A new 2-point hybrid block method for the numerical solution of first-order stiff systems of ordinary differential equations in initial value problems with optimal stability property is presented. The necessary and sufficient conditions for the convergence of the proposed implicit block numerical scheme for solving stiff ODEs are established. The stability and convergence analysis of the method show that it is consistent, zero-stable, and convergent. The absolute stability region of the method is plotted, indicating that the method is A-stable. The method is implemented in Microsoft Dev C++ environment using the C programming language and Newton’s iteration, and some selected first-order stiff initial value problems are solved. The numerical results obtained for the proposed method are compared with the existing fifth order fully implicit 2-point block backward differentiation formula and 2-point block backward differentiation formula with two off-step points methods. The comparison reveals that the new method outperforms both methods in terms of accuracy but are competing in terms of computation time as we reduce the step size. It is evident that the method converges faster.

Intelligent weighing systems play a significant role in guiding coal production and assisting production decisions. However, the traditional weighing method not only cannot guarantee efficiency, but also is prone to artificial fraud, causing economic losses to enterprises. In view of the needs of industrial production, this paper studies a visual weighing method for mining dump trucks with ResNet deep learning network as the core. Firstly, the collected dataset is processed by the Resize function and the Blend function, and then the ResNet neural network is trained with the processed dataset, and finally the cross-entropy loss function and Adam optimization strategy are used to improve the recognition accuracy. The results show that the final recognition accuracy is 60%.

Soft set theory gained popularity as a cutting-edge approach to handling uncertainty-related problems and modeling uncertainty when it was introduced by Molodtsov in 1999. It may be applied in a variety of contexts, both theoretical and practical. This paper introduces a new soft set operation called the “soft binary piecewise star operation.” Its basic algebraic characteristics are thoroughly examined. Moreover, this operation’s distributions over various soft set operations are obtained. We prove that the soft binary piecewise star operation is a commutative semigroup under certain conditions and is also a right-left system. Furthermore, we show that the collection of soft sets over the universe, along with the soft binary piecewise star operation and some other types of soft sets, form many important algebraic structures, such as semirings and near-semirings, by considering the algebraic properties of the operation and its distribution rules together.

This paper considers the conventional logistic model and how to obtain the solutions of fractional differential equations. It examines using a hybrid of Sumudu transform method, which is an approximate analytical method for solving fractional differential equations that are associated with time delay. Furthermore, the paper introduces the fractional Caputo-Fabrizio derivative and proportional time delay into the conventional logistic model to propose a general and more logistic model for the population growth. The paper considers different cases of the newly introduced general logistic model and using a hybrid of Sumudu transform method, their solutions were obtained. Using MATLAB, it displays and compares the behaviour of different cases of the general logistic model with fractional Caputo-Fabrizio derivative and proportional time delay.

The family of Burr distributions consists of twelve different distributions that result from solving a differential equation. This family is part of the family of continuous distributions and its applications have been investigated in various topics such as survival function, simulation problems, and economic and insurance analyses. Since the flexibility of the generalized distributions is often greater than the distribution itself, the generalization of the distributions of this family is of great interest. Also, due to the diversity of the distribution type, various generalizations of the Burr distribution have been presented. Regarding the importance of generalized distributions in this family, it is enough that the family of Burr distributions can be considered a parametric generalized family. In this article, it is intended to present a generalization of the Burr distribution, which results in the special case of the type II Burr distribution; In this way, we add a parameter in the type II Burr distribution structure and by changing this parameter, we reach different Burr distributions, including the type II Burr distribution. The mentioned parameter along with other distribution parameters is estimated by the maximum likelihood method.

A new complex derivative is defined for the first time. Some theorems linked to the definitions are given first. Applications of the new derivative to calculus and dynamics are discussed. The analysis may open newhorizons to undergraduate students and lecturers

Bernoulli bases are developed to approximate the solutions of two-point BVP in modelling viscoelastic flows in which the shifted Chebyshev collocation points are used as collocation nodes. Properties of Bernoulli bases are then used to reduce the two-point BVP in modelling viscoelastic flows to systems of nonlinear algebraic equations. The results show the agreement between the exact solutions and the approximate solutions. Form the numerical results we see that the proposed method gives accurate results.

The goal of this work is to use the T-R(y) family technique to create the Raleigh Weibull Distribution (RWD), a new probability distribution that may be used to fit real-world data. A Covid-19 data set that was acquired from Mexico was used to develop and fit some of the newly suggested distribution’s features. Different estimate methodologies were discussed, and the properties of the probability density function (pdf) and cumulative distribution function (CDF) were developed. The analysis shows that the extra form elements in the suggested model make the new distribution more flexible than the present distribution, which makes it more flexible than the current models. According to the fitted findings, the suggested RWD performed better than the existing distributions. Compared to the current Rayleigh Distribution, the recommended distribution (RWD) better fits real-world data. Consequently, a distribution (RWD) that can handle asymmetric datasets for both left- and right-skewed data was developed and different methods for estimating were explained. The analysis shows that the extra form elements in the suggested model make the new distribution more flexible than the present distribution, which makes it more flexible than the current models.

A new definition of the Fibonacci Matrix is given. The elements of the matrix consist of the Fibonacci numbers. First a preliminary knowledge on Fibonacci sequences and their properties are given. Then the new definition of the matrix is given together with some properties. The difference from the common definition is also discussed. The determinant of the matrix and its properties are posed and proven. Applications to systems of algebraic equations are also outlined.

The main teaching pain points of the course Linear Algebra include “students’ fear of difficulty”, “difficulty in igniting enthusiasm for learning”, “uneven levels of student proficiency”, “the political construction of basic course remaining a uphill battle” and so on. Aiming at facing the pain points of the course teaching and improving the effect of students’ learning, this paper designs the teaching program. Taking “eigenvalues and eigenvectors” as an example, based on the BOPPPS teaching model, multiple teaching methods are adopted such as flipped classroom, case study, hierarchical design. At the same time, the design combines the application of information technology, and integrates the ideology and political elements into the course.