“…We consider the properties of two specific enumeration operators: the HTP operator, mapping a set W of prime numbers to the set of polynomials realizing Hilbert’s Tenth Problem in the ring [Formula: see text]; and the root operator, mapping the atomic diagram of an algebraic field F of characteristic 0 to the set of polynomials in [Formula: see text] with roots in F. …”
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“…We applied this approach to redesigning an algebraic symbolization tutor. Our classroom study with 76 high school freshmen shows that, compared to the original tutor, the redesigned tutor led to higher learning efficiency on more difficult skills, higher learning gain on unscaffolded whole tasks, and more robust transfer to less practiced tasks. …”
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“…More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. …”
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“…For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.…”
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“…To further cement our results, our semantics is entirely based on a physically natural model of von Neumann algebras, which are mathematical structures used by physicists to study quantum mechanics.…”
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“…Furthermore, we also show that algebraic structure found in this prediction can be taken as a proxy for structure on the motor displacements, allowing for the discovery of the combinatorial structure of said displacements. …”
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“…In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. …”
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“…Stability of equilibria or critical points are analyzed by applying algebraic analysis. This model allows us to understand the process of cancer development and might help us design better treatment strategies to account for immunoediting.…”
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“…By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearized LS model equations. …”
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“…In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. …”
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“…Motivated by the recent realization of hyperbolic lattices in circuit quantum electrodynamics, we exploit ideas from algebraic geometry to construct a hyperbolic generalization of Bloch theory, despite the absence of commutative translation symmetries. …”
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“…Two sets of examples, including small and medium-sized problems, are implemented by general algebraic modeling language (GAMS) software to evaluate the model. …”
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“…Robust algorithms for this type of problem have been built by following algebraic approaches, but data-driven solutions are becoming more appealing due to their stochastic nature. …”
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“…In the case of a finite distributive or strongly modular consistent poset, this poset can be converted into a residuated structure and hence it can serve as an algebraic semantics of a certain non-classical logic with unsharp conjunction and implication. …”
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“…The core objective of this work is to construct some algebraic operations for PFSS such as OR-operation, AND-operation, and necessity and possibility operations. …”
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“…The methods we use are mostly drawn from the area of polynomial optimization and convex relaxation; we also use some results from real algebraic geometry, as well as Matlab optimization packages for PNP.…”
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“…The state vector can then be reconstructed by means of an algebraic-like observer through the computation of time derivatives using a Numerical Differentiation with Annihilatorsconsidering its inherent noise rejection properties. …”
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“…This paper focuses on the formulation of a reliable mathematical model represented by a series of differential and algebraic equations for the industrial batch MBT production process. …”
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“…The main advantage of our strategy is that it characterizes the approximate solution via some recurrence formulas, instead of solving a complex non-linear block algebraic system that requires high computational costs. …”
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“…However, in contrast to ‘almost-commutative manifolds’, the present framework, which we call gauge matrix spectral triples, employs only finite-dimensional algebras. In a path-integral quantization approach to the Spectral Action, this allows to state Yang–Mills–Higgs theory (on four-dimensional Euclidean fuzzy space) as an explicit random multimatrix model obtained here, whose matrix fields exactly mirror those of the Yang–Mills–Higgs theory on a smooth manifold.…”
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