In the article, we present new bounds for the function [Formula: see text] on the interval [Formula: see text] and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.

We refine a formula on values of multiple sine functions at division points. As applications we prove a formula on a sum of reciprocal trigonometric values, and obtain multiple modularity of a three variable modular function, which concerns a generalization of the Dedekind η function.

In this paper, based on the generalized Jacobi elliptic function expansion method,we obtain abundant new complex doubly periodic solutions of the double Sine-Gordon equation (DSGE), which are degenerated to solitary wave solutions and triangle function solutions in the limit cases,showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations i...

In the present paper polynomial interpolating scaling function and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function efficient algorithms based on fast discrete cosine and sine transforms are proposed.

This paper describes third aircraft model with 2 degrees of freedom. The aim of this study is to develop a mathematical model for investigation of adoptable landing gear vibration behavior and to design Proportional Integration Derivative (PID) classical techniques for control of active hydraulic nonlinear actuator. The parameters of controller and suspension system are adjusted according to be...

Kamesh Krishnamurthy, ∗ Ann M. Hermundstad, ∗ Thierry Mora, Aleksandra M. Walczak, and Vijay Balasubramanian † David Rittenhouse and Richards Laboratories, University of Pennsylvania, Philadelphia, PA 19104, USA Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, VA 20147, USA Laboratoire de physique statistique, UMR8550, CNRS, UPMC and École Normale Supérieure...

In this paper, we define a group of solutions x(t) that are sine and cosine to the upper limit integration in non-elementary integral can be arbitrary. We will also equal amplitude. This is generalized amplitude function. using Abel’s methods, described by Armitage Eberlein. And finally, an exponential function whose exponent product complex number At least three groups functions special cases

In this paper we design a CORDIC architecture for variable–precision, and a new algorithm is proposed to perform the interval sine and cosine functions. This system allows us to specify the precision to perform the sine and cosine functions, and control the accuracy of the result, in such a way that recomputation of inaccurate results can be carried out with higher precision. An important reduc...