首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 28 毫秒
1.
In a previous paper[1],S.T.Yau proved the following theorem:Theorem A Let M~n be an n-dimensional compact submanifold with parallel meancurvature in S~n p with p>1.If(3 n~(1/2)-1/p-1)S≤n,then M~n lies in a totally geodesicS~n 1.Lemma1[2]If a given set of n 1(n≥2)real numbers a_1,…,a_n and k satisfy thein(?)ality  相似文献   

2.
J.Lindenstrauss once gave a short proof of Liapounoff's Convexity Theorem by using induction [1]. Now we give a more direct way to prove the theorem other than using induction. Here is the Liapounoff'i theorem: Theorem Let μ_1,μ_2,…,μ_n,be finite positive non-atomic measures on some measure space X.Then M={(μ_1(A),μ_2(A),…,μ(A))|,measurable}is a closed and convex subset of R~n.  相似文献   

3.
In this paper, the author considers Lienard's equation, studies the properties of so-called characteristic functions and gives three theorems which ensure that the equation has at least one limit cycle. The theorems generlize Filippov's Theorem which is a repesentative result, Dragilev's Theorem, Theorem 1, 2 of[6], Theorem 9 of[8] and Theorems 1, 2 of[9] respectively.  相似文献   

4.
Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.  相似文献   

5.
This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.  相似文献   

6.
The object of this paper is twofold. First, a fixed point theorem of G.L. Cain, Jr. and M. Z. Nashed [1] is generalized. Second, the theorem (Theoreml) is utilized to obtain theorems on best approximation which extend and unify the results of Meinardus [2], Singh [ 3—4 ], and Sahney Singh-Whitfield [5].  相似文献   

7.
We develop the Radford's biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B ×βα H and derive a necessary and sufficient condition for B # ×βα H with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1] .  相似文献   

8.
In this paper we prove the following theorem.It is a generalization of Tenchel's theorem on theintegral curvature of curve.Theorem.If 1 is the length of a curve C=AB and φ is the angle between the tangent vectors ofC at A,B,then the integral curvature of C  相似文献   

9.
This paper comments that there exist some mistakes in the asymptotic expansion of the ?rst order Menikov function near a 3-polycycle given by Theorem 3.1 of [2]. We present a correction to the theorem, and then use it to show that only one limit cycle can be found near a 3-polycycle for a class of quadratic systems.  相似文献   

10.
1. The Main ResultsIn this paper we establish the following result concerning the Bessel functions Im(x):Theorem 1.1. (i) For any m ≥2 there exists a unique positive solution x=xm of theequationwhere(ii) If 2≤l < m, thenThis theorem is used in the study of free boundary problems[1]The following result will be used in the proof of (1.3):Theorem 1.2. The function G(x) is concave for 0 相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号