Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics

Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.

Qualia Role-Based Quantity Relation Extraction for Solving Algebra Story Problems

A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translate problem texts into math expressions,which lack quantity relation acquisition in sophisticated scenarios.To address the problem,the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects.Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems.Experimental result shows that the proposedmethod achieved an average accuracy of 82.2%on quantity relation extraction compared to 74.5%of baseline method.Another prompt learning result shows a 5%increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.

Lie symmetry and Hojman conserved quantity of a Nielsen equation in a dynamical system of relative motion with Chetaev-type nonholonomic constraint

The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints

The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.

生产力和生产关系的质量互变规律与混合所有制经济的产生及运行分析

生产力具有各要素发展的不平衡性与总体水平发展的一致性特点,各要素发展的量变积累会引起生产力总体发展的根本质变,生产力总体发展的全局量变又会引起生产关系要素的局部质变,这为混合所有制经济的产生和运行提供了可能性和现实性。混合所有制经济是社会主义公有制的重要实现形式,具有强大的生命力,在促进国民经济发展、推动技术创新、提供就业岗位、增加居民收入以及实现乡村振兴战略等方面发挥极其重要的功能。

逆变器启动工况下光伏直流串联电弧故障识别方法

光伏系统逆变器启动时,最大功率点跟踪(maximum power point tracking,MPPT)等内部控制算法会引起电流瞬态变化,从而干扰直流串联电弧故障诊断装置对故障特征的正确识别,造成误动作。为此,针对逆变器启动情况下电弧故障检测装置易出现误动作的问题,提出一种基于无量纲特征量和灰色关联度的故障检测方法。首先分析了电弧故障RLC等效振荡模型,得出电弧电流信号在频域具有较宽的频带;然后分别对逆变器工况与电弧故障实测电流的频域特性进行了对比,发现正常工况与故障在1~20 kHz和40~60 kHz范围内的频谱在波峰陡峭度、所处位置等方面存在差别,使用峭度、偏度、峰值因子、冲击因子、裕度因子、波形因子等提取频谱特征,计算灰色关联度并进行故障识别;最后,分别使用模拟平台和实际光伏系统进行了试验验证。结果表明,所提方法可有效避免逆变器启动造成的干扰,提高故障识别的准确度。

切割事件句中容器量词的语义功能

本文讨论切割事件句(如,“他切了一盘西瓜”)中容器量词的语义功能,首先分析切割事件句的歧义性,指出宾语的指称变化可导致切割类动词,如“切”在“切分”义和“切除”义之间波动,并从意象图式的角度对这一现象进行解释。然后,文章举出包含容器量词的切割事件句的歧义现象,并指出意象图式说所面临的困境;进而提出“同量指称”假设,并在该假设的基础上对相关问题进行解释。文章认为,容器量词属于开放类词汇,这一特性一方面为它们的同量指称性的产生提供先决条件,另一方面又造成它们与名词搭配方面的语义选择限制。最后,文章对语义最小论的相关观点进行了讨论。

悬浮电压在大型水电厂监控系统开关量中的应用及研究

经过隔离变压器输出的直流电压,没有与大地相连,对地测量到的浮动的电压就是悬浮电压。大型水电厂监控系统开关量电源一般采用直流24 V的悬浮电压,由于悬浮电压不接地,当开关量直流回路发生一点接地故障时并不马上产生后果,当出现第二点接地时,就可能发生短路造成继电保护、自动装置、开关等误动,严重时甚至导致事故停机。针对悬浮电压在水电厂监控系统开关量中的应用,研究并总结了一套快速排查开关量接地故障的技术。

Optimization of cutting parameters with Taguchi and grey relational analysis methods in MQL-assisted face milling of AISI O2 steel

This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different statistical methods.Vegetable oil was preferred as cutting fluid,and Taguchi method was used in the preparation of the test pattern.After testing with the prepared test pattern,cutting performance in all parameters has been improved according to dry conditions thanks to the MQL system.The highest tool life was obtained by using cutting parameters of 7.5 m cutting length,100 m/min cutting speed,100 mL/h MQL flow rate and 0.1 mm/tooth feed rate.Optimum cutting parameters were determined according to the Taguchi analysis,and the obtained parameters were confirmed with the verification tests.In addition,the optimum test parameter was determined by applying the gray relational analysis method.After using ANOVA analysis according to the measured surface roughness and cutting force values,the most effective cutting parameter was observed to be the feed rate.In addition,the models for surface roughness and cutting force values were obtained with precisions of 99.63%and 99.68%,respectively.Effective wear mechanisms were found to be abrasion and adhesion.

Effect of Rare Earth Elements on Quantity Growth of Crops

The effects of rare earth on the growth of rice, rape and soybean in three kinds of soils were studied with the method supposed by Economic Co-operation and Development organization (OECD), and the EC50(median growth concentration)values were obtained. The inhibition of RE on the growth of rice and rape in red soil and on the growth of soybean in yellow fluvo-aquic soil is higher with stronger poison effects. Compared with other heavy metals such as Hg, Cd, Pb, As, the poison of RE on crops is weaker.

电信网络诈骗关联犯罪法律适用疑难问题研究

以检察统一业务应用系统数据为依托,分析受案时间、简要案情、审结数额、审结罪名、一审宣告刑等“检察数字”,发现涉“两卡”类电信网络诈骗关联犯罪惩治对象多为犯罪链条末端的“卡农”,罪名集中于帮助信息网络犯罪活动罪和掩饰隐瞒犯罪所得罪,两罪不同发案时期出现同质变量、此消彼长的趋势,检视发现网络犯罪规制的刑法扩张和司法的扩大适用、电信网络诈骗关联犯罪?“主观明知”认定泛化,“客观行为”过度评价,罪名界限模糊,罪刑不适等问题。准确认定电信网络诈骗及其关联犯罪,提倡坚持形式与实质综合标准,以罪刑相适应原则进行调适的解决途径。

科技文献中4个不等二元关系符号的左边元素缺失及相关问题

探讨科技文献中用于比较实数(或同一类量)大小的不等二元关系符号(≥,≤,>,<)的左边元素(指实数或同一类量)缺失是否产生错误以及主要相关问题,其中同一类量指的是可以相互比较的物理量。根据数学基础知识论证了一个非空集合X上的二元关系符号R的左右两边元素缺一不可的结论,指出了关系符号用法上的注意问题;利用数学知识和国家标准相结合的方法,判定了二元关系符号(≥,≤,>,<)左边元素缺失是错误的,分析了产生错误的原因,给出了纠错方法;结合实例阐明了二元关系符号(≥,≤,>,<)用于变量范围表示时容易误判为关系符号左边元素缺失但实际并不缺失的问题。

灸法量效关系的研究进展与思考

灸法疗效不仅与施灸所用的材料和穴位的特异性有关,而且与灸量密切相关。近年来,很多学者在灸量与疗效的关系上进行了广泛研究。分别从影响灸量的各个因素概述了灸量和疗效关系的研究进展。希望对以后能更好的研究最佳灸量并指导临床提供帮助。

红花种质资源主要数量性状的灰色关联度分析

以26份红花种质资源为材料,应用灰色关联度分析方法,对红花的主要数量性状进行了分析。结果表明:对单株产量影响最大的是分枝总数,其后依次是单株有效果球数>茎粗>果球着粒数>顶花球直径>株高>生育期>千粒重。根据红花主要农艺性状间的关系,对产量影响最大的分枝总数与茎粗、株高、单株有效果球数和果球着粒数关系最为密切;对产量影响较大的单株有效果球数与分枝总数、茎粗、果球着粒数关系密切。因此,对红花高产育种而言,在保证适当的株高和茎粗的前提下,要注重选育分枝多、单株有效果球多、果球着粒数多和生育期适中的品种,同时不要忽略对品种千粒重和顶花球直径的选择。