The dually flat structure introduced by Amari–Nagaoka is highlighted in information geometry and related fields. In practical applications, however, the underlying pseudo-Riemannian metric may often be degenerate, such an excellent geometric rarely defined on entire space. To fix this trouble, present paper, we propose a novel generalization of for certain class singular models from viewpoint L...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

BACKGROUND Both Kaposi's sarcoma-associated herpesvirus (KSHV) and Epstein-Barr virus (EBV) are members of the human gamma herpesvirus family: each is associated with various human cancers. The majority of AIDS-associated primary effusion lymphoma (PEL) are co-infected with both KSHV and EBV. Dually-infected PELs selectively switch from latency to lytic replication of either KSHV or EBV in resp...

BACKGROUND New viruses pathogenic to plants continue to emerge due to mutation, recombination, or reassortment among genomic segments among individual viruses. Tospoviruses cause significant economic damage to a wide range of crops in many parts of the world. The genetic or molecular basis of the continued emergence of new tospoviruses and new hosts is not well understood though it is generally...

A class C of graphs is said to be dually compact closed if, for every infinite G ∈ C, each finite subgraph of G is contained in a finite induced subgraph of G which belongs to C. The class of trees and more generally the one of chordal graphs are dually compact closed. One of the main part of this paper is to settle a question of Hahn, Sands, Sauer and Woodrow by showing that the class of bridg...