复杂势场量子弹球中疤痕态的量子化条件

量子疤痕是波函数在经典不稳定周期轨道周围反常凝聚的一种量子或波动现象.人们对疤痕态的量子化条件进行了大量研究,对深入理解半经典量子化起到了一定的促进作用.之前大部分研究工作主要集中在硬墙量子弹球上,即给定边界形状的无穷深量子势阱系统.本文研究具有光滑复杂势场的二维量子弹球系统,考察疤痕态的量子化条件及其重复出现的规律,得到了与硬墙弹球不一样的结果,对理解这类现象是一个有益的补充.这些结果将有助于理解具有无规长程杂质分布的二维电子系统的态密度谱和输运行为.     

Hyperbolic Yamabe problem

In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.     

A Liouville theorem for weighted p−Laplace operator on smooth metric measure spaces

We prove that on a smooth metric measure space with m ?Bakry–Émery curvature bounded from below by ?(m ? 1)K for some constant K ≥0 (i.e., Ric_{f ,m} ≥?(m ? 1)K ), the following degenerate elliptic equation (0.1) has no nonconstant positive solution when p > 1 and constant λ _{f ,p} satisfies Our approach is based on the local Sobolev inequality and the Moser's iterative technique and is different from Cheng‐Yau's method, which was used by Wang‐Zhu in 2012 to derive a same Liouville theorem when 1 < p ≤2, Ric_{f ,m} ≥?(m ? 1)K and the sectional curvature is bounded from below. Copyright © 2016 John Wiley & Sons, Ltd.     

Blow‐up of the smooth solutions to the compressible Navier–Stokes equations

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

平面膜结构拓扑优化的有无复合体方法

将作者对桁架在应力约束下结构拓扑优化的有无复合体模型发展到平面膜结构在应力、位移约束下结构拓扑优化的建模与求解。同时提出了该模型的有效解法,获得了令人满意的数值结果。本文工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有意义的。     

融合伪距和载波相位的DGPS/惯性组合导航

本文利用卡尔曼滤波方法对码伪距测量和载波相位测量进行了最优融合，并得到了融合后的伪距测量误差标准差曲线，用融合后的伪距作为观测量和惯导系统进行组合，可以有效地提高导航精度，避免整周模糊度的确定。本文研究了这种组合导航系统，进行了仿真试验，仿真结果表明该组合系统的精度得到了很大的提高，定位精度在1m以内，是一种高精度的导航系统。     

广义双剪应力准则角隅模型

本文将广义双剪应力准则变换为π平面和静水应力轴的柱坐标方程,然后将其角隅光滑化,得到了新的光滑、外凸的广义双剪应力准则角隅模型,研究结果表明,近年来作为光滑化Mohr-Coulomb理论提出的各种角隅模型,实际上并不是光滑化的Mohr-Coulomb理论,而是光滑化的广义双剪应力理论。     

REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＳｕｐｐｏｓｅＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅａｎｄＴｉｓａｓｅｌｆｍａｐｏｆＥ .Ｓｕｐｐｏｓｅｘ0 ∈Ｅａｎｄｘｎ+1=ｆ(Ｔ ,ｘｎ)ｄｅｆｉｎｅｓａｎｉｔｅｒａｔｉｏｎｐｒｏｃｅｄｕｒｅｗｈｉｃｈｙｉｅｌｄｓａｓｅｑｕｅｎｃｅｏｆｐｏｉｎｔｓ ｘｎ ∞ｎ=0 ｉｎＥ .Ｆｏｒａｎｅｘａｍｐｌｅ ,ｔｈｅｆｕｎｃｔｉｏｎｉｔｅｒａｔｉｏｎｘｎ+1=ｆ(Ｔ ,ｘｎ) =Ｔｘ0 .ＳｕｐｐｏｓｅＦ(Ｔ) =ｘ∈Ｅ :Ｔｘ=ｘ ≠ ａｎｄｔｈａｔ ｘｎ ｃｏｎｖｅｒｇｅｓｓ…