On the fourth-order difference equation for the associated Meixner polynomials

Three equivalent forms of the fourth-order difference equation obeyed by the associated Meixner polynomials (with a nonnegative real association parameter) are derived from a refinement of a recent result due to Letessier et al. (1996).     

Molar excess free energy of mixing of 1-propanol or 2-propanol with cyclohexane at 298.15 and 308.15 K in terms of association model with a Flory contribution term

Excess molar Gibbs free energies of mixing for 1-propanol or 2-propanol + cyclohexane over the whole composition range at 298.15 and 308.15 K have been calculated from vapour pressure data measured by static method. The data have been analysed in terms of a Mecke-Kempter association model with a Flory contribution term.     

On noncommutative piecewise Noetherian rings

We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.     

Matrix analysis for associated consistency in cooperative game theory

Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. The Shapley value as well as the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix M^Sh and the associated transformation matrix M_λ, respectively. We develop a matrix approach for Hamiache’s axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality M^Sh = M^Sh · M_λ. The diagonalization procedure of M_λ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen’s axiomatization of a certain class of linear values. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory.     

湖北竹山黄绿色-绿色绿松石伴生矿的谱学研究

近年来绿松石市场上出现了俗称\"绿松石伴生矿\"的天然矿物,颜色丰富,有紫色、白色、褐黄色、黄绿色、绿色等,其中黄绿色-绿色系绿松石伴生矿相对其他颜色绿松石伴生矿与绿松石外观较为相似,鉴别难度较大.为探究其鉴别特征,选取两块来自湖北省竹山县市场的黄绿色-绿色系伴生矿原石(样品E和F),对其进行基础宝石学、电子探针、X射线粉...     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.