Peak Points for Pseudoconvex Domains: A Survey

This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been published elsewhere.      

Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement

Interactive vortex shedding in the multiply connected domain formed by a pair of circular cylinders is analysed by the FEM–FDM blending technique. The vorticity–streamfunction formulation is used to solve the incompressible Navier–Stokes equations at Re = 100, with the time-dependent wall streamfunctions determined from the pressure constraint condition and the far-field streamfunctions from the integral series formula developed earlier by the authors. The standard Galerkin finite element method is used in the relatively small FEM subdomain and the finite difference method based on the general co-ordinate system in the rest of the flow domain. Symmetric, antisymmetric and asymmetric wake patterns are obtained confirming the earlier experimental findings. The bistable nature of the asymmetric vortex shedding as well as the intermittent drifting from one status to the other between symmetric and antisymmetric wake patterns are reported.     

Abnormal thermal conductivity of [720]‐oriented BaTiO3 single crystal

The 3ω ‐scanning thermal microscopy and piezoresponse force microscopy techniques were combined to characterize the local thermal conductivity (λ) of ferroelastic domains in [720]‐oriented and [001]‐oriented BaTiO₃ single crystal. The [720]‐oriented BaTiO₃ showed a local λ value of 3.39 W/m·K, while it was 5.95 W/m·K for [001]‐oriented BaTiO₃. The underlying mechanism for such drastic thermal conductivity reduction in [720]‐oriented BaTiO₃ is ascribed to a stronger phonon‐scattering effect due to the high strains appearing in [720]‐oriented BaTiO₃ single crystals. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

不对称卟啉共价固载于硅基介孔薄膜材料模拟RS触发器的研究

合成了5-(4-氨基苯基)-10,15,20-三苯基卟啉(ATPP),并成功将其以共价嫁接的形式固载于介孔二氧化硅薄膜。基于卟啉化合物对酸碱的特异性响应,实现了对RS触发器逻辑功能的模拟。卟啉化合物被共价固载于介孔薄膜材料使得该分子逻辑器件具有相对较大的表面积、周期性排布的均一孔道结构以及高的光透过性等介孔薄膜材料的优异性质。这种混合多孔结构不但有利于嫁接于介孔材料中的卟啉与酸碱的更有效相互作用,而且还使酸碱输入能够被更加彻底地清除。     

Local attractors for weakly damped forced KdV equation in thin 2D domains

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓｍｕｃｈｐｒｏｇｒｅｓｓｈａｓｂｅｅｎｍａｄｅｏｎｔｈｅｈｉｇｈｅｒａｎｄｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ (ｓｅｅ ,ｅ .ｇ .[1 ]～ [1 0 ] ) ,ａｎｄｍａｉｎｌｙｂａｓｅｄｏｎｒｅａｃｔｉｏｎ＿ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｓ,Ｋｕｒａｍｏｔｏ＿ＳｉｖａｓｈｉｎｓｋｙｅｑｕａｔｉｏｎｓＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓ ,ｅｔｃ .Ｂｅｃａｕｓｅｏｆｔｈｅｆａｃｔｔｈａｔｔｈｅｐｒｉｎｃｉｐａｌｏｐｅｒ…     

The research of blow-up in 2D weakly damped forced KdV equation on thin domain

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｃｏｍｐｌｅｘｉｔｙｏｆｔｈｅｄｙｎａｍｉｃｓｏｆｔｈｅｈｉｇｈｅｒ＿ｄｉｍｅｎｓｉｏｎａｌｄｉｓｓｉｐａｔｉｖｅｓｙｓｔｅｍｓｏｌｉｔａｒｙｗａｖｅ ,ｔｈｅｒｅｉｓｍｕｃｈｄｉｆｆｉｃｕｌｔｙｉｎｓｔｕｄｙｉｎｇｔｈｅｓｅｐｒｏｂｌｅｍｓ.Ｔｈｅｐａｐｅｒｓ [1 ]～ [3]ｍｅｎｔｉｏｎｅｄｔｈｅｔｗｏ＿ｄｉｍｅｎｓｉｏｎａｌＫｄＶｅｑｕａｔｉｏｎｓｄｒｉｖｅｎｂｙＬａｘａｎｄ [3]ｏｂｔａｉｎｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｔｏｔｈｅｅｑｕａｔｉｏｎｓ…     

KdV-Burgers方程的级数解

给出ＫｄＶ－Ｂｕｒｇｅｒｓ方程的有界行波解的精确级数解,采用Ａｄｏｍｉａｎ算子分解法分别求行二个区域ζ〈０和ζ〉０的级数解,然后利用对接连续条件构成整体级数解。所得级数解能精确满足对接连续条件,并由此得到确定级数的系数递推公式,无需解非红性高阶代数方程组。与某些精确解及其它方法比较,计算简捷具在对接点处是收剑的。对某些非线性波动现象的研究,可作为计算和分析的数学依据。     

分组全连接的近红外光谱定量分析网络

全连接网络作为深度学习中的一种典型结构,几乎在所有神经网络模型中均有出现。在近红外光谱定量分析中,光谱数据样本数量较少,但每个样本的维度高。导致了两个问题：将光谱直接输入网络,网络的参数量会十分庞大,训练模型需要更多的样本,否则模型容易进入过拟合状态;在输入网络前对光谱进行降维,虽解决了网络参数量过大的问题,但会丢失一部分信息,无法充分发挥网络的学习能力。针对近红外光谱的特性,提出了一种分组全连接的近红外光谱定量分析网络GFCN。该网络在传统的两层全连接网络的基础上,用若干个小的全连接层替代第一个全连接层,克服了直接输入光谱导致网络参数量过大的缺点。采用Tecator和IDRC2018数据集对该方法进行测试,同时与全连接网络FCN和偏最小二乘PLS两种方法进行对比。结果显示：在两个数据集上,GFCN预测效果均优于FCN和PLS。在只有少量样本参与建模的情况下,GFCN依然能够保持较高的预测效果。表明,GFCN可以用于近红外光谱的定量分析,并且适应样本较少的场景,具有重要的研究价值和广泛的应用场景。     

有界凸圆型域上的准凸映照

本文研究星形映照的一类子族——有界凸圆型城上的准凸映照,并讨论了它与星形映照及凸映照的关系,建立其与凸映照同形的增长定理和掩盖定理．     

COMPOSITE LEGENDRE-LAGUERRE APPROXIMATION IN UNBOUNDED DOMAINS

1. IntroductionMany problems in science aam engineering are set in unbounded domains. There are severalways for their numerical simulatiolls. We may restrict calculations to some bounded domainswith certain artificial boundary conditions. But they induce errors. In particular, they ductshe wave Propagations in revolutionary problems. In opposite, if we use'spectral methods assorted with orthogonal systems of polynomials in Unbounded domains, then we could avoid tabstrouble, e.g., see Mad'ay,…