Extension Error Set Based on Extension Set

This paper gives the concepts of extension error set and fuzzy extension error set, discusses diverse extension error set and fuzzy extension error set based on extension set and error set, and puts forward the relevant propositions and operations. Finally, it provides proofs of the soundness and completeness for the propositions and operations.

Self-calibration and Compensation of Setting Errors for Surface Profile Measurement of a Microstructured Roll Workpiece

Microstructured roll workpieces have been widely used as functional components in the precision industries. Current researches on quality control have focused on surface profile measurement of microstructured roll workpieces, and types of measurement systems and measurement methods have been developed. However, low measurement efficiency and low measurement accuracy caused by setting errors are the common disadvantages for surface profile measurement of microstructured roll workpieces. In order to shorten the measurement time and enhance the measurement accuracy, a method for self-calibration and compensation of setting errors is proposed for surface profile measurement of microstructured roll workpieces. A measurement system is constructed for the measurement, in which a precision spindle is employed to rotate the roll workpiece and an air-bearing displacement sensor with a micro-stylus probe is employed to scan the microstructured surface of the roll workpiece. The resolution of the displacement sensor is 0.14 nm and that of the rotary encoder of the spindle was 0.15r~. Geometrical and mathematical models are established for analyzing the influences of the setting errors of the roll workpiece and the displacement sensor with respect to the axis of the spindle, including the eccentric error of the roll workpiece, the offset error of the sensor axis and the zero point error of the sensor output. Measurement experiments are carded out on a roll workpiece on which periodic microstructures are a period of 133 i^m along the circumferential direction. Experimental results demonstrate the feasibility of the self-compensation method. The proposed method can be used to detect and compensate the setting errors without using any additional accurate artifact.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

An Evaluation of Inter-Fractional Set-Up Errors in Patients Treated with Distinct Immobilization Equipment for Varying Anatomical Regions

This study aims to evaluate inter-fractional set-up errors in patients treated with distinct immobilization equipment (thermoplastic mask, knee-fix and feet-fix, wing board and vac-lok) for four anatomical regions including brain, head and neck (HN), thorax and pelvis. Data of randomly selected 140 patients who were treated for four anatomical regions were obtained using Hi-Art Helical Tomotherapy (HT) system. Pre-treatment planning was based on automatic registration readings of computed tomography (CT) and mega-voltage computed tomography (MVCT) on a daily basis. Distinct immobilization equipment was used for varying anatomical regions. Individual mean set-up error (M), systematic error (Σ), and random error (σ) values were calculated through daily translational and rotational deviation values. The size of translational, systematic and random error was 1.31 - 4.93 mm for brain, 2.28 - 4.88 mm for HN, 4.04 - 9.90 mm for thorax, and 6.34 - 14.68 mm for pelvis. Rotational values were as follows: 0.06&deg - 0.73&deg for brain, 0.42&deg - 0.6&deg for HN, 0.48&deg - 1.14&deg for thorax and 0.65&deg - 1.05&deg for pelvis. The highest translational, systematic and random error value was obtained from the pelvic regional. The highest standard and random error value in pitch and roll was produced in the rotational direction of the pelvis (0.05° and 0.71°), while the highest error value in yaw was (1.14°) produced from thorax. Inter-fractional set-up errors were most commonly produced in the pelvis, followed by thorax. Our study results suggest that the highest systematic and random errors are found for thorax and pelvis. Distinct immobilization equipment was important in these results. Safety margins around the clinical target volume (CTV) are changeable for different anatomical regions. A future work could be developed to new equipment for immobilization because of the reduced margins CTV.

胸部肿瘤三维适形调强放疗摆位误差相关因素分析

分析胸部肿瘤患者行三维适形调强放疗(IMRT)时产生摆位误差的相关因素,以准确计算出临床靶区(CTV)外放边界(摆位扩边(SM)值),从而实现安全放疗.以莆田学院附属医院接受IMRT治疗的83例胸部恶性肿瘤患者为研究对象,应用体位固定技术及电子射野影像装置(EPID)测量比较胸部恶性肿瘤IMRT的摆位误差,采用多元线性回归分析方法对摆位误差相关因素进行分析,进而分类计算出其SM值.结果显示,83例受试者在X轴、Y轴、Z轴上的SM值分别为0.31、0.28、0.28 cm;靶区定位、性别及肺容量分别为Y轴个体随机误差、Z轴个体系统误差、Z轴个体随机误差的独立影响因素.这表明肿瘤患者行IMRT治疗时靶区定位、性别及肺容量在不同方向上影响其摆位误差.

火炮远方瞄准点法误差分析研究

针对火炮方向瞄准时因周视瞄准镜与火炮回转中心不同心所造成的瞄准误差,使用几何建模方法对方向瞄准过程进行建模,并推导瞄准误差与标定点距离、装定角度和标定点位置之间的函数关系式。通过绘制和分析多组标定点距离、装定角度、标定点位置和瞄准误差数据图像,总结减小瞄准误差的若干方法。给出了装定角度、标定距离和对应瞄准误差极值之间的多项式拟合关系式,供相关人员使用。

BMI对乳腺癌放疗计划靶区外放边界的预判研究

目的:探讨体质量指数(body mass index,BMI)对乳腺癌患者治疗中位移误差的影响,为乳腺癌放射治疗中计划靶区外放边界提供数据支持。方法:回顾性分析本中心乳腺癌治疗的患者153例,利用CBCT获取摆位误差,并对数据进行挖掘,计算出两组因BMI的不同而导致的误差和PTV外放的差别。结果:从左乳和右乳的摆位误差分析计算得出:在考虑BMI情况下,左乳在腹背Z方向的摆位误差随BMI的增大而略有增大。右乳在Rx方向的摆位误差随BMI的增大而增大。左乳中,腹背Z方向外扩边界随BMI增大而逐渐增大。右乳中,头脚Y方向外扩边界随BMI增大而增大。结论:医师可根据乳腺癌的左右位置和BMI的大小来判断Mptv的扩大或者缩小,从而为患者提供更个性化精准化治疗。

乳腺癌保乳术后摆位误差对放疗计划剂量的影响

目的 分析乳腺癌保乳术后摆位误差对治疗计划剂量的影响。方法 选取左右保乳术后女性患者各15例为研究对象,通过移动治疗计划的治疗中心模拟摆位误差情况,分析不同摆位误差对临床靶区(Clinical Target Volume,CTV)和瘤床推量区(CTV-boost)95%体积的受量:CTV-D_(95)和CTV-boost-D_(95),以及危及器官(肺V5、肺V_(20)、健侧乳腺D_(mean)、左乳患者心脏Dmean)的影响。结果 单向摆位误差在0.5 cm以内时,在治疗中心偏患侧、头、腹3个方向上,CTV-D_(95)的平均值接近原计划,危及器官受量显著减小;在治疗中心偏健侧、脚、背3个方向上,CTV-D_(95)的平均值均显著降低,危及器官受量显著增加,其中治疗中心偏背方向剂量变化最大,但均在临床可接受范围。治疗中心同时偏向患侧、头、腹3个方向0.5 cm范围内,计划剂量变化可以接受。治疗中心同时偏向健侧、脚、背3个方向0.3 cm范围内,计划剂量变化可以接受;当这3个方向上的偏差同时达到0.5 cm时,CTV-D_(95)、CTV-boost-D_(95)受量小于处方剂量的95%,肺V_(20)受量平均值超出了要求的剂量限制,治疗实际受量不满足临床要求。结论 本中心的摆位平均误差在X、Y、Z方向均小于0.3 cm时,摆位误差导致的剂量偏差基本处于临床可接受范围。实际工作中,治疗中心同时偏向健侧、脚、背方向达到0.5 cm时,应引起治疗师高度重视,可适当增加锥形束CT次数。

组合电路SET传播特性与软错误率分析

通过研究单粒子瞬态(Single Event Transient,SET)在逻辑链路中的传输,表明输入脉冲宽度对脉冲在传输过程中的展宽和衰减有重要影响.在辐照环境下,采用SET的传输模型和软错误率的分析模型评估软错误率.基于这两种模型,从门级角度对组合电路的软错误率分析进行了改善,使得软错误率评估方法得到改进.由于电气掩蔽效应对软错误分析具有重要的影响,在运用SET传输模型中考虑了电气掩蔽特性.

A Study Regarding Solution of a Knowledge Model Based on the Containing-Type Error Matrix Equation

An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.

Correct a Wide Spread Conclusion of Cantor Set Theory

The Cantor’s conclusion that “there is a one-one correspondence between the points on n-dimensional space and the points on the line” appears in the numerous current documents. By introducing a monotonic and continuous function, a one-one correspondence between two intervals is built;and by using parametric equations of the curve, a one-one correspondence from the points on the curve to the points on the line is established. Specially, the meanings of multivariate functions are given. By using a n-variable equation with a parameter, a correspondence from n-dimensional space area to a interval is built, so the wrong conclusion is completely denied. The paper enriches calculus and can reduce the teaching difficulty of real function in some degree. The expression of moving curve (surface) limit is given in the paper. More importantly, after the conclusion is corrected, it will be necessary and possible to re-establish the theory and the approach about multivariable differential calculus.

COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.

一种基于错误集的极化码改进SCL译码算法

针对极化码在中短码长时纠错性能的不足,提出了一种基于错误集的极化码改进串行抵消列表(Successive Cancellation List of Polar Codes Based on Error Set,ES-SCL)译码算法。该算法首先根据极化码的信道特性构造错误集,在极化码编码时根据错误集中的元素设置奇偶校验(Parity Check,PC)位,其余位置则放置信息比特和冻结比特,译码器在译码PC位时,每条路径通过校验函数得到PC位的比特估计,不执行路径分裂和剪枝,其余位置则执行SCL译码。仿真结果表明,在加性高斯白噪声信道下,当码长为512,码率为0.5,误块率为10^(-5),最大译码列表数为8时,相较于PC-PSCL译码算法以及CA-SCL译码算法,所提出的ES-SCL译码算法获得了约0.18和0.15 dB的增益;当码长为256,码率为0.5,误码率为10^(-5),最大译码列表数为8时,相较于CA-SCL,PC-PSCL译码算法,获得了约0.3和0.35 dB的增益;此外,采用部分比特分裂译码的ES-SCL译码算法可以在误块率与PC-PSCL译码算法几乎相同的情况下,减少约50%的排序次数,具有更低的译码复杂度。

乳腺托架辅助装置设计及其在放射治疗摆位中的验证研究

目的:设计乳腺托架辅助装置,探讨其在左侧乳腺癌保乳术后全乳及锁骨上下区放射治疗中的应用价值。方法:选取医院收治的24例左侧乳腺癌保乳术后行放射治疗患者,按照随机数表法将其分为两种定位方式的乳腺托架组和乳腺托架辅助装置组,每组12例。两组患者均采用一体化静态调强放射治疗,统计分析两组患者主要危及器官(OAR)剂量学指标2%、50%靶区体积的受照剂量(D2、D50)、最大剂量(Dmax)、平均剂量(Dmean)、适形指数(CI)和均匀性指数(HI),使用锥形束CT(CBCT)测算患者摆位误差绝对值,并记录摆位时间。结果:两组患者剂量学指标D2、D50、CI及HI比较,差异无统计学意义;OAR左肺(V20、V30、Dmean)、心脏(V30、Dmean)、右乳腺Dmean、脊髓Dmax、肱骨头(Dmax、Dmean)和甲状腺Dmean比较,差异均无统计学意义。两组患者左右方向、头脚方向和腹背方向的摆位误差比较,差异均有统计学意义(Z=-2.112,Z=-8.061,Z=-2.228;P<0.035)。两组患者摆位时间比较,差异有统计学意义(t=5.181,P<0.001)。结论:乳腺托架辅助装置可提高摆位精度与效率,改造现有装备以适应技术的发展,提高放射治疗设备利用率,有较好的临床应用价值。

Efficient Information Set Decoding Based on Genetic Algorithms

In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.

STUDY ON A PRECISE ON-SPOT CALIBRATION METHOD FOR DISTRIBUTED STEREO REFERENCE POSITION-SETTING

A high precision method used for on-spot calibration of distributed stereoreference position setting is presented. The high measuring accuracy in stereo reference calibrationis derived from using a high precision water level instrument and an accurate height verniercaliper. It settles the problem of reference calibration effectively and accurately, without usinglarge coordinate measuring machines (CMM). It is more adaptable and precise than traditionalcalibration methods applying theodolites or autocollimators. The error sources of this method areanalyzed in detail and several methods are developed to eliminate the calibration error.Anoptimizing swallowtail-like anchor target is developed. Experiments show that the calibrationaccuracy can be limited within 0.06 mm in the range of 3～5 m and 0.03 mm with optimizing anchortarget. This method can be widely used in on-spot calibration.

不同固定技术对食管癌放射治疗精度的影响

目的探讨在线红外引导改良一体板联合颈胸膜固定技术减少食管癌患者的放射治疗摆位误差与提高摆位重复性。方法选择食管癌患者144例,其中男性68例,女性76例;年龄42~77岁,平均年龄60.5岁(标准差13.4岁);临床分期Ⅰ期42例,Ⅱ期65例,Ⅲ期37例。随机分为在线红外引导改良一体板联合颈胸膜固定组(试验组)72例,三维激光灯引导真空垫+翼型板固定组(对照组)72例。运用Elekta Synergy直线加速器机的锥形束CT(CBCT)对两组患者体位进行扫描,借助X射线容积成像系统对CBCT图像与定位CT图像进行配准得出摆位误差后对其进行统计学分析。结果试验组在X、Y、Z轴向平移误差为(1.76±0.99)mm、(1.45±0.78)mm、(1.38±0.81)mm,最大值为3.5 mm、3.7 mm、5.2 mm,验证通过率为98.61%、100.00%、98.61%;旋转误差为(1.37±0.90)°、(1.25±0.78)°、(1.39±0.90)°,最大值为2.5°、3.6°、3.7°,验证通过率为98.61%、100.00%、97.22%。对照组在X、Y、Z轴向平移误差为(1.95±1.07)mm、(2.08±1.40)mm、(2.23±1.08)mm,最大值为5.5 mm、6.4 mm、5.3 mm,验证通过率为97.22%、93.06%、97.22%;在X、Y、Z轴向旋转误差为(1.76±0.86)°、(1.60±0.78)°、(1.64±1.01)°,最大值为3.8°、3.4°、4.0°,验证通过率为95.83%、98.61%、97.22%。试验组与对照组摆位误差比较,在平移误差X轴向与旋转误差Z轴向差异无统计学意义(P>0.05),但在平移误差Y、Z轴向与旋转误差X、Y轴向差异有统计学意义(P<0.05)。结论在线红外引导下应用改良一体板联合颈胸膜对食管癌放射治疗患者进行体位固定相较于三维激光灯引导真空垫+翼型板能够提高摆位精度和重复性。

Estimation of the Population Mean Using Paired Ranked Set Sampling

In the situation where the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to SRS. In this paper we propose an estimator of the population mean using paired ranked set sampling (RSS) method. The proposed estimator is an unbiased estimator of the population mean when the set size is even. In case of odd set size the estimator is unbiased when the underlying distribution is symmetric. It is shown that the proposed estimator is more efficient than its counterpart SRS method for all distributions considered in this study.

An Efficient Class of Estimators for the Finite Population Mean in Ranked Set Sampling

In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.

非球面超精密车削对刀误差补偿

为提高非球面超精密车削的加工精度和加工效率,通过分析非球面的面形特点和超精密车削过程中对刀误差等因素的成因,建立了刀具对刀误差对非球面加工面形误差影响的仿真模型。仿真分析进一步揭示了刀具对刀误差所带来的面形误差变化规律。试验结果表明,通过刀具对刀误差补偿,非球面超精密车削后的面形精度PV=179 nm,表面粗糙度均方根RMS=45.4 nm。试验验证了理论分析和刀具对刀误差补偿方法的正确性。