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[Dimovski Ivan H.; Димовски Иван Х.]; [Spiridonova Margarita; Спиридонова Маргарита An approach to obtaining periodic and mean-periodic solutions of Linear Ordinary Dierential Equation (LODE) with constant coefficients is presented. The use of the Computer Algebra System (CAS) Mathematica for practical application of this approach is considered.

[Davidov Johann; Давидов Йохан]; [Ul Haq Absar; Ул Хак Абсар]; [Mushkarov Oleg; Muškarov Oleg; Мушкаров Олег] Every Walker 4-manifold M, endowed with a canonical neutral metric, admits a specific almost complex structure called proper. In this note we find the conditions under which a proper almost complex structure is harmonic in the sense of C. Wood and as a section of the bundle End(TM). 2000 Mathematics Subject Classification: Primary 53C15, Secondary 53C42, 53C43.

[Davidov Johann; Давидов Йохан] A manifold with an irreducible SО(3)-structure is a 5-manifold M whose structure group can be reduced to the group SО(3), non-standardly imbedded in SО(5). The study of such manifolds has been initiated by M. Bobieński and P. Nurowski who, in particular, have shown that one can define four СR-structures on a twistor-like 7-dimensional space associated to M. In the present paper it is observed that these CR-structures are induced by almost contact metric structures. The purpose of the paper is to study the problem of normality of these structures. The main result gives necessary and sufficient condition for normality in geometric terms of the base manifold M. Examples illustrating this result are presented at the end of the paper. 2000 Mathematics Subject Classification: 53C28; 53D15; 53B15.

[Rusev Peter; Russev Peter; Russev P.; Русев Петр; Русев Петър] It is shown that the use of the classical Taylor formula for obtaining sufficient conditions for existence of local extrema of real functions of real variables and for expanding the familiar elementary functions of a real variable in power series can be avoided. Suitable examples demonstrate the significance of this formula in other parts of the classical analysis.

[Apostolova Lilia N.; Apostolova Lilia Nik.; Апостолова Лилия Н.; Апостолова Лилия Ник.] Square roots of bicomplex number are found. Quadratic equation of bicomplex variable is solved. MS 2010 Classification: 30С10, 32A30, 30G35.

[Rusev Peter; Russev Peter; Russev P.; Русев Петр; Русев Петър]

[Kiryakova Virginia; Кирякова Виржиния]

Every almost Hermitian structure $(g,J)$ on a four-manifold $M$ determines a hypersurface $\Sigma_J$ in the (positive) twistor space of $(M,g)$ consisting of the complex structures anti-commuting with $J$. In this note we find the conditions under which $\Sigma_J$ is minimal with respect to a natural Riemannian metric on the twistor space in the cases when $J$ is integrable or symplectic. Several examples illustrating the obtained results are also discussed., Comment: 16 pages, typos corrected