Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1966"
585 citations
434 citations
80 citations
TL;DR: In this paper, the Popov criterion for the stability of a system containing a simple memoryless nonlinearity has been generalized to the case of systems containing an arbitrary number of nonlinearities, and the main result is established, with an application to deriving a subsidiary result, already discovered by other techniques.
Abstract: This paper generalizes the Popov criterion for the stability of a system containing a simple memoryless nonlinearity to the case of a system containing an arbitrary number of memoryless nonlinearities. In stating the problem formally, we point out two apparently distinct occurrences of nonlinearities which are really not different, so that both are in the ambit of the problem considered. The main result is established, with an application to deriving a subsidiary result, already discovered by other techniques, on the stability of second-order nonlinear systems.
70 citations
62 citations
TL;DR: In this paper, the convergence properties of the Volterra-Wiener functional series were investigated in the deterministic case and the stochastic case, and several theorems were presented with proofs.
Abstract: This paper gives new results on the application of Volterra-Wiener functionals to the analysis of nonlinear systems. Part I deals with the convergence properties of the Volterra-Wiener functional series both in the deterministic case and the stochastic case. Several theorems are presented with proofs. Part II deals with the determination of the kernels to satisfy the solution or response of the given system described by an ordinary nonlinear differential equation. Recurrence relations for the Volterra kernels are developed. Part III gives the cascade theorems with proofs which agree with the results of George and Van Trees. A Table of Associated Transforms and the derivation of two particular pairs are appended.
53 citations
TL;DR: In this paper, the optimum estimate of nonlinear process in presence of non-Gaussian noise and disturbances, deriving algorithm for correcting approximation was derived, and the algorithm was used for correcting the error.
Abstract: Optimum estimate of nonlinear process in presence of non-Gaussian noise and disturbances, deriving algorithm for correcting approximation
48 citations
TL;DR: In this paper, the Fowler-Nordheim field emission equation (FNE) was used to evaluate the slopes of logarithmic plots of the FNE and the related function s(y) is used in examining the slopes.
Abstract: The functions v(y) and t(y) are useful in evaluating the Fowler-Nordheim field emission equation. The related function s(y) is used in examining the slopes of logarithmic plots of this equation. Six-place tables of v(y), t(y), and s(y) are presented for values of y from 0 to 1.0 inclusive, at intervals of 0.01.
48 citations
47 citations
TL;DR: In this article, the formulation of stability problems in both elastic and aeroelastic systems in the framework of Lyapunov stability theory is explored, and specific examples are worked out so as to reveal some of the difficulties and to give some idea on the class of problems for which LyAPunov's direct method is readily applicable.
Abstract: This paper discusses the formulation of stability problems in both elastic and aeroelastic systems in the framework of Lyapunov stability theory. The application of Lyapunov's direct method to these problems is explored. This approach has the advantage over the conventional methods for it enables one to deal directly with the distributed mathematical model of the system without resorting to approximations. Specific examples are worked out so as to reveal some of the difficulties and to give some idea on the class of problems for which Lyapunov's direct method is readily applicable.
45 citations
TL;DR: In this paper, the general conditions that are necessary and sufficient far the existence of a (p, s)-digraph with prescribed degrees are presented. But they do not cover all the special cases derived in the literature for different assumptions.
Abstract: This paper presents the general conditions that are necessary and sufficient far the existence of a (p, s)-digraph with prescribed degrees. It reduces to all the special cases derived in the literature for different assumptions ( 2–11 ). This result allows the unification of all the existing results and provides an insight into the complicated cases.
TL;DR: The problem of optimum mean-square linear interpolation for random sampling is discussed and the technique of study is very simple and further extends the work done in periodic sampling and in periodic sampled with.
Abstract: Optimum mean square linear interpolation for random sampling, discussing periodic and Poisson sampling
TL;DR: In this paper, the root locus method is used to define a general stability criterion for any order linear systems, based on the distribution of real roots in even and odd parts of characteristic equations, the relative damping character of high order systems can be predicted.
Abstract: Using the root locus method a general stability criterion is defined for any order linear systems. According to the distribution of real roots in even and odd parts of characteristic equations, the relative damping character of high order systems can be predicted. By the manipulations of roots in even and odd parts of characteristic equations high order systems with multiple adjustable coefficients can be designed to meet specifications.
TL;DR: Using constant transformations and matrix embeddings, it is shown how to find all constant realizations of an arbitrary rational transfer function matrix as mentioned in this paper, and the theory is applied to finding essentially all equivalent networks.
Abstract: Using constant transformations and matrix embeddings it is shown how to find all constant realizations of an arbitrary rational transfer function matrix. Explicit means of calculating the transformations are given and the theory is applied to finding essentially all equivalent networks.
TL;DR: In this article, the driving point properties of the distributed RC ( RC ) network are utilized for realizing an impedance approximating (jw) − 1 2 over a wide frequency range ω0 RC network and those of the terminating impedance.
Abstract: The driving-point properties of the distributed RC ( RC ) network are utilized for realizing an impedance approximating (jw) − 1 2 over a wide frequency range ω0 RC network and those of the terminating impedance. We show that with suitable termination, the value of ω0 can be reduced by a factor of ten from the value for open or short-circuit conditions. Thin film or semiconductor realization is possible for the resulting networks, but they can also be approximated by combinations of lumped R's and C's. Two types of lumped-element approximations are suggested: one employs a finite ladder to approximate the three-terminal RC network while the other is based on truncation of the partial-fraction expansion of the two terminal RC impedances. It is found that the former type of structure gives better results than the latter type.
TL;DR: In this paper, the theory of linear algebra is used to obtain the transmission matrices of multi-conductor electrical transmission lines with constant distributed parameters in a direct manner, and general results pertaining to multichannel transmission lines have been deduced.
Abstract: In this paper the theory of linear algebra is used to obtain the transmission matrices of multi-conductor electrical transmission lines with constant distributed parameters in a direct manner. The transmission matrices of two-conductor transmission lines whose parameters vary continuously are also obtained by the use of a direct method in special cases of practical importance. General results pertaining to multi-conductor transmission lines with variable parameters are also deduced.
TL;DR: In this article, an analytical expression for the magnetization curve of the iron core with hysteresis is assumed and the amplitude characteristic and the frequency response curves of the oscillation are obtained by using the method of harmonic balance.
Abstract: This paper deals with the phenomenon of nonlinear resonance which occurs in an electrical oscillatory circuit containing a saturable iron core with hysteresis. An analytical expression for the magnetization curve of the iron core is assumed. The amplitude characteristic and the frequency response curves of the oscillation are obtained by using the method of harmonic balance. The stability of oscillations is discussed through the method of slowly-varying amplitude and phase of the oscillations. A noteworthy fact regarding the influence of hysteresis is the appearance of an isolated portion in the frequency response curves. A physical interpretation of this phenomenon is given.
TL;DR: In this article, the steady state and transient response characteristics of a new class of low-pass filters were investigated and compared with those of the Butterworth and Thomson filters and the recent class of filters due to Mullick.
Abstract: This paper presents the results of an investigation on the steady-state and transient response characteristics of a new class of low-pass filters. The natural frequencies of the proposed filters all lie on catenary contours and the transmission zeros are all at infinity. This class of ladder filters has some useful transmission properties when both time and frequency domain considerations are important. The response characteristics of this class of filters are compared with, those of the Butterworth and Thomson filters and the recent class of filters due to Mullick. We show that this class has some advantages when the rise-time, overshoot, and 3db frequency of the magnitude response (with no frequency peaking) are all of importance simultaneously.
TL;DR: In this paper, a slab of transparent methyl methacrylate plastic is irradiated by the sun and the time-temperature response of the slab is recorded, and a mathematical model of an irradiated transparent solid is solved for the temperature distribution in the slab as a function of time and distance in the solid.
Abstract: A slab of transparent methyl methacrylate plastic is irradiated by the sun, and the time-temperature response of the slab is recorded. Using the transmission spectrum of the plastic, a mathematical model of an irradiated transparent solid is solved for the temperature distribution in the slab as a function of time and distance in the solid. Comparison of the experiment and theory shows that the mathematical model predicts the thermal trap effect quite well.
TL;DR: It is shown that a bandlimited signal can be designed which eliminates intersymbol interference for signalling at Nyquist rate, and this signal is a solution to a quadratic integral equation.
Abstract: This paper considers the solution of a quadratic integral equation of the first kind arising in the design of bandlimited signals for binary communication using simple memory-less correlation detection. The signals are disturbed by additive white Gaussian noise. It is shown that a bandlimited signal can be designed which eliminates intersymbol interference for signalling at Nyquist rate. This signal is a solution to a quadratic integral equation. The existence of the solution, as well as a construction of the solution of this equation, are presented. The method of solution of the integral equation is applicable to a broad class of problems.
TL;DR: In this article, the authors considered nonhomogeneous boundary value problems of the Sturm-Liouville type with random forcing functions and found the statistical moments of the response in the case that the forcing function is stationary and weakly correlated, thereby extending previous work having to do with stochastic initial value problems.
Abstract: Nonhomogeneous boundary value problems of the Sturm-Liouville type having random forcing functions are considered. Estimates for the statistical moments of the response are found in the case that the forcing function is stationary and weakly correlated, thereby extending previous work having to do with stochastic initial value problems. The effect of an arbitrary parameter in the boundary conditions upon the second moment is studied in some detail in two typical problems.
TL;DR: In this paper, the absorbance of borohydride ion with acetone in aqueous solution is compared to that of a reagent blank from which the borhydride is omitted.
Abstract: The rapid, quantitative reaction of borohydride ion with acetone in aqueous solution is utilized to determine borohydride via an indirect spectrophotometric method. The absorbance of such a solution at Q66mμ is compared to that of a reagent blank from which the borohydride is omitted. The amount of acetone used up in the reaction with boro hydride is thus calculated and, from the stoichiometry of this reaction, the amount of borohydride initially present is determined. The method is applicable to the commercially available alkali metal and tetraalkylammonium borohydrides. Interference from active hydride impurities can be avoided.