Existence and iterative approximation of solutions of a system of general variational inclusions

In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature.     

The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition

The Dirichlet problem for a singularly perturbed parabolic reaction-diffusion equation with a piecewise continuous initial condition in a rectangular domain is considered. The higher order derivative in the equation is multiplied by a parameter ?², where ? ∈ (0, 1]. When ? is small, a boundary and an interior layer (with the characteristic width ?) appear, respectively, in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristic of the reduced equation passing through the discontinuity point of the initial function; for fixed ?, these layers have limited smoothness. Using the method of additive splitting of singularities (induced by the discontinuities of the initial function and its low-order derivatives) and the condensing grid method (piecewise uniform grids that condense in a neighborhood of the boundary layers), a finite difference scheme is constructed that converges ?-uniformly at a rate of O(N ^?2ln² N + n ₀ ^?1 ), where N + 1 and N ₀ + 1 are the numbers of the mesh points in x and t, respectively. Based on the Richardson technique, a scheme that converges ?-uniformly at a rate of O(N ^?3 + N ₀ ^?2 ) is constructed. It is proved that the Richardson technique cannot construct a scheme that converges in ?-uniformly in x with an order greater than three.     

一阶脉冲泛函微分方程非线性边值问题

考虑一阶脉冲泛函微分方程非线性边值问题,利用上下解方法和单调迭代技术得到了耦合解和唯一解存在的充分条件.所得结果改进和推广了文献的相关结果.     

OSCILLATION THEOREMS FOR A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER TYPE

Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.     

Synthesis of size-controlled acid-resistant hybrid calcium carbonate microparticles as templates for fabricating "micelles-enhanced" polyelectrolyte capsules by the LBL technique

Size-controlled, low-dispersed calcium carbonate microparticles were synthesized in the presence of the amphiphilic block copolymer polystyrene-b-poly(acrylic acid) (PS-b-PAA) by modulating the concentration of block copolymer in the reactive system. This type of hybrid microparticles have acid-resistant properties. By investigating the aggregation behaviors of PS-b-PAA micelles by transmission electron microscopy (TEM), the mechanism of hybrid calcium carbonate formation illustrated that the block copolymer served not only as "pseudonuclei" for the growth of calcium carbonate nanocrystals, but also forms the supramicelle congeries, a spherical framework, as templates for calcium carbonate nanocrystal growth into hybrid CaCO(3) particles. Moreover, this pilot study shows that the hybrid microparticle is a novel candidate as a template for fabricating multilayer polyelectrolyte capsules, in which the block copolymer is retained within the capsule interior after core removal under soft conditions. This not only facilitates the encapsulation of special materials, but also provides "micelles-enhanced" polyelectrolyte capsules.     

Reflection and transmission at normal incidence onto air-saturated porous materials and direct measurements based on parametric demodulated ultrasonic waves

The present work is related to the characterization of air-saturated porous media by using parametric demodulated ultrasonic waves. One uses two different powerful ultrasonic emitters working either at 47 kHz or at 162 kHz which are electronically amplitude modulated over the 200 Hz-4 kHz or 2 kHz-40 kHz bandwidths respectively. The demodulation process takes place in air, due to its nonlinearity enabling to generate audio range acoustical waves or alternatively low frequency ultrasonic waves which can be used to characterize porous materials in the reflection configuration at normal incidence. Some appropriate theoretical calculations are introduced for three configurations of interest, i.e. a porous slab, a porous layer mounted onto a rigid plate, and a porous half space, in the case of the equivalent-fluid model. Comparisons between theoretical modeling and experimental data are provided and prospective industrial applications are discussed.     

红宝石晶体光学浮区法生长及其缺陷研究

采用光学浮区法生长了φ7 mm×70 mm的红宝石晶体.晶体的生长界面为凸界面,生长方向为<001>方向.X射线双晶摇摆曲线表明晶体具有良好的质量.研究了生长温度、旋转速率、生长速率对晶体质量的影响,确定了合理的工艺条件.通过扫描电镜、能量散射光谱仪、X射线衍射、化学腐蚀结合偏光显微镜对红宝石晶体中气泡、位错、胞状组织和溶质尾迹等缺陷进行了分析.     

柔性曲梁多体系统的研究现状和展望

本文对近几年来柔性多体系统建模理论的研究进展进行了评述, 详细阐述了曲梁结构多体系统动力学研究的理论背景和工程意义. 结合连续介质力学和多体系统动力学理论, 介绍了平面曲梁、空间曲梁应变位移场的描述以及几何非线性问题研究现状. 通过国内外文献及已有的研究, 综述了现有曲梁的离散化方法, 以及这些方法对于定曲率、变曲率曲梁的适用性. 然后, 总结了曲梁刚柔耦合动力学建模和数值计算中的难点问题, 介绍了平面曲梁、空间曲梁实验研究的现状. 最后, 综合全文, 提出了目前研究存在的难点问题, 以及计划解决这些难点问题的方法.      

分子印迹壳聚糖/凹土分离富集-火焰原子吸收光谱测定痕量铅

建立了用分子印迹壳聚糖/凹凸棒石（MICA）分离富集-火焰原子吸收光谱（FAAS）测定痕量铅的新方法。 在动态吸附条件下,系统地研究了溶液pH值、流速、洗脱条件和干扰离子对痕量铅分离富集的影响;在pH=4.5,上样流速为0.60 mL/min的条件下,铅能被MICA定量富集;吸附的铅可用1.0 mol/L HCl-0.1 mol/L 甲基异丁酮的乙醇溶液在流速为0.96 mL/min条件下完全洗脱;在优化条件下,MICA对铅的动态吸附容量为36.78 mg/g。 线性范围为0～1.28 mg/L,r=0.999 7,检出限（3σ,n=11）为0.73 μg/L,相对标准偏差为1.69%(n=6,ρ=0.08 mg/L),回收率在98.7%～101.4%之间。 该方法操作简便、线性关系良好、灵敏度和精密度高,应用于实际水样中痕量铅的测定,结果满意。