赫师慎关于中国不定分析研究之探析

20世纪初期西方传教士赫师慎对中国不定分析进行了系统探讨,其论文《中国百鸡问题或不定分析》向西方世界展示了不定分析在中国发展历史的全貌,对于帮助西方了解中国数学及古代文明起到了重要作用。本文对此进行系统的分析,重新评价了赫氏在西方汉学研究中的历史地位,并对赫氏的若干论断提出质疑,辨明了其中若干不明文献的出处。

一次不定分析算法的比较研究

在前人研究的基础上,对中国大衍求一术、印度库塔卡和西方哥廷根抄本这三种古代一次不定分析算法进行全面的数理分析和比较,得出结论:大衍求一术、库塔卡是成熟的算法,哥廷根法是试探法.

中国的“大衍求一术”与古代印度不定分析理论比较研究

从分析Ｂａｇ的错误出发，将印度的“联合粉碎法”与中国的“大衍求一术”加以比校，从而阐明两者之间不存在承接关系．

两阶段不定核支持向量机

近年来,在机器学习的各个领域出现了越来越多不定的度量核矩阵,使得不定核支持向量机(IKSVM)得到了广泛关注。但是,现有IKSVM算法通常不能较好地解决高维数据所带来的信息冗余和样本稀疏等问题。针对此研究现状,对现有主流的IKSVM算法进行了研究,并基于再生核Kre?n空间(RKKS)中对IKSVM问题的稳定化定义,从理论上证明了IKSVM问题的本质为不定核主成分分析(IKPCA)降维后空间中的支持向量机(SVM)问题,进一步地提出求解IKSVM问题的新型学习框架TP-IKSVM。TP-IKSVM通过将IKSVM问题的求解拆分为IKPCA和SVM两个阶段,充分地发挥了IKPCA在处理高维数据的信息冗余和样本稀疏等方面的优势,同时结合SVM以有效分类。在真实数据集上的实验结果表明,TP-IKSVM的分类精度优于现有主流的IKSVM算法。

和算家的累约术

以和算家建部贤弘和中根元珪的累约术为例,通过探讨和算家的问题来源,复原其算法的构造思想,及其处理这些问题时与中算家的不同方法和态度,说明中日两国数学家在数学创造方面的一些异同之处.和算作为继承并发展中国古代数学的一个标本,对于深刻理解机械化程序算法体系的数学传统,颇有益处.

砖块铺地的故事

对于方程组fi(x1,x2,…xj)=0(i=1,2…,n;j=1,2,…,m,m>n)，一般情况下，当没有其他条件限制时，满足方程组的解无穷无尽，非常自由，真是“大海从鱼跃，长空任鸟飞”(宋代阮阅《诗总》)。如果附加一些条件(最典型的就是规定所有的xi均为整数，此时解这个方程叫做不定分析)。解域就显得碍手碍脚，必须小心探索，得来很费功夫。其中变幻多方、秘奥莫测：有的有通解，如勾股数公式；有的有若干组解，如百鸡问题；有的有唯一解；有的干脆在偌大一数集中无解，如费马大定理。

Application of uncertain type of AHP to condition assessment of cable-stayed bridges

In order to guarantee the safety service and life-span of long-span cable-stayed bridges, the uncertain type of analytic hierarchy process （AHP） method is adopted to access the bridge condition. The correlative theory and applied objects of uncertain type of AHP are introduced, and then the optimal transitive matrix method is chosen to calculate the interval number judgment matrix, which makes the weights of indices more reliable and accurate. Finally, with Harbin Songhua River Cable-Stayed Bridge as an example, an index system and an assessment model are proposed for the condition assessment of this bridge, and by using uncertain type of AHP, the weights of assessment indices are fixed and the final assessment results of the bridge are calculated, which proves the feasibility and practicability of this method. The application of this assessment method can provide the scientific basis for maintenance and management of long-span cable-stayed bridges.

Dynamic analysis and experimental study of vibro-acoustic system with uncertainties at middle frequencies

To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA） is proposed to analyze vibro-acoustics responses with uncertainties at middle frequencies. The mid-frequency dynamic response of the framework-plate structure with uncertainties is studied based on the hybrid FE-SEA method and the Monte Carlo（MC）simulation is performed so as to provide a benchmark comparison with the hybrid method. The energy response of the framework-plate structure matches well with the MC simulation results, which validates the effectiveness of the hybrid FE-SEA method considering both the complexity of the vibro-acoustic structure and the uncertainties in mid-frequency vibro-acousitc analysis. Based on the hybrid method, a vibroacoustic model of a construction machinery cab with random properties is established, and the excitations of the model are measured by experiments. The responses of the sound pressure level of the cab and the vibration power spectrum density of the front windscreen are calculated and compared with those of the experiment. At middle frequencies, the results have a good consistency with the tests and the prediction error is less than 3. 5dB.

基于Kreǐn空间的两阶段子空间学习

为了解决不定核Fisher判别分析(IKFDA)在处理高维小样本数据时的病态问题,基于Kreǐn空间提出了两阶段的IKFDA学习框架TP-IKFDA;为了解决不定核典型相关分析(IKCCA)在处理高维小样本数据时的过拟合问题,提出了两阶段的IKCCA学习框架TP-IKCCA.通过不定核主成分分析(IKPCA)进行降维处理,减弱高维特征所带来的负面影响;然后,在降维后的特征空间中进行Fisher判别分析(FDA)或典型相关分析(CCA).真实数据集上的试验结果表明,与IKPCA、IKFDA以及IKFDA的改进算法相比,TP-IKFDA的分类精度明显提高;TP-IKCCA相较于现有的IKCCA模型泛化性能得到了进一步改善.因此,在处理高维小样本数据时,TP-IKFDA和TP-IKCCA的实际泛化性能优于现有的不定核子空间学习技术.

A Generalization of Caristi Fixed Point Theorem

Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.

Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

Application of reliability-centered maintenance for productivity improvement of open pit mining equipment:Case study of Sungun Copper Mine

Equipment plays an important role in open pit mining industry and its cost competence at efficient operation and maintenance techniques centered on reliability can lead to significant cost reduction.The application of optimal maintenance process was investigated for minimizing the equipment breakdowns and downtimes in Sungun Copper Mine.It results in the improved efficiency and productivity of the equipment and lowered expenses as well as the increased profit margin.The field operating data of 10 trucks are used to estimate the failure and maintenance profile for each component,and modeling and simulation are accomplished by using reliability block diagram method.Trend analysis was then conducted to select proper probabilistic model for maintenance profile.Then reliability of the system was evaluated and importance of each component was computed by weighted importance measure method.This analysis led to identify the items with critical impact on availability of overall equipment in order to prioritize improvement decisions.Later,the availability of trucks was evaluated using Monte Carlo simulation and it is revealed that the uptime of the trucks is around 11000 h at 12000 operation hours.Finally,uncertainty analysis was performed to account for the uncertainty sources in data and models.

Regional Climate Change and Uncertainty Analysis based on Four Regional Climate Model Simulations over China

Four sets of climate change simulations at grid spacing of 50 km were conducted over East Asia with two regional climate models driven at the lateral bounda- ries by two global models for the period 1981-2050. The locus of the study was on the ensemble projection of cli- mate change in the mid-21st century （2031-50） over China. Validation of each simulation and the ensemble average showed good performances of the models overall, as well as advantages of the ensemble in reproducing present day （1981 2000） December-February （DJF）, June-August （JJA）, and annual （ANN） mean temperature and precipitation. Significant wanning was projected for the mid-21st century, with larger values of temperature increase found in the northern part of China and in the cold seasons. The ensemble average changes of precipitation in DJF, JJA, and ANN were determined, and the uncertainties of the projected changes analyzed based on the consistencies of the simulations. It was concluded that the largest uncertainties in precipitation projection are in eastern China during the summer season （monsoon pre-cipitation）.

Dynamic Radiographic Analysis of Sympathetic Cervical Spondylosis Instability

Objective To investigate the correlation between subaxial cervical spine instability and cervical spondylotic sympathetic symptoms as well as the difference of cervical spondylotic subaxial instability between male and female patients. Methods We analyzed retrospectively 318 surgical cases of cervical spondylosis treated at Department of Orthopedic Surgery of Peking Union Medical College Hospital between July 2003 and December 2007. All cases were divided into group A without sympathetic symptoms (n=284) and group B with sympathetic symptoms (n=34). Angular and horizontal translation values between two adjacent vertebral bodies from C2 to C7 were measured separately on hyperflexion and hyperextension lateral cervical spine radiographs. Fisher's exact test was used to evaluate the correlation between subaxial cervical instability and sympathetic symptoms. Intragroup correlation between patient gender and subaxial cervical instability was also evaluated. Results Subaxial instability incidences in groups A and B were 21.8% (62/284) and 55.9% (19/34), respectively. Statistical analysis indicated a definite correlation between subaxial cervical instability and sympathetic symptoms (P=0.000). Among patients without sympathetic symptoms, subaxial instability incidences were 21.4% (37/173) in males and 22.5% (25/111) in females, respectively (P=0.883). While among patients with sympathetic symptoms, subaxial instability incidences were 27.3% (3/11) in males and 69.6% (16/23) in females, respectively, indicating significant difference (P=0.030). Subaxial instability was most commonly seen at C4-C5 intervertebral space in sympathetic cervical spondylosis patients. Conclusions High correlation exists between subaxial cervical spine instability and cervical spondylotic sympathetic symptoms, especially in female patients. Hyperextension and hyperflexion radiographs of cervical spine are important to assess sympathetic cervical spondylotic subaxial instability.

Uncertainty analysis of ship model vertical center of gravity and transverse moment of inertia test

The usability of test results of ship model vertical center of gravity and transverse moment of inertia is generally depends on its uncertainty. Referring to the guidelines for uncertainty analysis in examination of liquid dynamic recommended by International Towing Tank Conference （ ITTC）, the results were analyzed, bias limits and precision limits were calculated and total uncertainty was estimated. The total uncertainty of six tests on ship model vertical center of gravity is is 0. 16% of the mean value, and the total uncertainty of six tests on ship model transverse moment of inertia is 5.66% of the mean value. The test results show that the total uncertainty of both the multiple tests and the single test is from the precision limits of ship model vertical center of gravity and transverse moment of inertia tests. Thus, the improved measurement system stability can enormously decrease the total uncertainty of multiple tests and the single test.

Sensitivity and Uncertainty Analysis of Regional Marine Ecosystem Services Value

Marine ecosystem services are the benefits which people obtain from the marine ecosystem,including provisioning services,regulating services,cultural services and supporting services. The human species,while buffered against environmental changes by culture and technology,is fundamentally dependent on the flow of ecosystem services. Marine ecosystem services become increasingly valuable as the terrestrial resources become scarce. The value of marine ecosystem services is the monetary flow of ecosystem services on specific temporal and spatial scales,which often changes due to the variation of the goods prices,yields and the status of marine exploitation. Sensitivity analysis is to study the relationship between the value of marine ecosystem services and the main factors which affect it. Uncertainty analysis based on varying prices,yields and status of marine exploitation was carried out. Through uncertainty analysis,a more credible value range instead of a fixed value of marine ecosystem services was obtained in this study. Moreover,sensitivity analysis of the marine ecosystem services value revealed the relative importance of different factors.

Study of Slope Reinforcement Force Based on FLAC

A slope will slide if the unbalanced force does not tend to zero when the stability of the slope is analyzed with the help of FLAC. Thus the ultimate reason of slope sliding is the unbalanced force determined by FLAC. The slope will remain stable if the unbalanced force is counterbalanced by a reinforcement force which is produced by a suitable reinforcement method. In this paper, the stability of the slope was analyzed by using FLAC, and the unbalanced force of the slope was obtained through the FISH function in FLAC. According to the equilibrium conditions, the relationship between the reinforcement force and unbalanced force was derived and accordingly the reinforcement force was determined. The reinforcement design was adopted by using pre-stressed anchor bars on the basis of the reinforcement force. An example is used to show that the effect of slope reinforcement based on the reinforcement force is safe and economical. The method doesn＇t need to suppose a sliding surface to obtain the reinforcement force, and it is also clear in physical meaning. So this method realized the organic unification of the stability analysis and the slope reinforcement.

Discussion of skill improvement in marine ecosystem dynamic models based on parameter optimization and skill assessment

Marine ecosystem dynamic models(MEDMs) are important tools for the simulation and prediction of marine ecosystems. This article summarizes the methods and strategies used for the improvement and assessment of MEDM skill, and it attempts to establish a technical framework to inspire further ideas concerning MEDM skill improvement. The skill of MEDMs can be improved by parameter optimization(PO), which is an important step in model calibration. An effi cient approach to solve the problem of PO constrained by MEDMs is the global treatment of both sensitivity analysis and PO. Model validation is an essential step following PO, which validates the effi ciency of model calibration by analyzing and estimating the goodness-of-fi t of the optimized model. Additionally, by focusing on the degree of impact of various factors on model skill, model uncertainty analysis can supply model users with a quantitative assessment of model confi dence. Research on MEDMs is ongoing; however, improvement in model skill still lacks global treatments and its assessment is not integrated. Thus, the predictive performance of MEDMs is not strong and model uncertainties lack quantitative descriptions, limiting their application. Therefore, a large number of case studies concerning model skill should be performed to promote the development of a scientifi c and normative technical framework for the improvement of MEDM skill.

Quantum Gravitational Effects on Tunneling Rate of Reissner-Nordstroum Black Hole Emission and Generalized Second Law

The semi-classical black hole tunneling radiation (Parikh-Wilczek tunneling proposal) is calculated undera minimal length uncertainty analysis.It is shown that,the generalized second law of thermodynamics may bound thetunneling probability radiation of a Reissner-Nordstrom black hole radiation.

Accurate estimation of soil shear strength parameters

The cost and safety of geotechnical engineering are highly depending on the accuracy of soil shear strength parameters.There are three methods often used to estimate soil shear strength parameters,i.e.,moment method,3-sigma rule and linear regression method.In this study,the accuracy of these three methods is compared.Traditional linear regression method(LRM)can only offer the mean of shear strength parameters.Some engineers misuse the standard error of shear strength indexes as the standard deviations.Such misuse may highly underestimate the uncertainty and induce high risk to the geotechnical design.A modified LRM is proposed to determine both the mean and variance of shear strength parameters.The moment method,three-sigma rule and LRM are used to analyze the tri-axial test data in Xiaolangdi Hydraulic Project and three numerical shear strength tests.The results demonstrate that:1)The modified LRM can offer the most accurate estimation to shear strength parameters;2)A dimensionless formula is much preferred in LRM rather than a dimensional formula.The stress ratio formula is much better than stress relation in the shear strength parameter analysis.The proposed method is applicable to shear strength parameter analysis for tri-axial test data,direct shear test and the un-drained shear strength test of stratified clay.