Blending Approximations with Sine Functions

1992 ◽  
pp. 1-19 ◽  
Author(s):  
G. Baszenski ◽  
F.-J. Delvos ◽  
S. Jester
Keyword(s):  
Sine Functions

scholarly journals Basis properties of the p , q -sine functions

2015 ◽  
Vol 471 (2174) ◽  
pp. 20140642 ◽  
Author(s):  
Lyonell Boulton ◽  
Gabriel J. Lord
Keyword(s):  
Shift Operators ◽  
The Family ◽  
The Subject ◽  
Infinite Multiplicity ◽  
Sine Functions

We improve the currently known thresholds for basisness of the family of periodically dilated p , q -sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing literature on the subject.

Extensions of Zeta Functions ? Examples and a Study of the Double Sine Functions

2005 ◽  
Vol 86 (1-2) ◽  
pp. 179-201
Author(s):  
Nobushige Kurokawa ◽  
Masato Wakayama
Keyword(s):  
Zeta Functions ◽  
Sine Functions

scholarly journals Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Giang
Keyword(s):  
Finite Element ◽  
Compressive Load ◽  
Shear Deformation Theory ◽  
Parameter Study ◽  
Compression Load ◽  
Large Structures ◽  
Geometrical Imperfection ◽  
Compressive Loads ◽  
Vibration Responses ◽  
Sine Functions

In practice, some components in large structures such as the connecting rods between the rotating parts in the engines, turbines, and so on, can model as beam structures rotating around the fixed axis and subject to the axial compression load; therefore, the study of mechanical behavior to these structures has a significant meaning in practice. This paper analyzes the vibration responses of rotating FGM beams subjected to axial compressive loads, in which the beam is resting on the two-parameter elastic foundation, taking into account the initial geometrical imperfection. Finite element formulations are established by using the new shear deformation theory type of hyperbolic sine functions and the finite element method. The materials are assumed to be varied smoothly in the thickness direction of the beam based on the power-law function with the porosity. Verification problems are conducted to evaluate the accuracy of the theory, proposed mechanical structures, and the calculation programs coded in the MATLAB environment. Then, a parameter study is carried to explore the effects of geometrical and material properties on the vibration behavior of FGM beams, especially the influences of the rotational speed and axial compressive load.

scholarly journals Comparing Activation Functions in Modeling Shoreline Variation Using Multilayer Perceptron Neural Network

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1281
Author(s):  
Je-Chian Chen ◽  
Yu-Min Wang
Keyword(s):  
Neural Network ◽  
Multilayer Perceptron ◽  
Activation Function ◽  
Aerial Survey ◽  
Activation Functions ◽  
Shoreline Changes ◽  
Extensive Evaluation ◽  
Aerial Vehicle ◽  
Sine Functions ◽  
Mlp Model

The study has modeled shoreline changes by using a multilayer perceptron (MLP) neural network with the data collected from five beaches in southern Taiwan. The data included aerial survey maps of the Forestry Bureau for years 1982, 2002, and 2006, which served as predictors, while the unmanned aerial vehicle (UAV) surveyed data of 2019 served as the respondent. The MLP was configured using five different activation functions with the aim of evaluating their significance. These functions were Identity, Tahn, Logistic, Exponential, and Sine Functions. The results have shown that the performance of an MLP model may be affected by the choice of an activation function. Logistic and the Tahn activation functions outperformed the other models, with Logistic performing best in three beaches and Tahn having the rest. These findings suggest that the application of machine learning to shoreline changes should be accompanied by an extensive evaluation of the different activation functions.

A Spatial and Temporal Harmonic Balance Method for Obtaining Periodic Solutions of a Nonlinear Partial Differential Equation With a Linear Complex Boundary Condition

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Xuefeng Wang ◽  
Weidong Zhu
Keyword(s):  
Boundary Condition ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Jacobian Matrix ◽  
Additional Function ◽  
Complex Boundary Condition ◽  
Complex Boundary ◽  
Hill’S Method ◽  
Sine Functions ◽  
Nonlinear String

Abstract A spatial and temporal harmonic balance (STHB) method is demonstrated in this work by solving periodic solutions of a nonlinear string equation with a linear complex boundary condition, and stability analysis of the solutions is conducted by using the Hill’s method. In the STHB method, sine functions are used as basis functions in the space coordinate of the solutions, so that the spatial harmonic balance procedure can be implemented by the fast discrete sine transform. A trial function of a solution is formed by truncated sine functions and an additional function to satisfy the boundary conditions. In order to use sine functions as test functions, the method derives a relationship between the additional coordinate associated with the additional function and generalized coordinates associated with the sine functions. An analytical method to derive the Jacobian matrix of the harmonic balanced residual is also developed, and the matrix can be used in the Newton method to solve periodic solutions. The STHB procedures and analytical derivation of the Jacobian matrix make solutions of the nonlinear string equation with the linear spring boundary condition efficient and easy to be implemented by computer programs. The relationship between the Jacobian matrix and the system matrix of linearized ordinary differential equations (ODEs) that are associated with the governing partial differential equation is also developed, so that one can directly use the Hill’s method to analyze the stability of the periodic solutions without deriving the linearized ODEs. The frequency-response curve of the periodic solutions is obtained and their stability is examined.

The remarkable sine functions

1968 ◽  
Vol 8 (4) ◽  
pp. 331
Author(s):  
I.G. Nidekker
Keyword(s):  
Sine Functions
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