有用信息,减少随机性,提高预测的准确性,采用了新的优化组合预测法对天然气需求量进行预测,预测结果比单一预测法好。但优化组合预测模型求解的权系数是固定的,对有众多影响因素的天然气需求量进行预测不是最适合的,为此采用自适应递推适时算法对其进行改进,使用变化的权系数进行预测。结果表明自适应递推优化组合预测模型比优化组合预测模型预测的结果还要好。