A note on q-analogue of Boole polynomials

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.Comment: 11 page

Barnes-type Daehee polynomials

In this paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.Comment: 34 page

A Daily Activity Monitoring System for Internet of Things-Assisted Living in Home Area Networks

In this paper, a daily activity monitoring system for Internet of Things (IoT)- assisted living in home area networks is proposed in order to provide care for elderly people who live alone. The proposed system consists of two main parts: an IoT-assisted living space with contactless activity sensors, a help trigger, and an emergency gateway and a daily activity monitoring server with a range of components including data collection, event and user management, activity analysis and reporting, and so on. The contactless activity sensors can be placed anywhere in the home, and the emergency gateway collects data from them, detects emergency situations reported through the help trigger, and communicates with the daily activity monitoring server. The server analyzes and reports the daily activities and activity patterns of elderly users using a predefined activity index. In addition, unexpected emergency situations can be estimated and prevented through analysis of the activity information

ESTIMATING THE CONVERGENCE RATE OF FUNCTIONAL ITERATIONS FOR SOLVING QUADRATIC MATRIX EQUATIONS ARISING IN HYPERBOLIC QUADRATIC EIGENVALUE PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

We consider Bernoulli's method for solving quadratic matrix equations (QMEs) having form Q(X) = AX^2 +BX+ C = 0 arising in hyperbolic quadratic eigenvalue problems (QEPs) and quasi-birth-death problems (QBDs) where A, B, C ∈ R^[m×m] satisfy Esenfeld's condition [8]. First, we analyze the exsistence of a solution and the convergence of the methods. Second, we sharpen bounds of the rates of convergence. Finally, in numerical experimentations, we show that the modified bounds give appropriate estimations of the numbers of iterations

Linear differential equations for families of polynomials

Abstract In this paper, we present linear differential equations for the generating functions of the Poisson-Charlier, actuarial, and Meixner polynomials. Also, we give an application for each case