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## 1. chinaXiv:202108.00116 [pdf]

Subjects: Mathematics >> Mathematics （General）

 In this paper, we discuss the properties of functions generated using Hausdorff metric.

## 2. chinaXiv:202108.00057 [pdf]

Subjects: Mathematics >> Mathematics （General）

 In this paper, we give some properties related to platform points of a fuzzy set and their applications.

## 3. chinaXiv:202107.00011 [pdf]

Subjects: Mathematics >> Mathematics （General）

 This paper discusses the properties the spaces of fuzzy sets in a metric s- pace equipped with the endograph metric and the sendograph metric, re- spectively. We fist discuss the level characterizations of the Γ-convergence and the endograph metric, and point out the elementary relationships among Γ-convergence, endograph metric and the sendograph metric. On the basis of these results, we present the characterizations of total boundedness, rel- ative compactness and compactness in the space of compact positive α-cuts fuzzy sets equipped with the endograph metric, and in the space of com- pact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these two kinds of spaces, respectively.

## 4. chinaXiv:202002.00021 [pdf]

Subjects: Mathematics >> Mathematics （General）

 2019年12月，新型冠状病毒肺炎(NCP，又称2019-nCoV)疫情从武汉开始爆发,几天内迅速传播到全国乃至海外，对我国的工农业生产和人民生活产生了重要影响。科学有效掌控疫情发展对疫情防控至关重要。本文基于中国卫健委及湖北省卫健委每日公布的累计确诊数，采用逻辑斯蒂模型对数据进行了拟合，以期给该疾病的防控治提供科学依据。通过公布的疫情数据，我们反演了模型的参数，进而有效地模拟了目前疫情的发展，并预测了疫情未来的趋势。我们预测，湖北省疫情还要持续至少2周，而在全国其他地区，疫情可望1周左右达到顶峰。

## 5. chinaXiv:201809.00178 [pdf]

Subjects: Mathematics >> Mathematics （General）

 The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_{\Omega}(G(|\nabla u|)+qF(u^+)+hu+\lambda_{+}\chi_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions $W^{1,G}(\Omega)$ with $u-\varphi\in W^{1,G}_{0}(\Omega)$, for a given function $\varphi$, where $W^{1,G}(\Omega)$ is the class of weakly differentiable functions with $\int_{\Omega}G(|\nabla u|)\text{d}x<\infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $\infty$. Given functions $q,h$ and constant $\lambda_+\geq 0$, we address several regularities for minimizers of $\mathcal {J}(u)$, including local $C^{1,\alpha}-$, and local Log-Lipschitz continuities for minimizers of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. We also establish growth rate near the free boundary for each non-negative minimizer of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. Furthermore, under additional assumption that $F\in C^1([0,+\infty); [0,+\infty))$, local Lipschitz regularity is carried out for non-negative minimizers of $\mathcal {J}(u)$ with $\lambda_{+}>0$.