For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition t...For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.展开更多
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝...应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。展开更多
The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means ...The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
Higher-order numeric solutions for nonlinear differential equations based on the Rach-Adomian-Meyers modified decomposition method are designed in this work. The presented one-step numeric algorithm has a high efficie...Higher-order numeric solutions for nonlinear differential equations based on the Rach-Adomian-Meyers modified decomposition method are designed in this work. The presented one-step numeric algorithm has a high efficiency due to the new, efficient algorithms of the Adomian polynomials, and it enables us to easily generate a higher-order numeric scheme such as a 10th-order scheme, while for the Runge-Kutta method, there is no general procedure to generate higher-order numeric solutions. Finally, the method is demonstrated by using the Duffing equation and the pendulum equation.展开更多
In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwis...In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.展开更多
In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propa...In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.展开更多
Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions...The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces.This technique makes it also possible to solve ill-posed initial value problems.展开更多
A general operational protocol which provides permanent macroscopic coherence of the response of any stable complex system put in an ever-changing environment is proposed. It turns out that the coherent response consi...A general operational protocol which provides permanent macroscopic coherence of the response of any stable complex system put in an ever-changing environment is proposed. It turns out that the coherent response consists of two parts: 1) a specific discrete pattern, called by the author homeostatic one, whose characteristics are robust to the statistics of the environment;2) the rest part of the response forms a stationary homogeneous process whose coarse-grained structure obeys universal distribution which turns out to be scale-invariant. It is demonstrated that, for relatively short time series, a measurement, viewed as a solitary operation of coarse-graining, superimposed on the universal distribution results in a rich variety of behaviors ranging from periodic-like to stochastic-like, to a sequences of irregular fractal-like objects and sequences of random-like events. The relevance of the Central Limit theorem applies to the latter case. Yet, its application is still an approximation which holds for relatively short time series and for specific low resolution of the measurement equipment. It is proven that the asymptotic behavior in each and every of the above cases is provided by the recently proven decomposition theorem.展开更多
文摘For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.
文摘应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。
文摘The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
文摘Higher-order numeric solutions for nonlinear differential equations based on the Rach-Adomian-Meyers modified decomposition method are designed in this work. The presented one-step numeric algorithm has a high efficiency due to the new, efficient algorithms of the Adomian polynomials, and it enables us to easily generate a higher-order numeric scheme such as a 10th-order scheme, while for the Runge-Kutta method, there is no general procedure to generate higher-order numeric solutions. Finally, the method is demonstrated by using the Duffing equation and the pendulum equation.
基金supported by the National Natural Science Foundation of China(Grant No.11771265).
文摘In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.
文摘In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
文摘S-R(strain-rotation)和分解定理克服了经典有限变形理论的一些缺点,使其可以为几何非线性数值分析提供可靠的理论基础.对于大变形问题,由于无网格法(element-free method)避免了对单元网格的依赖,从而从根本上避免了有限单元法(finite element method,FEM)的单元畸变问题,保证了求解精度.因此,将无网格法和S-R和分解定理结合起来势必能建立一套更加合理可靠的几何非线性数值计算方法.目前基于S-R定理的无网格数值方法研究较少并且只能用于二维平面问题的求解,但实际上绝大多数问题都必须以三维模型来进行处理,因此建立适用于三维情况的S-R无网格法是非常有必要的.本文给出了适用于三维情况的S-R无网格法:采用由更新拖带坐标法和势能率原理推导出来的增量变分方程,利用基于全局弱式的无网格Galerkin法(EFG)得到了用于求解三维空间问题的离散格式.利用MATLAB编制三维S-R无网格法程序,对受均布载荷的三维悬臂梁和四边简支矩形板结构的非线性弯曲问题进行了计算.最后将所得的数值结果与已有文献进行了比较,验证了本文的三维S-R无网格数值算法的合理性、有效性和准确性.本文的三维S-R无网格数值算法可以作为一种可靠的三维几何非线性数值分析方法.
文摘This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
文摘The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces.This technique makes it also possible to solve ill-posed initial value problems.
文摘A general operational protocol which provides permanent macroscopic coherence of the response of any stable complex system put in an ever-changing environment is proposed. It turns out that the coherent response consists of two parts: 1) a specific discrete pattern, called by the author homeostatic one, whose characteristics are robust to the statistics of the environment;2) the rest part of the response forms a stationary homogeneous process whose coarse-grained structure obeys universal distribution which turns out to be scale-invariant. It is demonstrated that, for relatively short time series, a measurement, viewed as a solitary operation of coarse-graining, superimposed on the universal distribution results in a rich variety of behaviors ranging from periodic-like to stochastic-like, to a sequences of irregular fractal-like objects and sequences of random-like events. The relevance of the Central Limit theorem applies to the latter case. Yet, its application is still an approximation which holds for relatively short time series and for specific low resolution of the measurement equipment. It is proven that the asymptotic behavior in each and every of the above cases is provided by the recently proven decomposition theorem.
