NORMAL REFLECTION SUBGROUPS OF COMPLEX REFLECTION GROUPS

We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linear factors involving generalised exponents. Our refinement gives a uniform proof and generalisation of a recent theorem of the second author.

Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs

We present closed-form solutions to some discounted optimal stopping problems for the running maximum of a geometric Brownian motion with payoffs switching according to the dynamics of a continuous-time Markov chain with two states. The proof is based on the reduction of the original problems to the equivalent free-boundary problems and the solution of the latter problems by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping boundaries are determined as the maximal solutions of the associated two-dimensional systems of first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of real switching lookback options with fixed and floating sunk costs in the Black–Merton–Scholes model.

Стабильные многослойные отражающие покрытия на длину волны lambda(HeI) = 58.4 nm для солнечного телескопа проекта КОРТЕС

Multilayer aluminum-based structures reflecting at λ(HeI) = 58.4 nm were studied. Spectral and angular dependences of the reflection coefficient of these coatings were determined using a laboratory reflectometer and at the ELETTRA and BESSY II synchrotrons. The optical characteristics of multilayer Ru/Al and Mo/Al mirrors with a protective MoSi_2 layer were found to be stable: the absolute change in the reflection coefficient within 18 months of storage in air was no larger than 1.5%. The peak near-normal reflection coefficient for Mo/Al mirrors at 58.4 nm was R = 26.1% with FWHM Δλ_0.5 = 10 nm of the reflection curve.

Normal Reflection Characteristics of One-Dimensional Unsteady Flow Shock Waves on Rigid Walls from Pulse Discharge in Water

Strong shock waves can be generated by pulse discharge in water, and the characteristics due to the shock wave normal reflection from rigid walls have important significance to many fields, such as industrial production and defense construction. This paper investigates the effects of hydrostatic pressures and perturbation of wave source (i.e., charging voltage) on normal reflection of one-dimensional unsteady flow shock waves. Basic properties of the incidence and reflection waves were analyzed theoretically and experimentally to identify the reflection mechanisms and hence the influencing factors and characteristics. The results indicated that increased perturbation (i.e., charging voltage) leads to increased peak pressure and velocity of the reflected shock wave, whereas increased hydrostatic pressure obviously inhibited superposition of the reflection waves close to the rigid wall. The perturbation of wave source influence on the reflected wave was much lower than that on the incident wave, while the hydrostatic pressure obviously affected both incident and reflection waves. The reflection wave from the rigid wall in water exhibited the characteristics of a weak shock wave, and with increased hydrostatic pressure, these weak shock wave characteristics became more obvious.