A new numerical model for simulations of wave transformation,breaking and long‐shore currents in complex coastal regions

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary‐conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high‐order upwind weighted essentially non‐oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two‐dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave‐induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Synthesis and characterization of highly conjugated side‐group‐substituted benzo[1,2‐b:4,5‐b′]dithiophene‐based copolymer for use in organic solar cells

A new donor–acceptor (D–A) conjugated copolymer based on benzo[1,2‐b:4,5‐b′]dithiophene (BDT) and thieno[3,4‐c]pyrrole‐4,6‐dione (TPD) was synthesized via a Stille cross‐coupling reaction. A highly conjugated thiophene‐based side group, tris(thienylenevinylene) (TTV), was incorporated into each BDT unit to generate the two‐dimensional D–A copolymer (PBDT‐TTV). An alkoxy‐substituted BDT‐based TPD copolymer (PBDT‐OR) was synthesized using the same polymerization method for comparison. PBDT‐TTV thin films produced two distinct absorption peaks. The shorter wavelength absorption (458 nm) was attributed to the BDT units containing the TTV group, and the longer wavelength band (567–616 nm) was attributed to intramolecular charge transfer between the BDT donor and the TPD acceptor. The highest occupied molecular orbital energy levels of PBDT‐OR and PBDT‐TTV were calculated to be −5.53 and −5.61 eV, respectively. PBDT‐TTV thin films harvested a broad solar spectrum covering the range 300–700 nm. A comparison with the PBDT‐OR films revealed stronger interchain π–π interactions in the PBDT‐TTV films and, thus, a higher hole mobility. A polymer solar cell device prepared using PBDT‐TTV as the active layer was found to exhibit a higher power conversion efficiency than a device prepared using PBDT‐OR under AM 1.5 G (100 mW/cm²) conditions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 653–660     

Cobalt‐based metal coordination polymers with 4,4′‐bipyridinyl groups: highly efficient catalysis for one‐pot synthesis of 3,4‐dihydropyrimidin‐2(1H)‐ones under solvent‐free conditions

Three new metal coordination complexes, namely [Co(BPY)₂(H₂O)₂](BPY)(BS)₂(H₂O)₄ ( 1 ), [Co(BPY)₂(H₂O)₄](ABS)₂(H₂O)₂ ( 2 ) and [Co(BPY)(H₂O)₄](MBS)₂ ( 3 ) (BPY = 4,4′‐bipyridine, BS = phenylsulfonic acid, ABS = p‐aminobenzenesulfonic acid, MBS = p‐methylbenzenesulfonic acid), were obtained under hydrothermal conditions. Complexes 1 , 2 , 3 were structurally characterized using single‐crystal X‐ray diffraction and infrared spectroscopy. All of them display low‐dimensional motifs: complex 1 displays a two‐dimensional structure; and complexes 2 and 3 exhibit a one‐dimensional tape structure. Through strong intermolecular hydrogen bonding interactions and weak packing interactions, all of them further stack to generate a three‐dimensional supramolecular architecture. Catalysts 1 , 2 , 3 were involved in the green synthesis of a variety of 3,4‐dihydropyrimidin‐2(1H)‐ones under solvent‐free conditions through Biginelli reactions. The corresponding catalytic product was obtained in quantitative yields (99%) under eco‐friendly synthesis conditions for the variety of reactions. Catalysts 1 , 2 , 3 exhibit excellent efficiency for the desired product, and their catalytic performance shows the following order: 2  >  1  ≈  3 , which can be ascribed to the hydrophobic interactions of different phenylsulfonate groups. The catalytic performance for the Biginelli reaction is not only dependent on the selected solvents, but also inversely proportional to the polarities of the solvents. Copyright © 2016 John Wiley & Sons, Ltd.     

A Crossed Immunoelectrophoretic Technique for the Detection of the Down's Syndrome Protein

Abstract

The sera of seventy-one women and twenty-six men of various ages were examined by a two dimensional (crossed) immunoelectrophoresis technique which was modified to detect a protein (the Down's Syndrome protein) originally found in the sera of mothers of trisomy 21 children. The sensitivity of the method is reported to be 0.1 to 1.0 mg/L. Modifications included use of a Tris-Tricine buffer, high voltage in the second dimension, and relatively low antibody concentration to allow easy detection of the Down's Syndrome (DS) protein.

Of twenty-eight mothers and twelve fathers of trisomy 21 children, eighteen mothers and five fathers were positive, while of forty-three women and fourteen men having unaffected or no children, only seven women and two men were positive for the DS protein.

Since the presence of the Down's Syndrome protein may indicate a propensity for giving birth to a trisomy 21 affected child, this crossed immunoelectrophoretic technique may be used as a screening procedure for the DS protein and, therefore, as a tool in genetic counseling.     

Efficient separation of high‐purity compounds from Oxytropis falcata using two‐dimensional preparative chromatography

The separation of high‐purity compounds from traditional Tibetan medicines plays an important role in investigating their bioactivity. Nevertheless, it is often quite difficult to isolate compounds with high purity because of the complexity of traditional Tibetan medicines. In this work, an offline two‐dimensional reversed‐phase preparative method was successfully developed for the separation of high‐purity compounds from Oxytropis falcata . Based on the analysis results, an ODS C18 prep column was used for first‐dimensional preparation, and 14.8 g of the crude sample was separated into five fractions with a recovery of 74.6%. Then, an XAqua C18 prep column was used to isolate high‐purity compounds in the second‐dimensional preparation because its separation selectivity is different with the ODS C18 stationary phase. As a result, eight compounds in the crude sample were isolated in more than 98% purity. This is the first report of trans‐cinnamic acid ( 1 ) and trifolirhizin ( 2 ) from Oxytropis falcata . This method has the potential to be an efficient separation method of high‐purity compounds from Oxytropis falcata and it shows great promise for the separation of high‐purity compounds from complex samples.     

黑体辐射公式的量纲分析

量纲分析是研究物理问题的重要方法之一.本文对量纲分析的解题步骤做了梳理归纳,并对于黑体辐射公式进行了量纲分析.     

一类特定的AF-代数

讨论了一类特定的AF-代数,其上的恒等同态可以用一列有限维值域的自同态逐点逼近.给出了这类AF-代数的K-理论刻画,并给出了一个不在这一类中的RFD AF-代数的例子.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.