Almost sure asymptotics for the continuous parabolic Anderson model

We consider the parabolic Anderson problem ∂ _t u = κΔu + ξ(x)u on ℝ₊×ℝ ^d with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constant and ξ is a random homogeneous potential. We concentrate on the two important cases of a Gaussian potential and a shot noise Poisson potential. Under some mild regularity assumptions, we derive the second-order term of the almost sure asymptotics of u(t, 0) as t→∞. Received: 26 July 1999 / Revised version: 6 April 2000 / Published online: 22 November 2000     

Amine-Reactive BODIPY Dye: Spectral Properties and Application for Protein Labeling

A boron-dipyrromethene (BODIPY) derivative reactive towards amino groups of proteins (NHS-Ph-BODIPY) was synthesized. Spectroscopic and photophysical properties of amine-reactive NHS-Ph-BODIPY and its non-reactive precursor (COOH-Ph-BODIPY) in a number of organic solvents were investigated. Both fluorescent dyes were characterized by green absorption (521–532 nm) and fluorescence (538–552 nm) and medium molar absorption coefficients (46,500–118,500 M⁻¹·cm⁻¹) and fluorescence quantum yields (0.32 – 0.73). Solvent polarizability and dipolarity were found to play a crucial role in solvent effects on COOH-Ph-BODIPY and NHS-Ph-BODIPY absorption and emission bands maxima. Quantum-chemical calculations were used to show why solvent polarizability and dipolarity are important as well as to understand how the nature of the substituent affects spectroscopic properties of the fluorescent dyes. NHS-Ph-BODIPY was used for fluorescent labeling of a number of proteins. Conjugation of NHS-Ph-BODIPY with bovine serum albumin (BSA) resulted in bathochromic shifts of absorption and emission bands and noticeable fluorescence quenching (about 1.5 times). It was demonstrated that the sensitivity of BSA detection with NHS-Ph-BODIPY was up to eight times higher than with Coomassie brilliant blue while the sensitivity of PII-like protein PotN (PotN) detection with NHS-Ph-BODIPY and Coomassie brilliant blue was almost the same. On the basis of the molecular docking results, the most probable binding sites of NHS-Ph-BODIPY in BSA and PotN and the corresponding binding free energies were estimated.     

Elementary Definability of the Class of Universal Planar Automata in the Class of Semigroups

Siberian Mathematical Journal - Universal planar automata are universal attracting objects in the category of semigroup automata whose set of states and set of output signals are equipped with...     

Effect of surface semichanneling on energy distributions of molecular ions reflected from single-crystal surface

Regularities in the energy distributions of molecular nitrogen ions reflected from (100)Cu crystal face are studied. The half-widths (FWHM) of the energy distributions of the reflected ions have been found to vary strongly near aligned orientations of the target with respect to the bombarding ion beam. A relationship has been found between the survival fraction of reflected molecular ions and the effect of ion focusing in surface semichanneling.     

Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

It is proven that the absolutely continuous spectrum of matrix Schrödinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The same result is also proven for some classes of slower decaying potentials if they are smooth.     

Study of the OZI selection rule in hadronic processes

In the experiments with LEPTON-F and SPHINX spectrometers the pion-induced charged exchange reactions π- + p → ? + n and π- + p → ω + n at Pπ-=32.5 GeV, as well as proton-induced diffractive reactions p + N → [p?] + N and p + N → [pω] + N at E _p =70 GeV were studied. The comparison of the cross-sections for ? and ω-production in these reactions is used for testing the OZI selection rule in hadronic processes. It has been demonstrated that in pion reactions the ratio of the yields of ? and ω-mesons R(?/ω) = (3 ± 1) · 10^?3 is in a good agreement with naive quark model prediction based on the mixing in vector meson nonet and on the OZI rule (R(?/ω)ozi = tg ²Δθ _V ? 4 · 10^?3). At the same time in proton reactions the effective ratio of ? and ω yields is ～ (4 ÷ 7) · 10^-2, i.e. a strong violation of the OZI rule is observed in proton-nucleon interactions. This violation can be in favor of possible existence of some exotic ss? component in the quark structure of protons.     

Divergent fourier series: Numerical experiments

An open problem in the theory of Fourier series is whether there are functions f L ₁ such that the partial sums S _n(f, x) diverge faster than log log n, almost everywhere in x. For a class of particularly bad functions Kahane proved that the rate of divergence is faster than o(log log n). We give here a probabilistic interpretation of the Kahane result, which shows that the record values of the sums S _n(f, x) should behave essentially as the record values of a sequence of independent identically distributed random variables, for which we deduce the divergence rate log log n. Numerical computation is in good agreement with the prediction. One can argue that the Kahane examples are in some sense optimal, and conclude that, under this assumption, ...(log log n) is the highest possible rate for divergence almost everywhere of the Fourier partial sums for L ₁ functions.     

Highly efficient and stereoselective cycloaddition of nitrones to indolyl- and pyrrolylacrylates

The reactions of various nitrones with indolyl- and pyrrolylacrylates proceeds regioselectively with high diastereoselectivity in the case of aldonitrones, and represents an effective method for obtaining new indolyl- and pyrrolyl-substituted isoxazolidine carboxylates stabilized by weak (CH?O) and moderate (NH?N) strength intramolecular hydrogen bonding. The resulting cycloadducts exhibit promising in vitro anti-influenza activities.