Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. …”
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A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems by A. Karimi Dizicheh, F. Ismail, M. Tavassoli Kajani, Mohammad Maleki

“…Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. …”
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Construction and Research of Lightweight Cryptography SOPT-S Boxes Based on Inverse Mapping in Galois Field by Zhaolong Fan, Qijian Xu, Yongju Xu, Fei Wang

“…It is shown that the SOPT-S boxes perform better in cryptographic properties such as differential uniformity, algebraic degree and avalanche effect than PRESENT, of which the algebraic degree achieves to n-1, avalanche effect to 1/2 and both of them achieve to the best, besides, it has an equivalent nonlinearity compared with PRESENT. …”
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Variable Weighted Ordered Subset Image Reconstruction Algorithm by Jinxiao Pan, Tie Zhou, Yan Han, Ming Jiang

“…We propose two variable weighted iterative reconstruction algorithms (VW-ART and VW-OS-SART) to improve the algebraic reconstruction technique (ART) and simultaneous algebraic reconstruction technique (SART) and establish their convergence. …”
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Fuzzy -Continuous Posets by S. P. Rao, Q. G. Li

“…The concept of fuzzy subset system on fuzzy posets is introduced; some elementary definitions such as fuzzy -continuous posets and fuzzy -algebraic posets are given. Furthermore, we try to find some natural classes of fuzzy -continuous maps under which the images of such fuzzy algebraic structures can be preserved; we also think about fuzzy -continuous closure operators in alternative ways. …”
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Research on trustworthiness measurement approaches of component based BPRAS by Qiang HAN, Yu-yu YUAN

“…Aiming at the absence of measurement methods about formalization on trustworthiness attributes of business process reengineering oriented application server (BPRAS),a cooperation framework of business process modeling and trustworthiness measurement based on BPRAS was proposed.Extracting the features of characteristics and behaviors of components consisting of the application server,an abstraction view of computing between those components based on the framework was presented through process algebraic approaches.Furthermore,relative concepts about its components computing operators were defined in order to construct algebraic model of its software trustworthiness (ST) to support the measurement of trustworthy BPRAS.Finally,an application case was also given.…”
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Restricted and extended plus operations for soft sets by Aslıhan Sezgin, Fitnat Aybek, Nurcan Güngör

“…By considering the algebraic properties of the operation and its distribution rules, we show that extended plus operation and other types of soft sets form many important algebraic structures, including semiring and near semiring in the collection of soft sets over the universe. …”
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Restricted and extended theta operations of soft sets: new restricted and extended soft set operations by Sezgin Aslihan, Aybek Fi̇tnat Nur

“…We demonstrate that, when coupled with other types of soft set operations, the extended theta operation forms numerous significant algebraic structures, such as semirings in the collection of soft sets over the universe, by taking into account the algebraic properties of the extended theta operation and its distribution rules. …”
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A Collocation Method for Solving Fractional Riccati Differential Equation by Yalçın Öztürk, Ayşe Anapalı, Mustafa Gülsu, Mehmet Sezer

“…Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. …”
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A characterisation of higher torsion classes by Jenny August, Johanne Haugland, Karin M. Jacobsen, Sondre Kvamme, Yann Palu, Hipolito Treffinger

“…The classification is furthermore extended to the setup of higher Nakayama algebras.…”
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Multiplicative Valency-Based Descriptors for Silicon Carbides Si2C3 − I[p, q], Si2C3 − II[p, q], Si2C3 − III[p, q], and SiC3 − III[p, q] in Drug Applications... by Jin Xu, Nasir Javaid, Shamas Bilal, Muhammad Rafaqat, Iskander Tlili

“…Topological indices help us to collect information about algebraic graphs and give us a mathematical approach to understand the properties of algebraic structures. …”
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Kemampuan Literasi Matematika Siswa dalam Memecahkan Soal TIMMS Konten Aljabar Ditinjau dari Pengetahuan Metakognitif by Laila Nur Cahyani, Lukman Jakfar Shodiq, Devi Rahayu Agustin

“…Students with procedural knowledge in solving TIMSS questions with algebraic content are classified as unable on all indicators. …”
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New restricted and extended soft set operations: restricted gamma and extended gamma operations by Aslıhan Sezgin, Fitnat Aybek

“…Considering the algebraic properties of the extended gamma operation and its distribution rules, we show that when combined with other types of soft sets, it forms several important algebraic structures, like semirings and nearsemirings, in the collection of soft sets over the universe. …”
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On the foundations of weak fuzzy complex-real functions by Lama Razouk, Suliman Mahmoud, Mohamad Ali

“…This paper aims to create a strong background of many algebraic structures dealing with Weak Fuzzy Complex (WFC) elements. …”
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Fano hypersurfaces in positive characteristic by Zhu, Yi

“…We prove that a general Fano hypersurface in a projective space over an algebraically closed field is separably rationally connected.…”
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Local Generalized (α,β)-Derivations by Ajda Fošner

“…We study local generalized (α,β)-derivations on algebras generated by their idempotents and give some important applications of our results.…”
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Higher-order differences based research on comparison between type-1 generalized Feistel-SP network and Feistel-SPSP network by ONGLe D, UJiao D, UWen-ling W

“…The powers against the higher-order differential cryptanalysis of the single-SP(substitution-permutation) model and the double-SP model are studied in the type-1 Feistel network by analyzing the growths of algebraic degrees. Combining the higher-order integral and the higher-order difference, a new method is exploited to estimate the upper bounds of algebraic degrees for the 4-line type-1 Feistel-SP scheme and the 4-line type-1 Feistel-SPSP scheme. …”
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Grassmannian Constellation Based on Antipodal Points and Orthogonal Design and Its Simplified Detecting Algorithm by Li Peng, Dacong Hu, Lin Zhang, Zhen Qin

“…A searching orthogonal USTM constellation based on the grid search algorithm is obtained under the presented framework and its minimum Frobenius chordal distance and simulation performance are be superior to those of the algebraic orthogonal USTM constellation.…”
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Approximate Cubic Lie Derivations by Ajda Fošner, Maja Fošner

“…We study the stability and hyperstability of cubic Lie derivations on normed algebras. At the end, we write some additional observations about our results.…”
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Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach by Sourav Mondal, Muhammad Imran, Nilanjan De, Anita Pal

“…The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. …”
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