First, we show the equivalence of two definitions left Riemann–Liouville fractional integral on time scales. Then, establish and characterize Sobolev space with help notion derivative At same time, define weak derivatives demonstrate that they coincide ones Next, prove kinds norms in introduced derive its completeness, reflexivity, separability, some embedding. Finally, as an application, by co...

The identity theorem of the sequent calculus exhibits one connection between the judgments A left and A right : If we assume A left we can prove A right . In other words, the left rules of the sequent calculus are strong enough so that we can reconstitute a proof of A from the assumption A. So the identity theorem is a global version of the local completeness property for the elimination rules....

Semantic completeness and syntax completeness are important characters of the general formal systems, two the completeness have different meaning for a formal system. This paper analyze the relation between semantic completeness of a formal system S and syntax completeness under certain condition and the relation between the syntax completeness of S and the syntax completeness of consistent ext...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...