A Quasilinear System Related with the Asymptotic Equation of the Nematic Liquid Crystal’s Director Field*

In this paper, the author studies the local existence of strong solutions and their possible blow-up in time for a quasilinear system describing the interaction of a short wave induced by an electron field with a long wave representing an extension of the motion of the director field in a nematic liquid crystal’s asymptotic model introduced in [Saxton, R. A., Dynamic instability of the liquid crystal director. In: Current Progress in Hyperbolic Systems (Lindquist, W. B., ed.), Contemp. Math., Vol.100, Amer. Math.Soc., Providence, RI, 1989, pp.325–330] and [Hunter, J. K. and Saxton, R. A., Dynamics of director fields, SIAM J. Appl. Math., 51, 1991, 1498–1521] and studied in [Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation I, Arch. Rat. Mech. Anal.,129, 1995, 305–353], [Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation II, Arch. Rat. Mech. Anal., 129, 1995, 355–383] and in [Zhang, P. and Zheng,Y., On oscillation of an asymptotic equation of a nonlinear variational wave equation,Asymptotic Anal., 18, 1998, 307–327] and, more recently, in [Bressan, A., Zhang, P. and Zheng, Y., Asymptotic variational wave equations, Arch. Rat. Mech. Anal., 183, 2007,163–185].     

二元热传导方程的Phragmén-Lindel?f型二择一结果

考虑了二元热传导方程在半无穷区域上解的渐近性质, 其中在柱体的侧面上施加局部非齐次Neumann条件.这种条件模拟了柱体侧面上的绝热材料受到局部破坏的情形.利用微分不等式技术和能量分析的方法, 得到了热传导模型的Phragmén-Lindel?f型二择一结果     

二维线性色散方程的色散量子化现象

研究了定义在平面有界矩形区域的二维线性KdV方程和二维线性Schr?dinger方程的色散量子化现象.证明了在有理时刻,方程周期初边值问题的解是初值条件的线性组合,而在无理时刻,解呈现类分形,连续不可微的状态.     

"生物数学"本、硕一体化系列课程的研究与探索 ——兼谈数学建模能力培养之途径

以东北林业大学本、硕两阶段"生物数学"系列课程的整体改革实践为例,针对数学本科专业和数学硕士点学科拔尖人才创新能力培养问题,通过构建"理论学习—专题研究—课外研讨班"一体化教学体系的教学法实践,探讨了如何以生物问题为背景,构建"问题—建模—求解"的研究型教学模式、搭建培养数学建模能力平台的问题,以实现培养学生数学建模能力的一体化教学体系和研究型教学模式的目标.     

神奇的海洋之旅

正海洋是生命的摇篮,然而,海水下面的一切,对人类来说又是那么陌生。海水下的风景是什么样的?那里生活着什么样的居民?它们又有什么奇特之处……想知道这一切吗?那就随我来一次快乐的海洋之旅吧!     

不同热解温度的秸秆源生物炭对Cd(Ⅱ)吸附机理

为了探究热解温度对生物炭吸附镉的性能及机制影响,以水稻秸秆为生物炭原料(BC),制备了300℃,500℃和700℃3种不同热解温度的生物炭(BC300、BC500和BC700)。通过灰分测定、元素分析、BET、FT-IR和XRD等方法,对所制备的材料进行表征。结果表明,与BC500、BC300相比,BC700具有较高的比表面积。静态吸附实验结果表明BC700具有更高的Cd2+去除能力。BC700对Cd2+吸附符合准二级动力学和Langmuir模型。最大理论平衡吸附量为20.3 mg·g-1。生物炭对Cd2+的主要吸附途径是离子交换作用(Qi)和沉淀作用(Qp),其中,离子交换作用是低温热解制备生物炭的主要吸附途径,沉淀作用在高温热解制备生物炭吸附Cd2+过程中所占比例最高。这项研究表明,热解温度不仅影响了生物炭对Cd2+的吸附能力,也影响了生物炭吸附Cd2+的作用途径。     

植物生长调节剂生物筛选方法的初步构建

通过对13种植物生长调节剂的试验，建立了用于筛选植物生长调节剂的生物检测方法，该方法第1步采用萝卜、黄瓜、小麦、油菜4种幼苗生长法联合筛选，第2步采用萝卜子叶扩张法、黄瓜子叶生根法联合筛选，这样能保证有生长调节剂活性的化合物在普筛中不被漏筛，而且方法简便，测试周期短。     

Commutators of Littlewood-Paley Operators on Herz Spaces with Variable Exponent

Let ? ∈ L~2(S~(n-1)) be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Operators and their higher-order commutators on Herz spaces with variable exponent.     

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

§1.IntroductionLet(?,F)be a measurable space and let Lb(F)be the space of F-measurable andbounded real functions.A nonlinear expectation is a continuous functionalE[·]:Lb(F)?→Rthat is order preserving(i.e.,E[X1]≥E[X2],if X1≥X2)and constant preserving     

Mechanical properties of double-stranded DNA biofilm with Gaussian distribution简

In microcantilever-based label-free biodetection technologies, deflection changes induced by adsorptions of double-stranded DNA （dsDNA） molecules on Au-layer surface are greatly affected by the mechanical, thermal and electrical properties of DNA biofilm. In this paper, the elastic properties of dsDNA biofilm are studied. First, the Parsegian＇s empirical potential based on a mesoscopic liq- uid crystal theory is employed to describe the interaction energy among coarse-grained DNA cylinders. Then, con- sidering a Gaussian distribution of DNA interaxial distance, the thought experiment method is used to derive an analyti- cal expression for Young＇s modulus of DNA biofilm with a stochastic packing pattern for the first time. Results show that Young＇s modulus of DNA biofilm is on the order of 10 MPa. These findings could provide a simple and effective method to evaluate the mechanical properties of soft biofilm on snbstrate.