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处处连续
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  everywhere continuous
    Relations among Almost Continuous, Almost everywhere Continuous and Fundamental Continuous
    几乎连续几乎处处连续基本上连续的关系
短句来源
    The Discussion of The Integrability Problems on the Almost Everywhere Continuous Essential Functions
    关于几乎处处连续的本性函数的可积性问题
短句来源
    In this paper,almost continuous concepts are given,and we have proved that {almost everywhere continuous functions } { almost continuous functions} {fundamental conti nuous functions } are proper inclusions.
    给出了几乎连续概念,并证明了几乎处处连续函数集合包含于几乎连续函数集合包含于基本上连续函数集合是真包含关系.
短句来源
    Based on that Lebesgue measurable function is almost everywhere equal to the almost everywhere continuous function on ,an equivalent definition and several properties on Lebesgue measurable function are given,and so is the tentative plan on Lebesgue measurable function to enter the mathematics teaching of the engineering course.
    由[a,b]上的勒贝格可测函数与几乎处处连续的函数几乎处处相等,给出勒贝格可测函数的等价定义及几个勒贝格可测函数的性质,提出一些关于勒贝格可测函数进入工科数学教学的设想。
短句来源
  “处处连续”译为未确定词的双语例句
    The theory of Riemann type integrals is established on compact Hausdorff measure spaces. It is proved that a function is Riemann integrable if and only if it is continuous almost everywhere.
    在紧Hausdorff测度空间上建立了Riemann型的积分理论,证明了函数可积的充要条件是该函数几乎处处连续.
短句来源
    On a Function Continuous and Non-differentiable Everywhere
    一个处处连续处处不可导的函数
短句来源
    A Continuous Function Without Derivatave at Anywhere
    一个处处连续无处可微的函数
短句来源
    An Elementary proof to Riemannian Integrability Theorem on Bounded, Almust Everywhese continuous Functions
    有界几乎处处连续函数Riemann可积定理的一个初等证明
短句来源
    On a Class of Function and Non Differen table Everywhere
    一类处处连续处处不可导函数
短句来源
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  everywhere continuous
We describe a class of locally convex spaces on which there exist everywhere infinitely b-differentiable real functions which are not everywhere continuous (and so are not everywhere HL-differentiable).
      
The method produces spinors which are everywhere continuous with continuous derivates which is particularly important for the relativistic case.
      
They are e.g.λn-almost everywhere continuous and therefore show satisfactorystability behaviour w.r.t.
      
Homomorphisms of topological measure spaces had been defined in [5] to be measure-preserving and almost everywhere continuous mappings; this induces a concept of isomorphic topological measures.
      
Thus constrained optimization algorithms cannot assume an everywhere continuous null space basis.
      
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In this paper an infinitely wide plate under pure plastic bending is discussed. The distribution ot stress and the relation between the couple acting on the plate and the corresponding deformation are found under the assumption that the relation between the intensity of shearing stress and shearing strain has the exponential form.The method suggested by the author is also compared with that proposed by R. Hill under the assumption that the plate is ideally plastic. Obviously the two have markeddifference. The...

In this paper an infinitely wide plate under pure plastic bending is discussed. The distribution ot stress and the relation between the couple acting on the plate and the corresponding deformation are found under the assumption that the relation between the intensity of shearing stress and shearing strain has the exponential form.The method suggested by the author is also compared with that proposed by R. Hill under the assumption that the plate is ideally plastic. Obviously the two have markeddifference. The latter gives rise to the discontinuity of stress in the neighbourhood ofthe "neutral layer", while the former always gives a continuous variation of stress.Also, the elastic recovery of plastic strain at the removal of the load is discussed. The result is compared with B. V. Ryabinin's experiment and is found to be in close agreement.It is believed that the present problem has its application in the cold working ofmetals.

本文中假定切应力强度和剪变形强度之间有冪函数的强化关系,从而推出了无限宽板在纯弯曲时的应力分布,及弯短和变形程度间的关系,它和理想塑性条件下得出的解有显著的差别。前者即本文的结果,应力分量是处处连续的,而后者引出的结果,应力分量在中性层处是不连续的。 本文又得出了无限宽板纯弯曲后,卸荷重时形状变化的解答,它和试验结果相当好地符合。显然这样的解答对冷冲压方面弯曲后的弹性回跳有重大意义。

There are some common difficulties encountered in elastic-plastic impact codes such as EPIC[1][2], NONSAP[3], etc. Most of these codes use the simple linear functions usually taken from static problems to represent the displacement components. In such finite element formulation, the strain and stress components are constants in every element. In the equations of motion, the stress components in general appear in the form of their space derivatives. Thus, if we use such form functions to represent the displacement...

There are some common difficulties encountered in elastic-plastic impact codes such as EPIC[1][2], NONSAP[3], etc. Most of these codes use the simple linear functions usually taken from static problems to represent the displacement components. In such finite element formulation, the strain and stress components are constants in every element. In the equations of motion, the stress components in general appear in the form of their space derivatives. Thus, if we use such form functions to represent the displacement components, the effect of internal stresses to the equations of motion vanishes identically. The usual practice to overcome such difficulties is to establish a self-equilibrium system of internal forces acting on various nodal points by means of transforming equations of motion into varia-tional form of energy relation through the application of virtual displacement principle. The nodal acceleration is then calculated from the total forces acting on this node from all the neighbouring elements. The transformation of virtual displacement principle into the varia-tional energy form is performed on the bases of continuity conditions of stress and displacement throughout the integrated space. That is to say, on the interface boundary of finite element, the assumed displacement and stress functions should be conformed. However, it is easily seen that, for linear form function of finite element calculation, the displacement continues everywhere, but not the stress components. Thus, the convergence of such kind of finite element computation is open to question. This kind of treatment has never been justified even in approximation sense. Furthermore, the calculation of acceleration of nodal points needs a rule to calculate the mass matrix. There are two ways to establish mass matrix, namely, lumped mass method and consistent mass method.141 The consistent mass matrix can be obtained naturally through finite element formulation, which is consistent to the assumed form functions. However, the resulting consistent mass matrix is not in diago-nalized form, which is inconvenient for numerical computation. For most codes, the lumped mass matrix is used, and in this case, the element mass is distributed in certain assumed proportions to all the nodal points of this element. The lumped mass matrix is diagonalized with the diagonal terms composed of the nodal masses. However, the lumped mass assumption has never been justified. All these difficulties are originated from the simple linear form functions usually used in static problems.

在EPIC、NONSAP等弹塑性撞击计算的有限元程序中,都有一些共同的弱点.所有这些程序,都采用静力学问题中常用的简单线性形状函数来描写各位移分量.在这样的有限元法中,应变和应力分量在每一有限元中都是常量.但在运动方程中,应力分量都是以它们的空间导数的形式出现的.于是,在采用了线性形状函数来表达的位移分量以后,应力分量对运动方程的贡献必恒等于零.克服这种困难的一般方法是通过虚位移原理,把运动方程化为能量关系的变分形式,从而建立既作用在结点上而又在每一有限元内自相平衡的人为内力平衡系统.把施加在某一结点上的所有相邻有限元的人为内力的作用叠加在一起,就能计算这一结点的加速度.但是从虚位移原理化为能量关系的变分形式时,要求位移和应力在积分域内处处连续.也就是说,要求位移和应力有限元都是协调的.我们很易看到,线性形状函数所描述的位移有限元是连续协调的,但其有关的应力分量在有限元界面上,则并不连续.所以,这样的有限元处理,是否收敛并无把握,即使从近似角度看,也是难以令人满意的.而且,为了计算结点的加速度,我们还应该有建立质量矩阵的计算规则.目前有两种计算方法:一种是集总(lumped)质量法,另一种是一致(...

在EPIC、NONSAP等弹塑性撞击计算的有限元程序中,都有一些共同的弱点.所有这些程序,都采用静力学问题中常用的简单线性形状函数来描写各位移分量.在这样的有限元法中,应变和应力分量在每一有限元中都是常量.但在运动方程中,应力分量都是以它们的空间导数的形式出现的.于是,在采用了线性形状函数来表达的位移分量以后,应力分量对运动方程的贡献必恒等于零.克服这种困难的一般方法是通过虚位移原理,把运动方程化为能量关系的变分形式,从而建立既作用在结点上而又在每一有限元内自相平衡的人为内力平衡系统.把施加在某一结点上的所有相邻有限元的人为内力的作用叠加在一起,就能计算这一结点的加速度.但是从虚位移原理化为能量关系的变分形式时,要求位移和应力在积分域内处处连续.也就是说,要求位移和应力有限元都是协调的.我们很易看到,线性形状函数所描述的位移有限元是连续协调的,但其有关的应力分量在有限元界面上,则并不连续.所以,这样的有限元处理,是否收敛并无把握,即使从近似角度看,也是难以令人满意的.而且,为了计算结点的加速度,我们还应该有建立质量矩阵的计算规则.目前有两种计算方法:一种是集总(lumped)质量法,另一种是一致(consistent)质量法.一致质量矩阵是通过正规的有限元计算求得的,它和?

In this paper,almost continuous concepts are given,and we have proved that {almost everywhere continuous functions } { almost continuous functions} {fundamental conti nuous functions } are proper inclusions.

给出了几乎连续概念,并证明了几乎处处连续函数集合包含于几乎连续函数集合包含于基本上连续函数集合是真包含关系.

 
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