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    and further, it implicates a significant improvement of the Lebesgue-Rademacher theorem: every Lipschitz mapping between two finitely dimensional spaces is C1 off a null set of first category.
    同时也是Lebesgue-Rademacher定理的一个本质的改进:有限维空间之间的Lipschitz映射在某个测度为零的第一类型集外是C~1映射,即有连续的微分映射。
    In addition, in the proof of the algebraic stability of waves with critical speeds, somekey properties of the Evans function D(λ) are obtained, in particular, D(0) = 0, but D_λ(0) ≠ 0, which is useful for semigroup estimates in the polynomially weighted spaces.
    在研究具有临界波速的行波解的稳定性时,我们验证Evans函数D(λ)具有某些重要性质,其在线性化算子的本质谱外不为零,尤其在原点处:D(0)=0,但D_λ(0)≠0,这对进行适当的空间分解及半群估计是非常有用的。
    The method to estimate the number n\ is proving that the two sides of a q-hypergeometric identity satisfy the same recurrence, and giving both an estimate of the order J of the recurrence and an estimate of the integer m_1 such that the leading coefficient of the recurrence is not identically zero, when n ≥ m_1. Therefore we have n_1=max{J,m_1}.
    估计n_1的方法是证明q超几何恒等式两边满足相同的迭代关系,并且给出迭代关系阶数J和m_1的估计,m_1满足当n≥m_1时,迭代关系的首项系数恒不为零,则我们有n_1=max{J,m_1}。
    Then we present three methods to estimate the number n_1.Firstly, we prove a proposition: the leading coefficient (regarded as a polynomial in q~n, q~(1/2)) of the recurrence is not equal to zero for all n ≥ [m/2] + 1, where m is the degree in q~(1/2) of the leading coefficient.
    首先,我们证明了一个命题:迭代关系的首项系数(关于q~n,q~(1/2)的多项式)对所有的n≥1[m/2]+1均不为零,其中m为首项系数中q~(1/2)的次数。
    If the sum of the vectors in each equivalence class is the 0-vector, we call P a special polygon.
    这种等价关系将P的边划分为有限个等价类。 若等价类中的边的向量和为零向量,则称多边形P为特殊多边形。
    i. e for an algebra of minimal representation-infinite type with preprojective component, it is simply connected if and only if the vanishing of 1 Hochschild cohomology group;
    在第二章中我们得到了极小无限表示型代数单连通性的一些结论:对于具有预投射分支的极小无限表示型代数,它是单连通当且仅当其一次Hochschild上同调群为零;
    We proofTheorem 3.1 Assume and satisfy:(H1) is non-negatively continuous function, 0; : is non-negatively continuous function and ;
    证明了定理3.1 如果 和 满足:(H1) 是不恒为零的非负连续函数, : 是非负连续函数且 ;
    It is comfirmed that the combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes, and that the combination parameter α( 0< α<1) plays an important role in the enhancement.
    能量误差为零的组合杂交格式可获得改进的粗网格精度,而其中组合参数α( 0<α<1)起着极其重要的作用。
    Founded upon Mankiw, Romer and Weil's (1990) neoclassical growth model of human resources, the paper tries to find that the supply elasticity of land is not zero, i,e, to studies the contribution of construction land to economic growth in the course of rapid industrialization and urbanization when the land supply is changing with the economic development.
    本研究将基于Mankiw,Romer and Weil(1990)包含人力资本的新古典增长模型,着力于研究土地的供给弹性不为零,也就是土地的供给随经济发展会发生变化情况下,快速工业化城市化进程中建设用地对经济增长的贡献。
    (2)if 0 →I → A → B→0 is (S) tracially quasidiagonal,then A is 2 — order tracial real rank zero if both I ,which is simple,and B are 1-order tracial rank zero
    (2)如果短正合列0→I→A→B→0是(S)迹拟对角化,如果I和B的1阶迹实秩为零,则A的2阶迹实秩为零。
    X_1 , , X_s are not all zero, where
    令X_1 , , X_s为不全为零的向量组,其中
    The approximate analytical solution is compared with the Burke-Schumann exact solution with the result that the flame shape is in good agreement, the error of flame height is zero and the maximum relative error of flame boundary is 0.1613%。
    近似理论解和Burke、Schumann精确解相比,火焰形状吻合得很好,火焰高度误差为零,火焰边界最大相对误差为—0.1613%。
    Ext_G(L(μ), L(λ)) is given in this paper for some irreducible highest weight g-modules, we show that the cohomology spaces are zero in many cases, but they need not be all vanish.
    本文我们得到了对于某些不可约最高权g-模的Ext_G(L(μ),L(λ)). 我们的结果证明在许多情况下Ext_G(L(μ),L(λ))为0,但是它们不全为零.
    It is shown, if the solution is two non-intersection secondary algebraic curve F=0 and d>=0, the necessary and sufficient condition is that (E)_3 may be simplified as the following form:
    F=0是椭圆、双曲线或抛物线,k_1、k_2是不为零的常数,从而推得这时(E)_3不可能存在极限环。 倘若F=0与φ=0都是圆轨线时,则有可能成为(E)_5的极限环。
    |z|=r Suppose that v>1, and letλ=(v-1)/v~v/(v-1),thenIf the right hand side of this equation is a positive finite number, then the order of f(z)is zero and f(z) can not be reduced to a polynomial, and f(z) has type function (logr).
    |z|=r 设v>1,并令λ=(v-1)/v~(v/(v-1)), 则如果这式右端为有限正数,则f(z)的阶为零,且不退化为多项式; 这时f(z)具有型函数(logr)~v。
    This paper studies the relationship between submatrices of A whose elements are all zero and the pointconnectivity of G, and that between majior submatrices of A whose elements are all one and point independence number of G.
    本文研究A中元素全为零的子矩阵与G的点连通度、A中元素全为1的主子矩阵与G的点独立数之间的关系。
    Theorem 1.Let M be an m-dimensional complex submanifoldimmersed into the complex projective space CP~(m+n),if n≤m,then theRicci curvature tensor of M(with the induced metric)is notidentically zero.
    定理1 设M是复射影空间CP~(m+n)的m维复子流形。 当n≤m时,M的诱导度量的Ricci张量不恒为零。
    The author gives a definition of weakly nilpotent graded radical for artinian graded rings and prove that an artinian graded ring A is semi- simple(i.e.the radical of A is zero)if and if A is a direct sum of finite number of simple artinian graded rings.
    定义了 Artin 分次环的弱幂零分次根,并证明了一个 Artin 分次环 A 是半单的(即 A 的根为零)当且仅当 A 是有限个单 Artin 分次环的直和.
    Let E_n(f) or E_n~k(f) be the best approximation to the function f∈C_[α,b] in space π_n or π_n~k, where In 1980, M. Hasson posed the following conjectures.
    分别记n次代数多项式和x~k的系数为零的n次代数多项式对函数f∈C[a,b]的最佳逼近为E_n(f)和E_n~k(f)。 1980年,M.
    Let M~u be a submanifold in the standard sphere S~(u+p). Forn=2 or p=1,its Gauss image in Grassmannian G(n+1,p)is minimal ifftr_Gh=0.
    本文证明对于标准球面 S~(n+p)中的子流形 M~n 当 n=n 或 p=1时,其高斯象是Grassmanniam G(n+1,p)中的极小流形当且仅当 tr_Gh=0,即曲面的二次基本形式关于Grassmanniam 子流形度量之迹为零。
 

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