In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.

Abstract Involution Schubert polynomials represent cohomology classes of K -orbit closures in the complete flag variety, where is orthogonal or symplectic group. We show they also $\mathsf {T}$ -equivariant subvarieties defined by upper-left rank conditions spaces symmetric skew-symmetric matrices. This geometry implies that these are positive combinations monomials variables $x_i + x_j$ , and ...

We have investigated the role of IL-6 in the initiation and progression of mouse mammary gland involution in IL-6-null mice. This study was based on the hypothesis that IL-6 is the activating cytokine for signal transducer and activator of transcription 3 (Stat), the transcription factor whose presence is required for controlled mammary gland involution. We now show that expression of IL-6 is l...

We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

Involution is the process of post-lactational mammary gland regression to quiescence and it involves secretory epithelial cell death, stroma remodeling and gland repopulation by adipocytes. Though reportedly accompanying apoptosis, the role of autophagy in involution has not yet been determined. We now report that autophagy-related (ATG) proteins mediate dead cell clearance and suppress inflamm...