Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System by José Carlos Martínez-Llario, Sergio Baselga, Eloína Coll

“…It is well known that both objectives are impossible to achieve by means of the traditional approach using local mathematical projections and Cartesian coordinates. This paper demonstrates in a quantitative methodological way that most of the spatial analysis software products make important deviations in calculations regarding to geodesics, being the users unaware of the magnitude of these inaccuracies, which can easily reach meters depending on the distance. …”
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Effective role of mineral oil and biological nanomaterial on thermal energy influenced by magnetic dipole and nanoparticle shape by Umar Nazir, Muhammad Sohail, Samaira Naz, Kanit Mukdasai, Manoj Singh, Abha Singh, Chandika Rama Mohan, Sayed M. Eldin, Ahmed M. Galal, Ahmed M. Galal

“…The concept of boundary layer was adopted to derive the physical problem in Cartesian coordinates, with results in the form of coupled partial differential equations (PDEs). …”
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An improved experimental-theoretical method for calculating the particle trajectory in a pneumatic separating channel by A. I. Burkov, A. L. Glushkov, V. A. Lazykm

“…At the third stage, the system of differential equations of particle motion in a pneumatic separating channel relative to a Cartesian coordinate system is made and their trajectories are calculated. …”
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RME-based local instructional theory for translation and reflection using of South Sumatra dance context by Dewi Rawani, Ratu Ilma Indra Putri, Zulkardi, Ely Susanti

“…This study produced a learning trajectory with three activities include: the students watched a dance video to describe the dancer’s’ positions in relation to floor tiles; the students were asked to determine the starting points of the dancers in Cartesian coordinates to learn concepts; and the students developed a formal concept based on their own knowledge.…”
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A New Method of Quantifying the Complexity of Fractal Networks by Matej Babič, Dragan Marinković, Miha Kovačič, Branko Šter, Michele Calì

“…In this paper, we introduce a new method for quantifying the complexity of a network based on presenting the nodes of the network in Cartesian coordinates, converting to polar coordinates, and calculating the fractal dimension using the ReScaled ranged (R/S) method. …”
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Design, Assembly and Control of a Differential/Omnidirectional Mobile Robot through Additive Manufacturing by Erick Axel Padilla-García, Raúl Dalí Cruz-Morales, Jaime González-Sierra, David Tinoco-Varela, María R. Lorenzo-Gerónimo

“…In this sense and based on Lyapunov’s method, a low-level controller is developed to control the angular speed of the wheels to a desired angular speed, and a medium-level controller controls the robot’s attitude to follow a desired Cartesian trajectory. Finally, the control strategies are implemented in both prototype configurations, and through experimental results, the theoretical analysis and the construction of the mobile robot are validated.…”
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Axisymmetric non-planar slicing and path planning strategy for robot-based additive manufacturing by Adrián López-Arrabal, Álvaro Guzmán-Bautista, William Solórzano-Requejo, Francisco Franco-Martínez, Mónica Villaverde

“…The algorithm is based on two coordinate systems, the Cartesian coordinate system {c} and a slicing coordinate system {s}. …”
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Real - Time Orbit Determination of Low Earth Orbit Satellites Using Radar System and SGP4 Model by Jae-Kwang Lee, Sung-Seub Lee, Jae-Cheol Yoon, Kyu-Hong Choi

“…To cope with this problem, we set state vector osculating to mean equinox and true equator cartesian elements with coordinate transformation. …”
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Modeling Effects of Heated Waste Water Discharge Rate on the Thermal Plume Pattern and Temperature at the Wastewater Discharge Site by parasto akbari, masood sadri nasab, y nikpor, a s

“…The model wasrun for two years to reach a steady state employing a Cartesian grid (40 × 120), five sigmalevels from the surface to the bottom, meteorological data, main components of the tide (O1,K1, M2, S2), and information related to the heated wastewater discharge rate and temperatureof water body. …”
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Comparison of Epistemological system's with Methodological Benchmarks in Spatial Planning by Ali Mkhtari Karchegani, morteza tavakoli, zahra ahmadipour

“…Research findings show that the concept of rationality in spatial planning is wider than its Cartesian meaning, and postmodern relativists attribute classical rationality to total rationality. …”
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Warehouse Drone: Indoor Positioning and Product Counter with Virtual Fiducial Markers by Murat Ekici, Ahmet Çağdaş Seçkin, Ahmet Özek, Ceyhun Karpuz

“…The output data are the cartesian position and yaw angle. All input and output data required for supervised learning in the simulation environment were collected along different random routes. …”
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Dirichlet-Neumann problem for the partial differential equations with deviation over the space argument by P.Ya. Pukach, S.M. Repetylo, M.M. Symotiuk, M.I. Vovk

“…Dirichlet-Neumann problem for the typeless high order partial differential equation with deviating over the space argument is studied in the domain, which is the Cartesian product of the segment $(0,T)$ and the unit circle $\Omega=\mathbb R/(2\pi \mathbb Z)$. …”
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Philosophical-mystical analysis of space in poetry and painting by Majid Rafati, Parviz Zia Shahabi, Abbas Masoudi, Malek Hosseini

“…This approach to language and literary theory has an essential relation to Cartesian subjectivism, which is based on the separation of the mind from the object, in contrast to Heidegger's improvisation of man-in-the-world and the ontology of language, as well as the intersection of man and world in Merleau-Ponty's body phenomenology. …”
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Numerical investigation of thermal enhancement using MoS2–Ag/C2H6O2 in Prandtl fluid with Soret and Dufour effects across a vertical sheet by Jie Liu, Umar Nazir, Muhammad Sohail, Kanit Mukdasai, Abha Singh, Mashael Alanazi, Gilbert Chambashi

“…The flow analysis has been developed in Cartesian coordinates considering variable thermal conductivity and non-uniform diffusion coefficient. …”
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Applications of triadic hybridized-cross nanomaterials suspended in engine oil using quadratic and linear convection with magnetic dipole by Fuzhang Wang, Muhammad Sohail, Umar Nazir, Essam R. El-Zahar, Manoj Singh, Abha Singh, Chandika Rama Mohan, Sayed M. Eldin

“…The flow of a cross model (CM) with mass and thermal transport has been modeled in Cartesian coordinates for the two-dimensional fluid flow problem. …”
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On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory by Parastoo Zangenehmehr, Ali Farajzadeh

“…Then some existence theorems for GIVEP are presented, also some suitable conditions in order the solution set of GIVEP is compact and convex for set-valued mappings whose are a subset of the cartesian product of Hausdorff topological vector space and their range is a subset of a topological space values (not necessarily locally convex or a topological vector space). …”
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Self-Directed Mobile Robot Navigation Based on Functional Firefly Algorithm (FFA) by Bhumeshwar K. Patle, Brijesh Patel, Alok Jha, Sunil Kumar Kashyap

“…This approach has two key advantages: first, the linear objective function performs efficiently with the single degree and finite-order polynomial time operation, and second, the cartesian constraint performs compactly with the chosen degree of freedom on the finite interval. …”
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Oil spill identification in X-band marine radar image using K-means and texture feature by Rong Chen, Bo Li, Baozhu Jia, Jin Xu, Long Ma, Hongbo Yang, Haixia Wang

“…First, the de-noised image was obtained by preprocessing the original image in the Cartesian coordinate system. Second, it was cut into slices. …”
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Boresight Calibration of Construction Misalignments for 3D Scanners Built with a 2D Laser Rangefinder Rotating on Its Optical Center by Jesús Morales, Jorge L. Martínez, Anthony Mandow, Antonio J. Reina, Alejandro Pequeño-Boter, Alfonso García-Cerezo

“…Moreover, aligning the extra rotation axis with the optical center allows the 3D device to maintain the same minimum range as the 2D scanner and avoids offsets in computing Cartesian coordinates. The paper proposes a practical procedure to estimate construction misalignments based on a single scan taken from an arbitrary position in an unprepared environment that contains planar surfaces of unknown dimensions. …”
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An Improved Immersed Boundary Method for Simulating Flow Hydrodynamics in Streams with Complex Terrains by Yalan Song, Yong G. Lai, Xiaofeng Liu

“…In this work, an immersed boundary method is developed in an existing terrain-conforming CFD model named U²RANS as an alternative, in which terrains are represented implicitly in the Cartesian background mesh. An improved two-layer wall function is proposed in the framework of the <i>k</i>-<i>ε</i> turbulence model, with the aim of producing accurate and smooth wall shear stress distribution and paving the way for future model development on sediment transport and scour modeling. …”
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