查看更多>>摘要：In this paper we investigate Erdos-Ko-Rado theorems in ovoidal circle geometries. We prove that in Mobius planes of even order greater than 2, and ovoidal Laguerre planes of odd order, the largest families of circles which pairwise intersect in at least one point, consist of all circles through a fixed point. In ovoidal Laguerre planes of even order, a similar result holds, but there is one other type of largest family of pairwise intersecting circles. As a corollary, we prove that the largest families of polynomials over F-q of degree at most k, with 2 <= k < q, which pairwise take the same value on at least one point, consist of all polynomials f of degree at most k such that f(x) = y for some fixed x and y in F-q. We also discuss this problem for ovoidal Minkowski planes, and we investigate the largest families of circles pairwise intersecting in two points in circle geometries. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper is, in a first stage, devoted to establishing a topological-algebraic characterization of the principal component, U0(M), of the set of unitary elements, U(M), in a unital JB*- algebra M. We arrive to the conclusion that, as in the case of unital C*-algebras, U0(M) = M-1 1 n U(M) ? ? = Ue.nn middotmiddotmiddot Ue.n1 (1) : n E N, hj E Msa v 1 < j < n = {u E U(M) : there exists w E U0(M) with ilu -wil < 2} is analytically arcwise connected. Actually, U0(M) is the smallest quadratic subset of U(M) containing the set eiMB6. Our second goal is to provide a complete description of the surjective isometries between the principal components of two unital JB*-algebras M and N. Contrary to the case of unital C*-algebras, we shall deduce the existence of connected components in 14(M) which are not isometric as metric spaces. We shall also establish necessary and sufficient conditions to guarantee that a surjective isometry & UDelta; : 14(M)-+ 14(N) admits an extension to a surjective linear isometry between M and N, a conclusion which is not always true. Among the consequences it is proved that M and N are Jordan *- isomorphic if, and only if, their principal components are isometric as metric spaces if, and only if, there exists a surjective isometry & UDelta; : 14(M)-+ 14(N) mapping the unit of M to an element in 140(N). These results provide an extension to the setting of unital JB*-algebras of the results obtained by O. Hatori for unital C*-algebras.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Byrne, EimearGluesing-Luerssen, HeideRavagnani, Alberto
19页
查看更多>>摘要：A B S T R A C T We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
查看更多>>摘要：We determine the tensor rank of all semifields of order 16 over F-2 and of all semifields of order 81 over F-3. Our results imply that some semifields of order 81 have lower multiplicative complexity than the finite field F-81 over F-3. We prove new results on the correspondence between linear codes and tensor rank, including a generalisation of a theorem of Brockett and Dobkin to arbitrary tensors, which makes the problem computationally feasible.(C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：An algebra A is said to be two-sided zero product determined if every bilinear functional phi : A x A &-> F satisfying phi(x, y) = 0 whenever xy = yx = 0 is of the form phi(x, y) = T-1(xy) + T-2(yx) for some linear functionals T-1, T-2 on A. We present some basic properties and equivalent definitions, examine connections with some properties of derivations, and as the main result prove that a finite-dimensional simple algebra that is not a division algebra is two-sided zero product determined if and only if it is separable. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue prob-lems of the same size as the matrices of the initial two-parameter eigenvalue problem. The method is applicable for right definite problems, possibly after performing an affine transformation. This includes a class of Helmholtz equations when separation of variables is applied. We provide a convergence proof for extremal eigenvalues and empirical evidence along with a local convergence proof for other eigenvalues. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
查看更多>>摘要：We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to matrices with positive imaginary part. We show that the principal pivot transform is matrix monotone by establishing Hermitian square representations for the imaginary part and the derivative.(c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
查看更多>>摘要：The concept of coherent configurations is a generalization of the concept of association schemes. In this paper, we introduce the concept of Q-polynomial coherent configurations and study the relationship among intersection numbers, Krein numbers, and eigenmatrices. The examples of Q-polynomial coherent configurations are provided from Delsarte designs in Q-polynomial schemes and spherical designs, Euclidean designs.(c) 2022 Published by Elsevier Inc.
查看更多>>摘要：The main concern of this paper is the Karcher mean of linearly independent triples (A, B, C) on the hyperbolic manifold of 2 x 2 positive definite matrices of determinant 1. We show that the Karcher mean is of the form (A, B, C) = xA + y(B + C), 0 < x, y and x + 2y < 1 under the trace condition tr(AB(-1)) = tr(AC(-1)). We further find an invertible hyperbolic matrix M depending only on the trace values tr(AB(-1)) and tr(BC-1) such that [x y] = M [cosh theta sinh theta] for some (unique) theta is an element of R. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this article the operator trace function Lambda(rr,s)(A)[K, M] := tr(K*A(tau)MA(T)K)(s) is introduced and its convexity and concavity properties are investigated. This function has a direct connection to several well-studied operator trace functions that appear in quantum information theory, in particular when studying data processing inequalities of various relative entropies. In the paper the interplay between Delta(r,s) and the well-known operator functions Gamma(p,s) and Psi(p,q,s) is used to study the stability of their convexity (concavity) properties. This interplay may be used to ensure that Lambda(s) is convex (concave) in certain parameter ranges when M = I or K = I. However, our main result shows that convexity (concavity) is surprisingly lost when perturbing those matrices even a little. To complement the main theorem, the convexity (concavity) domain of lambda itself is examined. The final result states that lambda(r,s) is never concave and it is convex if and only if r = 1 and s >= 1/2. (c) 2022 Elsevier Inc. All rights reserved.
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