scholarly journals Correction: Bustamante et al. Determining When an Algebra Is an Evolution Algebra. Mathematics 2020, 8, 1349

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1289
Author(s):  
Miguel D. Bustamante ◽  
Pauline Mellon ◽  
M. Victoria Velasco
Keyword(s):  
Natural Basis ◽  
Corrected Version ◽  
Evolution Algebra ◽  
Real Algebra

The authors wish to make the following corrections to this paper [1] (see corrected version in postprint [2]):On page 2, paragraph 4, complete the first sentence ‘In Theorem 2 we show that if A is a real algebra and B is a basis of A then B also is a basis of Aℂ, the complexification of A (with the same multiplication structure matrices) and that A is an evolution algebra if, and only if, Aℂ is an evolution algebra’ with the phrase ‘and has a natural basis consisting of elements of A’ [...]

scholarly journals Chains of three-dimensional evolution algebras: A description

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3175-3190
Author(s):  
Anvar Imomkulov ◽  
Victoria Velasco
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Natural Basis ◽  
3 Dimensional ◽  
Evolution Algebra ◽  
Fixed Rank ◽  
Weighted Digraph

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.

Ont he monodromy representation of polynomial maps in n variables

2002 ◽  
Vol 39 (3-4) ◽  
pp. 361-367
Author(s):  
A. Némethi ◽  
I. Sigray
Keyword(s):  
Cohomology Group ◽  
Jacobian Conjecture ◽  
Natural Basis ◽  
Generic Fiber ◽  
Monodromy Representation ◽  
Polynomial Maps ◽  
Polynomial Map

For a   non-constant polynomial map f: Cn?Cn-1 we consider the monodromy representation on the cohomology group of its generic fiber. The main result of the paper determines its dimension and provides a natural basis for it. This generalizes the corresponding results of [2] or [10], where the case n=2 is solved. As  applications,  we verify the Jacobian conjecture for (f,g) when the generic fiber of f is either rational or elliptic. These are generalizations of the corresponding results of [5], [7], [8], [11] and [12], where the case  n=2 is treated.

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

Expression of glycine and the glycine transporter Glyt-1 in the developing rat retina

2000 ◽  
Vol 17 (3) ◽  
pp. 484-484 ◽  
Author(s):  
DAVID V. POW ◽  
ANITA E. HENDRICKSON
Keyword(s):  
Cambridge University ◽  
Rat Retina ◽  
Glycine Transporter ◽  
Corrected Version ◽  
Developing Rat

Due to technical difficulties that have since been rectified, the photomicrographs in this article did not reproduce at the best resolution possible. Also, Figure 12 has been revised and a corrected version of the article is reproduced on pp. 1R–9R, which follows. Cambridge University Press regrets any inconvenience that this inadvertent error may have caused.

Corrigendum to: Establishment and In Vitro Evaluation of Porous Ion-Responsive Targeted Drug Delivery System. Protein & Peptide Letters, volume 27(11), (2020).

2021 ◽  
Vol 28 (3) ◽  
pp. 359-359
Author(s):  
Hongfei Liu ◽  
Jie Zhu ◽  
Pengyue Bao ◽  
Yueping Ding ◽  
Jiapeng Wang ◽  
...  
Keyword(s):  
Drug Delivery ◽  
Drug Delivery System ◽  
Delivery System ◽  
Targeted Drug Delivery ◽  
Electronic Version ◽  
In Vitro Evaluation ◽  
Corrected Version ◽  
Targeted Drug ◽  
Targeted Drug Delivery System

The authors are regretful for submitting and approving the publication of incorrect Figure 4 in this article. Below is the corrected version along with the revised caption. The electronic version of the article has already been corrected.

scholarly journals Casselman’s Basis of Iwahori Vectors and the Bruhat Order

2011 ◽  
Vol 63 (6) ◽  
pp. 1238-1253 ◽  
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Weyl Group ◽  
Bruhat Order ◽  
Group Element ◽  
The Other ◽  
Intertwining Operators ◽  
Transition Matrices ◽  
Natural Basis ◽  
Spherical Representation ◽  
Langlands Parameters ◽  
Combinatorial Condition

AbstractW. Casselman defined a basis fu of Iwahori fixed vectors of a spherical representation of a split semisimple p-adic group G over a nonarchimedean local field F by the condition that it be dual to the intertwining operators, indexed by elements u of the Weyl group W. On the other hand, there is a natural basis , and one seeks to find the transition matrices between the two bases. Thus, let and . Using the Iwahori–Hecke algebra we prove that if a combinatorial condition is satisfied, then , where z are the Langlands parameters for the representation and α runs through the set S(u, v) of positive coroots (the dual root systemof G) such that with rα the reflection corresponding to α. The condition is conjecturally always satisfied if G is simply-laced and the Kazhdan–Lusztig polynomial Pw0v,w0u = 1 with w0 the long Weyl group element. There is a similar formula for conjecturally satisfied if Pu,v = 1. This leads to various combinatorial conjectures.

Sign in / Sign up

Export Citation Format

Share Document