A High Accuracy Spatial Reconstruction Method Based on Surface Theory for Regional Ionospheric TEC Prediction by Jian Wang, Yi‐ran Liu, Ya‐fei Shi

“…The core theory of this method is as follows: (a) Any surface can be uniquely determined by its first and second fundamental quantities; (b) By direct difference approximation, differential equations are transformed into algebraic equations to solve Gauss equations faster. …”
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Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method by Cheng Li, Hongguang Li

“…A Galerkin projection of the governing equations for the approximate invariant manifolds yields a set of nonlinear algebraic equations in expansion coefficients, which can be solved numerically with a general choice of zero as initial guess for the cases in this work. …”
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Derivation of CaO-SiO2-Al2O3system slag viscosity equation by GP by Ri S.-C., Ra J.-H., Ryom K.-C.

“…The equation was automatically described as a simple algebraic equation with the basicity and content of Al2O3 and temperature. …”
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Enhancing the robustness of block ciphers through a graphical S-box evolution scheme for secure multimedia applications by Abdul Razaq, Muhammad Mahboob Ahsan, Hanan Alolaiyan, Musheer Ahmad, Qin Xin

“…A novel coset graph-based algebraic method was proposed to evolve a robust and efficient S-box in order to address the challenges of strong S-box generation. …”
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Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series by Erez Abrams, Michael Kasprzak, Gaurav Bhole, Tak-San Ho, Herschel Rabitz

“…This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. …”
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An Active Decoupling Method for 6R Robots Based on Denavit-Hartenberg Parameters by Yin Jie, Xi Wanqiang

“…Then, the D-H parameters with coupling are used in the forward kinematics, and the algebraic solution is used to obtain the inverse kinematics. …”
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Safety Evaluation for Highway Geometric Design Based on Spatial Path Properties by Lu Wang

“…After manipulating the curvature and torsion of the spatial curve algebraically, the correlation between geometric design variables and crash rate was ultimately established. …”
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Cycle Intersection for SOp,q-Flag Domains by Faten Abu Shoga

“…A real form G0 of a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold Z=G/Q. A maximal compact subgroup K0 of G0 has special orbits C which are complex submanifolds in the open orbits of G0. …”
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Extracting equations of motion from superconducting circuits by Christian Z. Pratt, Kyle J. Ray, James P. Crutchfield

“…First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion—complications that to date have precluded achieving these goals, let alone doing so efficiently. …”
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Influence of Turbulent Scalar Mixing Physics on Premixed Flame Propagation by H. Kolla, N. Swaminathan

“…The influence of reactive scalar mixing physics on turbulent premixed flame propagation is studied, within the framework of turbulent flame speed modelling, by comparing predictive ability of two algebraic flame speed models: one that includes all relevant physics and the other ignoring dilatation effects on reactive scalar mixing. …”
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Adaptive Fuzzy Consensus Tracking Control for Nonlinear Multiagent Systems with Time-Varying Delays and Constraints by Jie Lan, Tongyu Xu

“…Based on Lyapunov stability theory and algebraic graph theory, the constructed tracking control can ensure states within defined time-varying constraint bounds and eliminate the influence of time delays. …”
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A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations by M.H. Heydari, M. Razzaghi, M. Bayram

“…By applying the ψ-Hilfer fractional derivative operational matrix of the ψ-Chebyshev CFs, the classical derivatives operational matrices of the shifted CPs, and employing the collocation method, the solution of the equation under consideration is obtained by solving a system whose elements are algebraic equations. The accuracy of the presented strategy is examined by numerous examples.…”
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A Sliding Mode LCO Regulation Strategy for Dual-Parallel Underactuated UAV Systems Using Synthetic Jet Actuators by N. Ramos-Pedroza, W. MacKunis, M. Reyhanoglu

“…This difficulty is mitigated through careful algebraic manipulation in the regulation error system development, along with innovative design of the sliding surface. …”
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Dynamic Gust Load Analysis for Rotors by Yuting Dai, Linpeng Wang, Chao Yang, Xintan Zhang

“…Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. …”
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New version of Universal modeling method for centrifugal compressors calculation development by Yu. B. Galerkin, A. A. Drozdov

“…The math model of Universal modeling method is a sum of algebraic equations for calculation of head losses. …”
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Advanced ellipse overlap computation based on segment area of circles by Minhye Kim, Yongkuk Kim, Giphil Cho

“…To address the numerical limitations that may arise when calculating the overlapping area of two ellipses using algebraic and numerical methods, we propose a novel approach aimed at improving numerical accuracy. …”
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Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects by Subhankar Jana, Anjali Patel, Juthika Mahanta

“…Using these definitions, the paper proposes an algebraic model, namely the pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. …”
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Modeling Current Distribution Within Conductors and Between Parallel Conductors in High-Frequency Magnetics by Michael Solomentsev, Alex J. Hanson

“…In this article, we show that Maxwell's equations, in the high frequency limit, yield a set of linear algebraic equations that are rapidly solvable to yield both the current and magnetic field distribution and hence can be used to predict loss and leakage inductance. …”
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Heat and mass transfer performance of power-law nanofluid flow with thermal radiation and joule heating aspects: Surface heat flux analysis by Mhamed Benaissa, Zia Ullah, A. Dahshan, Md Mahbub Alam, Khadijah M. Abualnaja, Hanaa Abu-Zinadah, Abdullah A. Faqihi, Nidhal Ben Khedher

“…Utilizing the similarity transformation, thermal energy, mass, and momentum are reduced to an algebraic system. Dimensionless stretching surface functions are impacted by nanofluid parameters such as magnetic parameter, thermophoresis parameter Nt, Nb, joule heating J, thermal radiation Nr, Le, and Pr. …”
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Variationally Improved Bézier Surfaces with Shifted Knots by Daud Ahmad, Kanwal Hassan, M. Khalid Mahmood, Javaid Ali, Ilyas Khan, M. Fayz-Al-Asad

“…Instead of variational minimization of usual area functional, the quasi-minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points. The coefficients of these control points bear symmetry for the pair of summation indices as well as for the pair of free indices. …”
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