Nonspecific solvation and oscillator strengths for the long-wavelength vibronic absorption band of 4-dimethylaminochalcone solutions

The 4-dimethylaminochalcone molecule is one of the most efficient spectral-luminescent probes widely used in various medical and biological studies. Experimental data on the oscillator strengths in the long-wavelength vibronic band of 4-dimethylaminochalcone solutions in a series of individual solvents of different chemical nature are analyzed using the earlier derived refined equation describing the influence of nonspecific solvation processes on the matrix elements of the dipole moment of a purely electronic transition in organic dye molecules. It is shown that the semiempirical theory developed gives a satisfactory quantitative explanation to experimentally observed regularities indicative of a relatively weak influence of the solvent reaction field (orientation and induction forces) and dispersion interactions on the integrated intensity of the studied band belonging in the category of intramolecular charge transfer bands.     

The last subconstituent of the Hemmeter graph

We prove that when q is any odd prime power, the distance-2 graph on the set of vertices at maximal distance D from any fixed vertex of the Hemmeter graph Hem_D(q) is isomorphic to the graph Quad_D-1(q) of quadratic forms on .     

Reversible Modulation of Surface Plasmons in Gold Nanoparticles Enabled by Surface Redox Chemistry

Switchable surface redox chemistry is demonstrated in gold@iron/iron oxide core–shell nanoparticles with ambient oxidation and plasmon‐mediated reduction to modulate the oxidation state of shell layers. The iron shell can be oxidized to iron oxide through ambient oxidation, leading to an enhancement and red‐shift of the gold surface plasmon resonance (SPR). This enhanced gold SPR can drive reduction of the iron oxide shell under broadband illumination to reversibly blue‐shift and significantly dampen gold SPR absorption. The observed phenomena provide a unique mechanism for controlling the plasmonic properties and surface chemistry of small metal nanoparticles.     

On Asymptotics of Solutions of Nonlinear Differential Equations of the Second Order

We study the problem of asymptotics of unbounded solutions of differential equations of the form y″ = α₀ p(t)ϕ(y), where α₀ ∈ {−1, 1}, p: [a, ω[→]0, +∞[, −∞ < a < ω ≤ +∞, is a continuous function, and ϕ: [y ₀, +∞[→]0, +∞[ is a twice continuously differentiable function close to a power function in a certain sense.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 18–28, January–March, 2005.     

Decentralized optimal control of dynamical systems under uncertainty

The problem of optimal control of a group of interconnected dynamical objects under uncertainty is considered. The cases are examined in which the centralized control of the group of objects is impossible due to delay in the channel for information exchange between the group members. Optimal self-control algorithms in real time for each dynamical object are proposed. Various types of a priori and current information about the behavior of the group members and about uncertainties in the system are examined. The proposed methods supplement the earlier developed optimal control methods for an individual dynamical system and the methods of decentralized optimal control of deterministic objects. The results are illustrated with examples.