Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

用于高数值孔径物镜的可调光瞳滤波器

根据矢量衍射理论，提出了一种用于提高高数值孔径显微物镜纵向分辨率的可调二元环形光瞳滤波器，通过改变滤波器的环半径获得不同的纵向分辨率，并利用共焦显微术点扩散函数的乘积性大大地降低了旁瓣相对主瓣的比值。模拟结果表明，这种新型滤波器不仅可以提高高数值孔径物镜的纵向分辨率，同时基本上不影响横向分辨率。     

AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved.     

Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

Quantitative High Resolution Electron Microscopy

 With the resolution becoming sufficient to reveal individual atoms, HREM is now entering the stage where it can compete with X-ray methods to quantitatively determine atomic structures of materials without much prior knowledge, but with the advantage of being applicable to aperiodic objects such as crystal defects. In our view the future electron microscope will be characterised by a large versatility in experimental settings under computer control such as the illumination conditions (TEM-STEM), CBED, detecting conditions (diffraction, image, ptychography) and many other tunable parameters such as focus (g), voltage, spherical aberration (C _s ), beam tilt, etc. Since modern detectors can detect single electrons, also the counting statistics is known. The only limiting factor in the experiment will be the total number of electrons that interact with the object during the experiment due to the limitations in the exposure time or in the object damage. However, instrumental potentialities will never be exploited fully if not guided by an experimental strategy. Here intuitive guidelines can be very deceptive. For instance an image made with the best electron microscope (C _s  = 0) at the best focus (g = 0) from the best object (phase object) would show no contrast at all. Hence, questions such as what is the best C _s , focus, object thickness, etc. can only be answered properly if done using a method of experiment design.     

Partially concurrent eluent evaporation with an early vapor exit; detection of food irradiation through coupled LC-GC analysis of the fat

This paper reports two subjects. It describes LC-GC transfer by partially concurrent eluent evaporation at a greatly accelerated rate, as required for optimal compatibility with 2–3 mm i.d. LC columns and LC flow rates up to some 500 μl/min. Evaporation rates around 200 μl/min were obtained using a 0.53 mm. i.d. uncoated pre-column and an early vapor exit. A stationary-phasecoated “retaining” pre-column was used for preventing escape of volatile solutes through the vapor exit. The technique was used for the detection of food irradiation by analyzing selected radiolysis products of triglycerides, namely alkanes/alkanes and aldehydes. Extracted fat of chicken, hazel-nuts, and soup mixes was injected in LO and the relevant fractions were transferred on-line to GC. For chicken and nuts, detection of irradiation was possible down to doses below 0.5 kGy. Detection limits were higher for soup mixes due to interfering peaks.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Stability and other limit laws for exit times of random walks from a strip or a halfplane

We show that the passage time, T^*(r), of a random walk S_n above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that as n→∞ for a deterministic sequence B_n>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T^*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞.     

Variational principles for average exit time moments for diffusions in Euclidean space

Let be a smoothly bounded domain in Euclidean space and let be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from of a particle driven by where the average is taken over all starting points in