Covariant Differential Operator under General Coordinate Transformation and Structure of Lagrangian Operator

Some properties of a general integral operator

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎

Ozaki's conditions for general integral operator

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

On Humbert matrix function of two complex variables under differential operator

Operator ordering for generally covariant systems

An essential aspect of a generally covariant system is the invariance of its action under reparametrizations; this means that the label that parametrizes the trajectories of the system is not the time but a physically irrelevant parameter. As a consequence, the system is constrained to remain on the hypersurface of the phase space where the Hamiltonian is null. In fact, since the “evolution” ge...

Preclosure operator and its applications in general topology

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...