Reduced Multiplicative (BURA-MR) and Additive (BURA-AR) Best Uniform Rational Approximation Methods and Algorithms for Fractional Elliptic Equations by Stanislav Harizanov, Nikola Kosturski, Ivan Lirkov, Svetozar Margenov, Yavor Vutov

“…Assuming that the finite difference method (FDM) or the finite element method (FEM) is applied for discretization in space, the approximate solution is described by the system of linear algebraic equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">A</mi></mrow><mi>α</mi></msup><mi mathvariant="bold">u</mi><mo>=</mo><mi mathvariant="bold">f</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network by Bulat N. Galimzyanov, Maria A. Doronina, Anatolii V. Mokshin

“…An important result of the present work is the analytical equation relating the temperatures <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>g</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>m</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>A</mi></msub></semantics></math></inline-formula>, and that, from the algebraic point of view, is the equation for a second-order curved surface. …”
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2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings by Serkan Onar, Kostaq Hila, Sina Etemad, Ali Akgül, Manuel De la Sen, Shahram Rezapour

“…The aim of this study is to provide a generalization of prime vague <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-ideals in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-rings by introducing non-symmetric 2-absorbing vague weakly complete <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-ideals of commutative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-rings. A novel algebraic structure of a primary vague <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-ideal of a commutative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-ring is presented by 2-absorbing weakly complete primary ideal theory. …”
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UNLOADED OIL-SUBMERSIBLE CABLE REDUCED DYNAMIC MODEL ORDER OPTIMIZATION BASED ON THE FREQUENCY RESPONSE APPROXIMATION by Alexander S. Glazyrin, Yusup N. Isaev, Sergey N. Kladiev, Andrey P. Leonov, Ivan V. Rakov, Stanislav V. Kolesnikov, Sergey V. Langraf, Alexander A. Filipas, Vladimir A. Kopyrin, Rustam N. Khamitov, Vladimir Z. Kovalev

“…Methods: system of differential equations in Cauchy normal form, system of partial differential equations, nonlinear algebraic equations, Cramer's method, numerical methods, theory of four-poles, theory of long lines with distributed parameters, state space method, methods of frequency analysis, optimization methods. …”
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A Group Theoretic Approach to Cyclic Cubic Fields by Siham Aouissi, Daniel C. Mayer

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DIMG92 : un simulateur de formation pour le procédé DIMERSOL Dimg92: a Training Simulator for the Dimersol Process by Nica A., Capelle M., Galtier F.

“…In the static module the balances for the reactor form a system of nonlinear algebraic equations that is solved by a Newton-Raphson algorithm. …”
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Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions by Imtiaz Ali, Muhammad Javaid, Samuel Asefa Fufa

“…In this paper, we compute the fault-tolerant metric dimensions of three wheel related networks called by <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-level anti-web wheel <inline-formula> <tex-math notation="LaTeX">$AWW_{(n, r)}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-level Helm <inline-formula> <tex-math notation="LaTeX">$H_{(n, r)}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-level anti-web gear <inline-formula> <tex-math notation="LaTeX">$AWJ_{(2n, r)}$ </tex-math></inline-formula> networks in the form of different algebraic expressions consisting of the integral numbers <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>. …”
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Uncertainty quantification for integrated circuits and microelectrornechanical systems by Zhang, Zheng, Ph. D. Massachusetts Institute of Technology

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Equidistribution of values of linear forms on a cubic hypersurface by Chow, S

“…If the coefficients of the linear forms are algebraically independent over the rationals, then we may replace the <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>-invariant condition with the hypothesis <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi> <mo class="MathClass-rel">&gt;</mo> <mn>1</mn><mn>6</mn> <mo class="MathClass-bin">+</mo> <mn>9</mn><mi>r</mi></math> and show that the system has an integer solution. …”

Electronic structure of defects in crystals by Hunter, I

“…The calculation is along the lines of that of Smith (1965) for the F-centre in NaCl, but is algebraically more involved since the F-centre in alkaline earth fluorides is at a point of tetrahedral (T_d) symmetry in the crystal. …”

Vagueness, logic, and definite truth by Wall, L

“…Edgington’s suggestion is, however, that, although the semantics for vague language has the same algebraic structure as probability, the values are not to be interpreted as probabilities, but rather in a purely semantic manner as the degree to which a statement is close to being a clear case of truth.…”

Pentapartite Entanglement Measures of GHZ and W-Class State in the Noninertial Frame by Juan Luis Manríquez Zepeda, Juvenal Rueda Paz, Manuel Avila Aoki, Shi-Hai Dong

“…We study both pentapartite GHZ and W-class states in the noninertial frame and explore their entanglement properties by carrying out the negativities including 1-4, 2-3, and 1-1 tangles, the whole entanglement measures such as algebraic and geometric averages <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>π</mi><mn>5</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">Π</mi><mn>5</mn></msub></semantics></math></inline-formula>, and von Neumann entropy. …”
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Expression en termes d'énergie pour la perméabilité absolue effective. Application au calcul numérique d'écoulements diphasiques en milieu poreux Expression in Energy Terms for Abs... by Njifenjou A.

“…We compare our results with those obtained by a so-called algebraic equation (concerning the homogenized absolute permeability) used in some big industrial codes. …”
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On the Nature of Information: How FAIR Digital Objects are Building-up Semantic Space by Hans-Günther Döbereiner

“…This will proof to be a powerful tool to unravel the nature of information via analyzing its topological structure algebraically, especially when considering our conjecture concerning universality, classes of information and their possible instantiations on vastly different length and time scales, in effect explaining analogous structure formation.…”
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Un modelo bi-criterio para la ubicación de albergues, como parte de un plan de evacuación en caso de inundaciones by Juan Gaytán Iniestra, Pilar Ester Arroyo López, Ruth Enríquez Colón

“…The mathematical models were solved by using the General Algebraic Modeling System; first the minimal cost solution that satisfies all restrictions was generated, followed by the minimization of total evacuation. …”
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Securing smart contracts with formal verification and automated program repair by Tolmach, Palina

“…To perform a case study of two interacting DeFi protocols, we develop formal definitions for the key elements of DeFi applications and model their implementations and interactions using a process-algebraic formal modeling language. Based on this model, we perform model checking to verify relevant correctness properties of the analyzed protocols automatically. …”
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Studies of the electronic spectra and structure of some small molecules by Stone, T

“…</p> <p>Qualitative trends in the coupling constants of the ring protons were observed and discussed; for example, it was found that the algebraic sum of the <em>ortho</em> and <em>meta</em> coupling constants was approximately constant with different substituents at the <em>para</em> position. …”

Geometric rank of tensors and subrank of matrix multiplication by Swastik Kopparty, Guy Moshkovitz, Jeroen Zuiddam

“…That is, the matrices $M_k$ are the "slices" of $T$ perpendicular to the third axis. Now define an algebraic variety in $\mathbb F^{n_1}\times\mathbb F^{n_2}$ to be the set of all $(x,y)$ such that $x^TM_ky=0$ for every $k$. …”
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Terracini Loci of Segre Varieties by Edoardo Ballico

“…We study the dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></semantics></math></inline-formula> of the kernel at <i>S</i> of the differential of the associated algebraic map <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mrow><mo>(</mo><mi>Y</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mover><mo>→</mo><mrow><mspace width="4pt"></mspace><mspace width="4pt"></mspace></mrow></mover><mi mathvariant="double-struck">P</mi><mi>V</mi></mrow></semantics></math></inline-formula>. …”
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Discretized Finsler Structure: An Approach to Quantizing the First Fundamental Form by Abdel Nasser Tawfik

“…Whether an algebraic or a geometric or a phenomenological prescription is applied, the first fundamental form is unambiguously related to the modeling of the curved spacetime. …”
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