The Principle of Differentiation into Physical and Mathematical Theories

The article formulates the main principle of physics, which underlies this science. This principle has been called by the author of this article the Principle of differentiation into physical and mathematical theories. The article gives examples of the application of this principle in quantum mechanics and cosmology. A more detailed proof of the principle of equivalence of the electromagnetic field and the field of strong interaction to a free material particle is given. This principle, formulated in the article “Electrodynamics in Curvilinear Coordinates and the Equation of a Geodesic Line”, revealed the nature of the mass of elementary particles and became the basis for the formulation of the Principle of differentiation into physical and mathematical theories.

Mathematic principle of active jamming against wideband LFM radar

The inherent mathematic principle of active jamming against the wideband linear frequency modulated（LFM） radar is investigated. According to different generation strategies, the active jamming methods are reclassified into three groups, i.e.,non-coherent jamming（NCJ）, convolution jamming（CJ） and multiplying jamming（MJ）. Based on the classification, the mathematic principles of different active jamming groups are put forward, which describe the relationships between the modulated signals and the jamming results. The advantages and disadvantages of different groups are further analyzed, which provides a new perspective for the study of jamming/anti-jamming methods and a potential for engineers to integrate similar jamming methods into one jammer platform. The analyses and simulation results of some typical active jamming methods prove the validity of the proposed mathematics principle.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

A FINITE ELEMENT—MATHEMATICAL PROGRAMMING METHOD FOR ELASTOPLASTIC PROBLEMS BASED ON THE PRINCIPLE OF VIRTUAL WORK

By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

递归原理的思维特性及其数学应用

递归原理的基本思想隐含于数学知识或解题过程中,构造递归结构是运用递归方法进行解题的关键步骤,也凸显了递归方法解题的策略性和技巧性。递归原理具有结构化、条件性、有限性和辩证性等思维特性,在数学实践中,结合数学课程内容,通过强化递归原理的数学观念、思想方法、策略模式等进行解题思维训练,可引导学生达成思维自控,不断提升思维能力,完善数学认知结构。

电阻抗断层成像技术(EIT)的数学建模与其他应用场景

电阻抗断层成像(EIT)技术在医学成像和隐身技术等领域有着广泛的应用前景,本文首先对EIT的成像原理及其优缺点进行了论述;然后,对EIT在隐身技术和作为机械通气检测新技术的临床应用方面进行了介绍;最后,介绍了EIT的数学建模,尤其详细介绍了四种电极模型.EIT数学模型带来了偏微分方程的正问题、反问题、硬件系统设计以及图像去噪问题,成为这一技术的核心的“卡脖子”部分.

“双减”导向下小学数学课后作业设计的几点探究

教师只有科学合理地设计课后作业,才能减负提质、有效落实素质教育目标,真正将“双减”政策落到实处。基于此,文章从课后作业的概念及重要意义入手,探讨了小学数学课后作业的设计原则和有效设计策略,以期通过科学合理的课后作业设计,深入挖掘学生潜能、激发学生思维、丰富学生经验、加深学生对重要知识点的理解与记忆,从而打开全新的教学格局,使数学教学过程变得更加精彩,让课后作业在实现“双减”导向下的教学活动中发挥重要作用。

数学几何美学在服装设计中的应用

随着人们对服饰的艺术性和实用性要求的日益提高,设计师开始将数学引入服装设计中。数学中的形状、比例和对称性等几何美学为服装设计带来了新的视角。数学与服装设计跨学科的融合丰富了服装设计的表现形式,提高了功能性和审美性。

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

论《营造法式》开间、柱高的取值比例及其形式关联

关于中国古代建筑是否存在复杂精密、成熟稳定且可理性解析的立面构成法则,是建筑历史研究中一个经典的命题。本文在前人研究基础之上,进一步借由作图验算,以铺作层与柱高、间广赋值间的联动方式为考察对象,探索固有数理比例耦合特定图形关系的内因。提出以分°值控制铺作总高,继而以其作为基准、以檐高的■定出柱高,再由柱高间广关系扩展至整个立面设计的操作模型,并结合《营造法式》料例、功限章节所载数据,验证了该算法的可行性,以期将利用几何或代数方法分别解析宋式建筑立面的两种既有工作统合于同一逻辑框架之内。

基于AMESim的高压溢流阀特性分析

先导式高压溢流阀作为轴向柱塞变量泵或轴向柱塞变量马达的安全阀,其工作性能将直接关系到轴向柱塞变量泵、轴向柱塞变量马达及系统的安全性与可靠性。针对某型高压溢流阀,对其进行工作原理介绍以及数学计算,并通过AMESim建立仿真模型,探究节流孔直径、先导弹簧预紧力和主阀弹簧预紧力对高压溢流阀的开启压力、压力超调量、压力超调稳定时间及卸荷时间的影响,对高压溢流阀的设计具有指导意义。

OBE理念下“金课”建设原则与路径——以小学数学课程与教学为例

为提高小学数学课程的教学质量和效率,增强师范生综合素养,基于OBE理念,以小学数学课程与教学为例,结合“金课”建设原则,重点阐述“金课”建设路径,包括明确教学目标、完善教学内容、选择适合的教学方式、采用多种教学方法及健全评价机制等.这些“金课”建设措施,有利于满足师范生多元化的学习需求,提升师范院校人才培养质量.

利用游戏化方式构建技工院校数学活力课堂探析

游戏化方式在技工院校数学课堂上的应用,要求教师以游戏化元素激发学生的学习兴趣,吸引学生的注意力,调动学生的主观能动性,积极构建数学活力课堂。文章通过简析游戏化教学的内涵,探究游戏化方式融入技工院校数学课堂的意义,针对技工院校数学课堂上游戏化教学存在的问题,提出利用游戏化方式构建技工院校数学活力课堂的原则与策略,以此发挥游戏化方式的优势,提高数学课堂教学效率。

分层教学在中职数学教学中的应用探析

数学在中职教学中占据重要地位,既是学生学习的重点,也是学生学习的难点。为了更好地满足学生的数学学习需求,教师不断探索并实践各种教学方法。其中,分层教学在中职数学教学中的应用不仅能提高教学效果,还能促进学生的全面发展,具有重要的实践意义。文章阐述分层教学的内涵和原则,分析分层教学在中职数学教学中应用的优势,结合中职数学教学现状,对分层教学在中职数学教学中的应用策略进行探讨,旨在培养学生的自主学习能力,提升中职数学教学质量。

Mathematical modeling of elastic inverted pendulum control system

Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.

A Mathematical Approach to Develop the Distribution of Greenhouse Gas Emissions

A mathematical algorithm of the distribution of greenhouse gas emissions is proposed as a way to tackle the topical issue of climate change and develop approaches to attaining an agreement among emitters of greenhouse gases (on the global scale, in a country, a region, a megalopolis).

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

基于AHP-模糊模型的液压支架试验台中梁销轴节点优化研究

大吨位液压支架试验台加载试验中梁销轴节点端部孔壁区域峰值载荷过大,为改善销轴变形导致应力作用范围非连续性的状况,基于赫兹接触理论建立试验台销轴节点变形后峰值接触应力的数学理论模型,利用ANSYS软件对销轴节点模型仿真分析并与理论模型进行比对。结果表明:模拟结果与理论数据具有良好的一致性。结合实际工程现场应用,确定了降低销轴节点孔壁接触区域应力峰值的5个主要指标,即:轴孔缝隙、轴套管厚度、节点板厚、倒角长度、倒角角度,运用Minitab软件对3个评价指标:应力、切应力和应变建立主效应云图;根据模糊数学理论建立3个评价指标的隶属度函数,利用层次分析法(AHP)确定评价指标的权重向量,结合模糊综合评价和最大隶属度原则得到5个主要指标的最优解参数组合,并对该参数组合进行模拟。结果表明:优化后的销轴节点立柱峰值应力降比58.77%,耳板节点峰值应力降比12%。最优解参数组合在50 MN液压支架试验台的设计研发中得到了现场应用,验证了该优化参数的合理性,有效提升液压支架试验台加载试验时中梁销轴的使用寿命。进而证明:通过对销轴节点增设斜坡倒角,设置合理的初始间隙以及板材厚度,能够很大程度上减少销轴节点峰值载荷,并改善应力作用范围长度,为重型设备插拔定位销轴组件设计的实际工程应用提供了参考。