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A modular, cost-effective, versatile, open-source operant box solution for long-term miniscope imaging, 3D tracking, and deep learning behavioral analysis. [PDF]
Beacher NJ +6 more
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Propagation for Schrödinger Operators with Potentials Singular Along a Hypersurface. [PDF]
Galkowski J, Wunsch J.
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Critical metrology of minimally accessible anisotropic spin chains. [PDF]
Adani M +4 more
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Global Stability for Charged Scalar Fields in an Asymptotically Flat Metric in Harmonic Gauge. [PDF]
Kauffman C.
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Loschmidt echo for deformed Wigner matrices. [PDF]
Erdős L, Henheik J, Kolupaiev O.
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Commutativity and Homotopy-Commutativity [PDF]
The aim of this section is to show, by means of the methods developed in Chapter 3, that for an associative H-space G there exist maps G× G → G satisfying certain commutativity conditions (Theorem 4.5). As will be explained in Remarks 4.6 this result is related to the work of other authors on homotopy-commutativity.
M. Arkowitz, C. R. Curjel
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Commutators and the Commutator Subgroup
The American Mathematical Monthly, 1977(1977). Commutators and the Commutator Subgroup. The American Mathematical Monthly: Vol. 84, No. 9, pp. 720-722.
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American Journal of Mathematics, 1952
A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the ...
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A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the ...
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Commutativity of rings with constraints on commutators
Results in Mathematics, 1985Let F denote a commutative ring, \(F\) the corresponding ring of polynomials in two non-commuting indeterminates, and F[X,Y] the ring of polynomials in two commuting indeterminates. A polynomial \(f(X,Y)\in F\) is called admissible if each of its monomials has length at least 3 and f(X,Y) has trivial image under the natural F-algebra map from \(F\) to ...
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