ISSN 1439-8516 CN 11-2039/O1
The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in Hs(R2) for all 5/7 < s < 1 via using I-method in the context of atomic spaces. By means of the increment of modified energy, the existence of global attractor for the weakly damped, forced Zakharov-Kuznetsov equation is also established in Hs(R2) for 10/11 < s < 1.
Let Möb(Sn+1) denote the Möbius transformation group of Sn+1. A hypersurface f:Mn → Sn+1 is called a Möbius homogeneous hypersurface, if there exists a subgroup G ? Möb(Sn+1) such that the orbit G(p)={φ(p)|φ ∈ G}=f(Mn), p ∈ f(Mn). In this paper, we classify the Möbius homogeneous hypersurfaces in Sn+1 with at most one simple principal curvature up to a Möbius transformation.
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. In this paper, we propose a more generalized risk measure called quantile shortfall (QS) which includes MS as a special case. QS measures the conditional quantile loss of the tail risk and inherits the merits of MS. We construct an estimator of the QS and establish the asymptotic normality behavior of the estimator. Our simulation shows that the newly proposed measures compare favorably in robustness with other widely used measures such as ES and VaR.
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))||,
where ρ1 and ρ2 are fixed nonzero complex numbers with|ρ1|+|ρ2|< 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the above additive (ρ1, ρ2)-functional inequality in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in C*-ternary algebras.
A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I1 and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer.
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 isoparametric hypersurfaces, but in general, their isoparametric functions are different. We give a necessary and sufficient condition for an isoparametric function of (N, h) to be isoparametric on (N, F, dμBH), from which we get some examples of isoparametric functions.
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 different from the case of characteristic zero.
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 class of Abelian groups. In particular, we show that a finite Abelian group has the strong endomorphism kernel property if and only if it is cyclic.
