It is well known that determining the exact values of crossing number for circulant graphs is very difficult. Even so, some important results in this field are still proved. D.J. Ma was proved that the crossing number of C(2m + 2, m) is m + 1[8]. Then such problem for C(n, 3) was further solved [7]. Pak Tung Ho and X. Lin obtained accurate values for the crossover numbers of C (3m, m) and C (3m + 1, m)[4][5]. In this paper, as a complement, we show that the edges from the principal cycle of C(9, 3) do not cross each other in an optimal drawing.

The new oil derivatives transportation scheme proposed by the 2013 Mexican Energy Reform allowed new participants to enter the sector. The new legal framework requires fulfilling many requirements and corresponding duties for the transportation of oil products. The Mexican government already has an institution dedicated to measuring the regulatory cost of each federal procedure. This work aims to quantify the regulatory costs associated with the procedures and their compliance to obtain permits for transporting oil products by truck. We use the standard cost method to measure these costs, considering all associated costs. The results showed that two government offices did not adequately measure these costs. They did not consider relevant information on frequency and opportunity costs, resulting in undervaluation and leading to wrong expectations. As a result of this research, we provide a more accurate way of estimating these costs, which brings greater certainty in the budgeting of these projects and, therefore, increases the probability of survival and success.

Our main objective in this research is to affirm that philosophy, in its true essence and depth, has never been inherently opposed to religion. Rather, the turn toward atheism within philosophy represents isolated, personal stances, often reactionary in nature, and not rooted in genuine intellectual reflection, which the Qur’an encourages and calls people to adhere to. Our endeavor is to show that the call to atheism is foreign to reason, understood as a sound faculty or a sense linked to the pursuit of truth, as previously demonstrated by Descartes in his focus on the principles and methods of philosophical inquiry. To facilitate the achievement of these goals, we have employed several methodologies, primarily the structural method, which helps us analyze selected texts, this methodology enables the understanding of the elements within the studied positions, the relationships that link them, and the underlying implications upon which they are based. We will apply this method practically when analyzing conceptions that reject religion, uncovering the framework underpinning each conception. This approach facilitates comprehension by examining the rational foundations that support each interpretation of religion and later pave the way for its denial or transcendence. the historical method, which allows us to trace the development and dissemination of atheism, this approach is based on the premise that every sensory or intellectual phenomenon has an origin defined by time and place, evolving through transformations and additions over time. By employing this method, we can trace the development of various interpretations of religion and understand the intellectual accumulations shaped by successive historical periods, and the deconstructionist method, through which we identify the contradictions and flawed principles underlying atheistic arguments, this method allows for in-depth critique of the foundations, developmental trajectories, and final outcomes of phenomena. It also provides a means to establish new perspectives—whether by modifying the existing model, recontextualizing it, or replacing it with an entirely new framework. The importance of re-examining the relationship between philosophy and atheism stems from the profound influence of certain philosophical positions and their negative views on religion within various atheistic currents, especially contemporary ones. Contemporary atheism today poses a threat to religion as a symbolic human system, rich in a value-laden framework that upholds the essence of humanity in an era dominated by materialism and the absence of values. The central question of this research is: Can the human being truly achieve existence independently? Or can one live in this world isolated from all influential forces, including the creative and divine force?

Urban mobility in Grand Lomé is affected by several negative externalities, including road congestion, insecurity and environmental pollution. Traffic jams cause considerable economic losses, estimated at more than 13,000 CFA francs per month for some public officials, and represent a financial drain of several million CFA francs per day on the Togolese economy. These challenges are accentuated by rapid urbanization and a dizzying increase in the number of vehicles, especially motorcycle taxis. These factors not only cause economic losses, but also to the deterioration of the quality of life of the inhabitants. On average, motorists lose up to 49.5 min per day in traffic jams, with fuel and time costs estimated at hundreds of thousands of CFA francs per year for each user of the main boulevards. Through an in-depth analysis of the impacts of these negative externalities on mobility and sustainable development, this study reveals that traffic congestion, combined with the lack of road infrastructure, generates considerable economic and environmental costs. These traffic jams also worsen air pollution, making the transport sector responsible for 80% of greenhouse gas emissions. These proposed solutions include: 1) The modernization of road infrastructure, culminating in the construction of new lanes entirely dedicated to public and non-motorized transport. 2) The regulation of motorcycle taxis, inspired by regional examples, to improve safety and efficiency. 3) The introduction of rapid transit systems, such as Bus Rapid Transit (BRT), to make travel more fluid. 4) The implementation of strict environmental standards and regular technical controls to reduce greenhouse gas emissions. These proposals aim to reduce social and economic costs, while promoting sustainable mobility and a better quality of life for residents.

Lei's work explores the theme of existentialism, reflecting the anxiety and uncertainty that modern people experience in the face of a rapidly changing world. The stories explore the dislocation and suffering experienced by modern people in a heterogeneous cultural space, the anxiety of existential existence, and the alienation and dislocation of interpersonal relationships.

Based on instructional practice in badminton course teaching, this study expands the application of goal-directed behavior theory from management studies in the field of physical education, thereby supplementing the existing conditions for applying goal-directed behavior theory in the sports domain. Empirical evidence confirms that proactive college students, through the reconstruction of the badminton knowledge system, implementation of innovative teaching methods, and utilization of multidimensional assessment approaches, can effectively acquire proficient skills in major badminton techniques within a 32-hour instructional period. This accomplishment not only achieves the intended teaching objectives but also resolves the issue of students struggling to comprehend and acquire badminton techniques within a limited timeframe.