The Relativistic Linear Singular Oscillator

Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised taking into account referees suggestions

ICAR: endoscopic skull‐base surgery

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Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered

Effect of some factors on microbiota vitality and its reflection on the gut

The presence of microbiota in the Gut is very essential in the digestion process, and some factors may cause dysfunction in their activity. This review study is focused on effect of four factors on gut microbiota function, which includes ; intake of, antibiotics, alcohol, smoking, and mental issues such as; depression, anxiety, tension. The study went through the findings of a lot of researchers and came up with some conclusions such as; incorrect using of the antibiotics affect the functions of the GI microbiota causing disorder in the digestion system, Smoking cause disease in different organs, affecting the general health of the human being which reflect on nutrition and digestion, alcohol effects microbiota leading to liver fibrosis, hepatitis that effects digestion system