Polynomial cost for solving IVP for high-index DAE

We show that the cost of solving initial value problems for high-index differential algebraic equations is polynomial in the number of digits of accuracy requested. The algorithm analyzed is built on a Taylor series method developed by Pryce for solving a general class of differential algebraic equations. The problem may be fully implicit, of arbitrarily high fixed index and contain derivatives of any order. We give estimates of the residual which are needed to design practical error control algorithms for differential algebraic equations. We show that adaptive meshes are always more efficient than non-adaptive meshes. Finally, we construct sufficiently smooth interpolants of the discrete solution. AMS subject classification (2000) 34A09, 65L80, 68Q25     

The sequential differentiation and its applications in the optimal control problems

Using the sequential approach, we define a certain generalization of the operator derivative. We establish the necessary extremum condition in terms of the sequential derivative. As examples we consider the optimal control problems for systems governed by partial nonlinear differential equations of several kinds.     

Shank 2 expression coincides with neuronal differentiation in the developing retina

The retinal activity for vision requires a precise synaptic connectivity. Shank proteins at postsynaptic sites of excitatory synapses play roles in signal transmission into the postsynaptic neuron. However, the correlation of Shank 2 expression with neuronal differentiation in the developing retina remains to be elucidated regardless of previous evidences of Shank 2 expression in retina. Herein, we demonstrated that with progression of development, Shank 2 is initially detected in the inner plexiform layer at P2, and then intensively detected in inner plexiform layer, outer plexiform layer, and ganglion cell layer at P14, which was closely colocalized to the neurofilament expression. Shank 2 was, however, not colocalized with glial fibrillary acidic protein. Shank 2 expression was increased in the differentiated retinoblastoma cells, which was mediated by ERK 1/2 activation. Moreover, Shank 2 expression was colocalized with neurofilament at the dendritic region of cells. In conclusion, our data suggests that Shank 2 is expressed in the neurons of the developing retina and could play a critical role in the neuronal differentiation of the developing retina.     

张量概念的起源与演变

张量分析是现代数学物理学的基础工具.从广义相对论开始,到规范场论,以至后来的弦理论,这些理论的建立都是因为有了张量分析.张量分析所提供的对曲线坐标系的微分方法,真正实现了非欧几何从概念到演算的革命,而所有这一切都是以张量概念的产生为基础的.因此,着重分析从1841年到1913年张量概念的形成与发展,在原始文献中寻找它的历史线索,并考证″tensor″一词的提出者.     

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor analysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentiations. These progresses strengthen the tendency of the axiomatization of tensor analysis.     

中矩形公式与梯形公式的注记

将数值积分中的中矩形公式与梯形公式推广到两个函数的情形,并讨论了中间值的渐近性质.     

黄颡鱼MyoD基因的克隆及其表达

采用RT-PCR和RACE(cDNA末端快速扩增)方法克隆黄颡鱼MyoD(myogenic differentiation antigen,成肌分化抗原)基因的cDNA全长序列,对其进行生物信息学和在雌雄个体组织中的表达差异分析.结果表明,黄颡鱼MyoD基因编码区由810个碱基组成,编码269个氨基酸,其中第1～89个氨基酸为Basic区,第90～141个氨基酸为bHLH结构;黄颡鱼的MyoD基因与斑点叉尾鮰的同源性最高为93%.在雌雄成体组织中的表达分析显示,雄性个体中肌肉和胃组织中的表达量极显著高于雌性个体(p<0.01),雌性个体的肾脏和鳃组织中的表达量显著高于雄性(p<0.05).通过MyoD基因在雌雄个体中表现出的组织表达差异,认为这可能是造成黄颡鱼雌雄生长差异的重要因素之一.     

建兰组织培养及根状茎增殖的动力学

以建兰品种小桃红根状茎为外植体,研究植物生长调节剂对根状茎增殖、分化和生根的影响,以及根状茎的增殖对培养基中营养物质消耗的变化规律。结果表明,根状茎增殖的最佳培养基是MS+6-BA 0.5mg·L-1+蔗糖30g·L-1,根状茎生长速度为7.33;根状茎分化的最佳培养基是MS+NAA 0.6mg·L-1+TDZ 1.0mg·L-1+蔗糖30g·L-1,分化率为93.10%;生根的最佳培养基是1/2MS+NAA 1.0mg·L-1+蔗糖30g·L-1+AC 0.05%,生根率为96.3%。根状茎增殖的生长量变化呈S型曲线,与细胞培养不同,各时期界限并不是很明显。培养基中碳源、氮源和磷酸盐的消耗曲线与根状茎的生长曲线基本一致。pH由于根状茎先消耗碱性盐(铵态氮)而下降,后利用硝态氮而上升。更多还原     

大型圆形贮液池力学分析中的重心插值拟谱法

针对传统大型圆形贮液池力学分析方法计算复杂、精度不高的问题,用拟谱法对圆形贮液池的线弹性静力问题进行了研究.采用重心Lagrange插值多项式建立未知函数的微分矩阵,将池壁的控制方程表示为代数方程组.通过求解代数方程组,求得池壁各个离散点挠度,进而采用微分矩阵直接求得池壁内力.算例表明,该方法原理简单,易于程序实现和数值计算精度高.