Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

MOLECULAR STRUCTURE OF HETEROCYCLES: 17O NMR CHEMICAL SHIFTS: TORSION ANGLE RELATIONSHIPS IN 3-ALKYL SUBSTITUTED 4,5-DIHYDROISOXAZOLES AND ISOXAZOLES†

A quantitative relationship between the ¹⁷O substituent chemical shifts (SCS) of γ-alkyl substituents and the torsion angles calculated by the AM1 method is reported. A series of 3-alkyl substituted 5-trichloromethyl-5-hydroxy-4,5-dihydroisoxazoles and 5-trichloromethyl isoxazoles [where 3-alkyl substituents are Me, Et, n-Pr, iso-Bu, BrCH₂, iso-Pr, Br₂CH and tert-Bu] as model compounds were used.

     

New Exact Solution to (3+1)-Dimensional Burgers Equation

In this Letter, using Backlund transformation and the new variable separation approach, we find a new general solution to the (3 1)-dimensional Burgers equation. The form of the universal formula obtained from many (2 1)-dimensional systems is extended. Abundant localized coherent structures can be found by seclecting corresponding functions appropriately.     

Interaction between two folded solitary waves for a modified Broer--Kaup system

By means of a Painlevé-Baicklund transformation and a multi-linear separation-of-variable approach, abundant localized coherent excitations of a modified Broer-Kaup system are derived. There appear possible phase shifts for the interactions of the （2＋1）-dimensional novel localized structures, which are discussed in this paper.     

Theoretical Study of Formamide Tautomers—A Discussion of Enol-Keto Isomerizations and Their Corresponding Energies

In order to gain insight into the formamide molecule, seven tautomers and twelve transition states are found after being modeled by the density function theory of Becke's three-parameter hybride (B3LYP) type and ab initio Möller–Plesset second-order perturbation (MP2)-type methods. The isomerization phenomena between enol-keto tautomers and transition states via internal rotation or the proton transfer process are surveyed. A localized analysis is also introduced to ascertain the bond character caused by the delocalization of electrons, which will force the formamide tautomers to become planar. The trans effect in the molecule increases molecular stability.     

Reaction of dichloromaleic anhydride with 1,8-diaminonaphthalene: Synthesis and X-ray diffraction structure of 8,9-dichloropyrrolo[1,2-a]perimidin-10-one

The reaction of dichloromaleic anhydride with 1,8-diaminonaphthalene in refluxing toluene or 1,2-dichloroethane produces the new heterocyclic compound 8,9-dichloropyrrolo[1,2-a]perimidin-10-one in low yields. 8,9-Dichloropyrrolo[1,2-a]perimidin-10-one has been isolated by column chromatography and characterized in solution by IR, ¹H NMR, and UV/vis spectroscopies. The solid-state structure was unequivocally established by single-crystal X-ray diffraction analysis. 8,9-Dichloropyrrolo[1,2-a]perimidin-10-one crystallizes in the monoclinic space group P2 ₁/c, a = 7.475(1)Å, b = 10.650(2)Å, c = 14.468(2)Å, = 94.478(2)°, V = 1148.3(3) ų, Z = 4, and d _calc = 1.672 Mg/m³; R = 0.0289, R _w = 0.0762 for 1644 reflections with I > 2(I). The nature of the HOMO and LUMO in 8,9-dichloropyrrolo[1,2-a]perimidin-10-one has been determined by extended Hückel molecular orbital calculations, and these data are discussed relative to the cyclic voltammetric data obtained at a platinum electrode.     

(2+1)维非对称 Nizhnik-Novikov-Veselov系统的新映射解及其局域结构

映射法是一种非常经典、有效和成熟的求解非线性演化方程的方法，其最大的特点是可以有多种不同形式的设解，使得最终求得的解丰富多彩. 利用改进的 Riccati 方程映射法和变量分离法，得到了(2+1)维非对称 Nizhnik-Novikov-Veselov 系统的新显式精确解.根据得到的孤波解，构造出该系统的峰孤子和分形孤子等局域结构，研究了两个孤立波的“追碰”现象. 关键词： 改进的映射法 (2+1)维非对称 Nizhnik-Novikov-Veselov 系统 局域结构 “追碰”现象     

半壳结构金纳米膜的局域表面等离子体共振效应

采用纳米模版印刷术和化学自组装技术制备了半壳结构的金粒子膜.利用场发射扫描电子显微镜和光谱仪等测试手段对样品的结构和光学性质进行了分析.研究发现，该结构的金膜所具有独特的局域表面等离子体共振效应取决于样品的粒子大小、间距等微观结构，且其峰值吸收波长对其周围环境介质的介电常数变化十分敏感.实验结果表明，粒子排列均匀的亚单层膜结构是控制光学性质稳定的关键. 关键词： 局域表面等离子体共振 半壳结构 纳米模版印刷术     

Phosphorous disulfide and its ions in the electronic ground state: a gas phase theoretical study

Ab initio molecular orbital theory and density functional theory calculations were performed on the electronic ground states of the open-shell PS₂ molecule and its singly charged ions. A comparison of the optimized molecular structures indicates as the stepwise one-electron reduction of the PS₂⁺ ion, to yield PS₂ and PS₂⁻, provokes a symmetric elongation of both PS bonds along with a bending of its linear equilibrium geometry. The ionization potential (IP), adiabatic electron affinity (EA_ad), and atomization energy (AE) of the open-shell PS₂ molecule were calculated at different levels of theory. The following values were obtained at the more realistic UMP4SDTQ/6-311+G(3df)//UHF/6-311+G(3df) level of theory: IP=8.32 eV, EA_ad=3.03 eV and AE=12.40 eV. At the same level of theory, the calculated vertical detachment energy (VDE) of the PS₂⁻ anion is 3.22 eV. The donor–acceptor complexes formed in the gas-phase upon interaction of either one or two ammonia molecules with PS₂⁺ were also investigated. The calculated gas-phase binding energies indicate that the formation of the bis-adduct is favored over that of the mono-adduct by a binding energy gain of about 20 kcal/mol.