Hyperbolic sine and cosine functions on measure chains

Two distinct systems of commutative complex numbers inndimensions are described, of polar and planar types. Exponential forms ofn-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and this leads to the concept of residue for path integrals ofn-complex functions. The exponential function of ann-complex number is expanded in terms of functions called in this paper cosexponential functions, which are generalizations tondimensions of the circular and hyperbolic sine and cosine functions. The factorization ofn-complex polynomials is discussed.

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Some Mellin-type Definite Integrals Involving Sine and Cosine Functions

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/1001 ◽

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

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SINS Installation Error Calibration Based on Multi-Position Combinations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.383-390.4213 ◽

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.

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

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/prm.2020.11 ◽

2020 ◽

pp. 1-23 ◽

Cited By ~ 2

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.

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