Enhancing Critical Path Problem in Neutrosophic Environment Using Python

In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.

Local Radial Basis Function Methods: Comparison, Improvements, and Implementation

Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox.

Diophantine Quotients and Remainders with Applications to Fermat and Pythagorean Equations

Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pythagoras’- Fermat’s equation defined as follows. (1) when , it is well known that this equation has an infinity of solutions but has none (non-trivial) when . We also know that the last result, named Fermat-Wiles theorem (or FLT) was obtained at great expense and its understanding remains out of reach even for a good fringe of professional mathematicians. The aim of this research is to set up new simple but effective tools in the treatment of Diophantine equations and that of Pythagoras-Fermat. The tools put forward in this research are the properties of the quotients and the Diophantine remainders which we define as follows. Let a non-trivial triplet () solution of Equation (1) such that . and are called the Diophantine quotients and remainders of solution . We compute the remainder and the quotient of b and c by a using the division algorithm. Hence, we have: and et with . We prove the following important results. if and only if and if and only if . Also, we deduce that or for any hypothetical solution . We illustrate these results by effectively computing the Diophantine quotients and remainders in the case of Pythagorean triplets using a Python program. In the end, we apply the previous properties to directly prove a partial result of FLT. .

Animal representations in Margaret Atwood's novels:a study based on pan-indexicality model

Margaret Atwood is a Canadian author of more than thirty-five books and the winner of prestigious literary prizes,such as the Booker Prize,the Giller Prize,and the Governor General's Award.Her influence on Canadian literature and contemporary literature as a whole is phenomenal.Nevertheless,little is known with respect to how Atwood represents animals covering the full range of her novels.This paper reports on the analysis of animal representations in Atwood's seventeen novels through Python programming and close reading under the framework of a new semiotic research finding,a pan-indexicality model within the context of literature and the environment.This study investigates the frequencies of animal vocabulary in the seventeen novels,the changes of animal representations in her novels before 1990s and after 1990s,and the implication of the ever-changing animal representations during the fty years.This paper concludes that nonhuman animal descriptions in Atwood's novels of 1970s and 1980s run at a high level and decrease in her novels of 1990s,while scientific animal descriptions increase in her novels of 2000s and 2010s.Nonhuman animals in her novels of 1970s and 1980s are instrumentalized as a vehicle for indigenization and national individuation from the United States,and scientific animals in her novels of 2000s and 2010s are instrumentalized in the service of environmental apocalypticism.This study suggests that the pan-indexicality model can be employed to understand the meaning of signs in literature and the environment from the perspective of authorial intention,with reference to authors'encyclopedic knowledge,personal experience,social,and cultural background information.