‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

In 1902 Burnside [4] wrote "A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite while the order of every operation it contains is finite". This leads to the following problem, now called the Burnside problem: "If a group is finitely generated and of finite exponent, is it finite?" This is a very difficult question so a weaker form know...

This paper finds the Artin characters and exponent dependingon character table conjugacy classes of projective special lineargroup PSL (2,P*).Then we prove that (2, P*) isequal to p*' where P is a prime number , p=3 k> 0.