Fractional Integration via Picard Method for Solving Fractional Differential-Algebraic Systems by Susan H. Mohammad, Abdulghafor Mohammed Al-Rozbayani

“…In this paper, we applied an efficient integrative method called the fractional Picard method to find the approximate solution to a system of fractional algebraic differential equations (SFADEs). By comparing the results with the exact solution, it was found that this method is highly efficient for finding solutions. …”
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A Vector Algebraic Algorithm for Coverage Compensation in Hybrid Wireless Sensor Networks by Ning-ning Qin, Li-xia Guo, Zhi-guo Ding, Bao-guo Xu

“…Particularly, this paper proposes a vector algebra based algorithm by exploring redundant nodes as an extra dimension for coverage compensation. …”
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Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods by Zhongxuan Luo, Erbao Feng, Jielin Zhang

“…We present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. …”
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Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics by Gerd Niestegge

“…However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics, and Jordan algebras. This structure exhibits some similarities with Alfsen and Shultz's noncommutative spectral theory, but these two mathematical approaches are not identical. …”
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Discrete Waveform Relaxation Method for Linear Fractional Delay Differential-Algebraic Equations by Hongliang Liu, Yayun Fu, Bailing Li

“…Fractional order delay differential-algebraic equations have the characteristics of time lag and memory and constraint limit. …”
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Convergence of One-Leg Hybrid Methods for Implicit Mixed Differential Algebraic Systems by Iman H. Ibrahim, Fatma M. Yousry

“…This paper focuses on a hybrid multistep and its twin one-leg methods and implementing them on implicit mixed differential algebraic equations. The orders of convergence for the above methods are discussed and numerical tests are solved.…”
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Classification theorem on irreducible representations of the q-deformed algebra U′q(son) by N. Z. Iorgov, A. U. Klimyk

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Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order by Y. H. Cong, C. X. Jiang

“…A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. …”
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Connected algebraic subgroups of groups of birational transformations not contained in a maximal one by Fong, Pascal, Zikas, Sokratis

“…We prove that for each $n\ge 2$, there exist a ruled variety $X$ of dimension $n$ and a connected algebraic subgroup of $\mathrm{Bir}(X)$ which is not contained in a maximal one.…”
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Continuity in Teaching the Course Algebra and the Beginning of Analysis: Adaptation of Students to New Conditions by Azizkhan Umiralkhanov, Alma Abylkassymova, Yessenkeldy Tuyakov, Larissa Zhadrayeva, Almagul Ardabayeva

“…Also, an assessment of the effectiveness of continuity-based learning on the algebra and the beginning of analysis course was carried out based on the results of knowledge surveys. …”
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Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras by Seong-Hoon Cho

“…The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. …”
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Preimage attacks on reduced‐round Keccak hash functions by solving algebraic systems by Junling Pei, Lusheng Chen

Subjects: “…algebraic system…”
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Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability by Muhammad Ayub, Masood Khan, F. M. Mahomed

“…We present a systematic procedure for the determination of a complete set of kth-order (k≥2) differential invariants corresponding to vector fields in three variables for three-dimensional Lie algebras. In addition, we give a procedure for the construction of a system of two kth-order ODEs admitting three-dimensional Lie algebras from the associated complete set of invariants and show that there are 29 classes for the case of k = 2 and 31 classes for the case of k≥3. …”
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Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials by Deroin, Bertrand, Matheus, Carlos

“…The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura varieties), Klingler and Lerer recently showed that any bi-algebraic curve in a stratum of the moduli space of Abelian differentials is linear provided that the so-called condition $(\star )$ is fulfilled.In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus $7$, resp. $10$.…”
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Motion Modeling and Control of Lower Limb Exoskeleton Based on Max-Plus Algebra by Cuifeng Qin, Zuojun Liu

“…Max-plus algebra is a special method to describe the discrete event system. …”
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The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics by Yan Gu, Jiao Wang

“…As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. …”
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Dirac equation solution in the light front via linear algebra and its particularities by Jorge Henrique de Oliveira Sales, Gabriel de Oliveira Aragão, Diego Ramos do Nascimento, Ronaldo Thibes

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Motion Control of a Mobile Robot Using the Hedge–Algebras-Based Controller by Sy-Tai Nguyen, Thi-Thoa Mac, Hai-Le Bui

“…Hedge–algebras (HA) theory provides a useful mathematical tool for modeling the linguistic values of a linguistic variable. …”
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Algebraic Structures Based on a Classifying Space of a Compact Lie Group by Dae-Woong Lee

“…We analyze the algebraic structures based on a classifying space of a compact Lie group. …”
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Operator algebra, quantum entanglement, and emergent geometry from matrix degrees of freedom by Vaibhav Gautam, Masanori Hanada, Antal Jevicki

“…Abstract For matrix model and QFT, we discuss how dual gravitational geometry emerges from matrix degrees of freedom (specifically, adjoint scalars in super Yang-Mills theory) and how operator algebra that describes an arbitrary region of the bulk geometry can be constructed. …”
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