Leray’s inequality in general multi-connected domains in {\mathbb{R}^n}

Consider the stationary Navier–Stokes equations in a bounded domain whose boundary consists of L + 1 smooth (n − 1)-dimensional closed hypersurfaces Γ₀, Γ₁, . . . , Γ _L , where Γ₁, . . . , Γ _L lie inside of Γ₀ and outside of one another. The Leray inequality of the given boundary data β on plays an important role for the existence of solutions. It is known that if the flux on Γ _i (ν: the unit outer normal to Γ _i ) is zero for each i = 0, 1, . . . , L, then the Leray inequality holds. We prove that if there exists a sphere S in Ω separating in such a way that Γ₁, . . . , Γ _k (1 ≦ k ≦ L) are contained inside of S and that the others Γ _k+1, . . . , Γ _L are outside of S, then the Leray inequality necessarily implies that γ ₁ + · · · +  γ _k =  0. In particular, suppose that there are L spheres S ₁, . . . , S _L in Ω lying outside of one another such that Γ _i lies inside of S _i for all i = 1, . . . , L. Then the Leray inequality holds if and only if γ ₀ = γ ₁ = · · · = γ _L = 0.     

Stereoselective approach to potential scaffold of A-nor B-aromatic OSW-1 analogues via [4+2] cycloaddition of o-quinodimethane

A-nor B-aromatic steroidal skeleton was efficiently constructed by means of o-quinodimethane chemistry with exclusive stereoselectivity. The benzocyclobutene substrate for generation of the o-quinodimethane intermediate and subsequent [4+2] cycloaddition could be synthesized via (E)-selective Julia–Kocienski olefination and diastereoselective Grignard addition reactions. The synthesized tricyclic steroid-like compound with a trans-diol substructure would be utilized for divergent syntheses of potentially antitumor OSW-1 analogues with the truncated steroidal aglycone.     

Electronic structure of oxygen dangling bond in glassy SiO2: the role of hyperconjugation

The electronic structure and the nature of optical transitions in oxygen dangling bond in silica glass, the nonbridging oxygen hole center (NBOHC), were calculated. The calculation reproduced well the peak positions and oscillator strengths of the well-known optical absorption bands at 2.0 and 4.8 eV, and of the recently discovered absorption band at 6.8 eV. The 2.0 eV band was attributed to transition from the sigma bond between Si and dangling oxygen to nonbonding pi orbital on the dangling oxygen. The uniquely small electron-phonon coupling associated with the 2.0 eV transition is explained by stabilization of Si-O bond in the excited state by hyperconjugation effects.     

Domain wall dynamics driven by spin transfer torque and the spin-orbit field

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin-orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.     

Paramagnetic Inversion of the Sign of the Interference Contribution to the Transverse Relaxation of the Imido Protons of the Coordinated Imidazoles in the UniformlyN-Labeled Cytochromec3

In the spectrum of uniformly¹⁵N-labeled cytochromec₃, the relative linewidths of the doublet peaks of the¹⁵N-coupled imido proton of the coordinated imidazole group were reversed on oxidation. This inversion was explained by the interference relaxation process between the electron–proton dipolar and¹⁵N–¹H dipolar interactions. The inversion can be used to assign the imido protons of the coordinated imidazole groups in heme proteins.     

注氢纯铝中间隙型位错环一维迁移现象的原位观察

核聚变堆材料在高能粒子辐照过程中会产生大量点缺陷,导致辐照脆性和辐照肿胀等现象.因而,研究点缺陷在辐照过程中的演变过程至关重要.点缺陷团簇的一维迁移现象是这种演变过程的主要研究内容之一.本文采用普通低压(200 kV)透射电镜,在室温条件下对注氢纯铝中的间隙型位错环在电子辐照下的一维迁移现象进行了观察和分析.在200 keV电子辐照下,注氢纯铝中的位错环可多个、同时发生一维迁移运动,也可单个、独立进行一维迁移运动.位错环沿柏氏矢量1/3<111>的方向可进行微米尺度的一维长程迁移,沿柏氏矢量1/2<110>的方向一维迁移也可达数百纳米.电子束辐照时产生的间隙原子浓度梯度是引起位错环一维迁移并决定其迁移方向的原因.位错环发生快速一维迁移时,其后会留下一条运动轨迹;位错环一维迁移的速率越快,运动的轨迹则越长,在完成迁移过后的几十秒内这些运动轨迹会逐渐消失.     

Properties of a Thin-Film Optical Waveguide Using Fluorinated Silicon Oxide and Organic Spin-on-Glass Films

A thin-film optical waveguide using a fluorinated silicon oxide (SiOF) as a core layer was investigated. An organic spin-on-glass (SOG) film was used for a cladding layer. The SiOF films were formed at 23°C by a liquid-phase deposition (LPD) technique using a supersaturated hydrofluosilicic acid (H₂SiF₆) aqueous solution. A thin-film optical waveguide structure for single mode was designed and fabricated, based on the dispersion properties of refractive indices for the LPD-SiOF and organic SOG films. The refractive indices at a wavelength of 632.8 nm were 1.430 and around 1.400 for the LPD-SiOF and organic SOG films, respectively. The thickness of LPD-SiOF films deposited was 1.18 μm. Thicknesses of cladding organic SOG films cured at 300 and 400°C were 1.28 and 1.31μm, respectively. The effective refractive indices for single mode were 1.4169 and 1.4158 at a wavelength of 632.8 nm for the cladding organic SOG films cured at 300 and 400°C, respectively, and differences between the measured and calculated incident angles were 0.84° and 1.29° for the cladding organic SOG films cured at these respective temperatures. A streak of guided-light was observed for the LPD-SiOF/SOG structure optical waveguide. The transmission loss was 7.6-7.9 dB/cm.     

三线态二苯基卡宾的动力学稳定效应

通过对二苯基重氮甲烷进行光照射产生了一系列于邻位和对位具有不同大小取代基的三线态二苯基卡宾,用紫外可见光谱对其进行了直接观察,并利用激光闪光光解法测定了三线态二苯基卡宾在室温脱氧苯溶液中的寿命,由此表明在邻位和对位里引入庞大的取代基对三线态二苯基卡宾具有更好的稳定效应。     

Formation,growth and ageing of clathrate hydrate crystals in a porous medium

An experimental study was performed to visually observe the driving force dependence of hydrate growth in a porous medium filled with either liquid water and dissolved CO₂ or liquid water and gaseous CO₂. The given system subcooling, ΔT _sub, i.e. the deficiency of the system temperature from the triple CO₂?hydrate?water equilibrium temperature under a given pressure, ranged from 1.7?K to 7.3?K. The fine dendrites initially formed at ΔT _sub?=?7.3?K changed quickly into particulate crystals. For ΔT _sub?=?1.7?K, faceted hydrate crystals grew and the subsequent morphological change was hardly identified for an eight-day observation period. These results indicate that the physical bonding between hydrate crystals and skeletal materials becomes stronger with decreasing driving force, suggesting that the fluid dynamic and mechanical properties of hydrate-bearing sediments vary depending on the hydrate crystal growth process.