Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Effects of dust storms on microwave radiation based on satellite observation and model simulation over the Taklamakan desert

International audienceEffects of dust particles on microwave radiation over the Taklamakan desert are studied with use of measurements from the Advanced Microwave Scanning Radiometer (AMSR-E) on the EOS Aqua satellite and a microwave radiation transfer model. Eight observed cases show that the signal from atmospheric dust can be separated from the surface radiation by the fact that the dust particles produce stronger scattering at high frequencies and depolarize the background desert signature. This result of satellite data is consistent with the model simulation

Two-qubit Quantum Logic Gate in Molecular Magnets

We proposed a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled single-molecule magnets, $[\textrm{Mn}_4]_2$. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between the quantum computing bases and between the quantum computing bases and other excited states are evaluated and analyzed.Comment: 7 pages, 2 figure

A chemical mutagenesis approach to insert post-translational modifications in aggregation-prone proteins

Neurodegenerative diseases are a class of disorders linked to the formation in the nervous system of fibrillar protein aggregates called amyloids. This aggregation process is affected by a variety of post-translational modifications, whose specific mechanisms are not fully understood yet. Emerging chemical mutagenesis technology is currently striving to address the challenge of introducing protein post-translational modifications, while maintaining the stability and solubility of the proteins during the modification reaction. Several amyloidogenic proteins are highly aggregation-prone, and current modification procedures can lead to unexpected precipitation of these proteins, affecting their yield and downstream characterization. Here, we present a method for maintaining amyloidogenic protein solubility during chemical mutagenesis. As proof-of-principle, we applied our method to mimic the phosphorylation of serine-26 and the acetylation of lysine-28 of the 40-residue long variant of amyloid-β peptide, whose aggregation is linked to Alzheimer’s disease

Development of Novel EBSM System for High-Tech Material Additive Manufacturing Research

Electron beam is more appropriate for metal additive manufacturing (AM) than laser because of its high energy converting efficiency and high absorption for various materials. It becomes a preference for AM study of high-tech material with high melting point, high brittleness or graded material. A novel electron beam selective melting (EBSM) system with dual-material processing capability has been developed in Tsinghua University to meet the wide high-tech material AM research requirement. A vibration driven powder supplier was developed and the supplier had a high compatibility to various powders. A stable supplying rate and a supplying accuracy less than 7.5% were obtained with the supplier. Two powders can be supplied individually to obtain a mixture with tailored proportion for each powder layer. The mixture is homogenous and the actual proportion is close to the desired value. In order to prolong the spreading comb’s lifetime and avoid tooth breaking, a low deformation powder spreading device was designed based on dual inclined combs and a one-way scraping mechanism. The system provides exchangeable building tanks with sizes of 100 ×100 ×100 mm3 and 250 × 250 × 250 mm3, which can save powder when the part is small and the powder is expensive. The novel EBSM system is capable of building parts with single material and has a potential of dual-material processing.Mechanical Engineerin

Measuring the leptonic CP phase in neutrino oscillations with nonunitary mixing

Non-unitary neutrino mixing implies an extra CP violating phase that can fake the leptonic Dirac CP phase δCP of the simplest three-neutrino mixing benchmark scheme. This would hinder the possibility of probing for CP violation in accelerator-type experiments. We take T2K and T2HK as examples to demonstrate the degeneracy between the "standard" (or "unitary") and "non-unitary" CP phases. We find, under the assumption of non-unitary mixing, that their CP sensitivities severely deteriorate. Fortunately, the TNT2K proposal of supplementing T2(H)K with a µDAR source for better measurement of δCP can partially break the CP degeneracy by probing both cos δCP and sin δCP dependences in the wide spectrum of the µDAR flux. We also show that the further addition of a near detector to the µDAR setup can eliminate the degeneracy completely