The Security Weakness of Block Cipher Piccolo against Fault Analysis by Junghwan Song, Kwanhyung Lee, Younghoon Jung

“…Fault analysis is a type of side channel attack and cube attack is an algebraic attack finding sufficiently low-degree polynomials in a cipher. …”
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Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model by Yun Liu, Xijuan Liu

“…The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. Numerical simulations are conducted not only to illustrate analytical results but also to exhibit complex behaviors which include period-doubling bifurcation in period −2,−4,−8,−16 orbits, invariant closed cycles, and attracting chaotic sets. …”
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Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems by D. Baleanu, A. H. Bhrawy, T. M. Taha

“…The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. …”
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Biodiesel Production by Reactive Flash: A Numerical Simulation by Alejandro Regalado-Méndez, Sigurd Skogestad, Reyna Natividad, Rubí Romero

“…The RF was modeled by an index-2 system of differential algebraic equations, the vapor split (ϕ) was computed by modified Rachford-Rice equation and modified Raoult’s law computed bubble point, and the continuation analysis was tracked on MATCONT. …”
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Transient Response of Multiple Interface Cracks in Fine-Grained Coating Composite Structures under Impact Loading by Shuaishuai Hu, Junlin Li

“…Both the singular integral equation and single-valued conditions are simplified into an algebraic equation through the Chebyshev point placement method and solved by numerical calculation. …”
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Free Vibration Analysis of Simply Supported and Clamped Functionally Graded Rectangular Plate Using Coupled Displacement Field Method by Nathi Venkatalakshmi, Kalidindi Krishnabhaskar, Koppanati Meerasaheb

“…The trial functions signifying the displacement constituents of the cross-sections of the plate are stated in simple algebraic polynomial forms. The lateral displacement field is derived in terms of the total rotations with the help of coupling equations. …”
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Similarity analysis for natural convection from a vertical plate with distributed wall concentration by I. Mulolani, M. Rahman

“…It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. …”
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Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation by Bo Ren

“…As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. …”
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Sixth-Kind Chebyshev and Bernoulli Polynomial Numerical Methods for Solving Nonlinear Mixed Partial Integrodifferential Equations with Continuous Kernels by Abeer M. Al-Bugami, Mohamed A. Abdou, Amr M. S. Mahdy

“…Then, using different numerical methods, the Bernoulli polynomial method and the Chebyshev polynomials of the sixth kind, the nonlinear Fredholm integral equation has been reduced into a system of nonlinear algebraic equations. The Banach fixed-point theory is utilized in order to have a conversation about the nonlinear mixed integral equation’s solution, namely, its existence and uniqueness. …”
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A Vieta–Lucas collocation and non-standard finite difference technique for solving space-time fractional-order Fisher equation by Mohd Kashif

“…The non-standard finite difference (NSFD) method converts this system of ODEs into algebraic equations which have been solved numerically. …”
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Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity by Hongmei Wu, Zhiying Ou

“…According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. …”
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Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length by Guohua Cao, Xiang Cai, Naige Wang, Weihong Peng, Jishun Li

“…The variable-domain three-node elements of rope are employed and the corresponding differential algebraic equations (DAEs) are derived using Lagrange’s equations of the first kind. …”
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Evaluation of Cross-Coupling Decoupling in Islanded Microgrid Control with Inductor Current Feed-Forward Technique by Sunday Olayanju, Folasade Mojisola Dahunsi, Akinlolu Adediran Ponnle

“…This paper presents stepwise design and modelling of the inverter dynamics in the d-q reference frame. The systematic algebraic elimination method with inductor current feed-forward was employed for decoupling cross-coupling terms in the current and voltage loop controller design. …”
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Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative by Xin Liu, Kamran, Yukun Yao

“…We apply LT to the given fractional differential equation, which reduces it to an algebraic equation. The reduced equation is solved for the unknown in LT space. …”
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On Stability of Multi-Valued Nonlinear Feedback Shift Registers by Haiyan Wang, Qiuzhen Lin, Jianyong Chen, Jianqiang Li, Jianghua Zhong, Dongdai Lin, Jia Wang, Lijia Ma

“…Due to lack of efficient algebraic tools, the stability of multi-valued NFSRs has been much less studied. …”
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Fuzzy Hypervector Spaces by R. Ameri, O. R. Dehghan

“…In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. …”
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The Order of Hypersubstitutions of Type (2,1) by Tawhat Changphas, Wonlop Hemvong

“…There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of 𝑀-solid varieties. …”
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Accurate 2-D AOA Estimation and Ambiguity Resolution for a Single Source under Fixed Uniform Circular Arrays by Le Zuo, Jin Pan

“…This paper presents an analytic algorithm for accurate two-dimensional (2-D) angle of arrival (AOA) estimation of a single source under fixed uniform circular arrays (UCAs). Algebraic and explicit formulations for 2-D AOA estimation are first developed in the Fourier domain. …”
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Efficient Synthesis of Large Finite Patch Arrays for Scanning Wide-Angle Anomalous Reflectors by Sravan Kumar Reddy Vuyyuru, Risto Valkonen, Sergei A. Tretyakov, do-Hoon Kwon

“…Anomalous reflection into an arbitrary desired angle using purely reactive loads is numerically and experimentally validated. Owing to the algebraic nature of load optimization, the design methodology may be applied to the synthesis of large-scale reflectors of practical significance.…”
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Consensus Information Filtering for Large-Scale Systems with Application to Heat Conduction Process by Liguo Zhang, Ying Lyu

“…On diffusion processing, we fuse the common state estimations of the local information filters using consensus averaging algorithms and algebraic graph theory. Stability and performance analysis is provided for this distributed filtering algorithm. …”
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