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 ∞.     

二维图象中二阶导数滤波器边缘定位误差的理论分析

本文从理论上讨论了低通滤波后二维图象中弯曲边缘的定位误差问题.边缘位置通常由二阶导数算子的零交叉点定义.研究表明:梯度方向上的二阶导数算子(secondderivativein gradient direction SDGD)产生向心的、可预测的边缘偏移;而线性拉普拉斯算子(Laplacian Operator)产生相反方向(离心)的可预测位置偏移.由此可推断:两者之和——称之为PLUS,将产生比其组成成份(SDGD 和 Laplace)更为精确的边缘定位算子.文章讨论了常用的低通滤波器(如 Gaussian 滤波器及 Tepee 滤波器)对边缘定位精度的影响.     

Regularity Results for the Generalized Beltrami System

Abstract For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class (1 < r < n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved. Supported by the National Natural Science Foundation of China (49805005) and by the research foundation of Northern Jiaotong University (2002SM061)     

Non-destructive testing of tubes using a time reverse numerical simulation (TRNS) method

A method for the detection of defects in cylindrical structures and the determination of their positions and orientations is presented in this paper. The scattered field, which is generated by the interaction of excited guided waves with a defect, is evaluated with an approach named time reverse numerical simulation method (TRNS). Since the excited waves and the scattered field propagate along the sample, the time-consuming scanning of the whole tube can be eliminated. The scattered displacement field is measured in three dimensions over time with a laser vibrometer at different locations distributed equally around the circumference at a fixed axial coordinate far away from the defect. Instead of analyzing the complicated time signals directly, they are played back in time. If the recorded displacement histories of the scattered field are reversed in time and played back in an identical structure, the waves travel back the same path and interfere to a maximum at their origin. The result is an amplitude increase at the position of the defect where the scattered field was generated. Instead of playing back the recorded time signals in an experiment, this step is replaced by a numerical simulation. Only this enables the visualization and detection of the amplitude increase. As long as the simulation is of high accuracy, the position of the maximum interference corresponds exactly to the location of the defect in the experiment, although no defect is implemented in the simulation.     

Investigation into factors affecting precision in ion trap mass spectrometry using different scan directions and axial modulation potential amplitudes

Electrospray ionization mass spectra obtained from different scan directions are observed to be dependent on the axial modulation potential amplitudes used for resonant ejection and on the positive deviation caused by higher even-multipole fields present in most commercial ion traps. The axial modulation voltage influences the dissociation of ions during resonant ejection and the observed mass shifts. The higher even-multipole fields in commercial ion traps are known to influence resonant ejection from the ion trap and can cause a loss in mass resolution for peaks in reverse scan mass spectra compared with that obtained by the forward scan. However, along with the dissociation of ions during resonant ejection causing a loss in resolution, the possibility of resolving an isotopic distribution is also shown to be influenced by the mass shifts caused by the space charge. These mass shifts differ depending on the scan direction employed. A significant loss in resolution can also result from resonant ejection using non-optimal axial modulation voltages. We also present results showing the ejection of ions at betaz = 1/2 using the reverse scan mode without the axial modulation voltage. Ion ejection at betaz = 1/2 is uncommon in commercial (stretched ion traps) with the conventional analytical scan without the use of a frequency of the axial modulation voltage corresponding to this non-linear resonance.     

On Crossing Event Formulas in Critical Two-Dimensional Percolation

Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's bulk Cardy's formula is also studied.     

Specific Interaction of Coproporphyrin I with Antibodies in Water and Reverse Micelles: Dimerization of Antibodies Affects Antigen Binding Site

The antigen-antibody interaction between coproporphyrin I and anti-coproporphyrin antibodies was studied by a fluorescence method in water and a reverse micellar system: n-octane/Aerosol OT. Coproporphyrin fluorescence was quenched, and coproporphyrin emission maximum was shifted to the long-wavelength region after binding to the antibodies or Fab-fragments. The mechanism of this quenching is static, most probably, by a tryptophan residue (or maybe lysine or methionine). Apparent dynamic quenching, in this case, arises from protein backbone motion. A special kind of antibody Fab-Fab dimerization was proposed.     

Experimental determination of spin-rotation and spin-spin magnetic interactions in by nuclear spin conversion

When a gas sample of ¹³CH₃F is prepared with a population of isomers (ortho and para forms) far from the equilibrium given by nuclear spin statistics, it relaxes towards this equilibrium with an exponential decay rate. This phenomenon called nuclear spin conversion is mainly governed by intramolecular spin-spin and spin-rotation interactions. In the quantum relaxation model [P.L. Chapovsky, Phys. Rev. A 43, 3624 (1991)], two pairs of ortho-para levels (J = 9, K = 3; J' = 11, K' = 1) and (J = 20, K = 3; J' = 21, K' = 1) are principally responsible for the conversion. The levels of the second pair are coupled by both spin-spin and spin-rotation interactions. The application of an electric field (up to 10 kV/cm) induces a crossing of the Stark components of this pair, which is observed for the first time. A specific experimental set-up based on an electric field of alternating triangular shape is used, which allows the determination of the strength of both interactions via the measurement of the spin conversion decay rates. This work yields the first experimental value for the electronic contribution to the spin-rotation interaction in ¹³CH₃F. Received 23 May 2002 / Received in final form 18 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Patrice.Cacciani@univ-lille1.fr     

Dependence Properties of Multivariate Mixture Distributions and Their Applications

Consider a multivariate mixture model where the random variables X ₁, ..., X _n given (₁, ..., _n ), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X _i 's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.     

Fluorescence of jet-cooled naphthalene: Emission spectra, lifetimes and quantum yields

Fluorescence spectra of naphthalene, C₁₀H₈, were obtained in the laboratory under conditions which provide an appropriate simulation of the cometary conditions: super-cooled gas phase molecules in a collision-free environment. Five spectra were recorded, the excitation energies ranging from 1422 to 5293 cm⁻¹ above the first electronic state S₁ at 32 020 cm⁻¹. A comparison with previous jet-cooled naphthalene fluorescence spectra obtained by Beck et al. [1] and Hermine [2] shows that the former results are not consistent with the present ones. Spectra obtained by Beck et al. show weaker intensities at greater wavelengths compared to those obtained by Hermine and ourselves. We also measured the fluorescence lifetimes by recording the fluorescence decay as a function of time after the excitation of the molecules by monochromatic lasers and deduced the fluorescence quantum yields. A synthetic emission spectrum under solar irradiation is obtained for astrophysical implications.