Regularity criteria for the Euler equations with nondecaying data

The local-in-time existence and uniqueness of strong solutions to the Euler equations in the whole space with nondecaying and certainly regular initial velocity are concerned. It is obtained that the spatial regularity of solutions coincides with that of initial velocity under the suitable setting of external forcing terms. Regularity criteria focusing into the vorticity are also discussed due to the similar arguments of Beale-Kato-Majda.     

Anthracene-fused BODIPYs as near-infrared dyes with high photostability

An anthracene unit was successfully fused to the zigzag edge of a boron dipyrromethene (BODIPY) core by an FeCl(3)-mediated oxidative cyclodehydrogenation reaction. Meanwhile, a dimer was also formed by both intramolecular cyclization and intermolecular coupling. The anthracene-fused BODIPY monomer 7a and dimer 7b showed small energy gaps (～1.4 eV) and near-infrared absorption/emission. Moreover, they exhibited high photostability.     

Logarithmically Improved Regularity Criteria for the Navier�CStokes and MHD Equations

In this paper, logarithmically improved regularity criteria for the Navier–Stokes and the MHD equations are established in terms of both the vorticity field and the pressure.     

Graphene‐like Molecules with Four Zigzag Edges

An efficient synthetic method toward graphene‐like molecules (GLMs), having four zigzag edges, is described. They were obtained as stable materials and their structures were confirmed by X‐ray crystallographic analysis. They exhibit topology‐ and size‐dependent electronic properties and global aromaticity, which are all different from GLMs having either all‐armchair edges, or three zigzag edges, or two armchair/two zigzag edges. They can be reversibly oxidized and reduced into stable charged species, which show fragmental aromatic character to minimize anti‐aromaticity. Our studies give some new insights into the electronic structures and properties of a new type of rarely studied GLMs.     

碳纳米管的加入对聚偏氟乙烯/丙烯酸酯共混物形状记忆性能的影响

利用聚偏氟乙烯(PVDF)微小结晶的物理交联点作用,制备了形状记忆性能优异的聚偏氟乙烯/丙烯酸酯聚合物(PVDF/ACM)共混材料。为提高其形状回复应力,又将碳纳米管(CNT)引入该共混体系中,系统研究了PVDF/ACM/CNT三元体系纳米复合材料的制备、结构及性能。结果表明,碳纳米管在PVDF/ACM体系中分散均匀;在基本保持其形状记忆性能的前提下,加入质量分数为4%的CNT,材料在25℃时的储能模量由2000 MPa提高至3130 MPa。     

Toward Two‐Dimensional π‐Conjugated Covalent Organic Radical Frameworks

Reported is the synthesis, characterization, and material properties of the first π‐conjugated two‐dimensional covalent organic radical framework (CORF), PTM‐CORF , based on the stable polychlorotriphenylmethyl (PTM) radical. The covalent organic framework (COF) precursor ( PTM‐H‐COF ) was first synthesized by liquid/liquid interfacial acetylenic homocoupling of a triethynylpolychlorotriphenylmethane monomer, and showed crystalline features with a hexagonal diffraction pattern matching that of A‐B‐C stacking. Subsequent deprotonation and oxidation of the PTM units in PTM‐H‐COF gave PTM‐CORF . Magnetic measurements revealed that the neighboring PTM radicals in the PTM‐CORF are anti‐ferromagnetically coupled each other, with a moderate exchange interaction (J=?375 cm^?1). The PTM‐CORF has a small energy gap (ca. 0.88 eV) and a low‐lying LUMO energy level (?4.72 eV), and exhibits high electrocatalytic activity and durability toward the oxygen reduction reaction.     

High anisotropy of the field-effect transistor mobility in magnetically aligned discotic liquid-crystalline semiconductors

A magnetic field has been utilized for producing highly oriented films of a substituted hexabenzocoronene (HBC). Optical microscopy studies revealed large area HBC monodomains that covered the entire film, while wide-angle X-ray measurements showed that the HBC molecules are aligned with their planes along the applied field. On the basis of this method, solution-processed field-effect transistors (FET) have been constructed with charge carrier mobilities of up to 10(-3) cm2/V.s, which are significantly enhanced with respect to the unaligned material. Exceptionally high mobility anisotropies of 25-75 for current flow parallel and perpendicular to the alignment direction have been measured as a function of the channel length. Atomic force microscopy performed on the FET structures reveals fibril superstructures that are oriented perpendicularly to the magnetic field direction, consisting of molecular columns with a slippage angle of 40 degrees between the molecules. For channel lengths larger than 2.5 mum, the fibrils are smaller than the electrode spacing, which adversely affects the device performance.     

Combination of π-π stacking and electrostatic repulsion between carboxylic carbon nanoparticles and fluorescent oligonucleotides for rapid and sensitive detection of thrombin

On the basis of simultaneous electrostatic repulsion and π-π stacking interactions of carboxylic carbon nanoparticles (cCNPs) with single-stranded DNA, a noncovalent assembly of cCNPs and fluorescent aptamers is reported for rapid, sensitive, and selective detection of thrombin.     

Inverse viscosity problem for the Navier-Stokes equation

We consider an inverse problem of determining a viscosity coefficient in the Navier-Stokes equation by observation data in a neighborhood of the boundary. We prove the Lipschitz stability by the Carleman estimates in Sobolev spaces of negative order.     

Perylene-fused BODIPY dye with near-IR absorption/emission and high photostability

A N-annulated perylene unit was successfully fused to the meso- and β-positions of a boron dipyrromethene (BODIPY) core. The newly synthesized BODIPY dye 1b exhibits intensified near-infrared (NIR) absorption and the longest emission maximum ever observed for all BODIPY derivatives. In addition, this dye possesses excellent solubility and photostability, beneficial to practical applications.