Abstract:
As we know if D is a complete X-semilattice of unions then semigroup Bx(D)possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups B_{x}(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑_{2}(X,8) . Because the semilattice Q of the class ∑_{2}(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .

Abstract:
The paper gives description of regular elements of the semigroup B_{ X } (D) which are defined by semilattices of the class Σ_{2} (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B_{ X } (D) which is defined by semilattices of the class Σ_{2} (X, 8).

Abstract:
In this paper we give a full description of idempotent elements of the semigroup B_{X} (D), which are defined by semilattices of the class ∑_{1} (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.

Abstract:
Although it is well known that cloud cavitation shows unsteady behavior with the growing motion of an attached cavity, the shedding motion of a cloud, the collapsing motion of the cloud shed downstream and a reentrant motion in flow fields such as on a 2-D hydrofoil and in a convergent- divergent channel with a rectangular cross-section, observations for the periodic behavior of cloud cavitation in a cylindrical nozzle with a convergent-divergent part, which is mainly used in an industrial field, have hardly been conducted. From engineering viewpoints, it is important to elucidate the mechanism of periodic cavitation behavior in a cylindrical nozzle. In this study, a high-speed observation technique with an image analysis technique was applied to the cloud cavitation behavior in the nozzle to make clear the mechanism of unsteady behavior. As a result, it was observed in the nozzle that the periodic behavior occurs in the cloud cavitation and pressure waves form at the collapse of clouds shed downstream. Also, it was found through the image analysis based on the present technique that the pressure wave plays a role as a trigger mechanism to cause a reentrant motion at the downstream end of an attached cavity.

Abstract:
This
note provides the closed-form solution for the model by Lazear [1]. The employer adjusts
the performance standard for promotion when the employer observes only the
imperfect index of the employee’s ability. The adjustment margin is larger when
the performance depends heavily on luck and depends lightly on the employee’s
ability.

This
study aims to propose a method for quantitatively evaluating the influence
which the obstruction of sea breezes by clusters of high-rise buildings has on
the urban heat island effect using a weather simulation model and Geographic
Information Systems (GIS). Specifically, a method of evaluating the influence
of the obstruction of sea breeze by high-rise buildings on the urban heat
island effect was proposed. In the method, two scenarios that imagine urban
forms which differ with regard to whether or not they contain high-rise
buildings are created and weather simulation is conducted, and the results of
the simulations are comparatively analyzed focusing on temperature and wind
speed. Evaluation was conducted in two stages, and Shiodome of Minato City in
the Tokyo Metropolis was selected as the region for evaluation. In two stages
of evaluation, a rise in temperature of approximately 0.3 K and a reduction in
wind speed of approximately 1 m/s were observed in a region approximately five
to ten kilometers square downwind of high-rise buildings in the period 6 PM to
9 PM, and a higher temperature caused by the obstruction of sea breeze by
high-rise buildings was identified. The fact that such a higher temperature was
confirmed in the time period from 6 PM onwards, in which the temperature
decreases, reveals that obstruction of sea breeze by high-rise buildings dulls
the decrease in temperature which occurs from evening onwards, and influences
nighttime urban heat island formation.

Abstract:
Public management can and should be taught. Former Soviet Republics, including Georgia are facing this acute problem. Some attention is directed to management training, but public management stays in the background, although it is evident that major political and economic problems of Georgia and other countries of so-called “fledging democracies” arise due to the government theory neglect. The article considers development of administrative way of thinking starting from political doctrine to managerial approach, prospects for public management principles development, existing educational models. The epoch of classic universities is passing; with the help of textbooks students can only make courseworks. That’s why the use of innovative methods is necessary for students training.

Abstract:
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we consider the problem of nonparametric estimation of $f$ from low frequency observations from $X.$ The estimator of $f$ is constructed via Fourier inversion and kernel smoothing. Our main result deals with asymptotic normality of the proposed estimator at a fixed point.

Abstract:
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions becomes an entire function. Moreover, as an example of such functions, we study a function called Poincare function.

Abstract:
Given a discrete time sample $X_1,... X_n$ from a L\'evy process $X=(X_t)_{t\geq 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\gamma,\sigma^2,\rho)$ corresponding to the process $X.$ Based on Fourier inversion and kernel smoothing, we propose estimators of $\gamma,\sigma^2$ and $\rho$ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of $\gamma$ and $\sigma^2$ and an upper bound on the mean integrated square error of an estimator of $\rho.$