POSITIVE SOLUTIONS FOR NONHOMOGENEOUS ELLIPTIC EQUATIONSWITH CRITICAL GROWTH ON R~(2)

1IntroductionIntillspaper,weare(follccrlledwitlltileexistellccofPositly(tsollltiollsoftilefollowillgnonhonlogelleousellipticProblclll:whereg(x)EL'(R'),g(:v)Z0alldg(x)t0,f(x,t)=h(x,t).hi=withb>0,h(x,t)EC(R=xR,R)alldtilefollowing(CI)-(C3)11old:(CI)sliphillM0.linljfl- x,h(T,t)(t--if-=011llif'orllllyforxeR2.hill}t:l-:,t)(axle(~ltJ')= lx,11lliforllllyl'Ora:6RZ.ltl~la(C3)ThereexistM>0,aE(0,1]sucllthatFOllowing[1,5],wesaythatf(x,t)=h(x,f…     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

关于一个非线性椭圆特征问题的某些注记

讨论一个非线性椭圆特征问题，减弱了原有结果中的一个条件而得到同样的结果，并讨论了参数小于λ１的情形。     

Investigation of Scale Exponents of Complete and Incomplete Aggregation-Annihilation Processes

The complete and incomplete aggregation-annihilation processes are investigated with the method of generating function, and the scale exponents are obtained exactly. We find that the scale exponents of incomplete aggregation-annihilation process are different from the previous exponents obtained by different methods. The time dependence of the total number of clusters and the total mass of clusters are analytically obtained.     

CALCULUS OF VARIATIONS WITH DIRICHLET BOUNDARY VALUE PROBLEM FOR PERTURBED SECOND-ORDER DIFFERENTIAL EQUATIONS ON A HALF-LINE

Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.     

一类幂数列的单调性

关于一类幂数列的单调性已经有了一些特殊结果 ,而该文以导数为工具 ,通过对幂指型函数图象特征的讨论 ,构造出一个特殊的数列 { bk} ,解决了该类幂数列的单调性 ,得到了 2个有趣的结果。当 l 相似文献   

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.