Minimal ranks of some quaternion matrix expressions with applications

Suppose that p(X, Y) = A − BX − X^(∗)B^(∗) − CYC^(∗) and q(X, Y) = A − BX + X^(∗)B^(∗) − CYC^(∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y^(∗), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y = −Y^(∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed.     

Riemann problems for three-dimensional combustion models

We investigate Chapman-Jouguet models in three-dimensional space by means of generalized char- acteristic analysis. The interaction of detonation, shock waves and contact discontinuity is discussed intensively in this paper. If contact discontinuity appears, the structure of global solutions becomes complex. We deal with this problem when strength of detonation is small.     

Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

Stabilization of 4-manifolds

The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.     

常微分方程通解、特解、所有解的区别与联系

通过具体实例分析、讨论了高等数学中常微分方程的通解、特解和微分方程的所有解之间的区别与联系,并对高等数学教材中二阶线性微分方程的降阶法与二阶常系数非齐次线性微分方程特解求解过程中的作法进行了说明.     

STOCHASTIC SIMPLIFIED BARDINA TURBULENT MODEL： EXISTENCE OF WEAK SOLUTION

In this paper, we consider the stochastic version of the 3D Bardina model arising from the turbulent flows of fluids. We obtain the existence of probabilistie weak solution for the model with the non-Lipschitz condition.     

一类矩阵方程的Hermitian R-对称定秩解

本文研究了矩阵方程AX = B 的Hermitian R-对称最大秩和最小秩解问题. 利用矩阵秩的方法, 获得了矩阵方程AX = B有最大秩和最小秩解的充分必要条件以及解的表达式, 同时对于最小秩解的解集合, 得到了最佳逼近解.     

两大部类扩大再生产的充分必要条件与求解

两大部类扩大再生产的充分必要条件也就是马克思扩大再生产公式有解的充分必要条件.直到目前,由于还没有严谨地提出对于扩大再生产公式的一般求解方法,因而也没有严格地确定扩大再生产的充分必要条件.本文基于已经有研究获得的扩大再生产的一个必要条件,建立一种求解扩大再生产问题的一般方法,从而证明这个必要条件能够成为充分条件,由此确定它是充分必要条件.进而使用变量替换法,给出了通过直接求解两个部类的剩余价值积累率而求解扩大再生产问题的另一种方法.最后引用《资本论》中的两个实例,对所给出的两种求解扩大再生产问题的一般方法做了计算验证.     

One Nonparabolic End Theorem on Kahler Manifolds

In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.     

四阶椭圆方程的弱解(英文)

本文研究了一个四阶椭圆方程解的存在性问题.利用山路定理和喷泉定理,结合变分方法,获得了该问题弱解的几个存在性定理,推广了现有的一些结果.