近严格凸与最佳逼近

本文研究近严格凸与最佳逼近的关系．证明了Ｂａｎａｃｈ空间Ｘ是近严格凸的当且仅当Ｘ的每个子空间是紧－半－切比晓夫空间．     

（T＋λI）－1不一定是非扩张映射

设Ｔ是ｍ-增生算子，Ｉ是恒等映射．本文通过一个反例说明（Ｔ＋λＩ）^－1（λ＞０）不一定是非扩张映射．     

Semi‐classical formulation of time‐dependent discrete variable representation method

In this article, we apply a novel time‐dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi‐classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi‐classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Issue Information

An integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.     

The use of Sinc‐collocation method for solving Falkner–Skan boundary‐layer equation

The MHD Falkner–Skan equation arises in the study of laminar boundary layers exhibiting similarity on the semi‐infinite domain. The proposed approach is equipped by the orthogonal Sinc functions that have perfect properties. This method solves the problem on the semi‐infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, the governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by the Sinc‐collocation method. It is shown that the Sinc‐collocation method converges to the solution at an exponential rate. Copyright © 2010 John Wiley & Sons, Ltd.     

A novel synthetic strategy for preparing semi‐aromatic components modified polyamide 6 polymer

In this work, a novel synthetic path for preparing semi‐armotic components modified polyamide 6 was developed by caprolactam as solvent of purified terephthalic acid and 1,6‐hexanediamine. First, the ring opening reaction and poly‐addition of caprolactam were initiated by 1,6‐hexanediamine to generate a prepolymer containing amino groups in both ends, then followed by the poly‐condensation reaction with purified terephthalic acid, a long chain copolymer was produced, which the reaction time was reduced by 4 h compared with conventional hydrolytic ring‐opening polymerization of pure caprolactam. By varying the ratio of terephthalic acid and 1,6‐hexanediamine, a series of copolymers with different number average molecular weight and physical properties were prepared. Analytical results showed that the conversion percentage of caprolactam is significantly increased by the proposed method. Furthermore, this new copolymers exhibited excellent transparence and high decomposition temperature. Besides, the copolymers with average molecular weight ≥15,000 present good mechanical properties, making it a potentially useful application in plastics, textile yarn, and membranes. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 959–967     

Some results about zero‐cycles on abelian and semi‐abelian varieties

In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group.     

Photosensitive cholesteric copolymers with spiropyran-containing side groups II. Kinetic features of the photo- and thermo-chromic processes

Kinetic features of the photo- and thermo-chromic behaviour of new cholesteric triple copolymers with photosensitive spiropyran-containing side groups are considered. The kinetics of the back thermal process at different temperatures have been studied; activation energies for this process for the copolymers with different contents of the dye units have been obtained. The photochromic homopolymer and copolymers with a low content of dye units are shown to possess maximum values of the activation energy.     

Atom Exchange Versus Reconstruction: (GexAs4−x)x− (x=2, 3) as Building Blocks for the Supertetrahedral Zintl Cluster [Au6(Ge3As)(Ge2As2)3]3−

The Zintl anion (Ge₂As₂)^2? represents an isostructural and isoelectronic binary counterpart of yellow arsenic, yet without being studied with the same intensity so far. Upon introducing [(PPh₃)AuMe] into the 1,2‐diaminoethane (en) solution of (Ge₂As₂)^2?, the heterometallic cluster anion [Au₆(Ge₃As)(Ge₂As₂)₃]^3? is obtained as its salt [K(crypt‐222)]₃[Au₆(Ge₃As)(Ge₂As₂)₃]?en?2 tol ( 1 ). The anion represents a rare example of a superpolyhedral Zintl cluster, and it comprises the largest number of Au atoms relative to main group (semi)metal atoms in such clusters. The overall supertetrahedral structure is based on a (non‐bonding) octahedron of six Au atoms that is face‐capped by four (Ge_xAs_4?x)^x? (x=2, 3) units. The Au atoms bind to four main group atoms in a rectangular manner, and this way hold the four units together to form this unprecedented architecture. The presence of one (Ge₃As)^3? unit besides three (Ge₂As₂)^2? units as a consequence of an exchange reaction in solution was verified by detailed quantum chemical (DFT) calculations, which ruled out all other compositions besides [Au₆(Ge₃As)(Ge₂As₂)₃]^3?. Reactions of the heavier homologues (Tt₂Pn₂)^2? (Tt=Sn, Pb; Pn=Sb, Bi) did not yield clusters corresponding to that in 1 , but dimers of ternary nine‐vertex clusters, {[AuTt₅Pn₃]₂}^4? (in 2 – 4 ; Tt/Pn=Sn/Sb, Sn/Bi, Pb/Sb), since the underlying pseudo‐tetrahedral units comprising heavier atoms do not tend to undergo the said exchange reactions as readily as (Ge₂As₂)^2?, according to the DFT calculations.