Изучается геометрия кубических дифференциальных уравнений Абеля, задан- ных на одномерной вещественной кривой. Доказывается, что каждое такое уравнение яв- ляется ядром некоторого нелинейного дифференциального оператора, который в своюоче- редь задается кубикой на распределении Картана пространства 1-джетов. С помощьюэтого соображения строится контактно-инвариантная {e}-структура, ассоциированная с невырож- денным кубическим уравнением Абеля. Также приводится контактная классификация таких уравнений.

In this paper, we analyze an unreliable queueing system consisting of an infinite buffer and two heterogeneous servers. The main server (server 1) is unreliable, while the server 2 is considered as the reserve server and is assumed to be absolutely reliable. The service times have the PH-type (Phase-type) distribution. If both servers are able to provide the service, they serve a customer independently of each other. The service of a customer is completed when his/her service by any of two servers is finished. After the service completion, both servers immediately start the service of the next customer, if he/she presents in the system. If the system is idle, the servers wait for arrival of the new customer. The input flow is described by the BMAP (Batch Markovian Arrival Process). Breakdowns arrive to the server 1 according to a MAP (Markovian Arrival Process). After breakdown occurrence, repair of the server starts. The repair time also has the PH-type (Phase-type) distribution. The customers, which meet the servers busy upon arrival, join a buffer. They will be picked up for the service according to the First-In-First-Out discipline. The customers arrived at the same batch are picked up for the service in random order. If a customer arriving from outside or from a buffer sees only server 2 ready for service while the server 1 is under repair, only server 2 starts the service of this customer. But if server 1 is repaired before service completion of this customer, server 1 immediately begins the service of this customer. For this model, we derive ergodicity condition, calculate the key performance measures of the system and derive an expression for the Laplace-Stieltjes transform of the sojourn time distribution of an arbitrary customer.

Journal of Applied Spectroscopy v.78, #5, 2011 Resonant light-scattering spectra of molecules with double-well vibrational potentials by V. A. Morozov; Yu. M. Dubina (624-630). Examples of excitation spectra lines for resonant Rayleigh and Raman scattering by model molecules with a double-well potential in a vibrational subsystem in both the ground and excited states are calculated based on numerical solutions of a stationary Schrodinger equation for a particle in a double-well potential. The obtained results demonstrate that the given formalism can be used, e.g., to establish the mechanism for transferring the proton of an intramolecular H-bond in the excited molecular electronic state upon monochromatic irradiation using resonant light-scattering spectroscopic data. Keywords: excitation spectra of resonant scattering lines; Rayleigh and Raman scattering; double-well potential; hydrogen bond; proton transfer

A method for the rapid separate measurement of the vectors of jointly acting harmonic signals using frequencydependent sampling and summation of the samples is considered. A theoretical justification of the method is given and the measurement errors and the possibility of realizing the method in practice are discussed.

In order to measure aqueous solution concentration, radio frequency resonator sensors based on sections of a long line are proposed: two-conductor, coaxial and screened with a U-shaped inner conductor. Specific sensor structural features and the contents of their radio frequency measuring devices are described. Results are provided for experimental confirmation of the efficiency of these sensors for measuring the concentration of various two-component liquids with losses.