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<正> 本文将对重积分坐标变换时的积分微元变换作出一种新的解释。比如,众所周知,对二重积分,在直角坐标系下,积分微元ds=dxdy,在直角坐标系下,积分微元ds=dxdy,在极坐标系下,ds=rdrdφ。后者的证法常见有三 相似文献
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从一道考研试题入手,给出了当二重积分的被积函数或积分区域边界含x2-y2时的"双曲坐标变换"法.通过实例,对比说明该方法能够解决一类用直角坐标不易计算或不能计算的二重积分问题,并且可以运用到三重积分的计算上. 相似文献
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为避免确定累次积分的积分限之困难,介绍一种实用方法———代数定限法:利用不等式同解变换的办法将重积分的积分区域表示成累次积分所需要的形状 相似文献
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本文采用不同以往的方法;对正态定限(Orthant)概率积分施行线性变换与极坐标变换;得到了一个新的递推公式,使积分重数至少降低了3重;并推导了四维正态定限概率的表达式,这对进行数值计算是十分有意义的. 相似文献
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在本文中先给出了弧元素、面元索在坐标变换下的变换公式,然后给出了曲线、曲面积分在坐标变换下的变换公式,最后利用上述坐标变换公式推出了曲线曲面积分的对称性质. 相似文献
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《Chaos, solitons, and fractals》2001,12(3):617-621
This note shows how the 10 dimensions of heterotic strings arise naturally from the probabilistic character of the geometry of micro-space as the result of the standard deviation of the expectation value of an infinite-dimensional space using χ(n) and exponential statistical distribution. 相似文献
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Ryokichi Tanaka 《Mathematische Zeitschrift》2011,267(3-4):803-833
We discuss a large deviation principle of a periodic random walk on a covering graph with its transformation group of polynomial volume growth in view of geometry. As we shall observe, the behavior of a random walk at infinity is closely related to the Gromov?CHausdorff limit of an infinite graph and in the case where the graph admits an action of a group of polynomial volume growth, the Carnot-Carathéodory metric shows up in its limit space. 相似文献
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引进了第III类典型域上的内切超圆坐标;计算出了矩阵极坐标下相应于不变度量的体积元素;利用积分变换构造出了不变度量的Laplace-Beltrami算子的热核. 相似文献
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In transformation induced plasticity (TRIP) steel a diffusionless austenitic-martensitic phase transformation induced by plastic deformation can be observed, resulting in excellent macroscopic properties. In particular low-alloyed TRIP steels, which can be obtained at lower production costs than high-alloyed TRIP steel, combine this mechanism with a heterogeneous arrangement of different phases at the microscale, namely ferrite, bainite, and retained austenite. The macroscopic behavior is governed by a complex interaction of the phases at the micro-level and the inelastic phase transformation from retained austenite to martensite. A reliable model for low-alloyed TRIP steel should therefore account for these microstructural processes to achieve an accurate macroscopic prediction. To enable this, we focus on a multiscale method often referred to as FE2 approach, see [6]. In order to obtain a reasonable representative volume element, a three-dimensional statistically similar representative volume element (SSRVE) [1] can be used. Thereby, also computational costs associated with FE2 calculations can be significantly reduced at a comparable prediction quality. The material model used here to capture the above mentioned microstructural phase transformation is based on [3] which was proposed for high alloyed TRIP steels, see also e.g. [8]. Computations based on the proposed two-scale approach are presented here for a three dimensional boundary value problem to show the evolution of phase transformation at the microscale and its effects on the macroscopic properties. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The macroscopic material model, proposed by Papatriantafillou [1], is adopted to describe the rate dependent flow behaviour and the temperature and stress state dependent γ-α′ phase transformation of a newly developed cast TRIP-steel. Simple test of the implemented model revealed that the evolution of the martensite volume fraction is not predicted correctly in case of inelastic deformation and subsequent unloading. Therefore, we present an improved model for the γ-α′ phase transformation and show that these predictions are due to the choice of the corresponding thermodynamical driving force. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Yong-aiZheng De-binHuang Zeng-rongLiu 《应用数学学报(英文版)》2003,19(1):129-134
A geometric reduction procedure for volume-preserving flows with a volume-preserving symme-try on an n-dimensional manifold is obtained.Instead of the coordinate-dependent theory and the concrete coordinate transformation,we xhow that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space.More generally,if it admits an r-parameter volume-preserving commutable symmetry,then the reduced folw preserves the corresponding (n-r)-dimensional volume form. 相似文献
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In this paper, an extremal eigenvalue problem to the Sturm-Liouville equations with
discontinuous coefficients and volume constraint is investigated. Liouville
transformation is applied to change the problem into an equivalent minimization
problem. Finite element method is proposed and the convergence for the finite
element solution is established. A monotonic decreasing algorithm is presented
to solve the extremal eigenvalue problem. A global convergence for the algorithm
in the continuous case is proved. A few numerical results are given to depict the
efficiency of the method. 相似文献
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A method and an algorithm for determining the effective deformational properties of dispersely strengthened materials with a physically nonlinear matrix and quasi-spheroidal linearly elastic inclusions are elaborated based on the stochastic differential equations of the physically nonlinear theory of elasticity. Their transformation to integral equations and the application of the method of conditional moments reduce the problem to a system of nonlinear algebraic equations, whose solution is constructed by the iteration method. The deformation diagrams as functions of the volume content of inclusions are investigated. 相似文献
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We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic‐to‐tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like $\max \{ V^{2/3}, V^{9/11} \}$ in terms of the volume V. Moreover, our arguments illustrate the importance of self‐accommodation for achieving the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy. © 2012 Wiley Periodicals, Inc. 相似文献