The global Markov property for lattice systems

We prove the global Markov property for lattice systems of classical statistical mechanics, with bounded spins and finite range interactions. The method uses the one developed by two of us to prove the global Markov property of Euclidean generalized random fields. The result shows that the systems considered have a transition matrix, which together with a distribution on a hyperplane, describes completely the system.     

Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case

For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented.     

On the monotonicity of the power functions of tests based on traces of multivariate beta matrices

It is shown that for the MANOVA problem the power function of the test based on the trace of a multivariate beta matrix is monotonically increasing in each noncentrality parameter provided that the cutoff point is not too large. This result is also true for the problem of testing independence of two sets of variates.     

On the robustness of least squares procedures in regression models

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed.     

A time-decomposition algorithm for a stiff linear two-point boundary-value problem and its application to a nonlinear optimal control problem

An algorithm is proposed to solve a stiff linear two-point boundary-value problem (TPBVP). In a stiff problem, since some particular solutions of the system equation increase and others decrease rapidly as the independent variable changes, the integration of the system equation suffers from numerical errors. In the proposed algorithm, first, the overall interval of integration is divided into several subintervals; then, in each subinterval a sub-TPBVP with arbitrarily chosen boundary values is solved. Second, the exact boundary values which guarantee the continuity of the solution are determined algebraically. Owing to the division of the integration interval, the numerical error is effectively reduced in spite of the stiffness of the system equation. It is also shown that the algorithm is successfully imbedded into an interaction-coordination algorithm for solving a nonlinear optimal control problem.The authors would like to thank Mr. T. Sera and Mr. H. Miyake for their help with the calculations.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

光子晶体的带隙破缺随插入介质层变化规律的研究

采用文中图1所示的一维光子晶体的缺陷模,应用光学传输矩阵法,证明了由光子晶体的缺陷结构引起的光子禁带破缺,得出:"f"(禁带破缺处对应的入射光频率)随"nc"(插入介质层的折射率)的增加线性下降,数值模拟了它们的几何图形.并根据f-nc的对应关系提出了一种测量介质折射率的方法.     

Quark Masses in Terms of Gauge Constants and Cabibbo Angle

Fritzsch type of mass matrices for the 2×2 case and appropriate Lagrangians enable the choice of Yukawa constants of the Lagrangians in terms of the gauge constants. The mass matrices for the four quarks are shown to be proportional to V_L. The Cabibbo angle is computed to be 13^∘36′.     

Determination of the content and localization of magnesium in bioapatite of bone

Using x-ray diffraction, electrothermal atomization atomic absorption spectroscopy, and scanning electron microscopy with an x-ray microanalysis, we have studied the phase decomposition of biogenic and synthetic Mg-containing apatite at 900°C with formation of β-tricalcium-magnesium phosphate (β-TCMP). Employing simplified model representations, we obtained a relation that couples the initial Mg concentration with the degree of transformation of apatite into β-TCMP. It is shown that for the β-TCMP contents measured in bioapatite samples and on replacement of calcium by magnesium to about 8% in this phase the calculated range of Mg concentrations coincides with that available in literature sources (0.2–0.6 wt. %). A comparative investigation of the products of decomposition of biogenic and synthetic apatite by the methods of analysis of the composition and structure has established that the formation of β-TCMP is limited by both the insufficient concentration of magnesium and the small sizes of the crystals. The results of the investigations carried out together with the experimental data known from the literature are indicative of the nonuniform distribution of magnesium in the bulk of crystals of biogenic and synthetic apatite, with its predominant localization at the surface sites of the lattice. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 821–826, November–December, 2005.