Existence of Multistring Solutions of the Self-Gravitating Massive W−W-Boson

We consider a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in \cite{yan}Comment: 12 page

Light-Driven Hydrogen Production from Aqueous Solutions Based on a New Dubois-Type Nickel Catalyst

In this work, we report a new photocatalytic system that links multifunctional semiconductor nanocrystals with emerging water-soluble molecular catalysts made of earth-abundant elements for H2 generation [Ni(P2RN2R′)2(BF4)2]4−, R = Ph, R′ = [PhSO3]− (NiS). This noble metal free hybrid exhibits remarkable catalytic activity with a turnover number of 511 for H2 production and a photon-to-H2 conversion efficiency of 12.5%. The mechanistic insight into such high efficiency in this photocatalytic system was examined using a combination of steady-state emission and time-resolved absorption spectroscopy

Atomic electron tomography in three and four dimensions

Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. Here, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution

The geometry of Grassmannian manifolds and Bernstein type theorems for higher codimension

We identify a region \Bbb{W}_{\f{1}{3}} in a Grassmann manifold \grs{n}{m}, not covered by a usual matrix coordinate chart, with the following important property. For a complete $n-$submanifold in \ir{n+m} \, (n\ge 3, m\ge2) with parallel mean curvature whose image under the Gauss map is contained in a compact subset K\subset\Bbb{W}_{\f{1}{3}}\subset\grs{n}{m}, we can construct strongly subharmonic functions and derive a priori estimates for the harmonic Gauss map. While we do not know yet how close our region is to being optimal in this respect, it is substantially larger than what could be achieved previously with other methods. Consequently, this enables us to obtain substantially stronger Bernstein type theorems in higher codimension than previously known.Comment: 36 page