The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

Existence of Sign-changing Solution for Three-point Boundary Value Problems

In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.

Study on the Existence of Sign-Changing Solutions of Case Theory Based a Class of Differential Equations Boundary-Value Problems

By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.

RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVING-AVERAGE PROCESSES

In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

A New Method for Determining Threshold in Using PGCEVD to Calculate Return Values of Typhoon Wave Height

In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.

基于K-means的手肘法自动获取K值方法研究

典型的K-means算法利用手肘法选择合适的K值在实际项目中应用的较多,但是手肘法获取K值自动性低,以及面对海量数据的处理,效率上也有待提高。提出利用手肘法关系图初始点和末尾点连接的关系直线,求K值范围下直线y值与误差平方和的最大差值的方法,最大差值对应的K值为手肘法的最优肘点,由于手肘法需要多次迭代以及数据集稠密度对关系图的影响较小,提出利用数据集预抽样并且将程序部署在spark平台之上的方式自动获取手肘法的肘点K值,这样不仅根据此方法自动获取K-means最优K值而且提高了大数据集的处理效率。

改进CK-means+算法及并行实现

为降低K值的不确定性和初始聚类中心的随机性对聚类结果的影响,提出一种基于优化Canopy算法和均值计算法的改进K-means算法——CK-means+。优化Canopy算法,降低距离阈值T不确定性对最终输出K值的影响,通过Canopy算法和均值计算法得到K值和初始中心点。在UCI数据集上,结合Spark框架并行化,实验结果表明,相较其它算法,CK-means+算法效率更高,可以更好适应大规模数据应用场景。

Change-point Estimation of a Mean Shift in Moving-average Processes Under Dependence Assumptions

In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜ 〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.

AN APPROXIMATE EXPRESSION RELATED WITH RSA FIXED POINTS

Let T=T(n,e,α) be the number of fixed points o f RSA(n,e) that a re co prime with n=pq,and A,B be sets of prime numbers in (1,x) and (1,y) respectively. An estimation on the mean value M(A,B,e,α)=1 (#A)(#B)∑p∈A,q∈B,(p,q)=1logT(pq,e,α) is given.

一类Kirchhoff型四阶椭圆方程的无穷多个变号解（英文）

四阶Kirchhoff型椭圆问题来源于工程实际中的悬索桥模型.本文应用下降流不变集方法研究了一类四阶Kirchhoff型椭圆边值问题,在非线性项是奇函数且无穷远处超二次的条件下,证明了关于变号解存在性与多重性的两个定理.主要结果及其证明方法均不同于文献中的结果.

Characterizing the Seasonal and Directional Varying Properties in A Marine Environment

With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold（POT） method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated.

Trends of Shoreline Position: An Approach to Future Prediction for Balasore Shoreline, Odisha, India

The present study aims to analyze the shift in shoreline due to coastal processes and formulate available for best estimate of future shoreline positions based on precedent shorelines. Information on rates and trends of shoreline change can be used to improve the understanding of the underlying causes and potential effects of coastal erosion which can support informed coastal management decisions. In this paper, researchers go over the changes in the recent positions of the shoreline of the Balasore coast for the 38 years from 1975 through 2013. The study area includes the Balasore coastal region from Rasalpur to Udaypur together with Chandipur, Choumukh, Chandrabali as well as Bichitrapur. Transects wise shoreline data base were developed for approximately 67 kilometers of shoreline and erosional/accretional scenario has also been analysed by delineating the shoreline from Landsat imageries of 1975, 1980, 1990, 1995, 2000, 2005, 2010 and 2013. A simple Linear Regression Model and End Point Rate (EPR) have been adopted to take out the rate of change of shoreline and its future positions, based on empirical observations at 67 transects along the Balasore coast. It is found that the north eastern part of Balasore coast in the vicinity of Subarnarekha estuary and Chandrabali beach undergo high rates of shore line shift. The shoreline data were integrated for long- (about 17 years) and short-term (about 7 years) shift rates analysis to comprehend the shoreline change and prediction. For the prediction of future shoreline, the model has been validated with the present shoreline position (2013). The rate of shoreline movement calculated from the fixed base line to shoreline position of 1975, 1980, 1990, 1995, 2000, 2005 and 2010 and based on this, the estimated shoreline of 2013 was calculated. The estimated shoreline was compared with the actual shoreline delineated from satellite imagery of 2013. The model error or positional shift at each sample point is observed. The positional error varies from??4.82 m to 212.41 m. It has been found that model prediction error is higher in the left hand side of river Subarnarekha. The overall error for the entire predicted shoreline was found to be 41.88 m by Root Mean Square Error (RMSE). In addition, it was tested by means difference between actual and predicted shoreline positions using “t” test and it has been found that predicted shore line is not significantly different from actual shoreline position at (t132 = 0.278) p < 0.01.

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

ON DETECTION OF CHANGE POINTS USING MEAN VECTORS

In this paper,the authors consider the problem of change points within the framework of model selection and propose a procedure for estimating the locations of change points when the number of change points is known.The strong consistency of this procedure is also established. The problem of detecting change points is discussed within the framework of the simultaneous test procedure.The case where the number of change points is unknown will be discussed in another paper.

新时代大学生劳动教育的价值意蕴、现实困境和实践指向

对大学生开展劳动教育是中国特色社会主义教育制度的重要内容。作为建设社会主义现代化强国和实现中华民族伟大复兴的生力军,大学生能否成为“有理想、敢担当、能吃苦、肯奋斗”的新时代好青年,与劳动教育有着紧密的联系。当前,高校在贯彻落实劳动教育过程中面临着来自个体、家庭、社会以及学校自身等方面的挑战。应坚持系统观念,大学生个体的“意识扣”、家庭教育的“启蒙扣”、高校教育的“教育扣”、社会教育的“检验扣”要协同推进,方能取得实效。

基于点多边形的混合坐标

为了构造非负且光滑的广义重心坐标,提出一种基于点多边形的混合坐标构建方法.首先将原多边形三角剖分,计算所有网格顶点的重心坐标,并确定每个网格顶点的点多边形;然后分别计算原多边形内点关于其所在三角形的点多边形的重心坐标与混合系数,根据以上计算结果得到混合坐标;最后使用迭代坐标或调和坐标计算网格顶点的重心坐标,用均值坐标和迭代坐标计算原多边形内点关于点多边形的重心坐标.数值实例采用多个多边形的等高线图,以及其不同重心坐标的非负区域、光滑性、纹理映射对比,表明所提方法具有良好的光滑性,且在任意多边形内部具有非负性.

黄土地质灾害评价因子地形起伏度提取最佳尺度研究:以榆林市米脂县为例

目前地质灾害相关评价工作中,部分研究人员对于“地形起伏度”(也称相对坡高)选取最佳窗口单元进行提取存在着一定程度的随意性和主观性,致使取得的地形起伏度参数与研究区实际情况相比存在一定的误差。后续地灾评价中,无论采用以栅格为基础的信息量模型还是现今普遍流行的各类机器学习方法,其评价因子本身的误差甚至错误会导致评价结果可靠性降低。笔者基于Arc GIS平台,利用陕西省榆林市米脂县分辨率为2 m的DEM数据,采用均值变点分析法,通过两轮分析,数量分别为10×10和1×1的矩形窗口逐渐逼近研究区地形起伏度的最佳统计单元,计算出该县地形起伏度为0~256.60 m,最佳统计单元为59×59的窗格,栅格单元边长为2 m,提取窗格边长为118 m,对应提取面积为13924 m^(2)。随后依据陕北黄土地区历史滑坡及崩塌的易发坡高统计将米脂县地形起伏度等分为<20 m、20~40 m、40~60 m、60~80 m、>80 m等5个区间,受原始地形条件及削坡建房、建厂等综合影响,40~80 m为灾害隐患发育的主要区间,灾害隐患点占比为88.60%。结合米脂县地质灾害隐患点信息量值和灾害点密度对比曲线,结果显示二者有很好的相关性,体现了地形起伏度统计单元选取和区间划分的合理性。本研究所采用的高精度DEM数据的计算及分析结果,首先避免了目视寻找拐点的弊端,其次在黄土高原地区千沟万壑的地貌条件中能够满足数字地形分析与精细化地质灾害调查的需求,可为黄土高原区地质灾害评价防治及黄河中上游流域的水土流失治理与生态环境保护提供一定的技术支撑。

南海陆坡海底峡谷地形复杂度分析方法

地形复杂度指数是描述地形变化程度的综合指标,本文基于南海陆坡北港隆起区的水深网格数据,采用均值变点分析法确定地形起伏度的最佳统计单元,建立计算海底地形复杂度的模型,融合研究区坡度、地形起伏度、地表切割深度和高程变异系数4种地形因子,分析研究区的地形特征和地形复杂度。结果表明,研究区地形起伏度最佳分析窗口大小为19×19网格,最佳统计窗口面积为1.7689 km^(2);研究区北部及南部区域地形平坦,地形复杂程度较低,复杂度指数<2.35;中部区域存在规模不同的峡谷,地形复杂程度较高,复杂度指数平均>3.37,其中,中部偏东区域因海底峡谷最为发育,地形复杂度指数可达7.77。研究区地形复杂度的定量分析结果与海蚀作用的强弱程度呈现出较好的正相关性,这对系统开展南海海底峡谷形态特征及演化过程研究、维护海洋工程设施安全等具有重要借鉴意义。

基于ASTER GDEM的黑龙江省地形起伏度分析

地形起伏度是描述地貌形态的重要指标,反映了研究区域内地势起伏特征。以黑龙江省为研究区域、以30 m分辨率的ASTER GDEM(先进星载热发射和反射辐射仪全球数字高程模型)数据为基础,在ArcGIS平台上利用领域分析法分析不同窗口大小下的地形起伏度,通过均值变点法得出最佳统计单元面积为0.396 9 km^(2)。在此基础上对黑龙江省地势起伏度进行分析。结果表明黑龙江省地形起伏可分为4类,主要以台地、丘陵为主,平原占比次之。