Generalization of Retractable and Coretractable Modules

In this work, we extend the notion of retractability to  s- retractability. An R-module is called s-retractable if  for all nonzero . Also we extend coretractable modules to semi-coretractable modules. An R-module  is called semi-coretractable if  for all maximal essential submodule  of . We investigate theseclasses of modules and extend some of main theorems on retractable and coretractable modules to s-retractable and semi-coretractable modules, respectively

Some aspects in Noetherian modules and rings

Many authors have focused on the concept of Noetherian rings. M. Kosan and T. Quynh recently published an article on the Noetherian ring's new properties and their relation to the direct sum of injective hulls of simple right modules and essential extensions. Throughout this article, we extend the results of M. Kosan and T. Quynh to simple singular right modules and strongly singular injectivity

Doubt m-Polar Fuzzy Sets Based on BCK-Algebras

Doubt m-polar subalgebras (ideals) were introduced and some properties were investigated. Also, doubt m-polar positive implicative (commutative) ideals were defined and related results were proved

Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z. Several new connection formulae between some famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, and Fermat–Lucas polynomials, are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed

Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z. Several new connection formulae between some famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, and Fermat–Lucas polynomials, are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed

Deep Learning Methods Used in Remote Sensing Images: A Review

Undeniably, Deep Learning (DL) has rapidly eroded traditional machine learning in Remote Sensing (RS) and geoscience domains with applications such as scene understanding, material identification, extreme weather detection, oil spill identification, among many others. Traditional machine learning algorithms are given less and less attention in the era of big data. Recently, a substantial amount of work aimed at developing image classification approaches based on the DL model’s success in computer vision. The number of relevant articles has nearly doubled every year since 2015. Advances in remote sensing technology, as well as the rapidly expanding volume of publicly available satellite imagery on a worldwide scale, have opened up the possibilities for a wide range of modern applications. However, there are some challenges related to the availability of annotated data, the complex nature of data, and model parameterization, which strongly impact performance. In this article, a comprehensive review of the literature encompassing a broad spectrum of pioneer work in remote sensing image classification is presented including network architectures (vintage Convolutional Neural Network, CNN; Fully Convolutional Networks, FCN; encoder-decoder, recurrent networks; attention models, and generative adversarial models). The characteristics, capabilities, and limitations of current DL models were examined, and potential research directions were discussed