We show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real preHilbert space H. Adopting the language of Deza and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional...

abstract accurate prediction of hourly minimum temperature is required for various crop models which simulate photosynthesis and transpiration. such data can be used for crop protection and reducing the crops injuries due to freezing as well. our objective of this study is employing trigonometric and pattern recognition (k-nn) approaches to evaluate their potential in prediction of hourly tempe...

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.

The aim of this paper is to introduce the hybrid form hyperbolic Horadam function and investigate some its properties such as generating function. Another define sine cosine functions their symmetrical forms. For newly defined functions, recursive relations, derivatives, Cassini De Moivre type identities are examined. In addition, quasi-sine three-dimensional spiral defined.

In the paper, authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine tangent, composite incomplete gamma function with hyperbolic sine, in terms first kind Stirling numbers, apply a newly established expansion to derive closed-form formula specific partial Bell polynomials representation generalized logsine function, deduce combinatorial involving...

In this paper, it is shown that D. Shelupsky’s generalized sine function, and various general sine functions developed by P. Drábek, R. Manásevich and M. Ôtani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential...

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

A new approach for generating -scroll attractors is introduced. It is demonstrated that -scroll attractors can be generated using a simple sine or cosine function. A guideline is given so that a different number of scrolls can be designed easily by modifying two variables in the function. An electronic circuit is also designed for the implementation and the observation of a 9-scroll attractor i...