Cn中不同域的复合算子

令Ω1与Ω2与C^n中的两个有界齐性域，假设φ：1Ω→Ω2是一个全纯映射。在本中，我们研究相应的复合算子Cφ：β（Ω2）→β（Ω1）的有界性和紧性，特别地，我们讨论取B^n和U^n的情形。     

凸角域上的椭圆Neumann问题的H^2正则性

对凸角域上的Neumann问题△u au＝finΩ，эu/эn＝0onэΩ，这里α≥0是Ω上的有界可测函数且不恒为0，我们证明了：若f∈L^2（Ω)，则解u∈H^2(Ω)，且有正则性估计‖u‖2.0≤C‖f‖0.Ω。     

多面体k级中线的几个性质

全文约定：用Ω表示三维欧氏空间的多面体，其顶点集为{A1，A2，…，An}，重心为G，令{A1，A2，…，An}={A’1,A’2，…，A’n}，由Ω的任意k个顶点A’1，A’2，…，A’k组成的多面体为Ωjk，其重心为Gjk，由Ω的剩余n-k个顶点A’k＋1，A＇k＋2，…，A’n所组成的多面体为Ωjk，其重心为Gjk（j=1，2，…，Cn^k）．     

线性变换对带约束奇异线性模型的条件G—M估计的影响

考虑带约束奇异线性模型Y=Xβ＋ε，Lβ＝0，E（ε）＝0，cov（ε）＝σ~2V，其中V为非负定矩阵，X为任意秩．文章研究了观察向量Y的线性变换对回归系数条件可估函数Sβ的G－M估计的影响，并将条件可估子空间μ（X'L'）划分成Ω＋Ω_＋Ω_2.当μ（S'）Ω时，Sβ的条件G-M估计在模型变化后其优良性不变；当μ（S'）Ω_1时，模型变化后Sβ仍可估，但Sβ的条件G－M估计的方差要变大；当μ（S'）Ω_2时，Sβ不可估．     

二维Banach空间到L^1（Ω,μ）内的等距逼近

该文证明了B（E2，L1（Ω，μ））中的等距逼近问题，其中E2是二维Banach空间，（Ω，μ）是无原子的测度空间．     

关于Brocard角的yff的猜想

如果a_1、a_2、a_3是△A_1A_2A_3的三个内角,那么在△A_1A_2A_3内部存在一点Ω,使得 ω=∠ΩA_2A_3=∠ΩA_3A_1=∠ΩA_1A_2。 则称点Ω为这个三角形的一个Brocard     

基于半平面上自然边界归化的无界区域上的Schwarz交替法及其离散化

1．引言由于并行技术的不断发展，人们越来越重视区域分解法的研究．对于闭曲线o外部的无界区域Ω上的椭圆边值问题，近年来基于自然边界归化理论[2,5,6,10]，提出了无界区域上的一类重叠型和不重叠型区域分解算法［11，12。13］，即将无界区域Ω分解为一个很小的有界区域Ω1和一个圆外无界区域Ω2，在Ω1和Ω2上分别有限元法和自然边界元法交替求解．其中，对于连续情形的重叠型区域分解法可利用投影理论得到意义下的几何收敛性［11］．对于连续情形和离散情形的重叠型区域分解法还可利用极值原理证明在最大模意义下的几何收敛性113］本文…     

非局部半线性椭圆型方程奇摄动问题

今考虑如下奇摄动非局部半线性椭圆型方程边值问题：ε为正的小参数，x＝（x1，x2，…，xn）∈Ω，Ω为n维欧氏空间的有界域，Ω为Ω的光滑边界，L＝为Ω上的一致椭圆型算子，为外法向导数．假设：（H1）L的系数及f,g，Ki关于其变元在相应区域内为充分光滑的函数；（H2）fy（x,     

具临界Sobolev-Hardy指数的半线性椭圆方程的非平凡解

本文研究了如下问题：-div（｜x｜β△u）=｜x｜^a｜u｜^2（α,β）-2u＋λ｜x｜σ｜u｜^q-2,x∈Ω,u=0,x∈δΩ,这里Ω∪→R^N是有界光滑区域且0∈Ω，2（α，β）=2（N＋α）/N＋β-2，运用Sobolev-Hardy不等式和山路几何，证明了在一定的条件下方程至少存在一个非平凡解。     

多复变数完全拟凸映射的分解定理

设Ω1(∪) Cn1,Ω2(∪)Cn2为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))′为Ω1×Ω2上的正规化全纯映射.本文证明f为Ω1×Ω2上的正规化双全纯完全拟凸映射当且仅当f(z,w)=(Φ1(z),Φ2(W))′,其中ΦjΩj→Cnj是Ωj(j=1,2)上的正规化双全纯完全拟凸映射.     

非饱和土壤水流问题的CN有限元格式

首先给出二维非饱和土壤水流问题基于Crank-Nicolson(CN)方法的具有时间二阶精度的半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出误差估计,最后用数值例子说明全离散化CN有限元格式的优越性.这种方法可以绕开关于空间变量的半离散化格式的讨论,提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.     

Bilinear modeling solution approach for fixed charge network flow problems

We present a continuous, bilinear formulation for the fixed charge network flow problem. This formulation is used to derive an exact algorithm for the fixed charge network flow problem converging in a finite number of steps. Some preliminary computational experiments are reported to show the performance of the algorithm.     

非饱和土壤水流方程的CN广义差分法

首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便.     

非饱和土壤水流问题基于POD 方法的降阶有限体积元格式及外推算法实现

利用特征投影分解(proper orthogonal decomposition, 简记为POD) 方法对非饱和土壤水流问题的经典有限体积元格式做降阶处理, 建立一种具有足够高精度维数较低的降阶有限体积元格式, 并给出这种降阶有限体积元解的误差估计和外推算法的实现, 最后用数值例子说明数值结果与理论结果是相吻合的. 进一步表明了基于POD 方法的降阶有限体积元格式对求解非饱和土壤水流问题数值解是可靠和有效的.     

Existence of solutions to various rock types odel model of two-phase flow in porous media

We study the flow of two immiscible and incompressible fluids through a porous media c,onsisting of different rock types: capillary pressure and relative permeablities curves are different in each type of porous media. This process can be formulated as a coupled system of partial differential equations which includes an elliptic pressurevelocity equation and a nonlinear degenerated parabolic saturation equation. Moreover the transmission conditions are nonlinear and the saturation is discontinuous at interfaces separating different media. A change of unknown leads to a new formulation of this problem. We derive a weak form for this new problem, which is a combination of a mixed formulation for the elliptic pressure-velocity equation and a standard variational formulation for the new parabolic equation. Under some realistic assumptions, we prove the existence of weak solutions to the implicit system given by time discretization.     

OPERATOR－SPLITTING METHODS FOR THE SIMULATION OF BINGHAM VISCO－PLASTIC FLOW

IoductlonRom the early seventies to tUs Unlmely death In 2001,Jacqll6sLoms     

Routing of Railway Carriages

In the context of organizing timetables for railway companies the following railway carriage routing problem occurs. Given a timetable containing rail links with departure and destination times/stations and the composition of the trains, find a routing of railway carriages such that the required carriages are always available when a train departs. The problem is formulated as an integer multi-commodity network flow problem with nonlinear objective function. We will present a local search approach for this NP-hard problem. The approach uses structural properties of the integer multi-commodity network flow formulation of the problem. Computational results for a real world instance are given.     

Vortex-lines motion for the Ginzburg-Landau equation with impurity

In this paper,we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity.We prove that,asymptotically,the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.     

Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the presence of a potential field. The non-locality is due to the appearance of the ‘fractional Laplacian’ in the corresponding PDE, in place of the classical Laplacian which distinguishes the case of regular diffusion. We prove existence of weak solutions by combining a splitting technique together with a Wasserstein gradient flow formulation. An explicit iterative construction is given, which we prove weakly converges to a weak solution of this PDE.     

Effects of variable viscosity on pulsatile flow of blood in a tapered stenotic flexible artery

The objective of the present study is to investigate the effects of variable viscosity on incompressible laminar pulsatile flow of blood through an overlapping doubly constricted tapered artery. To mimic the realistic situation, wall of the artery is taken to be flexible, and physiologically relevant pulsatile flow is introduced. The governing equations of blood flow are made dimensionless. A coordinate transformation is used to make the overlapping doubly constricted wall geometry of tube to a straight tube. Taking advantage of the Stream function–Vorticity formulation, the system of partial differential equations is then solved numerically by finite difference approximations. Effects of Reynolds number, Strouhal number, degree of contraction, tapering angle, and viscosity parameters are presented graphically and analyzed. The results show that formation of stenosis and tapering disturb the flow field significantly, and degree of stenosis is more important in influencing blood flow compared with tapering.