It's considered that، the ring of linear operator of vector
space and stilled as a source of many mathematicians in general and
algebreians particularly in introducing a new concepts in algebra
and ring theory. In this subject I. Kaplansky proved
the following
theorem: "The ring of linear operators of finite dimension vector
space is regular".
The object of this paper is studying of ring of linear operator
of vector space in abstract algebra point of view.
We study in this paper one of functional analysis problems, involved with
construction a new class of functions, denoted by . The definition of the new
class depends on definition of Lebesgueclass of functions and on the Holder clas .
We study the
relation between the new class and approximation of the new class
to rational functions.
The supporting functions are powerful tools for studying several problems in mathematics and engineering sciences, since they have useful advantages.
In this paper, we prove that the following conditions and statements are equivalent:
1. is convex.
2. is supporting
3. is subadditive on the unit sphere.
Our aim of this paper is studying the problem on normal oscillations of system of capillary viscous fluids in vessel.
We prove results about the spectrum of the problem for rotating vessel and prove that the systems of root elements ( eigenelements
and associated elements ) form an Abel-Lidsky basis.
Also , we use some results from the theory of J-self adjoint operators in studying the spectrum of the problem for non-rotating vessel.
The aim of this research is to present the two new classes of complex functions . The first class is denoted , and the second one is denoted. The definition of both of them depends on the famous Lebesgue class ,and orlicz class .The relationship bet
ween the two new classes the two classes is studied. This study gives some properties .
Finally, this study is used for approximation of the class on group of wide curves.