In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...

We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.

Abstract In recent years, the Sine Cosine Algorithm (SCA) has become one of popular swarm intelligence algorithms due to its simple and convenient structure. However, standard SCA tends fall into local optimum when solving complex multimodal tasks, leading unsatisfactory results. Therefore, this study presents with communication quality enhancement, called CCEQSCA. The proposed algorithm includ...

Abstract In this paper, a hybrid algorithm called rough sine cosine (RSCA) is introduced for solving engineering optimization problems by merging the (SCA) with set theory concepts (RST). RSCA combines benefits of SCA and RST to focus search promising region where global solution can be found. Due imprecise information on problems, efficient algorithms roughly identify optimal type uncertain da...

In the present paper, we generalize Zygmund classes of functions with two variables defined by Móricz by means of modulus of continuity, and give the necessary and sufficient conditions for double sine, sine-cosine, cosinesine and double cosine series so that their sums belong to the generalized Zygmund classes. Some new results of Fülöp [1] and [2] on double trigonometric series are extended.

The Fourier spectra of circular gratings having sine or cosine radial profiles are derived, and their particular properties are discussed. These results are then extended to the most general form of circular sinusoidal gratings, namely: circular sine or cosine gratings with any arbitrary radial phase. q 1998 Elsevier Science B.V.

The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S + (x), S − (x), C + (x), and C − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x r + , x r are evaluated. 1. Introduction. The Fresnel integrals occur in the diffraction theory...