用代换法求解二重极限的类型和实例

对于二元函数的二重极限,重点是极限的存在性及其求解方法.由于二重极限较为复杂,判定极限的存在及求解,往往因题而异.依据变量(x,y)的不同变化趋势和函数f(x,y)的不同类型,探索得出了一些新的变量代换及应用.采用恰当的变量代换的求解方法后,对复杂的二重极限计算,就能简便、快捷地获得结果.     

一类修正Zhang H.C.非单调共轭梯度算法

为有效求解大规模无约束优化问题,本文基于RMFI共轭梯度法,结合Zhang H.C.非单调线搜索步长规则,提出了一类新的共轭梯度算法.在适当的条件下,证明了新算法的全局收敛性.数值算例表明,新算法比Zhang H.C.非单调规则下的标准RMFI方法收敛速度更快,更有效.同时,本文进一步研究了Zhang H.C.非单调线搜索步长规则的一个基于强迫函数的拓展模型,并从理论上证明了基于此拓展模型的新算法的全局收敛性.     

Facile fabrication of integrated three-dimensional C-MoSe<Subscript>2</Subscript>/reduced graphene oxide composite with enhanced performance for sodium storage

Scrupulous design and fabrication of advanced electrode materials are vital for developing high-performance sodium ion batteries. Herein, we report a facile one-step hydrothermal strategy for construction of a C-MoSe₂/rGO composite with both high porosity and large surface area. Double modification of MoSe₂ nanosheets is realized in this composite by introducing a reduced graphene oxide (rGO) skeleton and outer carbon protective layer. The MoSe₂ nanosheets are well wrapped by a carbon layer and also strongly anchored on the interconnected rGO network. As an anode in sodium ion batteries, the designed C-MoSe₂/rGO composite delivers noticeably enhanced sodium ion storage, with a high specific capacity of 445 mAh·g^-1 at 200 mA·g^-1 after 350 cycles, and 228 mAh·g^-1 even at 4 A·g^-1; these values are much better than those of C-MoSe₂ nanosheets (258 mAh·g^-1 at 200 mA·g^-1 and 75 mAh·g^-1 at 4 A·g^-1). Additionally, the sodium ion storage mechanism is investigated well using ex situ X-ray diffraction and transmission electron microscopy methods. Our proposed electrode design protocol and sodium storage mechanism may pave the way for the fabrication of other high-performance metal diselenide anodes for electrochemical energy storage.

Open image in new window

     

On the electro-osmotic flow in a saturated porous medium

Electro-osmosis in a saturated porous rigid medium is studied by both theoretical and experimental approach. Relationships giving liquid and electrical coupled macroscopic flows are obtained from the homogeneization method. They point out possible non symmetrical cross effects that explain deviations from Onsager reciprocal relations. Experiments on a kaolinite are reported which exhibit an important non symmetrical coupling.     

立井冻结坚硬基岩段深孔爆破技术应用试验研究

为提高深冻结立井坚硬基岩段掘进速度,在已有的研究和施工经验的基础上,进行了立井冻结坚硬基岩段深孔爆破技术应用试验研究。结合现场条件和岩石情况,优选具有良好技术性能的SJZ-6.7型伞形钻架和高威力抗冻型岩石水胶炸药,采用双阶筒形直眼掏槽,并配以大直径炮眼和大直径药卷、长延期毫秒非电雷管,以及PVC塑料管防结冰抗挤压技术,并重点试用了大直径中心空孔(中心空孔直径100 mm)。试验研究达到了预期效果,在如此坚硬的岩石(f=12~16)中,实现了炮眼利用率91.7%,掘进循环进尺3.85 m。研究结果表明,大直径中心空孔对提高了爆破效率起到了关键作用,同时,还有效的改善了破碎块度,降低了大块率,利于抓装。     

A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

In this article, we develop a dynamic version of the variational multiscale (D‐VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations.     

Forecasting with unequally spaced data by a functional principal component approach

The Principal Component Regression model of multiple responses is extended to forccast a continuous-time stochastic process. Orthogonal projection on a subspace of trigonometric functions is applied in order to estimate the principal components using discrete-time observations from a sample of regular curves. The forecasts provided by this approach are compared with classical principal component regression on simulated data.     

动态线性电极静电纺PVA纳米纤维的可纺性

为了解决传统针式静电纺针头易堵塞不易产业化的问题,采用铜丝动态线性电极静电纺丝技术对PVA纳米纤维的可纺性进行研究。利用扫描电子显微镜研究了PVA溶液浓度、电压和纺丝距离对PVA纤维形貌及直径分布的影响。结果表明:随PVA溶液浓度降低,溶液粘度和电导率减小,纤维直径及其分布变小。且随纺丝距离增大,纤维直径变细,纤维形貌变好。当PVA浓度为10%(质量分数),电压80 kV,距离30 cm时,可制备出形貌良好的纳米纤维,其直径为433 nm,产量高达 6.8 g/h ;当PVA浓度为5%(质量分数),电压80 kV,距离30 cm, 可纺最细纤维直径为96 nm。本研究可为未来PVA静电纺纳米纤维膜的规模化制备提供参考。     

块三对角线性代数方程组的一种迭代解法

建立求解系数矩阵为分块三对角矩阵的线性代数方程组的新型二次PEk方法以及其外插迭代二次EPEk方法,对系数矩阵为对称正定矩阵情形,证明了新型二次PEk方法和二次EPEk方法的可解性和收敛性.