We define interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals, interval valued (∈,∈∨q)-fuzzy k-bi-ideals and characterize k-regular and k-intra regular hemirings by the properties of interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals and interval valued (∈,∈∨q)-fuzzy k-bi-ideals. 2010 mathematics subject classification: 16Y60 • ...

Let $G$ be a finite group and $pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...

For integers k and n with k ≤ n a vector x ∈ R is said to be weakly k-majorized by a vector q ∈ R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1, . . . , k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P (q; k). We determine the vertices of both P (q; k) and its integer hull Q(q; k). Furthermore a ...

We give a combinatorial proof that k l-k-1 l + t q q q q a polynomial in q with nonnegative coefficients for nonnegative integers a, b, k, lwith a>~b and l~>k. In particular, for a=b=n and l=k, this implies the q-log-concavity of the Gaussian binomial coefficients k , which was conjectured q by BUTLER (Proc.

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

Let $$T(q) = \sum\limits_{k 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors natural k. We present monotonicity properties functions defined in terms T. More specifically, we prove that $$H(q) T(q) - {{\log (1 q)} \over {\log (q)}}$$ is strictly increasing on (0, 1), while $$F(q) {{1 q} q}H(q)$$ decreasing 1). These results are then ap...

Acute necrotizing inflammatory disease after intracerebral injection of LCM virus is largely dependent on the host immune response to the virus and is controlled, in part, by a dominant gene which is closely linked to the H-2 locus. The F(1) hybrid (H-2(q/k)) from mating a susceptible SWR/J mouse (H-2(q/q)) to a resistant C3H/HeJ mouse (H-2(k/k)) is susceptible to LCM virus disease. When such h...

Let us call a G (H, k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H, k) we will denote the minimum size of an (H, k) vertex stable graph. In this paper, we are interested in finding Q(C3, k), Q(C4, k), Q(K1,p, k) and Q(Ks, k).