Abstract In this paper, we study the structure of rational cohomology groups IA-automorphism group $\mathrm {IA}_3$ free rank three by using combinatorial theory and representation theory. particular, detect a nontrivial irreducible component in second , which is not contained image cup product map first groups. We also show that triple trivial. As corollary, obtain fourth term lower central se...

Let G be a finite p-group and F field of characteristic p. We filter the cochain complex free G-space with coefficients in by powers augmentation ideal FG. show that cup product induces multiplicative structure on arising spectral sequence compute E1-page as bigraded algebra. As an application, we prove recent counterexamples Iyengar Walker to algebraic version Carlsson's conjecture can not rea...

In Drosophila, germ cell formation depends on inherited maternal factors localized in the posterior pole region of oocytes and early embryos, known as germ plasm. Here, we report that heterozygous cup mutant ovaries and embryos have reduced levels of Staufen (Stau), Oskar (Osk) and Vasa (Vas) proteins at the posterior pole. Moreover, we demonstrate that Cup interacts with Osk and Vas to ensure ...

Background and purpose - Hip dislocation is one of the most common complications following total hip arthroplasty (THA). Several factors that affect dislocation have been identified, including acetabular cup positioning. Optimal values for cup inclination and anteversion are debatable. We performed a systematic review to describe the different methods for measuring cup placement, target zones f...

In this work, we demonstrate that the integral formula for a generalised Sato-Levine invariant is consistent in certain situations with Evans and Berger's fourth-order winding number. Also, found that, principle, one can derive analogous high-order numbers by which calculate entanglement of braids. The number Brunnian 4-braid calculated algebraically using cup product on cohomology finite regul...

The mixed metric dimension $$\textrm{mdim}(G)$$ of a graph G is the cardinality smallest set vertices that (metrically) resolves each pair elements from $$V(G)\cup E(G)$$ . We say max-mdim if $$\textrm{mdim}(G) = n(G)$$ It proved with $$n(G)\ge 7$$ contains vertex degree at least 5. Using strong product graphs and amalgamations, large families are constructed. one universal determined. cut boun...

AIMS To study the relation between optic nerve head topography (Heidelberg retina tomograph, HRT) and disc area, visual field index mean defect (MD), and intraocular pressure (IOP), and to see whether change in HRT parameters is associated with change in MD in a prospective follow up. METHODS 80 consecutive patients (69 patients with exfoliation glaucoma and 11 with ocular hypertension combin...