Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

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.     

Novel random poly(propylene isophthalate/adipate) copolyesters: Synthesis and characterization

Poly(propylene adipate) (PPA) and poly(propylene isophthalate/adipate) (PPI-PPA) random copolymers of various compositions were synthesized in bulk and characterized in terms of chemical structure and molecular weight. Furthermore, the thermal behavior was examined by thermogravimetric analysis and differential scanning calorimetry. All the polymers showed a good thermal stability. At room temperature they appeared as semicrystalline materials, except the copolymers containing 20 and 30 mol% of PI units: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of melting temperature with respect to homopolymers. The crystalline phase of PPI and PPA was evidenced at high content of propylene isophthalate or propylene adipate units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g as the content of PI units is increased was observed. This behavior was explained as due to the stiff phenylene groups in the polymeric chain. The Wood equation was found to describe well T_g-composition data. Lastly, the presence of a rigid-amorphous phase was evidenced in the copolymers, differently from PPA homopolymer.     

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

Rare numbers

Suppose thatX ₁,X ₂,... is a sequence of iid random variables taking values inZ ⁺. Consider the random sequenceA(X)(X ₁,X ₂,...). LetY _n be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn ^–(1–) Y _n for [0, 1].     

A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Random and cooperative sequential adsorption on infinite ladders and strips

We analyze various processes where particles are added irreversibly and sequentially at the sites of infinite ladders or broader strips (i.e., on terraces) of adsorption sites. For sufficiently narrow strips or ladders, exact solution in closed form is possible for a variety of processes. Often this is most naturally achieved by mapping the process onto an equivalent one-dimensional process typically involvingcompetitive adsorption. We demonstrate this procedure for sequential adsorption with nearest-neighbor exclusion on a 2× square ladder. For other select processes on strips slightly too broad for exact solution, almost exact analysis is possible exploiting an empty-site shielding property. In this way, we determine a jamming coverage of 0.91556671 for random sequential adsorption of dimers on a 2× square ladder. For broader strips, we note that the complexity of these problems quickly approaches that for × lattices.