Green approaches to heavy metal removal from wastewater: Microalgae solutions in a circular economy framework by Nikolaos A. Kazakis

“…A new research project (ALGEBRA) has been launched, offering a green approach to heavy metal removal from wastewater, aligning with the principles of circular economy. …”
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(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves by Chunlei Wang, Yong Zhang, Baoshu Yin, Xiaoen Zhang

“…By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. …”
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Calculation of ecological land-footprint - based on the input-output model and focusing on the imported commodities by Imre Dobos, Brigitta Tóth-Bozó

“…In addition, we allocate the latter again among final consumption and exports using the framework of linear algebra and matrix arithmetic. We also propose ways of extending the model to overcome the general but misleading assumption in the literature that imported commodities have an equal per unit ecological footprint to domestic products, an approach that is based on the idea that trading partners have the same technological background.…”
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Eigenvalues of Relatively Prime Graphs Connected with Finite Quasigroups by Muhammad Nadeem, Nwazish Ali, Hafiz Muhammad Bilal, Md. Ashraful Alam, M. I. Elashiry, Kholood Alnefaie

“…Spectral graph theory plays a very important role in understanding certifiable applications such as cryptography, combinatorial design, and coding theory. Nonassociative algebras, loop groups, and quasigroups are the generalizations of associative algebra. …”
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An Algorithm to Compute the H-Bases for Ideals of Subalgebras by Rabia, Muhammad Ahsan Binyamin, Nazia Jabeen, Adnan Aslam, Kraidi Anoh Yannick

“…The concept of H-bases, introduced long ago by Macauly, has become an important ingredient for the treatment of various problems in computational algebra. The concept of H-bases is for ideals in polynomial rings, which allows an investigation of multivariate polynomial spaces degree by degree. …”
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A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. by Niringiye, Richard

“…It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cholesky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions.…”
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Integrability of open boundary driven quantum circuits by Chiara Paletta, Tomaž Prosen

“…By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. …”
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When are the classes of Gorenstein modules (co)tilting? by Wang, Junpeng, Liu, Zhongkui, Zhao, Renyu

“…The second is to characterize Gorenstein modules via finitely generated modules, which provides a proof of that left Noetherian rings with finite left Gorenstein global dimension satisfy First Finitistic Dimension Conjecture and a result related to a question posed by Bazzoni in [J. Algebra 320 (2008) 4281-4299]. The last is to give some new characterizations of Dedekind and Prüfer domains and commutative Gorenstein Artin algebras as well as general (possibly not commutative) Gorenstein rings and Ding–Chen rings.…”
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A Closed Form of Higher-Order Cayley Transforms and Generalized Rodrigues Vectors Parameterization of Rigid Motion by Daniel Condurache, Mihail Cojocari, Ioan-Adrian Ciureanu

“…The approach uses only elementary algebraic calculations with Euclidean vectors and tensors. …”
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Complete verification of strong BSD for many modular abelian surfaces over ${\mathbf {Q}}$ by Timo Keller, Michael Stoll

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Lie symmetries, closed-form solutions, and conservation laws of a constitutive equation modeling stress in elastic materials by Rehana Naz, Willy Hereman

“…The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was investigated by Mason and his collaborators (Magan et al., 2018). The Lie algebra for the model is five-dimensional for the shearing exponent n>0, and it includes translations in time, space, and displacement, as well as time-dependent changes in displacement and a scaling symmetry. …”
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Space-Time Defects and Group Momentum Space by Michele Arzano, Tomasz Trześniewski

“…In particular, if we fix the direction of propagation of a massless defect in n+1-dimensional Minkowski space, then its space of holonomies is a maximal Abelian subgroup of the AN(n-1) group, which corresponds to the well known momentum space associated with the n-dimensional κ-Minkowski noncommutative space-time and κ-deformed Poincaré algebra. We also conjecture that massless defects in n-dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. …”
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(m, n)-Ideals in Semigroups Based on Int-Soft Sets by G. Muhiuddin, Abdulaziz M. Alanazi

“…Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. …”
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Critical spin chains and loop models with $PSU(n)$ symmetry by Paul Roux, Jesper Lykke Jacobsen, Sylvain Ribault, Hubert Saleur

“…This allows us to determine their spectra either by computing a twisted torus partition function, or by studying representations of the walled Brauer algebra. In the critical limit, our models give rise to a CFT that exists for any $n∈\mathbb{C}$ and has a global $PSU(n)$ symmetry. …”
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Thermodynamics of a Schwarzschild black hole surrounded by quintessence in the generalized uncertainty principle framework by Soham Sen, Abhijit Dutta, Sunandan Gangopadhyay

“…Considering the variance in the position to be of the order of the event horizon radius and equating the variance in the momentum to the Hawking temperature of the black hole, we substitute these variances in the deformed algebra. From there we obtained the generalized uncertainty principle-modified black hole temperature and eventually the specific heat of the black hole. …”
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NEW DESIGN METHOD FOR MAIN-AUXILIARY MODEL CONSTANT SPRINF SUPPORT HANGER by XING QingGuo, YANG LuLu, GANG XianYue, CHU ZhenMei

“…According to the Instant relationship between the outside force and the spring energy changes in the body coordinate system,The elliptic algebra Equation of cam rotation angle and load tube vertical displacement was derived by using energe method. …”
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Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations. by Akhtar Hussain, M Usman, Fiazuddin Zaman, Ahmed M Zidan, Jorge Herrera

“…We derived eight-dimensional symmetry algebra for the (3+1)-dimensional nonlinear elastic wave equation, which was used to obtain the optimal system. …”
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Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem by Minghua Xu, Yong Zhang, Qinglong Huang, Zhenhua Yang

“…This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. …”
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Difference equations: From Berry connections to the Coulomb branch by Andrea E. V. Ferrari, Daniel Zhang

“…We interpret the above action as that of the bulk Coulomb branch algebra on boundary twisted chiral operators. This relates our work to recent constructions of actions of Coulomb branch algebras on quantum equivariant cohomology, providing a novel correspondence between these actions and spectral data of generalised periodic monopoles. …”
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Exploring parameter dependence of atomic minima with implicit differentiation by Ivan Maliyov, Petr Grigorev, Thomas D. Swinburne

“…Here, the implicit derivative of functions defined as a fixed point is used to Taylor-expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. …”
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