A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group ${\text{Nil}}_3$, the universal covering of the Lie group $\text{PSL}(2,\mathbb{R})$ and the Lie group ${\text{Sol}}_3$) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.     

Frequency ratios of Sr,Yb, and Hg based optical lattice clocks and their applications

This article describes the recent progress of optical lattice clocks with neutral strontium (⁸⁷Sr), ytterbium (¹⁷¹Yb) and mercury (¹⁹⁹Hg) atoms. In particular, we present frequency comparison between the clocks locally via an optical frequency comb and between two Sr clocks at remote sites using a phase-stabilized fibre link. We first review cryogenic Sr optical lattice clocks that reduce the room-temperature blackbody radiation shift by two orders of magnitude and serve as a reference in the following clock comparisons. Similar physical properties of Sr and Yb atoms, such as transition wavelengths and vapour pressure, have allowed our development of a compatible clock for both species. A cryogenic Yb clock is evaluated by referencing a Sr clock. We also report on an Hg clock, which shows one order of magnitude less sensitivity to blackbody radiation, while its large nuclear charge makes the clock sensitive to the variation of fine-structure constant. Connecting all three types of clocks by an optical frequency comb, the ratios of the clock frequencies are determined with uncertainties smaller than possible through absolute frequency measurements. Finally, we describe a synchronous frequency comparison between two Sr-based remote clocks over a distance of 15 km between RIKEN and the University of Tokyo, as a step towards relativistic geodesy.     

Mercury forms and their transformation in pyrite under weathering

Pyrite is considered to be the major carrier of mercury in coal. Here, the chemical characteristics of two natural pyrite samples of different weathering degrees were characterized by time-of-flight secondary ion mass spectrometry (TOF-SIMS). Thermal stability of Hg was also analyzed via temperature programmed desorption experiment (TPD). Characteristic ions such as S⁻, Fe⁺, FeS⁻, and FeS₂⁻ were detected on the surface of fresh pyrite. The release temperature of Hg ranged between 180°C and 300°C, and the characteristic peak of black HgS was recorded. In addition, abundant Fe₂O₃⁻, FeSO⁻, SO₄⁻, and HSO₄⁻ were detected on the surface of weathered pyrite, and the release temperature of Hg therein was mainly distributed at 260°C to 380°C and 520°C to 600°C, corresponding to the characteristic peaks of red HgS and HgSO₄, respectively. The results show that pyrite is acidified during weathering and that Hg forms in pyrite are transformed from the original state (HgS) to HgSO₄.     

Properties of mono-weakly hyponormal 2-variable weighted shifts

In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers.     

On an open problem of Sankaranarayanan

Let λ(n) be the n-th normalized Fourier coeficient of a holomorphic Hecke eigenform f(z) ∈ Sk(Γ) for the full modular group.In one of his papers,Sankaranarayanan mentioned that it is an open problem to give a non-trivial estimate for the sum of λ(n) over cubes,i.e.n x λ(n3).In this paper,we are able to use the analytic properties of symmetric power L-functions to solve his problem.More precisely,we prove that Σn≤zλ(n3) x(3/4 +ε),Σn≤zλ(n4) x(97+ε).     

Depolarization properties of cirrus clouds from polarization lidar measurements over Hefei in spring

A new polarization lidar has been developed for detecting depolarization characteristics of aerosol and cirrus over Hefei (31.90°N, 117.16°E), China. The fundamental principle of polarization lidar is briefly introduced.     

Canonical Brownian Motion on the Diffeomorphism Group of the Circle

For infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric H^3/2, the associated Brownian motion has been constructed by Malliavin (C.R. Acad. Sci. Parist.329 (1999), 325-329). In this work, we shall give another approach and prove the invariance of heat measures under the adjoint action of S¹.     

An Elementary Proof of the Fundamental Theorem of Projective Geometry (Dedicated to Alfred Frölicher)

The following version of the fundamental theorem is proved: Let V, W be vector spaces and g: P(V)\E P(W) a morphism between the associated projective spaces. If the image of g is not contained in a line, then there exists a semilinear map f: V W which induces g. The difficulty lies in the fact that the homomorphism of division rings associated to the map f can be nonsurjective. As an application, a short proof of Wigner's theorem is also proposed.     

Decompositions of Fundamental Groups of Closed Surfaces into Free Constructions

Let T be a closed surface. It is proven that any decomposition of ₁(T,x) into an amalgamated product (or, more generally, into the fundamental group of a finite graph of groups) with f.g. edge group(s) is almost geometric. A problem of H. Zieschang is solved and the edge rigidity property is investigated.