### ON THE CORRECTNESS OF INVERSE PROBLEM OF DETERMINING COUPLE {u, σ} IN THE CASE OF A SIMPLE EQUATION FOR THE TRANSFER OF RADIATION

The article outlines the main research questions of the local properties of the collision integral and classical solutions of non-stationary radiative transfer equation, considered in the plain area of R3.

The paper studied and proved the correctness of questions “in the large” number of inverse problems for nonstationary transport equation, considered in a limited plain area of R3, for the simultaneous determination of the pair {u, σ}.

We present the smoothness of the area under consideration, taking into account the area of the prostate, to prove the lemma 1-4, on the basis of the lemma is proved Theorem 1.

Read More### ABOUT THE SPEED OF GRAVITY

The work describes a method to evaluate the speed of gravity interaction using space debris and asteroids. It demonstrates a technical implementation opportunity. Tentative analysis of experimental findings shows Newton’s model can be used in space navigation. The advantage of Newton’s model is confirmed by a seasonal deviation of a number of satellites from their expected location, as detected by a specialized laser location facility in Crimea, which provides high-precision detection of laser impulse direction. This deviation can be explained by Earth’s shift along the orbit while the light travels from the Sun to Earth.

Read More### A METHOD OF FORECASTING THE MOVEMENT OF MATTER

The article considers methods to forecast accelerated inertial movement of items, based on the understanding of the speed of gravity, which is much higher than the speed of light, and “the rain effect”. It offers a possible explanation for thirty phenomena of yet unexplained nature. These phenomena include accelerated expansion of the University; the increase in distance between the Sun and the center of the galaxy, between the Earth and the Moon; uniform explanation of experiments by Michaelson, Sagnac, Fizeau, Bradley; higher rotational speed at the equators of the Sun, Jupiter, Saturn compared to polar areas; spontaneous microparticle disintegration; tunnel effect; abrupt change in inertia moment on cooling solid helium, etc.

Read More### ABOUT SOME EXPERIMENTALLY FOUND OUT EFFECTS OF MICROWAVE RADIATION ON WHEAT

The experimental research results of the wheat seeds germination intensity dependence on the frequency of the external microwave radiation are considered. The experimental method consisted in the microwave irradiation with the given parameters of water, that in consequence soaked the wheat grains. As a experimental result the fact of microwave radiation influence on wheat seeds are established. It is shown the maximum positive effect of this wheat grain effect method was observed at frequency 8.9 GHz.

Read More### A NEW METHOD TO TRANSFORM SYSTEMS OF INEQUALITIES TO FIND THE INTERPOLATION OF MARTINGALE MEASURES

For one-step model of stochastic basis a random process is considered where is a trivial -field, and is a -field generated by a countable number of atoms. It is assumed that takes four different values , where either (this process admits an infinite number of martingale measures). This article takes up such martingale measures that satisfy the weakened noncoincidence barycenter condition (WNBC), – condition that makes it possible to interpolate with such martingale measure incomplete market to completel with respect to arbitrary interpolating special Haar filtering.

A new method of proof of the existence of the interpolation martingale measures is presented in the article. It is based on the replacement of complex inequalities of the WNBC that contains various undefined subsets of the set of natural numbers, into more simple inequalities containing specific components of martingale measures. In this article we obtain sufficient conditions on market parameters, which ensure the existence of a martingale measure.

The obtained results can be the basis for the algorithm and software complex. The program based on the method will allow to apply special Haar interpolations method to the calculations on the arbitrage-free financial markets, which will greatly facilitate the choice of optimal strategies of investors in the financial markets.

### OPTIMIZATION OF QUASI-LINEAR MODELS OF SYSTEMS WITH TWO STRUCTURES AND INDEPENDENT PRIORITIES

Explanation and mathematical model of the problem of optimal decision making is presented in the case when two independent priorities are distributed among two competing structures interacting in a single system. A model of quasi-linear type with independent priorities is investigated. Conditions of existence and uniqueness of points of global maximum and description of these points are given. Specific situations where sufficient conditions for the existence of extremum are not fulfilled or are fulfilled for only one of the priorities are considered. An example in the case of constant priorities is given.

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