Surface transient effects in ultralow‐energy Cs+ sputtering of Si

This study examines the dependence of the sputter rate and the transient width (z_tr) as a function of Cs⁺ primary ion energy (impact energy (E_p) = 320 eV, 500 eV and 1 keV) and incident angles between 0 and 70° . The instrument used was the ATOMIKA 4500 SIMS depth profiler and the sample was Si with ten delta layers of Si_0.7 Ge_0.3. We observed the narrowest transient widths of between 1.4 and 2.0 nm apparent depth. This was achieved at incident angles (θ) of 30–50° . An extended transient effect was observed when profiled at θ > 50° . Below this incident angle, the transient width is less than twice the penetration depth (z_tr < 2R_norm). At minimum z_tr, z_tr ≈ R_norm. The detection sensitivity is best achieved at θ ≈ 30° for all energies investigated. The sputter rate is lowest at normal incidence, rising gradually to a maximum at θ ≈ 50–60° . This is similar to that observed with ultralow‐energy O₂⁺ primary ion beams. 1 At ultralow energies, reducing E_p does not have a significant effect in reducing z_tr. We conclude that for E_p < 1 keV, the optimum condition to achieve minimum z_tr while maintaining good sensitivity and high sputter rate is at θ ≈ 30° . Copyright © 2007 John Wiley & Sons, Ltd.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

停留—催化反应速差动力学法同时测定Fe,Mo

根据Ｆｅ（Ⅲ）、Ｍｏ（Ⅵ）对Ｈ２Ｏ２氧化邻氨基酚的催化反应速率不同，结合流动注射停留技术，建立了同时测定Ｆｅ（Ⅲ）、Ｍｏ（Ⅵ）的速差动力学分光光度法．测定铁和钼的线性范围分别为０．１～２．５μｇ／ｍＬ和０．５～１５μｇ／ｍＬ．除Ｗ（Ⅵ）的允许量较小外，其它离子不干扰测定．用本法测定了合成样液中铁和钼含量，结果满意．     

烯烃加成反应活性与烷基极化效应的关系

烯烃的自由基加成和亲电加成速率受不同的因素控制.对于仅仅含烷基取代的简单烯烃:(1)与OH自由基加成速率-log kOH可由π键上烷基极化效应指数的几何平均值GMPEIπ关联:-log kOH=a bGMPEIπ c(GMPEIπ)2; (2)与亲电试剂加成速率log k可由π键两端碳原子所连基团极化效应指数PEI(L)和PEI(S)关联:log k=a bPEI(L) cPEI(S),其中的PEI(L)和PEI(S)分别表示极化效应较大和较小的一端.