Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ non-negative integer. $M$ $N$ two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators $\operatorname{Ext}^t_R(M, N)$ $\operatorname{H}^t_{\mathfrak a}(M)$ in terms minimal primary decomposition zero submodule which are independent choice decomposition. Then, by using...

Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic ...

Remote sensing object detection based on the combination of infrared and visible images can effectively adapt to around-the-clock changeable illumination conditions. However, most existing networks need two backbone extract features modalities, respectively. Compared with single modality network, this greatly increases amount calculation, which limits its real-time processing vehicle unmanned a...

Let g be a semisimple complex Lie algebra and k ⊂ g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V , we construct simple (g, k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V ′ ⊂ M, V ′ 6≃ V , is greater than the Vogan norm of V . The (g, k)-modules M are subquotie...

A combination of crystallography, biochemistry, and gene expression analysis identifies the coactivator subcomplex Med8C/18/20 as a functionally distinct submodule of the Mediator head module. Med8C forms a conserved alpha-helix that tethers Med18/20 to the Mediator. Deletion of Med8C in vivo results in dissociation of Med18/20 from Mediator and in loss of transcription activity of extracts. De...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...