Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

The importance of improving industrial transformation processes for more efficient ones is part of the current challenges. Specifically, the development of more efficient processes in the production of biofuels, where the reaction and separation processes can be intensified, is of great interest to reduce the energy consumption associated with the process. In the case of Biodiesel, the process is defined by a chemical reaction and by the components associated to the process, where the thermochemical study seeks to develop calculations for the subsequent understanding of the reaction and purification process. Thus, the analysis of the mixture of the components using the process simulator Aspen Plus V9^® unravels the thermochemical study. The UNIFAC-DMD thermodynamic method was used to estimate the binary equilibrium parameters of the reagents using the simulator. The analyzed aspects present the behavior of the components in different temperature conditions, the azeotropic behavior and the determined thermochemical conditions.

Salicylaldehyde imine transition metal catalyst is a kind of olefin polymerization catalyst that is widely used in the coordination of salicylaldehyde imine ligand and pre-transition metal. Salicylaldehyde imine ligands have the characteristic of easily inserting different substituents via organic synthesis. Therefore, the regulation of the polymerization activity, polymerization product, and product distribution can be achieved by changing the steric hindrance effect, the electronic effect, and the number of metal active sites near the catalytic active center. The development status of the transition metal catalyst of salicylaldehyde imide was summarized in this paper. The influence of the ligand structure of the salicylaldehyde imide transition metal catalyst on the catalytic performance, which involved the high selectivity of ethylene trimerization, ethylene/α-olefin, polar monomer copolymerization, ethylene polymerization production, ultra-high molecular weight polyethylene, and many other areas of olefin polymerization, was elaborated, providing references for further study and industrial applications of this catalyst.

The study aims to explore the role of artificial intelligence in enhancing the efficiency of public relations practitioners in Jordanian telecommunication companies. This study belongs to the category of descriptive research and adopted a survey methodology. The study surveyed (86) individuals representing the community of public relations practitioners and customer service personnel in the Jordanian telecommunication companies Zain and Orange.The study findings revealed that less experienced public relations personnel in Zain and Orange, with less than five years of experience, exhibit greater acceptance and enthusiasm for using artificial intelligence applications compared to their more experienced counterparts. The study also indicated that most public relations practitioners in Zain and Orange perceive artificial intelligence applications to have a moderate to significant contribution to achieving public relations functions and enhancing their work, reflecting technological advancement and the need to adapt to rapid changes in the business environment. Moreover, the study also discussed the limits, including that artificial intelligence can analyze large amounts of data related to the market and the audience, which provides further research and study.

The Corona epidemic, as a global crisis, and the Islamic State of Iraq and Syria) ISIS (war, as a regional crisis in Iraq, have significantly impacted the atmosphere of companies and the continuation of their activities. The present study examines the role of these crises in creating incentives for fraudulent reporting and reducing or improving audit quality. It also compares the results of these two relationships with each other. In other words, the current paper sought to answer these issues: What effect did the ISIS war and the COVID-19 pandemic have on the fraudulent reporting motives of companies, and how did it affect the quality of their audits? In the end, the answer to this question was addressed: What are the differences and similarities between the study results of the impact of COVID-19 and ISIS on fraudulent financial reporting and audit quality? For this purpose, the data of 33 companies from 2008 to 2021 (462 observations) were collected to examine six formulated hypotheses, and the hypotheses were tested using the method of structural equations and analysis of variance. Interviews with experts were also used to determine quality indicators of auditing and fraudulent financial reporting so that indigenous indicators were selected and finalized. The results showed no significant relationship between the epidemic of the COVID-19 crisis and the motives of fraudulent reporting and audit quality and between the crisis of the ISIS war and the motives of fraudulent reporting. However, the ISIS war crisis has negatively and significantly impacted audit quality. Finally, the results indicated no significant difference between the impact of the epidemic crisis of COVID-19 and ISIS on the motives of fraudulent reporting. Still, there is a significant difference in the impact of the epidemic crisis of COVID-19 and ISIS on the audit quality. The knowledge enhancement of the present study is the development of literature on the impact of the Corona and ISIS crises on corporate financial reporting and auditing. The current paper, by studying the consequences of COVID-19 and ISIS, showed that further investigations in this field, especially regarding the capital market environment and A company, can obtain essential results based on which practical suggestions can be made for possible future crises.