An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions by Yan Xia, Martin Berger, Sebastian Bauer, Shiyang Hu, Andre Aichert, Andreas Maier

“…The forward projection of the optimized ellipse can be used to complete the truncation data. …”
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Reflection of circularly polarized light from a CdS semiconductor crystal near the exciton resonance taking into account spatial dispersion by Valeriy V. Yatsyshen, Irina I. Borodina

“…The use of circularly polarized light carries additional information due to the change in the polarization ellipse upon reflection. Aim. The paper presents the results of calculations of the frequency and angular spectra of the ellipsometric parameters of reflected light for a CdS semiconductor crystal near the exciton resonance, taking into account spatial dispersion. …”
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A method for estimating the polymer gel granule volume by an optical technique by M.G. Tokmachev

“…It is shown that by estimating the outline of an ellipse-shaped granule, the algorithm determines its volume with a relative error of 0.4 %, which corresponds to an error in determining the granule diameter of 1 pixel.…”
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Elliptic Search of Self Healing Restoration on ATM Networks by Li Shiju Mei Liubo Dai Wenqi

“…Based on analyses of self healing restoration,this paper presents the elliptic algorithm which reduces search fields of useless messages,and simulates the process of selfhealing restoration by computes Results show that the search region of ellipse is less than the region of mono and dual direction,the effects on nodes number are small and the search area can be rational set The cost is that it must be to construct the table of minimal search region in every node…”
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Free In-Plane Vibration of Super-Elliptical Plates by Murat Altekin

“…A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. …”
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Finite Element Analysis of the Temperature Field of Face Gear Dish Wheel Grinding by Ming Xingzu, Zhao Lei, Wang Wei, Li Mande

“…According to the principle of face gear dish wheel grinding,by using the theory of instantaneous contact ellipse,the grinding basic parameters are solved,the finite element model of gear grinding temperature field is set up and the gear grinding transient temperature field finite element simulation is carried out.Through the simulation and experimental analysis,the basis for basic parameter optimization,improve the quality of grinding and further research of face gear grinding temperature field is provided.…”
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Hydraulic Performance Analysis and Design of Torus of Flat Hydraulic Torque Converter by Zhu Wenjie, Wu Guangqiang

“…The flat torus new design method based on the ellipse is used. Four kinds of different flatness ratio hydraulic torque converter are designed. …”
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Least Squares Problems with Absolute Quadratic Constraints by R. Schöne, T. Hanning

“…We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. …”
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Evaluation of CME Arrival Prediction Using Ensemble Modeling Based on Heliospheric Imaging Observations by Tanja Amerstorfer, Jürgen Hinterreiter, Martin A. Reiss, Christian Möstl, Jackie A. Davies, Rachel L. Bailey, Andreas J. Weiss, Mateja Dumbović, Maike Bauer, Ute V. Amerstorfer, Richard A. Harrison

“…We believe that by exploiting this capability, instead of relying on coronagraph observations only, it is possible to improve today's CME arrival time predictions. The ELlipse Evolution model based on HI observations (ELEvoHI) assumes that the CME frontal shape within the ecliptic plane is an ellipse and allows the CME to adjust to the ambient solar wind speed; that is, it is drag based. …”
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Optimal Tooth Surface Correction of Internal Helical Gear and Mesh Simulation by Su Jianxin, Deng Xiaozhong, Ren Xiaozhong, Wei Bingyang, Xu Zengjun

“…The numerical solution is substituted into the mesh equation to solve the transmission error,tooth contact trace and contact ellipse,consequently realized the mesh simulation of the internal helical gears which tooth surface is carried out.…”
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Simulation and Analysis of the Elliptical Gear Used in Rack Type Pumping Unit by Tian Zhenzhen, Peng Yong, Zhang Haokun

“…According to the geometric characteristics of the elliptical gear,with different eccentricity ratio of ellipse,the different transmission ratio curve is got,and then the variable speed motion of pumping unit is completed. …”
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Geometric Meshing Simulation Analysis of Zero Spiral Bevel Gear by Zhou Jiaojun

“…Then,the major axis of instantaneous contact ellipse is calculated based on differential geometry. …”
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Research of Steady State Temperature Field of Spiral Bevel Gear with Different Tooth Surface Structures by Hui Cheng, Zhouyang Li, Sanmin Wang

“…And the influence law of the direction of the bevel gear tooth surface contact trace，the length of the semi-major axis of the contact ellipse and the first derivative of the transmission ratio on the temperature field of the bevel gear is studied and analyzed.…”
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Analysis of the Influence of Roundness of Probe on the Accuracy of Gear Polar Coordinate Measuring Method by Yubin Teng, Tao Sun

“…In order to solve this problem，an ellipse ball probe is used to simulate the roundness error of the ball probe，and a calculation method is proposed to calculate the measurement error produced by the ellipsoid probe itself. …”
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Integrated ISPH approach with artificial neural network for magnetic influences on double diffusion of a non-Newtonian NEPCM in a curvilinear cavity by Weaam Alhejaili, Munirah Alotaibi, Abdelraheem M. Aly

“…Two cases of boundary conditions included $ \left({T}_{h}\&{C}_{h}\right) $ on top/bottom walls and $ \left({T}_{c}\&{C}_{c}\right) $ on vertical walls and inner ellipse for C1. The boundary walls of a curvilinear cavity were kept at $ \left({T}_{h}\&{C}_{h}\right) $ and the inner ellipse was maintained at $ \left({T}_{c}\&{C}_{c}\right) $ for C2. …”
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Study on the evolution of the spatial patterns and driving factors of national agricultural cultural heritage in China. by Lifei Xu, Yuyu Liao, Jun Liu

“…During the study period, the X axis of the standard deviation ellipse was always greater than the Y axis, but the difference between the X and Y axes was small, indicating that the spatial distribution direction was northeast-southwest, but the directionality was weak. …”
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Identification of failure behaviors of underground structures under dynamic loading using machine learning by Chun Zhu, Yingze Xu, Manchao He, Yujing Jiang, Murat Karakus, Lihua Hu, Yalong Jiang, Fuqiang Ren

“…Split Hopkins Pressure Bar (SHPB) tests on granite with holes of different shapes (rectangle, circle, vertical ellipse (elliptical short (ES) axis parallel to the impact load direction), and horizontal ellipse (elliptical long (EL) axis parallel to the impact load direction)) were carried out. …”
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Constraints for Jaccard index-based rotational symmetry focus position in binary images by N.A. Lomov, O.S. Seredin, D.V. Liakhov, O.A. Kushnir

“…The smallest circumscribed circle or ellipse and sets of concentric circles and ellipses produced by the principal component analysis were used as the approximating figure. …”
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Cycloid Gear Profile Modification based on Elliptical Method by Chen Zhilong, Wang Jun, Qin Zhengzheng, Zhao Daxing, Wang Quan

“…Compared with the commonly used method of tooth profile modification,the modified tooth profile curve is much closer to the complete conjugate tooth profile on the main meshing areas,and the meshing clearance between the cycloid wheel and the pin wheel can be made adjustment by controlling the shape parameters of the ellipse,which is simple and flexible. The normal tooth profile clearance,initial meshing clearance,contact stress and backlash are analyzed to verify the rationality of the modified method.…”
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A Milling Method for Elliptic-arc-tooth-trace Cylindrical Gear by Zhao Kunpeng, Song Aiping, Dou Chaoran, Zi Hao Chu, Yuegang

“…The profiles of the gear machined by the oblique mounting tools are all involute in the radial sections,and the expansion curve of the tooth trace on the reference cylindrical surface is part of the ellipse. The convex and the concave tooth trace have the same geometric parameters. …”
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