改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

含硫氨基酸与本征及缺陷石墨烯表面的相互作用

半胱氨酸及蛋氨酸是人体的两种含硫氨基酸,在生物活性中发挥着巨大的作用.本研究采用密度泛函理论方法对以上两种氨基酸在本征及缺陷石墨烯表面的吸附机理进行了详细研究.主要考虑了两种吸附体系:半胱氨酸及蛋氨酸平躺在两种石墨烯表面;两种氨基酸垂直地放置于两种石墨烯表面,且含硫的基团靠近表面.研究结果表明,半胱氨酸及蛋氨酸初始构型对它们之间的相互作用有一定的影响.两种氨基酸平躺时有较大的吸附能.此外,吸附能的结果显示两种氨基酸可以更好的与缺陷石墨烯表面紧密结合.同时,蛋氨酸与本征及缺陷石墨烯相互作用均大于半胱氨酸与本征及缺陷石墨烯相互作用.模拟结果有望为含硫氨基酸的石墨烯传感器提供有用的指导.     

Banach空间四阶两点问题正解的存在性

讨论了Banach空间E中的四阶边值问题:u~(4)(t)=f t(,u(t)),0≤t≤1,u(0)=u(1)=u″(0)=u″(1)=θ正解的存在性,其中f∶0,[1]×P→P连续,P为E中的正元锥.通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果.     

百年前的回望与启示——1923年诺贝尔化学奖得主弗里茨·普雷格尔的科研奇迹

弗里茨·普雷格尔因创立了有机物质的微量定量分析法而获得1923年诺贝尔化学奖,在获奖百年之际,本文回顾了他的相关研究背景和科研历程,并概述了微量定量分析技术的诞生情况。普雷格尔的成功体现了复合型知识结构的坚实基础、站立巨人肩膀上的继承创新、合作研究协同创新的重要性,其经历也引发了我们对于如何建立新时代理想研究生师生关系的思考。     

PROPERTIES OF THERMO-MOLDED GLUTEN/GLYCEROL/SILICA COMPOSITES

Environmentally friendly thermosetting composites were successfully prepared by conventional blending wheat gluten as matrix,glycerol as plasticizer and silica as filler followed by thermo-molding of the mixture at 120℃.The strong interfacial interaction between silica particles and gluten proteins leaded to an increase in storage modulus and a decrease in loss factor as revealed by dynamic mechanical analysis.The moisture absorption and elongation at break decrease while Young's modulus and tensile stre...     

SYNTHESIS, CHARACTERIZATION AND NANOPARTICLE FORMATION OF STAR-SHAPED POLY(L-LACTIDE) WITH SIX ARMS

Well-defined star-shaped poly(L-lactide)with six arms(sPLLA)was synthesized via the ring-opening polymerization of L-lactide using dipentaerythritol as initiator and stannous octoate as catalyst in bulk at 125~C.The effects of molar ratios of both monomer to initiator and monomer to catalyst on the molecular weights of as-synthesized sPLLA polymers were in detail investigated.The molecular weights of sPLLA polymers linearly increased with the molar ratio of monomer to initiator,and the molecular weight d...     

PREPARATION OF MICROPOROUS ULTRA HIGH MOLECULAR WEIGHT POLYETHYLENE (UHMWPE) BY THERMALLY INDUCED PHASE SEPARATION OF A UHMWPE/LIQUID PARAFFIN MIXTURE

Ultra-high molecular weight polyethylene (UHMWPE) with a microporous structure was prepared via thermally induced phase separation (TIPS).Liquid paraffin (LP) was used as a diluent in the preparation of microporous UHMWPE. Small angle laser light scattering (SALLS) and differential scanning calorimetry (DSC) were used to determine the phase separation temperatures,i.e.the cloud points and the dynamic crystallization temperatures,respectively.It was found that the cloudI points were coincident with the cr...     

PREPARATION AND CELL COMPATIBILITY OF FUNCTIONALIZED BIODEGRADABLE POLY(DL-LACTIDE-CO-RS-Β-MALIC ACID)

In order to create a functionalized biodegradable polymer for vascular tissue engineering application,poly(DL- lactide-co-RS-β-malic acid)(PDLLMAc)was synthesized.PDLLMAc was obtained after hydrogenolysis of poly(DL- lactide-co-RS-β-benzyl malolactonate)(PDLLMA),which was from the ring-opening polymerization of DL-lactide(DLLA) and RS-β-benzyl malolactonate(MA)using stannous octoate as catalyst.The copolymers were characterized by ~1H-NMR, FTIR,GPC and DSC.The tensile strength and water uptake of the cop...     

THERMOSENSITIVITY OF NARROW-DISPERSED POLY(N-n-PROPYLACRYLAMIDE) PREPARED BY ATOM TRANSFER RADICAL POLYMERIZATION

Controlled polymerization of N-n-propylacrylamide was achieved by atom transfer radical polymerization(ATRP) in a N,N-dimethylformamide-water mixture(50 vol%)at room temperature with methyl 2-chloropropinonate as initiator and CuCl/tris(2-dimethylaminoethyl)amine as the catalytic system in a ratio of 1:1:1.High molecular weight homopolymers(up to 3.7×10~4)with narrow molecular weight distribution(less than 1.2)were obtained.The living character of the polymerization was further demonstrated by self-block...     

SYNTHESIS, CHARACTERIZATION AND PROPERTIES OF ORGANOCLAY-MODIFIED POLYSULFONE/EPOXY INTERPENETRATING POLYMER NETWORK NANOCOMPOSITES

Organoclay-modified hydroxylterminated polysulfone (PSF)/epoxy interpenetrating network nanocomposites (oM-PSF/EP nanocomposites) were prepared by adding organophilic montmorillonite (oMMT) to interpenetrating polymer networks (IPNs) of polysulfone and epoxy resin (PSF/EP) using diaminodiphenylmethane (DDM) as curing agent.The mechanical properties like tensile strength,tensile modulus,flexural strength,flexural modulus and impact properties of the nanocomposites were studied as per ASTM standards.Differ...