Geometry of Numbers

We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of semi-stable lattices, and introduce non-abelian zeta functions for number fields.Comment: A paper by Tsukasa Hayashi is adde

Optical properties of 4 A single-walled carbon nanotubes inside the zeolite channels studied from first principles calculations

The structural, electronic, and optical properties of 4 A single-walled carbon nanotubes (SWNTs) contained inside the zeolite channels have been studied based upon the density-functional theory in the local-density approximation (LDA). Our calculated results indicate that the relaxed geometrical structures for the smallest SWNTs in the zeolite channels are much different from those of the ideal isolated SWNTs, producing a great effect on their physical properties. It is found that all three kinds of 4 A SWNTs can possibly exist inside the Zeolite channels. Especially, as an example, we have also studied the coupling effect between the ALPO_4-5 zeolite and the tube (5,0) inside it, and found that the zeolite has real effects on the electronic structure and optical properties of the inside (5,0) tube.Comment: 9 pages, 6figure

Assessment of in situ immobilization of Lead (Pb) and Arsenic (As) in contaminated soils with phosphate and iron: solubility and bioaccessibility

The effect of in situ immobilization of lead (Pb) and arsenic (As) in soil with respectively phosphate and iron is well recognized. However, studies on combined Pb and As-contaminated soil are fewer, and assessment of the effectiveness of the immobilization on mobility and bioaccessibility is also necessary. In this study, a Pb and As-contaminated soil was collected from an abandoned lead/zinc mine in Shaoxing, Zhejiang province of China, which has been treated with three phosphates, i.e., calcium magnesium phosphate (CMP), phosphate rock, and single super-phosphate (SSP) for 6 months in a field study. The ferrous sulfate (FeSO4) at 20 g kg-1 was then amended to the soil samples and incubated for 8 weeks in a greenhouse. The solubility and bioaccessibility tests were used to assess the effectiveness of the in situ immobilization. The result showed that phosphates addition decreased the concentrations of CaCl2-extractable Pb; however, the concentrations of water-soluble As increased upon CMP and SSP addition. With the iron addition, the water-soluble As concentrations decreased significantly, but CaCl2-extractable Pb concentrations increased. The bioaccessibility of As and Pb measured in artificial gastric and small intestinal solutions decreased with phosphate and iron application except for the bioaccessibility of As in the gastric phase with SSP addition. Combined application of phosphates and iron can be an effective approach to lower bioaccessibility of As and Pb, but has opposing effects on mobility of As and Pb in contaminated soil

Microscopic origin of local moments in a zinc-doped high-TcT_{c} superconductor

The formation of a local moment around a zinc impurity in the high-$T_{c}$ cuprate superconductors is studied within the framework of the bosonic resonating-valence-bond (RVB) description of the $t-J$ model. A topological origin of the local moment has been shown based on the phase string effect in the bosonic RVB theory. It is found that such an $S=1/2$ moment distributes near the zinc in a form of staggered magnetic moments at the copper sites. The corresponding magnetic properties, including NMR spin relaxation rate, uniform spin susceptibility, and dynamic spin susceptibility, etc., calculated based on the theory, are consistent with the experimental measurements. Our work suggests that the zinc substitution in the cuprates provide an important experimental evidence for the RVB nature of local physics in the original (zinc free) state.Comment: The topological reason of local moment formation is given. One figure is adde

Ductility enhancement of layered stainless steel with nanograined interface layers

Combination of surface mechanical attrition treatment (SMAT) and co-rolling is a promising experimental methodology to design metals with high strength and high ductility. Recent results have revealed that brittle nanograined interface layer (NGIL) can enhance the ductility of the co-rolled SMATed stainless steel (SS). In the present study, the cohesive finite element method is used to show that the SS ductility is significantly enhanced with the increase of fracture toughness of coarse-grained layers and failure strain of NGIL. However the ductility will not increase if the NGIL thickness goes beyond 60 μm. © 2011 Elsevier B.V. All rights reserved.postprin