Haar Wavelet Method for Nonlinear Vibration of Functionally Graded CNT-Reinforced Composite Beams Resting on Nonlinear Elastic Foundations in Thermal Environment by Jianyu Fan, Jin Huang

“…To evaluate the nonlinear natural frequencies, the obtained equations are discretized into a set of nonlinear algebraic equations through HWDM and then the direct iteration technique is employed to solve the resulting algebraic equations. …”
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On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields by Michail P. Markakis, Panagiotis S. Douris

“…The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. …”
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Hermite–Hadamard Type Inequalities via Generalized Harmonic Exponential Convexity and Applications by Saad Ihsan Butt, Muhammad Tariq, Adnan Aslam, Hijaz Ahmad, Taher A. Nofal

“…In addition, we elaborate the newly introduced idea by examples and some interesting algebraic properties. As a result, several new integral inequalities are established. …”
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On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators by Lajos Molnár

“…We conjecture that a similar assertion is true for general noncommutative C*-algebras and present a proof in the finite dimensional case.…”
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On Quantum Statistical Mechanics: A Study Guide by Wladyslaw Adam Majewski

“…These include the emergence of algebraic approach and the necessity of employment of infinite-dimensional structures. …”
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Combinatorics in N = 1 Heterotic Vacua by Seung-Joo Lee

“…The Calabi-Yau threefolds are algebraically realised as hypersurfaces in toric varieties, and a large class of vector bundles are constructed thereon as monads. …”
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THREE-DIMENSIONAL RECONSTRUCTION BY SART METHOD WITH MINIMIZATION OF THE TOTAL VARIATION by S. A. Zolotarev, M. A. Mirzavand

“…Computed tomography is still being intensively studied and widely used to solve a number of industrial and medical applications. The algebraic reconstruction method with simultaneous iterations SART considered in this work as one of the most promising of iterative methods, suitable for the tomographic problems. …”
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Modeling Dominant Height Growth in Planted Pinus pinea Stands in Northwest of Tunisia by Sghaier Tahar, Palahi Marc, Garchi Salah, Bonet José Antonio, Ammari Youssef, Pique Miriam

“…Six generalized algebraic difference equations (GADAs) derived from the base models of log-logistic, Bertalanffy-Richards, and Lundqvist-Korf were used to develop site index model for Pinus pinea plantations in north-west of Tunisia. …”
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On Refinements of Multidimensional Inequalities of Hardy-Type via Superquadratic and Subquadratic Functions by M. Zakarya, Ghada AlNemer, H. A. Abd El-Hamid, Roqia Butush, H. M. Rezk

“…By utilizing the peculiarities of superquadratic and subquadratic functions, we give the extensions for multidimensional inequalities of Hardy-type with general kernel. We use some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality to prove the essential results in this paper. …”
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A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method by Changqing Yang, Jianhua Hou

“…The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. …”
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Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique by Youssef Esmaiel, Magdi El-Azab, Galal El-Baghdady

“…By employing these polynomials, the singular Volterra integral equation is transformed into a set of algebraic equations that need to be solved. Subsequently, numerical analysis is introduced, followed by some examples and a comparison of them with existing methods to demonstrate the soundness and practicality of our method.…”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. …”
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Duality of (h,φ)-Multiobjective Programming Involving Generalized Invex Functions by GuoLin Yu

“…In the setting of Ben-Tal's generalized algebraic operations, this paper deals with Mond-Weir type dual theorems of multiobjective programming problems involving generalized invex functions. …”
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Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation by Binlu Feng, Yufeng Zhang

“…Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained. …”
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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. …”
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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. …”
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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. …”
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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.…”
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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. …”
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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. …”
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