Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

激光对生物分子的共振激发作用

在生物分子的“谐”和“非谐”振子势模型的基础上，用量子力学讨论了激光对生物分子的共振激作用；并用之对激光的生物激活、诱变机理的“共振吸收”定性理论作一解析分析。     

Extension of the measuring range of balances

The basic principle of comparing the sample mass with the mass of a reference body in equilibrium gives the equal-armed beam balance a unique accuracy. Main parameters characterising the suitability of the instrument are measuring range, resolution and relative sensitivity (resolution/maximum load). The historical development of the values of these parameters achieved depended strongly on the practical need in those times. Technically unfavourable scales of the oldest Egyptian dynasties (~3000 BC) could resolve mass differences of 1 g and had a relative sensitivity of at least 10^–3. More sophisticated instruments from the 18^th Dynasty (~1567–1320 BC) achieved a relative sensitivity of 10^–4 independent of the size of the instrument. In 350 BC Aristotle clarified the theory of the lever and at about 250 BC Archimedes used the balance for density determinations of solids. The masterpiece of a hydrological balance was Al Chazini’s 'Balance of Wisdom’ built about 1120. Its relative sensitivity was 2⋅10^–5. Real progress took place when scientists like Lavoisier (1743–1794) founded modern chemistry. At the end of the 19^th century metrological balances reached a relative sensitivity of 10^–9 with a maximum load of several kilogrammes. That seems to be the high end of sensitivity of the classical mechanical beam balance with knife edges. Improvements took place by electrodynamic compensation (Emich, Gast). In 1909 Ehrenhaft and Millikan could weigh particles of 10^–15 g by means of electrostatic suspension. In 1957 Sauerbrey invented the oscillating quartz crystal balance. By observing the frequency shift of oscillating carbon nanotubes or of silica nanorods, masses or mass changes in the attogram or zeptogram have been observed recently.     

Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

Crystallization and second harmonic generation in thermally poled niobium borophosphate glasses

Crystallization of glasses with compositions (1−x)(0.95 NaPO₃+0.05 Na₂B₄O₇)+xNb₂O₅, x=0.4, 0.43, 0.45, 0.48 was investigated by differential scanning calorimetry and X-ray powder diffraction. Crystallization of two phases was observed in the glasses with x=0.43-0.48. First phase is a sodium niobate with the structure of tetragonal tungsten bronze () and second phase is Na₄Nb₈P₄O₃₂ (). The crystallization of sodium niobate is correlated with increasing of nonlinear optical efficiency reported for thermally poled glasses with x>0.4. The results of Raman spectroscopy show the formation of three-dimensional (3D) niobium oxide framework in the glasses with increase of niobium concentration. This framework is supposed to have tetragonal tungsten bronze structure and to be responsible for nonlinear optical properties of the glass. Second harmonic generation signals of as prepared and crystallized glass after thermal poling are compared. The nucleation and crystallization do not improve the NLO properties of the glasses under study.     

（H2O）^＋n（n=1,2）的几何结构优化和振动光谱分析

采用Ｈａｒｔｒｅｅ－Ｆｏｃｋ和ＭＰ２方法在多种水平下优化了（Ｈ２Ｏ）＾＋ｎ（ｎ ＝１，２）的几何结构，并进行了振动光谱分析。结果表明：对（Ｈ２Ｏ）＾＋采用ＭＰ２／６－３１１＋＋Ｇ（ｄ，ｐ）可得出最满意的结论。     

The characterization of the capability of a balance

A survey is given on important standardized definitions by which the capability of balances may be characterized. Some modifications are proposed with regard to the use of mass sensors for the continuous determination of mass variations. An important supplement is the relative resolution introduced by Jenemann. Optimum values are presented.I am indepted to H. R. Jenemann for his critical remarks.     

花生中多菌灵残留量的高效液相色谱分析方法的研究

建立了测定花生中多菌灵残留量的高效液相色谱法，以乙酸乙酯提取，乙腈萃取分离，石油醚去酯，乙醇＋水（４＋１）沉淀蛋白质，在Ｒａｄｉｌ＿ＰａｋＣ１８柱上，甲醇＋水（５５＋４５）为流动相，采用外标法进行定量检测，相对标准偏差为０１８％，回收率在８００％～９８０％，最低检测限为０２ｍｇ／Ｌ。