As an innovative point of this work, the auxiliary functions are introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations.
Each of admissible functions, regardless of boundary conditions, is composed of a standard Fourier cosine series and several auxiliary functions introduced to ensure and accelerate the convergence of series representations.
Regardless of the boundary conditions, each of the displacement and rotation components of the sector plates is described as a linear superposition of a double Fourier cosine series and several supplementary functions introduced to accelerate the convergence of series representations.
Each of the shell displacements, regardless of boundary conditions, is constructed as a standard Fourier cosine series supplemented with auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the edges and accelerate the convergence of series representations.
Under the current framework, each of the shell displacements, regardless of boundary conditions, is expanded as a standard Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the edges and accelerate the convergence of series representations.
We study the Jacobson topology on the primitive ideal space Prim C* N) of the group C*-algebra of N. We are able to describe this topology in terms of convergence of subgroup-representation pairs, as used by the first author in an earlier work.
The modified Fourier series is expressed in the form of the linear superposition of a double cosine series and auxiliary functions which are introduced to ensure and accelerate the convergence of the series representations.
In our final analysis, we tested the convergence of schema component representations during the transfer test.
We present a comprehensive analysis of the convergence properties of the frame operators of Weyl–Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation.
Each of the displacement functions is here invariably expressed as a modified Fourier series, which consists of a standard Fourier cosine series plus several supplementary series/functions used to ensure and improve uniform convergence of the series representation.
And each of beam displacements, regardless of boundary conditions, is expanded as a modified Fourier series composed of a standard cosine Fourier series and certain supplementary terms introduced to remove the potential discontinuities at the ends, thus ensure and accelerate the convergence of the series representation.
