This paper deals with the localization of all the real roots of sine-polynomials. D. Richardson (1991, in ``effective Methods in Algebraic Geometry,'' pp. 427 440, Birkha user, Basel) has already studied this type of analytic function. He showed how to find the number of real roots in a bounded interval. Here we propose an algorithm which determines whether a sine-polynomial has a finite number...

The authors find some new inequalities of Jordan type for the sine function. These newly established inequalities are of new form and are applied to deduce some known results.

It should be remarked that asymptotic estimates of the behavior of the sine and of other integral transforms of regularly varying functions [6] in terms of the function f (1/x) had been obtained before [7–9], both as x → 0 and as x →∞. However, (1.1) is a global estimate that not only considers the endpoint behavior but also holds for all x > 0. Our aim in this article is to generalize (1.1) in...

Colliding Bodies Optimization (CBO) is a population-based metaheuristic algorithm that complies physics laws of momentum and energy. Due to the stagnation susceptibility of CBO by premature convergence and falling into local optima, some meritorious methodologies based on Sine Cosine Algorithm and a mutation operator were considered to mitigate the shortcomings mentioned earlier. Sine Cosine Al...

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink's inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017).

The fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with Uq(ŝl2) is constructed for |q| = 1. The formula for its determinant is given in terms of the double sine function.

In this paper by using numerical evaluation the effect of balancing drupes of water hammer on tunnels lining is considered. In case of not arrangment of these reservoirs, the tunnel lining will be damaged of cyclic powers of water hammer. In this research, function of balancing reservoir of water hammer on cover of tunnels to the barriers’ turbine is simulated by numerical methods and Plaxis 3D...

The brain produces dynamical rhythms at many frequencies that shift in amplitude and phase. To understand the functional consequences of mixtures of oscillations at the single cell level, we recorded the spike trains from single rat cortical neurons in vitro in response to two mixed sine wave currents. The reliability of spike timing was measured as a function of the relative power, phase and f...

Abstract In this paper the frequency distribution of quantization error in coherent sampling of digitizers will be investigated. As the distribution of the quantization error affects the values of THD and SNR, it is relevant for a correct interpretation of THD and SNR of sine waves in coherent sampling. The distribution of the quantization error will be analyzed as a function of N, total number...

We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield...