Scattering of a Gaussian beam by an anisotropically coated circular cylinder

A solution to the problem of Gaussian beam scattering by an anisotropically coated circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with a Tayor’s series. The transmitted field in the anisotropically coated region is expressed as a infinite summation of eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting the similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.     

Bilinear formalism,lump solution,lumpoff and instanton/rogue wave solution of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Nonlinear Dynamics - We consider the simplified (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. We use the binary Bell polynomial theory to construct a bilinear form of the...     

Organocatalytic and Scalable Syntheses of Unsymmetrical 1,2,4,5‐Tetrazines by Thiol‐Containing Promotors

Despite the growing application of tetrazine bioorthogonal chemistry, it is still challenging to access tetrazines conveniently from easily available materials. Described here is the de novo formation of tetrazine from nitriles and hydrazine hydrate using a broad array of thiol‐containing catalysts, including peptides. Using this facile methodology, the syntheses of 14 unsymmetric tetrazines, containing a range of reactive functional groups, on the gram scale were achieved with satisfactory yields. Using tetrazine methylphosphonate as a building block, a highly efficient Horner–Wadsworth–Emmons reaction was developed for further derivatization under mild reaction conditions. Tetrazine probes with diverse functions can be scalably produced in yields of 87–93 %. This methodology may facilitate the widespread application of tetrazine bioorthogonal chemistry.     

Proof of Sun’s conjectures on super congruences and the divisibility of certain binomial sums

The Ramanujan Journal - In this paper, we study the vanishing properties of Fourier coefficients of rth powers of the Dedekind eta function. We give a certain type of classification of this...     

高比能高功率全石墨烯锂离子电容器

石墨烯由于拥有超高比表面积和超高电导率而被作为电化学电容器材料广泛研究.本文采用树脂为碳源，通过一种方便快捷的树脂交换法制备一种具有高比表面积的多级孔三维石墨烯（3DG）.经过此种方法的催化、造孔、热处理等主要工艺步骤后，可显著增加石墨烯材料的小、介孔数量，从而提高材料的电化学性能.通过BET测试表明，3DG的比表面积可达2400 m²/g，孔体积达到2.0 cm³/g.以3DG作为正负极材料制备高比能量高功率型锂离子电容器（3DG-LIC），可使3DG-LIC的工作电压从传统超级电容器的2.5 V扩展到4.0 V，能量密度也从20 Wh/kg提高到105 Wh/kg.另外，相同的化学和微观结构能很好地平衡正负极的容量及速率，使高比能量高功率的3DG-LIC具有更宽阔的应用领域.     

Effects of monomer structure on the morphology of polymer networks and the electro-optical properties of polymer-dispersed liquid crystal films

Polymer-dispersed liquid crystal (PDLC) films were prepared by photochemical polymerisation with a series of (meth)acrylate monomers. The effects of monomer structure on the morphology of polymer networks in the PDLC films were studied. The acrylate monomers without sidegroup chain formed uniform polymer networks. The methacrylate monomers with methyl as their sidegroup chains formed lace-like networks. The size of the LC droplets increased with increasing the length of the flexible chain of both methacrylate and acrylate monomers. Meanwhile, the effects of the morphology of the polymer network on the electro-optical properties of PDLC films were also investigated.     

Strategic measures in optimal control problems for stochastic sequences

Controlled discrete–time stochastic processes axe studied using the convex–analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.