The Randić energy of generalized double sun
We show that the family of trees defined as generalized double sun of odd order satisfies the conjecture for the Randić energy proposed by I. Gutman, B. Furtula, S. B. Bozkurt (2014).
Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants and
I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by . Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values...
Triple positive solutions of fourth-order four-point boundary value problems for -Laplacian dynamic equations on time scales.
Permanence and global exponential stability of Nicholson-type delay systems
We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
On left --liberal semigroups
In this paper the equivalence on a semigroup in terms of a set of idempotents in is defined. A semigroup is called a -liberal semigroup with as the set of projections and denoted by if every -class in it contains an element in . A class of -liberal semigroups is characterized and some special cases are considered.
is not potentially nilpotent for
An sign pattern is said to be potentially nilpotent if there exists a nilpotent real matrix with the same sign pattern as . Let be an sign pattern with such that the superdiagonal and the entries are positive, the and entries are negative, and zeros elsewhere. We prove that for and , the sign pattern is not potentially nilpotent, and so not spectrally arbitrary.
Non-fragile estimation for discrete-time T-S fuzzy systems with event-triggered protocol
This paper investigates the non-fragile state estimation problem for a class of discrete-time T-S fuzzy systems with time-delays and multiple missing measurements under event-triggered mechanism. First of all, the plant is subject to the time-varying delays and the stochastic disturbances. Next, a random white sequence, the element of which obeys a general probabilistic distribution defined on , is utilized to formulate the occurrence of the missing measurements. Also, an event generator function...
Essential sign change numbers of full sign pattern matrices
A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign...
Rational realization of the minimum ranks of nonnegative sign pattern matrices
A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set (, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of . Using a correspondence between sign patterns with minimum rank and point-hyperplane configurations in and Steinitz’s theorem on the rational realizability of...
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