Modifying the existing probability models in literature and introducing new extensions of is a prominent interesting research topic. However, most recent era, via trigonometry methods have received great attention. This paper also offers novel trigonometric version Weibull model called alpha power cosine-Weibull (for short, “NACos-Weibull”) distribution. The NACos-Weibull distribution introduce...

The Review Opinion Diversification (Revopid-2017) shared task (Singh et al., 2017b) focuses on selecting top-k reviews from a set of reviews for a particular product based on a specific criteria. In this paper, we describe our approaches and results for modeling the ranking of reviews based on their usefulness score, this being the first of the three subtasks under this shared task. Instead of ...

In addressing the issue of text document clustering, a suitable function for measuring the distance between documents is needed. In this paper we explore a function for scoring document similarity based on probabilistic considerations: similarity is scored according to the expectation of the same words appearing in two documents. This score enables the investigation of different smoothing metho...

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity the chaotic behavior of two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine model (ACCM). 2D-ACCM is composed nonlinear bounded cosine function an absolute val...

In this note, we obtain a new multiplicative perturbation theorem for local Cregularized cosine function with a nondensely defined generator A. An application to an integrodifferential equation is given.

This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined when p is a Mersenne pri...

In this paper we characterize hypercyclic translation operators on $$B_{0}(\mathcal {H})$$ , the space of all compact linear a Hilbert $$\mathcal {H}$$ . Also, give some sufficient condition for related cosine operator function to be chaotic or topologically transitive.

Lehmer proved that the values of the cosine function evaluated at rational multiples of π are algebraic numbers. We show how to determine explicit, closed form expressions for the minimal polynomials of these algebraic numbers.