Results 41 to 50 of about 566,880 (282)
A non-self-adjoint Lebesgue decomposition
, 2013 We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space, and in particular the multiplier algebra of the Drury-Arveson space.
Kennedy, Matthew, Yang, Dilian
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, 2023 We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\ 5. Uniqueness of determinants up to a constant.\\ 6. $\det(A\cdot B)=\det(A)\cdot\det(B)$ for square matrices,\\ 7.
openaire +2 more sources
Demonstration of an All‐Optical AND Gate Mediated by Photochromic Molecules
Advanced Functional Materials, EarlyView.A logic AND gate that runs on photons is demonstrated. It relies on two spatially separated photochromic molecules that work in tandem. Abstract The realization of a photonic logic AND gate, i.e. a logic AND gate that runs on photons rather than electrons, and where all steps are controlled by light, is demonstrated. In a proof‐of‐principle experiment,
Heyou Zhang +7 more
wiley +1 more source
On derivations of linear algebras of a special type
Дифференциальная геометрия многообразий фигурIn this work, Lie algebras of differentiation of linear algebra, the operation of multiplication in which is defined using a linear form and two fixed elements of the main field are studied. In the first part of the work, a definition of differentiation
A. Ya. Sultanov +2 more
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A Simple and Practical Linear Algebra Library Interface with Static Size Checking [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime errors. While
Akinori Abe, Eijiro Sumii
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Backbone Heterojunction Photocatalysts for Efficient Sacrificial Hydrogen Production
Advanced Functional Materials, EarlyView.Herein, a ‘single‐component’ organic semiconductor photocatalyst is presented in which a molecular donor is bonded to a polymer acceptor. The resultant material demonstrates exceptional photocatalytic activity for hydrogen evolution in aqueous triethylamine with an outstanding external quantum efficiency of 38% at 420 nm.
Richard J. Lyons +11 more
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Generalised symmetries of remarkable (1+2)-dimensional Fokker–Planck equation
European Journal of Applied MathematicsUsing an original method, we find the algebra of generalised symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker–Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of ultraparabolic ...
Dmytro R. Popovych +2 more
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Topological characterizations of S-Linearity
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2007 We give several characterizations of basic concepts of S-linear algebra in terms of weak duality on topological vector spaces. On the way, some classic results of Functional Analysis are reinterpreted in terms of S-linear algebra, by an application ...
Carfi', David
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The Algebra of Non-Local Charges in Non-Linear Sigma Models
, 1993 We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$.
Abdalla, E. +3 more
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Anomalous Spin‐Optical Helical Effect in Ti‐Based Kagome Metal
Advanced Materials, EarlyView.The kagome lattice hosts diverse correlated quantum states, including elusive loop currents. We report spin‐handedness selective signals in CsTi3Bi5, termed the anomalous spin‐optical helical effect, surpassing conventional spin responses. Arising from light helicity coupled to spin‐orbital correlations, this effect provides a sensitive, indirect probe
Federico Mazzola +34 more
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