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1. chinaXiv:202107.00011 [pdf]

Properties of several fuzzy set spaces

Huan Huang
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.

submitted time 2021-11-27 Hits6894Downloads452 Comment 0

2. chinaXiv:202110.00083 [pdf]

Characterizations of compactness in fuzzy set space with Lp metric

黄欢
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.

submitted time 2021-10-25 Hits1596Downloads139 Comment 0

3. chinaXiv:202108.00116 [pdf]

Some discussions on Hausdorff metric

黄欢
Subjects: Mathematics >> Mathematics (General)

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

submitted time 2021-08-30 Hits2271Downloads258 Comment 0

4. chinaXiv:202108.00057 [pdf]

Properties of fuzzy set

黄欢
Subjects: Mathematics >> Mathematics (General)

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

submitted time 2021-08-10 Hits3600Downloads363 Comment 0

5. chinaXiv:202002.00021 [pdf]

关于新型冠状病毒感染人数的预测研究

吴宇宸
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。

submitted time 2020-02-18 Hits30589Downloads3303 Comment 0

6. chinaXiv:201809.00178 [pdf]

Regularity for a minimum problem with free boundary in Orlicz spaces

Jun Zheng; Leandro S. Tavares; Claudianor O. Alves
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 $\lambda_{+}>0$.

submitted time 2018-09-23 Hits18346Downloads1648 Comment 0

7. chinaXiv:201809.00180 [pdf]

Regularity in the two-phase free boundary problems under non-standard growth conditions

Jun Zheng
Subjects: Mathematics >> Mathematics (General)

In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_{\gamma}(u)=\int_{\Omega}\big(f(x,\nabla u)+(\lambda_{+}(u^{+})^{\gamma}+\lambda_{-}(u^{-})^{\gamma})+gu\big)\text{d}x\rightarrow \text{min}$ under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with $\gamma=0$, chemical reaction problems with $0<\gamma<1$, and obstacle type problems with $\gamma=1$. Our results hold not only in the degenerate case of $p> 2$ for $p-$Laplace equations, but also in the singular case of $1

submitted time 2018-09-22 Hits15633Downloads1477 Comment 0

8. chinaXiv:201809.00179 [pdf]

H\"{o}lder continuity of solutions to the $G$-Laplace equation

Jun Zheng; Yan Zhang
Subjects: Mathematics >> Mathematics (General)

We establish regularity of solutions to the $G$-Laplace equation $-\text{div}\ \bigg(\frac{g(|\nabla u|)}{|\nabla u|}\nabla u\bigg)=\mu$, where $\mu$ is a nonnegative Radon measure satisfying $\mu (B_{r}(x_{0}))\leq Cr^{m}$ for any ball $B_{r}(x_{0})\subset\subset \Omega$ with $r\leq 1$ and $m>n-1-\delta\geq 0$. The function $g(t)$ is supposed to be nonnegative and $C^{1}$-continuous in $[0,+\infty)$, satisfying $g(0)=0$, and for some positive constants $\delta$ and $g_{0}$, $\delta\leq \frac{tg'(t)}{g(t)}\leq g_{0}, \forall t>0$, that generalizes the structural conditions of Ladyzhenskaya-Ural'tseva for an elliptic operator.

submitted time 2018-09-22 Hits1059Downloads1059 Comment 0

9. chinaXiv:201611.00721 [pdf]

A Note on Elliptic Coordinates

Sun, Che
Subjects: Mathematics >> Mathematics (General)

Explicit equations are obtained to convert Cartesian coordinates to elliptic coordinates, based on which an elliptic-coordinate function can be readily mapped on a uniform Cartesian mesh.Application to Kirchhoff vortex is provided.

submitted time 2018-09-22 Hits39635Downloads2148 Comment 0

10. chinaXiv:201809.00176 [pdf]

一类高阶非线性微分方程Lyapunov不等式

郭旭; 王浩帆; 郑军
Subjects: Mathematics >> Mathematics (General)

本文研究一类高阶非线性微分方程的Lyapunov 不等式,是对《Lyapunov-type inequalities for $\psi$-Laplacian equations》有关结论的进一步探讨和推广.

submitted time 2018-09-18 Hits11265Downloads1559 Comment 0

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