Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…In such a way, linear algebras of extended hypernumbers are built. A special topology of conical neighborhoods in these algebras is introduced and studied. …”
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Surface Approximation using Growing Self-Organizing Nets and Gradient Information by Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano

“…Also, we show that in the adaptation stage the network utilizes efficient transformations, expressed as versors in the conformal geometric algebra framework, which build the shape of the object independent of its position in space (coordinate free). …”
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Optimization strategy on coverage control in wireless sensor network based on Voronoi by Chun-jiang ZHAO, Hua-rui WU, Qiang LIU, Li ZHU

“…Coverage holes directly reduce network performance and become a key problem of wireless sensor network.A detect-repair scheme for area coverage in wireless sensor network with Voronoi was proposed.The strategy achieves the network coverage rate optimization balance with a prerequisite of an acceptable coverage quality of network area.It uses the geometry theories and vector algebra to analyse the sensing range of nodes and the position feature of Voronoi polygon.It can calculate the accurate area of holes and ensure the connectivity of networks with the least number of odes.Simulation results show that the strategy can effectively reduce number of the nodes and the overlapped sensing regions and control redundant nodes.Meanwhile,the strategy has fast convergence speed.It not only realizes the control and optimization of the network coverage,but also outperforms existing algorithms with respect to the coverage of the target region.…”
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The dark side of double-tensor multiplets by L. Andrianopoli, G. Casale, L. Ravera, A. Santambrogio

“…Despite this fact, the supersymmetry algebra results to close only on-shell. Our analysis is conducted both in superspace, using the geometric (rheonomic) approach, and in spacetime, comparing how our results are obtained in the two approaches. …”
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A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models by Thierry E. Huillet

“…Next, using elementary algebra on CM functions, some suggested novel evolutionary mechanisms of potential interest are introduced and discussed.…”
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Non-invertible and higher-form symmetries in 2+1d lattice gauge theories by Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng

“…One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. …”
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Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums by Zoltán Kádár, Annalisa Marzuoli, Mario Rasetti

“…Equivalence of the previous models in the ground state is shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. …”
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Homological dimension based on a class of Gorenstein flat modules by Dalezios, Georgios, Emmanouil, Ioannis

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More on stubs in open string field theory by Martin Schnabl, Georg Stettinger

“…Abstract We continue our analysis of open string field theory based on A ∞ -algebras obtained from Witten’s theory by attaching stubs to the elementary vertex. …”
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A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II by Young Sik Kim

“…,(hn,x)∼), x∈B where μˆ:ℝn→ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ(ℝn), the Borel σ-algebra of ℝn with ‖μ‖<∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not always exist for bounded cylinder functions F(x)=f((h1,x)∼,...…”
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On the Number of Conjugate Classes of Derangements by Wen-Wei Li, Zhong-Lin Cheng, Jia-Bao Liu

“…Although we may obtain the value of hn in some computer algebra system, it is still meaningful to find an efficient way to calculate the approximate value, especially in engineering, since most people are familiar with neither programming nor CAS software. …”
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Modular representations of Loewy length two by M. E. Charkani, S. Bouhamidi

“…Let G be a finite p-group, K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. …”
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Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds by Mancho Manev

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Holographic Carrollian currents for massless scattering by Romain Ruzziconi, Amartya Saha

“…We then construct Carrollian CFT currents from the ascendants of the hard graviton operator, which satisfy the Lw 1+∞ algebra. We show that the large-time limit of their Ward identities implies an infinite tower of projected soft graviton theorems in the bulk, while their finite-time OPEs encode the collinear limit of scattering amplitudes.…”
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The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations by Xiaoyan Liu, Jin Xie, Zhi Liu, Jiahuan Huang

“…The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. …”
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Fuzzy BCI-subalgebras with interval-valued membership functions by Sung Min Hong, Young Bae Jun, Seon Jeong Kim, Gwang Il Kim

“…The purpose of this paper is to define the notion of an interval-valued fuzzy BCI-subalgebra (briefly, an i-v fuzzy BCI-subalgebra) of a BCI-algebra. Necessary and sufficient conditions for an i-v fuzzy set to be an i-v fuzzy BCI-subalgebra are stated. …”
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Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability by Carman Vlad

“…Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ. 𝒜(ℒ) is the algebra generated by ℒ and ℳ(ℒ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜(ℒ). …”
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Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. by Nzabonimpa, Godfrey

“…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 Cho!…”
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Real Root Polynomials and Real Root Preserving Transformations by Suchada Pongprasert, Kanyarat Chaengsisai, Wuttichai Kaewleamthong, Puttarawadee Sriphrom

“…The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. …”
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Path Transmissibility Analysis Considering Two Types of Correlations in Hydropower Stations by Baoping Zhi, Zhenyue Ma

“…In a complex situation, the application of the stochastic perturbation method is expanded using an algebra synthesis method the Hadamard product, and theoretical analyses, and numerical simulations of transfer paths in the new vibration model are carried out through the expanded perturbation method. …”
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