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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:202112.00129 [pdf]

Subjects: Mathematics >> Mathematics （General）

 最近，一种全新的集合被提出，名为随机排列集(Random Permutation Set RPS)。随机排列集考虑了某一集合的所有可能的排列，并可以看作是证据理论的一种推广。不确定性是随机排列集的一个重要特征。一个简单的问题是如何测量随机排列集的不确定度。为了解决这一问题，本文提出了随机排列集的信息熵(Entropy of Random Permutation Set)。当忽略排列事件(Permutation Event)中元素的顺序时，随机排列集的信息熵退化为证据理论中的邓熵。当每个排列事件只包含一个元素时，随机排列集的信息熵退化为概率论中的香农熵。因此，随机排列集的信息熵可以看作是邓熵和香农熵的推广。 本文用数值算例说明了随机排列集的信息熵的有效性。

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:202110.00083 [pdf]

Subjects: Mathematics >> Mathematics （General）

 In this paper, we give characterizations of compactness in fuzzy set space with Lpmetric. Based on these results, we present completions of fuzzy set spaces with Lpmetric. The fuzzy sets discussed in this paper are fuzzy sets in general metric space. We also point out that the results in this paper generalize the results given in our previous paper.

5. 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.

6. 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。

7. 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 $\lambda_{+}>0$.

8. chinaXiv:201809.00180 [pdf]

Subjects: Mathematics >> Mathematics （General）