Some New Results for the $\mathscr{M}$-Transform Involving the Incomplete $I$-Functions by Sanjay Bhatter, Nishant -, Sunil Purohit

“…The right choice of integral transforms aids in simplifying both integral and differential problems into a solution-friendly algebraic equation. In this paper, $\mathscr{M}$-transform is applied to establish the image formula for the multiplication of a family of polynomials and incomplete $I$-functions. …”
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A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 by Hasan Alnajjar

“…Let ℱ denote an algebraically closed field with a characteristic not two. …”
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Global Well-Posedness and Large-Time Behavior for the Equilibrium Diffusion Model in Radiation Hydrodynamics by Peng Jiang, Jinkai Ni, Lu Zhu

“…The global existence of classical solutions to the Cauchy problem in the whole space is established when initial data is a small smooth perturbation of a constant equilibrium state: moreover, an algebraic rate of convergence of solutions toward equilibrium is obtained under additional conditions on initial data. …”
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Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay by Zhanying Yang, Jie Zhang, Junhao Hu, Jun Mei

“…Moreover, the obtained criteria are expressed as some algebraic inequalities independent of the Mittag–Leffler functions, and thus, the calculation is relatively simple in both theoretical analysis and practical applications. …”
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Perihelion Precessions of Inner Planets in Einstein’s Theory and Predicted Values for the Cosmological Constant by Alvaro H. Salas S, Jairo E Castillo H, Lorenzo J. Martınez H

“…We give predictions about the value of the Cosmological Constant. Simple algebraic formulas allow to estimate perihelion shifts with high accuracy.…”
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Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness by Dongli Wu, Hao Zhang, Yunping Liu, Weihua Fang, Yan Wang

“…The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. …”
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A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations by A. H. Bhrawy, M. A. Alghamdi

“…The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. …”
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An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag by Behrooz Basirat, Hamid Reza Elahi

“…The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. …”
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Generalized affine transformation monoids on Galois rings by Yonglin Cao

“…The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x↦xu+a (for all x∈A), where u,a∈A. We study the algebraic structure of the monoid Gaff(A) on a finite Galois ring A. …”
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A note on rings of continous functions by J. S. Yang

“…We show that the theorem there is a completely regular space Y associated with a given topological space X such that C(Y,R) is isomorphic to C(X,R) may be extended to a fairly large class of topologlcal rings, and that, in the study of algebraic structure of the ring C(X,A), it is sufficient to study C(X,R) if A is path connected.…”
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On equivariant bundles and their moduli spaces by Damiolini, Chiara

“…Let $G$ be an algebraic group and $\Gamma $ a finite subgroup of automorphisms of $G$. …”
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Classes of Int-Soft Filters in Residuated Lattices by Young Bae Jun, Sun Shin Ahn, Kyoung Ja Lee

“…Finally, it is shown that the notion of an MV-int-soft filter coincides with the notion of a regular int-soft filter in BL-algebras.…”
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Universally catenarian domains of D+M type, II by David E. Dobbs, Marco Fontana

“…Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is universally catenarian. …”
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Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising by Yuying Shi, Qianshun Chang

“…For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. …”
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Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs by A. Pirkhedri, H. H. S. Javadi, H. R. Navidi

“…This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. …”
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On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS by Vakeel Khan, Zahid Rahman, Ayhan Esi, Amit Kumar

“…This paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot\|_G}, m_{\| \cdot \|_G} ^\mathcal{I}$ and $m_{0 \| \cdot \|_G} ^\mathcal{I}$ respectively. We discussed some algebraic and topological properties of these classes. …”
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SIMULATION OF THE ELECTROSTATIC DIPOLE FIELD IN THE PRESENCE OF A THIN UNCLOSED OBLATE ELLIPSOIDAL SHELL AND PLANE by G. Ch. Shushkevich

“…Using the addition theorems connecting spherical, ellipsoidal and cylindrical harmonic functions, the solution of the boundary problem is reduced to the solution of dual series equations by the Legendre polynomials that are transformed to an infinite system of linear algebraic equations of the second kind with a completely continuous operator. …”
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First Basic Problem of Elasticity Theory for a Composite Layer with Two Thick-Walled Tubes by Oleksandr Yu. Denshchykov, Valentyn P. Pelykh, Yaroslav V. Hrebeniuk, Vitalii Yu. Miroshnikov

“…Satisfying the boundary conditions and conjugation conditions between the layer and the tubes, an infinite system of integro-algebraic equations is formed, which is reduced to linear algebraic equations of the second kind, and the reduction method is applied. …”

Accelerated Modeling of Transients in Electromagnetic Devices Based on Magnetoelectric Substitution Circuits by Sergii Tykhovod, Ihor Orlovskyi

“…This helps to transform integro-differential state equations into linear algebraic equations for the representations of the solution functions. …”
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A note on a pair of derivations of semiprime rings by Muhammad Anwar Chaudhry, A. B. Thaheem

“…As an application, we show that noncommutative semisimple Banach algebras do not admit nonzero linear derivations satisfying the above central property. …”
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