Consensus of High-Order Nonlinear Multiagent Systems with Constrained Switching Topologies by Junwei Wang, Kairui Chen, Yun Zhang

“…A multistep algorithm for designing consensus protocol is then developed by solving the Lyapunov equation and algebraic Riccati equation. Finally, simulation examples are delineated to substantiate the effectiveness of the proposed algorithms.…”
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Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification by Jonas Maziero

“…Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. …”
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Design of a Dynamic Simulator for a Biped Robot by Diego A. Bravo M, Carlos F. Rengifo Rodas

“…The intermittent nature of these forces and the mathematical inequalities that they must satisfy lead to models described by hybrid algebraic differential equations. In this paper, a simulator was developed for a seven degrees of freedom planar biped robot, which was modeled using the Euler-Lagrange formulation. …”
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On q-Rung Orthopair Fuzzy Subgroups by Asima Razzaque, Abdul Razaq

“…In this work, we characterize the idea of a q-rung orthopair fuzzy subgroup and examine various algebraic attributes of this newly defined notion. …”
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Mathematical Formulation of Soft-Contact Problems for Various Rheological Models of Damper by Wiesław Grzesikiewicz, Artur Zbiciak

“…The main finding of the paper is a method of description of soft-contact phenomenon between rigid object and deformable rheological structure by the system of explicit nonlinear differential-algebraic equations easy for numerical implementation. …”
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Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications by Hongju Li, Ping Yu, Jing Liang, Feng Zhao

“…Cyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding. …”
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Operations on Soft Sets Revisited by Ping Zhu, Qiaoyan Wen

“…In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. …”
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Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions by Huaiqing Zhang, Yu Chen, Xin Nie

“…The improved method maintains the merit of Pravin method which can convert the Hankel integral to algebraic calculation. The simulation results reveal that the improved method has high precision, high efficiency, and good adaptability to kernel function. …”
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Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications by Artion Kashuri, Soubhagya Kumar Sahoo, Bibhakar Kodamasingh, Muhammad Tariq, Ahmed A. Hamoud, Homan Emadifar, Faraidun K. Hamasalh, Nedal M. Mohammed, Masoumeh Khademi

“…The main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues. …”
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Optimal Tracking Performance of MIMO Discrete-Time Systems with Network Parameters by Chao-Yang Chen, Weihua Gui, Zhi-Hong Guan, Shaowu Zhou, Cailun Huang

“…The best attainable regulation performance limitations can be obtained by the limiting steady state solution of the corresponding algebraic Riccati equation (ARE). The simulation results are given to demonstrate the main results of the theoretical development.…”
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A Novel Approach towards Bipolar Soft Sets and Their Applications by Tahir Mahmood

“…In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.…”
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On the relationship of interior-point methods by Ruey-Lin Sheu, Shu-Cherng Fang

“…In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic paths that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…The capacity of general triple integral transforms to change PDEs into simple algebraic equations is demonstrated.…”
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On the System of Diophantine Equations x2-6y2=-5 and x=az2-b by Silan Zhang, Jianhua Chen, Hao Hu

“…In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x2-6y2=-5 and x=az2-b for each pair of integral parameters a,b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals.…”
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A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions by E. H. Doha, D. Baleanu, A. H. Bhrawy, R. M. Hafez

“…A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. …”
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Singular LQ Problem for Irregular Singular Systems by Qingxiang Fang, Baolin Zhang, Jun-e Feng

“…The optimal control-state pair can be explicitly formulated via solving an algebraic Riccati equation and a Sylvester equation. …”
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Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets by Xiaoyong Xu, Fengying Zhou

“…The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. …”
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A Theory Approach towards Tradable Rail Freight Option by Jingwei Guo, Lutian Li, Ji Zhang, Qi Shen, Zhongqi Xie, Qinglin Li

“…The most significant feature of this method is its simplicity in analyzing the optimal pricing decision using only the algebraic category and Ito’s lemma.…”
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Numerical solution of nonlinear complex integral equations using quasi- wavelets by Ahmed Ayad Khudhair, Saeed Sohrabi, Hamid Ranjbar

“…The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. …”
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Sieve Method for Polynomial Linear Equivalence by Baocang Wang, Yupu Hu

“…Some cryptographic and algebraic properties of PLE are discussed, and from the properties we derive three sieves called multiplicative, differential, and additive sieves. …”
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