We investigate a number of coloring problems restricted to bipartite graphs with bounded diameter. First, we the $k$-List Coloring, $k$-Coloring, and $k$-Precoloring Extension on diameter at most $d$, proving $\textsf{NP}$-completeness in cases, leaving open only List $3$-Coloring $3$-Precoloring when $d=3$.
 Some these results are obtained $\textsc{through}$ proof that Surjective $C_6$-Ho...

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

background: small side branches, albeit less important than their larger counterparts, have not yet received due attention in the literature. nor has there ever been a comparison between drug-eluting stents and bare metal stents apropos side branch occlusion . the aim of this study was to compare the patency of small (≥0.5 and ≤1.5 mm in diameter) side branches with respect to bare metal vs. dr...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Background: The seeds of some medicinal plants and their compounds have long been valued for their numerous health benefits. Objective:To investigate some physical and chemical properties of Salvia spp. Methods: Some physico-chemical properties in five species of Salvia seeds (consisted of S. officinalis L., S. macrosiphon L., S. hypoleuca L., S. sclarea L. and S. nemorosa L.) were measured ...

due to the importance of weed control and the limitations of mechanical methods in some places, in this research the water jet cutting for weed control was investigated. the cutting tests were performed on camel thorn weed in shahid bahonar university of kerman. the water jet pressure of 90 bars was achieved with the aid of a suitable pump. the cutting time was studied in a completely randomize...