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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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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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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Probing the diversity of kink solitons in nonlinear generalised Zakharov-Kuznetsov-Benjamin-Bona-Mahony dynamical model by Naher Mohammed A. Alsafri, Hamad Zogan

“…With the incorporation of the Riccati equation, a close-form solution is then assumed for the resultant NODE by RMESEM, which converts the NODE into a set of algebraic equations. The fresh plethora of soliton results in the form of rational, exponential, rational-hyperbolic and periodic functional cases are obtained by addressing this set of equations. …”
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Noetherian and Artinian ordered groupoids—semigroups by Niovi Kehayopulu, Michael Tsingelis

“…Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). …”
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Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics by Renato Luz, Gustavo Petronilo, Ademir de Santana, Caroline Costa, Ronni Amorim, Rendisley Paiva

“…Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. …”
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Composite Operator Method Analysis of the Underdoped Cuprates Puzzle by Adolfo Avella

“…COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. …”
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