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The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
Then, we describe a numerical method to compute the dual function and give an estimate of the error.
      
The popularity of PSWFs seems likely to increase in the near future, as band-limited functions become a numerical (as well as an analytical) tool.
      
A numerical example illustrates that the method is available.
      
A numerical example is given to illustrate the solution procedure.
      
A numerical example is given to illustrate the procedures, prediction intervals are investigated via Monte Carlo method, and the accuracy of prediction intervals is presented.
      
Based on the basic principles of the micrometeorology of atmospheric boundary layers and vegetation canopy, a numerical model of the interaction between forest ecosystems and atmospheric boundary layers was developed.
      
Moreover, the new model was solved through a numerical method and was illustrated with typical values of some ecological factors; three groups of curves were acquired by calculation with the VisualBasic program.
      
A lightweight automotive prototype using alternative materials and gauge thickness is studied by a numerical method.
      
Based on the theory of heat transfer, this paper supplies a numerical solution to the non-homogeneous equation of heat transfer through the group explicit (GE) finite difference approach.
      
A numerical study of helium-heated inorganic membrane reformer coupling to HTGR
      
The flows were also analyzed using a numerical model of the three-dimensional turbulent flow in the pumps near the peak efficiency point using the k-? turbulence model and the VOF cavitation model.
      
The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves.
      
A numerical example was used to demonstrate effciency of the algorithm, the ways to improving it, and the differences between the suboptimal robust controllers with structured and nonstructured operator perturbations.
      
A numerical example is given to illustrate the efficiency of the approach.
      
A numerical method is set out for the determination of values of the probability distribution density of the time taken to fulfill the GERT network of a large dimension with the use of an inversion formula.
      
A numerical method of solution was proposed on the basis of the universal procedure of determining the spanning trees of the edge-weighted graph arranged in the nondecreasing order of their lengths.
      
The method was illustrated by a numerical example.
      
Results of a numerical modeling experiment are given.
      
The results of a numerical experiment corroborating the effectiveness of new methods are given.
      
 

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