A rotating holographic imager for stationary cloud droplet and ice crystal measurements

Optical Review - An optical cloud droplet and ice crystal measurement system ICEMET (icing condition evaluation method), designed for present icing condition monitoring in field conditions, is...     

Local independence of fractional Brownian motion

Let _σ(t,t′)${\sigma }_{(t,t^{\prime })}$ be the sigma-algebra generated by the differences _Xs−_Xs′$X_s-X_{s^{\prime }}$ with s,s^′∈(t,t^′)$s,s^{\prime }\in (t,t^{\prime })$, where _{(Xt)−∞<t<∞}${\left(X_t\right)}_{-\infty <t<\infty }$ is the fractional Brownian motion with Hurst index H∈(0,1)$H\in (0,1)$. We prove that for any two distinct timepoints _t1$t_1$ and _t2$t_2$ the sigma-algebras _{σ(t1−ε,t1+ε)}${\sigma }_{(t_1-\epsilon ,t_1+\epsilon )}$ and _{σ(t2−ε,t2+ε)}${\sigma }_{(t_2-\epsilon ,t_2+\epsilon )}$ are asymptotically independent as ε↘0$\epsilon \searrow 0$. We show the independence in the strong sense that Shannon’s mutual information between the two σ$\sigma$-algebras tends to zero as ε↘0$\epsilon \searrow 0$. Some generalizations and quantitative estimates are also provided.     

Cellulose--model films and the fundamental approach

This critical review describes the recent arrival of ultrathin films of cellulose. The methodology of preparation as well as the applications of the films for fundamental research is fully covered. The review places cellulose in a wider scientific context where cellulose research is no longer a field of interest for specialised scientists only. Cellulose and cellulosic materials should interest communities such as biochemists, physical chemists, surface chemists, organic chemists, polymer chemists and also physicists working close the disciplines mentioned. (149 references.).     

Inverse Scattering Problem for a Two Dimensional Random Potential

We study an inverse problem for the two-dimensional random Schrödinger equation (Δ + q + k ²)u = 0. The potential q(x) is assumed to be a Gaussian random function whose covariance operator is a classical pseudodifferential operator. We show that the backscattered field, obtained from a single realization of the random potential q, determines uniquely the principal symbol of the covariance operator of q. The analysis is carried out by combining harmonic and microlocal analysis with stochastic methods.     

Modification of olefin polymerization catalysts. I. Mechanism of the interaction between AIEt3 and silyl ethers

The interaction between AlEt₃ and silyl ethers, Ph_nSi(OMe)_4-n (n = 0–3), was followed by ¹³C- and ²⁹Si-NMR techniques in conditions close to those typical for an olefin polymerization reaction with supported Ziegler–Natta catalysts (A1Et₃:silyl ether ratios from 1 to 10, temperature range 25–75°C). A1Et₃ and silyl ethers form instantaneously at ambient temperature a donor-acceptor complex, which is stable at a 1:1 molar ratio. In the presence of excess A1Et₃ the complex decomposes via a mechanism consisting, in the case of PhSi(OMe)₃, of five consecutive steps: alternating complexation and ether reductions with the formation of alkylated silyl ethers, Ph(Et)_nSi(OMe)_3-n (n = 1,2), and dialkyl-aluminum alkoxides, (Et₂A1OMe₃)_n (n = 2,3). The rate of decomposition was enhanced by the increasing number of methoxy groups present in the silyl ether, heating, or a high A1Et₃:silyl ether ratio. The decomposition was not inhibited by the presence of 1-hexene.     

Separation of caffeine from antipyrine by means of cation exchanger in the ferric iron form

The ion exchange separation method presented in this paper is based upon the ability of antipyrine to form complexes with ferric iron. On passing an aqueous solution of caffeine and aratipyrine through a cation exchanger in the ferric iron form, antipyrine is quantitatively taken up. Caffeine, however, is completely displaced from the column on washing with water at elevated temperature and determined spectrophotometrically in the ultraviolet region. This procedure has been found to be simpler and more precise than others previously used.     

Two queues in tandem

A system consisting of two queues in series, the output of one queue being the input of the other, is described. General distributions are discussed, but the exponential distribution is given particular consideration.     

Core versus graded core, and global sections of line bundles

We find formulas for the graded core of certain -primary ideals in a graded ring. In particular, if is the section ring of an ample line bundle on a Cohen-Macaulay complex projective variety, we show that under a suitable hypothesis, the core and graded core of the ideal of generated by all elements of degrees at least (for some, equivalently every, large ) are equal if and only if the line bundle admits a non-zero global section. We also prove a formula for the graded core of the powers of the unique homogeneous maximal ideal in a standard graded Cohen-Macaulay ring of arbitrary characteristic. Several open problems are posed whose solutions would lead to progress on a non-vanishing conjecture of Kawamata.

     

A non-singular spherically symmetric separable copy of the vacuum in SU(2) Landau gauge

We give a new non-singular spherically symmetric and separable copy of the vacuum in Landau gauge for SU(2) Yang-Mills theories. The solution can be considered as a generalization of Gribov's solution in Coulomb gauge and thus it demonstrates the similarity between vacua in Coulomb and Landau gauges.