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.

Iran has one of the oldest civilizations in the world, and many elements of today’s urban planning and design have their origins in the country. However, mass country-city migration from the 1960s onwards brought enormous challenges for the country’s main cities in the provision of adequate housing and associated services, resulting in a range of sub-standard housing solutions, particularly in Tehran, the capital city. At the same time, and notably in the past decade, Iran’s main cities have had significant involvement in the smart city movement. The Smart Tehran Program is currently underway, attempting to transition the capital towards a smart city by 2025. This study adopts a qualitative, inductive approach based on secondary sources and interview evidence to explore the current housing problems in Tehran and their relationship with the Smart Tehran Program. It explores how housing has evolved in Tehran and identifies key aspects of the current provision, and then assesses the main components of the Smart Tehran Program and their potential contribution to remedying the housing problems in the city. The article concludes that although housing related issues are at least being raised via the new smart city technology infrastructure, any meaningful change in housing provision is hampered by the over centralized and bureaucratic political system, an out of date planning process, lack of integration of planning and housing initiatives, and the limited scope for real citizen participation.

Among the dental composites, Urethane Dimethacrylate (UDMA) is commonly used as a component in treating oral complications. Many molecular dynamics approaches are used to understand the behaviour of the material at room temperature as well as at higher temperatures to get a better insight after comparison with experimental values at the atomic level. There are three critical physical properties associated with these components, like abrasive wear, viscosity, and moduli, which play an essential role in determining the treatment and can be computed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), the general-purpose quantum chemistry program package (ORCA), and the General Utility Lattice Program (GULP) molecular dynamics methods. A radial distribution function plot is generated using visual molecular dynamics (VMD) for UDMA and BisGMA. A comparison of these parameters with BisGMA, another component of dental composites, along with experimental results, is carried out in the present investigation. Further, since radiation also matters for settling the materials in dental treatment, we have computed absorption spectra from 200 nm to 800 nm using LAMMPS/ORCA.

Considering the application of the polymer electrolyte membrane fuel cell (PEMFC), the separator thickness plays a significant role in determining the weight, volume, and costs of the PEMFC. In addition, thermal management, i.e., temperature distribution is also important for the PEMFC system to obtain higher performance. However, there were few reports investigating the relation between the temperature profile and the power generation characteristics e.g., the current density distribution of PEMFC operated at higher temperatures (HT-PEMFC). This paper aims to study the impact of separator thickness on the temperature profile and the current density profile of HT-PEMFC. The impact of separator thickness on the gases i.e., H₂, O₂ profile of HT-PEMFC numerically was also studied using CFD software COMSOL Multiphysics in the paper. In the study, the operating temperature and the relative humidity (RH) of the supply gas were varied with the separator thickness of 2.0 mm, 1.5 mm, and 1.0 mm, respectively. The study revealed that the optimum thickness was 2.0 mm to realize higher power generation of HT-PEMFC. The heat capacity of the separator thickness of 2.0 mm was the biggest among the separators investigated in this study, resulting in the dry-up of PEM and catalyst layer was lower compared to the thinner separator thickness. It also clarified the effects of separator thickness of profile gases, e.g., O₂, H₂O, and current density profile became larger under the higher temperature and the lower RH conditions.

Malaria is a mosquito-borne infectious disease that affects humans and poses a severe public health problem. Nigeria has the highest number of global cases. Geospatial technology has been widely used to study the risks and factors associated with malaria hazards. The present study is conducted in Ibadan, Oyo State, Nigeria. The objective of this study is to map out areas that are at high risk of the prevalence of malaria by considering a good number of factors as criteria that determine the spread of malaria within Ibadan using open-source and Landsat remote sensing data and further analysis in GIS-based multi-criteria evaluation (MCE). This study considered factors like climate, environmental, socio-economic, and proximity to health centers as criteria for mapping malaria risk. The MCE used a weighted overlay of the factors to produce an element at-risk map, a malaria hazard map, and a vulnerability map. These maps were overlaid to produce the final malaria risk map, which showed that 72% of Ibadan has a risk of malaria prevalence. Identification and delineation of risk areas in Ibadan would help policymakers and decision-makers mitigate the hazards and improve the health status of the state.