Scalar curvature,mean curvature and harmonic maps to the circle

Annals of Global Analysis and Geometry - We study harmonic maps from a 3-manifold with boundary to $$\mathbb {S}^1$$ and prove a special case of Gromov dihedral rigidity of three-dimensional cubes...     

Minimal surfaces in symmetric spaces with parallel second fundamental form

In this paper, we study geometry of isometric minimal immersions of Riemannian surfaces in a symmetric space by moving frames and prove that the Gaussian curvature must be constant if the immersion is of parallel second fundamental form. In particular, when the surface is \(S^2\), we discuss the special case and obtain a necessary and sufficient condition such that its second fundamental form is parallel. We also consider isometric minimal two-spheres immersed in complex two-dimensional Kähler symmetric spaces with parallel second fundamental form, and prove that the immersion is totally geodesic with constant Kähler angle if it is neither holomorphic nor anti-holomorphic with Kähler angle \(\alpha \ne 0\) (resp. \(\alpha \ne \pi \)) everywhere on \(S^2\).     

Minimal two-spheres in <Emphasis Type="Italic">G</Emphasis>(2, 4; (<Emphasis Type="Italic">C</Emphasis>)) with parallel second fundamental form

In this paper, we give a classification theorem of minimal two-spheres in G(2, 4; (C)) with parallel second fundamental form. Moreover, we also consider some special holomorphic two-spheres in G(2, n; (C)) and give the corresponding conditions of the parallel second fundamental form.     

How Does van der Waals Confinement Enhance Phonon Transport?

We study the mechanism of van der Waals(vdW)interactions on phonon transport in atomic scale,which would boost developments in heat management and energy conversion.Commonly,the vdW interactions are regarded as a hindrance in phonon transport.Here we propose that the vdW confinement can enhance phonon transport.Through molecular dynamics simulations,it is realized that the vdW confinement is able to make more than two-fold enhancement on thermal conductivity of both polyethylene single chain and graphene nanoribbon.The quantitative analyses of morphology,local vdW potential energy and dynamical properties are carried out to reveal the underlying physical mechanism.It is found that the confined vdW potential barriers reduce the atomic thermal displacement magnitudes,leading to less phonon scattering and facilitating thermal transport.Our study offers a new strategy to modulate the phonon transport.     

What are the Factors that Determine the Number of People Coming to China?

This paper studies the factors that affect people coming to China. We select the spending of United States and South Korea, GDP, railway transportation capacity of China as observations. Based on the data from 1988 to 2015, we use the ordinary least squares analysis regression model and present a most reasonable regression equation. It is found that South Korea’s spending is negative to the number of visitors, whereas the spending of US is positive. On comparing the effect of other variables, the growth of railway transportation capacity and the overseas travel expenses of South Korea or United States, have almost no significant impact on the number of people coming to China. However, as China economic growth increasing rapidly, more and more people are willing to come.     

Giant Asymmetric Transmission and Circular Dichroism with Angular Tunability in Chiral Terahertz Metamaterials

Inspired by the chiral structure from mode interaction, a chiral terahertz metamaterial and its complementary structure with the coexistence of asymmetric transmission and circular dichroism response are designed. The asymmetric transmission happens in the presence of electric and magnetic modes perpendicular to each other, resulting from intrinsic chirality under normal incidence. Circular dichroism exists in the presence of electric and magnetic modes parallel to each other under oblique incidence because of extrinsic chirality. Both asymmetric transmission and circular dichroism are enhanced by complementary structures, benefitting from the coupling between adjacent units. The maximum of chiral parameter κ can achieve 450, which is one hundred times higher than previously reported. The chiral response can be tuned by the incident angle and is sensitive to the environmental refractive index. The results highlight the potential applications of these metamaterials in chiral sensing and polarization transformation devices.     

Triple automorphisms of simple Lie algebras

An invertible linear map φ on a Lie algebra L is called a triple automorphism of it if φ([x, [y, z]]) = [φ(x), [φ(y), φ(z)]] for ∀ x, y, z ∈ L. Let g be a finite-dimensional simple Lie algebra of rank l defined over an algebraically closed field F of characteristic zero, p an arbitrary parabolic subalgebra of g. It is shown in this paper that an invertible linear map φ on p is a triple automorphism if and only if either φ itself is an automorphism of p or it is the composition of an automorphism of p and an extremal map of order 2.     

The study on microstructure and electrochemical properties of Al–Mg–Sn–Ga–Pb alloy anode material for Al/AgO battery

The microstructure of Al–Mg–Sn–Ga–Pb quinary aluminum alloy anode material and the influences of its electrochemical properties and self-corrosion rate in 4 mol/l NaOH +10 g/l Na₂SnO₃ medium were studied. The microstructure and morphology were characterized by metallographic microscope, transmission electron microscope, and scanning electron microscopy. The electrochemical properties were tested by electrochemical workstation, and the self-corrosion rate of Al alloy anode was studied by methods of recovery H₂ gas by discharge water. The results show that homogenization has not much impact on the electrochemical properties and the corrosion rate of the cast aluminum alloy anode material; besides, return annealing treatment of the cold-rolled Al–Mg–Sn–Ga–Pb quinary aluminum alloy anode material can reduce the rate of self-corrosion and make Al anodic potential shift negative steadily and improve the properties of the material.