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Creation of a stable vector vortex beam with dual fractional orbital angular momentum. [PDF]
Sci RepWang L, Wang G, Dong X, Gao X, Zhuang S.
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An explainable "family bucket" model for simultaneous prediction of K-edge XANES for multiple light transition metals. [PDF]
Chem SciHuang C +6 more
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Monolithic silicon carbide metasurfaces for engineering arbitrary 3D perfect vector vortex beams. [PDF]
Nat CommunLiu M +9 more
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Néel spin-orbit torque in antiferromagnetic quantum spin and anomalous Hall insulators. [PDF]
Nat CommunTang J, Zhang H, Cheng R.
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Topological Vector Spaces [PDF]
, 1982 Vector spaces will be considered as vector spaces over ℂ unless something else is specified. The symbols Hom(X, Y) resp. Sur(X, Y) will be reserved for sets of continuous homomorphisms resp. surjective homomor-phisms; End(X) is the set of continuous endomorphisms and Aut(E) is the set of continuous automorphisms (bijective and bicontinuous ...
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1994
One way to think of functional analysis is as the branch of mathematics that studies the extent to which the properties possessed by finite dimensional spaces generalize to infinite dimensional spaces. In the finite dimensional case there is only one natural linear topology.
Kim C. Border, Charalambos D. Aliprantis
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One way to think of functional analysis is as the branch of mathematics that studies the extent to which the properties possessed by finite dimensional spaces generalize to infinite dimensional spaces. In the finite dimensional case there is only one natural linear topology.
Kim C. Border, Charalambos D. Aliprantis
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Journal of the London Mathematical Society, 1965
Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables ...
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Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables ...
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