Consider the forward link of a mobile communications system with a single transmitter and rather arbitrary randomly time varying channels connecting the base to the mobiles. Data arrives at the base in some random way (and might have a bursty character) and is queued according to the destination until transmitted. The main issues are the allocation of transmitter power and time to the various q...

This paper deals with a delayed three-level food chain model with Beddington-DeAngelis functional response. By using the differential inequality theory, a set of sufficient conditions are obtained for the permanence of the system. By constructing a suitable Liapunov function, we derive that the system has a unique asymptotically periodic solution which is globally asymptotically stable. An exam...

An uncertain random variable is a measurable function from a probability space to the set of uncertain variables. In this paper, subadditivity property of chance measure and some inequalities on expected value for uncertain random variables including Jensen’s Inequality, Liapunov Inequality and cp Inequality are proved. Based on these inequalities, linear property and other properties of conver...

In this work, new approach to stability theory of impulsive differential equations is proposed. Instead of putting all components of the state variable x in one Liapunov function, several functions of partial components of x, which can be much easier constructed, are used so that the conditions ensuring that stability are simpler and less restrictive. Also, an example is given to illustrate the...

Uniform boundedness, ultimate boundedness, uniform stability, and asymptotic stability are studied by analyzing a Liapunov function satisfying v′(t) ≤ −αv(t) + √ v(t) ∫ t # ω(t, s) √ v(s)ds, t ≥ t0 ≥ 0, (# = 0 or −∞). The results are then applied to integrodifferential equations x′(t) = A(t) [ x(t) + ∫ t # F (t, s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), in real Hilbert space with unbounded linear...

It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum param...