An explicit solution of the large deformation of a cantilever beam under point load at the free tip

The large deformation of a cantilever beam under point load at the free tip is investigated by an analytic method, namely the homotopy analysis method (HAM). The explicit analytic formulas for the rotation angle at the free tip are given, which provide a convenient and straightforward approach to calculate the vertical and horizontal displacements of a cantilever beam with large deformation. These explicit formulas are valid for most practical problems, thus providing a useful reference for engineering applications. The corresponding Mathematica code is given in the Appendix.     

Stability of sets of functional differential equations with impulse effect

In this paper, we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous Lyapunov functions with Razumickhin techniques. Some sufficient conditions for stability of sets are established, and some known stability theorems also are generalized.     

Solitary wave and chaotic behavior of traveling wave solutions for the coupled KdV equations

Using the method of dynamical systems to study the coupled KdV system, some exact explicit parametric representations of the solitary wave and periodic wave solutions are obtained in the given parameter regions. Chaotic behavior of traveling wave solutions is determined.     

New exact solutions for the nonlinear wave equation with fifth-order nonlinear term

The purpose of this paper is to reveal the dynamical behavior of the nonlinear wave equation with fifth-order nonlinear term, and provides its bounded traveling wave solutions. Applying the bifurcation theory of planar dynamical systems, we depict phase portraits of the traveling wave system corresponding to this equation under various parameter conditions. Through discussing the bifurcation of phase portraits, we obtain all explicit expressions of solitary wave solutions and kink wave solutions. Further, we investigate the relation between the bounded orbit of the traveling wave system and the energy level h. By analyzing the energy level constant h, we get all possible periodic wave solutions.     

Allocating fixed costs and common revenue via data envelopment analysis

An issue of considerable importance involves the allocation of fixed costs or common revenue among a set of competing entities in an equitable way. Based on the data envelopment analysis (DEA) theory, this paper proposes new methods for (i) allocating fixed costs to decision making units (DMUs) and (ii) distributing common revenue among DMUs, in such a way that the relative efficiencies of all DMUs remain unchanged and the allocations should reflect the relative efficiencies and the input-output scales of individual DMUs. To illustrate our methods, numerical results for an example are described in this paper.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

便携式多源光谱融合水质分析仪的研制

采用光谱信息融合理论,研制了一种新型便携式多参数水质分析仪,自行设计了仪器的分析方法、硬件结构、内部工作原理及软件功能.可作为一种无须化学试剂、体积小、快速、易于野外现场作业的绿色水质检测工具.通过对少量水质样品的光谱测量分析,快速检测了总有机碳(TOC)、化学需氧最(COD)等6类水质有机污染物指标.实际测量结果表明,本仪器采用的基于多源光谱信息融合的水质分析方法测量精度显著优于目前市场上普遍采用的常规紫外吸收光谱法.     

基于低分辨率色散型拉曼光谱仪的汽油苯含量快速分析

针对汽油苯含量的快速分析问题,提出了基于低分辨率色散型拉曼光谱仪的新的检测方法.由于色散型拉曼光谱中存在着严重的测量噪声和荧光背景干扰,应用多项式平滑滤波除噪声和迭代多项式拟合基线校正方法减少荧光背景的干扰.随后,分别采用岭回归,主成分同归、偏最小二乘回归方法,对炼油厂的汽油样本建立了三个苯含量的快速分析模型并对其进行验证.实验表明,基于低分辨率色散型拉曼光谱仪进行汽油苯含量分析,结合常规建模方法,重复性和再现性均满足SH/T0713-2002标准的要求,此外由于其具有低成本、小型易携带等优点,适用于日常快速分析.     

Super quasiperiodic wave solutions and asymptotic analysis for $$ \mathcal{N} = 1 $$ supersymmetric KdV-type equations

Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method to construct explicit super quasiperiodic (multiperiodic) wave solutions of $ \mathcal{N} = 1 $ \mathcal{N} = 1 supersymmetric KdV-type equations in superspace. We show that the supersymmetric KdV equation does not have an N-periodic wave solution with arbitrary parameters for N ≥ 2. In addition, an interesting influencing band occurs among the super quasiperiodic waves under the presence of a Grassmann variable. We also observe that the super quasiperiodic waves are symmetric about this band but collapse along with it. We present a limit procedure for analyzing the asymptotic properties of the super quasiperiodic waves and rigorously show that the super periodic wave solutions tend to super soliton solutions under some “small amplitude” limits.