A New Spectral Mittag-Leffler Weighted Method to Solve Variable Order Fractional Differential Equations by Abdulrazzaq T. Abed, Ekhlass S. Al-Rawi

“… Background: In many studies, spectral methods based on one of the orthogonal polynomials and weighted residual methods (WRMs) have been used to convert the variable-order fractional differential equation (VO-FDEs) into a system of linear or nonlinear algebraic equations, and then solve this system to obtain the approximate solution. …”
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On Decompositions of Matrices over Distributive Lattices by Yizhi Chen, Xianzhong Zhao

“…We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.…”
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Separation effectiveness of ideal ion exchange membranes: Application of the Gibbs-Donnan theory. by Jacek Waniewski, Leszek Pstras, Mauro Pietribiasi

“…For both cases, the presented nonlinear algebraic equations require in general the use of numerical methods to approximate their mathematical solutions, although we present as well some closed solutions for simple cases with ideal ionic mixtures. …”
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Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques by A. El-Mesady, Omar Bazighifan

“…Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they encapsulate the structure of finite groups and more general algebraic objects known as quasigroups, and they produce optimal density error-correcting codes. …”
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Not Your Usual Analog Electronics Course—Generalized Analysis of Single-Transistor Amplifiers Uncovers Hidden Reciprocities and Equivalences by Brian Hong

“…Unlike the formulas that students typically learn and designers typically use, the equations presented in this tutorial assume the most general set of conditions: finite output resistance and base-collector current gain, a load resistor at each non-input terminal of the transistor, and a “feedback” resistor between the base and collector terminals. Although perhaps algebraically complex at first glance, emphasis is placed on mathematical elegance and ease of use—expressions are formulated in terms of sub-terms that capture important aspects of the circuit’s behavior. …”
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Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder by G. Ch. Shushkevich

“…It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. …”
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Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section by Zhongmin Wang, Rongrong Li

“…Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. …”
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Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

“…The main goal of the presented technique is to transform these problems into a nonlinear system of algebraic equations using the operational matrix obtained from the integration, which can be solved by a proper numerical method; thus, the solution procedures are either reduced or simplified accordingly. …”
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…The vanishing condition is reduced to a system of algebraic constraints, which can then be solved for unknown control points in terms of known boundary control points. …”
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Topology of 3-dimensional manifolds by Eaman Eftekhary

“…Starting with the work of Poincare in the last years of 19th century and first few years of 20th century, we review the major steps in putting 3-manifolds and their algebraic topology in a solid mathematical framework, and the important theorems which strengthened the understanding of 3-manifolds, including the prime decomposition theorem and JSJ decomposition of 3-manifolds. …”
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Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System by Yuan-Wei Tseng, Jer-Guang Hsieh

“…It will be shown that linear quadratic regulator (LQR) design for linear time-invariant SDS systems using state derivative feedback can be obtained via an algebraic Riccati equation. Furthermore, this optimal state derivative feedback may also be implemented using an equivalent state feedback. …”
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Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods by S. Valton, F. Peyrin, D. Sappey-Marinier

“…We consider the α-FDK algorithm, the shift-variant FBP method derived from the T-FDK, an FBP method based on the Grangeat formula, and an iterative algebraic method (SART). The results show that the low contrast artifacts can be efficiently corrected by the shift-variant method and the SART method to achieve good quality images at the expense of increased computation time, but the geometrical deformations are still not compensated for by these techniques.…”
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The Feyn-structure of Yangian symmetry by Florian Loebbert, Harshad Mathur

“…The considered bilocal constraints on Feynman integrals resemble the definition of conformal partial waves via Casimir operators, but are based on a different algebraic structure.…”
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Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method by Ying Zhang, Dongyan Shi, Dongze He, Dong Shao

“…After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. …”
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Investigation and evaluation of economic variables affecting the national power of countries by Reyhaneh SalehAbadi, Mohammad Reza HafezNia, Seyyed Hadi Zarghani, syrus ahmadi

“…The national strength of algebraic aggregation is a large number of positive and negative factors that are composed of numerous sources and resources. …”
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Filters in 2D and 3D Cardiac SPECT Image Processing by Maria Lyra, Agapi Ploussi, Maritina Rouchota, Stella Synefia

“…SPECT images are then reconstructed, either by filter back projection (FBP) analytical technique or iteratively, by algebraic methods. The aim of this study is to review filters in cardiac 2D, 3D, and 4D SPECT applications and how these affect the image quality mirroring the diagnostic accuracy of SPECT images. …”
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New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations by Jian Rong Loh, Chang Phang, Abdulnasir Isah

“…This reduces the FIDE into a system of algebraic equations to be solved for the Genocchi coefficients of the solution f(x). …”
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Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks by Hung-Tsai Huang, Ming-Gong Lee, Zi-Cai Li, John Y. Chiang

“…In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. …”
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Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making by Omid Nikan, Jalil Rashidinia, Hossein Jafari

“…It allows for significant sparsification of the algebraic system, leading to a lower condition number and reduced computational effort, while keeping high accuracy. …”
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Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information by Baolin Li, Lihua Yang

“…Additionally, Hamacher operations as a generalization of Algebraic operations and Einstein operations demonstrate good smooth approximate. …”
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