in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

A time-dependent bosonic string configuration is discussed, in graviton and dilaton backgrounds, leading to Weyl-symmetry beta-functions which are homogeneous in X, to any order in α ′ . As a consequence, a string reparametrization can always be implemented, such that beta functions can be cancelled, to any order in α ′ . This non-perturbative conformal invariance is valid for any target space ...

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

In this paper, we look at the notion of cohomological triviality fibrations homogeneous spaces affine algebraic groups defined over \({\mathbb {C}}\) and use topological methods, primarily theory covering spaces. This is made possible because structure groups. Further, generalize our results for arbitrary connected their As an application give a result quasi- reductive (i.e., whose unipotent ra...