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2.
Jamil Chaker 《Mathematische Nachrichten》2019,292(11):2316-2337
We consider systems of stochastic differential equations of the form for with continuous, bounded and non‐degenerate coefficients. Here are independent one‐dimensional stable processes with . In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices. 相似文献
3.
Johannes Wittmann 《Mathematische Nachrichten》2019,292(7):1627-1635
Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels . 相似文献
4.
As is known, Alternating-Directional Doubling Algorithm (ADDA) is quadratically convergent for computing the minimal nonnegative solution of an irreducible singular M-matrix algebraic Riccati equation (MARE) in the noncritical case or a nonsingular MARE, but ADDA is only linearly convergent in the critical case. The drawback can be overcome by deflating techniques for an irreducible singular MARE so that the speed of quadratic convergence is still preserved in the critical case and accelerated in the noncritical case. In this paper, we proposed an improved deflating technique to accelerate further the convergence speed – the double deflating technique for an irreducible singular MARE in the critical case. We proved that ADDA is quadratically convergent instead of linearly when it is applied to the deflated algebraic Riccati equation (ARE) obtained by a double deflating technique. We also showed that the double deflating technique is better than the deflating technique from the perspective of dimension of the deflated ARE. Numerical experiments are provided to illustrate that our double deflating technique is effective. 相似文献
5.
We consider a Schrödinger operator on , where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU). 相似文献
7.
基于单粒子导心运动代码ORBIT,采用测试粒子模拟方法,研究了托卡马克等离子体内部不同径向位置处局域磁场扰动对高能量离子的损失的影响。研究表明,在局域磁扰动主要分布在某磁面附近、其环向具有类似纹波场形式下,可造成一些靠近等离子体中心区域的高能量离子损失,但对靠近等离子边界的离子损失影响相对不大。这些损失的高能量离子均为捕获离子,离子的投掷角越大就越容易损失。此外,造成高能量离子最大损失率的局域场径向位置与这些损失离子的初始径向位置通常存在一定的偏移,而且这个偏移与这些离子的能量密切相关。当局域场出现在某些位置时,能量较低的离子会有一定的损失,能量较高的离子反而不会损失。 相似文献
8.
研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的. 相似文献
9.
Shigeaki Koike Takahiro Kosugi Makoto Naito 《Journal of Mathematical Analysis and Applications》2018,457(1):436-460
The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans. 相似文献
10.
《中国化学快报》2020,31(9):2353-2357
NiS2 has become a research hotspot of anode materials for Na-ion batteries due to its high theoretical specific capacity. However, the volume effect, the dissolution of polysulfide intermediates and the low conductivity during the charge/discharge process lead to the low specific capacity and poor cycling stability. NiS2/rGO nanocomposite was prepared by a facile two-step process: GO was prepared by modified Hummers method, and then NiS2/rGO nanocomposite was synthesized by l-cys assisted hydrothermal method. NiS2/rGO nanocomposite shows excellent cycle performance and rate performance, which could be attributed to the mesoporous structure on the graphene skeleton with high conductivity. Besides, the chemical constraint of a unique SO bond on NiS2 could inhibit the dissolution of intermediates and the loss of irreversible capacity. 相似文献