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oscillatory

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oscillatory
oscillatory, a. (ˈɒsɪlətərɪ, əˈsɪlət(ə)rɪ) [f. L. type *oscillātōri-us, f. oscillāre, oscillāt- to oscillate: see -ory.] 1. Characterized by swinging or moving to and fro like a pendulum.1738 Gray Let. in Poems (1775) 35 My motions at present..are much like those of a pendulum or (Dr. Longically spe... Oxford English Dictionary
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Oscillatory integral
In mathematical analysis an oscillatory integral is a type of distribution. Conversely, any oscillatory integral is a Lagrangian distribution. wikipedia.org
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Oscillatory neural network
An oscillatory neural network (ONN) is an artificial neural network that uses coupled oscillators as neurons. Oscillatory neural networks have been trained to recognize images. wikipedia.org
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Oscillatory Solutions of Differential Equation Show that the DE $$y'' +q(x)y = 0 \; (*)$$ is oscillatory if one of the following condition is satisfied: i) $q(x) \geq m^2 > 0$ eventually ii) $q(x) = 1 + \phi(x)$ w...
Conditions ii) or iii) imply condition i). Under condition i), the angle $φ$ of $y=r\cos φ$, $v=r\sin φ$ for the first order system $y'=mv$, $v'=-q/m·y$ follows the differential equation $$ φ'=\frac{yv'-y'v}{y^2+v^2}=-\frac{mv^2+q/m·y^2}{y^2+v^2}=-m-\frac{(q-m^2)/m}{y^2+v^2} $$ Thus the angular velo...
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Oscillatory integral operator
In mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form where the function S(x,y) is called Properties of oscillatory integral operators have been studied by Elias Stein and his school. wikipedia.org
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Definition of purely oscillatory This is question about a term whose definition I can find anywhere. I am given to solve a differential equation and one of the questions asks to show that the solution (we are given in...
"Purely oscillatory" typically refers to a lack of damping, meaning that the spring does not lose amplitude as it oscillates. This means that there is no first derivative term in the diff eq defining the oscillatory motion.
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Oscillatory baffled reactor
A Continuous Oscillatory Baffled Reactor (COBR) is a specially designed chemical reactor to achieve plug flow under laminar flow conditions. There are typically two pumps in a COBR; one pump is reciprocating to generate continuous oscillatory flow and a second pump creates net flow through the wikipedia.org
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Is $a_n = (-1)^{[ \log n]}$ is oscillatory sequence? I know that $a_n =(-1)^n$ is oscillatory sequence as sequence osciallate between $-1$ and $+1 $ I have some doubt in my mind that Is $a_n = (-1)^{[ \log n]}$ is os...
$a_n=1$ if $e^{2k} \leq n <e^{2k+1}$ and $a_n=-1$ if $e^{2k-1} \leq n <e^{2k}$ (for any positive integer $k$) so the sequence oscillates.
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Analyticity of infinitely oscillatory functions I have a simple question: if $f:[-1,1]\to\mathbb{R}$ is analytic, can it be infinitely oscillatory (by which I mean something like $\sin(1/x)$ ?
No, if $U=f^{-1} (f(x))$ is the preimage of $f(x)$ then $x$ must be isolated in $U$.
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SensorMedics high-frequency oscillatory ventilator
The SensorMedics High-Frequency Oscillatory Ventilator is a patented high-frequency (>150 Rf) mechanical ventilator designed and manufactured by SensorMedics 3100B measure actual tidal volumes, it is impossible to wean with precision; as a result, some clinicians find it problematic to use these machines for oscillatory wikipedia.org
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differential equation for oscillatory phase The differential equation $$\frac{d^2 x}{dt^2} + k x = 0$$ leads to harmonic solution like $x = \sin(\omega t + \phi)$. Is there a differential equation that leads to a harm...
You can start by taking the first and second derivatives of your solution: $$\frac{d}{dt}\sin(\omega_a t + \sin(\omega_b t + \phi_b))=(\omega_b \cos(\omega_b t+\phi_b)+\omega_a)\cos(\sin(\omega_b t+\phi_b)+\omega_at)\\\\\frac{d^2}{dt^2}\sin(\omega_a t + \sin(\omega_b t + \phi_b))= −(\omega_b \cos(\o...
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oscillatory period sound - oscillatory period pronunciation - how to ...
oscillatory period 's definition：a punctuation mark (.) placed at the end of a declarative sentence to indicate a full stop or after abbreviations; "in England they call a period a stop"; oscillatory period in Chinese：振荡周期
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[A Meta analysis of the efficacy of high-frequency oscillatory ...
The results of the Meta analysis showed that there were no significant differences between the HFOV and CMV groups in the in-hospital or 30-day mortality rate, incidence of barotrauma, mean ventilation time, and oxygenation index (P>0.05). However, compared with CMV, HFOV increased the PaO 2 /FiO 2 ratio by 17%, 24%, and 31% at 24, 48, and 72 ...
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L 2 estimates for oscillatory singular integral operators with analytic ...
L 2 estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of almost orthogonality, oscillatory estimates and size estimates.
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Highly oscillatory sums Is there a way of calculating sums of (highly) oscillatory functions? _Example._ How can we calculate the following series? (At least asymptotics of it.) $$ \sum_{n=1}^{x} \frac{1}{\sin^2(1/n...
$$\csc^2{(1/n)}=n^2+\frac13+O(1/n^2)$$ So for large $x$ your summation becomes $$\sum_{n=1}^x \left(n^2+\frac13+O(1/n^2)\right)=\frac16x(x+1)(2x+1)+\frac13x+O(1)$$
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