具有对流项的一类非线性椭圆型问题爆炸解的精确渐近行为

设Ω是RN中的有界光滑区域.应用Karamata正规变化理论和摄动方法.构造比较函数.得到了问题△u+|▽u|q=b(x)g(u),x∈Ω,u|(а)Ω=+∞的解在边界附近的精确渐近行为和解的唯一性,其中g在无穷远处以指数1+ρ(ρ＞0)正规变化.b在Ω内非负非平凡并且允许在边界为0.     

具有奇异耗散项的非线性双曲方程的混合问题

本文考虑具有奇异耗散项的非线性方程的混合问题。 Ω(?R~n)是具有光滑边界?Ω的有界开集。H~s(Ω),(H_0~s(Ω))表示Ω上的Sobolev     

拟线性椭圆型问题有限元近似解的迭代加速分析

一、问题的提出 我们考察二阶拟线性椭圆型第一边值问题: -?(α(x,u)?u)=f(x,u),在Ω内, u(x)=0,在?Ω上,其中Ω是R~n(n=2,3)中有界开区域,?Ω是Ω的光滑边界。若u(x),α(x,u(x))和f(x,u(x))有足够正规性,则问题(1)的等价弱形式方程是:对于u∈H_0~1(Ω), (α(x,u)?u,?v)=(f(x,u),v),?v∈H_0~1(Ω)。 (2)这里假设α(x,u)在Ω×R中为正的且有界,内积     

一个非线性抛物型方程正解的性质

考虑一个具有非线性吸收项和非线性边界流的拟线性抛物型方程正解的性质．得到了解整体存在的充要条件．此外，借助于Chasseigne和Vázquez的结论以及比较原理，导出了爆破解只可能在区域的边界¶Ω上发生爆破．对于有界的Lipschitz型区域Ω, 还估计了在a=0时爆破解的爆破速率.     

位移障碍下一个四阶变分不等式的某些强间断非协调元逼近

考虑[1]中四阶变分不等式问题:其中为非空闭凸集,而障碍函数φ∈C~2(Ω),φ<0,在?Ω上.关于解的性质,有下述结果:当Ω?R~2是具有光滑边界?Ω的有界凸区域且f∈L~2(Ω)时,问题(1)存在唯     

零理想边界的素端上某类椭圆型方程的非负解

考虑具有零理想边界的非紧镶边Riemann曲面Ω=Ω∪ aΩ及其上的Dirichlet积分有限的非负局部Holder连续的二重共变量P.用F表示方程△u=Pu在aΩ取极限值0的非负连续解全体.本文讨论拟Picard原理成立的充要条件并证明若Ω的每一理想边界点都有端邻域满足广义Heins条件,则Martin函数全体所成之集是F中的极小正解全体所支撑的子半线性空间P的一个Hamel基,而且F可表示为与P相关的直和形式.     

基于拟法锥条件的非凸非线性规划问题的同伦内点法

1 引言 考虑如下的非线性规划问题: min f(x) (1) 8.t.gi(x)≤0,i=1,…,m,其中xR~n,我们总假定f,gi是二次连续可微的。 称Ω={xR~n|gi(x)≤0,i=1,…,m}为(1)的行域;Ω~0={xR~n|gi(x)<0,i=1,…,m}为(1)的严格可行域;Ω=Ω\Ω~0为Ω的边界。 此外,记     

零理想边界的素端上某类椭圆型方程的非负解

考虑具有零理想边界的非紧镶边Ｒｉｅｍａｎｎ曲面Ω＝Ω∪　Ω及其上的Ｄｉｒｉｃｈｌｅｔ积分有限的非负局部Ｈｏｌｄｅｒ连续的二重共变量Ｐ．用Ｆ表示方程上Δｕ＝Ｐｕ在 Ω取极限值０的非负连续解全体．本文讨论拟Ｐｉｃａｒｄ原理成立的充要条件并证明：若Ω的每一理想边界点都有端邻域满足广义Ｈｅｉｎｓ条件,则Ｍａｒｔｉｎ函数全体所成之集是Ｆ中的极小正解全体所支撑的子半线性空间Ｐ的一个Ｈａｍｅｌ基,而且Ｆ可表示为与Ｐ相关的直和形式．     

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．     

R~n中具有非负曲率的封闭超曲面的充要条件

设Ω为R~n中有界单连通开集.其边界Ω是无限可微的封闭超曲面.在[7]中建立了同Ω的平均曲率有关的积分等式.本文给出Ω具有非负平均曲率的充要条件.给出Ω具有非负Gauss曲率的充要条件.引用[8]的一个结果,给出Ω具有各阶非负平均曲率的充要条件.     

Determining a Rotation of a Tetrahedron from a Projection

The following problem, arising from medical imaging, is addressed: Suppose that T is a known tetrahedron in ?³ with centroid at the origin. Also known is the orthogonal projection U of the vertices of the image ?T of T under an unknown rotation ? about the origin. Under what circumstances can ? be determined from T and U?     

Symmetry-based solution of a model for a combination of a risky investment and a riskless investment

Benth and Karlsen [F.E. Benth, K.H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stoch. Anal. Appl. 23 (2005) 687-704] treated a problem of the optimisation of the selection of a portfolio based upon the Schwartz mean-reversion model. The resulting Hamilton-Jacobi-Bellman equation in 1+2 dimensions is quite nonlinear. The solution obtained by Benth and Karlsen was very ingenious. We provide a solution of the problem based on the application of the Lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions.     

On a mapping of a projective space into a sphere

We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.     

Folding a surface to a polygon

A concept of folding for compact connected surfaces, involving the partition of the surface into combinatorially identical n-sided topological polygons, is defined. The existence of such foldings for given n and given surfaces is explored, with definitive results for the sphere and the torus. We obtain necessary conditions for the existence of such foldings in all other cases.Supported by Kuwait University Grant SM 043.     

Calculating a function of a matrix with a real spectrum

Let T be a square matrix with a real spectrum, and let f be an analytic function. The problem of the approximate calculation of f(T) is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that T is triangular and its diagonal entries t_ii are arranged in increasing order. To avoid calculations using the differences t_ii ? t_jj with close (including equal) t_ii and t_jj, it is proposed to represent T in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the f(T) entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform some scalar operations (such as the building of interpolating polynomials) with an enlarged number of significant decimal digits.

     

Approaching a vertex in a shrinking domain under a nonlinear flow

We consider here the homogeneous Dirichlet problem for the equation , in a noncylindrical domain in space-time given by . By means of matched asymptotic expansion techniques we describe the asymptotics of the maximal solution approaching the vertex x=0, t=T, in the three different cases p>1/2, p=1/2(vertex regular), p<1/2 (vertex irregular).