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The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new techn...
Let $A_1:=K\langle x, \frac{d}{dx} \rangle$ be the Weyl algebra and $\mI_1:= K\langle x, \frac{d}{dx}, \int \rangle$ be the algebra of polynomial integro-differential operators over a field $K$ of cha...
For the algebra $\mI_1= K\langle x, \frac{d}{dx}, \int \rangle$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It i...
Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r_f its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1_f i...
We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic ...
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential ...
We define leaves and trajectories for schemes endowed with a vector field. With the help of these tools, we are able to give a geometrical interpretation and to generalize several results and constru...
Sachs [16] showed that a Boolean algebra is determined by its lattice of subalgebras.We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determin...
Using a bidifferential graded algebra approach to integrable partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix N...
B-收敛和D-收敛的概念被推广到了变时滞微分代数方程问题,给出了$D_A$-收敛的定义,讨论了该类问题的$D_A$-收敛性,并给出了相应的误差估计,证明了如果G-稳定的单支方法对于常微分方程初值问题在经典意义下是p阶相容的且$\frac{\beta _k}{\alpha_k}>0$,那么具有线性插值过程的该方法是p阶$D_A$-收敛的,这里p=1或2.
论述了在随机Lipschitz条件下倒向随机微分方程解的性质.通过解的先验估计,分别得到了在随机Lipschitz条件下倒向随机微分方程的解关于终端值和生成元的连续性质.
研究分数阶微分方程多点边值问题正解的存在性,利用动点定理,得到了边值问题至少存在1个正解和3个正解的充分条件.
针对一类非线性微分代数系统,利用M导数方法,给出了受控不变分布的概念,并讨论了此类微分代数系统受控不变分布的一些性质.给出了一个计算包含在系统输出核(kerE(h))内的最大受控不变分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用给出的算法计算微分代数系统的包含在系统输出核内的最大受控不变分布.
讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD), 利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度, 从而按$ L^{\infty}(L^2({ \it \Omega})$ 模达到最优.
证明同调有界的连通微分分次代数(简称为DG代数)上的紧致DG模的amplitude与基代数的amplitude的差恰为该DG模的投射维数. 由此可得非平凡的正则DG代数是同调无界的. 对正则DG代数$A$, 若它的同调代数$H(A)$是分次Koszul代数, 则证明$H(A)$有有限的整体维数; 如果把条件减弱为$A$是Koszul DG代数, 则给出了一个$H(A)$的整体维数为无限的例子. 对...

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