Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, changing paradigm can highly simplify envisioning and explaining three-dimensional rotations. This change allows high school student with an understanding geometry to develop matrix explain at collegiate level. The proposed method includes assumption point (P) within initial frame axe...

Abstract The set of points that escape to infinity under iteration a cosine map, is, the form $C_{a,\,b} \colon z \mapsto ae^z+be^{-z}$ for $a,\,b\in \mathbb{C}^\ast$ , consists collection injective curves, called dynamic rays . If critical value $C_{a,\,b}$ escapes infinity, then some its overlap pairwise and split at points. We consider large subclass maps with escaping values, including map ...

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal t...

Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family {Ft : t ∈ R} of linear continuous multifunctions Ft : K → cc(X) there exists a linear continuous multifunction H : K → cc(K) such that Ft(x) ⊂ ∞ X n=0 t (2n)! H(x). Let X be a real normed vector space. We will denote by n(X) the family of all nonempty subsets of X and by cc(...

ABSTRACT A commonly used decimation filter is the cascadedintegrator-comb (CIC) filter, which consists of two main sections: an integrator and a comb, separated by a down-sampler. This ffilter is attractive in many applications because of its very low complexity which requires no multipliers and storages. The magnitude characteristic of this filter has a low attenuation in the stopband, and a d...

This paper presents a feature extraction scheme called multichannel flexible local discriminant bases (MF-LDB) for left/right index finger movement imagery classification of a multi-channel electroencephalogram (EEG). The MF-LDB is obtained by calculating the local cosine packets (LCP) of the decided channel over nonuniform time-segments. The proposed method combines information from neighborin...

ABSTRACT In this paper, we propose a new numerical method for solving a rib waveguide TE-mode problem. In the proposed method, the cross-section of the waveguide is divided into several regions and the refractive index profile and field distribution in each region are expanded into Fourier cosine series, and then are substituted in the wave equation. A second-order differential matrix equation ...