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     Let f(w) be an analytic and univalent function in a convex domain D. Sharp bounds on the estimates of |f(n)(w)/f'(w)| are found for all w in D and 2≤n≤8. These estimates generalize several known results.
     设函数f(w)为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f(n)(w)/f'(w)|的精确上界. 这个结果推广了一些已知的结论.
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     Let X be a real Banach space which is both p uniformly convex and uniformly smooth, T:D(T)X be a Lipschitzian m accretive operator. Under the natural setting that the domain of T , D(T) is a proper subset of X ,method of approximating a solution of the equation x+Tx=f is studied. The results extend several known results.
     设X是p一致凸和一致光滑的Banach空间,T:D(T)→X是Lipschitz的m增生算子,其中T的定义域D(T)是X的闭真子集,文中研究了逼近非线性方程x+Tx=f解的方法,其结果扩展了几个已知的结论
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     in this paper,we first established three differential identity,and then discussed the oscillation comparison theorems of prepared solutions and derivative function of prepared solutions forsystem (P(t)Y') ' + Q(t)Y= 0,and grneralized some known results.
     研究了二阶线性微分系统的预备解及其导函数的振动性.首先建立三个微分恒等式,然后利用它们研究了系统(P(t)Y’)+Q(t)Y=0的预备解及导函数的振动比较定理,推广了若干已知的结论
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     Studied the point comparison theorem of solutions for two classes of nonlinear differential equation by establishing differential identity and generalized some known results.
     通过建立微分恒等式,研究二类非线性微分方程与线性方程之间解的零点比较定理及解的导函数的零点比较定理,推广了一些已知的结论
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     The uniqueness and two uniqueness of limit cycles of Liénand type system x··+ (f(x) +k(x)x·)x·+g(x)=0 are discussed. Some new results are given,and some known results are improved and extended.
     研究了Liénard型系统x··+(f(x)+k(x)x·)x·+g(x)=0的极限环的唯一性与唯二性,得到了新的结果,推广和改进了一些已知的结论
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  known result
     When the mean of random variables is zero, the solution is shown to reduce a known result for the value of the integral over the first quadrant.
     当随机变量的均值为零时 ,这个解在第一象限上的积分值可简化为一个已知的结论 .
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     In this short note, a new algebraic inequality is given, and by its application, a known result is generalized.
     给出了一个新的代数不等式,作为应用推广了文[1]中的一个已知的结论.
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  “已知的结论”译为未确定词的双语例句
     Our result includes many known conclusions.
     所得的结果包含了许多已知的结论.
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     C2n(1,n) for n≥2;
     关于循环图C_(2n)(1,k)的导出匹配可扩性,已知的结论如下:
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     Chapter 3: In this chapter, the author is to study the existence theorems of random solutions for random semi-closed 1-set contraction operators equation A(co,x)=ux (u>l) in different border condition and obtains some new results.
     第三章:本章主要研究随机半闭1-集压缩算子方程A(ω,x)=ux,(u≥1)的随机解的存在性。 我们通过利用一个已知的结论,在不同的边界条件下研究上述方程的随机解,得到几个随机解的存在性定理。
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     In this paper,we consider the Fekete-Szego problem for the family B(α,β) of Bazilevie function of type B. The results we obtained are sharp and we extend some known conclusions.
     本文我们引入了一类巴西列维奇函数,讨论了该类函数上的Fekete-Szego问题,所获得的结论是准确的.一些已知的结论是本文的特例.
短句来源
     Fourth, simple reasoning, using experiments to confirm the known conclusions.
     四是简单推理,只是采用一定的实验证实已知的结论
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  known results
We also use known results about canonical bases forUq2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.
      
These estimates not only improve, but also extend some known results in the related topics.
      
The exact soliton solutions are given and the relation between this condition and the known results in the literature is also discussed.
      
In addition, some known results about the Cartesian products of two directed cycles are also deduced.
      
In this paper, a new criterion of the non-existence of periodic solutions for a generalized liénard system is given, which generalizes and extends some known results of Sugie et al.
      
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  known result
As applications, we prove a partial converse of a well-known result of Nagel et al.
      
So the structure of attractors is clear and simple in some sense by the known result.
      
Optimization by the generalized work functional using the Bellman quasilinearization method is shown to yield the well-known result due to A.A.
      
The well-known result of Kaplansky (for compact spaces) is a corollary of this theorem.
      
We amplify the well-known result due to Dlab and Ringel on the reduction of a real rectangular matrix to canonical form by formally complex transformations of rows and columns.
      
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