1. ### A Study of Sensitivity of Nonlinear Oscillations of a CLD Parallel Circuit to Parametrization of Tunnel Diode

Haiduke Sarafian

The Pennsylvania State University, University College, York, PA, 17403.

Abstract: Tunnel diode aka Esaki diode [1] is a peculiar nonlinear electronic element possessing negative ohmic resistance. We consider a multi-mesh circuit composed of three elements: a charged capacitor, C, a self-inductor, L, and an Esaki diode, D, (CLD) all three in parallel. We parametrize the I-V characteristics of the diode and derive the circuit equation; this is a nonlinear differential equation. Applying a Computer Algebra System (CAS) specifically Mathematica [2] we solve the circuit equation numerically conducive diode dependent parametric solution; in general the solution has a damped oscillatory character. In this note we investigate the sensitivity of the oscillations as a function of diode’s parameters. We establish the fact that for a set of parameters the tunnel diode behaves almost as an ohmic resistor and that the circuit equation tends toward classic CLR-parallel circuit with linear damped oscillations. Mathematica simulation assists visualizing the transition.

Keywords: Tunnel Diode, Electrical Nonlinear Oscillations, Computer Algebra System, Mathematica.

2. ### Interswitching of Transmuted Gamma Autoregressive Random Processes

Rasaki Olawale Olanrewaju1, Johnson Funminiyi Ojo2, Adekola Lanrewaju Olumide3

1. Department of Mathematical Sciences, Pan African University Institute for Basic Sciences, Technology and Innovation. P.O. Box 62000-00200, Nairobi, Kenya.
2. Department of Statistics, University of Ibadan, Ibadan, P.O. Box 200284, Oyo state, Nigeria.
3. Department of Physical Sciences, Bells University of Technology, Ota, Nigeria.

Abstract: We study the assortment of autoregressive random processes via a transmuted Gamma distributed noise. We consider a transmuted re-parameterization of the Gamma parameters in terms of μ and σ2, afterwards ascertained that the transmuted Gamma is a proper probability density function, then proceeded to spelt-out the structural form and traits of the Gamma Mixture Autoregressive generalization in its k-components. The mean and variance of the Gamma Autoregressive model were ascertained coupled with its first and second-order stationarity. The ingrained k-components’ autoregressive coefficients, re-parameterization Gamma coefficients, k-regime transitional weights were estimated via Expectation-Maximization (EM) algorithm. However, some step ahead predictions were derived as well as the model sub-setting estimation via Levinson-Durbin recursive technique.

Keywords: Expectation-Maximization (EM) algorithm, Gamma Autoregressive model, k-components, k-regime transitional weights, Levinson-Durbin recursive, Transmuted.