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It is well known that Gabor expansions generated by a lattice of Nyquist density are numerically unstable, in the sense that they do not constitute frame decompositions.
      
Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT).
      
Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
      
This makes them numerically attractive for applications in geophysical modeling.
      
It is simple in structure, implementable, numerically efficient and has global convergence.
      
In particular, when the new shape parameter of the distribution under progressive stress is given (or estimated in advance), the closed forms of these estimators are relatively simple and are numerically accessible on computers.
      
Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically.
      
Spatial soliton solutions of a class of generalized nonlinear Schr?dinger equations in N-space are discussed analytically and numerically.
      
Option prices are computed numerically in a Markov chain approximation for the case of exponential utility.
      
A new method based on the finite difference time domain (FDTD) method is presented to numerically analyze the transmission and reflection characteristic of composite materials with negative effective permittivity.
      
Here, the actuation mechanism of the sandwiched-configuration EWOD chips was carefully studied, and the movement of droplets was numerically analyzed by using the computational fluidic software, CFD-ACE+.
      
The design was investigated numerically to obtain proper dimensions for the antenna and a prototype was constructed.
      
The modified Reynolds equation is numerically calculated using super over relaxation method.
      
This paper attempted to numerically analyze the action process based on damage mechanics when a jet created by bubble collapse acted on the bearing surface in the process of cavitation erosion.
      
Furthermore, influences of the Péclet number (Pe) and Brinkman number (Br) on temperature, Nusselt number (Nu) and thermal stress are revealed numerically.
      
Moreover, the general case of incident electron with any given momentum and spin state are studied numerically in detail, including the abrupt changes of spin direction and the two-step characters for reflection.
      
Firstly, the distributions of welding temperature field and residual stress on a butt joint were numerically simulated with the sequentially coupled method.
      
The spray characteristics of methanol and ethanol with high-pressure swirl injector were explored experimentally and numerically.
      
In this paper, the premixed combustion of CH4/air mixture in a porous medium is numerically simulated with a laminar combustion model.
      
The performance graphs of a centrifugal compressor under different diffuser stagger angles were measured, and the influence of different stagger angles of vanes on the stage performance as well as flow field was investigated numerically.
      
 

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