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 continuous development of emerging economies represented by China and Russia has exacerbated the changes in the world political and economic landscape, and international organizations represented by the United Nations have led to inefficient dispute resolution mechanisms in international affairs due to their formalism and pluralism. On the contrary, G-groups has shown its flexibility and efficiency in global governance. However, the international community has been questioned G-group’s legitimacy for many years. This paper will take the G7 and G20 as examples, analyze the legitimacy problems in G-groups, explain their reform measures, and propose future reform directions to promote the development of G-groups, so as to help the international community to conduct global governance more effectively.

Online transportation is a new type of service equipped with an internet network, and its presence in Indonesia is considered a service that disrupts the transportation sector. The government is faced with a complex policy problem to regulate online transportation. This article aims to reveal the role of policy actors in the media regarding policy issues and online transportation policy solutions. This article used qualitative analysis and the NPF policy narrative framework approach. This study found that licensing issues and Permenhub were problems that the DIY and Riau governments shared. More specific problems in Riau Province are related to violence issues, and that in DIY are related to congestion problems. The policy solution recommended by policy actors to the media is to make regional level regulations that technically regulate online transportation according to the area conditions.

This paper provides a comprehensive review of SURF (speeded up robust features) feature descriptor, commonly used technique for image feature extraction. The SURF algorithm has obtained significant popularity because to its robustness, efficiency, and invariance to various image transformations. In this paper, an in-depth analysis of the underlying principles of SURF, its key components, and its use in computer vision tasks such as object recognition, image matching, and 3D reconstruction are proposed. Furthermore, we discuss recent advancements and variations of the SURF algorithm and compare it with other popular feature descriptors. Through this review, the aim is to provide a clear understanding of the SURF feature descriptor and its significance in the area of computer vision.

Nanomaterials stand as transformative elements across diverse domains, ranging from biotechnology, aircraft, aviation, and space exploration to medicine, health, environmental preservation, resources, energy, and aerospace. This issue, comprising nine original research articles and two insightful reviews, we embark on a journey to unravel the multifaceted uses of nanomaterials, with a special emphasis on their contributions to environmental protection and medicine. Delving into the unique traits of various nanomaterials, our aim is to provide readers with a comprehensive understanding that transcends conventional boundaries, fostering a deeper appreciation for the impact of nanomaterials.

The study focused on investigating the effects of varying levels of HA (HA₁ = 0, HA₂ = 25, HA₃ = 50, HA₄ = 75, and HA₅ = 100) on Red Dragon, Red Prince, and Red Meat varieties of red radish. This analysis aimed to unravel the relationship between different levels of HA and their impact on the growth and productivity of red radish genotypes. The findings revealed that the Red Prince genotype attained the utmost plant height of 24.00 cm, an average of 7.50 leaves per plant, a leaf area of 23.11 cm², a canopy cover of 26.76%, a leaf chlorophyll content of 54.60%, a leaf fresh weight of 41.16 g, a leaf dry weight of 8.20 g, a root length measuring 9.73 cm, a root diameter of 3.19 mm, a root fresh weight of 27.60 g, a root dry weight of 6.75 g, and a remarkable total yield of 17.93 tons per hectare. The implications of this study are poised to benefit farmers within the Dera Ismail Khan Region, specifically in the plain areas of Pakistan, by promoting the cultivation of the Red Prince variety.