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.     

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.     

On the distribution of the number of packets in the fluid flow approximation of packet arrival streams

Fluid flow approximations are widely used for approximating models of communication systems where packet arrival streams are generated in a regular manner over certain intervals (constant rate). The appropriate mathematical model for describing those bursty arrival streams in the fluid flow framework are the well-known Markov modulated rate processes (MMRP). The paper deals with the distribution of the numberN(t) of packets in the interval [0,t] of MMRP. For two-state MMRPs and their superpositions we derive formulas for the distribution ofN(t) and its density. Further we give asymptotic results. The presented numerical results and simulation studies illustrate the goodness of the fluid flow approximation and show that the proposed numerical algorithms work well even in the case of multiplexing a large number of burst silence sources.This work was partially supported by a grant from the Deutsche Bundespost TELEKOM.     

基于流率入树枝向量行列式算法的循环经济系统增长反馈分析

设计了江西省萍乡市兰坡村“猪-沼-粮”循环经济系统工程的流率入树模型,并利用流率入树枝向量行列式算法得到了系统的反馈环,在反馈环基础上,构造了系统增长基模,得到结论,以沼气工程（沼肥）为纽带,发展养殖业能实现生猪养殖、稻谷种植和蔬菜种植之间的良性循环,能够达到稻谷增产和收入增长,在微观层面上实现粮食安全和农民增收双赢。     

241Am-Be中子参考辐射的蒙特卡罗模拟研究

研究用于校准场所中子剂量监测仪表的241Am-Be中子参考辐射场计量特性。采用蒙特卡罗方法模拟了空气自由中子参考辐射(FRNR),GB/T 14055规定的最小尺寸中子参考辐射(SRNR)和实际中子参考辐射(ARNR)中不同检验点处中子周围剂量当量率、散射中子占比和能谱分布特征。研究结果表明,空气对FRNR中的剂量率和能谱分布影响小,近似为理想中子参考辐射;采用5%含硼聚乙烯作屏蔽的最小尺寸SRNR可减少热中子,降低散射中子占比,影锥法不适用于小尺寸中子参考辐射中对散射中子的修正;ARNR中的散射中子更少、占比更低,影锥法所得散射中子占比与理论值基本一致。     

超越SNOM探针通光孔径尺寸的金属纳米间隙超分辨测量

采用电磁场有限元方法,数值模拟了孔径型扫描近场光学显微镜(aperture Scanning Near-field Optical Microscopy,a-SNOM)在照明模式下的工作过程.针对金偶极天线结构,改变天线长度和纳米间隙尺寸,计算了a-SNOM探针孔径的远场辐射速率随探针端面中心坐标变化的扫描曲线,实现了超越a-SNOM探针通光孔径尺寸的天线金属纳米间隙的超分辨测量,对于100nm通光孔径的探针,可分辨最小尺寸为10nm(0.016倍波长)的金属间隙.通过对比金属和介质偶极天线的a-SNOM探针远场辐射速率测量的计算结果,表明天线金属纳米间隙的超分辨测量的实现是由于金属间隙表面等离激元的激发.     

Investigation of ammonia stripping with a hydrodynamic cavitation reactor

Ammonia is a commonly used compound in the domestic and industrial fields. If ammonia found in wastewater after use is not treated, even at low concentrations it may cause toxic effects in the receiving environment. In this study, a hydrodynamic cavitation reactor (HDC) was designed with the aim of removing ammonia. The effect of parameters like different cavitation numbers, airflow, temperature and initial concentration on NH₃ removal was researched. The potential of hydrodynamic cavitation for removal of volatile gases, like NH₃, was assessed with the aid of two film theory mathematical equations. Experimental studies were performed at fixed pH = 11. Under the conditions of 0.12 cavitation number, 25 L/min airflow, 30 °C temperature and 2500 mg/L initial concentration, in 24 h 98.4% NH₃ removal efficiency was achieved. With the same experimental conditions without any air, the HDC reactor provided 89.5% NH₃ removal at the end of 24 h.The HDC reactor is very effective for the removal of volatile gases from wastewater and it was concluded that even in the absence of aeration, the desired NH₃ removal efficiency was provided.     

Effects of multi-frequency ultrasound on freezing rates and quality attributes of potatoes

The effects of multi-frequency ultrasound assisted freezing on the freezing rate, microstructure, quality properties (drip loss, firmness, total calcium content, l-ascorbic acid content and total phenol content) of potatoes were studied. The results indicated that the freezing effects of multi-frequency ultrasound was better than those of single-frequency ultrasound. Multi-frequency ultrasound could significantly increase the freezing rate and preserve the quality of frozen samples better. With increase in the number of ultrasonic frequencies, the freezing effect was more obvious. In addition, scan electron microscopy (SEM) images showed that the ice crystals formed by the multi-frequency ultrasonic treatment were fine and uniformly distributed, which caused less damage to the frozen potato samples. From the analysis of the quality attributes, the nutritional values of the samples after multi-frequency ultrasonic treatment was higher, but attention should be paid to the negative influence of the hydroxyl radical generated by the multi-frequency ultrasound.     

On the Variability of Heart Rate Variability—Evidence from Prospective Study of Healthy Young College Students

Heart rate variability (HRV) has been widely used as indices for autonomic regulation, including linear analyses, entropy and multi-scale entropy based nonlinear analyses, and however, it is strongly influenced by the conditions under which the signal is being recorded. To investigate the variability of healthy HRV under different settings, we recorded electrocardiograph (ECG) signals from 56 healthy young college students (20 h for each participant) at campus using wearable single-lead ECG device. Accurate R peak to R peak (RR) intervals were extracted by combing the advantages of five commonly used R-peak detection algorithms to eliminate data quality influence. Thorough and detailed linear and nonlinear HRV analyses were performed. Variability of HRV metrics were evaluated from five categories: (1) different states of daily activities; (2) different recording time period in the same day during free-running daily activities; (3) body postures of sitting and lying; (4) lying on the left, right and back; and (5) gender influence. For most of the analyzed HRV metrics, significant differences (p < 0.05) were found among different recording conditions within the five categories except lying on different positions. Results suggested that the standardization of ECG data collection and HRV analysis should be implemented in HRV related studies, especially for entropy and multi-scale entropy based analyses. Furthermore, this preliminary study provides reference values of HRV indices under various recording conditions of healthy young subjects that could be useful information for different applications (e.g., health monitoring and management).     

氩气感应耦合等离子体速度与温度数值模拟

为了获得用于研究再入飞行器热防护系统的感应耦合等离子体风洞流场数据,基于流场、电磁场和化学场的多场耦合建立了非平衡态感应耦合等离子体数值模型。利用该模型对不同入口质量流率和不同工作压力下的感应耦合等离子体进行了数值模拟,得到了相应工作参数下感应耦合等离子体温度与速度的分布特性。计算结果表明:等离子体中心线上的速度随着入口质量流率的增大而增大,而随着工作压力的增大而减小;同时,等离子体中心线上的温度随着入口质量流率的增大而减小,而随着压力的增大先减小后增大。这些结果可为感应耦合等离子体风洞优化设计及其工业应用提供理论指导。