Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation

In this paper, a generalized variable-coefficient Gardner equation arising in nonlinear lattice, plasma physics and ocean dynamics is investigated. With symbolic computation, the Lax pair and Bäcklund transformation are explicitly obtained when the coefficient functions obey the Painlevé-integrable conditions. Meanwhile, under the constraint conditions, two transformations from such an equation either to the constant-coefficient Gardner or modified Korteweg-de Vries (mKdV) equation are proposed. Via the two transformations, the investigations on the variable-coefficient Gardner equation can be based on the constant-coefficient ones. The N-soliton-like solution is presented and discussed through the figures for some sample solutions. It is shown in the discussions that the variable-coefficient Gardner equation possesses the right- and left-travelling soliton-like waves, which involve abundant temporally-inhomogeneous features.     

Isomers and [2,3]-Sila-wittig Rearrangement of [(Allyloxy)sily]lithium Silylenoid in the Gas Phase and THF Solvent

Theoretical calculations of the [2,3]-sila-wittig rearrangement of isomers of [(allyl-oxy)silyl]lithium (C3H50)H2SiLi have been performed in the gas phase and THF solvent using theG3MP2B3 method.Seven isomers of silylenoid (C3H5O)H2SiLi, 1～7, are found.The [2,3]-sila-wittig rearrangement paths are followed using two isomers, 2 and 4, to yield the transition states as well as the products.In the transition state, the silicon center functions as a nucleophile and the allyl as an electrophile.The interaction between the silicon and allylic sites leads to the formation of Si-C[3] bond and the break of O-C[1] bond.Finally, the (allylsilyl)oxylithium (C3H5)H2SiOLi is obtained.The rearrangement paths are confirmed by the intrinsic reaction coordinate (IRC)calculations.The rearrangement mechanisms of reactions of 2 and 4 are similar, and the latter reaction is more favored in the gas phase and THF solvent.Also, the solvent effects are analyzed in this work.     

Theoretical Study on the Inclusion Complex of β-Cyclodextrin and Nitrobenzene

Quantum chemical calculations were carried out to investigate the structures and properties for the inclusion complexes of nitrobenzene (NB) into β-cyclodextrin. Two low-energy conformations of β-cyclodextrin (A and B) in the gas phase were initially investigated by the PM3 and B3LYP/6-31+G(d,p) calculations, respectively. Three different orientations were considered in the inclusion process of A and B with NB to form 1:1 complexes. Potential energy scan by PM3 calculations indicated that the phenyl orientation Ab for conformation A and the equator orientation Bc for conformation B are more favorable in energy, respectively. We also considered the 2:1 inclusion complexes of host A or B with guest NB in the gas phase. PM3 calculation indicated that the host-guest interaction energies to form 1:1 complexes are more negative than those to form 2:1 NB/B complexes. Finally, we studied the solvent effect of NB/CD complex, and PM3 results show that the influence of water molecules on the inclusion process is very important. The driving forces for the inclusion process and the geometries of complexes were discussed in detail.     

基于液氮喷雾式食品流态化速冻机的青刀豆速冻实验研究

速冻是用来保存食品的常用方法之一,而在食品的长期保存的过程中人们一直关心的一个问题是如何能够保持食品的外观、完整性和品质。流态化速冻是实现单体快速冻结的最有效方法之一。我所自行研制了液氮喷雾式食品流态化速冻机。本文便是基于此速冻装置的基础之上,对青刀豆进行速冻试验研究,来分析在不同的冻结条件下对物料的冻结时间、干耗和品质的影响。通过冻结青刀豆复温后的电镜照片,来分析速冻过程中冰晶生长对食品品质的影响。     

基于聚苯胺纳米纤维复合膜界面构建电化学细胞传感器及其对癌细胞的识别检测

合成了聚苯胺纳米纤维,直径在50～70 nm之间;基于静电作用构建聚苯胺纳米纤维-纳米金复合膜界面,并在此界面上层层组装修饰叶酸分子,构建叶酸功能化传感界面,基于叶酸分子与癌细胞表面过量表达的叶酸受体之间的特异性识别作用,将此传感界面应用于对癌细胞的识别和捕获。结果表明:叶酸功能化传感界面能够特异性识别和捕获叶酸受体过量表达的癌细胞。采用电化学阻抗技术,以HeLa细胞为模型,应用于对癌细胞的识别和检测,细胞在1.0×104～6.4×106cells/mL浓度范围内与阻抗变化值ΔRct呈良好的线性关系;检出限为2000 cells/mL。本方法简单、快速灵敏、重现性和稳定性良好;制备的传感器可以再生使用。     

Darboux Transformation and Grammian Solutions for Nonisospectral Modified Kadomtsev-Petviashvili Equation with Symbolic Computation

In the present paper, under investigation is a nonisospectral modified Kadomtsev-Petviashvili equation, which is shown to have two Painleve branches through the Painleve analysis. With symbolic computation, two Lax pairs for such an equation are derived by applying the generalized singular manifold method. Furthermore, based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the N-th-iterated potential transformation formula in the form of Grammian is also presented.     

Darboux Transformation and Grammian Solutions for Nonisospectral Modified Kadomtsev-Petviashvili Equation with Symbolic Computation

In the present paper, under investigation is a nonisospectral modified Kadomtsev-Petviashvili equation, which is shown to have two Painlevé branches through the Painlevé analysis. With symbolic computation, two Lax pairs for such an equation are derived by applying the generalized singular manifold method. Furthermore, based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the N-th-iterated potential transformation formula in the form of Grammian is also presented.     

Symbolic-computation study of integrable properties for the (2 + 1)-dimensional Gardner equation with the two-singular manifold method

The singular manifold method from the Painlevé analysiscan be used to investigate many important integrable propertiesfor the non-linear partial differential equations. In this paper,the two-singular manifold method is applied to the (2 + 1)-dimensionalGardner equation with two Painlevé expansion branchesto determine the Hirota bilinear form, Bäcklund transformation,Lax pairs and Darboux transformation. Based on the obtainedLax pairs, the binary Darboux transformation is constructedand the N x N Grammian solution is also derived by performingthe iterative algorithm N times with symbolic computation.     

碳排放气体浓度遥感监测研究

结合国际碳排放气体浓度遥感监测最新研究进展,介绍了碳排放监测方法,以及碳排放气体浓度遥感监测技术(包括热红外、太阳波谱、主动遥感监测技术)。并详细介绍了目前已在使用和未来将采用的监测主要碳排放气体的几种星载传感器,并对这些传感器已获取的监测结果进行了详细分析。