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points theorem
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  点定理
     By using the fixed points theorem of twist map, the author proves that the biomathematical model of muscular blood vessel: x+B+Ax+γx 3=E cos ωt has at least one 2π /ω periodic solution under condition: B/2<1 where A, B, γ, E, ω are positive constant.
     运用扭转映射的不动点定理 ,证明了肌型血管生物数学模型 x+Bx+Ax+γx3 =E cosωt,( B/ 2 <1 )至少存在一个 2 π/ ω周期解 ,其中 A,B,γ,E,ω都是正常数
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     In this paper, using Fixed points theorem of twist map, the author proves that the biomathematical model of aneurysm of circle of Willis: +μ+ax-βx~2+γx~3=Fcosωt (where μ,α,β,γ,F,ω are positive constant). There is at least one (2π)/ω-periodic solution under condition: μ/2+β~/(4γ)<1 by Poincare' map.
     本文运用扭转映射的不动点定理,通过Poincare'映射,在(μ/2)+((β~2)/(4a))<1的条件下,证明了Willis环状脑动脉瘤生物数学模型 +μ+αx-βx~2+γx~3=Fcosωt(其中μ,α,β,γ,F,ω都是正常数)至少存在一个(2π)/ω周期解。
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     A fixed points theorem of Ray Avoiding mappings on a finite dimensional space
     有限维空间中Ray Avoiding映射的不动点定理
短句来源
     A Random Fixed Points Theorem in Banach Space
     Banach空间中的一个随机不动点定理
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     The existence and uniqueness of common fixed points for two pairs of compatible mappings are considered,a new common fixed points theorem is given. The theorem let (f,A) and (g,B) are compatible self-mappings in X,and (f,A) and (g,B) are continuous mapping pair,fXBX,gXAX.
     研究了两对相容映射的公共不动点的存在性和唯一性,获得一个新的公共不动点定理:设(f,A)和(g,B)都是X上相容自映射,且(f,A)或(B,g)连续,fX BX,gX AX。
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  “points theorem”译为未确定词的双语例句
     A Generalization of the Fan - Browder Fixed Points Theorem and Application
     Fan-Browder不动点定理的一个推广及其应用
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     In this paper, by use of the pseudo-gradient vector field, the three critical points theorem in [2] is extended to the C1 function in the Ba-nach space, and therefore the three critical, points theorem in [5] is strengthened and the existence of the saddle point of the C2 function is discussed.
     本文利用伪梯度向量场,将〔2〕中的三临界点定理推广到Banach空间上的C~1函数,由此加强了〔5〕中的三临界点定理,并讨论了C~2函数的鞍点的存在性问题。
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     THREE CRITICAL POINTS THEOREM AND ITS APPLICATIONS
     三临界点定理及其应用
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     Since Banach's fixed points theorem was proved by Banach in 1992, the iterative approximations methods of fixed points for nonlinear mapping have formed unity by contractive mappings theorems and the Mann and Ishikawa iterative sequences now.
     关于对不动点问题的研究,从20世纪20年代起,由经典的压缩映象原理到现在用Ishikawa迭代序列去逼近算子的不动点已经形成了一个比较系统、完善的体系。
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     Finally, under the condition that C2 real function defined on Hilbert space has the compact gradient field, a strenthening form of the three critical points theorem in 〔 1 〕 is given.
     最后,在Hilbert空间上的C~2实值函数有紧梯度场的假设条件下,给出了文[2]中的三临界点定理的一种加强形式。
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  相似匹配句对
     Theorem.
     定理:设Ω(?)
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     D theorem.
     A. D提出的结论。
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     THREE CRITICAL POINTS THEOREM AND ITS APPLICATIONS
     三临界点定理及其应用
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     ON SADDLE POINTS IN MINI-MAX THEOREM
     关于极小极大定理中的鞍点
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     Points Of Innovation
     西门子创新文化四要素
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  points theorem
On the other hand, any connected (finite) graph can be realized in the above sense by means of a smooth function of three variables having a minimal number of stationary points (Theorem B).
      
A Critical Points Theorem and Nonlinear Differential Problems
      
The technical approach is mainly based on a three critical points theorem.
      
In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:????Our main tool is a recent three critical points theorem of B.
      
Saint Raymond ([6]), we improve the three critical points theorem established in [5].
      


In the present paper,we study the boundedness and stability of solutions of the following n-dimensional system of differential equations: dx/dt=A(t)x+f(t,x) x(t_0)=x_0 (1.1) where A(t)is a contiouous n×n matrix for t≥t_0≥0 and f(t,x)is a con- tinuous vector function for t≥t_0,x∈D={x||x|

In the present paper,we study the boundedness and stability of solutions of the following n-dimensional system of differential equations: dx/dt=A(t)x+f(t,x) x(t_0)=x_0 (1.1) where A(t)is a contiouous n×n matrix for t≥t_0≥0 and f(t,x)is a con- tinuous vector function for t≥t_0,x∈D={x||x|theorem.FUNDANENTAL THEOREN.Assume 1)(1.1)satisfies the conditions(1.4)and(1.5);2)the maximum solution y(t)of the equation dy/dt=(t)y+KG(t,y) (2.7) passing through(t+0,K|x_0|)can be continued to the interval[t_0,t_0+α],where K|x_0|0 is a certain constant or+∞.Then the solution of(1.1)passing through(t_0,x_0)can be continued to the interval(t_0,t_0+α)and |x(t)|≤y(t) for t∈[t_0,t_0+α In §3,§4,we use the fundamental theorem to obtain some ratiher general criteria for boundedness and stability of solutions of(1.1)which include a series of results concerned [1] [2] [3] [6],and in this manner one may see the internal relation between these results.In this paper we also come to a similar result obtained by Stokes [16]which relies on a fixed point theorem for locally convex topological linear space due to Tychonoff.

本文討論n维方程组(1.1)。在假設(1.4)与(1.5)之下,得基本定理——若方程(2.7)的最大解要延拓,則方程组(1.1)的解的范不超过它,且也可延拓。由此给出(1.1)的解的有界性和稳定性的判別法,这概括了一系列的有关結果,如文献[1]、[2]、[3]、[6]、[16]、从而看出这些結果的相互关系。

This paper has established fixed point index for condensing maps inordered Banach Spaces and deduced some positive fixed point theorems.

本文对半序Banach空间中锥上的凝聚映射建立了不动点指数,并用其导出了一些正不动点定理,给出了存在正解的条件。

To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By...

To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By using the double integral of Cauchy typeWhere be 4×4 matrices, they are transpose of each other.γ_(PQ)=γ(P,Q)=((x-ξ)~2+(y-η)~2+(z-ζ)~2)~(1/2) be the distance of two points p(ξ,η,ζ,) and Q(x,y,z).By ■(α,β,γ) denote the outer normal of D~+ on the surface ∑ at the poinr Q. The matrix M(P,Q) is Called a Cauchy kernel matrix, the point P=Q is an isolated singular point of second order of M(P,Q).Reducing the Hilbert boundary problem in space (H)_l to the System of singulra integral equations with Cauchy kernel matrix;WhereUsing the Banach fixed point theorem to prove the existence and uniqueness theorem for the system of singuler integral equations (I)_l, then the above Hilbert boundary value problem in space (H)_l has a unique solutiou under some conditions.By means of the Schauder fixed-point theorem, which enables us to prove existence theorem for nonliean Hilbert boundary value problem in space:(H)_n G■~+(P_0)+K■~-(P_0)+λ■(P_0,■~+(P_0),■~-(P_0))=0Where G(P_0)=[G_(ij)(P_0)]i,j=1,2,3,4; K(P_0)=[K_(ij)(P_0)]i,j=1,2,3,4, which are the given nonsingular function matrices on ∑, and det|G±K|≠0, λ≠0 is a parameter, ■≡■(f_1,f_2,f_3,f_4) is a given non-linear Continuous function vector of ■~+(P_0) and■~-(P_0) and satisfying H(Hlder) condition on ∑.Supposing that also satisfies some supplementary conditions, it is shown that the non-linear Hilbert boundary value problem in space (H)_n has a uniquc solution also.

本文是研究空间的线性与非线性的Hilbert边值问题,该问题是提出的,但他只解决了常系数的情形。作者首先证得了H((?),Σ)是Banach空间,再用Banach不动点定理证得变系数的空间线性Hilbert边值问题解的存在性与唯一性。同时用Schauder不动点原理证得空间非线性Hilbert边值问题解也是存在的,然后加上适当条件便可证得解亦呈唯一的。

 
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