Application of the Cesaro Mean to the Transient Interaction of a Spherical Acoustic Wave and a Spherical Elastic Shell

1972 ◽  
Vol 39 (2) ◽  
pp. 623-625 ◽  
Author(s):  
B. S. Berger ◽  
D. Klein
Keyword(s):  
Acoustic Wave ◽  
Elastic Shell ◽  
Cesàro Mean ◽  
Transient Interaction ◽  
Spherical Elastic Shell ◽  
Cesaro Mean

scholarly journals Neoclassical Solution of Transient Interaction of Plane Acoustic Waves with a Spherical Elastic Shell

1996 ◽  
Vol 3 (2) ◽  
pp. 85-98 ◽  
Author(s):  
Hanson Huang ◽  
Hans U. Mair
Keyword(s):  
Laplace Transform ◽  
Acoustic Waves ◽  
Separation Of Variables ◽  
Elastic Shell ◽  
Time Derivative ◽  
Time History ◽  
Inverse Laplace Transform ◽  
Transient Interaction ◽  
Time Histories ◽  
Spherical Elastic Shell

A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.

scholarly journals Some subordination involving polynomials induced by lower triangular matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saiful R. Mondal ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Unit Disk ◽  
Triangular Matrices ◽  
Cesàro Mean ◽  
Cesaro Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

Deferred Cesàro summability and statistical convergence for double sequences of sets

2021 ◽  
pp. 1-9
Author(s):  
Uğur Ulusu ◽  
Esra Gülle
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean

The main purpose of this paper is introduced the concept of deferred Cesàro mean in the Wijsman sense for double sequences of sets and then presented the concepts of strongly deferred Cesàro summability and deferred statistical convergence in the Wijsman sense for double sequences of sets. Also, investigate the relationships between these concepts and then to prove some theorems associated with the concepts of deferred statistical convergence in the Wijsman sense for double sequences of sets is purposed.

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