Solutions of the Yang-Baxter matrix equation for an idempotent
A. Cibotarica Jiu Ding J. Kolibal Noah H. Rhee
Numerical Algebra, Control & Optimization 2013, 3(2): 347-352 doi: 10.3934/naco.2013.3.347
Let $A$ be a square matrix which is an idempotent. We find all solutions of the matrix equation of $AXA=XAX$ by using the diagonalization technique for $A$.
keywords: Jordan form Yang-Baxter matrix equation commuting matrices diagonalizable matrices. idempotent
A unified maximum entropy method via spline functions for Frobenius-Perron operators
Jiu Ding Noah H. Rhee
Numerical Algebra, Control & Optimization 2013, 3(2): 235-245 doi: 10.3934/naco.2013.3.235
We present a general frame of finite element maximum entropy methods for the computation of a stationary density of Frobenius-Perron operators associated with one dimensional transformations, based on spline function approximations. This gives a unified numerical approach to the density recovery for this class of positive operators by combining the principle of maximum entropy with the idea of finite elements. The norm convergence of the method is proved and the numerical results with the piecewise cubic method show its fast convergence.
keywords: Frobenius-Perron operator Markov approximations. basic spline maximum entropy stationary density
Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions
Jiu Ding Aihui Zhou
Discrete & Continuous Dynamical Systems - A 2000, 6(2): 451-458 doi: 10.3934/dcds.2000.6.451
In this paper, by using a trace theorem in the theory of functions of bounded variation, we prove the existence of absolutely continuous invariant measures for a class of piecewise expanding mappings of general bounded domains in any dimension.
keywords: Frobenius-Perron Operators Invariant Measures Variation.
Jiu Ding Bingsheng He Qin Ni Wenyu Sun
Numerical Algebra, Control & Optimization 2013, 3(2): i-ii doi: 10.3934/naco.2013.3.2i
This special issue is dedicated to the memory of the late Professor Xuchu He of Nanjing University, China. Professor He passed away on April 30, 1990 at the age of 69. An international workshop was held at Nanjing Normal University in May 2011 on the occasion of his 90th birthday.

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