Dynamics of semigroup actions of linear fractional transformations

Positive continued fractions are viewed as the orbit of 1 under the action of the semigroup of functions generated by r(x) = 1/x and s(x) = x + 1. The fixed points of the elements of this semigroup contain purely periodic continued fractions (which are the reduced surds by Lagrange's theorem on continued fractions). In this article, we study the fixed points of the elements of semigroups generated by general pairs of linear fractional transformations and show that topological transitivity of a non-commutative semigroup action implies that the fixed point set is dense. We also prove a similar result for two-generator semigroups of affine transformations on the real line.     

Central limit theorem for the estimator of the value of an optimal stopping problem

We consider an optimal stopping problem defined on a finite Markov chain whose transition probabilities are unknown. We prove a central limit theorem for the maximum likelihood estimator and the stretch estimator of the optimal value of the optimal stopping problem. Also, we propose a perturbation technique to weaken the hypotheses of the central limit theorem. The author was supported by a grant from the SpanishScretaría de Estado de Educación y Universidades in cooperation with the European Social Funds.     

On the distribution of the estimated process yield index Spk

This paper considers an asymptotic distribution for an estimate of the process yield index proposed by Boyles (1994). The asymptotic distribution of is useful in statistical inferences for . An illustrative example is given for hypothesis testing and for interval estimation on the yield index . Copyright © 2002 John Wiley & Sons, Ltd.     

Measurement of the pulse parameters of silicon transistors under avalanche operating conditions

Equipment for measuring the dynamic parameters of transistors under avalanche operating conditions is described. The equipment enables the amplitude of the rise time and fall time of pulses generated by a relaxation generator with an avalanche transistor to be measured, and also enables the shape of the discharge current and voltage on the collector to be monitored. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 51–54, July, 2007.     

基于统计技术改进PVC材料均匀性研究

材料均匀性会直接影响PVC挤出加工和注塑加工的一致性。不均匀材料会造成制品表面粒点、流线和花纹等缺陷。改进材料均匀性可以提高顾客满意度和过程效率。选择材料均匀性评价指标、调查材料均匀性和改进材料均匀性是本文研究的三个方面。利用方差分析对材料均匀性的评价指标进行分析,通过方差分析,确定将灰分作为材料均匀性的评价指标。利用假设检验对材料生产的均匀性进行分析。通过假设检验,证明材料在不同时间的均匀性是不稳定的。利用TRIZ和中心极限定理,对改性PVC材料生产流程进行改进,确定将增加均质化过程以改进材料均匀性。     

雪崩光电二极管高精度三维微调架结构设计与分析

通过利用计算机软件实体建模及有限元分析和测试实验的方法,为某卫星激光测距系统的雪崩光电二极管接收器设计了新型结构的高精度三维微调架.首先,使用UG软件进行三维实体建模;然后,利用有限元分析软件MSC.Patran对微调架模型进行静力分析和模态分析;最后,对微调架实物进行振动和精度测试实验.实验结果和有限元分析结果较为吻合,验证了有限元分析的可靠性.软件设计及分析和测试实验的结果表明微调架的设计满足预期的设计要求,能够实现对雪崩二极管的精密调整,使其正常工作.     

Cumulative detection probabilities and range accuracy of a pulsed Geiger-mode avalanche photodiode laser ranging system

Cumulative pulses detection with appropriate cumulative pulses number and threshold has the ability to improve the detection performance of the pulsed laser ranging system with GM-APD. In this paper, based on Poisson statistics and multi-pulses cumulative process, the cumulative detection probabilities and their influence factors are investigated. With the normalized probability distribution of each time bin, the theoretical model of the range accuracy and precision is established, and the factors limiting the range accuracy and precision are discussed. The results show that the cumulative pulses detection can produce higher target detection probability and lower false alarm probability. However, for a heavy noise level and extremely weak echo intensity, the false alarm suppression performance of the cumulative pulses detection deteriorates quickly. The range accuracy and precision is another important parameter evaluating the detection performance, the echo intensity and pulse width are main influence factors on the range accuracy and precision, and higher range accuracy and precision is acquired with stronger echo intensity and narrower echo pulse width, for 5-ns echo pulse width, when the echo intensity is larger than 10, the range accuracy and precision lower than 7.5 cm can be achieved.     

The performance of control charts for large non‐normally distributed datasets

Because of digitalization, many organizations possess large datasets. Furthermore, measurement data are often not normally distributed. However, when samples are sufficiently large, the central limit theorem may be used for the sample means. In this article, we evaluate the use of the central limit theorem for various distributions and sample sizes, as well as its effects on the performance of a Shewhart control chart for these large non‐normally distributed datasets. To this end, we use the sample means as individual observations and a Shewhart control chart for individual observations to monitor processes. We study the unconditional performance, expressed as the expectation of the in‐control average run length (ARL), as well as the conditional performance, expressed as the probability that the control chart based on estimated parameters will have a lower in‐control ARL than a specified desired in‐control ARL. We use recently developed factors to correct the control limits to obtain a specified conditional or unconditional in‐control performance. The results in this paper indicate that the control chart should be applied with caution, even with large sample sizes.     

Classical Statistical Inference Extended to Truncated Populations for Continuous Process Improvement: Test Statistics,P‐values,and Confidence Intervals

Statistical hypothesis testing is useful for controlling and improving processes, products, and services. This most fundamental, yet powerful, continuous improvement tool has a wide range of applications in quality and reliability engineering. Some application areas include statistical process control, process capability analysis, design of experiments, life testing, and reliability analysis. It is well‐known that most parametric hypothesis tests on a population mean, such as z‐test and t‐test, require a random sample from the population under study. However, there are special situations in engineering, where the specification limits, such as the lower and upper specification limits, on the process are implemented externally, and the product is typically reworked or scrapped if the performance of a product does not fall in the range. As such, a random sample needs to be taken from a truncated distribution; however, there has been little work on the theoretical foundation of statistical hypothesis procedures under this special situation. The objective of this paper is twofold. First, we provide the mathematical justifications that the central limit theorem works quite well for a large sample size, given samples taken from a truncated distribution. We also verify this finding using simulation. Second, we then develop the new one‐sided and two‐sided z‐test and t‐test procedures, including their test statistics, confidence intervals, and P‐values, using appropriate truncated statistics. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of the wavefield generated by a gas exploder used for artificial avalanche release

A study of the entire wavefield (3D) generated by the detonation of a Gazex® device performed on the Gamsleiten slope, at Obertauern, Austria is presented. The main aim of the study was to determine whether the detonation can trigger snow avalanches in remote locations. A linear array of sensors in the vicinity of the blasting point combining six 1D and two 3D seismic sensors was deployed. Three independent Gazex® detonations were subsequently triggered in intervals of approx. 15 min. The signals obtained were similar. Waves propagating through the ground (P waves) and sound waves were clearly detected. The corresponding ground velocities and accelerations were determined. The frequency content of the whole signals was band-limited to 10-40 Hz, although the frequency content of P waves was lower than that of sound waves in the three components. A different behaviour in the frequency content evolution of the two wave groups was observed. P waves suffered distortion and attenuation with distance. This was not observed in the sound waves which showed local amplifications. The maximum values of the velocity and acceleration measured correspond to the sound waves observed in the horizontal components. The values of the ground accelerations obtained for the whole signals were 6 times lower than the value of the critical acceleration, which is the value that is required for the inclined snow slab to be stable. Cumulative snow slab displacements caused by long vibrations were also considered. The results suggest that in this case the likelihood of a snow avalanche release due the Gazex® device detonations is low. However, this result cannot be generalized to other snow and terrain conditions and to other conventional explosives. Specific studies should be carried out at the target sites/situations. Another important finding was the significant contribution of the horizontal components to the ground movement. This indicates that it is necessary to consider the whole wave field (3D) in this type of study.     

Mechanism of avalanche precursors in inclining granular layers using a continuum model obtained by discrete element method

How do large shear stress and stress ratio peaks, which are avalanche precursors, occur in granular layers in an inclining box and why do the precursors have periodicities? The answers are our main objectives. The large and small shear stress peaks which are constituted by the large and small sticks and slips are found in our simulation results. Small sticks and slips, which occur after the large slip, change the granular structure until the stress ratio becomes equal to or larger than the frictional coefficient of granular materials. Here the next large slip with the large stick and slip, which shows the precursor, occurs. The precursors which are constituted by the series of the large stick–slip events have naturally periodicities because the stick–slip events are oscillation phenomena. Our 3-dimensional simulation results using the smoothed particle hydrodynamics (SPH) method based on our constitutive equations obtained by the 3-dimensional discrete element method (DEM) present the precursors in the bulk and on the surface and show the difference between them. The precursors are also found in the longitudinal and the depth directions of the granular layer. The simulated periodicities agree with the published experimental results.     

A circuit modeling of SAGCM avalanche photodiode with additional layer and nonuniform electric field profile

This paper presents a new way to improve the speed of the separated absorption grading charge multiplication avalanche photodiode by adding a new thin charge layer between absorption and grading layers. In this method, we assume a nonuniform electric field in different regions of the structure. In addition, based on carrier rate equations, a circuit model of the proposed structure is extracted. Considering the trade-offs between thicknesses of layers, we try to acquire the optimum structure by setting the physical parameters. Finally, it is shown that, in comparison with the conventional structure, considerable improvements in the gain-bandwidth product and also breakdown voltage are achieved.     

The Half-Half Plot

The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online.     

Role of stacking faults in solid state transformations

This article illustrates the two different roles played by stacking faults in solid state transformations viz. (i) in accommodating part of the transformation strains as observed in the noble metal-based alloys undergoing martensitic transformations, and (ii) in providing a mechanism for changing the stacking sequence of layers in a variety of materials like SiC, ZnS, Co and its alloys, and certain steels. Diffraction patterns taken from the martensitic phases of noble-metal-based alloys as well as from SiC and ZnS crystals undergoing transformation from one close-packed modification to another reveal the presence of characteristic diffuse streaks. It is shown that from a theoretical analysis of the observed intensity distribution along streaked reciprocal lattice rows in terms of physically plausible models for the geometry and distribution of faults, one can make a choice between various possible routes for transformation. From simple computer simulation studies, it is shown that the observed arrest of transformations in SiC is essentially due to the insertion of stacking faults in a random space and time sequence leading to an irregular distribution of solitons.     

Analysis of deformation induced martensitic transformation in stainless steels

Abstract

Many studies monitoring the formation of martensite during the tensile deformation of austenite report data which are, in principle, affected by both the applied stress and the resulting plastic strain. It is not clear in these circumstances whether the transformation is stress induced (i.e. the stress provides a mechanical driving force) or whether the generation of defects during deformation helps nucleate martensite in a scenario better described as strain induced transformation. The authors demonstrate in the present work that a large amount of published data relating the fraction of martensite to plastic strain can in fact be described in terms of the pure thermodynamic effect of applied stress.     

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm''s theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm''s theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.     

The kinetics of pressure-induced polymorphic transformations

The various methods of obtaining the kinetics data in pressure-induced transformations have been briefly reviewed. Some of the recent results obtained for the pressure-induced alpha-omega transformation in titanium, and fcc-bcc transformation in ytterbium have been discussed. The general features of the kinetics data have been compared with those for other transformations available in literature.     

Failure time distributions for complex equipment

The exponential distribution is inadequate as a failure time model for most components; however, under certain conditions (in particular, that component failure rates are small and mutually independent, and failed components are immediately replaced or perfectly repaired), it is applicable to complex repairable systems with large numbers of components in series, regardless of component distributions, as shown by Drenick in 1960. This result implies that system behavior may become simpler as more components are added. We review necessary conditions for the result and present some simulation studies to assess how well it holds in systems with finite numbers of components. We also note that Drenick's result is analogous to similar results in other systems disciplines, again resulting in simpler behavior as the number of entities in the system increases.     

Computer simulations of martensitic transformations in NiAl alloys

Ni_{1 − x}Al_x alloys in the concentration range 34% < x < 40% exhibit a martensitic transformation from an austenitic phase with bcc structure to a close-packed structured martensitic phase. Above the transformation temperature electron microscopy shows the occurrence of tweed like structures which are accompanied by a considerable softening of the phonon energies at . We have done molecular dynamics simulations employing a semi-empirical model which allows us to study the transformation on an atomistic length scale. Our results show that local distortions of the crystal lattice, which come from the atomic disorder of the alloys, are responsible for the occurrence of tweed phenomena.