Using elementary methods we give a new proof of a result concerning the special form of the character of the bounded peripheral element which arises at an end of a curve component of the character variety of a knot complement. 1991 Mathematics subject classification (Amer. Math. Soc): 57 M 25, 57 N 10.

The problem of the holomorphic contractibility Teichmüller spaces T(0,n) punctured spheres (n>4) arose in 1970s connection with solving algebraic equations Banach algebras. Recently it was solved by author. In present paper, we give a refined proof for all T(0,n), n>4 and provide two independent proofs low-dimensional spaces, which has intrinsic interest.

Graph modification problems such as vertex deletion, edge deletion or edge contractions are a fundamental class of optimization problems. Recently, the parameterized complexity of the contractibility problem has been pursued for various specific classes of graphs. Usually, several graph modification questions of the deletion variety can be seen to be FPT if the graph class we want to delete int...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...