A method for eternally dominating strong grids by Alizée Gagnon, Alexander Hassler, Jerry Huang, Aaron Krim-Yee, Fionn Mc Inerney, Andrés Zacarías, Ben Seamone, Virgélot Virgile

“…In this paper, we continue the study of the eternal domination game on strong grids. Cartesian grids have been vastly studied with tight bounds for small grids such as 2×n, 3×n, 4×n, and 5×n grids, and recently it was proven in [Lamprou et al., CIAC 2017, 393-404] that the eternal domination number of these grids in general is within O(m + n) of their domination number which lower bounds the eternal domination number. …”
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Dynamics of Tri-Hybrid Nanoparticles in the Rheology of Pseudo-Plastic Liquid with Dufour and Soret Effects by Enran Hou, Fuzhang Wang, Umar Nazir, Muhammad Sohail, Noman Jabbar, Phatiphat Thounthong

“…The physical model was developed upon Cartesian coordinates, and boundary layer theory was utilized in the simplification of the modelled problem, which appears in the form of coupled partial differential equations systems (PDEs). …”
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Determinism, well-posedness, and applications of the ultrahyperbolic wave equation in spacekime by Yuxin Wang, Yueyang Shen, Daxuan Deng, Ivo D. Dinov

“…The solutions to the Cauchy boundary value problem in multiple time dimensions are derived in Cartesian, polar, and spherical coordinates. These include both bounded and unbounded spatial domains. …”
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In-Situ Process Monitoring and Defects Detection Based on Geometrical Topography With Streaming Point Cloud Processing in Directed Energy Deposition by Muhammad Mu'az Imran, Young Kim, Gisun Jung, Liyanage Chandratilak De Silva, Jeong-Hun Suh, Pg Emeroylariffion Abas, Yun Bae Kim

“…By transforming raw signals into spatially equidistant points representing clad height in a 2-D Cartesian plane, a heatmap tomography of each layer is generated. …”
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Numerical Simulation of the Thermally Developed Pulsatile Flow of a Hybrid Nanofluid in a Constricted Channel by Amjad Ali, Zainab Bukhari, Gullnaz Shahzadi, Zaheer Abbas, Muhammad Umar

“…The laminar flow simulations are carried out in 2D for simplicity as the flow profiles are assumed to vary only in the 2D plane represented by the 2D Cartesian geometry. The streamlines and vorticity contours are also shown to demonstrate the flow behviour along the channel. …”
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Design and characterisation of a cell exposure system with high magnetic field homogeneity: RILZ coils by Marco-Xavier Rivera González, Marco-Xavier Rivera González, Isabel López de Mingo, Isabel López de Mingo, Alexandra Amuneke Ramírez, Ceferino Maestú Unturbe, Ceferino Maestú Unturbe, Ceferino Maestú Unturbe

“…These differences are statistically significant compared to the Helmholtz configuration for the three Cartesian directions: x (p < 0.01), y (p < 0.01), z (p < 0.01). …”
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Dual-Manipulator Optimal Design for Apple Robotic Harvesting by Zicong Xiong, Qingchun Feng, Tao Li, Feng Xie, Cheng Liu, Le Liu, Xin Guo, Chunjiang Zhao

“…In order to ensure canopy area coverage with the most compact mechanical configuration possible, this paper proposes a configuration optimization design method of dual-manipulator to meet the research and development needs of an apple-efficient harvesting robot using the typical tree shape of a “high spindle” in China as the object. A Cartesian coordinate dual-manipulator with two groups of vertically synchronous operations and a three-degree range of motion based on the features of the spatial distribution of fruits under a typical canopy of dwarf and close planting was designed. …”
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Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars by Gerrit M. Horstmann, George Mamatsashvili, André Giesecke, Teimuraz V. Zaqarashvili, Frank Stefani

“…The tachocline is modeled as a shallow plasma atmosphere with an effective free surface on top that we describe within the Cartesian β -plane approximation. As a novelty to former studies, we equip the governing equations with a conservative tidal potential and a linear friction law to account for viscous dissipation. …”
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Mapping and Analysis of the Connectome of Sympathetic Premotor Neurons in the Rostral Ventrolateral Medulla of the Rat Using a Volumetric Brain Atlas by Dempsey, Bowen, Le, Sheng, Turner, Anita, Bokiniec, Phil, Ramadas, Radhika, Bjaalie, Jan G., Menuet, Clement, Allen, Andrew M., Goodchild, Ann K., McMullan, Simon, Neve, Rachael L.

“…We infected bulbospinal RVLM neurons with a recombinant rabies variant that drives reporter expression in monosynaptically connected input neurons and mapped their distribution using an MRI-based volumetric atlas and a novel image alignment and visualization tool that efficiently translates the positions of neurons captured in conventional photomicrographs to Cartesian coordinates. We identified prominent inputs from well-established neurohumoral and viscero-sympathetic sensory actuators, medullary autonomic and respiratory subnuclei, and supramedullary autonomic nuclei. …”
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Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm by Marzouk, Youssef M., Schlegel, Fabrice, Ghoniem, Ahmed F.

“…The method is based on Taylor series expansion in Cartesian coordinates, as initially proposed by Lindsay and Krasny [J. …”
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Thermal perturbations caused by large impacts and consequences for mantle convection by Zuber, Maria, Watters, Wesley A., Hager, Bradford H

“…We examine the effects of thermal perturbations on a convecting layer of incompressible fluid with uniform viscosity in the limit of infinite Prandtl number, for two upper boundary conditions (free- and no-slip) and heat sources (100% volumetric heating and 100% bottom heating) in 2-D Cartesian finite element simulations. Small, low-temperature perturbations are swept into nearby downflows and have almost no effect on the ambient flow field. …”
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Measurement of the distance between corneal apex and pupil center in patients following small-incision lenticule extraction or implantable collamer lens implantation and its correl... by Yishan Qian, Lan Ding, Yanlan Ding, Lin Jiang, Zesheng Liu, Xingtao Zhou

“…The angle kappa was measured using a Scheimpflug imaging device (Pentacam) and represented as Cartesian values between the pupil center and the corneal vertex (X, Y) and chord u ( $$ \sqrt{{X}^{2}+{Y}^{2}}@ $$ orientation), and was compared pre- and post-operative. …”
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KINEMATICS ANALYSIS OF A PARALLEL ROBOT WITH A PASSIVE SEGMENT ANÁLISIS DE LA CINEMÁTICA DE UN ROBOT PARALELO CON UN SEGMENTO PASIVO by Abdelhakim Cherfia, Abdelouahab Zaatri, Max Giordano

“…Further, we determine the reciprocal relations between cartesian and angular velocities of the end-effector via articular velocities by simple derivation of the direct geometrical model expressions. …”
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Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer by Xusheng Wang, Yonghua Xie, Chongxi Chen

“…Methods In this study, a 2D numerical model is proposed for the steady state well-flow in an unconfined aquifer, in which the control equation of seepage in the cylindrical coordinates is transformed equivalently to the Cartesian coordinates through parameter transformation, and the sectional 2D modelling is implemented via the MODFLOW finite-difference grid of cubic blocks. …”
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Robot Time-Optimal Trajectory Planning Based on Quintic Polynomial Interpolation and Improved Harris Hawks Algorithm by Jing Xu, Chaofan Ren, Xiaonan Chang

“…Finally, the robot end-effector trajectory passes through the pose points steadily and continuously under the cartesian space optimal time.…”
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Analysis of the Stress State of a Layer with Two Cylindrical Elastic Inclusions and Mixed Boundary Conditions by Vitalii Yu. Miroshnikov, Oleksandr B. Savin, Mykhailo M. Hrebennikov, Oleksandr A. Pohrebniak

“…Thus, the layer is considered in the Cartesian coordinate system, the inclusions – in the local cylindrical ones. …”

A Novel Velocity-Based Control in a Sensor Space for Parallel Manipulators by Antonio Loredo, Mauro Maya, Alejandro González, Antonio Cardenas, Emilio Gonzalez-Galvan, Davide Piovesan

“…All camera space manipulation (CSM) models in the literature are position-based, where the mapping between the end effector position in the Cartesian space and sensor space is established. Such models are not appropriate for tracking moving targets because the relationship between the target and the end effector is a fixed point. …”
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Investigation of composed charged particles with suspension of ternary hybrid nanoparticles in 3D-power law model computed by Galerkin algorithm by Umar Nazir, Kanit Mukdasai, Muhammad Sohail, Abha Singh, Mohammed Theeb Alosaimi, Mashael Alanazi, Ayele Tulu

“…The phenomenon of momentum and energy balance is derived in Cartesian coordinates and developed PD (partial differential)-equations. …”
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Computerized three-dimensional cephalometric template for Thai adults by Jeenarat Duangsuwan, Somchart Raocharernporn, Sasipa Thiradilok, Somchai Manopatanakul

“…Manual affine transformation of all landmarks was used to transfer medical image coordinates (Digital Imaging and Communications in Medicine [DICOM] or Right-Anterior-Superior [RAS] systems) to Cartesian universal coordinates. Intraclass correlation coefficients (ICC) and Bland-Altman (BA) plots were used to assess inter- and intra-examiner reliability (ICC = 0.961–1.000, BA mean errors = −0.1 mm). …”
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A Table of Some Coherency Matrices, Coherency Matrix Factors, and Their Respective Mueller Matrices by Colin J. R. Sheppard, Artemi Bendandi, Aymeric Le Gratiet, Alberto Diaspro

“…For the general homogeneous deterministic case, expressions for the Mueller matrix have particularly simple forms for Cartesian or stereographic coordinates in generalized retardation space.…”
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