We will develop some inequalities which let us bound the probability of a random variable taking a value very far from its expectation. This is the most basic inequality we will use. This is useful if the only thing we know about a random variable is its expectation. It will also be useful to derive other inequalities later.

We study maximal inequalities for demisubmartingales and N-demisupermartingales and obtain inequalities between dominated demisubmartingales. A sequence of partial sums of zero mean associated random variables is an example of a demimartingale and a sequence of partial sums of zero mean negatively associated random variables is an example of a Ndemimartingale.

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This consists, given a conditional differential-algebraic system, in verifying if the system is structurally solvable for every state, and if not in finding a state in which the system is structurally singular. We give an integer linear programming formulation for the problem...

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs. AMS 2000 subject classifications: Primary 60B20, 60E15; secondary 60G09, 60F10.

It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years, a number of integral inequalities had been established by many scholars, which are motivated by certain applications. For de...

* Correspondence: volodin@math. uregina.ca Department of Mathematics and Statistics, University of Regina, Regina Saskatchewan S4S 0A2, Canada Full list of author information is available at the end of the article Abstract Some exponential inequalities for a sequence of acceptable random variables are obtained, such as Bernstein-type inequality, Hoeffding-type inequality. The Bernsteintype ineq...