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  表达
    By using the BFGS correction to approximate the inverse of the Hessian matrix of the Lagrangian function, the subproblem that positive definite quadratic programming with only one linear constraint is formulated, it is always uniquely solveable and the explicit solution is obtained. Thus, the general quadratic programming or the linear equations subproblem which is usually required in the exisiting constrained nonlinear programming methods is avoided and the fast convergence property of the BFGS method is preserved.
    用BFGS法修正光滑逼近问题Lagrange函数Hesse矩阵的逆的近似,导出只含一个线性约束的正定二次规划子问题,其解存在唯一且可显式表达,因而免除了现有约束非线性规划方法中二次规划或线性方程组子问题求解,节省每次迭代计算量,同时保持BFGS拟牛顿法的快速收敛性质。
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    In this Paper We Propose and demonstrate a Constrction Of magic hyper-Cubes Of the nth Order in Euclidean K dimensional Space. It is Proved thate there exists an infinite number Of the magic hgper-cubes in Euclidean K dimensional space for any positive integer K≥2. Finally, We give formulae for the representation Of all magic Cubes Of the Pth Oder, where P is an arbitrary odd integer and P≥7.
    本文提出和证明了一种构造n阶幻k方的方法、证明了对任意正整数k≥2,都存在无穷多个幻K方、最后、给出了所有奇数阶p≥7的幻立方的一组表达公式。
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    Some sufficient conditions, in terms of positive definite matrix, for stability of linear systems are given. Based on the obtained stability results, stability of second order differential systems is considered, the result proposed by [3-5] is generalized.
    给出了利用矩阵广义正定性表达的线性系统稳定性的充分条件,并利用所得条件考虑了二阶微分系统的稳定性问题,推广了[3—5]中的结果。
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    This paper studies some function that is expressed by means of inner product and analysis their convex. The hredominant result that followed: This kind of inner function on vector x in made of A_(n×n) which is a positive semi-definite matrix,vector α and x which are belong to n-dimension Euolidecm space. Then this kind of function is a convex function over n-dimen- sion Eulerian space.
    本文研究用内积表达的某些函数,分析它们的凸性,其主要的结论如下:由一个实的半正定矩阵 An×n 及属于 n 维欧氏空间的向量 a,x 构成[x,Ax]+[a,x]+b(b 为常量)型关于向量 x 的一类内积函数,则此类函数为n 维欧氏空间上的凸函数。
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    Radial symmetry of positive solutions for a semilinear elliptic equation of the plolyharmonic operator involving critical exponent are proved, their explicit expressions are get and they are also the minimizers for the best constant of some Sobolev embedding theorem.
    证明了一类含高阶调和算子的半线性椭圆型方程的正解都是径向对称的,由此得到显式表达.这些正解也是达到某类Sobolev最佳嵌入常数的极小元
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    Positive Solutions of Nonlinear Boundary Value Problems
    非线性边值问题的
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    Positive Solutions for Nonlinear Boundary Value Problems and Random Fixed Points Theorems
    非线性边值问题的解及随机不动点定理
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    Positive Fixed Points of Nonlinear Operators and Distribution of Polynomial Zeros
    非线性算子的不动点及多项式零点的分布
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    Extension of Positive Functionals and Farkas Lemma
    泛函延拓与Farkas引理
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    THE NUMBER OF POSITIVE SOLUTIONS OF HAMMERSTEIN NONLINEAR INTEGRAL EQUATIONS
    Hammerstein型非线性积分方程解的个数
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  positive
Tilting modules for classical groups and howe duality in positive characteristics
      
In this note we present a very simple method of proving that some hyperbolic manifoldsM have finite sheeted covers with positive first Betti number.
      
For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesski? and Sere?kin.
      
Semistable principal bundles-II (positive characteristics)
      
Computing invariants of reductive groups in positive characteristic
      
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