Link Homology in 4-Manifolds

We define link homology in 4-manifolds, and show that it hasa close connection to linking numbers and intersection matricesof 4-manifolds. We also define null-homologous links in 4-manifolds.We give a necessary and sufficient condition for links to benull-homologous in 4-manifolds. This condition implies thatfor any 4-manifold with second Betti number n, there are (n+ 2)-component links which are not nullhomologous in the 4-manifold.     

On a first-passage problem for a cumulative process with exponential decay

A first-passage problem for a cumulative process is investigated. The cumulative process is assumed to be generated by a Poisson process, and the amplitude generated by an event is assumed to decay exponentially. An integral equation for the probability density of the first-passage time until the total amplitude exceeds a pre-specified threshold level is derived. The Laplace transform of the probability density of the first-passage time is obtained explicity when each amplitude generated by an event is distributed exponentially. The mean first-passage times are given in a closed form and plotted versus the threshold level.     

The theorem for semisimple Hopf algebras

We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra of dimension , where is a prime and , over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if , is isomorphic to a group algebra.

     

Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

硫化锰电子结构的软X射线共振非弹性散射研究

利用软X射线共振非弹性散射谱(resonant inelastic soft X-ray scattering, RIXS)对3d过渡金属硫化物中的硫化锰(MnS)电子结构进行了研究.通过分析Mn²⁺的2p⁶3d⁵→2p⁵3d⁶→2p⁶3d⁵二次光子过程，得到了共振非弹性散射谱中的两类非弹性峰，d-d电子跃迁和电荷转移(charge-transfer)跃迁.这两部分跃迁分别共振增强于L边附近及伴随峰附近.基于Hartree-Fock方法的多重态计算分别模拟了原子近似下和立方体O_h对称群下共振非弹性散射谱及吸收谱.计算得MnS实际晶体场10Dq值介于0.80eV—0.85eV之间.对MnS和MnO CT跃迁差异的讨论表明MnS较强的CT跃迁来源于其较窄的能隙宽度. 关键词： 软X射线共振非弹性散射 软X射线吸收谱 d-d跃迁 电荷转移     

Graphite–boron composite heater in a Kawai-type apparatus: the inhibitory effect of boron oxide and countermeasures

We have investigated the performance of a graphite–boron composite (GBC) with 3?wt % boron as a precursor for a boron-doped diamond heater in a Kawai-type apparatus at 15?GPa. We first tested a machinable cylinder of GBC sintered at 1000°C in Ar/H₂ gas (99:1 molar ratio). Boron oxide (B₂O₃) formed during sintering frequently hindered the GBC heater from stable operation at temperatures higher than 1400°C by producing melt throughout the heater together with oxide and/or silicates. We then rinsed the GBC heater in hydrochloric acid to remove B₂O₃. After rinsing, we succeeded in stably generating temperatures higher than 2000°C. We also improved a molding process of different-sized GBC tubes for convenient use and tested the molded GBC heater. It was free from the B₂O₃ problem. The electromotive force of the W/Re thermocouple was successfully monitored up to 2400°C.     

Reminiscence of 40-year research on nitrogen metabolism

This article summarizes my research over 40 years. The main theme of my work is nitrogen metabolism of amino acids, though later I focused on protein turnover in the cell. In the first years of my research work, I was busy dissecting the pathways involved in the metabolism of certain amino acids and their related enzymes. Then I became interested in the physiology and regulation of matabolism of these amino acids. For that, I used primary cultured hepatocytes, which contain many liver-specific enzymes. However, this play field was very rough around 1970 and hence I had to smooth them (differentiated) first. We discovered a specific growth factor (hepatocyte growth factor, HGF) in rat platelets. Exceptionally, I also worked on branched chain amino acids (valine, leucine and isoleucine). These amino acids are not efficiently metabolized in the liver, so I had to consider the physiology of extrahepatic tissues as well. Finally, I came across a huge protease complex, the proteasome. Whether these players, small amino acid metabolizing enzymes and the huge protease complex, danced well in harmony on my playground or not, I still do not know.     

A compact optical heterodyne interferometer by optical integration and its application

A compact high-resolution optical heterodyne interferometer combining a two-frequency light module and a minute optical system is described. The light module, which generates two independent frequencies of light, is fabricated by proton exchange method on LiNbO₃ substrate. We report an experiment evaluating measurement accuracy using a micro-displacement measurement system which incorporates this interferometer. Results of the experiment with a standard thickness sample show high thermal stability with maximum measurement error of 1.8 nm at a temperature from 19°C to 33°C. The system was used to measure the hysteresis of a piezoelectric element for displacements of several nm, thereby making it possible to analyze the system quantitatively in practice.     

Ultrasonic intensity microscopy for imaging of living cells

Ultrasound intensity microscopy was developed for in vivo imaging. This paper describes the preliminary results obtained using 300 MHz ultrasound intensity microscopy for in vitro characterization of cell cultures. The novelty of the approach lies in the fact that it allows remote, non-contact and disturbance-free imaging of cultured synovial cells and the changes in the cells’ properties due to external stimulants such as transforming growth factor beta-1 (TGF-β1). The intensity imaging method has potential for extracting mechanical cell properties and monitoring the effects of drugs.Ultrasound propagates through a thin specimen such as cultured cells and is reflected at the interface between the specimen and substrate. A two-dimensional distribution of the ultrasonic intensity, which is closely related to the mechanical properties, is visualized to analyze cell organs, such as the nucleus at the central part and the cytoskeleton at the peripheral zone. After stimulation with TGF-β1, the ultrasonic intensity at the actin zone was significantly increased compared with the control.     

Measurement of non-DLVO force on a silicon substrate coated with ammonium poly(acrylic acid) using scanning probe microscopy

The repulsive force originating from steric hindrance of polymers in aqueous solvent was investigated using scanning probe microscopy (SPM). The contact angle (CA) of ammonium poly(acrylic acid) (PAA) solution on the Si surface was measured to estimate the state of the Si substrate. Results of CA measurement show that the Si surface was fully covered with PAA at 0.1 mass% in aqueous solution. The interaction force between the Si tip and the wafer was estimated using the SPM force curve mode. The force curve measured in the ion-exchanged purified water showed the typical relation predicted by Derjaguin-Landau-Verway-Overbeek (DLVO) theory. However, the force curve shape in the 0.1 mass% PAA solution was significantly different. Only a repulsive force was observed at less than about 4 nm of separation distance between the Si wafer and cantilever tip. This distance originated from the steric repulsions of PAA adsorbed onto the Si wafer and cantilever tip.