the aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $s_{h}$ and  $t_{h},$ respectively. it is shown that $t_{h}=s_{h}$ if and only if $beta=beta^{*}.$ we also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

• The in-plane mechanical properties of 7 semi-regular lattices were derived analytically. We found a stretching-dominated topology with an elastic buckling strength 43% higher than regular triangular lattice. One bending-dominated tessellation is 85% stiffer and 11% stronger hexagonal seven analytically for uniaxial compression shear. These analytical expressions then validated using Finite El...