scholarly journals A New Application of the $${\bar{\partial }}$$-Method

2021 ◽  
Vol 28 (4) ◽  
pp. 492-506
Author(s):  
Shiyin Zhao ◽  
Yufeng Zhang ◽  
Xiangzhi Zhang
Keyword(s):  
Soliton Solutions ◽  
Nonlinear Schrödinger ◽  
Lie Bracket ◽  
Dirac Function ◽  
Formula Method

AbstractBy constructing a new calculating rule of Lie bracket, we construct a new nonlinear Schrödinger hierarchy and its reduction equations via using the $${\bar{\partial }}$$ ∂ ¯ -method. Furthermore, some soliton solutions of such the equation are obtained by making use of Dirac function.

Computation of the integral Fermi-Dirac function

2012 ◽  
Vol 4 (5) ◽  
pp. 464-470 ◽  
Author(s):  
R. V. Golovanov ◽  
K. I. Lutskii
Keyword(s):  
Dirac Function

scholarly journals Pole-Based approximation of the Fermi-Dirac function

2009 ◽  
Vol 30 (6) ◽  
pp. 729-742 ◽  
Author(s):  
Lin Lin ◽  
Jianfeng Lu ◽  
Lexing Ying ◽  
E. Weinan
Keyword(s):  
Dirac Function

Numerical Studies on Resistive Wall Instabilities in Cylindrical Plasma Confined by Surface Current

2011 ◽  
Vol 50-51 ◽  
pp. 785-789
Author(s):  
Shao Yan Cui ◽  
Peng Xie
Keyword(s):  
Plasma Flow ◽  
Initial Perturbation ◽  
Surface Current ◽  
Cylindrical Plasma ◽  
Resistive Wall Mode ◽  
Numerical Studies ◽  
Function Distribution ◽  
Resistive Wall ◽  
Dirac Function ◽  
The Stability

The stability of resistive wall mode is studied in cylindrical plasma confined by surface current, which is Dirac -function distribution. For Dirac -function distribution case, it is shown that the perturbations oscillate and even decline wherever the initial perturbation seed is placed. The whole system is stable and the plasma flow has little effect on it.

scholarly journals The Dirac function in non-linear differential equations

1958 ◽  
Vol 03 (5) ◽  
pp. 348-359
Author(s):  
Václav Doležal ◽  
Jaroslav Kurzweil ◽  
Zdeněk Vorel
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Dirac Function ◽  
Linear Differential

scholarly journals Optimal Execution considering Trading Signal and Execution Risk Simultaneously

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yuan Cheng ◽  
Lan Wu
Keyword(s):  
Kernel Function ◽  
Price Impact ◽  
Value Functions ◽  
Feedback Form ◽  
Bellman Equations ◽  
Impact Function ◽  
Optimal Execution ◽  
Dirac Function ◽  
Hamilton Jacobi Bellman ◽  
Optimal Execution Problem

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

Critical exponent in a Stefan problem with kinetic condition

1997 ◽  
Vol 8 (5) ◽  
pp. 525-532 ◽  
Author(s):  
ZHICHENG GUAN ◽  
XU-JIA WANG
Keyword(s):  
Free Boundary ◽  
Critical Exponent ◽  
Global Solution ◽  
Stefan Problem ◽  
Finite Time ◽  
Blow Up ◽  
One Dimensional ◽  
Kinetic Condition ◽  
Dirac Function ◽  
The One

In this paper we deal with the one-dimensional Stefan problemut−uxx =s˙(t)δ(x−s(t)) in ℝ ;× ℝ+, u(x, 0) =u0(x)with kinetic condition s˙(t)=f(u) on the free boundary F={(x, t), x=s(t)}, where δ(x) is the Dirac function. We proved in [1] that if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some M>0 and γ∈(0, 1/4), then there exists a global solution to the above problem; and the solution may blow up in finite time if f(u)[ges ] Ceγ1[mid ]u[mid ] for some γ1 large. In this paper we obtain the optimal exponent, which turns out to be √2πe. That is, the above problem has a global solution if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some γ∈(0, √2πe), and the solution may blow up in finite time if f(u)[ges ] Ce√2πe[mid ]u[mid ].

Sign in / Sign up

Export Citation Format

Share Document