Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order by A. Kazemi Nasab, A. Kılıçman, Z. Pashazadeh Atabakan, S. Abbasbandy

“…The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. …”
Get full text

On the Vector Degree Matrix of a Connected Graph by Nasr A. Zeyada, Anwar Saleh, Majed Albaity, Amr K. Amin

“…A matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. …”
Get full text

Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed Point Method by Tianxiang Yao, Xianghong Lai

“…By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. …”
Get full text

On Copson Ideal Convergent Sequence Spaces by Mohammad Idrisi, Nazneen Khan, Kavita Saini, Mobeen Ahmad, ‌ Yasmeen, Manal Labadi

“…Also, I will define some algebraic, topological properties and inclusion relations in these spaces.…”
Get full text

Finite AG-groupoid with left identity and left zero by Qaiser Mushtaq, M. S. Kamran

“…It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

Mapping Iterative Medical Imaging Algorithm on Cell Accelerator by Meilian Xu, Parimala Thulasiraman

“…Algebraic reconstruction techniques require about half the number of projections as that of Fourier backprojection methods, which makes these methods safer in terms of required radiation dose. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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)”. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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.…”
Get full text

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.…”
Get full text

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.…”
Get full text

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. …”
Get full text

Advanced technique for flexible cable analysis by A. V. Chesnokov, V. V. Mikhailov

“…The differential equation of cable equilibrium is thus transformed into the set of algebraic equations. The cable length is expressed in algebraic form by means of the power expressions for the sum of the series.Results. …”
Get full text