Nonosculating Sets of Positive Reach

For integral geometric and local topological properties of two sets of positive reach, one fixed and the other moving or translating, certain exceptional relative positions have to be excluded. We give a measure geometric justification in form of a Sard-type theorem which extends to more general singular sets. A slightly stronger result has been proved by Schneider for the special case of convex bodies.     

Pressure dependence of spectral positions and widths of emission lines related to DJ→FJ electronic transitions in Sm ions doped into SrFCl single crystal

The pressure dependence of the peak positions and widths of the fluorescence lines corresponding to the ⁵D_J→⁷F_J electronic transitions in Sm²⁺-doped SrFCl crystals was measured at room temperature (RT) with a diamond anvil cell (DAC) and a high-pressure gas system, using silicone oil and gaseous helium as the pressure-transmitting medium, respectively. At RT and ambient pressure the electronic transitions ⁵D₀→⁷F_J (J= 0, 1, 2, 3) and ⁵D₁→⁷F_J (J=0, 1, 2) in Sm²⁺ ions yielded rather sharp spectral lines peaked at 14490, 14206, 13685, 13012 cm⁻¹ and 15823, 15533, 15012 cm⁻¹, respectively. At pressures up to 45 kbar in the DAC all these peaks shifted linearly to lower energies at the rates −2.36, −2.10, −2.43, −2.22 cm⁻¹/kbar and −2.35, −2.33, −2.47 cm⁻¹/kbar. Under purely hydrostatic gas pressure up to 7 kbar at RT the initial (normal pressure) widths of the ⁵D₀→⁷F₀, ⁵D₀→⁷F₁ and ⁵D₁→⁷F₀ lines having a Lorentzian profile (with corrected FWHM values of 1.55, 5.71 and 1.97 cm⁻¹) decreased linearly with increasing pressure at the rates −0.009(2), −0.077(3) and −0.034(2) cm⁻¹/kbar, respectively. Possible mechanisms of the observed pressure effects are discussed. For further studies of linewidth variations with the pressure, gaseous helium as a best possible high-pressure medium is strongly recommended.     

Electrochemical deposition: the concept of residence times in structure development

The concept of the residence time of an atom in a kink position was introduced to predict the structure of electrochemically deposited surface coatings. The residence time is obtained from the reciprocal value of the rate constant for separation from the kink position. Residence times and deposition rates determine the density of kink positions [ksp] on the growing metal film. For equilibrium conditions (Nernst potential), the density of kink positions [ksp]₀ depends on the exchange current density i₀ and on the residence time by the equation:

非均匀激光场中氢分子离子高次谐波的增强

通过数值求解非波恩-奥本海默近似下的一维含时薛定谔方程,研究了蝴蝶结型纳米结构基元中氢分子离子高次谐波的产生.研究表明,在蝴蝶结型纳米结构基元内部产生的非均匀场的空间位置对高次谐波的发射有较大影响.当非均匀场的空间位置从30 a.u.平移到-30 a.u.时,高次谐波的截止位置被延展且形成光滑的超连续的谐波谱,并应用时频分析方法、经典三步模型以及电离概率等解释了高次谐波发射的物理机理.研究了高次谐波谱对非均匀场空间位置的依赖性与载波包络值的关系,发现随着载波包络值的变化,非均匀场在不同空间位置处的高次谐波谱变化趋势相同.     

Point processes in general position

The aim of this note is to introduce for point processes in ? ^d the notions general position and reinforced general position, and to characterize these processes. As a consequence we show that Poisson processes P _ρ with an infinite intensity measures ρ are in general position iff ρ is diffuse in the sense that any affine subspace of dimension d ? 1 is a ρ-nullset. Moreover, P _ρ is in reinforced general position iff in addition any (d ? 1)-sphere is a ρ-nullset.