Exponential absolute stability of discrete systems
Nonlinear discrete systems absolute stability exponential property proved by modified frequency condition, applying analog transformation to Szego-Kalman equations
Siljak, D. D.↗
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Use of exponentials in the integral solution of the parabolic equations of boundary layer, wake, jet, and vortex flows
Incompressible laminar boundary layer, vortex and axisymmetric wake/jet flow parabolic equations solution by weighted residuals method, describing use of exponentials
Bossel, H. H.↗
Junction capacitance as a function of voltage for diffused p-n diodes with exponential doping gradients
Capacitance calculation for diffused p-n junction with exponential doping gradients
Been, J. F.↗
Exponential downweighting of past data in a single stage, weighted-least-squares trajectory processor
Exponential downweighting of past data in single stage, weighted least squares trajectory processor for coasting spacecraft
Rich, R. G.↗
Exponential absolute stability of discrete systems
Exponential absolute stability of nonlinear discrete systems of Lure type, deriving modified frequency condition
Siljak, D. D.↗
Vortex computation by the method of weighted residuals using exponentials
Rotationally symmetric quasi-cylindrical viscous incompressible vortex flow, using method of weighted residuals approximating axial velocity and circulation profiles by series of exponentials
Bossel, H. H.↗
Exponential decontamination models for count data
Mathematical models for microorganism exponential die-off rate and variance estimation from decontamination data
Bansal, A. K.↗
Maximization of the region of exponential absolute stability.
The problem of selecting a regulator vector which yields the largest estimate of the region of exponential absolute stability is considered. Reformulation of an extended version of the Popov frequency condition in terms of a nonnegative polynomial gives the desired algorithm in mathematical programming format.
Karmarkar, J. S.↗
A note on exponential absolute stability.
A new sufficient condition is formulated for the Lur'e type nonlinear continuous system to be exponentially absolutely stable. The condition relaxes the assumptions on the nonlinear characteristic by modifying the requirements on the linear part of the system.
Siljak, D. D.↗
Exponential stability of large-scale discrete systems
The concept of vector Liapunov functions is used to obtain conditions for the exponential stability of large-scale discrete systems which can be decomposed into a number of interconnected subsystems with the same stability property. Both the structurally invariant composite systems and the large-scale systems under structural perturbations are considered. Connective absolute stability of a large-scale system composed of the interconnected Lur'e-type subsystems is defined and resolved in this context, resulting in a computationally and conceptually attractive alternative to a straightforward stability analysis of the system by frequency-domain criteria.
Grujic, L. T.↗
Neural pulse frequency modulation of an exponentially correlated Gaussian process
The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.
Hutchinson, C. E.↗
Curve fitting of aeroelastic transient response data with exponential functions
The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.
Bennett, R. M.↗
A new algorithm for the integration of exponential and logarithmic functions
An algorithm for symbolic integration of functions built up from the rational functions by repeatedly applying either the exponential or logarithm functions is discussed. This algorithm does not require polynomial factorization nor partial fraction decomposition and requires solutions of linear systems with only a small number of unknowns. It is proven that if this algorithm is applied to rational functions over the integers, a computing time bound for the algorithm can be obtained which is a polynomial in a bound on the integer length of the coefficients, and in the degrees of the numerator and denominator of the rational function involved.
Rothstein, M.↗
Investigation of the double exponential in the current-voltage characteristics of silicon solar cells
Difficulties in relating observed current-voltage characteristics of individual silicon solar cells to their physical and material parameters were underscored by the unexpected large changes in the current-voltage characteristics telemetered back from solar cells on the ATS-1 spacecraft during their first year in synchronous orbit. Depletion region recombination was studied in cells exhibiting a clear double-exponential dark characteristic by subjecting the cells to proton irradiation. A significant change in the saturation current, an effect included in the Sah, Noyce, Shockley formulation of diode current resulting from recombination in the depletion region, was caused by the introduction of shallow levels in the depletion region by the proton irradiation. This saturation current is not attributable only to diffusion current from outside the depletion region and only its temperature dependence can clarify its origin. The current associated with the introduction of deep-lying levels did not change significantly in these experiments.
Wolf, M.↗
Turbulent scattering in an exponential atmosphere - A wave-optical solution
The thin-screen model for scattering of radiation by a turbulent atmosphere is generalized to the case where the mean phase change decreases exponentially as a function of distance across the screen. This is of interest because it models the effect of turbulent scattering in an isothermal average atmosphere. We present both the change in average intensity and average bending angle in terms of the r-m-s scattering angle introduced by the turbulence. We find, for example, that the effect of turbulent scattering on the mean scattering angle (and hence Doppler residuals) is approximately the same as that obtained from more heuristic calculations. The effect depends on wavelength only to the extent that the refractivity is a function of wavelength.
Hubbard, W. B.↗
Simulation study of the power of the Kolmogoroff-Smirnoff and Z tests for the exponential distribution
Simulation tests were carried out to compare the power of the Kolmogoroff-Smirnoff and Z tests for the exponential distribution against a wide range of alternative distributions. The results indicate that both tests should be used for applications for which detailed knowledge regarding the possible classes of alternative distributions is lacking.
Gayle, J. B.↗
Numerical method for boundary layers with blowing - The exponential box scheme
The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.
El-Mistikawy, T. M.↗
On the atmosphere with exponential turbulence
An exact calculation is presented for the photon-average bending angle and intensity produced during occultation of a point source by an isothermal atmosphere with an exponential height dependence of turbulent power. The calculation is performed via an expansion in powers the gradients of average refractivity and turbulent power. Attention is given to conditions for the validity of the expansion. The results are compared with other expressions recently presented by Eshleman and Haugstad for the same distribution of refractivity, and discrepancies are noted. Finally, certain properties of photon averages which may be of importance for the reduction of occultation data, are discussed.
Hubbard, W. B.↗