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आयतन 9, मुद्दा 6 (2020)


On H-Open Sets and H-Continuous Functions

Fadhil Abbas

The aim of this paper is to introduce a new class of open sets called h-open sets. Also, introduce and study topological properties of h-interior, h-closure, h-limit points,

h-derived, h-interior points, h-border, h-frontier and h-exterior by using the concept of h-open sets. Moreover introduce the notion of h-continuous functions, h-open

functions, h-irresolute functions, h-totally continuous functions, h-contra-continuous functions, h-homeomorphism and investigate some properties of these functions

and study some properties, remarks related to them


The Optimal Tax Model

Valeria Bondarenko

In this paper we analyze and propose new method and algorithm of selecting the optimal labor time as a function of skills following our main references. The optimal

labor time is a situation when the utility function of individual reaches a maximum. One of the main differences with is our algorithm for creation the skill distribution.

Saez proposed and considered the distribution of skills with using empirical distribution of income and the approximation the labor income tax by linear model. The

author proved that with using the presented utility function of consumption and labor effort, it will be possible to obtain some level of skills which will be adaptable with

observed (public information) taxable revenue which corresponds proposed linear tax schedule


Intuitionistic Fuzzy Ideals Supra Topological Spaces

Fadhil Abbas

In this paper we introduce the notion of intuitionistic fuzzy ideals in intuitionistic fuzzy supra topological spaces. The concept of an intuitionistic fuzzy s-local function is

also introduced here by utilizing the s-neighbourhood structure for an intuitionistic fuzzy supra topological space. These concepts are discussed with a view to find new

intuitionistic fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated intuitionistic fuzzy supra topologies and several

relations between different intuitionistic fuzzy ideals and intuitionistic fuzzy supra topologies are also studied here. Moreover, we introduce an intuitionistic fuzzy set




and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy

-supra dense-in-itself sets, fuzzy S

-supra closed

sets, fuzzy

-supra perfect sets, fuzzy regular-I-supra closed sets, fuzzyI-supra open sets, fuzzy semi-I-supra open sets, fuzzy pre-I-supra open sets, fuzzy



open sets, fuzzy


-I-supra open sets) and study some characteristics of theses sets and then we introduce some fuzzy ideal supra continuous functions


The Stability of a Oscillating Rotating Streaming Fluid Jet with an Self-Gravitating Force

Hamdy M. Barakat*

The stability of a oscillating rotating streaming fluid jet with an self-gravitating force is discussed. The problem is formulated and the basic equations are solved. A general Eigen-value relation is derived studied analytically and results are confirmed numerically. The fluid jet is purely stable in the non-ax symmetric perturbation while in the ax symmetric mode it is unstable for small wave number. The streaming has the effect of reducing the stable states not only in the ax symmetric mode but also in those of non-ax symmetric. The self-gravitating force is destabilizing only in the symmetric mode (m=0) for a small range of wave numbers, but it is stabilizing for all other perturbation. This phenomenon is interest, academically and during the geological drilling in the crust of the earth as we have superposed gas-oil layer mixture fluids. The stability behavior of the model comes after destabilizing behavior of the model when it be reduced and suppressed.


The Fundamental Principles of Gyroscope Theory

Ryspek Usubamatov* and Marek Bergander

Beginning from the Industrial Revolution, outstanding and ordinary scientists of the past and present time tried to formulate mathematically the dynamics of rotating objects. However, only the famous mathematician L. Euler expressed one component of the dynamics of a rotating body which is presented by the change in the angular momentum or precession torque. To date, his decision in publications presented as a fundamental principle of the gyroscope theory. Other scientists and researchers presented intuitive interpretations of the gyroscopic effects without mathematical models. All scientists considered the forces and motion acting on the spinning disc, which is the simplest mechanism in classical mechanics that created so many problems for a long time. This is an unusual phenomenon in the physics of mechanics, in which analytical methods enable us to solve more complex problems than inertial forces acting on a simple spinning disc

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