Abstract:
The association between hemodynamic and biochemical parameters of cerebral blood flow have been studied in man, using mathematical methods of statistics. The values have been obtained through catheterization using a probe jammed at the level of the bulb of the superior jugular vein. Relationships with central hemodynamic parameters have been evaluated, including the right atrium, the right ventricle, and the left ventricle, as well as with pressure and biochemical values of the arterial bed. Data have been acquired in patients with stable arterial hypertension. Analysis of all relationship between hemodynamic and biochemical parameters has shown that the uniform hemodynamic zone: Sin.P. – SJV – SEV – the right atrium, normally participates in regulation of gaseous exchange in the human brain depending on the minimum pressure on the way of outflow from the brain. In stable arterial hypertension, this type of regulation is lost. On the basis of the results of this study, it has been concluded that blood viscosity is normally a primary controlled parameter of homeostasis. In stable arterial hypertension, homeostatic control of factors determining rheological and thrombogenic properties of blood, as well as participating in the development of brain ischemic conditions is lost. This increases risk of disturbances in central hemodynamics.

Abstract:
The present study was conducted to examine the interaction of biochemical parameters within the blood flow, their effect on the cerebral blood flow, as well as the mechanisms of cerebral ischemia by stable arterial hypertension. The hemodynamics and biochemical indicators of cerebral blood flow without the additives of the extracranial blood were obtained by the catheterization method via a probe wedged at the level of the bulb of the superior jugular vein. Sampling of the arterial blood was done in the thoracic aorta. Correlation and factor analysis of the relationship of the biochemical substances within the blood flow, and of the hemodynamic indicators of the cerebral inflow and outflow of blood were conducted by stable arterial hypertension compared with similar data of the control group. The differences thus identified led to the conclusion that by stable arterial hypertension, there is a loss of the homeostatic control of the factors determining the rheological and thrombogenic properties of the blood involved in the formation of cerebral ischemic events.

Abstract:
At long-term count rate measurements of beta sources 3H, 56Mn, 32Si, 36Cl, 60Co, 137Cs, 90Sr-90Y and decay products of 226Ra the rhythmic changes with amplitude 0.1% 0.3% from average magnitude and period 1 year, and up to 0.01 % with period about one month are detected. Magnitude of diurnal oscillations did not exceed 0.003%. Analysis of measurements data for alpha radioactive sources 238Pu and 239Pu did not reveal any statistically reliable periodic patterns. Sporadic drops in the count rate were detected while registering the activity of 54Mn, 60Co and 90Sr-90Y sources. Bursts in the count rate were registered when scanning the celestial sphere by a reflecting telescope with 60Co or 40K radioactive sources at the focus point. Possible factors underlying these deviations in beta-radioactivity are discussed.

Abstract:
The attainability problem with “asymptotic constraints” is considered. Concrete variants of this problem arise in control theory. Namely, we can consider the problem about construction and investigation of attainability domain under perturbation of traditional constraints (boundary and immediate conditions; phase constraints). The natural asymptotic analog of the usual attainability domain is attraction set, for representation of which, the Warga generalized controls can be applied. More exactly, for this, attainability domain in the class of generalized controls is constructed. This approach is similar to methods for optimal control theory (we keep in mind approximate and generalized controls of J. Warga). But, in the case of attainability problem, essential difficulties arise. Namely, here it should be constructed whole set of limits corresponding to different variants of all more precise realization of usual solutions in the sense of constraints validity. Moreover, typically, the above-mentioned control problems are infinite-dimensional. Real possibility for investigation of the arising limit sets is connected with extension of control space. For control problems with geometric constraints on the choice of programmed controls, procedure of this extensions was realized (for extremal problems) by J. Warga. More complicated situation arises in theory of impulse control. It is useful to note that, for investigation of the problem about constraints validity, it is natural to apply asymptotic approach realized in part of perturbation of standard constraints. And what is more, we can essentially generalize self notion of constraints: namely, we can consider arbitrary systems of conditions defined in terms of nonempty families of sets in the space of usual controls. Thus, constraints of asymptotic character arise.

Abstract:
In a number of experiments, when detecting particles emitted in beta decays, periodic oscillations of count rate with an amplitude up to tenths of a percent and short bursts vastly exceeding the usual count rate are found. At the same time, several experiments did not detect any differences from the “normal” course of beta decays greater than 0.01%. The article shows that the inconsistency of the experimental results is due to different measurement technique. The assumption is made of the possible participation in the beta decay processes of cosmic slow neutrinos, which makes it possible to explain in a comprehensive manner not only periodic and sporadic changes in the beta decay rate, but also a number of other incomprehensible phenomena associated with beta radioactivity. On the basis of the experiments carried out, an estimate is made of the flux density of slow cosmic neutrinos.

Abstract:
Necessary and sufficient conditions are given for the complete convergence of maximal sums of identically distributed negatively associated random variables. The conditions are expressed in terms of integrability of random variables. Proofs are based on new maximal inequalities for sums of bounded negatively associated random variables. 1. Introduction The paper by Hsu and Robbins [1] initiated a great interest to the complete convergence of sums of independent random variables. Their research was continued by Erd？s [2, 3], Spitzer [4], and Baum and Katz [5]. Kruglov et al. [6] proved two general theorems that provide sufficient conditions for the complete convergence for sums of arrays of row-wise independent random variables. In the paper of Kruglov and Volodin [7], a criterion was proved for the complete convergence of sums of independent identically distributed random variable in a rather general setting. Taylor et al. [8] and Chen et al. [9, 10] demonstrated that many known sufficient conditions for complete convergence of sums of independent random variables can be transformed to sufficient conditions for the complete convergence of sums of negatively associated random variables. Here we give necessary and sufficient conditions for the complete convergence of maximal sums of negatively associated identically distributed random variables. They resemble the criterions presented by Baum and Katz [5] and by Kruglov and Volodin [7] for the complete convergence of sums of independent identically distributed random variables. Theorems 2.3 and 2.5 are our main results. Theorem 2.3 is new even for independent random variables. In what follows we assume that all random variables under consideration are defined on a probability space We use standard notations, in particular, denotes the indicator function of a set Recall the notion of negatively associated random variables and some properties of such random variables. Definition 1.1. Random variables are called negatively associated if for any pair of nonempty disjoint subsets and of the set and for any bounded coordinate-wise increasing real functions and Random variables are negatively associated if for any random variables are negatively associated. In this definition the coordinate-wise increasing functions and may be replaced by coordinate-wise decreasing functions. Indeed, if and are coordinate-wise decreasing functions, then and are coordinate-wise increasing functions and the covariance (1.1) coincides with the covariance for and Theorem A. Let be negatively associated random variables. Then for

Abstract:
We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam are evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.

Abstract:
The effective Lagrangian of electromagnetic fields at the cubic order in field strength has been considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical energy-momentum tensors and show that they possess non-zero traces. The propagation of a linearly polarized laser beam in the external transverse magnetic field is investigated. We evaluate the induced ellipticity which allows us to obtain a constraint on parameters introduced from the PVLAS experimental data.

Abstract:
The article determines that without regard to research and suggestions of many foreign and domestic scientists who study the issue of the size of the state sector and the national estate administration, in Ukraine the effective model of state sector is not formed.As a result the country has no valid system of control of estate administration. As the existing system of management shows, the regulative functions of the state in the field of property are performed by a number of different state institutions. Though the world experience demonstrates, that it is more reasonable to deal with such matters by a unique authorized body.The article determines a number of problems related to the development of the estate administration and gives suggestions for solving the problems. Having analysed the estate system of control it is possible to draw a conclusion, that the state pattern of ownership has low efficiency. In today's terms privatization exists not only as a process of changing the proprietor but also as a separate source of receipt of funds to the state budget which enables the state to conduct certain social programs. But lately the privatization process has been complicated by the legislative innovations, namely by the necessity of privatization of the premises together with the land. Taking into account the duration of land estimation, it prolongs the procedure of privatization considerably and in addition increases the cost of the object.It should be noticed that for some time past lease, which is also one of the sources of inpayments to the state budget, has come forward as a widespread method of estate administration. Although in terms of financial crisis the demand on the objects of lease of public domain diminishes and the tendency of decrease of the market property objects of lease grows. It is therefore necessary to pay attention to the market calls and stimulate subjects of leasing relations at legislative level.As a result of analysis the steps to perfection of the existing legislative base were determined, conducting the monitoring of estate administration, acceleration of passing of the acts that regulate the sphere of estate administration.