Al-Nahrain Journal of Science

In this study, the exact Bullet solutions for the (3+1)-dimensional Schrödinger equation which demonstrates the Bullet behaviour in optical fibers can be accumulated through the extended simple equation method, and Csch method. The applied strategies may retrieve several kinds of optical Bullet solutions within one frame, which is quite simple and reliable. As a result, we are able to develop a variety of traveling wave structures namely the periodic, singular Bullet wave. The extended simple equation method, and Csch method approaches were implemented perfectly and can be extended to deal with many advanced models in contemporary areas of science and engineering.

We present in this work the concepts of fuzzy AlmostNearlyprime submodules and fuzzy AlmostNearly2Absorbiing submodules as popularizations of fuzzy Nearly prime submodules and fuzzy 2-Absorbing submodules. Numerous additional fundamental characteristics, attributes, and connections between these ideas and other ideas are provided.

The aim of this study is to make a comparison between the Markov model and the mixed model to predict future values, based on monthly data of the exchange rates of the US dollar against the Iraqi dinar for the period from January 2017 to December 2022. By comparing the two models using MAD, RMSE, and MAPE prediction accuracy measures to find the most appropriate model for analyzing the data of interest, the study concluded that the mixed model (ARIMA) (0,2,1) with the lowest values of the prediction accuracy measures is the most suitable and appropriate model for analyzing the study data, in order to predict the future exchange rates of the US dollar against the Iraqi dinar compared to the Markov model. Based on this model, the exchange rates of the US dollar against the Iraqi dinar were predicted until the end of June 2023 AD, and the predictive values were consistent with the original values of the series, which indicates the efficiency of the model. Two statistical models were used: the Markov model, the autoregressive model, and ARIMA. The two models were applied to the data under study in order to compare them with the exchange rates of the dollar against the Iraqi dinar the importance of studying.

In this research we introduced a new concept, which is coc-preopen set, with some properties, theorems, and functions related to this concept. We also benefited from the properties of some spaces in order to find new results related to the concept of coc-preopen.

In this work, we introduce a new type of topology associated to directed graph on vertices set, which is named as non-adjacency incompatible vertices topology (-topology) of directed graph. A sub-basis family of this topology is generated on the set of vertices, and formed via taking the non-adjacency vertices which arises (path of length two) in different direction to each vertex. We investigate some properties and discuss it on an important and certain types of directed graphs. Our motivation is to giving fundamental steps toward investigation of various properties of directed graphs via their corresponding non-adjacency incompatible vertices topology. Some results are obtained, the presence of the isolated vertex is not necessary in our definition, observations about the specification of this new topology with certain types of digraphs (which type of digraphs achieves the discrete non-adjacency incompatible vertices topology and which does not, and when it achieves and -space). Furthermore, application (applied example in biomathematics) to the Pulmonary circulation in humans is introduced in this paper.

This article relies on the Caputo fractional derivative for the objective of is to examine an interconnected system of fractional differential equations. The problem under consideration involves four fractional-Caputo-derivatives underneath initial conditions. We state and prove the existence and uniqueness theorem of solution by application of Banach fixed point theorem. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions for this result are established by means of the fixed-point theorem of Schaefer. We end the paper by presenting to the reader by illustrative example.

The increasing use of panel data across various fields necessitates robust estimation methods that can resist the influence of outliers, which often lead to biased and ineffective estimates when using traditional methods like least squares. This research investigates two robust estimation techniques within fixed and random effects models for panel data, comparing their performance using the mean square error. Through a simulation experiment with varying sample sizes and contamination levels, the results for the fixed effects model indicate that the Weighted Likelihood Estimator consistently outperformed other methods across all sample sizes at a 10% contamination rate, while the S method excelled at a 20% contamination rate. For the random effects model, the former was most effective with a sample size of 200, while the latter proved superior at a sample size of 800, regardless of contamination levels.