The first high-resolution infrared study of diazirinone, N2CO: Analysis of the Fermi-coupled ν1 and 2ν5 bands

The first validated detection of the elusive diazirinone molecule (N₂CO) in the gas phase was performed using high-resolution infrared spectra recorded in the 1810–2100 cm⁻¹ region. The ν₁ and 2ν₅ bands were identified at 2043.8 and 1863.3 cm⁻¹ close to the ab initio prediction [X.Q. Zeng, H. Beckers, H. Willner, J.F. Stanton, Angew. Chem. Int. Ed. 50 (2011) 1720–1723]. For these two bands, the individual lines exhibit a (2:1) intensity alternation, confirming a three membered ring structure (C_2V symmetry) for N₂CO. The major output of the ν₁ and 2ν₅ bands analysis is the first experimental determination of the ground-state rotational constants of cyclic N₂CO. The observed intensity pattern of the ν₁ and 2ν₅ bands is in agreement with the existence of a strong Fermi resonance coupling the 1¹ and 5² energy levels.     

Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules

A convenient, Peierls-type approach to obtain low-temperature phases is to use the method of an m-potential. In this paper we show that, for more complex systems where it may be rather difficult to rewrite the Hamiltonian as an m-potential and whose configurations are subject to linear constraints, the verification of the Peierls condition can be reformulated as a linear programming problem. Before introducing this novel strategy for a general lattice system, we compare it with the m-potential method for a specific model molecular system consisting of an equimolar mixture of a chiral molecule and its non-superimposable mirror image that occupy all the sites of a honeycomb lattice. In one range of interactions, we prove that a racemic low-temperature phase occurs (containing equal numbers of each enantiomer). However, in a neighboring range of interactions, we show that a homochiral low-temperature phase (containing a single enantiomer) exists, and thus chiral segregation occurs in the system. Our linear programming technique yields these results in wider ranges of interactions than the m-potential method.     

Indestructibility,HOD, and the Ground Axiom

Let φ₁ stand for the statement V = HOD and φ₂ stand for the Ground Axiom. Suppose T_i for i = 1, …, 4 are the theories “ZFC + φ₁ + φ₂,” “ZFC + ¬φ₁ + φ₂,” “ZFC + φ₁ + ¬φ₂,” and “ZFC + ¬φ₁ + ¬φ₂” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, …, 4, A_i = _df{δ < κ∣δ is an inaccessible cardinal which is not a limit of inaccessible cardinals and V_δ?T_i} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing four models in which A_i = ?? for i = 1, …, 4. In each of these models, there is an indestructibly supercompact cardinal κ, and no cardinal δ > κ is inaccessible. We show it is also the case that if κ is indestructibly supercompact, then V_κ?T₁, so by reflection, B₁ = _df{δ < κ∣δ is an inaccessible limit of inaccessible cardinals and V_δ?T₁} is unbounded in κ. Consequently, it is not possible to construct a model in which κ is indestructibly supercompact and B₁ = ??. On the other hand, assuming κ is supercompact and no cardinal δ > κ is inaccessible, we demonstrate that it is possible to construct a model in which κ is indestructibly supercompact and for every inaccessible cardinal δ < κ, V_δ?T₁. It is thus not possible to prove in ZFC that B_i = _df{δ < κ∣δ is an inaccessible limit of inaccessible cardinals and V_δ?T_i} for i = 2, …, 4 is unbounded in κ if κ is indestructibly supercompact. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Ground state solutions for a semilinear elliptic problem with a convection term

By a sub-supersolution method and a perturbed argument, we improve the earlier results concerning the existence of ground state solutions to a semilinear elliptic problem −Δu+p(x)q|∇u|=f(x,u), u>0, x∈RN, , where q∈(1,2], for some α∈(0,1), p(x)?0, ∀x∈RN, and f:RN×(0,∞)→[0,∞) is a locally Hölder continuous function which may be singular at zero.     

CⅠ等电子序列离子组态能量Z相关修正的改进

以相对论多体微扰理论为基础,利用屏蔽理论的思想和方法,引入并改进了与核电荷数Z相关的能量修正函数,计算了CⅠ等电子序列离子（6<=Z<=55）基组态(1s2 2s2 2p2)和第一激发组态(1s2 2s2 2p1)能量.计算过程基于自编的C语言和Mathematica程序,所得结果与实验值符合的很好,大大减小了由于忽略能量高阶项产生的误差,证明此项改进适用于等电子序列离子组态能量的计算.     

Soliton dynamics for the generalized Choquard equation

We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation   where the nonlinear term is (|x|^θ−N?|u|^p)|u|^p−2u$({|x|}^{\theta -N}?{|u|}^p){|u|}^{p-2}u$. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.     

基态原子与理想金属Au表面间的范德瓦尔斯作用

研究了基态碱金属原子与理想金属Au表面间的范德瓦尔斯(vdW)作用.通过分析电四极跃迁对vdW的贡献,构建了计算超精细能级碱金属原子与理想金属表面间vdW作用系数C3的理论模型.以85Rb、133Cs为例,计算了其基态原子超精细能级的C3系数.其中85Rb: 52S1/2 (F=2)及52S1/2 (F=3)对应的C3系数分别为:2.2409 及2.2425 ;133Cs: 62S1/2 (F=3)及62S1/2 (F=4)分别对应 2.4480 及2.4538 .研究还发现随着 的增大,C3增大,z (原子与金属表面之间的距离)不变时,原子与理想金属表面间vdW作用增强. 这一研究在实现原子囚禁及介质表面量子反射等方面具有重要意义     

Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.     

Evaluation and Optimization of the Oxidation efficiency of a UV-Persulphate-Oxidation Toc-Analyzer for the Determination of Oil Contamination from Forestry in Ground Water

Different chain oils (tall, rape seed and mineral oils) have been used as model compounds to evaluate and optimize the applicability of UV-persulphate TOC-analyzer for quantitative determination of forestry oils and to follow the progress of their biodegradability. It was shown, that K 2 S 2 O 8 -UV-oxidation method is not sufficient to oxidize chain oils completely. There were differences in oxidation efficiency between different oils, changing from about 46% measured for tall oil to about 25% observed for rape seed chain oil. The addition of Triton X-100 surfactant up to 2% (w/w) was observed to increase the oxidation efficiency, e.g. to 75% for tall oil. The observations can be explained by assuming that in the presence of surfactant the emulsions are more homogeneous and stable. Optimization using two-level full factorial design (temperature of the oxidation chamber and the amount of persulphate) was studied. The results show that the UV-persulphate-oxidation TOC-analyzer is not suitable method to monitor biodegradability of chain oils.     

Bichromophoric hemicyanine dyes as fluorescence probes applied for monitoring of the photochemically initiated polymerization

The spectroscopic properties of series homodimmeric hemicyanine dyes based on (p-N,N-dimethylaminostyryl)benzothiazolium, (p-N,N-dimethylaminostyryl)benzoxazolium, (p-N,N-dimethylaminostyryl)-2,3,3-trimethyl-3H-indolium residues were determined. The absorption and fluorescence spectra of the dyes under study were measured in different polarity solvents at room temperature. On the basis of the solvatochromic behavior the ground state (μ_g) and excited state (μ_e) dipole moments of bis-(N,N-dimethylaminostyryl) derivatives were evaluated. The dipole moments (μ_g and μ_e) were estimated from solvatochromic shifts of absorption and fluorescence spectra as function of dielectric constant (ε) and refractive index (n) of applied solvents. The absorption and fluorescence spectra are only slightly affected by the solvent polarity. The analysis of solvatochromic behavior of the fluorescence spectra as a function of Δf (ε, n) revealed that the emission occurs from a high polarity excited state. The large dipole moment changes along with the red-shifted fluorescence, as the solvent polarity is increased, demonstrates the formation of an intramolecular charge transfer state (ICT). Six bichromophoric hemicyanine dyes, possessing benzothiazole, benzoxazole or indolinium group linked by 5 or 10 methylene groups were evaluated as fluorescence probes applied for monitoring of the polymerization process. The study on the changes in fluorescence intensity and spectroscopic shift of studied compounds were carried out during photochemically initiated polymerization of 2-ethyl-2-(hydroxymethyl)-propane-1,3-diol triacrylate (TMPTA).