Related papers: A note on relationship between some bounding inequ…
We present an analysis of the structure of Bell inequalities, mainly for the case of N qubits with two observables each. We show that these inequalities are related to Hadamard matrices and define Bell polynomials (in one variable) as an…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We study exponential stability for a kind of neural networks having time-varying delay. By extending the auxiliary function-based integral inequality, a novel integral inequality is derived by using weighted orthogonal functions of which…
We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of…
We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be…
Starting from the definition of a stiffness matrix, the authors present a new formulation of the Cartesian stiffness matrix of parallel mechanisms. The proposed formulation is more general than any other stiffness matrix found in the…
At the occasion of Eduardo D. Sontag's 70 th birthday, we provide here an overview of the tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation of the…
A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing…
We present a technique to resolve a Gaussian density matrix and its time evolution through known expectation values in position and momentum. Further we find the full spectrum of this density matrix and apply the technique to a chain of…