Effect of LiCl in Polymer Solution on the Instable Part of Electrospinning Nanofibers:Theoretical Analysis and Experimental Verification

In this paper,the theoretical analysis proves that the relationship between radius r of jet and the axial distance z from the onset of whipping instability follows an allometric law in the form r∝z-1/4 whatever surface charge parameter α is.Polyvinylalcohol(PVA)was used to study the effect of surface charge on the variation of jet diameter with axial coordinate after the onset of whipping instability during electrospinning by adding LiCl.The experiment shows that the relationship between radius r of jet and the axial distance z from the onset of whipping instability also follows the law in the form r∝z-1/4 when the content of LiCl is from 0.2 wt% to 4 wt%.That is,the law does not depend upon the content of salt,and the theoretical prediction agrees quite well with the experimental data.     

节理岩体对P波传播的影响

应力波在节理岩体中的传播规律是十分复杂的,不仅会受到岩石物理力学参数的影响,还会受到节理性质及分布特征的影响.以含平行双节理的岩体作为研究对象,采用数值模拟的方式探讨了平面P波在节理岩体中传播规律.首先,对含平行双节理的岩体进行了分析,探讨了节理刚度、归一化节理间距、节理倾角、节理刚度比对质点振速缩放系数(VSF)在节理前、节理间和节理后分布特征的影响.结果表明:对于节理岩体,节理刚度越大,平面P波的透射性越好,能量衰减的越少;在一定范围内,归一化节理间距越大,能量衰减的越多;节理倾角对不同位置的监测点的影响各不相同;不同刚度比下,对节理2附近的监测点影响较大,其余监测点基本上没有影响.     

一种双正交小波代数构造方法

提出了一种B样条双正交小波的代数构造方法.对同一个尺度函数来说,可通过自由选择参数构造多种不同的对偶尺度函数的系数,从而可以构造不同的B样条双正交小波.在此基础上用同一尺度函数的多种双正交小波分别作了信号消噪和图像的分解与重构实验,取得了小波系数在信号消噪和图像处理中如何按照应用目的选优的相关结论.     

d+1维生长方程的奇异动力学标度性质研究

将López基于Hentschel和Family的直接标度分析理论提出的判别连续性动力学生长方程标度奇异性的解析方法,本文推广应用到d 1维生长方程动力学标度奇异性质的研究中,分别判断出d 1维的Kardar-Parisi-Zhang(KPZ)、线性molecular-beam epitaxy(MBE)、Sun-Guo-Grant(SGG)以及Lai-Das Sarma-Villain(LDV)等生长方程在弱耦合和强耦合区域内的奇异标度性质.当生长方程出现奇异标度性质时,使用标度关系lαoc=α-zκ可以得到各方程的局域粗糙度指数,并与数值模拟的结果相吻合.     

机器学习在座逾渗相变问题中的应用

机器学习理论区别于传统方法,因其在对于复杂的数据集识别、分类的准确性和高效性而被广泛应用于各个领域.识别相变是机器学习和统计物理领域相结合的最有代表性的工作.到目前为止,机器学习完成的相变识别几乎都是基于具有动力学演化过程的自旋模型,如Ising模型等,而其在另一类不具有动力学演化过程而完全由系统结构特征决定的相变模型,如逾渗模型等,仍未有细致研究.本文结合现有的机器学习技术,卷积神经网络和一般向量机,对二维方格子上的座逾渗问题进行了研究,发现能以高正确率对不同相的构型进行识别,证明了机器学习在这类问题上研究的可行性.通过已完成训练的学习机对不同参数下构型预测的正确率计算,发现正确率在相变点附近会出现急剧衰减,与系统参数呈幂律衰减.这与传统相变理论一致.通过定量计算,还发现2种学习机的正确率衰减规律都满足同一个幂律指数.这不仅进一步从全新的角度揭示了相变的普适性,而且为找寻相变点提供了新的方法.     

一类多元双正交向量值小波包的构造

文章研究了一类多元双正交向量值小波包的构造及其性质。     

广义Boussinesq方程的不变集与精确解

不变集方法是一种构造非线性偏微分方程精确解的有效方法.文章利用不变集思想方法,讨论了一类非线性偏微分方程utt=A(u)uxxxx+B(u)uxx+C(u)(uux)x+D(u)u2d的问题,得到了一些情况下对应方程的精确解,从而丰富了这类方程解的研究.     

Convergence of the majorization method for multidimensional scaling

In this paper we study the convergence properties of an important class of multidimensional scaling algorithms. We unify and extend earlier qualitative results on convergence, which tell us when the algorithms are convergent. In order to prove global convergence results we use the majorization method. We also derive, for the first time, some quantitative convergence theorems, which give information about the speed of convergence. It turns out that in almost all cases convergence is linear, with a convergence rate close to unity. This has the practical consequence that convergence will usually be very slow, and this makes techniques to speed up convergence very important. It is pointed out that step-size techniques will generally not succeed in producing marked improvements in this respect.     

Bronchial asymmetry and Fibonacci scaling

Summary The irregular branching pattern of the bronchial tree in multiple mammalian species is consistent with a process of morphogenetic self-similarity described by Fibonacci scaling.     

微分方程的小波解

构造了尺度因子为3的正交尺度函数，应用它求解微分方程，实验结果表明此方法有效。