Group Twisted Tensor Bipro ducts over Hopf Group Coalgebras

In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and su？cient conditions for the new object to be a Hopf group coalgebra.     

A variational formula for controlled backward stochastic partial differential equations and some application

An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.     

旁侧序列对端粒DNA G-quadruplex热稳定性和折叠与去折叠动力学的影响

从热力学和动力学两个方面研究了旁侧序列对人端粒核心序列G3（T2AG3）3在钠离子溶液中所形成的Cr-quadruplex结构的影响．紫外吸收熔解实验表明G3（T2AG3）3一侧或两侧加上6个胸腺嘧啶核苷酸序列（T6）会明显降低G-quadruplex的相变温度（Tm）．在3′端加上T6时Tm降低约5℃，在5′端加上T6时Tm降低约10℃，两侧同时加上T6时L降低16℃．采用表面等离子体共振（surface plasmon resonance，SPR）测定G-quadruplex折叠和去折叠动力学的结果表明旁侧序列的加入同时降低了折叠和去折叠的速率常数（kf，ku），使折叠平衡常数（KF）由9．01降至7．44．上述结果表明旁侧序列的存在降低了G-quadruplex结构的稳定性．     

A new method to find homoclinic and heteroclinic orbits

A new series method is provided for continuous-time autonomous dynamical systems, which can find exact orbits as opposed to approximate ones. The method can reduce the connecting orbit problem as a boundary value problem in an infinite time domain to the initial value problem. It consists of transforming time to the logarithmic scale, substituting a power series around each fixed point of interest for each of the unknown functions into the system, and equating the corresponding coefficients. When solving for the power series coefficients, additional parameters are used in order to find the intersections of the unstable manifold and the stable manifold of the equilibria. This paper demonstrates how the new method allows to obtain heteroclinic and homoclinic orbits in some well-known cases, such as Nagumo system, stretch-twist-fold flow or mathematical pendulum.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

大黄素联合5AzA-cdR对胰腺癌抑癌基因p16、RASSF1A去甲基化作用研究

目的研究大黄素是否可增强5AzA-cdR对胰腺癌Panc1细胞抑癌基因p16、RASSF1A的去甲基化作用。方法采用细胞增殖实验检测不同浓度大黄素对Panc1细胞的生长抑制情况,焦磷酸盐测序PCR（BSP）分别检测大黄素、5AzA-cdR及大黄素联合5AzA-cdR对Panc1细胞抑癌基因p16、RASSF1A甲基化状态的影响,并用荧光定量PCR（FQ-PCR）和Westernblot分别检测p16、RASSF1A及甲基转移酶DNMT1、DNMT3a在mRNA和蛋白水平的表达情况。结果大黄素以时间和浓度梯度依赖性抑制Panc1细胞生长。BSP结果显示大黄素具有微弱的去甲基化作用,5AzA-cdR具有一定程度的去甲基化作用,当两者联用时,去甲基化作用更加显著;FQ-PCR和Westernblot结果显示大黄素与5AzA-cdR联用时,p16、RASSF1A的表达水平均较空白对照明显增高（均P＜0.05）,DNMT1、DNMT3a的表达水平均较空白对照明显降低（均P＜0.05）。结论大黄素与5AzA-cdR联用可通过降低DNMT1和DNMT3a的表达水平来增强5AzA-cdR对胰腺癌抑癌基因p16、RASSF1A的去甲基化作用。     

具有5个不同素因子的Nicol数数数

通过计算机辅助,利用元素的阶、欧拉函数、因子和函数等数论函数的性质,继续研究了具有5个不同素因子的Nicol数,证明了具有5个不同素因子的Nicol数只能是3-Nicol数和4-Nicol数.