Scientific Research Publishing

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52590#.VJujVcCAM4 Author(s)    Ismail Ibragimovich Safarov , Maqsud Sharipovich Akhmedov , Zafar Ihterovich Boltaev Affiliation(s) Bukhara Technological-Institute of Engineering, Bukhara, Republic of Uzbekistan . ABSTRACT The main features are the length of the waveguide in one direction, as well as limitations and localization of the wave beam in other areas. There is described the technique of the solution of tasks on distribution of waves in an infinite cylindrical waveguide with a radial crack. Also numerical results are given in the article. Viscous properties of the material are taken into account by means of an i...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=51410#.VGlR1WfHRK0 Author(s)   Lufeng Ling * Affiliation(s) School of Mathematics and Information Science, Shangqiu Teachers College, Shangqiu, Henan, China . ABSTRACT In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α -times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α -times Integrated Cosine Function by the approximation theorem of n -times integrated semigroups. If the semigroups are equicontinuous at each point   , we give different methods to prove the theorem. KEYWOR...