ﻻ يوجد ملخص باللغة العربية
We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all of these pairs reduce to the same pair (C, D) from this family, except for pairs whose arbitrary entries are zeros of a certain polynomial. The polynomial and the pair (C D) are constructed by a combinatorial method based on properties of a certain graph.
Let $(A,B)$ be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum [ (underline{underline A},underline{underline B})oplus (A_1,B_1)oplusdotsoplus(A_t,B_t) ] that is congruent to $(A
For $G={rm GL}(n,q)$, the proportion $P_{n,q}$ of pairs $(chi,g)$ in ${rm Irr}(G)times G$ with $chi(g) eq 0$ satisfies $P_{n,q}to 0$ as $ntoinfty$.
According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nil
We establish a relative spannedness for log canonical pairs, which is a generalization of the basepoint-freeness for varieties with log-terminal singularities by Andreatta--Wisniewski. Moreover, we establish a generalization for quasi-log canonical pairs.
Balanced pairs appear naturally in the realm of Relative Homological Algebra associated to the balance of right derived functors of the $mathsf{Hom}$ functor. A natural source to get such pairs is by means of cotorsion triplets. In this paper we stud