Mitigating Neural Habituation in Insect Bio-Bots: A Dual-Timescale Adaptive Control Approach. [PDF]
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Optical solutions to the time fractional Akbota equation arising in nonlinear optics via two distinct methods. [PDF]
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Unraveling the Link Between n-Back Working Memory and Algebraic Ability in Adolescents: Correlations and Training Effects. [PDF]
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Dynamic modeling and adaptive variable constraint optimization for integrated energy systems based on double-loop framework. [PDF]
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The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics. [PDF]
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Global Optimization of Polynomials over Real Algebraic Sets
Journal of Systems Science and Complexity, 2019This paper deals with the problem of optimizing a polynomial function \(f\) over an arbitrary given real algebraic set: \(f^{*}=\inf_{x\in V} f(x)\) where \(V = \{x \in \mathbb{R}^n | g_1(x) = 0, \dots , g_s(x) = 0\}\). The authors present an algorithm to compute the global infimum \(f^*\) of \(f\) over an arbitrary given real algebraic set \(V\) where
Chu Wang, Zhi-Hong Yang, L. Zhi
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Points near real algebraic sets
Proceedings of the American Mathematical Society, 2014Summary: Given a real algebraic set \( X\) and a box \( \mathcal{B}\) in \( \mathbb{R}^n\), which is a union of cubes of equal size and with disjoint interiors, we bound the number of cubes that intersect \( X\). As a consequence, we bound the volume of the set of points having distance at most \( \delta \) from \( X \cap \mathcal{B}\), and we estimate
W. Schmidt, U. Zannier
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Voronoi Diagrams of Real Algebraic Sets
Geometriae Dedicata, 2003This paper considers Voronoi diagrams of \(n\) semialgebraic sets in \(\mathbb{R}^d\) of dimension \(d-1\). Bounds are given on the cell complexity of \(k\)th order Voronoi diagrams.
J. H. Rieger
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The topology of real algebraic sets with isolated singularities
The Annals of Mathematics, 1981In this paper we give a topological classification of real algebraic sets with isolated singularities, showing that they are exactly smooth closed manifolds with smooth subpolyhedra crushed to points. The question of which topological spaces are homeomorphic to real algebraic sets (solutions of polynomial equations in Euclidean space) has been long ...
S. Akbulut, H. King
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Approximation of smooth manifolds by real algebraic sets
Russian Mathematical Surveys, 1982This is a survey article on \(C^ r\)-approximation (with ...
N. V. Ivanov
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