For a semi-bounded operator with defect index (1, 1 ), we solve von Neumann s problem in a explicit way based on Krein s formula and rank one perturbation theory of a positive selfadjoint operator, only assuming the Friedrichs extension is obtained.
对亏指数(1，1)的下半有界闭对称算子的von Neumann问题，作者利用实参数形式的Krein公式和自伴正算子的秩1扰动理论给出了一个仅依赖于Friedrichs延拓的显式解答，并且证明了对每个这类算子，在它的全体自伴延拓集合到单位圆周S~1的一个自然的双射下，它的von Neumann问题解集的像一定处于1/4单位圆周内。
The semibounded operators in Menger PN spaces;
Menger PN空间上的半有界算子(英文)
On von Neumann s Problem of a Semi-bounded Operator with Defect Index (1, 1);
具亏指数（1，1）的下半有界对称算子的von Neumann问题
Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems;
拟线性双曲组在半有界初始轴上的柯西问题
Probabilistic Formula of Strongly Continuous Equi-bounded C-Semigroups;
强连续等度有界C半群的概率型公式
Invariant and Admissible Subspaces of the exponentially bouned C-Somigroups;
指数有界C-半群的不变和容许子空间
Other signs include uneven borders or one half different from the other.
黑素瘤的)其它征兆包括不均匀界线，即一半有别于另一半。
Relatively Bounded Perturbations of Eventually Differentiable and Eventually Norm-continuous Semigroups;
最终可微半群与最终范数连续半群的相对有界扰动
Using matrix theory, we present a sharp upper bound on the spectral radius of digraphs and strongly connected diagraphs.
利用矩阵理论，给出了简单有向图的谱半径可达上界和强连通有向图的谱半径上界。
About half of the world's known supply of copper ore is already in use.
全世界已知的铜矿储量，大约有一半已在使用了。
Miss World Contest has a history of more than50 years.
世界小姐评选活动已经有半个世纪的悠久历史。
Bounded Positive Entire Solutions of Semilinear Elliptic Partial Differential Equations;
半线性椭圆型偏微分方程的全局有界正解
The Positive Cone and Semi-order Yielded by the Bounded Linear Functional in Banach Spaces;
Banach空间上非零有界线性泛函导出的正锥与半序
The Existence of Positive Solutions of Semilinear Elliptic Systems;
有界洞型区域内一类半线性椭圆方程组的正解
Two Note on Generates Opertaor of the Exponentially Bounded C-Semigroup;
指数有界C-半群的生成算子的两个结果
Positive solutions for semilinear elliptic equations with critical Sobolev exponents
具有Sobolev临界指数的半线性椭圆方程的正解(英文)
The developed nations, with about onefourth of the world's population, possess almost half the arable land of the earth.
发达国家人口占世界的四分之一，拥有耕地将近世界之半。
There is every probability of..
多半有，多半会…。
Mustering half of the earth's population and sixty percent of its natural resources.
亚洲有占世界一半的人口和百分之六十的自然资源。
Africa contains 6.3 million refugees, half of the world's total.
非洲地区存在的难民有630万，占世界难民总数的一半。