算子代数上2-局部Lie三重导子的结构

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

一种新的岩石非线性黏弹塑性蠕变模型研究

为了克服传统元件组合模型不能描述岩石蠕变过程中非线性特征的缺陷，首先根据加速蠕变阶段的应变和应变率随蠕变时间急剧增大的特点，建立黏塑性应变与蠕变时间的指数函数关系并提出非线性黏塑性体．将该非线性黏塑性体与广义Burgers蠕变模型串联，建立可以描述岩石全蠕变过程的非线性黏弹塑性蠕变模型，根据叠加原理得到一维应力状态下的轴向蠕变方程．然后基于塑性力学理论指出岩石三维蠕变本构方程建立过程中的不足之处，并给出非线性黏弹塑性蠕变模型合理的三维蠕变方程．最后采用不同应力水平下砂岩轴向蠕变试验对模型合理性进行验证，结果表明：拟合曲线与试验曲线吻合度较高，所建蠕变模型能够很好地描述砂岩在不同应力水平下的蠕变变形规律，尤其对加速蠕变阶段的非线性特征描述效果很好，验证了模型的合理性．     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

     

一类含参广义集值拟变分包含组的解的灵敏性分析

本文引入了一类新的含参广义集值拟变分包含组,应用隐预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,在适当的条件下,分析了含参广义集值拟变分包含组的解的灵敏性,所得结果推广改进了最新文献中的许多结果．     

矩阵的广义特征值及特征向量的神经网络方法

矩阵特征值及特征向量计算在实际问题中有广泛的应用.应用神经网络方法来计算广义特征值及对应的特征向量,给出了相应的算法,并对给出的算法在数学上进行了严格证明.并用实例验证了其正确性.     

(Anti-)de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in (anti)-de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.     

Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.