జర్నల్ ఆఫ్ జెనరలైజ్డ్ లై థియరీ అండ్ అప్లికేషన్స్

The automorphism groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.

In the work different fields of applications of mathematics are examined, namely: Mathematics and music, Mathematics and education, Mathematics and sport, Mathematics and modern technologies. The purpose of this work is to demonstrate on particular examples, the way mathematics has penetrated all spheres of human activities, in one form or another. The use of mathematics in sports is represented by the example of basketball (strategy and tactics of the game, calculation of results). Mathematics in music reveals itself in symmetry, euphony and the construction of scales. The application of mathematics in education is exemplified by the development of the schools of ancient Greece and Rome and schools of a later period. The relation of Mathematics with modern life is shown in the section “Mathematics and modern technologies”. Computing heavily relies on mathematics. Such algebras as elementary, abstract and Boolean are the most commonly used in coding. Mathematics is also applied in scientific software. Mathematics together with computers assists in physics, chemistry, biology, geology and even mathematics themselves. Computers are also used to teach mathematics to children. Thousands of programs are designed to help children with mathematics.

It is difficult to name at least one kind of human activity which is not related to mathematics anyhow. Of course, it is impossible to disclose all the spheres of application of mathematics in one work, but the students used the analytical and research approach to the given task, and the corresponding conclusions were formulated by them.

In this paper we prove that left multiplicative generalized Jordan derivation and left multiplicative generalized Jordan triple derivation of 2-torsion free semiprime rings are left multiplicative generalized derivation.

Magnetohydrodynamic and chemical reaction effects of variable viscosity on heat generation and mass transfer viscous dissipation fluid in the presence of suction/injection through porosity is solved numerically. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. Finally, numerical results are presented for velocity, temperature and concentration profiles for different parameters of the problem are studied. In addition, the effects of the pertinent parameters on the skin friction, the rate of heat transfer and mass fluxes are also discussed numerically.