A law of the iterated logarithm for random walk in random scenery with deterministic normalizers

LetX, X _i ,i≥1, be a sequence of independent and identically distributed ? ^d -valued random vectors. LetS _o=0 and \(S_n = \sum\nolimits_{i = 1}^n {X_i } \) forn≤1. Furthermore letY, Y(α), α∈? ^d , be independent and identically distributed ?-valued random variables, which are independent of theX _i . Let \(Z_n = \sum\nolimits_{i = 0}^n {Y(S_i )} \) . We will call (Z _n ) arandom walk in random scenery. In this paper, we consider the law of the iterated logarithm for random walk in random scenery where deterministic normalizers are utilized. For example, we show that if (S _n ) is simple, symmetric random walk in the plane,E[Y]=0 andE[Y ²]=1, then $$\mathop {\overline {\lim } }\limits_{n \to \infty } \frac{{Z_n }}{{\sqrt {2n\log (n)\log (\log (n))} }} = \sqrt {\frac{2}{\pi }} a.s.$$      

Total Synthesis of Indole and Dihydroindole Alkaloids. XVIII. Isomers and analogues of vinblastine

The synthesis and conformational analysis of (3′R)-3-hydroxyleurosidine ( 5 ), (3′S)-3-hydroxyleurosidine ( 10 ), (3′S)-3-acetoxy-4′-deoxyleurosidine ( 15 ), (3′R)-3-acetoxy-4′-deoxyleurosidine ( 23 ), (3′R)-3-acetoxy-4′-deoxyvinblastine ( 16 ), (3′S)-3-acetoxy-4′-deoxyleurosidine ( 28 ) is discussed.     

Molecular sensing of 3-chloro-1,2-propanediol by molecular imprinting

A covalent interaction-based molecularly imprinted polymer (MIP) material for 3-chloro-1,2-propanediol (3-MCPD), a post-testicular anti-fertility agent and possible carcinogen and mutagen in food products containing acid-hydrolyzed vegetable proteins, has been successfully fabricated using 4-vinylphenylboronic acid as the functional monomer. Rebinding assay revealed that the binding constant, K_B, for the receptor sites and non-specific sites are 1.93±0.1×10⁴ and 2.74±0.7×10² M⁻¹, respectively. The estimated number of receptor site, B_max, imprinted is 123.3±3 μmol/g of MIP. The MIP material is able to act as a potentiometric chemosensor for 3-MCPD via increase in Lewis acidity of the receptor sites upon reaction of the arylboronic acid with 3-MCPD to form the more acidic arylboronic acid esters. A simple pH glass electrode is sufficient to monitor the analyte-specific rebinding. In unbuffered aqueous media, linear potentiometric response from 0 to 350 ppm of 3-MCPD can be achieved. The MIP-based chemosensing in a soya sauce matrix has also been attempted. It is found that the dynamic range of the potentiometric chemosensing response of the MIP material is much reduced, probably due to the blocking or deactivation of receptor sites by interferents in soya sauces. Nevertheless, the present work demonstrated the feasibility of using MIP-based chemosensors as semi-quantitative analytical tools for screening purposes in quality control of food products.     

Sequence distribution and intramolecular excimer formation in styrene-acrylonitrile copolymers

Styrene-acrylonitrile copolymers, like many other copolymers containing styrene, exhibit both normal and excimer fluorescence. We have shown that the ratio of the excimer to monomer fluorescence intensities in random styrene-acrylonitrile copolymers is linearly dependent upon the concentration of styrene-styrene bonds in the copolymer. This observation is consistent with a photophysical model which allows the energy absorbed by styrene units to migrate freely along the copolymer chain. Some of the energy is emitted in the form of normal fluorescence; some of the energy, trapped by neighbouring styrene-styrene pairs suitably oriented to allow excimer formation, is emitted as excimer fluorescence. The fluorescence characteristics of acrylonitrile-styrene copolymers are contrasted with those of methyl methacrylate-styrene copolymers, in which the methylmethacrylate sequences are believed to present partial barriers to energy migration along the copolymer chains.