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Oscillation Condition of Quartz-Oscillating Circuit in High Frequency (1)

IEEJ Transactions on Electronics, Information and Systems, 2009
A novel oscillation condition of quartz oscillating circuit with 622 MHz AT-Cut HFF-Xtal (=High Frequency Fundamental-crystal) oscillator is established. A circuit analysis is performed by combining a shunt capacitance (C0) with a negative resistance (-Rci) and a combination capacitance (Ct). A load resistance (RL) is obtained by combining C0 with -Rci.
Tomio Sato   +2 more
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Start-oscillation conditions in modulated and unmodulated O-type oscillators

IRE Transactions on Electron Devices, 1961
The starting conditions for the O-type backward-wave oscillator are computed for large values of C, QC and d, using both digital and analog methods. A general method of solving complex polynomials called the "downhill" method is applied both to the secular equation and then to the RF voltage equation to obtain starting conditions.
J.E. Rowe, H. Sobol
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RHEED oscillations at special diffraction conditions

Surface Science, 1993
Abstract It is suggested that analysis of RHEED intensity oscillations can be simplified when diffraction conditions are chosen appropriately and two cases are presented as supporting evidence. The first is an out-of-phase condition where the specular reflection from the substrate is very weak. At this condition the oscillations can be described by a
P.A. Maksym, Z. Mitura, M.G. Knibb
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Backward-wave oscillator starting conditions

IRE Transactions on Electron Devices, 1957
Detailed calculations of the starting conditions for backward-wave oscillations were carried out in the region 0 < QC < 0.25. The coupled-mode theory is called upon to explain the complex nature of the propagation constants for backward-wave interaction.
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Extraction under vacuum-oscillation boiling conditions

Pharmaceutical Chemistry Journal, 2006
Anew method is proposed for the extraction of biologically active substances from raw plant materials, which makes use of an apparatus featuring the periodic formation and collapse of vapor bubbles in the processed suspension. The influence of the boil-up frequency, the amplitude of volume variations, and the temperature of extractant on the mechanism ...
E. V. Ivanov   +3 more
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Oscillation Conditions in Single Tuned Amplifiers

Journal of Applied Physics, 1946
An application of the calculus of finite differences has been made in obtaining the complete expression for the voltage gain of an n-stage amplifier having identical grid-to-plate impedances and plate loads when driven by a generator of any given internal impedance.
William R. Faust, Hugo M. Beck
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Sharp conditions for rapid nonlinear oscillations

Nonlinear Analysis: Theory, Methods & Applications, 2000
The authors consider the equation \[ \ddot x + g(x)=f(t,x,\dot x) \tag{1} \] where \(g:{\mathbb{R}}\to {\mathbb{R}}\) and \(f:[a,b]\times {\mathbb{R}}\times {\mathbb{R}}\to{\mathbb{R}}\) are \(C^1\)-functions, \(xg(x)>0\) for \(|x|\) large. \(g(x)\) is superlinear and associated boundary value problems are referred to as superlinear also. One says that
Klokov, Yu. A., Sadyrbaev, F. Zh.
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Klein's Oscillation Theorem for Periodic Boundary Conditions

Canadian Journal of Mathematics, 1971
Multiparameter eigenvalue problems for systems of linear differential equations with homogeneous boundary conditions have been considered by Ince [4] and Richardson [5, 6], and more recently Faierman [3] has considered their completeness and expansion theorems.
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SUFFICIENT CONDITIONS FOR OSCILLATION OF THE LIÉNARD EQUATION

Chinese Annals of Mathematics, 2000
Sufficient conditions for the oscillation of all solutions to the generalized Liénard equation \[ \dot{x}=h(y)-F(x),\quad \dot{y}=-g(x), \tag{*} \] with \(F(0)=0\), \(yh(y)>0\), \(xg(x)>0\) for \(x,y\neq 0\), \(h(y)\) is strictly increasing, \(\lim_{y\to \pm\infty}h(y)=\pm \infty\) and \(\lim_{|x|\to \infty}G(x)=\infty\), with \(G(x)=\int_0^x g(s) ds\).
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Nonlinear Langmuir oscillations under nonequilibrium conditions

Physics of Plasmas, 2000
The influence of external ionization sources on the characteristics of Langmuir oscillations in a partially ionized plasma is considered. It is demonstrated that in the case of continuous sources of ionization the nonlinear Langmuir oscillations are nonharmonic and are determined by the Airy equation.
A. R. Karimov, V. A. Shcheglov
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