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. …”

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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A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators by Zhaoxia Chen, Xiong You, Xin Shu, Mei Zhang

“…New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. …”
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Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta’s Substitution by Y. Y. Lee

“…The aim of the modification in the solution procedures is to develop the analytic formulations, which are used to calculate the vibration amplitudes of a nonlinear multimode damped beam without the need of nonlinear equation solver for the nonlinear algebraic equations generated in the harmonic balance processes. …”
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Some Graph-Based Encryption Schemes by Baizhu Ni, Rabiha Qazi, Shafiq Ur Rehman, Ghulam Farid

“…This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages.…”
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Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems by Yuangong Sun, Zhaorong Wu, Fanwei Meng

“…We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.…”
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New Inner Product Quasilinear Spaces on Interval Numbers by Hacer Bozkurt, Yılmaz Yilmaz

“…Secondly, we present Is,Ic0,Il∞, and Il2 quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.…”
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A Survey on the Integral Means Spectrum for Conformal Mappings by I.R. Kayumov

“…Estimates of the integral means spectrum in the class of functions mapping the exterior of the unit disk onto the attraction basins of the infinity of algebraic polynomials are presented.…”
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Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications by Artion Kashuri, Sajid Iqbal, Saad Ihsan Butt, Jamshed Nasir, Kottakkaran Sooppy Nisar, Thabet Abdeljawad

“…In this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and ϕ are proved. …”
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Orthogonal Polynomials of Compact Simple Lie Groups by Maryna Nesterenko, Jiří Patera, Agnieszka Tereszkiewicz

“…Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. …”
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A Survey on Generalized Topological Indices for Silicon Carbide Structure by Sajid Mahboob Alam, Fahd Jarad, Abid Mahboob, Imran Siddique, Taner Altunok, Muhammad Waheed Rasheed

“…Topological indices facilitate the collection of beneficial information and provide an approach to understanding the properties of chemical structure by providing information about algebraic graphs. Let G be a graph with u-vertices and Ωu be the degree of uth vertex. …”
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Applications of a New q-Difference Operator in Janowski-Type Meromorphic Convex Functions by Bakhtiar Ahmad, Muhammad Ghaffar Khan, Mohamed Kamal Aouf, Wali Khan Mashwani, Zabidin Salleh, Huo Tang

“…Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. …”
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New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds by W. M. Abd-Elhameed, E. H. Doha, Y. H. Youssri

“…The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. …”
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Syntheses of differential games and pseudo-Riccati equations by Yuncheng You

“…For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.…”
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Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature by Yawei Chu, Dehe Li, Jundong Zhou

“…The arguments mainly rely on algebraic curvature estimates and several analysis tools on Mn,g,f, such as the property of f-parabolic and a Liouville type theorem.…”
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