Sigmoidal functions are usually used to characterize the behavior of dynamical systems, in particular, for neural networks. Recently, multilevel piecewise linear functions have been employed in cellular neural networks (CNN). In this paper, we first use the inverse trigonometric function, tan−1(x), to generate a series of trigonometric functions to obtain one-, twoand three-directional multi-sc...

The goal of this work was to answer one simple question: given that the trigonometric functions take hundreds of clock cycles to execute on a Pentium IV, can they be computed faster, especially given that all Intel processors now have fast floating-point hardware? The streaming SIMD extensions (SSE/SSE2) in every Pentium III and IV provide both scalar and vector modes of computation, so it has ...

In this paper, we present a new primal-dual interior-point algorithm for linear optimization based on a trigonometric kernel function. By simple analysis, we derive the worst case complexity for a large-update primal-dual interior-point method based on this kernel function. This complexity estimate improves a result from [1] and matches the one obtained in [2].

Equivariant function with respect to symmetries of the wallpaper group is constructed by trigonometric functions. A proper transformation is established between Euclidean plane and hyperbolic spaces. With the resulting function and transformation, wallpaper patterns on the Poincaré and Klein models are generated by means of dynamic systems. This method can be utilized to produce infinity of bea...

The issue is uniqueness of representation by multiple trigonometric series. Two basic uniqueness questions, one about series which converge to zero and the other about series which converge to an integrable function, are asked for each of four modes of convergence: unrestricted rectangular convergence, spherical convergence, square convergence, and restricted rectangular convergence. Thus there...

Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes method based on the trigonometric function to derive updated form existing models. The proposed family called cotangent trigonometric-G distributions. Based method, version Weibull model, namely, distribution, studied. Certain mathematical properties are deri...

Reasoning has been extensively studied by many experts. However, Research on student reasoning in trigonometric problem solving, particularly those related to logical thinking skills is still sorely needed. This study aimed explore students' solving function problems regarding skills. The research was conducted using a qualitative approach. subjects involved high school students Palopo, Indones...

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (∨-system) and we determine all trigonometric ∨-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a fact...