STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｉｅｓｏｆｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｆｏｒｆｏｌｌｏｗｉｎｇｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ(Ｐ)　Δｕ(Ｘ) +ｇ( ｜Ｘ｜)ｆ(ｕ(Ｘ) ) =0 ,　　Ｒ1<｜Ｘ｜<Ｒ2 ,ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ1 =ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ2 =0(ｗｈｅｒｅＲ1>0 ,Ｘ ∈Ｒｎ,ｎ ≥ 2 )ａｒｅｂｅｉｎｇｃｏｎｔｉｎｕｅｄｆｏｒｒｅｃｅｎｔ 2 0ｙｅａｒｓｗｉｔｈｏｕｔｉｎｔｅｒｒｕｐｔｉｏｎ[1- 11],ｂｅｃａｕｓｅｔｈｅｐｒｏｂｌｅｍ (Ｐ)ｈａｓｗｉ…     

Iterative construction of solutions to nonlinear equations of lipschitzian and local strongly accretive operators

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. Let T: X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions of the equation Tx=f be nonempty. We show that sol(T) is a singleton and the Ishikawa sequence converges strongly to the unique solution of the equation Tx=f. In addition, whenever T is a Lipschitzian and local pseudocontractive mapping from a nonempty convex subset K of X and the set F(T) of fixed points of T is nonempty, we prove that F(T) is a singleton and the Ishikawa sequence converges strongly to the unique fixed point of T. Our results are the improvements and extension of the results of Deng and Ding⁽⁴⁾ and Tan and Xu⁽⁵⁾.     

Mann and Ishikawa iterative approximation of solutions form-accretive operator equations

The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors’ recent results.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

Direct calculation of AGMA geometry factor J by making use of polynomial equations

The available sources and procedures for determination of AGMA geometry factor J are tables, charts and semi-analytical methods. When computerized gear design is considered, usage of tables requires a number of interpolations; usage of charts requires curve fitting; and usage of semi-analytical methods needs a numerical algorithm and may have convergence problems. As an alternative to these, polynomial equations for direct calculation of AGMA geometry factor J are derived for external spur gears. Thus, it is made possible to evaluate the J factor easily and with minimum process time. J factors are determined being independent of the highest point of single tooth contact (HPSTC). Derived equations can be used to calculate the tooth root stresses corresponding to loads acting on any point on the involute tooth profile. Thus, cases where the center distance is increased for providing backlash or for operating the gears at a desired exact center distance can easily be handled by determining the corresponding new HPSTC. A computer program is developed to demonstrate the usage of the derived equations. The method can also be used for determination of the J factors for gears with non-standard proportions.     

Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

中频磁控溅射制备不同S/W原子比WSx薄膜的结构和摩擦学性能研究

采用中频磁控溅射制备了WS_x薄膜,通过X射线衍射 (XRD)、场发射扫描电子显微镜(FESEM)、原子力显微镜(AFM)和X射线光电子能谱 (XPS)对其结构进行了分析,采用纳米压入仪(Triboindenter)和真空球-盘摩擦试验机分别考察了薄膜的力学性能和摩擦磨损性能.结果表明:改变溅射功率密度和气压,将引起选择性溅射与薄膜氧化程度的变化,致使薄膜S/W原子比随之变化,薄膜的S/W原子比随着溅射功率密度的增加先减小后增大,而随着溅射气压的增大逐渐增大.薄膜S/W原子比较低时,薄膜W含量较高,薄膜结构较致密、硬度较高,但摩擦系数较大、耐磨性能较差;随着S/W原子比的增大,薄膜中WS₂含量显著增加,W含量明显下降,摩擦系数降低,耐磨性能明显改善.     

A study of the in situ transverse tensile lamina strength and the classical solution of the opening mode crack in a 0/90/0 laminate

In this paper, the classical solution of the opening mode crack in the 90° layer of 0/90/0 laminates has been determined by means of Fourier transformations and the procedure of Copson for a pair of dual integral equations. The fracture behavior and the in situ transverse strength of the 90° layer have been quantitatively studied in graphite/epoxy laminates, based on the solution obtained above. The results show that the stress intensity factor of this kind of laminates, which is different from that of a single unidirectional 90° layer, decreases with the increase in thicknessb, or modulusE _L orG _LT of the 0° layer and also decreases with the decrease in the thickness of the 90° layer. So the lamination effect manifests itself and thein situ transverse strength of the 90° layer is thereby enchanced. The theoretical calculations agree with the experimental data presented by D.L. Flaggs. Supported by National Natural Science Fundation of China.