Projective varieties have countably many real forms by Labinet, Timothée L.

“…In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. …”
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Triangular Function Method is Adopted to Solve Nonlinear Stochastic It o^–Volterra Integral Equations by Guo Jiang, Dan Chen, Fugang Liu

“…Integral operator matrixes of triangular functions are used to convert the nonlinear stochastic integral equations into a system of algebraic equations. Meanwhile, we gain the error of the current method, and it is demonstrated that the error accuracy of this method is higher than that of the BPFs. …”
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Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation by K. R. Raslan, Khalid K. Ali, Reda Gamal Ahmed, Hind K. Al-Jeaid, Amira Abd-Elall Ibrahim

“…The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. …”
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Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet by Fuqiang Zhao, Jiaquan Xie, Qingxue Huang

“…The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. …”
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Solving Partial Integro-Differential Equations via Double Formable Transform by Bayan Ghazal, Rania Saadeh, Abdelilah K. Sedeeg

“…By solving numerous cases, the double formable transform’s ability to turn the PIDE into an algebraic equation that is simple to solve is demonstrated.…”
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The condition number associated with ideal lattices from odd prime degree cyclic number fields by de Araujo Robson Ricardo

“…The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Polynomial Learning With Errors (PLWE)”. …”
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The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor by Radek Matušů, Jana Závacká, Roman Prokop, Monika Bakošová

“…The paper focuses on robust stabilization where the suitable parameters of a simple continuous-time PI controller are determined through a combination of the Kronecker summation method, sixteen plant theorem, and an algebraic approach to control design in the ring of proper and stable rational functions. …”
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A New Generalized Chebyshev Matrix Algorithm for Solving Second-Order and Telegraph Partial Differential Equations by Waleed Mohamed Abd-Elhameed, Ramy M. Hafez, Anna Napoli, Ahmed Gamal Atta

“…This approach uses the operational matrix of derivatives of the generalized Chebyshev polynomials and applies the collocation method to convert the equations with their underlying conditions into algebraic systems of equations that can be numerically treated. …”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…Using matrix representation of a function and their derivatives, the problem is reduced to a system of algebraic equations in a simple way. From the computational point of view, the results are in excellent agreement with those presented in published works.…”
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Geometric Representations of Interacting Maps by Tsuyoshi Kato

“…In particular we discover a new duality on the set of automata which arise from the projective duality in algebraic geometry.…”
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On Bernstein Polynomials Method to the System of Abel Integral Equations by A. Jafarian, S. Measoomy Nia, Alireza K. Golmankhaneh, D. Baleanu

“…Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.…”
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Formal Lagrangian Operad by Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder

“…Following this idea, we provide a deformation theory for symplectic groupoids analog to the deformation theory of algebras. It turns out that the semiclassical part of Kontsevich's deformation of C∞(ℝd) is a deformation of the trivial symplectic groupoid structure of T∗ℝd.…”
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Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions by Saad Ihsan Butt, Saima Rashid, Muhammad Tariq, Miao-Kun Wang

“…We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. …”
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Application of Müntz Orthogonal Functions on the Solution of the Fractional Bagley–Torvik Equation Using Collocation Method with Error Stimate by S. Akhlaghi, M. Tavassoli Kajani, M. Allame

“…By using the Riemann–Liouville fractional integral operator that we define for the Müntz orthogonal functions, the process of numerically solving the fractional Bagley–Torvik equation that is solved using Müntz orthogonal functions is reduced, and finally, we reach a system of algebraic equations. By solving algebraic equations and obtaining the vector of unknowns, the fractional Bagley–Torvik equation is solved using Müntz orthogonal functions, and the error value of the method can be calculated. …”
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Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source by V. S. Malyar, A. V. Malyar

“…The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. …”
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A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR by O. N. Zhdanov, A. V. Sokolov

“…Practical application of advanced algebraic constructions in modern communication systems based on MC-CDMA (Multi Code Code Division Multiple Access) technology and in cryptography necessitates their further research. …”
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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…The resulting nonlinear system of algebraic equations is a discrete analogue of the initial system of differential equations. …”
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Quasi-discreted dynamics of a neural net: The lighthouse model by Hermann Haken

“…Because of the δ-functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. …”
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A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation by Yonglei Fang, Qinghong Li, Qinghe Ming, Kaimin Wang

“…The two RK methods in the pair have algebraic orders five and four, respectively. The two methods of the embedded pair are derived by nullifying the phase lag, the first derivative of the phase lag of the fifth-order method, and the phase lag of the fourth-order method. …”
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Note on the Solution of Transport Equation by Tau Method and Walsh Functions by Abdelouahab Kadem, Adem Kilicman

“…The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.…”
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