Whole space case for solution formula of Korteweg type fluid motion in R3 by Bagus Suhada Dede, Maryani Sri, Renny Renny, Triyani Triyani, Hendriya Guswanto Bambang, Kartiwi Mira

“…In this paper we consider the solution formula of linearized diffusive capillary model of Korteweg type without surface tension in three-dimensional Euclidean space ℝ3 using Fourier transform. Firstly, we construct the matrix of differential operators from the model problem. …”
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Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric by Atamurat Kuchkarov, Gafurjan Ibragimov, Massimiliano Ferrara

“…We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of m groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. …”
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A Flexile and High Precision Calibration Method for Binocular Structured Light Scanning System by Jianying Yuan, Qiong Wang, Bailin Li

“…Initial extrinsic parameters in projective space are estimated with the method of factorization and then upgraded to Euclidean space with orthogonality of rotation matrix and rank 3 of the absolute quadric as constraint. …”
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The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics by Yan Gu, Jiao Wang

“…As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. …”
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Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system by Kanagaraj Muthuselvan, Baskar Sundaravadivoo, Shankar Rao Munjam, Kottakkaran Sooppy Nisar

“…Abstract The primary focus of this paper is to explore the concept of an initial condition for a noninstantaneous impulsive fractional integro-differential equation of order 0 < ϑ < 1 $0<\vartheta <1$ in an n-dimensional Euclidean space. Using the Laplace transform method, we derive the solution representation of the given dynamical system and investigate the existence and uniqueness of the mild solution through the topological degree method and Gronwall’s inequality. …”
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Bi-GRCN: A Spatio-Temporal Traffic Flow Prediction Model Based on Graph Neural Network by Wenhao Jiang, Yunpeng Xiao, Yanbing Liu, Qilie Liu, Zheng Li

“…First, aiming at the spatial dependence between traffic flow data and traffic roads, Graph Convolution Network (GCN) which can directly analyze complex non-Euclidean space data is selected for spatial dependence modeling, to extract the spatial dependence characteristics. …”
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The Effect of COVID-19 Pandemic on Emitted PM2.5 in Urban Road Networks: Using Loop Data and Kriging Method for Passenger Cars in the Central Part of the City of Lodz by Marta Borowska-Stefańska, Michał Kowalski, Paulina Kurzyk, Alireza Sahebgharani, Szymon Wiśniewski

“…Second, the traffic flow for the whole network system is estimated using an isometric transformed network and the Euclidean space, and the representative one is selected. …”
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Multi-Sensor Information Fusion with Multi-Scale Adaptive Graph Convolutional Networks for Abnormal Vibration Diagnosis of Rolling Mill by Rongrong Peng, Changfen Gong, Shuai Zhao

“…However, most of the existing deep learning (DL) based methods exploit only single sensor information and Euclidean space data, which results in incomplete information contained in the features extracted by in-depth networks. …”
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On eigenfunctions corresponding to first non-zero eigenvalue of the sphere $ S^n(c) $ on a Riemannian manifold by Sharief Deshmukh, Amira Ishan, Olga Belova

“…First, we consider the compact $ \left(M^{n}, g\right) $ as the hypersurface of the Euclidean space $ \left(R^{n+1}, \langle, \rangle \right) $ with isometric immersion $ f:\left(M^{n}, g\right) \rightarrow $ $ \left(R^{n+1}, \langle, \rangle \right) $ and a constant unit vector $ \overrightarrow{a} $ such that the function $ \rho = \langle f, \overrightarrow{a}\rangle $ satisfying $ \Delta \rho = -nc\rho $ for a positive constant $ c $ is isometric to $ S^{n}(c) $ if and only if $ \left(M^{n}, g\right) $ is isometric to $ S^{n}(c) $ provided the integral of Ricci curvature $ Ric\left(\nabla \rho, \nabla \rho \right) $ has an appropriate lower bound. …”
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A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model by Mark Kelbert, Yurii Suhov

“…We assume that a connected Lie group G acts on M, represented by a Euclidean space or torus of dimension d'≤d, preserving the metric and the volume in M. …”
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Principal component analysis and its generalizations for any type of sequence (PCA-Seq) by V. M. Efimov, K. V. Efimov, V. Y. Kovaleva

“…The result will always be PCs in some Euclidean space. We called this method ‘PCA-Seq’. It is certainly an exploratory method, as is its particular case SSA. …”
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Topology of Locally and Non-Locally Generalized Derivatives by Dimiter Prodanov

“…The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduces a generalization of the derivatives from the perspective of the modulus of continuity and characterizes their sets of discontinuities. …”
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