On quasi-integrable deformation scheme of the KdV system by Kumar Abhinav, Partha Guha

“…The standard abelianization process based on the inherent sl(2) loop algebra leads to an infinite number of anomalous conservation laws, that yield conserved charges for definite space-time parity of the solution. …”
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Glossários de matemática como veículo de integração de saberes em sala de aula by Iran Abreu Mendes, Evanildo Costa Soares

“…A pesquisa foi realizada em uma escola pública, em três etapas: pesquisa bibliográfica sobre terminologias referentes aos termos matemáticos e suas relações e significados conceituais; experiências didáticas com alunos 9o ano do Ensino Fundamental, com foco em vocábulos relacionados à geometria e trigonometria, e experiências com professores dos Anos Iniciais, com enfoque em termos relacionados à aritmética, à álgebra e à geometria. Em ambos os momentos investigamos as conexões entre os termos do glossário, os vocábulos do dicionário de língua portuguesa e os termos que evidenciavam conceitos matemáticos nos livros didáticos. …”
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A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling by Ying Li, Musheng Wei, Fengxia Zhang, Jianli Zhao

“…In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image.…”
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A Quantum Space behind Simple Quantum Mechanics by Chuan Sheng Chew, Otto C. W. Kong, Jason Payne

“…The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. …”
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Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory by Rocco Amorosso, Sergey Syritsyn, Raju Venugopalan

“…We show that FTE2 can be expressed in terms of correlators of Polyakov loops, is manifestly gauge-invariant, and therefore free of the ambiguities in computations of the entanglement entropy in gauge theories related to the choice of the center algebra. Employing the replica trick, we compute FTE2 for SU(2) Yang-Mills theory in (2+1)D and demonstrate that it is finite in the continuum limit. …”
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Math-Phys-Chem Approaches to Life by Hitomi Kitaojima, Shigeru Kanemitsu

“…They correspond to three mathematical dsciplines—probability, linear algebra and free groups, respectively. We shall give some basics for the Rényi (𝛼)-entropy, Chebyshev polynomials and the notion of free groups inrespective places. …”
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Algebrization of Nonautonomous Differential Equations by María Aracelia Alcorta-García, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, Elifalet López-González

“…Given a planar system of nonautonomous ordinary differential equations, dw/dt=F(t,w), conditions are given for the existence of an associative commutative unital algebra A with unit e and a function H:Ω⊂R2×R2→R2 on an open set Ω such that F(t,w)=H(te,w) and the maps H1(τ)=H(τ,ξ) and H2(ξ)=H(τ,ξ) are Lorch differentiable with respect to A for all (τ,ξ)∈Ω, where τ and ξ represent variables in A. …”
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Fração: conceito e aplicação da unidade de medida por professores e futuros professores by Maria Alice Veiga Ferreira de Souza

“…Pesquisas indicam que a compreensão de frações restrita à alguma(s) interpretação(ções) compromete a ampla construção conceitual e o desempenho da Álgebra e da Matemática futura. Independentemente da interpretação, existem traços centrais que as integram, como a identificação da unidade de medida. …”
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On the 75th birth anniversary of Marat Mirzaevich Arslanov by I.Sh. Kalimullin, V.L. Selivanov

“…The paper describes the biography and the main scientific achievements of Marat Mirzaevich Arslanov, the Head of the Department of Algebra and Mathematical Logic of Kazan Federal University, Professor, who is the founder of the Kazan School of Mathematical Logic and Computability Theory. …”
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Web Accessibility Analysis of Massive Open Online Courses in Mathematical Disciplines by E. A. Kosova, M. Yu. Khalilova

“…By automatic testing using Web Accessibility Checker, the accessibility of the functional and informational content of the MOOCs was evaluated. 73% of MOOCs were found to conform to the syllabus subjects “Probability Theory and Mathematical Statistics”, “Discrete Mathematics” and “Algebra and Geometry”; 8 basic disciplines of higher mathematics education are not covered by online education; 96,4% of the courses have accessibility limitations, especially for people with visual impairment. …”
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Transfer functions of a time-varying control system by Volt Avdieiev

“…This makes it possible to transform differential equations into algebraic ones, as a result to use the developed apparatus of linear algebra to solve problems of analysis and synthesis. …”
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Classical eikonal from Magnus expansion by Joon-Hwi Kim, Jung-Wook Kim, Sungsoo Kim, Sangmin Lee

“…The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. …”
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Some features of mathematical education in Lithuania during the years of dependence by Juozas Banionis

“…In V–XI forms mathematics as a subject consisted of systemic arithmetic, algebra, geometry and trigonom­etry courses, which were sufficient for students entering the institutions of higher education. …”
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RDF Knowledge Graphs Designed with Axiomatic Methodology to Enhance Industry 4.0 by Fernando Rolli, Chiara Parretti, Riccardo Barbieri, Alessandro Polidoro, Bianca Bindi

“…It allows the selection of the most reliable data sources, thereby optimizing the knowledge graph construction process using matrix algebra, minimizing redundancy and improving the efficiency of query response. …”
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Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions by Ricardo Abreu Blaya, Juan Bory Reyes, Richard Delanghe, Frank Sommen

“…Let ℝ0,m+1(s) be the space of s-vectors (0≤s≤m+1) in the Clifford algebra ℝ0,m+1 constructed over the quadratic vector space ℝ0,m+1, let r,p,q∈ℕ with 0≤r≤m+1, 0≤p≤q, and r+2q≤m+1, and let ℝ0,m+1(r,p,q)=∑j=pq⨁ ℝ0,m+1(r+2j). …”
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(SPT-)LSM theorems from projective non-invertible symmetries by Salvatore D. Pace, Ho Tat Lam, and Ömer M. Aksoy

“…This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)× Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. …”
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Applying cognitive diagnostic models to mechanics concept inventories by Vy Le, Jayson M. Nissen, Xiuxiu Tang, Yuxiao Zhang, Amirreza Mehrabi, Jason W. Morphew, Hua Hua Chang, Ben Van Dusen

“…As part of a broader project to develop a cognitive diagnostic assessment for introductory mechanics within an evidence-centered design framework, we identified and tested the student models of four skills that cross content areas in introductory physics: apply vectors, conceptual relationships, algebra, and visualizations. We developed the student models in three steps. …”
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Extensions of Riordan Arrays and Their Applications by Paul Barry

“…The methods used include generating functions, linear algebra, weighted compositions, and linear recurrences. …”
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Arbitrary 3D multi-body road vehicle modeling for vehicle-infrastructure interaction by Shiyi Mei, Colin Caprani, Daniel Cantero

“…By avoiding imposing traditional force and moment equilibrium, this approach can be easily applied to a Computer Algebra System (CAS): an open-source Python script based on CAS is provided for constructing symbolic matrices across various road vehicle configurations. …”
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External barycentric coordinates for arbitrary polygons and an approximate method for calculating them by Ivan S. Polyansky

“…The algorithmic features of the implementation of an approximate analytical solution with a structured representation of pseudocodes of programs for calculating external barycentric coordinates, formed mainly for the MathCad computer algebra system, are clarified. The efficiency is demonstrated by specific examples. …”
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