# Natural sciences

Number of the journal, №: 2017. № 1

Annotation:
The article deals with the application of information and communication technologies in the teaching of mathematics. These technologies contribute to the development of independent thinking, help to rationally use time, form interdisciplinary communication.

The application of combinatorics to the solution of certain tasks

Annotation: This article reveals the possibility of solving life situations with combinatorial coefficients and shows the practicality of applying formulas on the theory of probability and mathematical statistics. The solution of tasks with combinatorial coefficients consists mainly in the decomposition of these coefficients by the basic formulas and their manipulations.

Number of the journal, №: 2016. № 4

Research of one numerical series

Annotation: In the paper, we consider some fractional and irrational expressions, and prove the assertion that leads them to fractional and rational expressions, and also consider one general lower and upper bound (two-sided estimate) for a one numerical series. In obtaining some congruencies, we used the formula for binomial coefficients, then from the sum of the left side we cancel each other, and the summons with even numbers, where everywhere in an even degree in an uneven degree are doubled even after multiplier was put outside, all the summons remain free from the square root. Several variants of proofs are considered in the solution of certain problems and theorems.

Some examples of the application of complex numbers in geometry

Annotation: The article deals with the geometric interpretation of complex numbers, the possibilities of applying a transformation of the plane, and examples of solving problems.

Number of the journal, №: 2016. № 3

Graphite laminated materials strength properties and energy characteristics of polymer binders

Annotation:
The approach which was proposed earlier for composite materials strength prediction using

contact angle measurements was applied for graphite laminated materials. It was shown that the calculation of

the work of adhesion to polar and non-polar model liquids can be applied to the choice of polymer binder.

Some processes of irrational rationalization and two-sided evaluation of a single number series

Annotation: In this article we consider some fractional-irrational expressions and prove the assertion that reduce them to fractional-rational expressions and also consider one general lower-and-upper bound (two-sided estimate) for one numerical series.

Number of the journal, №: 2015. № 2

Methods of integro-differential equations solution.

Annotation:
This article is intended for those who are faced with the task of the integro-differential equation solution

where y(x) is the desired function, K(x, t) and f(x) are known functions defined on the interval [a, b]. To solve

the integro-differential equation, in the article it is first encouraged to review the definitions and theorems of

integral-differential equations. Next, methods of integral-differential equations solution and some examples of

their solution are considered

On solution of geometric problems with a complex figure

Annotation:
In the article it is highlighted a unconventional approach to problem solving method with ambiguous

geometry figure in a school course allowing a complex figure according to the source data. Some problems of

this type are presented; the different approaches to drawing of each figure to each of these problems are sited;

tips on their solution are given. The interpretation of these problems applying The Geometer's Sketchpad

developed by Nicholas Jackiw and Scott Steketee should draw the interest of teachers and students.

Antimicrobial effects of natural honey

Annotation:
This article is written in line with the important questions on antimicrobial effects of natural honey

against gram-positive bacteria to reveal the therapeutic properties. These circumstances demonstrate the

medical and social significance of solving the science-oriented task of developing high-quality pharmaceutical

product on the basis of honey as well as its application not only as a preventive and medicinal agent to treat

many illnesses but also as in beauty treatment.

Number of the journal, №: 2014. № 3

Outstanding German researches of mountains of Kazakhstan

Annotation:
Activity of German scientists who explored mountain systems of Kazakhstan and Russia is considered in

the article. Scientific biographies of P.S. Pallas and H. Merzbacher is presented.