scholarly journals A large probability averaging theorem for the defocusing NLS

Nonlinearity ◽  
2019 ◽  
Vol 32 (10) ◽  
pp. 3661-3694 ◽  
Author(s):  
D Bambusi ◽  
A Maiocchi ◽  
L Turri
Keyword(s):  
Large Probability ◽  
Averaging Theorem

scholarly journals Second-order differential equations with random perturbations and small parameters

2017 ◽  
Vol 147 (4) ◽  
pp. 763-779
Author(s):  
M. Kamenskii ◽  
S. Pergamenchtchikov ◽  
M. Quincampoix
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Random Perturbation ◽  
Stochastic Averaging ◽  
Second Order ◽  
Random Perturbations ◽  
Existence And Uniqueness Theorem ◽  
Second Order Differential Equations ◽  
Averaging Theorem ◽  
Small Parameters

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

Generalized proof of the modified averaging theorem

1980 ◽  
Vol 35 (6) ◽  
pp. 1462-1463 ◽  
Author(s):  
Ismail Tosun ◽  
Max S. Willis
Keyword(s):  
Averaging Theorem

On the Number of Limit Cycles of Discontinuous Liénard Polynomial Differential Systems

2018 ◽  
Vol 28 (14) ◽  
pp. 1850175
Author(s):  
Fangfang Jiang ◽  
Zhicheng Ji ◽  
Yan Wang
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Upper Bounds ◽  
Second Order ◽  
Discontinuous Differential Equations ◽  
Differential Systems ◽  
Lower Upper ◽  
First Order ◽  
Polynomial Differential Systems ◽  
Averaging Theorem

In this paper, we investigate the number of limit cycles for two classes of discontinuous Liénard polynomial perturbed differential systems. By the second-order averaging theorem of discontinuous differential equations, we provide several criteria on the lower upper bounds for the maximum number of limit cycles. The results show that the second-order averaging theorem of discontinuous differential equations can predict more limit cycles than the first-order one.

A Time-Interleaved Statistically-Driven Two-Step Flash ADC for High-Speed Wireline Applications

2017 ◽  
Vol 26 (07) ◽  
pp. 1750118 ◽  
Author(s):  
Dengbao Liu ◽  
Lin He ◽  
Fujiang Lin ◽  
Ting Li ◽  
Yu-Kai Chou
Keyword(s):  
Probability Distribution ◽  
Input Signal ◽  
High Speed ◽  
Small Probability ◽  
Flash Adc ◽  
Analog To Digital ◽  
Second Stage ◽  
Large Probability ◽  
Interleaved Adc ◽  
Time Interleaved

This paper presents a statistically-driven two-step flash sub-analog-to-digital converter (ADC) to construct the high-speed time-interleaved ADC in wireline communication applications. The comparators in the flash sub-ADC are divided into the large probability first stage and the small probability second stage to take advantage of the nonuniform probability distribution of the input signal. At the first step of operation, the large probability first stage is activated while the small probability second stage is suspended. If the input signal is beyond the input range of the first stage, the segment selection signal will trigger proper segment in the second stage. Feed-forward equalization is proposed to manipulate the probability distribution of the ADC input signal. A possible implementation of the proposed ADC as well as the modulation and equalization scheme is presented to comply with the IEEE 802.3ap 10[Formula: see text]G Ethernet standard. In the case of a PAM-4 pseudorandom signal, the proposed solution achieves [Formula: see text] reduction on the average number of activated comparators compared to a conventional flash ADC.

scholarly journals An abstract averaging theorem

1976 ◽  
Vol 23 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Thomas G Kurtz
Keyword(s):  
Averaging Theorem
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