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A matrix Fredholm integral equation of neuronal networks is transformed into a Cauchy system suited for numerical and analytical studies. A special case is discussed, and a connection with the classical renewal integral equation of stochastic point processes is presented.
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An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.
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The acoustic power transmitted by a variable-area duct section which carries a steady subsonic flow is investigated under the conditions of both upstream- and downstream-propagating incident plane waves. It is found that the ratio of the power transmitted by incident waves moving against the flow to the power transmitted by incident waves moving with the flow is equal to the ratio of the difference between the Mach number and unity to the square of the sum of the Mach number and unity.
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Computations based on several second-order turbulence models, including full Reynolds stress and two-equation models, are compared with a number of boundary-layer experiments. In general, the models represent the data reasonably well, with skin friction tending to be somewhat overpredicted in the far downstream region of the adverse pressure gradient experiments. A discussion of the behavior of the ARAP full Reynolds stress model in predicting the components of the Reynolds stress tensor is given. It is concluded that compatibility at the wall may necessitate the use of more than one length scale.
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A definition of centralized fixed modes of a system, which is an adoption of the definition of fixed modes for a decentralized system is made. It is shown that the centralized fixed modes of a system can be easily and efficiently calculated in terms of the eigenvalues of the system, and that the calculation of such fixed modes enables one to determine, in a numerically efficient way, whether a system is controllable, observable, stabilizable, or detectable. An efficient algorithm for reducing a system to minimal realization form is then given. The algorithms have been effectively used on systems of order up to 100.
A coefficient-assignability theorem is presented for systems defined over a commutative ring with 1. The conditions examined include all the general results on coefficient-assignability available in the literature. It is concluded that the proposed techniques are not effective for the case of the weaker property of pole placement when it is assumed that the commutative ring is a PID. Morse's well-known theorem seems to be the best result available for this situation.
The paper deals with robotic manipulator control systems with dynamic characteristics. It is shown that using model reference adaptive control techniques makes it possible to develop control algorithms which will maintain uniformly high performance over a wide range of system motions and payloads.
Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.
In 1977 Canuto et al. proposed a formalism to deal with the possible difference between gravitational and atomic clocks (or times). The formalism was incomplete since the authors only dealt with the gravitational Lagrangian LG, leaving the specific form of the matter Lagrangian Lm for a later study. Kembhavi and Pollock (1981) have proposed a matter Lagrangian which they define as 'the only possible one' or 'the inescapable form of Lm'. Adding this Lm to Lg, they claim that the theory does not allow for a variable G. The present paper gives a mathematical proof that the proposed matter Lagrangian, far from being 'the only one' or 'the inescapable form', is actually a very special case which already contains imprinted all the conclusions Kembhavi and Pollock claim to have discovered. Their results are therefore erroneous.