scholarly journals A Few Conditions for aC*-Algebra to Be Commutative

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Lajos Molnár
Keyword(s):  
Power Functions ◽  
Exponential Functions ◽  
Algebraic Properties ◽  
Sine And Cosine Functions ◽  
Cosine Functions

We present a few characterizations of the commutativity ofC*-algebras in terms of particular algebraic properties of power functions, the logarithmic and exponential functions, and the sine and cosine functions.

scholarly journals Relation of Some Known Functions in terms of Generalized Meijer G -Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Syed Ali Haider Shah ◽  
Shahid Mubeen ◽  
Gauhar Rahman ◽  
Jihad Younis
Keyword(s):  
Bessel Functions ◽  
Logarithmic Function ◽  
Trigonometric Functions ◽  
Modified Bessel Functions ◽  
Modified Bessel Function ◽  
Exponential Functions ◽  
Hyperbolic Functions ◽  
Binomial Expansion ◽  
Sine And Cosine Functions ◽  
Cosine Functions

The aim of this paper is to prove some identities in the form of generalized Meijer G -function. We prove the relation of some known functions such as exponential functions, sine and cosine functions, product of exponential and trigonometric functions, product of exponential and hyperbolic functions, binomial expansion, logarithmic function, and sine integral, with the generalized Meijer G -function. We also prove the product of modified Bessel function of first and second kind in the form of generalized Meijer G -function and solve an integral involving the product of modified Bessel functions.

Some Mellin-type Definite Integrals Involving Sine and Cosine Functions

2019 ◽  
Vol 10 (1) ◽  
pp. 222-237
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Dilshad Ahamad
Keyword(s):  
Definite Integrals ◽  
Sine And Cosine Functions ◽  
Cosine Functions

SINS Installation Error Calibration Based on Multi-Position Combinations

2011 ◽  
Vol 383-390 ◽  
pp. 4213-4220
Author(s):  
Zhen Huan Wang ◽  
Xi Jun Chen ◽  
Qing Shuang Zeng
Keyword(s):  
Theoretical Analysis ◽  
Least Squares ◽  
Rotation Rate ◽  
Scale Factor ◽  
New Method ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Error Calibration ◽  
Sine And Cosine Functions ◽  
Cosine Functions

A new method is proposed to calibrate the installation errors of SINS. According to the method, the installation errors of the gyro and accelerometer can be calibrated simultaneously, which not depend on latitude, gravity, scale factor and earth's rotation rate. By the multi-position combinations, the installation errors of the gyro and accelerometer are modulated into the sine and cosine functions, which can be identified respectively based on the least squares. In order to verify the correctness of the theoretical analysis, the SINS is experimented by a three-axis turntable, and the installation errors of the gyro and accelerometer are identified respectively according to the proposed method. After the compensation of the installation error, the accuracy of the SINS is improved significantly.

Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

2020 ◽  
pp. 1-23 ◽  
Author(s):  
T. Sathiyaraj ◽  
JinRong Wang ◽  
D. O'Regan
Keyword(s):  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Second Order ◽  
Delay Systems ◽  
Stochastic Delay ◽  
Finite Dimensional ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Theoretical Results

Abstract In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.

Activities: Sine and Cosine Functions with A Calculator

1980 ◽  
Vol 73 (7) ◽  
pp. 521-529
Author(s):  
Dorothea D. Bone ◽  
Evan M. Maletsky ◽  
Christian Hirsch ◽  
Daniel Yates
Keyword(s):  
Sine And Cosine Functions ◽  
Cosine Functions
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