Exponential stability of triangular differential inclusion systems

We consider a differential inclusion system of the form , where is a collection of upper triangular matrices. Conditions for exponential stability of all the possible solutions are given.     

Limitations on infants' response to rate-based auditory-visual relations.

To study rate-based intersensory matching, infants first were familiarized with different auditory-visual relations and then were tested for detection of auditory visual equivalence. Across several different experiments, 4-, 6-, and 8-mo-old infants first were habituated with (1) a single, temporally concordant auditory-visual compound stimulus, (2) a single, temporally discordant compound stimulus, (3) 2 different temporally concordant compounds, or (4) a silently moving visual stimulus. A consistent and robust finding was a preference for the visual stimulus that moved at a novel velocity, indicating that the temporal attributes of the visual component dominated responsiveness. Only 1 experiment yielded evidence, albeit limited, of intersensory matching; infants habituated with a silently moving visual stimulus preferred the sound-specified visual stimulus in the presence of the rapid sound but not in the presence of the slow sound. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A necessary condition for quantitative exponential stability of linear state-space systems

For an arbitrary n×n constant matrix A the two following facts are well known:

• (1/n)Re(traceA)−max_j=1,…,nRe λ_j(A)0;

• If U is a unitary matrix, one can always find a skew-Hermitian matrix A so that U=e^A.

In this note we present the extension of these two facts to the context of linear time-varying dynamical systemsAs a by-product, this result suggests that, the notion of “slowly varying state-space systems”, commonly used in literature, is mathematically not natural to the problem of exponential stability.     

Optimization of Thermal-Flow Processes in a System of Conjugate Cooling Towers

Abstract

The paper presents the thermal-flow study of a closed cooling system with special emphasis on the working parameters of natural draft wet cooling towers. The authors analyze the possibility of the improvement of the overall cooling efficiency of a closed cooling system consisting of several cooling towers by the proper redistribution of cooling water between individual units. The problem of the optimal redistribution of circulating water between cooling towers is formulated as a mathematical issue involving finding the extrema of the multivariate function with constraints fixing the total mass flow rate of cooling water circulated in the hydraulic installation and the ranges of the hydraulic loads of individual cooling towers. The optimization process requires information about the individual characteristics of each cooling tower, which is achieved by experimental measurements done on real objects. The research done inside the cooling towers enables the identification of the heat and mass transfer processes across its radius. Next, these characteristics are used to calculate the optimal cooling water flow rates to the cooling towers, giving the highest possible mean cooling water temperature drop in the system.