关于地轴二分点进动的讨论

地球自转轴相对于黄道法线的进动,天文学上叫二分点进动。这种进动的周期很长,到目前为止测量值约为25800年。对于这种进动,过去曾有人进行了研究,但得出的是近似不变的力矩公式。本文采用另一种方法,得出了变化的力矩公式,并与前一种方法得出的结果进行了对比。

聚焦过程追本溯源优化策略浸润思想--对一道新定义“二分点”问题的评析与思考

一、问题提出笔者以2022年朝阳区九年级第一学期期末学业水平调研新定义“二分点”为载体,展现学生获取、理解、应用新定义“二分点”进行画图、运算、推理,进而解决问题的全貌,聚焦过程;透析解法的不同思路,追本溯源;提炼解题的一般步骤,优化策略.

例说“二分法”思想的应用

"二分法"是高中数学必修内容之一,是现代信息技术与函数、方程知识的有机整合,是求方程近似解的常用方法.利用"二分法"可以帮助我们轻松、快捷解决一些相关的问题.

铅球 链球 铁饼投掷区的简易划法

《田径竞赛规则》规定,铅球和链球投掷圈内沿直径是2.135米(公差为±0.5厘米),铁饼投掷圈内沿直径是2.50米(公差为±0.5厘米)。三者的投掷区角度均为40°,角度线的交点在投掷圈的中心。根据《田径竞赛规则》规定,这个40°角的投掷区如何划法?下面介绍两种简易方法供参考。 1.等分圆圈法(如图一) 铅球和链球投掷区的划法:铅球和链球投掷圈内沿直径是1.0675米(公差为±0.

广西河池供电局:减少停电时间 管理出实招

山险崖石横,停电难下降,怎么办？河池供电局三招制敌,剑指县级供电企业客户平均停电时间,2014年各县指标平均下降70%左右,截至目前同比下降74.57%。第一招：推行停电管控时钟针对县级供电企业客户平均停电时间关键指标居高难下的难题,该局以大化供电公司为试点,结合公司管理实际,总结分析指标管控存在的问题,指导其设计完成供电所客户停电时间停电管控时钟,并在各供电所试点应用。

世界自然科学发展史上的遗憾

世界自然科学发展史上的遗憾在世界自然科学发展的历史长河中，物理学家牛顿可称为一颗耀眼的明星。但是在他大量的科学发现背后，曾有过不义之举，此为世人所始料不及。公元１６８７年，牛顿的《自然哲学的数学原理》一书确立了现代科学的目标、方法和范围。就是这样一位...

Limit cycle problem for quadratic differential system x = -y + lx^2 + mxy, y =x(1 +ax +by)

The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.

HESSIAN MATRIX BASED SADDLE POINT DETECTION FOR GRANULES SEGMENTATION IN 2D IMAGE

Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ago. In this paper, a new granule segmentation algorithm is developed using saddle point as the cutting point. The image is binarized and then sequentially eroded to form a gray-scale topographic counterpart, followed by using Hessian matrix computation to search for the saddle point. The segmentation is performed by cutting through the saddle point and along the maximal gradient path on the topographic surface. The results of the algorithm test on the given real images indicate certain superiorities in both the segmenting robustness and execution time to the referenced methods.

The Existence of Solutions of Three-point Boundary Value Problems for Second Order Impulsive Differential Equation

We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.

Enthalpy and Heat Capacity Data for 1,2-Cyclohexanediol

The thermodynamic properties of different geometric structures of 1,2-cyclohexanediol which were rarely reported in literature, such as combustion enthalpy, formation enthalpy, melting enthalpy and heat ca-pacities, were determined by NETZSCH DSC 204 Scanning Calorimeter. The relationship between the melting point and the composition for the mixture system of cis-1,2-cyclohexanediol and trans-1,2-cyclohexanediol was investigated and corresponding phase diagram was obtained. 'The melting enthalpies of both cis-1,2-cyclohexanediol and trans-1,2-cyclohexanediol are 20.265kJ·mol-1 and 16.368kJ·mol-1 respectively. The standard combustion enthalpies of cia- and trans-1,2-cyclohexaneddiol were determined by calorimeter. They are respec-tively -3507.043 kJ·mol-1 and - 3497.8 kJ·mol-1 at 298.15 K.The standard formation enthalpies are respectively 568.997 kJ·mol-1 and 578.240 kJ·mol-1 for cia- and trans -1,2-cyclohexaneddiol.

Support vector machine for prediction of meiotic recombination hotspots and coldspots in Saccharomyces cerevisiae

A novel method for predicting hotspots and coldspots using support vector machine （SVM） based on statistical learning theory is developed. This method is applied to published 303 hot and 48 cold open reading frames （ORFs） in Saccharomyces cerevisiae. The sequence features of general dinucleotide abundance and dinucleotide abundance based on codon usage are extracted, and then the data sets are classified with different parameters and kernel functions combined with the method of two-fold cross validation. The result indicates that 87.47% accuracy can be reached when classifying hot and cold ORF sequences with the kernel of radial basis function combined with dinucleotide abundance based on codon usage.

Morphogenetic Processes in Division of Uronemella filificum (Ciliophora, Scuticociliatida)

The morphogenetic processes of Uronemella filificum (Kahl, 1931) Song and Wilbert ①, were studied using protargol method. The stomatogenesis of U. filificum can be summarized as follows: membranelles 1-2, paroral membrane and scutica of the opisthe originate from the parental paroral membrane, while membranelle 3 in the opisthe develops from the parental scutica. The paroral membrane of the proter developes from the parental paroral membrane. The stomatogenetic sequences are similar to the previous descriptions for other related taxa. The phylogenetic position of Uronematidae is discussed in the light of morphogenetic data obtained.

Design of Wind Turbine Torque Controller with Second‑Order Integral Sliding Mode Based on VGWO Algorithm

A robust control strategy using the second-order integral sliding mode control(SOISMC)based on the variable speed grey wolf optimization(VGWO)is proposed.The aim is to maximize the wind power extraction of wind turbine.Firstly,according to the uncertainty model of wind turbine,a SOISMC torque controller with fast convergence speed,strong robustness and effective chattering reduction is designed,which ensures that the torque controller can effectively track the reference speed.Secondly,given the strong local search ability of the grey wolf optimization(GWO)and the fast convergence speed and strong global search ability of the particle swarm optimization(PSO),the speed component of PSO is introduced into GWO,and VGWO with fast convergence speed,high solution accuracy and strong global search ability is used to optimize the parameters of wind turbine torque controller.Finally,the simulation is implemented based on Simulink/SimPowerSystem.The results demonstrate the effectiveness of the proposed strategy under both external disturbance and model uncertainty.

Rapid determination of production date for green tea by near-infrared spectroscopy

Coupled with partial least squares(PLS),near infrared(NIR)spectroscopy was applied to develop a fast and nondestructive method to identify the production date of Rizhao green tea aiming at the deficiencies of the existing methods.In the modeling process,the raw spectra were first processed by five-point smoothing and first derivative.And then,moving window back propagation artificial neural network(MW-BP-ANN)was applied to select the characteristic spectral variables.After that,the calibration model was built by PLS,and the optimum model was achieved when 9 principal component scores(PCs)were included.The performances of the calibration models were evaluated according to root mean square error of predictionεRMSEP,correlation coefficient(C p)and residual prediction deviation(σRPD).The optimum results of the calibration model was achieved,andεRMSEP=19.965,C p=0.943 andσRPD=3.07.The overall results sufficiently demonstrate that NIR spectroscopy combined with PLS can be efficiently applied in the rapid identification of green tea production date.

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM (III)_(m=0) HAVING THREE ANTI-SADDLES (I)

For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 the system has one saddleN(0,1/n) and three anti-saddles.

Judicious partitions of weighted hypergraphs

Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.

L_p-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE

The notion of Lp-dichotomy for linear differential equations with possibly unbounded oper-ator is introduced. By help of Banach fixed point theorem sufficient conditions for the existenceof bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part areobtained.