Resonances with the complex rotation method: a study of an exactly soluble two-channel model

The complex rotation method is applied to the determination of widths and shifts of an harmonic oscillator predissociated by a linear potential, for when exact analytical formulas are available in the limit of small interchannel coupling. Excellent agreement is obtained.     

Rotational diffusion of dyes in solvents of low viscosity from transient-dichroism experiments

Rotational diffusion data from pulsed laser experiments are presented for dye molecules dissolved in alcohols and non-alcohols. Cresyl violet and fluorescein both exhibit strong dependence of the rotational motion upon solvent molecular structure. In complete contrast the rotational diffusion of the oblong dyes pyronine G and acridine orange do not reveal any specific solute-solvent interaction.     

未决赔款准备金评估的随机性Munich链梯法

精算实务界通常采用链梯法等确定性方法评估未决赔款准备金,这些评估方法存在一定缺陷,一方面不能有效考虑保险公司历史数据中所包含的已决赔款和已报案赔款数据信息,另一方面只能得到未决赔款准备金的均值估计,不能度量不确定性。为了克服这些缺陷,本文结合Mack模型假设和非参数Bootstrap重抽样方法,提出了未决赔款准备金评估的随机性Munich链梯法,并应用R软件对精算实务中的实例给出了数值分析。     

Surface-enhanced raman scattering as a function of molecule-surface separation

The dependence of Raman enhancement on molecule-surface separation is measured for pyridine on roughened Ag surfaces in UHV. Results follow predictions for local field enhancement by small Ag spheroid resonances by McCall, Platzman and Wolff, showing multi-layer enhancement. Isotopic studies confirm that several layers contribute to the enhanced Raman signal.     

Robust mean–variance hedging via G-expectation

In this paper we study mean–variance hedging under the $G$-expectation framework. Our analysis is carried out by exploiting the $G$-martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric $G$-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.     

To be or not to be constructive,that is not the question

In the early twentieth century, L.E.J. Brouwer pioneered a new philosophy of mathematics, called intuitionism. Intuitionism was revolutionary in many respects but stands out – mathematically speaking – for its challenge of Hilbert’s formalist philosophy of mathematics and rejection of the law of excluded middle from the ‘classical’ logic used in mainstream mathematics. Out of intuitionism grew intuitionistic logic and the associated Brouwer–Heyting–Kolmogorov interpretation by which ‘there exists $x$’ intuitively means ‘an algorithm to compute $x$ is given’. A number of schools of constructive mathematics were developed, inspired by Brouwer’s intuitionism and invariably based on intuitionistic logic, but with varying interpretations of what constitutes an algorithm. This paper deals with the dichotomy between constructive and non-constructive mathematics, or rather the absence of such an ‘excluded middle’. In particular, we challenge the ‘binary’ view that mathematics is either constructive or not. To this end, we identify a part of classical mathematics, namely classical Nonstandard Analysis, and show it inhabits the twilight-zone between the constructive and non-constructive. Intuitively, the predicate ‘$x$ is standard’ typical of Nonstandard Analysis can be interpreted as ‘$x$ is computable’, giving rise to computable (and sometimes constructive) mathematics obtained directly from classical Nonstandard Analysis. Our results formalise Osswald’s longstanding conjecture that classical Nonstandard Analysis is locally constructive. Finally, an alternative explanation of our results is provided by Brouwer’s thesis that logic depends upon mathematics.     

Observation of a spin 4 boson resonance at 2050 MeV

We report the observation of a spin 4 resonance from the analysis of the reaction π^?p→ K⁺K^?n. The mass and width of the h-meson were determined to be 2050 MeV and 225 MeV. The quantum numbers are J^P = 4⁺, C = +1 and very probably I^G = 0⁺.     

Vibrational coupling in collision-induced raman scattering

The observed splitting of the collision-induced Raman band v₃ in liquid SF₆ is interpreted as vibrational exciton line splitting The bandwidth of the collision-induced Raman bands v₃ and v₆, in liquid SF₆ and v₂ and v₃ in liquid CO₂ and CS₂ can be explained by contributions from reonentational motion and from transition dipole-transition dipole vibrational coupling.