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The "determining modes" concept introduced by Foias and Prodi in 1967 say that if two solutions agree asymptotically in their P projection, then they are asymptotical in their entirety. In this paper, we consider the 2D g-Bénard problem in domains satisfying the Poincaré inequality with homogeneous Dirichlet boundary conditions. We present an improved upper bound on the number of determining modes. Moreover, we slightly improve the estimate on the number of determining modes and obtain an upper bound of the order G. These estimates are in agreement with the heuristic estimates based on physical arguments, that have been conjectured by O.P. Manley and Y.M. Treve. The Gronwall lemma and Poincaré type inequality will play a central role in our computational technique as well as the proof of the main result of the paper. Studying the properties of solutions is important to determine the behavior of solutions over a long period of time. The obtained results particularly extend previous results for 2D g-Navier-Stokes equations and 2D Bénard problem.

Vietnam is one of the five countries in the world most severely affected by climate change, particularly the north central coastal provinces of Vietnam. In the near future, millions of citizens in these coastal hazard areas will experience difficulties in socio-economic activities and face poverty due to the loss of their agricultural land and even their homes. Therefore, this research study focuses on proposing key components of spatial planning of the north central coastal alluvial zones in Vietnam for adaptation to climate change and sea-level rise to protect inhabitants’ quality of life as well as their agricultural land. The research uses the typical case study of Dong Chau Ngoai village, Dong Minh town, Tien Hai district, Thai Binh province, Vietnam.

Currently, the situation of establishment and participation of criminal groups in Vietnam is increasing in number and has complicated happenings, causing serious consequences to social and economic security, especially criminal groups are also linked outside the territory. The United Nations Convention against Transnational Organized Crime provides for the criminalization of acts of establishing and joining organized crime groups in two mandatory or optional directions, depending on economic conditions, international, political and legislative traditions of each country. In Vietnam's criminal law, the 2015 Penal Code provides for the establishment and participation of criminal groups in Article 14, which is one of the acts in the stage of preparation for crimes, as well as the acts join criminal groups in specific crimes in Article 109, Article 113, Article 299. However, the Penal Code 2015 does not have specific provisions on acts of establishing and joining organized crime groups. Therefore, the addition of this provision on the basis of the provisions of the Convention is extremely necessary.

Radial Visualization technique is a non linear dimensionality reduction method. Radial Visualization projects multivariate data in the 2-dimensional visual space inside the unit circle. Radial Visualization supports display both the samples and the attributes that provides useful information of data structures. In this article, we introduced a new variant of Radial Visualization for visualizing high dimensional data set that named Arc Radial Visualization. The new proposal that modified Radial Visualization supported more space to display high dimensional datasets. Our method provides an improvement in visualizing cluster structures of high dimensional data sets on the Radial Visualization. We present our proposal method with two quality measurements and proved the effectiveness of our approach for several real datasets.