Algebraic cycles and EPW cubes

Let X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a 19‐dimensional family of hyperkähler sixfolds that are “double EPW cubes” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). This has interesting consequences for the Chow ring of the quotient , which is an “EPW cube” (in the sense of Iliev–Kapustka–Kapustka–Ranestad).     

Research on the composition center of a class of rigid differential systems

In this paper, we answer the question: under what conditions a class of rigid differential systems have a composition center. We give the sufficient and necessary conditions for these systems to have a center at origin point. At the same time, we give the formula of focal values and the highest order of fine focus.     

Yau's uniformization conjecture for manifolds with non-maximal volume growth

The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed by G. Liu in [23]. In the first part, we will give a survey on the progress.In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number C_1~n is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that,under bounded curvature conditions, C_1~n is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on K¨ahler manifolds with minimal volume growth.     

多复变数一类α次星形映射齐次展开式各项的精细估计

本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.     

The Bateman–Horn conjecture: Heuristic,history, and applications

The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau’s conjecture. We discuss the Bateman–Horn conjecture, its applications, and its origins.     

Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

The family of pairwise independently determined(PID) systems, i.e., those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether mixing implies mixing of all orders, has a positive answer. We show that in the class of weakly mixing PID one finds a positive answer for another long-standing open problem, whether the multiple ergodic averages 1/N N-1∑n=0 f_1(T~nx)···f_d(T~(dnx)),N→∞,almost surely converge.     

对测量气体热导率实验中压强影响的分析

在测量气体热导率的实验中,发现气压在0．133～1．33kPa内1／Q和1/p并不完全符合线性关系,分析发现这是由于分子定向运动所致．随着测量室内气压的升高,测量室内气体分子温度也随之升高,当P〉1．33 kPa时,1／Q再次偏离1/p的一次函数关系．     

Third generation photovoltaics

We review recent progress towards increasing solar cell efficiencies beyond the Shockley‐Queisser efficiency limit. Four main approaches are highlighted: multi‐junction cells, intermediate‐band cells, hot carrier cells and spectrum conversion. Multi‐junction cells use multiple solar cells that selectively absorb different regions of the solar spectrum. Intermediate‐band cells use one junction with multiple bandgaps to increase efficiencies. Hot‐carrier cells convert the excess energy of above‐bandgap photons into electrical energy. Spectrum conversion solar cells convert the incoming polychromatic sunlight into a narrower distribution of photons suited to the bandgap of the solar cell.     

冲击作用下炸药热点形成的3维离散元模拟

为了探讨非均质炸药在冲击作用下的细观响应特性,分别对以HMX为基的PBX塑料粘接炸药和含孔洞的HMX炸药在活塞推动下热点的形成过程进行了3维离散元模拟(未考虑化学反应)。结果表明,塑料粘接炸药中的热点集中在炸药晶体与粘结剂的结合部,晶体温升低于粘结剂,且晶体边界温升高于内部。对于含孔洞炸药,热点温度与孔洞的尺寸和形状有关,大孔洞塌缩形成的热点温度高于小孔洞塌缩形成的热点温度,球形孔洞塌缩形成的热点温度高于立方体孔洞塌缩得到的热点温度。     

Plasmonic hot electron tunneling photodetection in vertical Au–graphene hybrid nanostructures

Plasmon‐induced hot‐electron generation provides an efficient way to convert light into electric current. The investigation of the optoelectronic response in two‐dimensional materials and metallic hybrid nanostructure attracts increasing research interest. Here, we present a tunneling effect of plasmonic hot electrons that is generated from Au nanoparticles, which can vertically tunnel through graphene monolayers. A strong photocurrent induced by the hot electrons was measured in this graphene‐based vertical photodetector with its intensity maximum reached at the plasmon resonance wavelength. The tunneling effect of plasmonic hot electrons was investigated by gradually increasing the incident laser power and bias voltage between the top and bottom electrodes. The dynamic attenuation of plasmonic hot electrons in an excited state was further investigated with multilayered graphene sheets. These results show that our vertical hybrid structure can function as an effective design for the tunneling photodetector, and enable the realization of complex nanophotonic devices that are based on graphene and other 2D materials, such as optical transistors and plasmonic hot‐electron sensors.