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— Emily Weinstein Nation's Restaurant News: A new survey reveals that nationwide, restaurant operators' expectations for the next six months have soured, thanks to declining sales in July and August as well as the drought-driven rising cost of food prices.
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This reduces the infinitely high dimensional Hilbert space to a small number of dimensions and hence allows for the numerical calculation of all operator expectation-values.
We show that Kitaev's Toric code model and Wen's plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain, demonstrating that despite the spectral gap in these systems the toric operator expectation values may vanish once thermal fluctuations are present.
He said that high roaming prices in Europe, especially for downloading data, reflected the operators' profit expectations, not the true costs of service.
Nonetheless, because of the consistency between the environmental data and the operator's expectations, one event can be taken to be the cause of the other.
The symbol of ({mathbb{E}}) denotes the operator for expectation.
The first approximation is based on interchanging the minimization and expectation operators.
However, user and operator requirements and expectations are continuously evolving, and competing radio access technologies are emerging.
Railroad operator CSX matched expectations with $2.3 billion in revenue after the close and its shares shot up 2.8% in after-hours trading.
The symbols †, ∗, Tr denote Hermitian, complex-conjugate and transpose operations, respectively and E denotes expectation operator.
The symbol ‖. ‖ F is the Frobenious norm, E stands for the expectation operator, T denotes the transpose operator, and H denotes the conjugate transpose operator.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com