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mathematical argument
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  数学论证
     In order to gain insight into the Theological phenomena of matter by strict mathematical argument and to provide a better ground for further guide to practice, a brief introduction of the view on matter, time, space, motion within the area of rheological mechanics and the basic principles to be followed when establishing the constitutive relations between continuous and discrete rheological mechanics are given.
     为对物质流变现象进行严格的数学论证以便深刻地理解它,从而进一步指导实践,本文简要地介绍了流变力学中的物质观、时空观、运动观,以及在这个基础上建立连续统和离散统流变力学本构方程时所遵循的基本原理.
短句来源
     In order to gain insight into the rheological phenomena of matter by strict mathematical argument and to provide a better ground for further guide to practice, a brief introduction of the view on matter, time-space, motion within the area of rheological mechanics are given.
     为对物质流变现象进行严格的数学论证以更深刻地理解它,从而进一步指导实践,我们简要地介绍了流变力学中的物质观、时空观、运动观。
短句来源
     which not only concerned with thermodynamic first law but second law. require explanation and mathematical argument if rheological fracture is to be given a proper theoretical basis.
     为给流变断裂学以正确的理论基础,对这里提出的不仅涉及热力学第一定律而且涉及第二定律的一些看法,就需要加以解释和数学论证
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  “mathematical argument”译为未确定词的双语例句
     Then, eight pieces suggestions are given in how to cultivate creativity in mathematics, such as encouraging in mathematical spread, mathematical conjecture, mathematical argument, mathematical image, etc.
     其次,就培养数学创造性思维的途径,提出八点建议,例如:鼓励进行数学推广,数学猜想,数学反驳,数学想像等等。
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  相似匹配句对
     ARGUMENT
     论点
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     On Mathematical Debate
     数学争论浅析
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     ON MATHEMATICAL INTUITION
     论数学直觉
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     On Argument Functions
     辐角函数的研究
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     whole course system is composed of logic of argument(informal logic)and mathematical(formalized)logic;
     整个逻辑学的课程体系由论证逻辑(非形式逻辑)和数理(形式化)逻辑构成;
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  mathematical argument
The purpose of this note is to point out that the mathematical argument presented for a dynamic generalization of a known elastostatic solution representation in [1] involves faulty steps.
      
We then show by a rigorous mathematical argument that the unique solution of this microscopic problem converges as ε → 0 to the solution of a double-porosity model of the global macroscopic flow.
      
Our results justify the uniqueness of Bader's partition of atoms in molecules on the basis of an a priori mathematical argument implicitly contained in the theory rather than on an a posteriori chemical one as done so far.
      
Recently, a mathematical argument was given that the motion at the critical frequency is bounded for bodies with nonzero cross-section area.
      
A clinical methodology was used to investigate the perceptions which pupils of secondary school age have concerning modes of mathematical argument which have an agreed status within the world of mathematics.
      
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In order to gain insight into the Theological phenomena of matter by strict mathematical argument and to provide a better ground for further guide to practice, a brief introduction of the view on matter, time, space, motion within the area of rheological mechanics and the basic principles to be followed when establishing the constitutive relations between continuous and discrete rheological mechanics are given.

为对物质流变现象进行严格的数学论证以便深刻地理解它,从而进一步指导实践,本文简要地介绍了流变力学中的物质观、时空观、运动观,以及在这个基础上建立连续统和离散统流变力学本构方程时所遵循的基本原理.

In this paper gives the view of what the basic concepts and principle of modern rheological mechanics are and put these concepts directly into mathematical language. In order to gain insight into the rheological phenomena of matter by strict mathematical argument and to provide a better ground for further guide to practice, a brief introduction of the view on matter, time-space, motion within the area of rheological mechanics are given. The task of rheological mechanics is to connect with one another these...

In this paper gives the view of what the basic concepts and principle of modern rheological mechanics are and put these concepts directly into mathematical language. In order to gain insight into the rheological phenomena of matter by strict mathematical argument and to provide a better ground for further guide to practice, a brief introduction of the view on matter, time-space, motion within the area of rheological mechanics are given. The task of rheological mechanics is to connect with one another these three primitive elements—body, configuration, and force—in such a way as to yield good mathematical models (constitutive equations) for the rheological behavior of mateials, ad hoc the basic principles to be followed when establishing the constitutive relations of continuum or discrete rheological mechanics are given also.

本文给出什么是现代流变力学的基本概念和原理的见解,并把这些概念直接写成数学语言。为对物质流变现象进行严格的数学论证以更深刻地理解它,从而进一步指导实践,我们简要地介绍了流变力学中的物质观、时空观、运动观。流变力学的任务就是把三个本原要素——物体、运动和力——这样的彼此连系起来,以得到材料流变特性的好的数学模式(本构方程),为此也给出了建立连续系统或离散统流变力学本构方程所遵循的基本原理。

First, we cannot but talk in a few words about rheological fracture, because of this subject is generally understood as a self-contradictory one. In fact, Griffith's works just sixty years ago signaled the beginnings of a mechanics of fractcture, he realized and investigated the beginnings of a mechanics of fracture, he realized and investigated the phenomena of rupture and flow in solids. However it must be remembered that rheological mechanics sixty years ago was not well developed. Today from rheological...

First, we cannot but talk in a few words about rheological fracture, because of this subject is generally understood as a self-contradictory one. In fact, Griffith's works just sixty years ago signaled the beginnings of a mechanics of fractcture, he realized and investigated the beginnings of a mechanics of fracture, he realized and investigated the phenomena of rupture and flow in solids. However it must be remembered that rheological mechanics sixty years ago was not well developed. Today from rheological mechanics we know that any material may be caused to flow by varying temperature and force field. If defined as isotropy group of the material at particle Ⅹ, with respect to the reference configuration, then solid is a material whose isotropy group is the orthogonal group and fluid whose isotropy group is the full unimodular group. All continuous deformations form a symmetric group. At rupture, the nature of the group changes. In other words, the change into a state of rupture may be interpreted as an asymptotic phenomenon which imposes a constraint on the invariants of the field tensor. In this new light, flow and rupture are all physical quantities, and any physical quantity has a mathematical background itself. The mathematical background of flow can be in terpreted as a mapping of one topological space into another and of rupture is then the corresponding mapping should become singlar, because of at rupture the macro-element breaks down, and the mo Julus of transformation tends to infinite. Therefore. they are relative, with one another. Rheological fracture is rest upon this mathematical background.The conclusion of our other article is that the fracture is a purely rheological process not influenced by surface energy, but yet the introduction of surface energy into the continuum description of the fracture process forces a major departure from the mechanics appropriate to the non-separation body. We realized that by virtue of this additioncd term however, the possibility of obtaining a corresponding local balance equation directly as a derived consequence of the global balance statement, as is customary in classical continuum mechanics, is lost. They must instead be imposed additional postulates about separating. When a separating body is viewed as a non-equilibrium irreversible thermodynamic process, the full thermodynamic nature of the surface energy induced by crack propagation becomes apparent.Aug mechanical process in a rheological material produees dissipated energy. Thus, in order to properly describe the propagation of a crack it is necessary to consider the rheological solid mechanically as a dissipature type media, and so in the global energy balance law must inclusion the rate-of-energy dissipation term which represent the behavior of rheological materials. According to the character of the surfaces of a propagating crack, the balance equations are material rate equations.Moreover, we have already known from continuum thermodynamics that irreversible processes must be associated with entropy production. Irreversible crack propagation will then, under some conditions, contribute the entropy content to the separationg body, and fracture, in order to be properly viewed, should be viewed as a rhological process with memory.The insights that have been raised here. which not only concerned with thermodynamic first law but second law. require explanation and mathematical argument if rheological fracture is to be given a proper theoretical basis. In this paper, this theoretical basis of rheological fracture is given.We have shown that the thermorheological material with memory can be defined as aviscoelastic material with memory according as thermorheological material response, it only necessary exists certain relation between the time and the temperature history. By virtue of the planestrain crack growth relations can be applied even when the global state of body is one of plane stress, it is only necessary that the failure zone be small enough for the neighborhood of the crack-tip to be in plane strain. Th

首先,关于流变断裂我们不能不说几句,因为这个课题一般被理解是自相矛盾的。实际上,整六十年前Griffifh的工作标志着断裂力学的开始,他那时就认识到并研究了固体中的破裂和流动现象。可是必须提及,流变力学在六十年前还没有很好发展起来。今天,我们从流变力学知道,由于温度和力场的变化可引起任一材料发生流动。若将(?)定义为质点×存参考构形(?)的实质迷向群,则固体是迷向群为正交群的材料,而流体就是迷向群为全幺模群的材料。整个连续变形形成对称群。破裂时,群的性质改变。换句话说,可以把变到破裂状态看作是一种渐近现象,它给场张量不变量以限制。在这个新的看法中,流动和破裂都是物理量,而任一物理量都有它自身的数学背景。流动的数学背景可视为从一个拓扑空间到另一拓扑空间的映射,而破裂的数学背景则是相应的映射变为奇异的,这是由于破裂时宏观组元破坏,变换模趋于无穷大的缘故。从而,它们是彼此相关的。流变断裂学就是建立存这个数学背景上。我们另一文的结论是,断裂是不受表面能影响的一个纯粹流变过程。可是,把表而能引入断裂过程的连续统力学描述中,才主要地使它从适用于未裂体的力学独立出来。但我们认为,由于这项引入,使得经典连续统力学惯刚的把相应...

首先,关于流变断裂我们不能不说几句,因为这个课题一般被理解是自相矛盾的。实际上,整六十年前Griffifh的工作标志着断裂力学的开始,他那时就认识到并研究了固体中的破裂和流动现象。可是必须提及,流变力学在六十年前还没有很好发展起来。今天,我们从流变力学知道,由于温度和力场的变化可引起任一材料发生流动。若将(?)定义为质点×存参考构形(?)的实质迷向群,则固体是迷向群为正交群的材料,而流体就是迷向群为全幺模群的材料。整个连续变形形成对称群。破裂时,群的性质改变。换句话说,可以把变到破裂状态看作是一种渐近现象,它给场张量不变量以限制。在这个新的看法中,流动和破裂都是物理量,而任一物理量都有它自身的数学背景。流动的数学背景可视为从一个拓扑空间到另一拓扑空间的映射,而破裂的数学背景则是相应的映射变为奇异的,这是由于破裂时宏观组元破坏,变换模趋于无穷大的缘故。从而,它们是彼此相关的。流变断裂学就是建立存这个数学背景上。我们另一文的结论是,断裂是不受表面能影响的一个纯粹流变过程。可是,把表而能引入断裂过程的连续统力学描述中,才主要地使它从适用于未裂体的力学独立出来。但我们认为,由于这项引入,使得经典连续统力学惯刚的把相应局部平衡方程作为整体平衡描述的直接结论的可能性就丧失掉。它们必须代以作为裂开的附加假设。当把物体的开裂视作为一个非平衡不可逆热力学过程,表面能的整个热力学性质也就清楚了。流变性材料的任何力学过程都要耗散能量。因此,为能正确地描述裂纹扩展,就需要把流变固体从力学上看作是耗能型介质,从而在整体能量平衡规律中必须计及标志流变性材料特性的耗能率。根据扩展裂纹表面的特征,平衡方程是实质率型方程。此外,我们从连续统热力学知道,不可逆过程必然伴有熵产生。在某种情况下,不可逆的裂纹扩展向开裂体提供了熵含量,从而为了正确的看待,应将断裂视作为带有记忆的流变过程。为给流变断裂学以正确的理论基础,对这里提出的不仅涉及热力学第一定律而且涉及第二定律的一些看法,就需要加以解释和数学论证。本文给出流变断裂学的这样理论基础。我们表明,根据热流变性材料响应,只要时间和温度历史间存在一定关系,热流变性记忆材料就可定义为一种粘弹性记忆材料。由于甚至物体的整体状态是一种平面应力状态时,平面应变裂纹增长公式也适用,这仅要求对于是平面应变的裂纹尖端邻域来说,衰坏区足够小。所以,我们应用Graham的广义粘弹对应性原理,从而简化了流变体的断裂问题。

 
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