Closed-form solutions to sensitivity equations in the frequency and time domains for linear models of ecosystems

1983 ◽  
Vol 18 (3-4) ◽  
pp. 209-221 ◽  
Author(s):  
James R. Kercher
Keyword(s):  
Closed Form ◽  
Linear Models ◽  
Closed Form Solutions ◽  
Sensitivity Equations ◽  
Time Domains

Closed Form Solutions to Nonlinear Heat Conduction Problems

2012 ◽  
Vol 326-328 ◽  
pp. 115-119
Author(s):  
J. Zabadal ◽  
R. Garcia ◽  
V. Ribeiro ◽  
F. Van Der Laan
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Closed Form ◽  
Control Systems ◽  
Analytical Method ◽  
Linear Models ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Heat Conduction ◽  
Closed Form Solutions ◽  
Standard Techniques

This work presents a new analytical method for solving nonlinear heat conduction problems in arbitrary domains. The method is based on approximate mappings which transforms nonlinear partial differential equations into linear models which can be solved using standard techniques. In order to verify whether the proposed formulation can be employed to conceive new online control systems, numerical results are reported.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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