Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Evaluation of dead time calculation in liquid chromatography using a linearization procedure for homologous series

A mathematical method for the calculation of the dead time (t_m) in HPLC was evaluated using a computer simulation approach, in which artificial perturbations were introduced to Simulated homolog retention times. The calculation was based on a modified and extended Grobler and Bálisz (GB) method. Investigated wav how the precision of the calculated t_M is affected by: statistical fluctuations in retention times and which, and how many homolog retention times are used. Based on these simulations a two-step procedure for the t_M calculation is proposed: In the first step the linearity of log t_{R, n} vs carbon number n is checked using as many homolog retention times as possible. The slope value b^o of the first linear regression in the GB method is used for the selection of homolog retention times in the final t_M calculation. In the second step the optimal selection of homologs is made and the final t_M calculation is carried out. Guidelines for homolog selection are given.     

Hole doping and superconductivity characteristics of the s=1, 2 and 3 members of the (Cu,Mo)-12s2 homologous series of layered copper oxides

Superconductivity characteristics have been systematically evaluated for a two-CuO₂-plane copper oxide system, (Cu,Mo)-12s2, upon increasing the number of fluorite-structured layers, s, between the two CuO₂ planes. Essentially single-phase samples of (Cu_0.75Mo_0.25)Sr₂YCu₂O_7+δ (s=1), (Cu_0.75Mo_0.25)Sr₂(Ce_0.45Y_0.55)₂Cu₂O_9+δ (s=2) and (Cu_0.75Mo_0.25)Sr₂(Ce_0.67Y_0.33)₃Cu₂O_11+δ (s=3) were synthesized through a conventional solid-state route in air. To make the samples superconductive an additional high-pressure oxygenation (HPO) treatment was required. Such treatment (carried out at 5 GPa and 500 °C in the presence of 75 mol% Ag₂O₂ as an oxygen source to maximize the T_c) compressed the crystal lattice for the three members of the (Cu_0.75Mo_0.25)-12s2 series equally, i.e., by 0.01 Å for the a parameter and by 0.07 Å for the c parameter per formula unit. From both Cu L-edge and O K-edge XANES spectra the s=1 sample was found to possess the highest overall hole-doping level among the HPO samples. Accordingly it exhibited the best superconductivity characteristics. With increasing s, both the T_c (s=1: 88 K, s=2: 61 K, s=3: 53 K) and H_irr values got depressed, being well explained by the trend of decreasing CuO₂-plane hole concentration with increasing s as revealed from O K-edge XANES spectra for the same samples. Hence, the present results do not suggest any significant (negative) impact on the superconductivity characteristics from the gradually thickened fluorite-structured block itself.     

LC and LC-MS Separation of Peptides on Macrocyclic Glycopeptide Stationary Phases: Diastereomeric Series and Large Peptides

Previous work on the LC separation of peptides had shown that macrocyclic glycopeptide stationary phases to be selective for peptides of five to thirteen amino acids in length. In this work, the selectivity of the teicoplanin stationary phase is compared to that of a C18 stationary phase for seven diastereomeric enkephalin peptides. The teicoplanin stationary phase separated all seven diastereomeric enkephalin peptides in a single chromatographic run. The insertion of d-amino acids into the primary enkephalin sequence produced areas of hydrophobicity that influenced retention order on the C18 stationary phase. However, analogous trends are not observed on the teicoplanin stationary phase, which is more polar and structurally diverse. Optimization of the mobile phase and the use of a step-gradient for the enkephalin separation on the teicoplanin stationary phase is discussed. Also, the selectivity of macrocyclic glycopeptide stationary phases for peptides of 14, 28, 30, and 36 amino acids also is investigated and compared to separation on a C18 stationary phase. A method for eluting peptides with multiple basic amino acids, which tend to be strongly retained on the macrocyclic glycopeptide stationary phases, is presented.     

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