In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...

Austenite is a semi-stable phase in most stainless steels that deforms to martensite under Md30 and forms martensitetype ά and ε due to the deformation in the steels. Since the distribution of strain induced martensite plays animportant role in achieving desired properties, the main objective of the present work is to model martensitedistribution of ά during cold rolling using...

 ‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...

Throughout the paper all graphs G = (V,E) are undirected and simple. An induced biclique of G is a complete bipartite induced subgraph of G. A noninduced biclique is a complete bipartite (not necessarily induced) subgraph of G. Equivalently, the pair (X, Y ) of disjoint vertex subsets X ⊆ V and Y ⊆ V is a non-induced biclique of G if {x, y} ∈ E for all x ∈ X and y ∈ Y . If, additionally, X and ...