Chen, You Li Liu, Yan Yan Mao, Guang Cai Wu, Yuan Shan Yan, Fei
Published in
Acta Mathematica Sinica, English Series

Among recent measures for risk management, value at risk (VaR) has been criticized because it is not coherent and expected shortfall (ES) has been criticized because it is not robust to outliers. Recently, [Math. Oper. Res., 38, 393–417 (2013)] proposed a risk measure called median shortfall (MS) which is distributional robust and easy to implement...

Fang, Jie Sun, Zhong Ju
Published in
Acta Mathematica Sinica, English Series

An endomorphism h of a group G is said to be strong whenever for every congruence θ on G, (x,y) ∈ θ implies (h(x), h(y)) ∈ θ for every x, y ∈ G. A group G is said to have the strong endomorphism kernel property if every congruence on G is the kernel of a strong endomorphism. In this note, we study the strong endomorphism kernel property in the clas...

Duan, Fei Fei Shu, Bin Yao, Yu Feng
Published in
Acta Mathematica Sinica, English Series

Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac’s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very differen...

Shan, Min Jie
Published in
Acta Mathematica Sinica, English Series

The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in Hs(ℝ2) for all 57\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...

He, Qun Dong, Pei Long Yin, Song Ting
Published in
Acta Mathematica Sinica, English Series

In this paper, we give the complete classifications of isoparametric hypersurfaces in Randers space forms. By studying the principal curvatures of anisotropic submanifolds in a Randers space (N, F) with the navigation data (h, W), we find that a Randers space form (N, F, dµBH) and the corresponding Riemannian space (N, h) have the same isoparametri...

He, Jun An, Guang Yu Li, Jian Kui Qian, Wen Hua
Published in
Acta Mathematica Sinica, English Series

A linear mapping ϕ from an algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal A}$$\end{document} into its bimodule ℳ\documentclass[12pt]{minimal} \usepackag...

Jin, Yuan Feng Park, Choonkil Rassias, Michael Th.
Published in
Acta Mathematica Sinica, English Series

In this paper, we introduce and solve the following additive (ρ1,ρ2)-functional inequalities ‖f(x+y+z)−f(x)−f(y)−f(z)‖≤‖ρ1(f(x+z)−f(x)−f(z))‖+‖ρ2(f(y+z)−f(y)−f(z))‖,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...

Chen, Ya Yun Ji, Xiu Li, Tong Zhu
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Acta Mathematica Sinica, English Series

Let Möb(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{S}^{{n + 1}}$$\end{document}) denote the Möbius transformation group of \documentclass[12pt]{minimal} \u...

Iranmanesh, Mahdeyeh Jafarpour, Morteza Aghabozorgi, Hossien Zhan, Jian Ming
Published in
Acta Mathematica Sinica, English Series

In this paper, first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism. Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4. Moreover, we propose a hyperfield of order 4 which is not as a quotient hyperfield FG\documentclass[12pt]{min...

Kahraman, Tanju
Published in
Acta Mathematica Sinica, English Series

In this study, by using moving frame along frontal of Legendre curve, we define frontal partner curves on unit sphere S2. We give the relationships between curvatures of Legendre curves and frontal partner curves are strengthen by an example.