A subcube partition is a of the Boolean cube $\{0,1\}^n$ into subcubes. irreducible if only sub-partitions whose union are singletons and entire partition. tight it “mentions” all coordinates.
 We study extremal properties partitions: minimal size, weight, maximal number points, minimum dimension. also consider existence homogeneous partitions, in which subcubes have same dimensions. addit...

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible de...

Abstract Let $X \subset \mathbf {P}^n$ be an irreducible hypersurface of degree $d\geq 3$ with only isolated semi-weighted homogeneous singularities, such that $\exp (\frac {2\pi i}{k})$ is a zero its Alexander polynomial. Then we show the equianalytic deformation space $X$ not $T$-smooth except for finite list triples $(n,d,k)$. This result captures very classical examples by B. Segre families...

Assumed that (S,+,.) is a semiring. Semiring algebra structure as generalization of ring. A set I⊆S called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I every s in S. Based on this definition, there special condition namely prime P, when αβ∈P, then could prove α or β are elements P. Furthermore, I irreducible Ia intersection from B S, I=A I=B. We also know the strongly no...

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.