The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field

In this article, we will study the isoperimetric problem by introducing a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow preserves the volume of the bounded domain enclosed by a star-shaped hypersurface and decreases the area of hypersurface under certain conditions. We will prove the long time existence and convergence of the flow. As a result, the isoperimetric inequality for such a domain is established. Especially, we solve the isoperimetric problem for the star-shaped hypersurfaces in the Riemannian manifold endowed with a closed, non-trivial conformal vector field, a wide class of warped product spaces studied by Guan, Li and Wang is included

High-yield TiO(2) nanowire synthesis and single nanowire field-effect transistor fabrication

We report a facile method for synthesizing single-crystal rutile TiO 2 nanowires using atmospheric-pressure, chemical vapor deposition with Ti and TiO as precursors. The synthesis is found to depend critically on the predeposition of a layer of metallic Ti on the Ni catalysts layer. The omission of this step seems previously to have impeded the efficient synthesis of titania nanowires. Single-nanowire field-effect transistors showed the TiO2 nanowires to be n -type semiconductors with conductance activation energy of ???58 meV.open242

Gold nanoprisms as a hybrid in vivo cancer theranostic platform for in situ photoacoustic imaging, angiography, and localized hyperthermia

The development of high-resolution nanosized photoacoustic contrast agents is an exciting yet challenging technological advance. Herein, antibody (breast cancer-associated antigen 1 (Brcaa1) monoclonal antibody)- and peptide (RGD)-functionalized gold nanoprisms (AuNprs) were used as a combinatorial methodology for in situ photoacoustic imaging, angiography, and localized hyperthermia using orthotopic and subcutaneous murine gastric carcinoma models. RGD-conjugated PEGylated AuNprs are available for tumor angiography, and Brcaa1 monoclonal antibody-conjugated PEGylated AuNprs are used for targeting and for in situ imaging of gastric carcinoma in orthotopic tumor models. In situ photoacoustic imaging allowed for anatomical and functional imaging at the tumor site. In vivo tumor angiography imaging showed enhancement of the photoacoustic signal in a time-dependent manner. Furthermore, photoacoustic imaging demonstrated that tumor vessels were clearly damaged after localized hyperthermia. This is the first proof-of-concept using two AuNprs probes as highly sensitive contrasts and therapeutic agents for in situ tumor detection and inhibition. These smart antibody/peptide AuNprs can be used as an efficient nanotheranostic platform for in vivo tumor detection with high sensitivity, as well as for tumor targeting therapy, which, with a single-dose injection, results in tumor size reduction and increases mice survival after localized hyperthermia treatment.National Basic Research Program of China (No. 2015CB931802)National Natural Science Foundation (China) (Nos. 81225010, 81327002, 31170961, 20771075, and 20803040)National High-Tech R&D Plan of China (No. 2014AA020700)Shanghai Science and Technology Fund (Nos. 13NM1401500 and 15DZ2252000

Toward Fundamentals of Confined Catalysis in Carbon Nanotubes

An increasing number of experimental studies have demonstrated that metal or metal oxide nanoparticles confined inside carbon nanotubes (CNTs) exhibit different catalytic activities with respect to the same metals deposited on the CNT exterior walls, with some reactions enhanced and others hindered. In this article, we describe the concept of confinement energy, which enables prediction of confinement effects on catalytic activities in different reactions. Combining density functional theory calculations and experiments by taking typical transition metals such as Fe, FeCo, RhMn, and Ru as models, we observed stronger strains and deformations within the CNT channels due to different electronic structures and spatial confinement. This leads to downshifted d-band states, and consequently the adsorption of molecules such as CO, N-2, and O-2 is weakened. Thus, the confined space of CNTs provides essentially a unique microenvironment due to the electronic effects, which shifts the volcano curve of the catalytic activities toward the metals with higher binding energies. The extent of the shift depends on the specific metals and the CNT diameters. This concept generalizes the diverse effects observed in experiments for different reactions, and it is anticipated to be applicable to an even broader range of reactions other than redox of metal species, CO hydrogenation, ammonia synthesis and decomposition discussed here