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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 017 820 97X  
Author(s):  
Chen, Mufa  
Shorttitle:  
Variational formulas and approximation theorems for the first eigenvalue in dimension one.  
Source:  
Sci. China, Ser. A 44, No. 4, 409  418 (2001).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
elliptic linear differential/difference operators; first Dirichlet/Neumann eigenvalues; the lowest eigenvalue; bothsided estimates  
Review:  
On a finite or semiinfinite interval the author considers a general superposition L of the first and second derivative with xdependent coefficients and with Dirichlet or Neumann boundary condition in the origin. The work is a continuation of its seven (all self) references [this makes it less easy to put this paper in broader context since just one of them (but Trans. Amer. Math Soc.!) is extraterritorial] but offers very nice results (their essence being well characterized by the title, and they look ``final"). Amazingly enough, these explicit bounds are complete (i.e., bothsided)! Three illustrative examples demonstrate their power in applications. The study is complemented by its discrete, Markovchain parallel considering the birthdeath process mediated by the purely secondorder difference operator D (personally, I would recommend to read this supplement first).  
Remarks to the editors:  