Necessary first-order conditions for optimal crossing of a given region

We consider a nonlinear optimal control problem with an integral functional in which the integrand is the characteristic function of a closed set in the phase space. An approximation method is applied to prove the necessary conditions of optimality in the form of a Pontryagin maximum principle without any prior assumptions on the behavior of the optimal trajectory. Similarly to phase-constrained problems, we derive conditions of nondegeneracy and pointwise nontriviality of the maximum principle. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 179–204, 2004.     

Developing methods for observing processes induced by femtosecond laser pulses with high spatiotemporal resolution

A combination of femtosecond laser techniques and nanomicroscopy creates promising new possibilities for studying both matter and a whole number of ultrafast physical processes. The results obtained at the Institute for Spectroscopy as a result of developing a new area of femtosecond nanomicroscopy are presented.     

Thermodynamics of electrostatic forces interaction in concentrated electrolyte solutions

The potential of interactions of particles in concentrated solutions of electrolytes in the steady state is calculated taking into account the electrostatic and solvation (hydration) interactions and weak chemical bonding between the hydration shells.     

Formation of nanolocalized tungsten photoion packets by femtosecond laser pulses

Nanolocalized ion packets have been produced due to the transmission of photoions, which are emitted from a refractory metal emitter irradiated by femtosecond laser radiation with a high repetition rate, through a quartz nanocapillary. With the use of such a pulsed nanobeam, a miniature ion microscope has been created and the image of a dielectric-nanoaperture fragment has been obtained.     

Formation of extended periodic microstructures by “Point” irradiation of gold film by femtosecond laser pulses

Extended periodic microstructures are formed on a thin gold film by femtosecond laser radiation. The structure length is an order of magnitude larger than the typical size of the irradiated region. The detection of gold photoions generated in the process of the microstructuring ensures a high-sensitivity on-line diagnostics of this phenomenon.     

Photochemical oxidation of persistent cyanide-related compounds

Russian Journal of Physical Chemistry A - Kinetic regularities of the photolysis of thiocyanate solutions using of mono- and polychromatic UV radiation sources with different spectral ranges are...     

A quasiconformal analog of Carathéodory’s criterion for the Möbius property of mappings

In 1937, Carathéodory proved that every injective mapping f: G → f(G) ? $\bar C$ of a domain G ? $\bar C$ , taking circles to circles, is Möbius. The present article shows that if each injective mapping takes circles onto k-quasicircles then it is K-quasiconformal with $K \leqslant k + \sqrt {k^2 - 1} $ .     

On Selfsimilar Jordan Curves on the Plane

We study the attractors of a finite system of planar contraction similarities S _j (j=1,...,n) satisfying the coupling condition: for a set {x ₀,...,x _n} of points and a binary vector (s ₁,...,s _n ), called the signature, the mapping S _j takes the pair {x ₀,x _n} either into the pair {x _j-1,x _j } (if s _j =0) or into the pair {x _j , x _j-1} (if s _j =1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis.