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1
Christensen, A. P., and A. A. Shabana. "Exact Modeling of the Spatial Rigid Body Inertia Using the Finite Element Method." Journal of Vibration and Acoustics 120, no. 3 (1998): 650–57. http://dx.doi.org/10.1115/1.2893879.
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In the classical finite element literature beams and plates are not considered as isoparametric elements since infinitesimal rotations are used as nodal coordinates. As a consequence, exact modeling of an arbitrary rigid body displacement cannot be obtained, and rigid body motion does not lead to zero strain. In order to circumvent this problem in flexible multibody simulations, an intermediate element coordinate system, which has an origin rigidly attached to the origin of the deformable body coordinate system and has axes which are parallel to the axes of the element coordinate system in the undeformed configuration was introduced. Using this intermediate element coordinate system and the fact that conventional beam and plate shape functions can describe an arbitrary rigid body translation, an exact modeling of the rigid body inertia can be obtained. The large rigid body translation and rotational displacements can be described using a set of reference coordinates that define the location of the origin and the orientation of the deformable body coordinate system. On the other hand, as demonstrated in this investigation, the incremental finite element formulations do not lead to exact modeling of the spatial rigid body mass moments and products of inertia when the structures move as rigid bodies, and such formulations do not lead to the correct rigid body equations of motion. The correct equations of motion, however, can be obtained if the coordinates are defined in terms of global slopes. Using this new definition of the element coordinates, an absolute nodal coordinate formulation that leads to a constant mass matrix for the element can be developed. Using this formulation, in which no infinitesimal or finite rotations are used as nodal coordinates, beam and plate elements can be treated as isoparametric elements.
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Templeton, G. H., G. B. Seibert, M. Ramanathan, S. S. Cassidy, and R. Johnson. "Left ventricular coordinate systems." American Journal of Physiology-Heart and Circulatory Physiology 257, no. 3 (1989): H1025—H1031. http://dx.doi.org/10.1152/ajpheart.1989.257.3.h1025.
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Three-dimensional kinematics of radiopaque markers in anterior, posterior, septal, and lateral regions of a major equatorial plane were evaluated in anesthetized dogs by biplane fluoroscopy. Stationary coordinate systems measured marker locations recorded during diastole and systole from a contractile origin at the center of contraction at end systole and from a geometric origin at the intersection with the equatorial plane of the ventricular long axis at end diastole. A time-indexed system measured marker locations at end diastole and at end systole, respectively, from the locations of the geometric origin at end diastole and end systole. Compared to the stationary system with the geometric origin, both the stationary system with the contractile origin and the time-indexed system reduced the variability of the radial components of the contractile displacements between ventricular regions. In contrast to the other two systems, the system with the contractile origin reduced circumferential components to values not significantly different from zero. These results indicate that 1) abnormally contracting regions of the ventricle may be located and their size measured by determining the region where the radial component differs from that in the rest of the equatorial plane and 2) rotation in a major equatorial plane of the ventricle is significant, but the influence of rotation can be minimized by referencing ventricular dimensions to a coordinate system with an origin at the center of contraction.
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Vinogradov, A. V. "Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011." Geodesy and Cartography 929, no. 11 (2017): 2–10. http://dx.doi.org/10.22389/0016-7126-2017-929-11-2-10.
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Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.
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Bhagavatula, Ramkamal, Olu A. Fashesan, Lloyd R. Heinze, and James F. Lea. "A Computational Method for Planar Kinematic Analysis of Beam Pumping Units." Journal of Energy Resources Technology 129, no. 4 (2007): 300–306. http://dx.doi.org/10.1115/1.2790981.
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A generalized computational method for planar kinematic analysis of pumping units is presented in this study. In this method, a local coordinate system is assigned to each body with respect to a fixed global coordinate system. The position of each point in a body is determined by specifying the global translational coordinates of the local coordinate system origin and its rotational angle relative to the global coordinate system. Constraint equations of motion are developed using the vector of coordinates of the connected bodies. These equations are solved to yield the position, velocity, and acceleration of the individual linkages at each instance of time. Both rotational and translational types of joints are considered in the analysis. The translational joint analysis is not discussed in this paper as they are not applicable for beam pumping units. This method can be used as an effective tool for pumping unit design and optimization. An example is provided to show the application of this method.
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Chunmei, Chen, Li Qingyuan, and Jia Huiling. "Effect on Application by Mechanism of GDI Rendering Functions and Solutions." International Journal of Geology and Earth Sciences 1, no. 3 (2015): 24–45. https://doi.org/10.5281/zenodo.1494775.
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GDI drawing-functions in Windows API were analyzed and found that GDI drawing-function mapped the world coordinate system (Cartesian coordinate system) origin (0, 0) to the pixel center between (0, 0) and (1, 1) of the device coordinate system (screen coordinates). It pointed out that in order to maintain the same graphic geometric characteristics and avoiding overprinting, GDI drawing functions compromised with the endpoints and the boundary pixels, which caused some strange phenomenon many programmers have not found and it was difficult to understand. In response to these phenomena, explanations are given. In addition, the effect on some applications is pointed out and solutions are proposed.
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Murray, C. A. "The Origin of Celestial Coordinates." Symposium - International Astronomical Union 141 (1990): 51–59. http://dx.doi.org/10.1017/s0074180900086162.
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In 1978, Guinot proposed that, for studies of Earth rotation, the zero point of the apparent “right ascension” coordinate on the true equator should be so chosen that the rate of change of its hour angle is exactly proportional to the inertial rate of rotation of the Earth. It has been subsequently suggested that this concept of the “non-rotating origin” supersede the equinox quite generally as the origin of celestial coordinates. Since this proposal was first put forward, there has been much discussion, and some criticism, from Aoki and his colleagues, both published and in private correspondence. Some of the arguments for and against Guinot's proposal are discussed, as a contribution to the wider debate on reference systems now being carried out under the auspices of the IAU.
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Wang, Xian Feng, Feng Xing, Makoto Obata, and Yoshiaki Goto. "Position Determination in Three Dimensional Structural Testing System." Advanced Materials Research 163-167 (December 2010): 4478–81. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.4478.
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A three dimensional structural testing system for static and pseudo dynamic test is developed, in which a coordinate system has been used in the measurement. The center of the ball joint hinge in an almost neutral position for the displacements of three actuators was the origin. However n process since the initial error cannot be controlled. This makes it difficult to exactly compare the results for different coordinate systems though the error is small. In this paper, to eliminate this difference, we set up a new coordinate system with the origin being the point of absolute zero of the actuator displacements. Since the origin usually cannot be measured directly, the new coordinate system is determined by appending three unknowns and a set of equations at the origin. The transformation between the new coordinate system and the previous one is obtained using a shift and Eulerian angles.
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Zhang Zhong-Zheng and Cheng Xiao-Fang. "Dual-origin coordinate system for solar cells." Acta Physica Sinica 63, no. 11 (2014): 118801. http://dx.doi.org/10.7498/aps.63.118801.
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Delčev, Siniša, Gábor Timár, and Miran Kuhar. "The origin of the d48 coordinate system." Geodetski vestnik 58, no. 04 (2014): 681–94. http://dx.doi.org/10.15292/geodetski-vestnik.2014.04.681-694.
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Vinogradov, A. V. "Determining the parameters of a local coordinate system with a non-standard longitude of the central meridian. Analysis of existing methods." Geodesy and Cartography 960, no. 6 (2020): 2–12. http://dx.doi.org/10.22389/0016-7126-2020-960-6-2-12.
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Processing the results of topographic and geodetic works is performed in local coordinate systems. The parameters of the local coordinate systems were established on the basis of SK-42 or SK-63 systems. At present, it is necessary to set new communication parameters with coordinate systems SK-95 and GSK-2011. In many MCSs, the central meridians do not coincide with the origin, and the coordinates of the starting points were obtained from the catalogs of the preliminary calculation geodetic network. To establish the new communication parameters, it is necessary to determine the longitude of the central meridian MCS in SK-95 and GSK-2011 systems. To find the errors in calculating the longitude of the central meridian, MCS the models were constructed with different positions of the central meridian relative to the origin. The longitude was calculated using well-known and new formulas and methods. Errors in calculating the longitude of the MSC are systematic. An increase in the calculation volume does not exclude the influence of systematic errors, reaching 4ʺ. For some lines, they make 8ʺ.
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Cui, Gang Wei, Jia Lu, Yu Feng Gu, Dong Gao, Hong Cai Wang, and Chun Cheng Li. "Research on Real-Time Synthetic Error Compensation Principle for CNC Machine Tool." Advanced Materials Research 314-316 (August 2011): 2454–57. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.2454.
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Synthetic error of CNC machine tool, mainly including geometric error and thermal error, is generally affected by many factors. And temperatures that include environment temperature and temperature asymmetry of machine tool are most important factor. Aiming at geometric error and thermal error mainly, this paper proposed a real-time synthetic error compensation solution for CNC machine tool based on Differential Resolver Function (DRF). The principle of this solution is offsetting the origin of workpiece coordinate system when implementing the NC code in machine tool. After real-timely collecting machine tool coordinates position and thermal key points’ temperatures, synthetic errors are calculated by the synthetic model that is beforehand constructed and stored in compensation equipment, and then the pulses that represent coordinate system origin offsetting value are generated and sent into NC system by DRF to realize synthetic error compensation of CNC machine tool.
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Iversen, Einar, Bjørn Ursin, Teemu Saksala, Joonas Ilmavirta, and Maarten V. de Hoop. "Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: transformation between Cartesian and ray-centred coordinates." Geophysical Journal International 226, no. 2 (2021): 893–927. http://dx.doi.org/10.1093/gji/ggab151.
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SUMMARY Within the field of seismic modelling in anisotropic media, dynamic ray tracing is a powerful technique for computation of amplitude and phase properties of the high-frequency Green’s function. Dynamic ray tracing is based on solving a system of Hamilton–Jacobi perturbation equations, which may be expressed in different 3-D coordinate systems. We consider two particular coordinate systems; a Cartesian coordinate system with a fixed origin and a curvilinear ray-centred coordinate system associated with a reference ray. For each system we form the corresponding 6-D phase spaces, which encapsulate six degrees of freedom in the variation of position and momentum. The formulation of (conventional) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between Cartesian and ray-centred phase-space perturbations. Such transformation can also be used for defining initial conditions for dynamic ray tracing in Cartesian coordinates and for obtaining the coefficients involved in two-point traveltime extrapolation. As a step towards extending dynamic ray tracing in ray-centred coordinates to higher orders we establish detailed information about the higher-order properties of the transformation between the Cartesian and ray-centred phase-space perturbations. By numerical examples, we (1) visualize the validity limits of the ray-centred coordinate system, (2) demonstrate the transformation of higher-order derivatives of traveltime from Cartesian to ray-centred coordinates and (3) address the stability of function value and derivatives of volumetric parameters in a higher-order representation of the subsurface model.
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Wang, Yuezong, Zhaodong Wang, Mengfei Guo, and Xin Zhang. "Research on an automatic leveling method with a feedback mode for a parallel 3D printer." Rapid Prototyping Journal 25, no. 7 (2019): 1250–65. http://dx.doi.org/10.1108/rpj-03-2019-0052.
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Purpose The purpose of this study is to propose an automatic leveling method for a printing platform based on a three-point coordinate feedback. The proposed method is used in fused deposition modeling additive manufacturing systems. The coordinate error of the leveled plane is constrained to within  ± 0.2 mm, which is less than the printed layer thickness. Design/methodology/approach First, the model of the forward and inverse solutions of the parallel arm is obtained based on the principles of vector algebra. Second, the automatic leveling mechanism for collecting the z-coordinate is designed. The best position of the virtual origin plane is obtained by comparing the z-coordinates of the test points. Finally, after making multiple adjustments through a closed-loop z-coordinate feedback, the parallelism of the printing plane and the virtual origin plane is limited to an effective range. Findings The experimental results show that after three leveling attempts, the z-coordinate of the test points can be constrained to within  ± 0.2 mm, which shows that this method can effectively achieve automatic leveling in a delta three-dimensional (3D) printer. Originality/value This study presents a novel and distinctive delta 3D printer leveling system by designing a leveling mechanism and a leveling algorithm. The method uses a closed-loop feedback mode to make the leveling process simple, convenient and efficient without requiring major changes to the printer. The error after leveling is less than the printed layer thickness, which fully guarantees the accuracy of the leveling process.
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Zhou, Xiaobing. "Analytic solution of the gravity anomaly of irregular 2D masses with density contrast varying as a 2D polynomial function." GEOPHYSICS 75, no. 2 (2010): I11—I19. http://dx.doi.org/10.1190/1.3294699.
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The analytic solution of the gravity anomaly caused by a 2D irregular mass body with the density contrast varying as a polynomial function in the horizontal and vertical directions is extrapolated from a historical version in which the analytic solution for the gravity anomaly was given only at the origin of the coordinate system to any point for the density function in terms of variables relative to that origin. To calculate the gravity anomaly at stations that are not at origins, a coordinate transformation is performed, in which case the polynomial density contrast function must also be expressed in the transformed coordinates, or a transformed solution must be obtained. These analytic solutions can be obtained at any station using (1) a solution transformation method, in which the density function and boundary of a mass body are kept intact, or (2) a coordinate transformation method, in which polynomial coefficient and boundary of a mass body are transformed accordingly. The issue of singularity and instability of the analytic methods has been related to case studies. Caution should be exercised in modeling or interpreting the gravity survey data using the analytic methods for large target-distance-to-target-size ratios outside the range of numerical stability. Compared with other published methods, the analytic solution results agree very well with other numerical or seminumerical methods, indicating the solution is correct and can be applied for any gravity anomaly calculation caused by an irregular 2D mass body with the density-contrast approximated as a polynomial function of horizontal position and/or vertical position when the observation is within the range of numerical stability.
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Zhao, Hao, Renbo Xia, Yueling Chen, Liming Tao, Daixian Zhao, and Tianyu Zhang. "A Fast Conversion Method of Tube Coordinates." Highlights in Science, Engineering and Technology 15 (November 26, 2022): 16–21. http://dx.doi.org/10.54097/hset.v15i.2197.
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Inspired by the idea of the coordinate transformation of the robot arm, the tube structure is analogized to the robot arm structure, and the conversion method of the tube bend processing parameters LRA to the three-dimensional coordinate points is obtained. The method first regards the tube as a “mechanical arm”; then, using the similarity of the LRA processing parameters and D-H parameters, all the LRA parameters are converted into D-H parameters; finally, the D-H parameter method is applied to calculate the distance between each axis of the " mechanical arm ". If the first space coordinate point is defined as the origin of the base coordinate system , then the position of the origin of other coordinate systems in the base coordinate system can be obtained; It has been proved by experiments that this method fast and feasible.
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Halynskyi, V. P. "Marching algorithm to calculate supersonic flow past a tilting-nose rocket." Technical mechanics 2022, no. 1 (2022): 16–25. http://dx.doi.org/10.15407/itm2022.01.016.
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This paper presents a marching algorithm for the calculation of supersonic flow past a tilting-nose rocket. A feature of the algorithm is that the marching direction of supersonic flow calculation for the nose does not coincide with that for the main part of the rocket surface. Because of this, at first flow past the nose is calculated in a cylindrical coordinate system, the flow field parameters being stored at marching cross-sections. The start and the end of the parameter storage interval in the flow field are determined from the condition of the intersection of the bow shock wave with a plane in which an initial flow field is to be specified for the calculation of flow past the main part of the rocket surface. The flow field is interpolated in two stages, First, in the cylindrical coordinate system bound to the main part of the rocket surface in the initial data plane, the radial coordinates of the bow shock wave are determined at meridional sections. From the radial coordinates of points on the rocket surface and the bow shock wave, new computational grid node coordinates are determined at meridional sections in the cylindrical coordinate system of the main part. Using the new computational grid coordinates specified in the cylindrical coordinate system of the main part, old coordinates specified in the cylindrical coordinate system of the nose are determined with the use of expressions that relate the two coordinate systems to each other. The flow parameters at a point with the calculated coordinates are calculated using linear interpolation of the stored flow field parameters in the cylindrical coordinate system bound to the nose. The calculated flow field is used as initial data for the marching calculation of the main part of the rocket, The paper presents the results of calculation of the aerodynamic characteristics of a tilting-nose rocket in a supersonic flow at different values of the nose angle. The proposed algorithm may be used in a prompt calculation of the aerodynamic characteristics of rockets with tilting elements. In doing so, use may be made of a standard program of rocket flow calculation with an added block for the storage and interpolation of the flow field in a tilted cylindrical coordinate system with a shifted origin, which allows the marching direction to be changed.
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Li, Pengfei, Fan Yang, Peng Wang, Jinfeng Zhao, and Zheng Zhong. "A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation." Applied Mathematics and Mechanics 43, no. 11 (2022): 1641–56. http://dx.doi.org/10.1007/s10483-022-2928-7.
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AbstractAcoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.
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BARKER, B. M., and R. F. O'CONNELL. "ON TOLMAN'S MASS-ENERGY RELATION AND A NEW TOLMAN-TYPE RELATION." International Journal of Modern Physics A 04, no. 02 (1989): 327–34. http://dx.doi.org/10.1142/s0217751x89000133.
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Tolman derived the mass-energy relation [Formula: see text] using a particular choice of coordinates, viz. the Schwarzschild solution for the metric tensor in isotropic coordinates for a body of mass m at rest at the origin. Here we show that this relation retains the same form for the case of a very general coordinate system. The latter includes the Schwarzschild and harmonic coordinates as special cases. In addition, we give a new Tolman-type relation [Formula: see text]. The quantities [Formula: see text] and [Formula: see text] are the energy-momentum densities for matter and the gravitational field, respectively.
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Yu, Hefu, and Bo-Qiang Ma. "Origin of fermion generations from extended noncommutative geometry." International Journal of Modern Physics A 33, no. 29 (2018): 1850168. http://dx.doi.org/10.1142/s0217751x18501683.
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We propose a way to understand the three fermion generations by the algebraic structures of noncommutative geometry, which is a promising framework to unify the standard model and general relativity. We make the tensor product extension and the quaternion extension on the framework. Each of the two extensions alone keeps the action invariant, and we consider them as the almost trivial structures of the geometry. We combine the two extensions, and show the corresponding physical effects, i.e. the emergence of three fermion generations and the mass relationships among those generations. We define the coordinate fiber space of the bundle of the manifold as the space in which the classical noncommutative geometry is expressed, then the tensor product extension explicitly shows the contribution of structures in the non-coordinate base space of the bundle to the action. The quaternion extension plays an essential role to reveal the physical effect of the structure in the non-coordinate base space.
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Sun, Huarui, Zhichao Sun, Tianfu Chen, Yuxuan Miao, Junjie Wu, and Jianyu Yang. "An Efficient Backprojection Algorithm Based on Wavenumber-Domain Spectral Splicing for Monostatic and Bistatic SAR Configurations." Remote Sensing 14, no. 8 (2022): 1885. http://dx.doi.org/10.3390/rs14081885.
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This paper introduces a fast backprojection synthetic aperture radar (SAR) imaging algorithm based on wavenumber-domain spectral splicing. The traditional fast backprojection (FBP) algorithm establishes the polar coordinate system with the center of the sub-aperture as the origin. Therefore, the coordinates of the image obtained from each sub-aperture are different. Sub-aperture images must be projected to a uniform coordinate system before they can be coherently superimposed to form the final image, which requires a large amount of calculation. In order to deal with this problem, this paper proposes a novel imaging method, which uses the same polar coordinate system for each sub-aperture. The sub-aperture images are then spliced in the wavenumber-domain, and directly added after upsampling. This method avoids the projection from each sub-aperture to the uniform coordinate system, thus improving the imaging accuracy and efficiency. At the same time, the algorithm is suitable for various configurations, and can achieve good imaging results for bistatic forward-looking SAR and high-speed mobile platform. Finally, simulations are presented to demonstrate the effectiveness of the algorithm.
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Odo, Satoru, and Kiyoshi Hoshino. "Hand Shape Recognition using Higher Order Local Autocorrelation Features in Log Polar Coordinate Space." Journal of Robotics and Mechatronics 15, no. 3 (2003): 286–92. http://dx.doi.org/10.20965/jrm.2003.p0286.
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The friendly communication can be more promoted between the human and computer if the function of gesture recognition is implemented to the computer system as the input interface along with the keyboards and mice. We propose a mouse-like function for estimating hand shape from input images with a monocular camera, with which a computer user feels no restraint or awkwardness. Our system involves conversion of sequential images from Cartesian coordinates to log-polar coordinates. Temporal and spatial subtractions and color information are used to extract the hand region. The origin of log-polar coordinates is chosen as the center of the acquired image, but once the hand has been extracted, the estimated centroid position of the hand region in the next frame, obtained from the current hand position and speed, is used as the origin to convert. Recognition of the hand shape is carried out by multiple regression analysis using higher order local autocorrelation features of log-polar coordinate space. Mouse-like functions are realized according to the hand shape and motion trajectory. Compared to conventional Cartesian coordinates, conversion to log-polar coordinates enables us to reduce image date and computation time, remove the variability by the scaling, and improve antinoise characteristics.
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Avila, Ruben, and Shoaib Raza Syed. "On the Elliptical Orbit of the Earth and Position of the Sun in the Sky: An Engineering Approach." Nucleus 61, no. 1 (2024): 10–15. https://doi.org/10.71330/thenucleus.2024.1330.
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The position of the Sun as seen by an observer on the Earth’s surface and the position and velocity vectors of the Earth revolving in an elliptical orbit around the Sun can be calculated using several computational approaches. These approaches include (but are not limited to) the use of an analytical approach; a numerical approach, and the use of a Solar Position Algorithm (PSA). In the analytical methodology, the Earth’s momentum equation is transformed to eliminate its time dependence, and the equation is solved analytically. Whereas, using the numerical approach, the dimensionless momentum equation of the revolving Earth is written in the polar coordinate system (r, θ) and solved numerically. The solar position algorithm known as PSA (Plataforma Solar de Almeria, abbreviated from its Spanish origin: https://www.psa.es), is a numerical algorithm that uses several empirical relations to calculate the solar declination and the ecliptic longitude angles, etc. The algorithm uses Cartesian coordinate system to calculate the dimensionless coordinates of the pole star (Polaris) and its declination angle to calculate the position vector of an observer that rotates with the Earth. This coordinate system is referred to as a new Cartesian coordinate system whose origin is located at the center of the Earth. The solar elevation angle and azimuth angle are obtained by performing a set of rotations of this new Cartesian coordinate system. In this article, we have used basic physical principles (analytical approach) to obtain the main parameters of the Sun’s trajectory and position, at certain time in the sky. The methodology presented here can easily be used by professionals and engineers working in the area of solar/alternate energy, as well as for the design of intelligent/green buildings/cities for a sustainable environment.
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Avila, Ruben, and Shoaib Raza Syed. "On the Elliptical Orbit of the Earth and Position of the Sun in the Sky: An Engineering Approach." Nucleus 61, no. 1 (2024): 10–15. https://doi.org/10.71330/nucleus.61.01.1330.
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The position of the Sun as seen by an observer on the Earth’s surface and the position and velocity vectors of the Earth revolving in an elliptical orbit around the Sun can be calculated using several computational approaches. These approaches include (but are not limited to) the use of an analytical approach; a numerical approach, and the use of a Solar Position Algorithm (PSA). In the analytical methodology, the Earth’s momentum equation is transformed to eliminate its time dependence, and the equation is solved analytically. Whereas, using the numerical approach, the dimensionless momentum equation of the revolving Earth is written in the polar coordinate system (r, θ) and solved numerically. The solar position algorithm known as PSA (Plataforma Solar de Almeria, abbreviated from its Spanish origin: https://www.psa.es), is a numerical algorithm that uses several empirical relations to calculate the solar declination and the ecliptic longitude angles, etc. The algorithm uses Cartesian coordinate system to calculate the dimensionless coordinates of the pole star (Polaris) and its declination angle to calculate the position vector of an observer that rotates with the Earth. This coordinate system is referred to as a new Cartesian coordinate system whose origin is located at the center of the Earth. The solar elevation angle and azimuth angle are obtained by performing a set of rotations of this new Cartesian coordinate system. In this article, we have used basic physical principles (analytical approach) to obtain the main parameters of the Sun’s trajectory and position, at certain time in the sky. The methodology presented here can easily be used by professionals and engineers working in the area of solar/alternate energy, as well as for the design of intelligent/green buildings/cities for a sustainable environment.
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Zhaba, V. I. "Modeling of the deuteron wave function in coordinate representation and calculations of polarization characteristics." Revista Mexicana de Física 67, no. 1 Jan-Feb (2021): 137–45. http://dx.doi.org/10.31349/revmexfis.67.137.
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Modeling of the deuteron wave function in coordinate representation for the nucleon-nucleon potential Reid93 were performed. For this purpose, the asymptotics of the radial wave function near the origin of coordinates and at infinity are taken into account. The most simple and physical asymptotics were applied. In this case, the superfluous knots of both components of the deuteron wave function for the coordinate value r=0.301 fm were compensated. Taking into account the asymptotics of the wave function has little effect on the general behavior of the calculated polarization characteristics of t20 and Ауу. Particular points of the transmitted momentum have been identified, where the tensor deuteron polarization t20 and the tensor analyzing power Ауу show a clear difference.
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Zhaba, V. I. "Modeling of the deuteron wave function in coordinate representation and calculations of polarization characteristics." Revista Mexicana de Física 67, no. 1 Jan-Feb (2021): 137. http://dx.doi.org/10.31349/revmexfis.67.137.
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Modeling of the deuteron wave function in coordinate representation for the nucleon-nucleon potential Reid93 were performed. For this purpose, the asymptotics of the radial wave function near the origin of coordinates and at infinity are taken into account. The most simple and physical asymptotics were applied. In this case, the superfluous knots of both components of the deuteron wave function for the coordinate value r=0.301 fm were compensated. Taking into account the asymptotics of the wave function has little effect on the general behavior of the calculated polarization characteristics of t20 and Ауу. Particular points of the transmitted momentum have been identified, where the tensor deuteron polarization t20 and the tensor analyzing power Ауу show a clear difference.
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Wang, Jing Jing, Hong Jun Wang, and Yong Yin. "Comparison of Multi Freedom Degrees for Patient Positioning Using Kilovoltage Cone Beam CT in Image-Guided Radiotherapy." Applied Mechanics and Materials 195-196 (August 2012): 480–84. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.480.
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Kilovoltage Cone Beam CT (kV CBCT) based image guided radiotherapy (IGRT) is an important approach to correct patient setup which can generate 3D patient anatomy image in radiotherapy process. This paper discusses multi degrees of freedom patient positioning using CBCT based IGRT and presents a new coordinate system classification method. We can conclude that it is essential for correct patient setup to overlap three key points, namely the center of mass (CM) of tumor target, the origin of treatment planning CT image coordinate system, the origin of CBCT image coordinate system). In addition, this paper gives the implementing method of overlapping these three points.
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ZHENG Li-gong, 郑立功, 李龙响 LI Long-xiang, 王孝坤 WANG Xiao-kun, 薛栋林 XUE Dong-lin, and 张学军 ZHANG Xue-jun. "Coordinate-origin calibration of removal function in Magnetorheological Finishing." Optics and Precision Engineering 25, no. 1 (2017): 8–14. http://dx.doi.org/10.3788/ope.20172501.0008.
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Jiang, Shuai, Lei Wang, and Yuanyuan Dong. "Application of Virtual Reality Human-Computer Interaction Technology Based on the Sensor in English Teaching." Journal of Sensors 2021 (November 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/2505119.
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In order to improve the online English teaching effect, the paper applies the sensor and human-computer interaction into the English teaching. The paper improves the sensor information by applying Kalman Filter, combines sensor positioning algorithm to trace the students in the English teaching online, and turns the kernels by the skeleton algorithm into corresponding coordinates of space rectangular coordinate system taking the waist as a coordinate origin to get a human-computer interaction skeleton model in the virtual reality. According to the actual needs of English teaching human-computer interaction, the paper builds a new English teaching system based on the sensor and the human-computer interaction and tests its performance. The experiments suggest that the smart system in the paper can effectively improve English teaching effects.
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Gulyaev, A. P. "Celestial Coordinate System and the FK5 Catalogue." Symposium - International Astronomical Union 141 (1990): 383–84. http://dx.doi.org/10.1017/s0074180900087106.
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To study the motion of the celestial objects in a reference frame one should Know the evolution of the frame itself, In our case it the motion of the origin of coordinates and the proper motions of the objects, the system is based upon.
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Ponizy, B., F. Noblesse, M. Ba, and M. Guilbaud. "Numerical Evaluation of Free-Surface Green Functions." Journal of Ship Research 38, no. 03 (1994): 193–202. http://dx.doi.org/10.5957/jsr.1994.38.3.193.
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A very simple and efficient method for computing the nonoscillatory near-field terms in the expressions for the Green functions, and their gradients, for wave diffraction/radiation by an offshore structure and steady ship waves in deep water is presented. The Green functions are decomposed into three terms corresponding to simple (Rankine) singularities, wave fields, and nonoscillatory near-field (local) flow components. The method which is presented for approximating the latter nonoscillatory near-field components is based on the use of a coordinate-transformation and a function-transformation. The coordinate-transformation maps the unbounded domain of definition of the Green function into a finite domain (unit square or cube) of transformed coordinates. The function-transformation expresses the near-field components, which are singular at the origin, in terms of functions that are regular everywhere. Proper coordinate and function transformations reduce the problem of approximating singular functions in unbounded domains into that of approximating smoothly varying functions within finite domains. The latter task can be accomplished in a number of ways, including the use of linear table interpolation presented in the study.
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Nikolić, Hrvoje. "The Origin of the Difference between Space and Time." Symmetry 15, no. 4 (2023): 957. http://dx.doi.org/10.3390/sym15040957.
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All differences between the role of space and time in nature are explained by proposing principles in which none of the spacetime coordinates has an a priori special role. Spacetime is treated as a non-dynamical manifold, with a fixed global RD topology. The dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it follows that one coordinate takes a special role. It is proposed that any boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the (1,D−1) signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized.
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Hoekstra, Eric. "On the Origin and Development of an Embedded v-Initial Construction in Frisian." Amsterdamer Beiträge zur älteren Germanistik 77, no. 1-2 (2017): 171–90. http://dx.doi.org/10.1163/18756719-12340071.
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Frisian features an embedded v-First construction, which is semantically equivalent to an infinitival clause. The construction comes in two varieties. The coordinated variety involves a clause functioning as a second clause of a coordination in the scope of a modal verb. It used to feature an infinitival verb until it started to appear in the 18th century with (unambiguously) imperative verbs. The subordinated variety involves a clause functioning as a verbal argument. It developed out of the coordinated variety in the 18th century. The grammatical properties of both varieties of this construction in present-day Frisian are presented and understood as a result of their origin and subsequent development out of a coordinate construction in Old Frisian. To the extent that the analysis is successful, it provides support for the notion ‘construction’ and for examining the origin and evolution of constructions, as is customary in construction grammar (Goldberg 2006, Givon 2009).
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Zhu, Jun Feng, Xin Yan, Ling Ling Zhou, and Xiao Xin Zhao. "Measurement of Helmholtz Coil." Applied Mechanics and Materials 738-739 (March 2015): 893–98. http://dx.doi.org/10.4028/www.scientific.net/amm.738-739.893.
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Based on the basic principles of electromagnetism, the application of Shanghai Fudan-day Welcomes UNESCO Instruments Ltd. THQHC-1 type Helmholtz coil magnetic field measuring instrument for measuring coil uniform magnetic field generates a magnetic field on the carrier to get round the coil axis, online circle center at (coordinate origin) at the maximum magnetic field strength. Starting from the coordinate origin, to the sides, the magnetic field lines accelerate the decline, when the distance exceeds the coil radius, the decelerating decline. Conclusions for the understanding of a uniform magnetic field reference.
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Arjun, Tan. "From the Pear-shape of the Earth to a Tetrahedroid-shape of the Earth." APPLIED SCIENCE PERIODICAL XXVI, no. 4, November 2024 (2024): 15–23. https://doi.org/10.5281/zenodo.14802427.
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<em>The notion of the ‘Pear-shape of the Earth’ is widely known to the public at large. However, a similar concept called the ‘Tetrahedroid-shape of the Earth’, is not. This concept was recently revived by Mentock, who argued that the tetrahedroid Earth was more appropriate than the pear-shaped Earth. In this study, we construct three model orientations of the tetrahedron within a circumscribed spherical Earth to see which orientation best locates the geoid highs with its four vertices. In the first model (Model A), one vertex is situated at the North Pole, a second on the Greenwich meridional plane and the two others at azimuthal angles of 120° and 240° respectively. Two other models are generated from Model A to better locate the vertices with the geoid highs. The method consists of converting the spherical coordinates of the vertices to rectangular coordinates; then rotating the coordinates system by a desired angle; and finally, converting the new rectangular coordinates back to the spherical coordinates. The origin of the rectangular coordinate system is at the center of the Earth, with z-axis pointing towards the North Star, the x-axis lying in the Greenwich meridional plane, and y-axis fixed by the right-hand rule. Model B is created by rotating the coordinate system about the y-axis counter-clockwise by -20°; and Model C is created by rotating the coordinate system about the x-axis counter-clockwise by -20°. The locations of the vertices in Models B and C show improved agreements with the geoid highs.</em>
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J. Dimitrijevic, Nebojsa. "CREATING GEOMETRIC SHAPES IN AUTODESK INVENTOR USING OF BORN (BASE ORPHAN REFERENCE NODE) TECHNIQUE." Knowledge International Journal 28, no. 4 (2018): 1341–48. http://dx.doi.org/10.35120/kij28041341n.
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The basic concept of BORN (Base Orphan Reference Node) technique is the use of a Cartesian coordinate system as a first shape, which preceded the creation of any geometrical shape. After the establishment a Cartesian coordinate system, are obtained by three mutually normal working plane (XY, YZ and ZX), which can be used as a sketching plane, three working axes (X, Y, and Z) and a working point (the origin). Three working planes are used as a reference for dimensions and geometric constructions. Autodesk Inventor automatically adjust set of reference geometry, which consists of three working-plane, three working axes and the origin when we begin to create a new part. All of the following geometric shapes can be used by the coordinate system and / or reference geometry as sketching plane.
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MOSEMAN, ELIZABETH R., and PETER WINKLER. "On a Form of Coordinate Percolation." Combinatorics, Probability and Computing 17, no. 6 (2008): 837–45. http://dx.doi.org/10.1017/s0963548308009474.
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Let ai,bi, i = 0, 1, 2, . . . be drawn uniformly and independently from the unit interval, and let t be a fixed real number. Let a site (i, j) ∈ $\N^2$ be open if ai + bj ≤ t, and closed otherwise. We obtain a simple, exact expression for the probability Θ(t) that there is an infinite path (oriented or not) of open sites, containing the origin. Θ(t) is continuous and has continuous first derivative except at the critical point (t=1), near which it has critical exponent (3 − $\sqrt{5}$)/2.
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Lee, D. G., and S. P. Bell. "Architecture of the yeast origin recognition complex bound to origins of DNA replication." Molecular and Cellular Biology 17, no. 12 (1997): 7159–68. http://dx.doi.org/10.1128/mcb.17.12.7159.
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In many organisms, the replication of DNA requires the binding of a protein called the initiator to DNA sites referred to as origins of replication. Analyses of multiple initiator proteins bound to their cognate origins have provided important insights into the mechanism by which DNA replication is initiated. To extend this level of analysis to the study of eukaryotic chromosomal replication, we have investigated the architecture of the Saccharomyces cerevisiae origin recognition complex (ORC) bound to yeast origins of replication. Determination of DNA residues important for ORC-origin association indicated that ORC interacts preferentially with one strand of the ARS1 origin of replication. DNA binding assays using ORC complexes lacking one of the six subunits demonstrated that the DNA binding domain of ORC requires the coordinate action of five of the six ORC subunits. Protein-DNA cross-linking studies suggested that recognition of origin sequences is mediated primarily by two different groups of ORC subunits that make sequence-specific contacts with two distinct regions of the DNA. Implications of these findings for ORC function and the mechanism of initiation of eukaryotic DNA replication are discussed.
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Sun, Ning, Huan Yu Li, and Jing Jing Gong. "A New Method to Solving the Internal Mass of Rigid Body Based on the Principle of Inertia Parameters." Applied Mechanics and Materials 344 (July 2013): 37–40. http://dx.doi.org/10.4028/www.scientific.net/amm.344.37.
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On the basis of Coordinate transformation analysis of the inertia parameters in three-dimensional space, according to the characteristic that the coordinate direction is existed and unique which the product of inertia is 0 when rotating the coordinate system, a new method to judge and calculate the particle information by searching for the intersection of the two lines that lead from two different coordinate origin is proposed. The processes and procedures to calculate the internal mass of rigid body are deduced theoretically. A special numerical example is given to verify the correctness of the theory. The error factors are analyzed qualitatively as well.
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Konopatskiy, E. V., S. I. Rotkov, M. V. Lagunova, and V. A. Tyurina. "GRAPHICAL AND ANALYTICAL DEFINITION OF PARAMETRIC CURVES IN EXPLICIT FORM." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 233 (November 2023): 3–8. http://dx.doi.org/10.14489/vkit.2023.11.pp.003-008.
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The aim of the work is to establish the relationship between graphical and analytical methods of solving problems on the example of the definition of parametric curves in explicit form. The idea is to represent the system of parametric equations of a plane curve in the space of Otxy coordinate system as a system of two projections of the curve on a complex Monge drawing. Then the desired curve can be obtained explicitly as a discrete set of points on the profile plane of projections in the Otxy coordinate system. If we consider the system of curve projections as a single curve in three-dimensional space Otxy, then this curve can be flat and spatial. For planar curves located in a partial position plane, it is easy to make the transition from parametric setting of the curve to an explicit form due to the linear relationship between one of the variables (x or y) and the parameter t. If the curve in the Otxy coordinate system belongs to the general position plane, we can use the projection plane replacement method to transform it to a projecting position. This allows a linear relationship to be established between one of the variables and a parameter to obtain the equation of the curve in explicit form, followed by an inverse transformation of the planes of projections. Mathematically, replacing the plane of projections is equivalent to replacing the coordinate system and reduces it to a rotation around the origin of the coordinates. Formulas for transforming the coordinate system, taking into account the peculiarities of using Monge's complex drawing and for determining the angle of rotation of the coordinate system are given.
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XU, TINGTING, PENGCHENG LI, SHANGBIN CHEN, and WEIHUA LUO. "TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX." Journal of Innovative Optical Health Sciences 03, no. 01 (2010): 75–80. http://dx.doi.org/10.1142/s1793545810000873.
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Cortical spreading depression (CSD), which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia, has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5 mm/min. Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique, the variation of propagation speed of CSD across different regions of cortex was not well-concerned, partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex. Here, we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex. In this method, temporal clustering analysis (TCA) and least square estimation (LSE) were first used to detect origin site where CSD was induced. Taking the origin site of CSD as the origin of coordinates, the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation. Then, two fixed-distance regions of interest (ROIs) are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm. Finally, we could draw a two-dimensional image, in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex. The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.
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Uozumi, Yosuke, Kouki Nagamune, Naoki Nakano, et al. "Fully Automated Determination of Femoral Coordinate System in CT Image Based on Epicondyles." Journal of Advanced Computational Intelligence and Intelligent Informatics 19, no. 3 (2015): 372–80. http://dx.doi.org/10.20965/jaciii.2015.p0372.
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We propose a fully automated determination of the femoral coordinates in computerized tomography (CT) imaging based on epicondyles. The challenge point of this paper is that we take up how to calculate the femoral coordinate system (FCS), which is difficult to determine automatically. Our proposed method automatically determines the FCS based on anatomical reference points. We evaluated 10 subjects (six men and four women 28.9 ± 9.3 years old, three left-handed and seven right-handed) who had no history of joint injury. We examined the proposed method by comparing the expert and algorithm. The medial epicondyle was 1.41 ± 0.75 mmp= 0.42 > 0.05, student’sttest) in positioning accuracy. The lateral epicondyle was 1.36 ± 0.70 mmp= 0.42) in positioning accuracy. The origin was 0.87 ± 0.40 mmp= 0.71). in positioning accuracy. The lateral axis angle accuracy was 0.53 ± 0.84°p= 0.44). In short, the proposed method constructed patient-specific coordinate systems more accurately than expert manual.
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Soechting, J. F., S. I. H. Tillery, and M. Flanders. "Transformation from Head- to Shoulder-Centered Representation of Target Direction in Arm Movements." Journal of Cognitive Neuroscience 2, no. 1 (1990): 32–43. http://dx.doi.org/10.1162/jocn.1990.2.1.32.
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In a previous study (Soechting and Flanders 1990a) we suggested that subjects used a coordinate system centered at the shoulder while pointing to targets in extrapersonal space. In particular, we suggested that this coordinate system was used to define target location in terms of its distance and the direction from the shoulder. In this paper we examine this suggestion in more detail. We show that when subjects make errors in the distance of a pointing movement, the computed errors in direction will depend on the origin of the coordinate system chosen to measure direction. From an analysis of the computed error, we estimate the origin of each subject's coordinate system. We artificially induced large errors in pointing distance by asking subjects to point half-way to a target on a line from the shoulder or from the head, that is, in directions from two possible centers. The subjects' performance on both these tasks was comparable to the performance of subjects asked to point directly to the target. From this finding we argue that there exists both a head-centered and a shoulder-centered representation of target location within the central nervous system.
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Klemm, Richard D., Richard J. Austin, and Stephen P. Bell. "Coordinate Binding of ATP and Origin DNA Regulates the ATPase Activity of the Origin Recognition Complex." Cell 88, no. 4 (1997): 493–502. http://dx.doi.org/10.1016/s0092-8674(00)81889-9.
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Yildirim, Faruk, and Fatih Kadi. "Proposed single-zone map projection system for Turkey." Reports on Geodesy and Geoinformatics 112, no. 1 (2021): 35–45. http://dx.doi.org/10.2478/rgg-2021-0006.
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Abstract The coordinate base of the maps or sheets produced is the Universal Transversal Mercator (UTM) conformal projection, and it is not possible to work in a single coordinate system in Turkey. Therefore, a transition from UTM to other conformal projections is required. For the countries extending in an east–west UTM zone width like Turkey, composite projection (CP), a double standard paralleling Lambert Conformal Conic (LCC) and double map projections (DP) are used widely. However, this process causes increase in working load and processing errors by users. This study aims to determine a common projection system that can be used in the whole country. In this context, a composite projection from UTM and LCC projection has been defined for the first time. According to the results obtained, map projection CP with the least distortion values in both east–west and north–south directions has been chosen. With the CP selection, a single coordinate system has been determined for medium- and large-scale maps. Projection correction formulas, scale factor and false origin have been determined for map coordinates in CP. These distortions are obtained with a difference of less than 1 cm for 1 km long sides and less than 0.003″ for the azimuth value of this side, when the correction formulas are used.
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Koc, Wladyslaw. "Determination of Track Axis Coordinates in the Analytical Method of Designing Railway Route Geometry." Advances in Image and Video Processing 12, no. 5 (2024): 339–62. https://doi.org/10.14738/aivp.125.17740.
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The article presents the final version of the analytical method for designing railway route geometry, in which individual elements of geometric system (straight sections, circular arcs and transition curves) are described using mathematical equations. The design of the route change section is carried out in an appropriate local Cartesian coordinate system, the basis of which is the symmetrically arranged adjacent main directions. The described method is adapted to the technique of mobile satellite measurements, which provide, in a very short time, a huge number of track axis coordinates, incomparable to traditional geodetic measurements. By locating the origin of the local coordinate system at the intersection point of the main directions of the route, the basis for a universal design variant was created. This variant includes both symmetrical cases and asymmetrical ones resulting from different types and lengths of transition curves. Two situations that may arise when using the local coordinate system were considered, related to the position of the designed geometric system to the main point of the route. A number of specific issues were also clarified. After determining the basic characteristic values, the computational algorithm described in the work leads to solving the problem in a sequential way, much more convenient than before. The obtained possibilities are illustrated by two computational examples.
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Kim, Tae Woo, Hong Sik Yun, Dong Ha Lee, Gun Soo Kim, and Young Chang Koh. "Establishment of New Single Origin Plane Rectangular Coordinate System in Korea." Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography 31, no. 3 (2013): 183–92. http://dx.doi.org/10.7848/ksgpc.2013.31.3.183.
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Mesón, Alejandro M., Francisco M. Fernández, Eduardo A. Castro, Alberto Maltz, and Rodolfo Rodriguez. "Shift of the coordinate origin in calculating resonances by dilatation transformation." Journal of Computational Physics 57, no. 3 (1985): 491–94. http://dx.doi.org/10.1016/0021-9991(85)90192-5.
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Chang, Bilin, and A. A. Shabana. "Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates." Journal of Applied Mechanics 57, no. 3 (1990): 707–18. http://dx.doi.org/10.1115/1.2897081.
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In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.
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Shrestha, Sanju, Shanti Thapa, and Bed Prasad Pandey. "Structural Properties of Graphene." Pragya Darshan प्रज्ञा दर्शन 5, no. 2 (2023): 81–84. http://dx.doi.org/10.3126/pdmdj.v5i2.59615.
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Graphene, a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice with six carbon atoms, are of two types due to their bonding. Due to its structural uniqueness, properties of the grapheme is found to be very different and important in application point of view. Hence, the authors have studied the structural properties as co-ordination number, coordinates, distances of nearest atoms from 1st to 5th, analytically using two dimensional coordinate system taking one atom of a unit cell at the origin. Furthermore, packing fraction is also calculated, as the property is very important to study absorption/adsorption of different atoms into the sheet of it.
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Guo, Huaijian, Hanshuo Song, Zhengyu Zhou, Lingrui Lv, and Chang Zang. "Research on multi-beam problems based on geometric modeling and underwater detection." Highlights in Science, Engineering and Technology 82 (January 26, 2024): 323–32. http://dx.doi.org/10.54097/b64zqt45.
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This paper aims to establish and solve the mathematical model of coverage width under multi-beam bathymetry, rising from a one-dimensional sea area measurement problem to a two-dimensional sea area measurement problem. First, this paper takes the center of the sea area as the coordinate origin, establishes a one-dimensional coordinate system, and derives the functional relationship between the coordinate position of the measured ship axis and the angle of the seabed slope through the triangle edge relationship. At the same time, the mathematical relationship between the depth of the water body and the position of the measuring ship is constructed, and the relationship between the single coverage width of the detection system and the depth of the water body is found using the sine theorem. Subsequently, this paper established a two-dimensional sea area measurement model. Taking the center point of the sea area to be measured as the coordinate origin, a three-dimensional coordinate system was constructed. The normal vector projection direction was taken into account to obtain the new slope angle, and the two-dimensional sea area measurement was converted into a one-dimensional sea area. Measurement. Finally, this article uses MATLAB to conduct simulation experiments and gives the relationship between the coverage width and the position of the survey ship at different angles between survey line directions, providing an effective reference for the multi-beam sounding strategy.