We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov pro...

We previously reported the importance of connective tissue growth factor (CTGF) in rheumatoid arthritis (RA). CTGF contains four distinct modules connected in tandem, namely insulin-like growth factor-binding protein (IGFBP)-like, von Willebrand factor (vWF) type C repeat, thrombospondin type 1 (TSP-1) repeat, and carboxyl-terminal (CT) modules. The relationships between each of these modules o...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

Starting from allyl 2-O-acetyl-3-O-benzyl-α-l-rhamnopyranoside (3), allyl (2,3,4,6-tetra-O-benzoyl-β-d-galactopyranosyl)-(1→4)-2-O-acetyl-3-O-benzyl-α-l-rhamnopyranoside (5) was synthesized under Helferich conditions. Module 5 was converted to 2,3,4,6-tetra-O-benzoyl-β-d-galactopyranosyl-(1→4)-2-O-acetyl-3-O-benzyl-α-l-rhamnopyranosyl bromide (8) which was then coupled with methyl (allyl 2,3-di...

let r be a commutative ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained

in this paper, we give a generalization of the integral dependence from rings to modules. we study the stability of the integral closure with respect to various module theoretic constructions. moreover, we introduce the notion of integral extension of a module and prove the lying over, going up and going down theorems for modules.

michael addition of pyrimidine and purine nucleobases to substituted as well as unsubstituted α,β-unsaturated esters efficiently proceeds in the presence of catalytic amount of zinc oxide in ionic liquid 1-butyl-3-methylimidazolium bromide (zno/[bmim]br) under microwave irradiation to afford carboacyclic nucleosides, as biologically important compounds, in good to excellent yields and in short ...

Michael addition of pyrimidine and purine nucleobases to substituted as well as unsubstituted α,β-unsaturated esters efficiently proceeds in the presence of catalytic amount of zinc oxide in ionic liquid 1-butyl-3-methylimidazolium bromide (ZnO/[bmim]Br) under microwave irradiation to afford carboacyclic nucleosides, as biologically important compounds, in good to excellent yields and in short ...

An environmentally friendly, facile and solvent-free synthetic route for aluminum sulfate octadecahydrate (Al2(SO4)3.18H2O) catalyzed one-pot multi-component synthesis of 12-aryltetrahydrobenzo[α]xanthene-11-ones, 1,8-dioxo-octahydroxanthenes and 14-aryl-14Hdibenzo[α,j]xanthenes has been developed. The readily, easy to handle, non-toxic, environmental friendly and low-cost catalyst, easily sepa...

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.