We prove that if cf(λ) > א0 and 2 cf(λ) < λ then λ → (λ, ω + 1) in ZFC

Let w0 denote the permutation [n, n − 1, . . . , 2, 1]. We give two new explicit formulae for the Kazhdan-Lusztig polynomials Pw0w,w0x in Sn when x is a maximal element in the singular locus of the Schubert variety Xw. To do this, we utilize a standard identity that relates Px,w and Pw0w,w0x.

It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kähler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves. We derive a ...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...