Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

Chase’s lemma and its context

Chase’s lemma provides a powerful tool for translating properties of (co)products in abelian categories into chain conditions. This note discusses the context in which the lemma is used, making explicit what is often neglected in the literature because of its technical nature.     

偏缠绕模的Frobenius性质

主要给出了偏缠绕模的Frobenius性质，推广了缠绕模相应的性质。     

An Upper Bound for the w-Weak Global Dimension of Pullbacks

Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}.     

Structural insights of a cellobiose dehydrogenase enzyme from the basidiomycetes fungus Termitomyces clypeatus

Filamentous fungi secrete various oxidative enzymes to degrade the glycosidic bonds of polysaccharides. Cellobiose dehydrogenase (CDH) (E.C.1.1.99.18) is one of the important lignocellulose degrading enzymes produced by various filamentous fungi. It contains two stereo specific ligand binding domains, cytochrome and dehydrogenase - one for heme and the other for flavin adenine dinucleotide (FAD) respectively. The enzyme is of commercial importance for its use in amperometric biosensor, biofuel production, lactose determination in food, bioremediation etc. Termitomyces clypeatus, an edible fungus belonging to the basidiomycetes group, is a good producer of CDH. In this paper we have analyzed the structural properties of this enzyme from T. clypeatus and identified a distinct carbohydrate binding module (CBM) which is not present in most fungi belonging to the basidiomycetes group. In addition, the dehydrogenase domain of T. clypeatus CDH exhibited the absence of cellulose binding residues which is in contrast to the dehydrogenase domains of CDH of other basidiomycetes. Sequence analysis of cytochrome domain showed that the important residues of this domain were conserved like in other fungal CDHs. Phylogenetic tree, constructed using basidiomycetes and ascomycetes CDH sequences, has shown that very surprisingly the CDH from T. clypeatus, which is classified as a basidiomycetes fungus, is clustered with the ascomycetes group. A homology model of this protein has been constructed using the CDH enzyme of ascomycetes fungus Myricoccum thermophilum as a template since it has been found to be the best match sequence with T. clypeatus CDH. We also have modelled the protein with its substrate, cellobiose, which has helped us to identify the substrate interacting residues (L354, P606, T629, R631, Y649, N732, H733 and N781) localized within its dehydrogenase domain. Our computational investigation revealed for the first time the presence of all three domains - cytochrome, dehydrogenase and CBM - in the CDH of T. clypeatus, a basidiomycetes fungus. In addition to discovering the unique structural attributes of this enzyme from T. clypeatus, our study also discusses the possible phylogenetic status of this fungus.