基于交通拥堵信息的高速公路拥堵路段ACK-Means聚类

为了充分利用实际高速公路路段交通拥堵信息,更合理地聚类交通拥堵的内在规律和特征变化,提出自适应确定聚类中心C和类别K值(adaptive center and K-means value,ACK-Means)的聚类算法,进行高速公路拥堵路段聚类。ACK-Means算法借助簇类密度、簇类间距以及簇类强度,同时又考虑到数据样本的偶然性,对离群点进行合理分配,ACK-Means算法可实现自适应确定聚类中心C和类别K值。基于实际交通拥堵信息构建数据集,Python编程实现高速公路拥堵路段ACK-Means聚类,巧妙解决了高速公路拥堵路段聚类数目K和聚类中心C设定问题。聚类结果表明,ACK-Means算法实现高速公路拥堵路段无监督聚类,聚类结果完全基于实际的高速公路交通拥堵信息,具有更高的实用性。

基于SVD-K-means算法的软扩频信号伪码序列盲估计

针对通信中软扩频信号伪码序列盲估计困难的问题,提出一种奇异值分解(singular value decomposition,SVD)和K-means聚类相结合的方法。该方法先对接收信号按照一倍伪码周期进行不重叠分段构造数据矩阵。其次对数据矩阵和相似性矩阵分别进行SVD完成对伪码序列集合规模数的估计、数据降噪、粗分类以及初始聚类中心的选取。最后通过K-means算法优化分类结果,得到伪码序列的估计值。该算法在聚类之前事先确定聚类数目,大大减少了迭代次数。同时实验结果表明,该算法在信息码元分组小于5 bit,信噪比大于-10 dB时可以准确估计出软扩频信号的伪码序列,性能较同类算法有所提升。

GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE

In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p.

On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime

In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.

THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS

For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

A Note on the Mean Value Theorems

The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point P on the graph such that the tangent at P is parallel to the secant through the two endpoints. The mean value theorem for definite integrals says that the area under the function is equal to the area of a rectangle whose base is the length of the interval and height of some point Q on the graph. These two theorems have been studied and utilized extensively and they form the backbone of many important theorems in different branches of mathematics. In this note, we pose the question: for what functions do the two points P and Q always coincide? We find that the only analytic functions satisfying this condition are linear or exponential functions.

Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem

This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.

基于K-means聚类算法的烘烤烟叶图像分割研究

目前我国烟叶烘烤过程主要依赖人工监测,存在主观性、模糊性和高成本等问题,使用机器视觉方法对烘烤过程烟叶质量变化进行实时监测与判断的研究逐渐增多,实时监测需建立在高效且准确的烘烤烟叶图像分割之上,因此烘烤烟叶图像分割的研究变得尤其重要。提出了基于K-means聚类算法的烘烤烟叶图像分割方法,首先读取图像并将RGB转换为CYMK颜色空间,然后提取CYMK颜色空间下的K通道灰度化图像,再对此单通道图像进行聚类,根据聚类中心确定图像分割阈值,最后利用图像处理方法对图像进行分割。研究比较了K-means、模糊C均值聚类(FCM)和高斯混合聚类(GMM)3种聚类方法,结果表明K-means算法的像素准确率为97.8%、交并比为96.43%、Dice系数为98.2%,均优于其他2种方法。K-means算法能够更好地提取烤烟的烟叶轮廓,去除冗余信息,使得分割结果更清晰。

基于改进SOM+K-means算法的客户价值研究

为提高多特征参数聚类相似度,针对多特征参数相关性和分布不等问题,提出一种改进的聚类算法,并以此算法研究RFM客户价值模型。此改进算法,通过矩阵旋转和压缩变换以及协方差矩阵处理,构造一种聚类相似度目标的距离函数,以此距离函数结合SOM算法和K-means算法各自优点,设计改进SOM+K-means组合聚类算法。应用该算法创建RFM客户价值模型,并实验验证。通过轮廓系数法评估,该算法聚类的轮廓系数相比原K-means和SOM算法聚类的轮廓系数,分别提高约0.129和0.126。该聚类算法提高了RFM客户价值聚类效果,为客户价值研究提供了一种新的聚类方法。

基于优化模糊C-means算法的不平衡大数据分类研究

针对不平衡大数据的分类问题,提出一种优化模糊C-means算法的不平衡大数据分类算法。先计算C-means模糊交叉算子,定义优化函数,并求解大数据不平衡增益。利用Spark分类平台,确定大数据样本压缩模糊近邻值的取值范围,再通过放大近邻值的处理方式,定义不平衡阈向量,从而完善整个分类流程,完成基于优化模糊C-means算法的不平衡大数据分类方法的设计。实验结果表明,上述分类方法的应用,可将正例信息、负例信息的取样长度区间完全分离开来,能有效解决因不平衡大数据分类不精准造成的信息样本混淆的问题,符合实际应用需求。

Estimation of Return Level for Maximum Daily and Hourly Precipitation in Nagano Prefecture, Japan, Using the Extreme Value Theory

The weather in Nagano Prefecture, Japan, can be roughly classified into four types according to principal component analysis and k-means clustering. We predicted the extreme values of the maximum daily and hourly precipitation in Nagano Prefecture using the extreme value theory. For the maximum daily precipitation, the vales of ξ in Matsumoto, Karuizawa, Sugadaira, and Saku were positive;therefore, it has no upper bound and tends to take large values. Therefore, it is dangerous and caution is required. The values of ξ in Nagano, Kisofukushima, and Minamishinano were determined to be zero, therefore, there was no upper limit, the probability of obtaining a large value was low, and caution was required. We predicted the maximum return levels for return periods of 10, 20, 50, and 100 years along with respective 95% confidence intervals in Nagano, Matsumoto, Karuizawa, Sugadaira, Saku, Kisofukushima, and Minamishinano. In Matsumoto, the 100-year return level was 182 mm, with a 95% CI [129, 236]. In Minamishinano, the 100-year return level was 285 mm, with a 95% CI [173, 398]. The 100-year return levels for the maximum daily rainfall were 285, 271, and 271 mm in Minamishinano, Saku, and Karuizawa, respectively, where the changes in the daily maximum rainfall were larger than those at other points. Because these values are large, caution is required during heavy rainfall. The 100-year return levels for the maximum daily and hourly precipitation were similar in Karuizawa and Saku. In Sugadaira, the 100-year return level for a maximum hourly rainfall of 107.2 mm was larger than the maximum daily rainfall. Hence, it is necessary to be careful about short-term rainfall events.

A Number Theoretic Function and Its Mean Value Computation

Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements

In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.

EXISTENCE THEOREMS FOR A SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH IMPULSES

In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).

Non-Acceleration Theorem in a Primitive Equation System: I. Acceleration of Zonal Mean Flow

Non-acceleration theorem in a primitive equation system is developed to investigate the influences of waves on the mean flow variation against external forcing. Numerical results show that mechanical forcing overwhelms thermal forcing in maintaining the mean flow in which the internal mechanical forcing associated with horizontal eddy flux of momentum plays the most important roles. Both internal forcing and external forcing are shown to be active and at the first place for the mean flow variations, whereas the forcing-induced mean meridional circulation is passive and secondary. It is also shown that the effects on mean flow of external mechanical forcing are concentrated in the lower troposphere, whereas those due to wave-mean flow interaction are more important in the upper troposphere. These act together and result in the vertically easterly shear in low latitudes and westerly shear in mid-latitudes. This vertical shear of mean flow is to some extent weakened by thermal forcing.

THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN

We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.

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.

An Existence Theorem of Solution for a Singular Third-order Two-point Boundary Value Problem

By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.

Some Hybrid Mean Values of a New Number Theoretic Function

Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）

Use of Support Vector Regression Based on Mean Impact Value Model to Identify Active Compounds in a Combination of Curcuma longa L.and Glycyrrhiza extracts

A support vector regression based on the mean impact value (MIV) model was constructed to identify the bioactive compounds inhibiting proliferation of HeLa cells in a combination of turmeric (Curcuma longa L.) and liquorice (Glycyrrhiza) extracts. The quantitative chemical fingerprint from 50 batches of turmeric and liquorice extracts was established using high performance liquid chromatography hyphenated to an ultraviolet visible detector. Qualitative results were obtained using ultra performance liquid chromatography coupled with electrospray ionization quadrupole time-of-flight tandem mass spectrometry. A total of 46 peaks (peaks 1–15 from turmeric and 16–46 from liquorice) were selected as “common peaks” for analysis. The inhibitory effect of the combined extracts on HeLa cells was measured by MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay. It was found that 15 compounds (peaks: 8, 12, 30, 24, 46, 11, 14, 9, 3, 1, 44, 18, 7, 45 and 43) possessing high absolute MIV exhibited a significant correlation with the cytotoxicity against HeLa cells; most of these have already been confirmed with potential cytotoxicity in previous research. The important potential application of the present model can be extended to help discover active compounds from complex herbal medicine prior to traditional bioassay-guided separation. It is considered that this could be a useful tool for re-developing herbal medicine based on the use of these active compounds. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.