We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of graphs called path-comple...

How do bureaucracies pattern durable inequalities? Predominant approaches emphasize the role of administrative categories, which prioritize certain populations for valued resources based on broader regimes human worth. This article extends this body work by examining how categorical inequalities become embedded within infrastructures and institutional pathways. I develop argument through a case...

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

This paper addresses the path-following problem of steering an autonomous air vehicle along a predefined 3-D path, while tracking a desired velocity profile. The presented solution relies on the definition of a path-dependent error space to express the dynamic model of the vehicle, which exhibits a high degree of directional accuracy. The proposed methodology adopts a polytopic Linear Parameter...

Considering sustainability a matter of intergenerational welfare equity, this paper examines whether an optimal development path can also be sustainable. It argues that the general “zero-net-aggregateinvestment” condition for an optimal development path to be sustainable in the sense of the maximin criterion of intergenerational justice is too demanding to be practical, especially in the contex...

In a binary tree T of N leaves, the left (right) level l i (r i) of leaf i is the number of left (right) edges in path from the root to that leaf. The level n i of leaf i is n i = l i +r i. Kraft-McMillan's characteristic inequality gives a necessary and suucient condition for a multiset of integers fn 1 ; n 2 ; :::; n N g to be the length ensemble of a binary tree T. Similarly, Yeung's charact...

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantu...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.