Deterministic homogenization of nonlinear degenerate elliptic operators with nonstandard growth

We study the deterministic homogenization of nonlinear degenerate elliptic equations with nonstandard growth.One fundamental in this topic is to extend the classical compactness results of theΣ-convergence method to the Orlicz spaces.We also show that one can homogenize nonlinear Dirichlet problems in a general way by leaning on a simple abstract hypothesis contrary to what has been done in the determinstic homogenization theory.     

几何体网对随机模拟的影响

随着计算机的迅速发展,统计模拟常用于解决实际问题.在几何概率问题中,代表几何体网的构造十分重要。本文考虑四种不同的产生网的方法对三种不同几何体(球带、圆饼、圆环)进行模拟试验,得到一些有用的结果,并推荐数论方法,特别是好格子点(GLP)方法。本文指出代表几何体的网十分重要,若选择不当,可能会导致有偏估计。     

润滑油的指标评价及配方优化

本文首先基于优选理论中的TOPSIS法,较好地评价了润滑油各实验指标,缩小了添加剂和基础油种类的选择范围,然后采用均匀设计,得到了润滑油的最优配方.研究表明,将TOPSIS法和均匀设计结合、运用到润滑油优质配方的寻找及优选中,有助于企业降低实验成本,提高实验效率,具有较高的应用价值.     

由均匀染色导出的强Chernoff界

本文研究了相关变量的Chernoff问题. 利用相关变量构造图的方法, 利用均匀染色的结果, 获得了更强的Chernoff界, 推广了Chernoff不等式在相关随机变量的不等式下的界.     

HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT

We study the homogenization of the incompressible Navier-Stokes equations with periodic oscillating coefficient in a bounded non-homogeneous media. To do that, we introduce a generalized compensate compactness result and a suitable class of test function to this problem. By passing the limit, we obtain the homogenized model of this problem.     

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

变围压-孔压条件下含气煤岩应力应变关系研究

为研究围压及孔压对含气煤岩本构关系的影响,基于弹性力学及破坏理论,建立了细观非均匀弹脆性模型,利用FEPG数值模拟软件,编制了有限元计算程序,用数值方法模拟了含气煤岩体在变围压-孔压条件下的变形及破坏规律.结果表明,围压增大时,煤岩体由脆性逐渐转呈柔性,且承载能力有所增强,而孔压的影响则恰好相反.将数值模拟结果分别与变围压、变孔压实验数据进行了对比,两者基本相符,充分验证了力学模型的适用性及计算程序的正确性.     

高锰酸钾溶液标准物质的研制

介绍高猛酸钾溶液标准物质的研制过程。对研制的溶液标准物质进行了均匀性和稳定性考察。结果表明,该标准物质均匀性良好,定值稳定期为6个月。用称量滴定法定值,定值结果为c(1/5 KMnO4)=0.100 7 mol/kg(k=2)。该标准溶液满足二级标准物质的技术要求,已被批准为国家级二级标准物质。     

Cisplatin-loaded polymer/magnetite composite nanoparticles as multifunctional therapeutic nanomedicine

Multifunctional nanocarriers with multilayer core-shell architecture were prepared by coating superparamagnetic Fe3O4 nanoparticles with diblock copolymer folate-poly（ethylene glycol）-b-poly（glycerol monomethacrylate） （FA-PEG-b- PGMA）, and triblock copolymer methoxy poly（ethylene glycol）-b-poly（2-（dimethylamino） ethyl methacrylate）-b- poly（glycerol monomethacrylate） （MPEG-b-PDMA-b-PGMA）. The PGMA segment was attached to the surfaces of Fe304 nanoparticles, and the outer PEG shell imparted biocompatibility. In addition, folate was conjugated onto the surfaces of the nanocarriers. Cisplatin was then loaded into the nanocarrier by coordination between the Pt atom in cisplatin and the amine groups in the inner shell of the multilayer architecture. The loaded cisplatin showed pH-responsive release： slower release at pH 7.4 （i.e. mimicking the blood environment） and faster release at more acidic pH （i.e. mimicking endosome/lysosome conditions）. All of the cisplatin-loaded nanoparticles showed concentration-dependent cytotoxicity in HeLa cells. However, the folate-conjugated cisplatin-loaded carriers exhibited higher cytotoxicity in HeLa cells than non-folate conjugated cisplatin-loaded carriers.     

沥青混凝土级配曲线的数值设计方法与对有效弹性模量影响的研究

沥青混凝土有效性能的预测和评估是其在道路工程与大坝防渗等应用中的关键问题。本文利用细观随机建模技术和有限元方法研究了级配曲线对沥青混凝土有效弹性模量的影响。首先,基于改进的蒙特卡洛法分别实现了服从工程筛分级配曲线或给定函数级配曲线的沥青混凝土细观随机模型的高效生成;然后,利用建立的模型分析了骨料的含量、弹性模量和试样尺寸对沥青混凝土的有效弹性模量的影响,并与实验结果进行对比,验证了所建模型的可靠性;从而,预测了在AC-13级配范围内级配曲线的凹凸程度,即粗细骨料的组成比例对沥青混凝土有效弹性模量的影响。结果表明,级配曲线的凹凸程度对其有效弹性模量影响存在较大差异,级配曲线的下凹(粗骨料占比增大)会导致有效弹性模量迅速增大,级配曲线的上凸(细骨料占比增大)也会引起有效弹性模量略有上升;另外提出的随机建模方法可实现对级配曲线,即对粗细骨料组成比例的定制设计.