New Results and Matrix Representation for Daehee and Bernoulli Numbers and Polynomials

In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on Daehee numbers and polynomials. Moreover, we obtained some new results for Daehee and Bernoulli numbers and polynomials

New Results on Higher-Order Daehee and Bernoulli Numbers and Polynomials

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and short proofs of many previous results on higher order Daehee numbers and polynomials. Moreover, we obtained recurrence relation, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigated the relation between these numbers and polynomials and Stirling numbers, Norlund and Bernoulli numbers of higher order. The results of this article gives a generalization of the results derived very recently by El-Desouky and Mustafa [6]

Forecasting the Climate Change through the Distributions of Solar Radiation and Maximum Temperature

The climate change crisis is negatively affecting the world and is the focus of many researchers attention for its life-threatening economic and climate impact on Earth. Therefore, this study aims to estimate the joint distribution function (EFXY) of both daily solar radiation (S) and daily maximum temperature (T) along with the Markov property. In this study, three-parameter distributions have been utilized with S and T, which are generalized extreme value (GEV) and Weibull (W-3P), respectively. Each of these parameters and the joint distribution function ((, )) have been estimated. Four real data of S and T in Queensland, Australia during two consecutive years are applied. The method of maximum likelihood estimation (MLE) is applied on the proposed distributions of S and T to estimate their parameters, which was validated using Goodness-of-Fit tests. In addition, the logarithmic (LFXY) model and the multi-regression model (MFXY) for (, ) are obtained. The results have been compared and the EFXY and LFXY are found to be non-equivalently, while the EFXY and MFXY are equivalent and homogeneous, confirming the validity of the joint distribution function estimate with the least error. Thus, the climate change probabilities are more accurately predictable by knowing both X and Y or by knowing both () and () with minimal error