Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

基于Ni-SnO2纳米颗粒的GS-PUF设计

气敏传感器具有气体识别、探测和监测等功能, 广泛应用于工业生产等领域, 但在泄漏预警时缺乏迅速识别和定位等功能. 本文基于传感器制备工艺偏差分析, 通过对传感器气敏机制的研究, 提出一种基于Ni-SnO2纳米颗粒的气敏传感器物理不可克隆函数(Gas Sensor-Physical Unclonable Function, GS-PUF)设计方案. 该方案利用掺杂Ni元素的方法, 结合静电喷雾沉积技术制备Ni-SnO2气敏传感器, 以获取更加稳定可靠的物理特征值, 然后采集气敏传感器对不同浓度下气体的响应数据, 最后利用随机阻值多位平衡算法比较不同组气敏传感器响应电信号值, 实现PUF数据输出. 制备每组样本可产生128位二进制数据的多组PUF样本, 进行对比实验. 结果表明, 所设计的GS-PUF具有气体泄漏源头识别定位的功能, 且随机性提升至99%, 唯一性达49.80%.     

A Criterion of Nonparabolicity by the Ricci Curvature

A complete manifold is said to be nonparabolic if it does admit a positive Green’s function. To ?nd a sharp geometric criterion for the parabolicity/nonparbolicity is an attractive question inside the function theory on Riemannian manifolds. This paper devotes to proving a criterion for nonparabolicity of a complete manifold weakened by the Ricci curvature. For this purpose, we shall apply the new Laplacian comparison theorem established by the ?rst author to show the existence of a non-constant bounded subharmonic function.     

On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem. We then use that result to obtain an interval where a certain Mittag–Leffler function has no real zeros.     

Nonrigid image registration using similarity measure based on spatially weighted global probability distribution function

In nonrigid image registration, similarity measures including spatial information have been shown to perform better than those measures without spatial information. In this work, we provide new insight to the relationships among regional mutual information, regional probability distribution functions (PDFs) and global PDFs, and propose a novel nonrigid registration scheme with spatially weighted global probability distribution function (SWGPDF). Similarity measures based on SWGPDF (SWGPDFSM) are constructed. Three different spatial sub-region division methods are compared: the equally spaced sub-region (ESSR), the local binary pattern sub-region (LBPSR) and the gradient sub-region (GSR). The registration scheme applies B-spline based free form deformations (FFDs) as the transformation model. A Parzen window and linear interpolation are used to construct histograms. The SWGPDFSM registration scheme with ESSR space division is compared with the traditional global mutual information (gMI), the traditional global normalized mutual information (gNMI), regional mutual information and the SWGPDFSM with LBPSR or GSR space division. The test results show that SWGPDFSM scheme with ESSR space division outperforms the other schemes for elastically aligning images in the presence of big geometrical transformations, bias fields and illumination changes.     

从头计算方法比较研究B_2Au_4,Al_2Au_4和BAlAu_4的几何和电子结构(英文)

Au/H相似性的研究是现代化学中的一个热门话题.我们从理论上报道Au/H相似的新成员:共价化合物B2Au4,离子化合物Al2Au4和BAl Au4.采用密度泛函和波函数理论方法对比研究了缺电子体系B2Au4、Al2Au4和BAl Au4的几何和电子结构.详细讨论了它们基态结构的轨道、适应性自然密度划分(Ad NDP)和电子局域函数(ELF)分析.计算结果表明稍微扭曲变形的C2B2Au4是基态结构,在这个共价化合物中含有两个B―Au―B三中心二电子(3c-2e)键.然而C3vAl+(Al Au4)-和C3vAl+(BAu4)-被研究证明是含有三个X―Au―Al三中心二电子键的类盐化合物(在Al2Au4中X=Al,BAl Au4中X=B).Al2Au4和BAl Au4是至今为止首例报道的在离子缺电子体系中含有金桥键的化合物.同时计算了B2Au4-、Al2Au4-和BAl Au4-阴离子基态结构的绝热剥离能和垂直剥离能,为实验表征提供依据.文中报道的金桥键为共价键和离子键相结合的缺电子体系提供了一个有趣的键合模式,有助于设计含有高度分散金原子的新材料和催化剂.     

Chitosan/Ce(IV) redox polymerization‐based amplification for detection of DNA point mutation

Polymerization‐based signal amplification, a technique developed for use in rapid diagnostic tests, hinges on the ability to localize initiators as a function of interfacial binding events. We report here a new DNA detection method in which polymer growth in redox‐polymerization is used as a means to amplify detection signals. The introduction of biotin‐labeled chitosan (biotin‐CS) with highly dense amino groups into the polymerization amplification as macromolecular reducing agent, beneficially simplifies amplification operation, as well as, provides a large amount of initiation points to improve the sensitivity of detection. DNA hybridization, SA and biotin binding reactions led to the attachment of CS on a solid surface where specific DNA sequences were located. With the addition of the mixture containing monomer AM, crosslinker PEGDA and oxidant CAN onto the CS location, the growth of polymer films was triggered to render the corresponding spots readily distinguishable to the naked eye. Direct visualization of 0.21 fmol target DNA molecules of interest was demonstrated. Non‐small cell lung cancer p53 sequence was further selected as a proof‐of‐principle to detect DNA point mutation. The proposed method exhibited an efficient amplification performance for molecule detection, and paved a new way for visual diagnosis of biomolecules. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1929–1937