The interplay between viruses and host immune responses is critical to determine either a successful infection or resolution. Mammalian cells have developed different mechanisms to recognize invading pathogens via their pathogen-associated molecular patterns (PAMPs), which are often nucleic acid products (e.g., doublestranded RNAs or dsRNA) generated during viral genome replication [1]. To evad...

For a mixed hypergraphH= (X,C,D), where C andD are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’such that everyC ∈ Cmeets some class in more than one vertex, and everyD ∈ D has a nonempty intersection with at least two classes.A vertex-order x1, x2, . . . , xn onX (n=|X|) is uniquely colorable if the subhypergraph induced by {xj : 1 j i} has precisely on...

Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k–list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2–list colorable graphs. Here we state some results which will pave the way in character...

A mixed hypergraph is a triple H = (X, C,D) where X is the vertex set and each of C, D is a family of subsets of X, the C-edges and D-edges, respectively. A k-coloring of H is a mapping c : X → [k] such that each C-edge has two vertices with the same color and each D-edge has two vertices with distinct colors. H = (X, C,D) is called a mixed hypertree if there exists a tree T = (X, E) such that ...

Let ~1,22 . . . . . ~,; n/>2 be any properties of graphs. A vertex (~L, ~2 . . . . . J~,,)-partition of a graph G is a partition (V1, l~,...,/7,,) of V(G) such that for each i = 1,2 . . . . . n the induced subgraph G[Vi] has the property ~i. A graph G is said to be uniquely (~1,~2 . . . . . ~,)-partitionable if G has unique vertex (2~1, ~2 , . . . , ~,)-partition. In the present paper we invest...

We show that for any infinite cardinal κ , every complete lattice where each element has at most one complement can be regularly embedded into a uniquely complemented κ-complete lattice. This regular embedding preserves all joins and meets, in particular it preserves the bounds of the original lattice. As a corollary, we obtain that every lattice where each element has at most one complement ca...

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...