Notion of Complex Spherical Fuzzy Graph with Application by Muhammad Shoaib, Waqas Mahmood, Weded Albalawi, Faria Ahmad Shami

“…This research study introduces some operations, namely, strong product, composition, Cartesian product, and semi-strong product, on CSFG. …”
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On semilattices of groups whose arrows are epimorphisms by M. El-Ghali M. Abdallah, L. N. Gab-Alla, Sayed K. M. Elagan

“…This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended to idempotent separating congruences on S, it is proved that Q(ρK)=ρQ(K) for every normal K in S. …”
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Focusing a cylindrical vector beam and the Hall effect by V.V. Kotlyar, S.S. Stafeev, A.A. Kovalev, V.D. Zaitsev

“…It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). …”
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IMPROVE OF UNCERTAIN MICROSATELLITE MAGNETIC CLEANLINESS BASED ON MAGNETIC FIELD SPATIAL HARMONICS COMPENSATION by Б.І. Кузнецов, Т.Б. Нікітіна, І.В. Бовдуй, К.В. Чуніхін, В.В. Коломієць, Б.Б. Кобилянський

“…Vector payoff calculated based on development method for analytical calculation of magnetostatic field induction of spherical sources in the Cartesian coordinate system (CCS) using Wolfram Mathematica ® software. …”
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Constraint Trajectory Surface-Hopping Molecular Dynamics Simulation of the Photoisomerization of Stilbene by Yibo Lei, Shaomei Wu, Chaoyuan Zhu, Zhenyi Wen, Sheng-Hsien Lin

“…Classical trajectories are carried out in Cartesian coordinates with constraints in internal coordinates, while nonadiabatic switching probabilities are calculated separately in free internal coordinates by Landau-Zener and Zhu-Nakamura formulas along the seam. …”
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Focusing of linearly polarized optical vortex and a Hall effect by V.V. Kotlyar, A.A. Kovalev, A.G. Nalimov

“…It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). …”
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GA Based Adaptive Singularity-Robust Path Planning of Space Robot for On-Orbit Detection by Jianwei Wu, Deer Bin, Xiaobing Feng, Zhongpu Wen, Yin Zhang

“…The tracking accuracy of the space manipulator end-effector is crucial to the detection precision. In this paper, the Cartesian path planning method of velocity level inverse kinematics based on generalized Jacobian matrix (GJM) is proposed. …”
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Safety Evaluation for Highway Geometric Design Based on Spatial Path Properties by Lu Wang

“…This will necessitate an analytical investigation into the effects of higher-order properties, such as curvature and torsion, on the geometry of spatial Cartesian curves. First, these combinations of horizontal and vertical alignments were categorized into six classifications, each with its own spatial expression in mathematical form. …”
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Propagation of Transverse Wave for the Piezoelectric Radial Phononic Crystal Annular Plate in a Fibonacci Order by Wei Liu, Guangbin Yu

“…Based on the previous conventional phononic crystal (PC) structures infinitely periodic in Cartesian coordinates, this paper addresses a new radial phononic crystal annular plate (RPCAP) modeled in a Fibonacci order along the radial direction. …”
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Writing in movement: movement-based performing arts for developing physical education teachers’ identity by Nicoletta Cappello, David Rodriguez, Esther Hernández, Dolors Cañabate

“… Introduction: This study highlights the relevance of surpassing Cartesian paradigms for a holistic development of Physical Education Teachers' identity through embodied pedagogies. …”
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Numerical Study of Violent Impact Flow Using a CIP-Based Model by Qiao-ling Ji, Xi-zeng Zhao, Sheng Dong

“…The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. …”
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Complex Atanassov's Intuitionistic Fuzzy Relation by Abd Ulazeez M. Alkouri, Abdul Razak Salleh

“…We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. …”
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Modeling the hydrodynamics of the OWC device placed over an undulated seabed in the presence of ocean current by Santanu Kumar Dash, Kshma Trivedi, Santanu Koley, Shrabani Mondal

“…The mathematical problem is investigated within the framework of the two-dimensional Cartesian coordinate system by incorporating the classical linear wave-structure theory. …”
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Analisa Strategi Teknologi Informasi Pemasaran UKM Kuliner di Media Sosial Menggunakan Metode SWOT by Fahmi Ajismanto, Andika Widyanto

“…The stages are from weighting and rating every item in questionneire, IFAS and EFAS calculations, Cartesian SWOT diagrams, combined strategy matrice, and SWOT matrices. …”
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Spatially Formulated Connected Automated Vehicle Trajectory Optimization with Infrastructure Assistance by Ran Yi, Yang Zhou, Xin Wang, Zhiyuan Liu, Xiaotian Li, Bin Ran

“…As an alternative of temporal domain and Cartesian coordinate formulation, our formulation provides the constrained trajectory optimization flexibility to describe complex road geometries, traffic regulations, and road obstacles, which are usually spatially varying rather than temporal varying, with assistances vehicle to infrastructure (V2I) communication. …”
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Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1:1:1 Simultaneous Resonance by Ali Kandil, Y. S. Hamed, Jan Awrejcewicz, Nasser A. Saeed

“…These deflections are governed by a system of two ordinary differential equations in order to describe their Cartesian directions. Based on multiple time-scales analysis, truncated asymptotic expansions are assumed to be approximate solutions to the given problem. …”
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Investigation of Blockchain Technology by Using the Innovative Concepts of Complex Pythagorean Fuzzy Soft Information by Naeem Jan, Jeonghwan Gwak, Younghoon Jeon, Bushra Akram

“…In this analysis, we aim to diagnose the innovative idea of complex Pythagorean fuzzy soft relations (CPyFSRs) by using the Cartesian product (CP) of two complex Pythagorean fuzzy soft sets (CPyFSSs), which are computed with the help of two different ideas, called complex Pythagorean fuzzy relation and soft sets. …”
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Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques by A. El-Mesady, Omar Bazighifan

“…Proposed product techniques are the half-starters’ vectors Cartesian product, half-starters’ function product, and tensor product of graphs. …”
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Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture by T. Anuradha, T. Lakshmi Surekha, Praveena Nuthakki, Bullarao Domathoti, Ganesh Ghorai, Faria Ahmed Shami

“…Vizing’s conjecture from 1968 proves that the Cartesian fabricated from graphs domination variety is at least as big as their domination numbers production. …”
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Application of CAD Technology in Extracting Line Feature of Industrial Part Image by Fei Li

“…Based on 3D computer-aided design (CAD) data, by solving the parameter transformation relationship between the CAD 3D Cartesian coordinate system and the image coordinate system, the target line feature is projected onto the image, and the initial value range of the image line feature is obtained. …”
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