Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Comparative Characteristics of Some Physicochemical Properties of Azoles

We have carried out a correlation analysis of some physicochemical characteristics of pyrrole, pyrazole, imidazole, triazole, and tetrazole, calculated by the semiempirical quantum-chemical AM1 method. We have found the linear dependences of the ionization potential, the dipole moment, and the acidity on the -electron excess, and also the dependence of the ionization potential on the enthalpy of formation of the studied azoles.     

Solvatochromism of 3-[2-(aryl)benzoxazol-5-yl]alanine derivatives

The photophysical properties of N-Boc-3-[2-(9-anthryl)benzoxazol-5-yl]-l-alanine methyl ester (BoxAnt) and N-Boc-3-[2-[4-(9′-(10′-butyl)anthryl)phenyl]benzoxazol-5-yl]-l-alanine methyl ester (BoxPhAnt) were studied in a series of solvents. Their absorption spectra are less sensitive to the solvent polarity than the corresponding fluorescence spectra which show a pronounced solvatochromic effect leading to large Stokes shifts. Using an efficient solvatochromic method, based on the empirical solvent polarity parameter , a large change of the dipole moment on excitation for BoxPhAnt has been found. From an analysis of the solvatochromic behaviour of the absorption and fluorescence spectra in terms of bulk solvent polarity functions, f(_r, n) and g(n), a larger excited-state dipole moment (about 8 D, ψ = 56) was obtained for BoxPhAnt than for BoxAnt (about 3 D, ψ = 0). Both applied methods gave similar values of the excited-state dipole moments for both compounds studied.     

Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

下承式梁拱组合桥梁的梁拱协作机理研究

文章将外部静定、内部高次超静定的梁拱组合桥梁分解成梁拱闭合体和吊杆两种构件,并且将吊杆力假定为膜张力,求解出了梁拱组合桥梁在均布荷载作用下拱肋分担的荷载大小及其修正系数,明确了其传力途径,定量地求出了梁拱分担的荷载比例,拱梁的拉压力偶矩大小以及梁拱截面的弯矩,并讨论了拱梁荷载比、弯矩比的影响因素及其关系,完整地揭示了下承式梁拱组合桥梁的梁拱协作机理.     

关于有消失矩的函数的Hilbert变换的加权范数不等式

为刻划一类权函数W,使具有N阶消失矩的函数f的Hilbert变换f满足带权L~P强型不等式Adams给出了一个充要条件。利用A_P权的性质,本文进一步完善了这个结果。     

p调和函数正则性的一个注记

若p调和函数u属于W^1,q〉p-1〉0,且满足｜p-2｜或｜p—g｜足够小,证明了△↓一定是Holder连续的．这个结果推广了调和函数（p=2）的正则性结论,其证明主要运用了Hodge分解及反Holder不等式．