Random walks on inhomogeneous lattices

For lattices with two kinds of points (black and white), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Preparation of light-stable micelles with azo dyes from a nonamphiphilic random block copolymer

Light-stable micelles with azo dyes were prepared by micelle formation of a nonamphiphilic diblock copolymer containing azobenzene and UV absorbent at ca. 1 mol% as the unit ratios. The nonamphiphilic block copolymer consists of two different kinds of random copolymer blocks: poly[4-(phenylazophenoxymethyl)styrene-co-vinylphenol] (P(AS-co-VPh)) and poly[4-(2-hydroxybenzophenoxymethyl)styrene-co-styrene] (P(HBS-co-St)). This random block copolymer, P(AS-co-VPh)-b-P(HBS-co-St) formed the micelles in the presence of 1,4-butanediamine (BDA) through hydrogen bond cross-linking between the VPh units via BDA. The micelles had the azobenzene moieties at the cores and the UV absorbents at the coronas. The micelles showed a small color difference in color fading experiments, in comparison with the unimers and with micelles having no UV absorbent at the coronas. It is significant that the diblock copolymer forms the micelles and has the UV absorbents at the coronas to suppress the color fading. Furthermore, the chain length of ,-diamines had no effect on the hydrodynamic radius of the micelles, but affected the aggregation number and the cmc.     

An efficient Stille cross-coupling reaction catalyzed by Pd(OAc)2/DAB-Cy catalytic system

An efficient palladium-catalyzed Stille cross-coupling reaction has been developed. In the presence of 3 mol% of Pd(dba)₂ and 6 mol% of DAB-Cy (1,4-dicyclohexyl-diazabutadiene), various aryl halides (iodides and bromides) were coupled with organotin compounds to afford the corresponding biaryls and alkyne in good to excellent yields. Furthermore, high TONs [turnover numbers, TONs up to 950,000 for the reaction of 1-iodo-4-nitrobenzene and tributyl(phenyl)stannane] for the Stille cross-coupling reaction were observed.     

Interactions of Some Amino Acids with Aqueous N,N-Dimethylacetamide Solutions at 298.15 and 308.15 K: A Volumetric Approach

The apparent molar volumes, V _φ , of glycine, L-alanine and L-serine were obtained in aqueous 0 to ∼4 mol⋅kg⁻¹ N,N-dimethylacetamide (DMA) solutions from density measurements at 298.15 and 308.15 K. The standard partial molar volume, V _φ ^o, and standard partial molar volumes of transfer, Δ_tr V _φ ^o, were determined for these amino acids. It has been shown that hydrophilic-hydrophilic interactions between charged groups of the amino acids and the —CON= group of DMA are predominant in the case of glycine and L-serine, but for L-alanine the interactions between its side group (—CH₃) and DMA are predominant. An increase in temperature increases the standard partial molar volumes but decreases the transfer volumes of the amino acids. The results have been interpreted in terms of cosphere overlap model.     

Vibrational Spectroscopic Study on Ion Solvation and Association of Lithium Perchlorate in 4-Methoxymethyl-ethylene Carbonate

Solvation interaction and ion association in solutions of lithium perchlorate/4-methoxymethyl-ethylene carbonate （MEC） have been studied by using Infrared and Raman spectra as a function of concentration of lithium perchlorate. The splitting of ring deformation band and ring ether asymmetric stretching band, and the change of carbonyl stretching band suggest that there should be a strong interaction between Li^＋ and the solvent molecules, and the site of solvation should be the oxygen atom of carbonyl group. The apparent solvation number of Li^＋ was calculated by using band fitting technique. The solvation number was decreased from 3.3 to 1.1 with increasing the concentration of LiClO4/MEC solutions. On the other hand, the band fitting for the ClO4^- band revealed the presence of contact ion pair, and free ClO4^- anion in the concentrated solutions.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Transference numbers for ultra concentrated solutions of aqueous hydrochloric acid at 25°C

Transference numbers of HCl(aq) solutions at 25°C, from 0.01 to 13.6 mol-kg^–1(m) have been obtained by measuring the emf of cells with transference using hydrogen gas/platinum electrodes. Good agreement is obtained at concentrations up to 1 m with all previous data, and our results strongly corroborate those of King and Spiro over the 2–8m concentration range. The transference numbers of the hydronium ion fit the empirical equation, _H ^HCl = 0.821 + 0.0457m ^1/2 – 2.476×10^–2m – 1.90×10^–4 m ² – 1.45×10^–5 m ³ the maximum deviation in T _H ^HCl being 0.003.     

稳态荧光探针法测定三聚季铵盐表面活性剂的胶束聚集数

以芘为荧光探针, 十六烷基氯化吡啶(CPC)为猝灭剂, 以芘的饱和水溶液为溶剂配制表面活性剂溶液, 根据芘的荧光强度之比I1/I3随表面活性剂水溶液浓度的变化, 测定了三聚季铵盐表面活性剂CTTTA的cmc值, 测定值与表面张力法测定的cmc值一致；当猝灭剂CPC的浓度取0.1~0.3 mmol·L-1范围时, 用稳态荧光探针法测定了CTTTA的胶束聚集数. 实验数据表明, 表面活性剂溶液浓度为6~10倍cmc时, 胶束聚集数N随表面活性剂浓度增大而线性增大, 并用外推法得到CTTTA的临界胶束聚集数.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

大气闪烁对自适应光学校正的影响

 激光在大气湍流中长距离近水平传输时，闪烁加强，限制了常规自适应光学的校正能力。数值研究了大气闪烁对自适应光学校正的影响，拟合得到了在Fresnel数一定时，Strehl比与Rytov方差的表达式，以及Rytov方差一定时，Strehl比与Fresnel数的表达式。结果表明，在Rytov方差较小时，纯相位校正Ｓtrehl比只与Rytov方差有关；随着Rytov方差的增加，Strehl比不仅与Rytov方差有关，还与Fresnel数有关，Fresnel数越大，校正Strehl比越大；大发射和接收孔径有利于提高校正Strehl比；在一定的Rytov方差下，Stregl比随Fresnel数增大而增加，逐步趋于饱和，达到纯相位校正的极限。