In this paper, a notion of principal $2$-bundle over Lie groupoid has been introduced. For such $2$-bundles, we produced short exact sequence VB-groupoids, namely, the Atiyah sequence. Two notions connection structures viz. strict connections and semi-strict on arising respectively, from retraction up to natural isomorphism have We constructed class $\mathbb{G}=[G_1\rightrightarrows G_0]$-bundl...

This research identifies lexical bundles which are connected to move analysis in article of Science & Technology. The corpus-based was used acquire qualification frequency and range. A number were listed the corpus identified structurally functionally using taxonomy approach by Biber et al., (2004). Further conducted connect expression with rhetorical move. Connecting articles aims test whe...

This article examines idiomatic expressions as sources of both regularity and irregularity in language. Some morphological, lexical, syntactical, and semantical characteristics of idioms are discussed. It is shown how a lexical licensing mechanism, which is formulated within a formal grammar framework, can deal with the data. After that, this proposal is extended to the phenomenon of negative p...

M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.