Study on the estimation of Euler angles for Macao Science Satellite-1

The Euler angle estimation is a calibration method for vector data measured by the magnetometer on a satellite.It is used to find the relative rotation between the coordinate system of the magnetometer and the satellite(usually determined by Star Imagers).Before launch of the low-orbit,low-inclination Macao Science Satellite-1(known as MSS-1),we simulated the estimation of Euler angles by using the magnetic measurements of the in-orbit Swarm and China Seismo-Electromagnetic Satellite(noted as CSES),with various data combinations.In this study,11 data sets were designed to analyze the estimation results for the MSS-1 orbit by using a joint estimation method of the geomagnetic field model parameters and Euler angles.For the model results,we found that all the spatial power spectral lines showed behavior consistent with that of the CHAOS-7.8 model at low degrees(corresponding to large-scale magnetic signals).The spectra of models without global data coverage deviated much more(by a maximum of~10^(4) nT^(2))from those of the CHAOS-7.8 model at higher degrees.For models with global data coverage and with various data combinations,the spectral lines were distributed similarly.Moreover,the models with accordant power spectral distributions demonstrated different Euler angle estimations.As more vector data at higher latitudes were included,the estimated Euler angles varied monotonically in all three directions.The models with vector data in the same latitude range showed similar Euler angle results,regardless of whether the poleward scalar data were included.The largest value difference was found between the models using vector data within±40°latitudes and those using vector data within±60°latitudes,which reached to~28″.Therefore,we concluded that the inversion of the spherical harmonic Gauss coefficients in our tests was mainly affected by the spatial coverage range of the data,whereas the estimation of Euler angles largely depended on the latitude range where the vector data could be obtained.These results can be used for future in-flight data testing.We expect the estimation of Euler angles to improve as other methods are adopted.

Coupled DEM-FDM analyses of the effects of falling rock’s shape and impact angle on response of granular cushion and rock shed

Rock shed is an effective protection measure against rockfall.To investigate the influences of falling rock’s shape and impact angle on the impact effect of the cushioned rock shed,a modeling approach for a rock shed with a cushion layer using PFC-FLAC.The granular cushion is modeled as an aggregate of discrete non-cohesion particles,while the concrete plate and the beam are modeled as zones.The falling rock with different sphericities and impact angles is modeled as a rigid assembly.The numerical model is validated by comparing the simulation results with experimental and numerical results from previous literature.This model is applied to analyze the effects of rock shape and impact angle on the dynamic interaction effects between falling rock and cushioned rock shed,including the impact force,transmitted bottom force,penetration depth,and plate deflection.The numerical results show that the variation in the falling rock’s shape has different effects on the falling rock with different impact angles.These findings could support rock shed design by revealing the limitations of the assumptions in the past research,which may result in unsafe rock sheds for some rockfall cases.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

A Procedure for Trisecting an Acute Angle (Method 2)

This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.

Combination of Tilt-Angle and Euler Deconvolution Approaches to Determine Structural Features from Aeromagnetic Data Modeling over Akonolinga-Loum Area (Centre-East, Cameroon)

Aeromagnetic data for center-east Cameroon between the latitudes 3.5° to 4.5°N and longitudes 12° to 12.5°E are used to further study the subsurface area of this part of the geological Province of Central Africa and the Congo Craton. The GIS and GEOSOFT v6.5 softwares are used to treat the data. This analysis enabled us to explore our study area from surface right to the base. The Tilt Angle method is used to delineate geological structures and to estimate the depth. The Euler’s deconvolution method is used to estimate the specific depth of structural contacts. We estimate the northern boundary of the Congo Craton and southern boundary of the Pan-African starting from 3°7'N of West to 3°75'N of East. Its depth is estimated around 2.6 km for deep and 0.1 km for shallow while the direction is WSW-ENE and the NW slope varies from 30° to 60°. We obtain that main and minor lineaments exist throughout, from the surface to the base of the area with their principal direction being SW-NE. We also obtain the vertical gradient contact and the quasihorizontal contact. This is proof of the subduction of the Pan-African belt under the Congo Craton due to the intense collision which caused the rejuvenation of the crust. The main consequence of this collision is the formation of pudding and fold structures, beginning from the superficial part right to the base and which caused the intrusion of schistose, chlorite-schist, quartzite in the micaschist and the intrusions of gneiss and garnetiferous schist in the migmatite. In our study, we highlight the presence of 37 major and 523 minor lineaments that localize the circulation of minerals. The probable slope of the lineaments in the northern part of the region varies from 30° to 60° in a SE direction while in the southern part, and it varies from 30° to 60° in a NW direction.

基于Euler/N-S方程的跨音速非线性静气动弹性问题研究

在C-H网格的基础上,采用Jam eson的中心差分有限体积法求解Eu ler/N-S方程,采用结构影响系数法计算结构的弹性变形,用三角元面积加权法和常体积转换法(CVT)实现流固耦合。

任意曲线坐标系Euler方程S2流面的计算方法

为提高S2流面计算方法对涡轮复杂几何的适应性和计算能力,详细推导了任意正交曲线坐标系下应用于流道中心S2流面计算的Euler方程,提出了任意曲线坐标系Euler方程S2流面的计算方法,发展了适用于三阶精度总变差减小的差分格式的数学模型,结合了隐格式时间推进、Riemann问题求解等技术。在应用于带弧形凸起的流道及某直叶栅气动参数计算,并对某三级低压涡轮进行性能预测的结果表明:所提方法对激波具有较高的捕捉精度,能够较准确地获得叶栅气动参数分布,且与实验结果吻合良好;对于多级涡轮总性能参数和气动参数分布均有较高的计算精度,是一种可为涡轮设计提供快速、可靠的计算方法。

骨性Angle′s Ⅲ类错患者正畸手术前后下颌角矢量点位置的变化及意义

目的观察骨性Angle′sⅢ类错患者下颌角矢量点(Gov点)位置变化,并探讨其临床意义。方法取天津地区健康人29例为对照组,接受正手术治疗的骨性Angle′sⅢ类错畸形患者15例为观察组。均拍摄头颅侧位X线片,测量Gov点的座标。结果观察组术前、术后及对照组Gov点横坐标分别为(-4.54±0.51)、(-5.10±0.69)、(-5.02±0.35)cm,纵坐标分别为(-7.76±0.40)、(-7.65±0.57)、(-7.50±0.43)cm,观察组术前Gov点横、纵坐标与术后及对照组比较P均<0.05,观察组术后与对照组Gov点横、纵坐标比较P均>0.05。对照组下颌神经孔与Gov点间距为(1.35±0.16)cm,观察组术前为(1.27±0.19)cm,两组相比P>0.05。结论骨性Angle′sⅢ类错患者Gov点位置向前下移位,正手术后得以纠正。Gov点位置可能与下颌功能状态存在内在联系,可以作为正手术术前制定手术计划及术后评估矫治效果的指标。

应用Euler—Savary方程求盘形凸轮廓线的曲率半径

应用Euler-savary方程导出直动滚子从动件盘形凸轮廓线上任意点曲率半径的公式,解决平面机构啮合理论在凸轮机构中应用的问题。该公式不仅先于凸轮廓线方程求出廓线的曲率半径,还显示了曲率半径和压力角之间的内在联系,从而直接把强度条件和传力性能结合起来考虑,有利于简化该种凸轮机构的优化设计。

关于Euler函数的Makowski猜想

对于正整数n,设φ(n)是n的Euler函数.该文证明了:如果φ(n+3)=φ(n)+2,则n=2pr或2pr-3,其中p是适合p≡3(mod 4)的素数,r是正整数.

Some Kind of Equations Involving Euler＇s Function

For any given positive integer n ≥ 1, the Euler function φ（n） is defined to be the number of positive integers not exceeding n which are relatively prime to n. w（n） is defined to be the number of different prime divisors of n. Some kind of equations involving Euler＇s function is studied in the paper.

Modified viscocanalostomy in the Chinese population with open angle glaucoma: a 10-year follow-up results

AIM: To study the long-term efficacy and safety of modified viscocanalostomy in Chinese people with open angle glaucoma(OAG).METHODS: This retrospective study included a total of 100 eyes from 100 Chinese patients with medically uncontrolled OAG. All the patients underwent modified viscocanalostomy with injection of viscoelastic material in the surgically created ostia of Schlemm's canal(SC). The modifications included peeling of the inner wall of SC and the juxtacanalicular meshwork, use of mitomycin C, and loosely suturing the superficial scleral flap. Intraocular pressure(IOP), visual acuity, number of medications, laser goniopuncture data and complications were recorded. The definition of complete(qualified) success was an IOP equal to or lower than 21, 18, 16 mm Hg without(with or without) anti-glaucoma medications. RESULTS: The mean IOP was 33.5±9.9 mm Hg before surgery, 15.2±3.6 mm Hg(mean IOP reduction of 51%) at 5 y after surgery, and 15.6±2.8 mm Hg(mean IOP reduction of 49.9%) at 10 y after surgery(P<0.001). The number of anti-glaucoma medications dropped from 2.39±0.5 preoperatively to 0.47±0.8 at 5 y and 0.67±0.8 at 10 y postoperatively(P<0.001). The follow-up period was 104.5±37.0 mo. The qualified success rate for an IOP of 21, 18 or 16 mm Hg or less was 84% [95% confidence interval(CI): 0.80-0.88], 73%(95%CI: 0.68-0.78), and 59%(95%CI: 0.52-0.66) after 5 y, and 80%(95%CI: 0.76-0.84), 69%(95%CI: 0.64-0.74), 51%(95%CI: 0.44-0.58) after 10 y, respectively. There was a relationship between age, preoperative IOP and success rate(P<0.01, P<0.05). A total of 31 eyes(31.3%)in 31 patients underwent laser goniopuncture, decreasing the IOP from 22.9±4.3 mm Hg to 16.3±2.5 mm Hg(P<0.01). Neither blebitis nor endophthalmitis occurred.CONCLUSION: Modified viscocanalostomy could be performed to lower IOP, decrease multiple anti-glaucoma drops use as well. It's a safe procedure with less complications over 10 y in Chinese individuals with OAG.

Elevated urine formaldehyde in elderly patients with primary open angle glaucoma

AIM：To investigate the risk factor of primary open angle glaucoma（POAG）,which is the leading cause of irreversible blindness worldwide.An abnormally high level of endogenous formaldehyde（FA） has recently been found correlated with cell death and neurodegenerative disease,raising the possibility of a putative correlation of abnormal endogenous FA with POAG.· METHODS：Thirty-four elderly patients with POAG and sixteen healthy controls were enrolled.Glaucomatous visual defects were present at both the functional（visual field） and structural[retinal nerve fiber layer（RNFL）thickness]levels.Morning urine samples were obtained and were analyzed by high-performance liquid chromatography（HPLC） to detect the endogenous FA level in a double blind manner.· RESULTS：Patients with POAG（P 〈0.05） had significantly higher urine FA levels.The urine FA level of patients with severe visual field defects[mean deviation（MD）≥12 dB]was significantly（P〈0.001） greater than that of patients with mild to moderate defects（MD〈12 dB）.By optical coherence tomography（OCT）,the superior and inferior RNFL thickness of POAG group was significantly（P〈0.001） thinner than in controls.Furthermore,the superior and inferior thinning of the RNFL was correlated with the elevation of urine FA concentration.CONCLUSION：Endogenous FA level is positively correlated with the neuronal defects of POAG.

高阶熵条件格式下Euler方程与N-S方程的混合算法

针对在工程问题中使用N S方程计算量大的问题 ,提出只在粘性作用显著的局部区域求解N S方程 ,在流场的其余部分采用Euler方程计算的办法来模拟具有复杂外形的流动问题 ,并提出了一种基于高阶熵条件格式的算子分裂算法 .应用所构造的算法对绕迫击炮弹的亚、跨超声速流动进行了模拟计算 .计算结果与试验数据的对比表明 ,所提出的方法是切实可行的 .

Some Remarks for the Relationships between the Generalized Bernoulli and Euler Polynomials

In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.

颅骨点云曲面重建的Euler’s Elastica模型

为从具有复杂拓扑关系的颅骨点云数据中重建精确、光滑的隐式曲面,提出了基于Euler’s Elastica的变分水平集方法.首先,将Euler’s Elastica作为正则化约束引入变分能量泛函,采用增广拉格朗日方法将变分能量泛函最小化问题转化为一系列子问题;其次,分别采用广义软阈值公式、解析公式和快速傅里叶变换求解;最后,在计算过程中采用投影算法,有效地避免了水平集函数的重新初始化过程.实验结果表明,相较于现有方法,所提基于Euler’s Elastica的变分水平集方法具有更好的收敛性和有效性,能够提高重建的精确性,避免曲面边缘的缺失.

包含广义Euler函数φ3（n）和Smarandache函数S（n）的一方程的解

令φe(n)为广义Euler函数,S(n)为Smarandache函数,其中e为正整数。探讨包含广义Euler函数φ3(n)和Smarandache函数S(n)的方程φ3(n)=S(n8)的可解性问题,利用这2个数论函数的有关性质,给出了这一方程在φ3(n)=3-1φ(n)条件下无正整数解的结论。

The Use of Edge Enhancement Methods and Euler Deconvolution to Estimate an Ore Deposit Depth from Gravity Data

The Hercynian massif of the central Jebilet (Morocco) is characterized by the outcrop of many gossans with great economic importance. This work focuses on interpreting gravity data of Benslimane gossan, located about thirty kilometres to the North-West of Marrakech. The residual gravity map of the study area highlights several anomalies which coincide with the mining and geological contexts. Applying edge detection methods, for example, tilt angle derivative (TDR), the total horizontal derivative of the tilt angle derivative (HDR_TDR) and the 3D Euler deconvolution, allowed us to estimate the depth of the Benslimane deposit. As a result, the average depth of the ore deposit was estimated to exceed 200 m. The results are promising, and the processing methods must be applied to the other gossan in the Jebilet massif for further exploration studies.

Automatic DEXP method derived from Euler’s Homogeneity equation

The depth from extreme points(DEXP)method can be used for estimating source depths and providing a rough image as a starting model for inversion.However,the application of the DEXP method is limited by the lack of prior information regarding the structural index.Herein,we describe an automatic DEXP method derived from Euler’s Homogeneity equation,and we call it the Euler–DEXP method.We prove that its scaling field is independent of structural indices,and the scaling exponent is a constant for any potential field or its derivative.Therefore,we can simultaneously estimate source depths with diff erent geometries in one DEXP image.The implementation of the Euler–DEXP method is fully automatic.The structural index can be subsequently determined by utilizing the estimated depth.This method has been tested using synthetic cases with single and multiple sources.All estimated solutions are in accordance with theoretical source parameters.We demonstrate the practicability of the Euler–DEXP method with the gravity field data of the Hastings Salt Dome.The results ultimately represent a better understanding of the geometry and depth of the salt dome.

Solution to Stokes-Maxwell-Euler Differential Equation

Solutions to the differential equation in Smith’s Prize Examination taken by Maxwell are discussed. It was a competitive examination using which skill full students were identified and James Clerk Maxwell was one of them. He later formulated the theory of Electromagnetism and predicted the light speed & its value was subsequently confirmed by experiments. Light travel in a direction perpendicular to oscillating electric and magnetic field through a vacuum from sun. In the same exam paper, Maxwell answered the question related to Stokes Theorem of vector calculus which was used in the formalism of Electromagnetic theory.