Some coincidence theorems of set-valued mappings

Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].     

On the degree theory for multivalued (S+) type mappings

This paper is to generalize the results of Zhang and Chen^[1]. We construct a topological degree for a class of mappings of the form F=L+S where L is closed densely defined maximal monotones operator and S is a nonlinear multivalued map of class (S+) with respect to the domain of L. Project supported by the Foundation of State Educational Commission of China for Returned Scholars from Abroad (1995806).     

Extending Circle Mappings to the Annulus

We show that any monotone degree one C mapping of the circle can be realized as the induced mapping on the boundary by a C area preserving diffeomorphism of the open annulus. The circle mapping may have critical points, allowing the possibility of Denjoy behavior on the boundary.     

Global structure of a kind of predator-prey system

In this paper we prove a theorem, theorem 2, on nonexistence of closed trajectory for a general predator-prey system. Then, using this theorem and another theorem on existence and uniqueness of limit cycle for predator-prey system, we complete the investigation of a concrete model of predator-prey system (?)=γx(1-x/K)-yx~n/(a+x~2) (?)=y(μx~n/(a+x~2)-D)(n=1,2)under the conditions of all kinds of parameters.     

Univalent σ-Harmonic Mappings

We study mappings from ℝ² into ℝ² whose components are weak solutions to the elliptic equation in divergence form, div (σ∇u)= 0, which we call σ-harmonic mappings. We prove sufficient conditions for the univalence, i.e., injectivity, of such mappings. Moreover we prove local bounds in BMO on the logarithm of the Jacobian determinant of such univalent mappings, thus obtaining the a.e. nonvanishing of their Jacobian. In particular, our results apply to σ-harmonic mapping associated with any periodic structure and therefore they play an important role in homogenization. Accepted October 30, 2000?Published online April 23, 2001     

Dynamics of inner mappings

We study properties of invariant sets of dynamical systems generated by inner mappings. We prove that if x is a nonwandering point of a finitely multiple inner mapping, then not only its positive trajectory O⁺(x) consists of nonwandering points but also the negative trajectory O⁻(x) contains at least one partial semitrajectory consisting of nonwandering points.     

BPNN用于含氮、硫杂环润滑油添加剂抗磨性能的定量构效关系研究

采用反向传播神经网络法(Back Propagation Neural Network,简称:BPNN)对31种含氮、硫的2-烷基黄原酸酯类润滑油添加剂的抗磨性能进行了摩擦学定量构效关系(Quantitative Structure Tribo-ability Relationship,简称:QSTR)的研究,得到了具有良好的稳定性和预测能力的BPNN-QSTR模型(R~2=0.998 4,R~2(LOO)=0.695 9,q~2=0.879 1).参考输入层的12种2D和3D结构描述符的敏感度,对影响抗磨性能的分子结构进行了相应的探讨.结果表明:分子中的N和S杂原子对其抗磨损性能有显著的影响;同时,分子长度、所含双键S原子和芳香环数量以及分子支化程度等都是影响抗磨性能的主要因素.     

On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart(a shift mapping),but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.     

Bäcklund transformations for the equation ∂2u/∂x1∂x1 + ∂2u/∂x2∂x2−f (u)

Bäcklund transformations for the equation ² u/x¹x ¹+ ²u/x ² x ²=f (u)here f is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d ² f/du ²=f is sufficient for the existence of Bäcklund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt ^[1,2].     

The double and triple velocity correlations of small vortexes in three-vortex model theory and the decay of grid-produced turbulence

In the three-vortex model theory of turbulence ^[1,2] and double and the triple velocity correlation functions of small vortexes were employed. In this paper, the double and the triple velocity correlation functions of small vortexes are further discussed, and the expressions of some coefficients in the expansions in terms of relative displacement of two points are given. Finally, by using these coefficients, the decay of grid-produced trubulence is calculated. The result of calculations gives good agreement with the experimental data of G.K. Batchelor and A.A.Townsend ^[3].The projects Supported by the National Natural Science Foundation of China.     

Fixed points of a pair of asymptotically regular mappings

I.IntroductionTheconceptofasymptoticregularitywasintroducedbyBrowderandPetryshynl'].LetEbearealBanachspacewithnorn11l'l'AmappingT:E-Eissaidtobeasymptotical1yregulariflimijT" 'x~T'x:l=ofora1lxinE,whereTffxdenotesthenthiteratio11of--ooT.ltiswell-knownthatif…     

Fixed pansystems theorems and pansystems logic conservation of chaos

The study of nonlinear problems was developed in works ^[1,2] by means of the pansystems methodology (PM) which does not need the condition related to differential manifolds and linear space. In work [2], within the framework of PM, we proved that study of panchaos, panattractor and strange panattractor can be transformed conditionally into some forms of fixed subsets. As a continuation of work [2], we now research the pansystems logic conservation of panchaos, panattractor, strange panattractor and some other fixed subsets.     

Quasilinear Equations for Viscoelasticity of Strain-Rate Type

We consider the quasilinear m ×  m system of partial differential equations that governs the motion of a viscoelastic material of strain-rate type on a bounded domain in . The dependence of the stress on both the strain and strain-rate is nonlinear, and our hypotheses allow for a potential energy which is a nonconvex function of the strain. The critical hypothesis is that the dependence of the stress function on the strain rate is uniformly strictly monotone (in the sense of Minty and Browder). We prove the existence and uniqueness of weak solutions to a natural initial-boundary value problem for a large class of constitutive functions. We then treat the question of H ²-regularity of solutions and show that, while regularity in the initial data is preserved, solutions do not, in general, become more regular than their initial data. This generalizes a result for the semilinear case due to Rybka.     

The numerical solution of the unsteady natural convection flow in a square cavity at high Rayleigh number using SADI method

The unsteady natural convection flow in a square cavity at high Rayleigh number Ra=10 ⁷ and 2×10 ⁷ has been computed using cubic spline integration. The required solutions to the two dimensional Navier-Stokes and energy equations have been obtained using two alternate numerical formulations on non-uniform grids. The main features of the transient flow have been briefly discussed. The results obtained by using the present method are in good agreement with the theoretical predictions ^[1,2].The steady state results have been compared with accurate solutions presented recently for Ra=10 ⁷.     

Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems

We classify new classes of centers and of isochronous centers for polynomial differential systems in \mathbb R²{\mathbb R^2} of arbitrary odd degree d ≥ 7 that in complex notation z = x + i y can be written as

Minimizers of Caffarelli–Kohn–Nirenberg Inequalities with the Singularity on the Boundary

Let Ω be a bounded smooth domain in ${{\bf R}^N, N\geqq 3}Let Ω be a bounded smooth domain in R^N, N\geqq 3{{\bf R}^N, N\geqq 3}, and D_a^1,2(W){D_a^{1,2}(\Omega)} be the completion of C₀^￥(W){C_0^\infty(\Omega)} with respect to the norm:

||u||a2=òW |x|-2a|?u|2dx.||u||_a^2=\int_\Omega |x|^{-2a}|\nabla u|^2{d}x.      18. Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces   总被引：1，自引：0，他引：1   邓磊  杨明歌 《应用数学和力学(英文版)》2007,28(1):103-109 In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.      19. Positive solution of a class of equations involving noncompact mappings      兰坤泉  丁协平 《应用数学和力学(英文版)》1988,9(8):727-736 In this paper, we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P1-compact mappings. Next, we show several existence theorems of positive solutions for the equations involving these mappings. Our theorems improve and extend some recent results.      20. Computation of recirculating swirling flow with the GLM Reynolds stress closure      Fu Song  S. B. Pope 《Acta Mechanica Sinica》1994,10(2):110-120 A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope[3,4], is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson[11] and the computational results obtained with the typical isotropization of production model (IPM) and thek-ε type Boussinesq viscosity model.

Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces

In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.     

Positive solution of a class of equations involving noncompact mappings

In this paper, we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P₁-compact mappings. Next, we show several existence theorems of positive solutions for the equations involving these mappings. Our theorems improve and extend some recent results.     

Computation of recirculating swirling flow with the GLM Reynolds stress closure

A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope^[3,4], is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson^[11] and the computational results obtained with the typical isotropization of production model (IPM) and thek-ε type Boussinesq viscosity model.