UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by
for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.     

拉卡（Racah，Giulic，1909-1965）以色列物理学家（Physicist，Israel）

拉卡在将群论用于原子光谱和原子核结构方面做了许多工作，量子力学中角动量耦合理论中的拉卡系数就是用他的名字命名的。拉卡出生于意大利的弗罗伦斯，得到博士学位后在罗马为费米做过1年助手，又到慕尼黑跟泡利进修1年，然后在比萨大学任教。1938年意大利法西斯政权颁布反犹法律，他因是犹太人被解职，就去了巴勒斯坦，任教于耶路撒冷的希伯来大学，还担任过以色列的军区司令。     

BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0     

An explanation of the△D35（1930） as a ρ△ bound state

Constituent quark models based on two-body potentials systematically overpredict the mass of △D35 （1930）. A possible solution to this problem comes out from the application of a schematic hybrid model, containing three-quark as well as meson-baryon components, to the light-quark baryon spectrum. The △D35（1930） and its partners △D33（1940） and△s31（1900） are found to contain a significant pA component. Then, through the use of the hidden gauge formalism, it is shown that these resonances can be dynamically generated from the ρ-△ interaction. In particular △D35（1930） can be interpreted as being essentially a ρ△ bound state. This interpretation suggests that the inclusion of ρ△ as an effective inelastic channel in data analyses could improve the extraction and identification of the resonance.