Vol 22, No 1-2 (2016)

In the article we prove structure theorems for spaces of cusp forms with characters of a level p. The spaces are decomposed in the direct sum of three subspaces. The first subspace is essencial. The eta-quotions play an important role in the investigations. The divisor of the functions is concentrated in cusps. The theorem about the structure of spaces of modular forms with characters is proved. We discuss the question about generators of these spaces and K.Ono’s problem. Dimensions of spaces are calculated by the Cohen — Oesterle formula, the orders in cusps are calculated by the Biagioli formula.

In this paper, we consider a problem for one-dimensional hyperbolic equation with second kind integral conditions and prove unique solvability. To prove this statement we suggest a new approach. The main idea of it is that given nonlocal integral condition is equivalent with a different condition, nonlocal as well but this new condition enables us to introduce a definition of a generalized solution bazed on an integral identity and derive a priori estimates of a required solution in Sobolev space. This approach shows that integral conditions are closely connected with dynamical conditions.

The paper considers the problem of injecting gas into the porous layer initially saturated with gas and water, accompanied by formation of hydrate. We have investigated case where the intensity of hydrate is limited by diffusion of water through the hydrate layer formed between water and gas in the core of the pore of the channel. As part of this scheme kinetics of hydrate is determined one empirical parameter D having the dimension of the diffusion coefficient (m²/s). We have analyzed effect of the value of this parameter on the features of the process of hydrate formation, depending on the parameters that define the initial state of porous reservoir and reservoir characteristics.

This work is aimed for justification of quantitative effect of radiation defect concentration decreasing in materials depending on density of edge dislocation which are their outlet. The results of defect kinetics modeling with taking into account their recombination on dislocation loops, edge dislocations and pores are given. The summery of this work is useful in the frame of solving problem of decreasing radiation swelling and material properties degradation during neutron irradiation.

We have discussed the development of models of dynamics of formation of reserves juveniles from natural spawning sturgeon Acipenser gueldenstaedtii of theCaspian Seaon historical data. Working hypotheses are based on the graph conceptual scheme aimed chain links. Structuring multivariate analytical conclusions about the quality of the interaction of 12 natural and anthropogenic factors in the ecosystem of the Caspian Sea have allowed us to recharge from the general ideas of the theory on to describe the specific situation of the tragic consequences of overfishing of anadromous fish with a long lifecycle. Reducing the word was swiftly enough and not consistent with the expectations of the replenishment of stocks by artificial reproduction. Dedicated contact circuit pulse propagation cognitive digraph where arcs contains the power of influence, says an indirect strengthening of action depends on the density of mortality. Interestingly, the relationship did not have a permanent independent sign «+» or «–». Recessions manifested dramatically on both boundaries of the range of optimum number of spawning manufacturers. Perhaps the decline in the efficiency of the reproduction right of the balance associated with the migration routes overlap. It is more intense withdrawal of fish more prolific race hibernating until spring in the river. The model takes into account the additional effect of increasing variations in the pace of development of the size on the survival of migrating hatchery. The system of differential equations is investigated in an iterative discrete continuous hybrid form with alternative position of equilibrium trajectory. One of the equilibrium is unstable, and is the starting point for the degradation of reproductive activity. The proposed model of reproduction under supercritical level seizures shows subtle transition from the brink of fading fluctuation to the permanent historical perspective depletion, the way into the Red Book.