On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

HyperFLOW软件非结构网格亚跨声速湍流模拟的验证与确认

计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度.      

水胁迫下典型盐生植被梭梭光谱特征分析

荒漠地区由于气候干燥，降水稀少，水分常成为制约植被生长的因素之一，水分胁迫对植物长势和产量的影响比任何其他胁迫都要大。随着高光谱技术的发展，国内外已有众多学者利用高光谱数据研究植被遭受胁迫作用，然而这些研究对象多集中于甜菜、棉花、玉米、水稻等作物，针对干旱区盐生植被遭受胁迫作用的研究较少。梭梭作为荒漠、半荒漠地区的典型盐生植被之一，具有极高的经济和生态效益。选择梭梭作为研究对象，培育一年生梭梭，并设置三个水分梯度，形成受不同水分量胁迫的梭梭。使用原始光谱、红边位置参数，结合植被指数及二维相关光谱研究其叶片光谱特征，为干旱区利用高光谱遥感监测盐生植被提供借鉴。结果表明：(1)分析梭梭叶片反射光谱曲线发现，在可见光至中红外各波段范围内，受不同水分量胁迫作用的梭梭叶片光谱反射率有显著差异。在可见光(350～610 nm)波段，各水分处理的梭梭叶片反射率依次为100 mL>500 mL>200 mL，这是由于100和200 mL水分促进梭梭内部叶绿素合成，使该波段反射率降低，而过多的水分(500 mL)对梭梭内部的叶绿素合成没有更大的促进作用。在红光区(611～738 nm)，随着水分量的增多，受不同水分量胁迫的梭梭叶片光谱反射率依次减小。在738～1 181和1 228～1 296 nm波段，受不同水分量胁迫作用的梭梭叶片光谱反射率为：200 mL>100 mL>500 mL；在1 182～1 227 nm波段，受不同水分量胁迫作用的梭梭叶片光谱反射率为：100 mL>200 mL>500 mL。这是由于植被细胞结构对近红外区域的反射率影响较大，因而受不同水分胁迫作用的梭梭叶片光谱反射率有显著差异。在1 300～1 365和1 392～1 800 nm波段，受各水分胁迫作用的梭梭叶片反射率为：100 mL>200 mL>500 mL。这表明在500 mL水分胁迫量范围内，水分越多，叶子的细胞液、细胞膜对水分的吸收能力越强，使得反射率下降。通过对原始光谱求取一阶导数并提取红边位置参数发现，各水分处理下的梭梭叶片一阶微分光谱曲线中红边位置未发生移动。这是由于梭梭在长期的干旱环境影响下，形成了特殊的适应机制，水分对其红边位置影响不敏感。(2)选取若干植被指数分析各水分处理下的梭梭光谱指数变化。当水分胁迫量由100 mL增至200 mL时，WI/NDWI，MSI和NDII指数值变化显著，可用于研究水分胁迫下梭梭的光谱特征。(3)使用二维相关光谱技术分析受各水分胁迫作用的梭梭光谱特征，得出在100 mL水分胁迫下，在536，643，1 219和1 653 nm波段处，吸收峰对水分的微扰敏感；在200 mL水分胁迫下，在846和1 083 nm波段处，吸收峰对水分的微扰敏感；在500 mL水分胁迫下，在835和1 067 nm波段处，吸收峰对水分的微扰敏感。总之，在近红外波段，与100 mL水分量相比，梭梭受200和500 mL水分量胁迫时，吸收峰对水分的微扰敏感度上升。由100 mL水分胁迫下梭梭的二维同步相关谱图可知，1 044和1 665 nm，1 072和903 nm，903和1 264 nm，1 230和1 061 nm波段处形成正交叉峰，表明这些波段处光谱强度随水分的干扰同时变化。     

Synthesis and characterization of 9,9‐bis(4‐hydroxyphenyl and 4‐aminophenyl)dibenzofluorenes: Novel fluorene‐based monomers

Two novel 9,9‐difunctionalized fluorene‐type monomers, 9,9‐bis(4‐hydroxyphenyl‐ and 4‐aminophenyl)‐2,3:6,7‐dibenzofluorenes, are synthesized by the reaction of dibenzenzofluorenone with phenol and aniline. These monomers are used for the preparation of polyester and polyimide as the typical polymers to evaluate the property change such as thermal stability caused by the benzene rings fused to the fluorene skeleton with keeping good solubility, in comparison with the polymers derived from simple fluorenone. In fact, these two new polymers have the fairly enhanced thermal stability and refractive index value along with satisfactory solubility in organic solvents, enough to emphasize the fusion effect. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2602–2605     

Estimator of a change point in single index models

This paper considers the problem of change point in single index models. In order to obtain asymptotically valid confidence intervals for the estimation of the change point, the convergence rate and asymptotic distribution of the change point estimate is studied. Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.     

Synthesis of polydithiourethanes and their thermal,optical, and mechanical properties originated from monomers structure

Polyaddition of various diisothiocyanates and dithiols was achieved with triethylamine in dimethylformamide at 25 °C for 12 h under nitrogen, and then the corresponding polydithiourethanes (PDTUs) were obtained with high yield and molecular weight without depending on the monomer structures, although the dithiol monomer of the low nucleophilicity was unsuitable for polyaddition in this system. The chemical and physical properties of the obtained PDTUs such as solvent solubility, glass transition temperature, thermal stability, transparency, refractive index, and tensile strength, were analyzed in detail by gel permeation chromatography, nuclear magnetic resonance, Fourier transform infrared–attenuated total reflection, ultraviolet–visible, differential scanning calorimetry, thermogravimetric analysis, and tensile testing measurements. These results proved that PDTUs and their cast films having the aliphatic diisothiocyanate and dithiol moieties exhibited excellent chemical and physical properties compared to that of the aromatic PDTUs. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2255–2262     

Synthesis of palladium concave Nanocubes with high‐index facets and their catalytic properties

Palladium nanocrystals with a variety of shapes have received particular interest in recent years due to their unique properties in catalysis. Herein, Pd concave nanocubes with high‐index facets (Pd‐CNs) was synthesized by a simple water‐based route without seeds using L‐ascorbic acid (AA) as the reduction agent in the presence of CTAB. X‐ray diffraction and transmission electron microscopy were employed to demonstrate the formation of concave structures with high‐index facets of the Pd‐CNs with an average size of 17.5 nm. The as‐prepared Pd‐CNs presented significantly higher catalytic activity than commercial Pd/C (an average particle size of 4.7 nm) in the electro‐oxidation of methanol, but exhibited weaker property in Suzuki coupling reaction, which provided an evidence for the effect of shape and size on different reactions.     

Comparative molecular field analysis of chromatographic hydrophobicity indices for some coumarin analogs

The chromatographic hydrophobicity index (CHI) is an HPLC‐based parameter that provides reliable guidance in optimization of pharmacological efficiency and adsorption, distribution, metabolism and exertion (ADME) profile of drug candidates. In the present work, classical and three‐dimensional quantitative structure–property relationship (QSPR) models were developed for prediction of CHI values of some 4‐hydroxycoumarin analogs on immobilized artificial membrane column. Comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) as 3D–QSPR methods were performed to gain insight into the key structural factors affecting on the chromatographic hydrophobicity of interested chemicals. The calculated parameters of Q ², R ² and standard error were 0.545, 0.996 and 0.773 for CoMFA model and 0.815, 0.986 and 1.44 for CoMSIA model, respectively. The contour maps for steric fields of the CoMFA model illustrate that the hydrophobicity of chemicals will be higher when the positions of R6, R7 and R8 in the 4‐hydroxycuomarin ring are substituted by alkyl groups. Moreover, by the analysis of the plots of electrostatic fields, it was concluded that the CHI value greatly increases if one hydrogen on coumarin ring is substituted by the F, Cl, Br, OH or OCH₃ group.