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.

This study examines the challenges and needs faced by non-profit organisations (NPOs) in Colombia regarding the adopting of the International Financial Reporting Standards (IFRS) for small and medium enterprises (SMEs), particularly focusing on sections 3 and 4. Employing a mixed-method approach, the research combines qualitative and quantitative methods. Surveys were conducted with Colombia NPOs, official documents were analysed, and comparative case studies were performed. In-depth interviews and participant observation were also utilised to gain a comprehensive understanding of the obstacles and current practices within the Colombian context. The findings reveal that NPOs in Colombia encounter significant difficulties in adopting IFRS due to the complexity of the standards, lack of specialised resources, and the need for specific training. Internal challenges such as deficiencies in staff qualifications and training, resistance to change, and technological limitations were identified. Externally, ambiguities in the legal framework and donor requirements were highlighted. The case study illustrated that, while there are similarities between IFRS for SMEs and the IFR4NPO project, specific adaptations are essential to address the unique needs of NPOs. This research underscores the necessity of developing additional guidelines or modifying existing ones to enhance the interpretation and application of IFRS in Colombia NPOs. It is recommended to implement proactive strategies based on education and legislative reform to improve the transparency and comparability of financial information. Adopting a more tailored and supported accounting framework will facilitate a more relevant and sustainable implementation, benefiting Colombian NPOs in their resource management and accountability efforts.

Accurate prediction of US Treasury bond yields is crucial for investment strategies and economic policymaking. This paper explores the application of advanced machine learning techniques, specifically Recurrent Neural Networks (RNN) and Long Short-Term Memory (LSTM) models, in forecasting these yields. By integrating key economic indicators and policy changes, our approach seeks to enhance the precision of yield predictions. Our study demonstrates the superiority of LSTM models over traditional RNNs in capturing the temporal dependencies and complexities inherent in financial data. The inclusion of macroeconomic and policy variables significantly improves the models’ predictive accuracy. This research underscores a pioneering movement for the legacy banking industry to adopt artificial intelligence (AI) in financial market prediction. In addition to considering the conventional economic indicator that drives the fluctuation of the bond market, this paper also optimizes the LSTM to handle situations when rate hike expectations have already been priced-in by market sentiment.

India has experienced notable advancements in trade liberalization, innovation tactics, urbanization, financial expansion, and sophisticated economic development. Researchers are focusing more on how much energy consumption of both renewable and non-renewable accounts for overall system energy consumption in light of these dynamics. In order to gain an understanding of this important and contentious issue, we aim to examine the impact of trade openness, inventions, urbanization, financial expansion, economic development, and carbon emissions affected the usage of renewable and non-renewable energy (REU and N-REU) in India between 1980 and 2020. We apply the econometric approach involving unit root tests, FE-OLS, D-OLS, and FM-OLS, and a new Quantile Regression approach (QR). The empirical results demonstrate that trade openness, urbanization and CO₂ emissions are statistically significant and negatively linked with renewable energy utilization. In contrast, technological innovations, financial development, and economic development in India have become a source of increase in renewable energy utilization. Technological innovations were considered negatively and statistically significant in connection with non-renewable energy utilization, whereas the trade, urbanization, financial growth, economic growth, and carbon emissions have been established that positively and statistically significant influence non-renewable energy utilization. The empirical results of this study offer some policy recommendations. For instance, as financial markets are the primary drivers of economic growth and the renewable energy sector in India, they should be supported in order to reduce CO₂ emissions.