This paper presents the derivations of the voltage transfer functions of the amplifier A, the feedback network β, and the loop gain T of the common-drain (CD) Colpitts oscillator, using the small-signal model of the CD Colpitts oscillator. The derivation of the characteristic equation of the CD Colpitts oscillator is presented. Using the characteristic equation, the equation for the oscillation...

The soil-water characteristic curve can be used to estimate various parameters used to describe unsaturated soil behaviour. A general equation for the soil-water characteristic curve is proposed. A nonlinear, least-squares computer program is used to determine the best-fit parameters for experimental data presented in the literature. The equation is based on the assumption that the shape of the...

In this paper we develop numerical methods for integrating general evolution equations ut = F (u), u(0) = u0, where F is defined on a dense subspace of some Banach space (generally infinite dimensional) and is equivariant with respect to the action of a finite dimensional (not necessarily compact) Lie group. Such equations typically arise from autonomous PDE’s on unbounded domains that are inva...

This document describes how one can derive the solutions to a linear constant coefficient homogeneous differential equation with repeated roots in the characteristic equation with Abel’s Theorem.

In this paper a modified transcendental equation is proposed, and we analyzed its chaotic characteristics and periodic. It is a simple non-linear mode, l but it has complex dynam ics.Then it was used in gray image encryption. This is a digital image encryption algorithm, dual scrambling that based on chaos of pixel position and pixel value.Compared with the traditional transcendental equation, ...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

Cooker’s sloshing experiment is a prototype for studying the dynamic coupling between fluid sloshing and vessel motion. It involves a container, partially filled with fluid, suspended by two cables and constrained to remain horizontal while undergoing a pendulum-like motion. In this paper the fully-nonlinear equations are taken as a starting point, including a new derivation of the coupled equa...

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems. Given an irreducible non-negative power series system with m equations, let ρ be the radius of convergence of the solution power series and let τ be the values of the solu...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...