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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：带有内部跳跃条件的ODE特征值问题和logistic扩散方程
内部跳跃条件 ODE特征值问题 logistic扩散方程
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2023/5/16
在本报告中, 我们首先介绍一个带有内部跳跃条件的二阶常微分方程特征值问题, 并将说明该特征值问题等价于一个带有 Dirac 势测度的测度微分方程特征值问题. 进而我们考虑更一般的带有 Dirac 势测度的测度微分方程特征值问题, 并且给出主特征值的存在性定理. 其次, 我们介绍带有内部跳跃条件的 logistic 扩散方程, 并且给出解的存在性定理. 此外, 我们还将讨论这些问题的生物学意义。
DistFlow ODE: Modeling, Analyzing and Controlling Long Distribution Feeder
Modeling, Analyzing and Controlling Long Distribution Feeder Dist Flow ODE
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2012/11/26
We consider a linear feeder connecting multiple distributed loads and generators to the sub-station. Voltage is controlled directly at the sub-station, however, voltage down the line shifts up or down...
Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
Point classification the second order ODE's Ruslan Sharipov Painleve equations
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2012/4/17
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter...
q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE
q-damped Oscillator degenerate roots coefficients q-difference ODE
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2011/9/5
Abstract: The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It i...
Voltage Collapse and ODE Approach to Power Flows: Analysis of a Feeder Line with Static Disorder in Consumption/Production
ODE Voltage Collapse Feeder Line Power Flows Static Disorder
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2011/7/6
We consider a model of a distribution feeder connecting multiple loads to the sub-station. Voltage is controlled directly at the head of the line (sub-station), however, voltage anywhere further down ...
Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE
Differential equations probability theory random coefficients
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2011/1/18
We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector.We also prove a “pointwise” large ...
A finite time blowup result for quadratic ODE's
blowup quadratic ODE's
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2010/11/9
This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems.
An ode to Phipps' jeep convoys
The jeep problem Phipps’ jeep caravans
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2010/12/7
The jeep problem was first solved by O. Helmer and N.J. Fine. But not much later, C.G. Phipps formulated a more general solution. He formulated a so-called convoy or caravan variant of the jeep proble...
On the 7th order ODE with submaximal symmetry
7th order ODE contact curves integral curves
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2010/4/2
We find a general solution to the unique 7th order ODE admitting ten dimensional group of contact symmetries. The integral curves of this ODE are rational contact curves in $\PP^3$ which give rise to ...
A hybrid, PDE-ODE control strategy for intercepting an intelligent, well-informed target in a stationary, cluttered environment
Pursuit Evasion Potential Field Game Theory
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2010/9/16
In [15], [16] a new class of intelligent controllers that can semantically embed an agent in a spatial context constraining its behavior in a goal-oriented manner was suggested. A controller of such a...