Search results for "Involution"
showing 10 items of 73 documents
Avoiding patterns in irreducible permutations
2016
We explore the classical pattern avoidance question in the case of irreducible permutations, <i>i.e.</i>, those in which there is no index $i$ such that $\sigma (i+1) - \sigma (i)=1$. The problem is addressed completely in the case of avoiding one or two patterns of length three, and several well known sequences are encountered in the process, such as Catalan, Motzkin, Fibonacci, Tribonacci, Padovan and Binary numbers. Also, we present constructive bijections between the set of Motzkin paths of length $n-1$ and the sets of irreducible permutations of length $n$ (respectively fixed point free irreducible involutions of length $2n$) avoiding a pattern $\alpha$ for $\alpha \in \{13…
Standard polynomials and matrices with superinvolutions
2016
Abstract Let M n ( F ) be the algebra of n × n matrices over a field F of characteristic zero. The superinvolutions ⁎ on M n ( F ) were classified by Racine in [12] . They are of two types, the transpose and the orthosymplectic superinvolution. This paper is devoted to the study of ⁎-polynomial identities satisfied by M n ( F ) . The goal is twofold. On one hand, we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew-symmetric matrices for both types of superinvolutions. On the other, in case of M 2 ( F ) , we find generators of the ideal of ⁎-identities and we compute the corresponding sequences of cocharacters and codimensions.
The exponent for superalgebras with superinvolution
2018
Abstract Let A be a superalgebra with superinvolution over a field of characteristic zero and let c n ⁎ ( A ) , n = 1 , 2 , … , be its sequence of ⁎-codimensions. In [6] it was proved that such a sequence is exponentially bounded. In this paper we capture this exponential growth for finitely generated superalgebras with superinvolution A over an algebraically closed field of characteristic zero. We shall prove that lim n → ∞ c n ⁎ ( A ) n exists and it is an integer, denoted exp ⁎ ( A ) and called ⁎-exponent of A. Moreover, we shall characterize finitely generated superalgebras with superinvolution according to their ⁎-exponent.
Thymus pathology observed in the MGTX trial
2012
The MGTX trial is the first prospective, randomized clinical trial that aims to evaluate the impact of extended transsternal thymectomy on myasthenic symptoms, prednisone requirements, and quality of life in patients with nonthymomatous, anti-acetylcholine receptor autoantibody-positive myasthenia gravis (MG). Here, we give an overview of the rationale of thymectomy and the standardized macroscopic and histopathological work-up of thymectomy specimens as fixed in MGTX standard operating procedures, including the grading of thymic lymphofollicular hyperplasia and the morphometric strategy to assess thymic involution.
On Codimensions of Algebras with Involution
2020
Let A be an associative algebra with involution ∗ over a field F of characteristic zero. One associates to A, in a natural way, a numerical sequence \(c^{\ast }_n(A),\)n = 1, 2, …, called the sequence of ∗-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In this paper we focus our attention on \(c^{\ast }_n(A),\)n = 1, 2, …, by presenting some recent results about it.
Superinvolutions on upper-triangular matrix algebras
2018
Let UTn(F) be the algebra of n×n upper-triangular matrices over an algebraically closed field F of characteristic zero. In [18], the authors described all abelian G-gradings on UTn(F) by showing that any G-grading on this algebra is an elementary grading. In this paper, we shall consider the algebra UTn(F) endowed with an elementary Z2-grading. In this way, it has a structure of superalgebra and our goal is to completely describe the superinvolutions which can be defined on it. To this end, we shall prove that the superinvolutions and the graded involutions (i.e., involutions preserving the grading) on UTn(F) are strictly related through the so-called superautomorphisms of this algebra. We …
Calpains mediate epithelial-cell death during mammary gland involution: mitochondria and lysosomal destabilization.
2012
Our aim was to elucidate the physiological role of calpains (CAPN) in mammary gland involution. Both CAPN-1 and -2 were induced after weaning and its activity increased in isolated mitochondria and lysosomes. CAPN activation within the mitochondria could trigger the release of cytochrome c and other pro-apoptotic factors, whereas in lysosomes it might be essential for tissue remodeling by releasing cathepsins into the cytosol. Immunohistochemical analysis localized CAPNs mainly at the luminal side of alveoli. During weaning, CAPNs translocate to the lysosomes processing membrane proteins. To identify these substrates, lysosomal fractions were treated with recombinant CAPN and cleaved produc…
Bing meets Sobolev
2019
We show that, for each $1\le p < 2$, there exists a wild involution $\mathbb S^3\to \mathbb S^3$ in the Sobolev class $W^{1,p}(\mathbb S^3,\mathbb S^3)$.
On the Asymptotics of Capelli Polynomials
2020
We present old and new results about Capelli polynomials, \(\mathbb {Z}_2\)-graded Capelli polynomials, Capelli polynomials with involution and their asymptotics.
On multiplicities of cocharacters for algebras with superinvolution
2021
Abstract In this paper we deal with finitely generated superalgebras with superinvolution, satisfying a non-trivial identity, whose multiplicities of the cocharacters are bounded by a constant. Along the way, we prove that the codimension sequence of such algebras is polynomially bounded if and only if their colength sequence is bounded by a constant.