Synthesis and structures of 4,6-disubstituted 2-(5-methyl-1,2,4-oxadiazol-3-yl)-1,3,5-triazines

New 1,2,4-oxadiazolyl-1,3,5-triazines were synthesized from amidoximes derived from sym-triazine mononitriles. The structure of one of the resulting compounds was studied in detail by X-ray diffraction. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1845–1850, August, 2005.     

阶梯扫描伏安法与线性扫描伏安法相关性的理论研究——简单可逆体系

本文采用Ｒｅｉｍａｎｎ－Ｓｔｉｅｌｔｉｅｓ（黎曼－斯堤杰斯）级数展开法，指导了简单可逆电极体系的线性扫描伏安法和阶梯扫描伏安法的电流方程式，得到了能有机地统一的这两种最大为基本的伏安法的电流函数表达式，表达式简明直观，在无因次电流函数的基础详细讨论了制约阶梯扫描伏安法和线性扫描伏安法之间相关性程度的各因素，获得了一些新的结论。     

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.     

Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ _n ^∞ =1a_n λ _n ^−s be a generalized Dirichlet series with 1 =λ ₁ <λ ₂ < …,λ _n≤Dn, andλ _n+1 -λ _n ≥D ^{− 1} λ _n+1 ^{− a} where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.     

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

Computer-assisted optimization of selectivity by tuning temperature and carrier gas pressure drop in two GC capillary columns coupled in series

The paper shows a computer-assisted procedure for the optimization of selectivity of two columns coupled in series by tuning the working temperature (using the isothermal mode) and columns coupling-point pressure at constant inlet and outlet carrier gas pressures. The optimization procedure validation was tested by the separation of 32 hydrocarbons in a column series with the aim to resolve the maximum number of components in the shortest possible analysis time.Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday     

Flow and heat transfer with prescribed skin friction in a rotating fluid

This paper investigates the rotating flow and heat transfer of a viscous fluid induced by a stretching surface. The nonlinear problem subject to a given skin friction at the boundary is solved. Analytic solution is obtained using homotopy analysis method. The velocity, temperature, and stretching velocity is calculated for different values of the rotation parameter (λ). The obtained results are compared with the well known results of rotating flow induced by a stretching surface by using four sets of boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Cholesteric induction power of β-galactose derivatives

Galactose derivatives were explored as chiral dopants, effective for inducing chiral nematic liquid crystal (LC) phases. Galactose bearing O-isopropylidene substituents at the C3 and C4 and butoxybiphenyl substituents at the C2 and C6 positions exhibits a high helical twisting power (HTP) value of ?74.4 μm^?1. Such a high HTP value for the galactose derivative is attributed to (1) linkage of the C3 and C4 carbons with the O-isopropylidene substituent, which places the C2 and C6 substitutes in a skew arrangement at a large angle and (2) enhancement of the affinity with the host nematic LCs by incorporating aromatic substituents at the C2 and C6 positions that are similar to those in the host.     

Tuning the mesogenic properties of 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals: the effect of a phenoxy end-group in two sterically equivalent series

Two sterically equivalent series of phenoxy-terminated 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals were synthesised, and their mesogenic properties were characterised by polarised optical microscopy and differential scanning calorimetry (DSC). The phenoxy end-group causes a significant increase in melting point and inhibits – at least partially – the mesomorphism of these materials relative to the parent isomers; in most cases, the broad enantiotropic SmC phase formed by the parent isomers is suppressed by the addition of the phenoxy end-group. However, detailed analyses by small-angle X-ray scattering and monodomain 2D X-ray scattering suggest that these compounds form a SmA phase with a partially intercalated bilayer structure in which the phenoxy end-groups are nanosegregated. Such an intercalated bilayer structure might enable the tuning of smectogenic properties by appropriate substitution of the phenoxy end-groups.     

On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates