Coarse-grained model for spring friction study of micron-scale iron by smoothed particle hydrodynamics

The paper constructs a coarse-grained model to investigate dry sliding friction of the body-centered-cubic Fe micron-scale system by smoothed particle hydrodynamics simulations and examines influences of the spring force on the characters of friction. The N_atom = 864 \times 10^12 atoms Fe system is coarse-grained into the two different simple-cubic particle systems, one of 432000 and the other of 16000 particles. From the detection of stick-slip motion, friction coefficient, dependence of friction coefficient on isotropy or anisotropy of the spring force and externally applied normal load, we find that the coarse-grained model is a reasonable modeling process for study of friction of the Fe system and the anisotropic behavior presents better friction of the system than the isotropic one

Sperner Lemma, Fixed Point Theorems, and the Existence of Equilibrium

In characterizing the existence of general equilibrium, existing studies mainly draw on Brouwer and Kakutani fixed point theorems and, to some extent, Gale-Nikaido-Debreu lemma. In this paper, we show that Sperner lemma can play a role as an alternative powerful tool for the same purpose. Specifically, Sperner lemma can be used to prove those theorems as well as the lemma. Additionally, Kakutani theorem is shown as a corollary of Gale-Nikaido-Debreu lemma. For a demonstration of the use of Sperner lemma to prove general equilibrium existence, we consider two competitive economies marked either by production goods or financial assets. In each case, we successfully provide another proof on the existence of a general equilibrium using only Sperner lemma and without a need to call on the fixed point theorems or the lemma

REQUIREMENTS IN THE PROCESS OF BUILDING A CONTINGENT OF ETHNIC MINORITY CADRES IN THE MOUNTAINOUS AREAS OF NGHE AN PROVINCE, VIETNAM

Nghe An is a province in Vietnam, with 10 mountainous districts and 1 mountainous town, accounting for 83.31% of the province's natural area. The mountainous area of Nghe An is a place with complicated and dangerous terrain and poor infrastructure; the lowest human development index (HDI) in the province; economic situation is extremely difficult, but it is a place with an important strategic position in terms of socio-economic development and protection of national border security. Therefore, building a contingent of ethnic minority cadres has a very important position and role in the development of the mountainous area of Nghe An. However, the work of building a contingent of ethnic minority cadres in mountainous districts of Nghe An currently has many shortcomings and limitations that need to be overcome, and possible solutions are needed so that the construction building a contingent of ethnic minority cadres in mountainous areas to achieve good results in the coming time.  Article visualizations

INGREX: An Interactive Explanation Framework for Graph Neural Networks

Graph Neural Networks (GNNs) are widely used in many modern applications, necessitating explanations for their decisions. However, the complexity of GNNs makes it difficult to explain predictions. Even though several methods have been proposed lately, they can only provide simple and static explanations, which are difficult for users to understand in many scenarios. Therefore, we introduce INGREX, an interactive explanation framework for GNNs designed to aid users in comprehending model predictions. Our framework is implemented based on multiple explanation algorithms and advanced libraries. We demonstrate our framework in three scenarios covering common demands for GNN explanations to present its effectiveness and helpfulness.Comment: 4 pages, 5 figures, This paper is under review for IEEE ICDE 202

Demand and equilibrium with inferior and Giffen behaviors

We introduce a class of differentiable, strictly increasing, strictly concave utility functions exhibiting an explicit demand of a good which may have Giffen behavior. We provide a necessary and sufficient condition (bases on prices and consumers’ preferences and income) under which this good is normal, inferior or Giffen good. Interestingly, with this utility, the equilibrium price of a good may increase in the aggregate supply for this good