国际地下实验室发展综述

地下实验室是开展粒子物理学、天体物理学及宇宙学等领域一些重大基础性前沿课题的重要研究场所和良好的低本底环境,建设和发展地下实验室对于一个国家的基础科学研究具有重要科学意义.目前,国际上许多国家都已经建立起地下实验室,而中国一直没有很好的地下实验室,特别是极深地下实验室.2009年,清华大学与二滩水电开发有限责任公司开展战略合作,利用锦屏山隧道建立中国首个世界最深的地下实验室--中国锦屏地下实验室(China Jinping Underground Laboratory,CJPL),并于2010年12月12日正式启用.中国锦屏地下实验室的建成,标志着中国已经具备开展物理学重大基础前沿科学研究的自主地下实验平台,对于推动我国相关领域的重大基础前沿课题的自主研究意义重大.文章对国际上一些重要地下实验室的情况进行了介绍,并对中国锦屏地下实验室的基本情况进行了介绍.     

软科学:自然科学与人文社会科学的综合应用——科学与人文漫话之十六

给出了软科学的界定及软科学内容简介;从软科学研究项目一览出发,根据软科学研究的主要对象与软科学研究的方法特点分析并论证了软科学要求自然科学与人文社会科学的综合应用.     

Hydrogenation mechanism in lanthanum-activated magnesium films

With density-functional theory, the dissociative chemisorptions and diffusion processes of hydrogen on both pure and La-doped Mg(0001) surfaces are studied. Calculation results show that the energy barrier obtained for hydrogen dissociation on the La-doped Mg(0001) surface is smaller due to back-donated bonding between molecular H₂ and doped La atom. The obtained diffusion barriers (0.8–0.22 eV) imply a fast motion of atomic H on La-doped Mg(0001) surface.     

Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model

This paper proposes a novel extended traffic network model to solve the logit-based stochastic user equilibrium (SUE) problem with elastic demand. In this model, an extended traffic network is established by properly adding dummy nodes and links to the original traffic network. Based on the extended traffic network, the logit-based SUE problem with elastic demand is transformed to the SUE problem with fixed demand. Such problem is then further converted to a linearly constrained convex programming and addressed by a predictor–corrector interior point algorithm with polynomial complexity. A numerical example is provided to compare the proposed model with the method of successive averages (MSA). The numerical results indicate that the proposed model is more efficient and has a better convergence than the MSA.     

Backward stochastic differential equations associated with the vorticity equations

In this paper we derive a non-linear version of the Feynman–Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2. A particular class of terminal values provide, via these probabilistic methods, solutions for the vorticity equation.     

Non-stretch mappings for a sharp estimate of the Beurling–Ahlfors operator

In this paper we identify certain classes of non-stretch mappings that enjoy a sharp estimate of the Beurling–Ahlfors operator. We first make use of a property of subharmonic functions to prove that the Bañuelos–Wang conjecture and the Iwaniec conjecture are true for a class of mappings that satisfy a quasilinear conjugate Beltrami equation. By utilizing the principal solutions of Beltrami equations, we further explicitly construct some classes of non-stretch mappings for which the Bañuelos–Wang conjecture and the Iwaniec conjecture are true.     

On the Hochschild cohomology ring of tensor products of algebras

We prove that, as Gerstenhaber algebras, the Hochschild cohomology ring of the tensor product of two algebras is isomorphic to the tensor product of the respective Hochschild cohomology rings of these two algebras, when at least one of them is finite dimensional. In case of finite dimensional symmetric algebras, this isomorphism is an isomorphism of Batalin–Vilkovisky algebras. As an application, we explain by examples how to compute the Batalin–Vilkovisky structure, in particular, the Gerstenhaber Lie bracket, over the Hochschild cohomology ring of the group algebra of a finite abelian group.     

The elementary symmetric functions of a reciprocal polynomial sequence

Erdös and Niven proved in 1946 that for any positive integers m and d, there are at most finitely many integers n   for which at least one of the elementary symmetric functions of 1/m,1/(m+d),…,1/(m+(n−1)d)$1/m,1/(m+d),\dots ,1/(m+(n-1)d)$ are integers. Recently, Wang and Hong refined this result by showing that if n?4$n?4$, then none of the elementary symmetric functions of 1/m,1/(m+d),…,1/(m+(n−1)d)$1/m,1/(m+d),\dots ,1/(m+(n-1)d)$ is an integer for any positive integers m and d. Let f   be a polynomial of degree at least 2 and of nonnegative integer coefficients. In this paper, we show that none of the elementary symmetric functions of 1/f(1),1/f(2),…,1/f(n)$1/f(1),1/f(2),\dots ,1/f(n)$ is an integer except for f(x)=x^m$f(x)=x^m$ with m?2$m?2$ being an integer and n=1$n=1$.     

Approximation of monogenic functions by higher order Szeg kernels on the unit ball and half space

We study the adaptive decomposition of functions in the monogenic Hardy spaces H2by higher order Szeg kernels under the framework of Clifford algebra and Clifford analysis,in the context of unit ball and half space.This is a sequel and a higher-dimensional generalization of our recent study on the complex Hardy spaces.     

Graphic Sequences with an A-Connected Realization

A non-increasing sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer \({\sigma (A, n)}\) such that each graphic sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) with d _n ≥ 2 and \({\sigma (\pi) = d_1 + d_2 + \cdots +d_n \ge \sigma (A, n)}\) has an A-connected realization. In this paper, we determine \({\sigma (A, n)}\) for |A| ≥ 5 and n ≥ 3.