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    Based on this inferred consequence from them, the paper shows us that any finite set A of nonzero elements being characterized by 0 contains a sum-free subset B, with |B|>13|A|.
    作为它们的一个推论,证明了特征为零的任何非零元素的有限集合都包含一个sum-free子集B,|B|>13|A|.
    Let M be the ideal in Z[v] generated by v-1 and a odd prime p, U be a quantum algebra over A-Z[V]M with a symmetric Cartan matrix.
    令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子代数. k是特征为零的代数闭域,A→k(v(?)
    Let {X(t),T1≤t≤T2 } be a seperable measurable Gaussian process with mean zero and differentiable covariance function. For u ↑+∞,this paper discusses sajourn limiting theorem of process above Level u.
    设{X(t),T1≤t≤T2}是可分、可测的高斯过时程,均值函数为零,而协方差函数г(s,t)=EX(s)X(t)具有连续一阶编导.对于水平u↑+∞,本文讨论X(t)在u之上的逗留极限定理,
    We study the following initial valueproblem ut-1tΔu=u γ u(ε 0,x)=φ(x) t>ε 0>0 x∈R n (0.1) x∈R n.
    本文讨论下面的初值问题ut-1tΔu=uγu(ε0,x)=φ(x){t>ε0>0x∈Rn(0.1)x∈Rn.(0.2)其中γ1,φ(x)连续有界,且φ(x)0但不恒为零。
    The paper shows that detEn is a Maximum Determinant. The En=(eij)nxn, eij =0 only if i=j + 1 or i
    取En=(eij)nxn,其中eij=即En是一个主对角线之下的第一条对角线的元素为零,其余元素均为1的lowerhessenberg(0,1)矩阵,则对于任意给出的A∈Mn,必有detA≤detEn。
    When A (t) is a 2×2 matrix, and one of its eigenvalues is Zero, and the other is negativel We Study the Stability of System x=A (t)x and give Sufficient conditions that guarantee the Stabilityof the trivialSolution of the system.
    在A(t)为2×2矩阵,而其特征根一个为零,另一个为负数的情况下讨论了系统x=A(t)x零解的稳定性,给出了保证该系统零解稳定的若干充分条件.
    The full indispensable ekistent condition of the equation AxB-CxD=E is that it is zero when arbitrary (λ1, λ2)≠ (0.0). Det (λ1A-λ2C) is different from Det (λ1D, λ2B). This article presents the algorithm to solve the equation AxB-CxD=E.
    方程AxB-CxD=E存在唯一解的充分必要条件是:对任意的(λ1,λ2)≠(0,0),Det(λ1A-λ2C)和Det(λ1-λ2B)不同时为零,并给出了求解方程AxB-CxD=E的算法.
    In this paper,by applying the distance of plane R 2 and level importance function g(λ),we establish the LG pd metric D [pg] on fuzzy number space E 1,and show that (E 1,D [pg] ) is a metric space if and only if g(λ)≠0 almost everywhere on [0,1].
    以平面R2 上的距离d 为基础,结合水平λ的重要性函数g(λ),在Fuzzy 数空间E1 上建立了LGpd-度量D[pg],证明了(E1,D[pg])为度量空间的充分必要条件是g(λ)在[0,1]上几乎处处不为零。
    The surn of the coefficients in f(X1,…, Xn) (denoted by fsc) isnonzero. If d(fsc) =δ(fsc) and d(f(X1,…, Xn)) f(X1,…, Xn ) - f(X,1…,Xn ).
    如果f(X1,X2,…,Xn)的各单项式的系数之和(记为fsc)不为零,d(fsc)=δ(fsc)且在R的边上是中心值的。
    An approximate checking method to judge whether the variance of random coefficient AR(1) equals to zero or not was presented in this paper.
    给出随机系数AR(1)的随机系数方差是否为零的一个近似检验方法
    The generalized curve regression model, y i=g(t i)+ε i; (1≤i≤n), is considered, where g(·) is an unknown smooth function defined [0, 1] and {ε i} is statuary series.
    考虑广义回归模型 yi=g( ti) +εi,1≤ i≤n,其中 g(· )为 R上的未知函数 ,误差 εi 是均值为零的平稳序列 .
    \$\; (ii) \$λ\-1=0,\$ but \$λ\-2≠0,\$ then\$ m\-1=1,\$ or \$λ\-1≠0,\$ but \$λ\-2=0,\$ then\$ m\-2=1\$;
    (ii) λ1,λ2 中有一个为零 ,不妨设 λ1=0 ,λ2 ≠ 0 ,则 m1=1 ;
    The present paper proves that a ring R is a periodic ring if and only if for any a,b∈R, there exist positive integers m,n,k and a polynomial f(x) with integer coefficients and the constant term being zero such that a mb k=a nb kf(b).
    证明环 R是周期环的充分必要条件是对 a,b∈ R,均有自然数 m,n,k及常数项为零的整系数多项式 f ( x) ,使得 ambk=anbkf ( b)
    In this paper we get the following results: Let (z) be a meromorphic function in domain G which is not identically zero, a1(z), a2(z), …,ak(z) be holomorphic function in domain G, F={f} be a family of meromorphic functions in G.
    本文获得如下结果:设(z)为区域G内一不恒为零的亚纯函数,a1(z),a2(z),…,ak(z)为区域G内的全纯函数,F={f}为G内一亚纯函数族.
    We show that the nonparametric MLE Fn of F obeys the central limit theorem in the sense that for measurable g(x), the integrals n~1/2 ∫ g(x)[dFn(x)- dF(x)] converges to a normal distributon with mean zero and variance σ2 as n tends to infinity.
    本文证明,F的非参数最大似然估计Fn在下述意义下服从中心极限定理. 对任何可测函数g(x),n~(1/2)∫g(x)[dFn(x)-dF(x)]依分布收敛到均值为零方差为σ2的正态分布.
    Especially, when Q(s) ≡ 0 and A(t, x) = A(t), the conditions which guarantee the existence of unique and stable periodic solutions are derived.
    特别地,当Q(s)为零矩阵,A(t,x)=A(t)时给出了存在唯一稳定的周期解的条件.
    Let U be a quantum group over A=Z Ω with a symmetric Cartan matrix, where Ω is the ideal of Z generated v-1, k be an algebraically closed of characteristic zero. Consider a ring homomorphism A→k(v|→ξ), let U k=U? 瑼 k.
    A=Z[v] Ω,Ω是 Z[v]的由 v- 1和奇素数 p生成的理想 ,U是 A上的量子群 ,设 k是特征为零的代数闭域 ,A→ k(v|→ ξ)是代数同态 ,ξ是 p次本原根 ,命 Uk=U Ak,W是 weyl群 ,X+是支配权集 ,本文的主要结果是如下的定理
    Based on Hopf's maximum principles,a class of fourth-order elliptic equationsΔ\+2u+h(x,u,Δu)=0and some boundary-value problems were studied. Some properties of the solutions were obtained,which the corresponding results of the chapter 10 of Maximum Principles and Their Applications by R.
    应用 Hopf极值原理 ,对四阶椭圆型方程Δ2 u +h(x,u,Δ u) =0及其边值问题进行研究 ,给出解的泛函的极值原理 ,并证明了在一些边界条件下解恒为零 . 同时推广了 R.
    Moreover, we also give a classification of the surfaces with vanishing Moebius form in Sn.
    在此基础上,进一步给出了Sn中Moebius形式为零的曲面的分类.
    We discuss derivation on infinite matrix rings, and prove that every derivation of
    讨论无穷矩阵环上的导子,证明了环R上有限个元素不为零的无穷矩阵坏的每个导子均可表示为两个特殊导子之和。
 

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