We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that structure constants of Kazhdan–Lusztig basis are unimodal. explain why implies tensor category associated by Lusztig to any two-sided cell in a Coxeter group is rigid and pivotal.

Domain adaptation (DA) aims to transfer knowledge from a label-rich and related domain (source domain) label-scare (target domain). Pseudo-labeling has recently been widely explored used in DA. However, this line of research is still confined the inaccuracy pseudo labels. In paper, we explore imbalance issue performance among classes in-depth observe that worse performances all are likely furth...

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...