MLAPM - a C code for cosmological simulations by Knebe, A, Green, A, Binney, J

“…The code is purely grid-based and uses a recursively refined Cartesian grid to solve Poisson's equation for the potential, rather than obtaining the potential from a Green's function. …”

A new interpretation of the Keller-Segel model based on multiphase modelling. by Byrne, H, Owen, MR

“…By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. …”

Variational modelling of cavitation and fracture in nonlinear elasticity by Henao Manrique, D

“…We show, further, that the creation of surface can be modeled by carefully analyzing the jump set of the inverses, and we point out some connections between the analysis of cavitation and fracture, the theory of SBV functions, and the theory of Cartesian currents of Giaquinta, Modica, and Soucek. …”

Numerical simulation of the time-fractional Fokker--Planck equation and applications to polymeric fluids by Beddrich, J, Suli, E, Wohlmuth, B

“…The key challenge associated with the numerical solution of the TFNSFP system is that, in addition to it being nonlocal in time, it is, even in its simplest form, posed on a spatial domain that is the Cartesian product of two d-dimensional domains, for d ∈ {2, 3}, the d-dimensional flow domain and the d-dimensional configuration space domain. …”

Numerical linear approximation involving radial basis functions by Zhu, S

“…The main contributions of this thesis include sufficient conditions for the sovability of compactly supported radial basis functions with different shapes, near points preconditioning techniques for high dimensional interpolation systems with compactly supported radial basis functions, a heterogeneous hierarchical radial basis function interpolation scheme, which allows compactly supported radial basis functions of different shapes at the same level, an <em>O</em>(<em>N</em>) algorithm for constructing hierarchical scattered data set andan <em>O</em>(<em>N</em>) algorithm for sparse kernel summation on Cartesian grids. Besides the main contributions, we also investigate the eigenvalue distribution of interpolation matrices related to radial basis functions, and propose a concept of smoothness matching. …”

Self-supervised video representation learning by uncovering spatio-temporal statistics by Wang, J, Jiao, J, Bao, L, He, S, Liu, W, Liu, YH

“…In order to alleviate the learning difficulty, we employ several spatial partitioning patterns to encode rough spatial locations instead of exact spatial Cartesian coordinates. Our approach is inspired by the observation that human visual system is sensitive to rapidly changing contents in the visual field, and only needs impressions about rough spatial locations to understand the visual contents. …”

Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation by Van Gorder, R

“…One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. …”

Flat electroencephalography’s cluster centers movement tracking during epileptic seizure by Mukhni, Syu’aiba, Tan, Lit Ken, Nor Azwadi, Che Sidik, Goh, Chien Yong, Lee, Kee Quen, Chuan, Zun Liang, Asako, Yutaka

“…Through fEEG, the signals can be viewed in a Cartesian plane which consists of EEG’s channels and cluster center of electrical potential during epilepsy. …”
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Analysing the Stock Market as an Economic Lever, Using a Qualitative and a Quantitative Model by Marian-Pompiliu Cristescu, Raluca-Andreea Nerișanu, Maria Flori, Florin Stoica, Florentina Laura Stoica

“…Additionally, the quantitative method offers a strictly cartesian perspective for determining future scenarios, while the sustainable vector model, based on a fractalized vision of reality, manages to capture a plurality of perspectives, as well as the interrelationships between the determining parameters, thus being a complex system of simple equations, as opposed to the quantitative method which is defined as a simple system of complex equations.…”
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Prediction Model of a Generative Adversarial Network Using the Concept of Complex Picture Fuzzy Soft Information by Sami Ullah Khan, Esmail Hassan Abdullatif Al-Sabri, Rashad Ismail, Maha Mohammed Saeed Mohammed, Shoukat Hussain, Arif Mehmood

“…Complex picture fuzzy soft relations are defined in this study by taking the Cartesian product of two complex picture fuzzy soft sets. …”
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Stiffness Modeling and Dynamics Co-Modeling for Space Cable-Driven Linkage Continuous Manipulators by Hejie Xu, Xinliang Li, Yanan Li, Deshan Meng, Xueqian Wang

“…Secondly, the stiffness components of the SCCM are discussed, and the stiffness modeling method of each part is given. Finally, the Cartesian space equivalent stiffness model of the end was established. …”
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LPNet: Retina Inspired Neural Network for Object Detection and Recognition by Jie Cao, Chun Bao, Qun Hao, Yang Cheng, Chenglin Chen

“…An encoder extracts images which feature in log-polar coordinates while a decoder eliminates image noise in cartesian coordinates. Moreover, according to the movement of center points, LPNet has stable and sliding modes. …”
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Size-Dependent Free Vibration of Non-Rectangular Gradient Elastic Thick Microplates by Bo Zhang, Cheng Li, Limin Zhang, Feng Xie

“…The DQ rule is extended to the straight-sided quadrilateral domain through a coordinate transformation between the natural and Cartesian coordinate systems. The Gauss–Lobato quadrature rule and DQ rule are jointly used to discretize the strain and kinetic energies of a generic straight-sided quadrilateral plate element. …”
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Intelligent Calibration of a Heavy-Duty Mechanical Arm in Coal Mine by Yunhong Jia, Xiaodong Zhang, Zhenchong Wang, Wei Wang

“…It also shows the maximum absolute error (MAXE) between the actual mast end position and the nominal mast end position is reduced by more than 58.72% in the three directions of Cartesian coordinate system.…”
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Linear Diophantine fuzzy graphs with new decision-making approach by Muhammad Zeeshan Hanif, Naveed Yaqoob, Muhammad Riaz, Muhammad Aslam

“…We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. …”
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Thermal Improvement in Pseudo-Plastic Material Using Ternary Hybrid Nanoparticles via Non-Fourier’s Law over Porous Heated Surface by Ebrahem A. Algehyne, Essam R. El-Zahar, Muhammad Sohail, Umar Nazir, Hussein A. Z. AL-bonsrulah, Dhinakaran Veeman, Bassem F. Felemban, Fahad M. Alharbi

“…The modeled phenomenon is derived in the Cartesian coordinate system under the usual boundary-layer approach proposed by Prandtl, which removes the complexity of the problem. …”
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A Non-Linear Non-Planar Coupling Mechanism of Suspended Cables in Thermal Conditions by Zhirui Guo, Henghui Lin, Weilong Ni, Yaobing Zhao

“…Introducing a two-mode expansion and applying the multiple scale method, the polar and Cartesian forms of modulation equations are obtained. …”
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Reply to Comment on ‘Physics-based representations for machine learning properties of chemical reactions’ by Puck van Gerwen, Matthew D Wodrich, Ruben Laplaza, Clemence Corminboeuf

“…By studying several datasets that vary in the type of chemical (i.e. high-quality atom-mapping) and structural information (i.e. Cartesian coordinates of reactants and products) contained within, we illustrate that physics-based representations combined with kernel models are competitive with deep learning models. …”
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The Generalized Inverse Sum Indeg Index of Some Graph Operations by Ying Wang, Sumaira Hafeez, Shehnaz Akhter, Zahid Iqbal, Adnan Aslam

“…In this paper, we provided the bounds related to this index for some graph operations, including the Kronecker product, join, corona product, Cartesian product, disjunction, and symmetric difference. …”
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Determining horizontal curvature of railway track axis in mobile satellite measurements by Władysław Koc, Andrzej Wilk, Cezary Specht, Krzysztof Karwowski, Jacek Skibicki, Krzysztof Czaplewski, Slawomir Judek, Piotr Chrostowski, Jacek Szmagliński, Paweł Dąbrowski, Mariusz Specht, Sławomir Grulkowski, Roksana Licow

“…The method is based on inclination angle changes of a moving chord in the Cartesian coordinate system. In the presented case, the variant referred to as the method of two virtual chords is applied. …”
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