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On the alternative structures for a three-grade Markov manpower system

Amenaghawon Vincent A., Ekhosuehi Virtue U., Osagiede Augustine A.

Journal of Mathematics and Applications

2020

Vol. 43

5--17

This paper considers a manpower system modelled within the Markov chain context under the condition that recruitment is doneto replace outgoing flows. The paper takes up the embeddability problem in a three-grade manpower system and examines it from the standpoint of generating function (i.e., the z-transform of stochastic matrices). The method constructs a stochastic matrix that is made up of a limiting-state probability matrix and a partial sum of transient matrices. Examples areprovided to illustrate the utility of the method.

An Approach to Design Broadband Air Backed Piezoelectric Sensor

Ali M. G. S., Elsayed N. Z., Eid E. A.

Archives of Acoustics

2015

Vol. 40, No. 1

3--10

In this work, an approach to the design of broadband thickness-mode piezoelectric transducer is presented. In this approach, simulation of discrete time model of the impulse response of matched and backed piezoelectric transducer is used to design high sensitivity, broad bandwidth, and short-duration impulse response transducers. The effect of matching the performance of transmitting and receiving air backed PZT-5A transducer working into water load is studied. The optimum acoustical characteristics of the quarter wavelength matching layers are determined by a compromise between sensitivity and pulse duration. The thickness of bonding layers is smaller than that of the quarter wavelength matching layers so that they do not change the resonance peak significantly. Our calculations show that the −3 dB air backed transducer bandwidth can be improved considerably by using quarter wavelength matching layers. The computer model developed in this work to predict the behavior of multilayer structures driven by a transient waveform agrees well with measured results. Furthermore, the advantage of this this model over other approaches is that the time signal for optimum set of matching layers can be predicted rapidly.