The spontaneous emission of submicronic particles from a surface of highradioactive dielectrics has been under the experimental study for the first time. Formation of disordered regions due to intrinsic irradiation and electron sputtering of surface clusters processes turned out to be responsible for the phenomenon under observation.

In this paper we construct a mathematical model of securities market. The results obtained are a good basis for an analysis of any stock market.

A new stochastic model of economy is developed that takes into account the choice of consumers are the dependent random fields. Axioms of such a model are formulated. The existence of random fields of consumer's choice and decision making by firms are proved. New notions of conditionally independent random fields and random fields of evaluation of information by consumers are introduced. Using the above mentioned random fields the random fields of consumer choice and decision making by firms are constructed. The theory of economic equilibrium is developed.

Conditions for a phase transition from the paramagnetic state to the modulated structure are found in a class of anisotropic Ising models with an external magnetic field. The critical value of the external magnetic field is obtained. Branching equations are derived and small branching theorems are proven for commensurate and incommensurate configurations. Here we consider a class of anisotropic Ising models with an external magnetic field and show a phase transition from the paramagnetic state to spatially inhomogeneous commensurate configuration or incommensurate one below the critical magnetic field. To be more exact, we illustrate the method on the ANNNI model [1,2], but one can apply it to models with an arbitrary number of interacting neighbours.Any N 1 -periodic configuration x can be expressed [3] aswhere