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In differential geometry, the four-gradient (or 4-gradient) is the four-vector analogue of the gradient from vector calculus. In special relativity and in quantum mechanics , the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors .
G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist.
As with the conjugate gradient method, biconjugate gradient method, and similar iterative methods for solving systems of linear equations, the CGS method can be used to find solutions to multi-variable optimisation problems, such as power-flow analysis, hyperparameter optimisation, and facial recognition.
Germany's state-owned railway operator, Deutsche Bahn, said Thursday that it has agreed to sell its European public transport subsidiary, Arriva, to U.S.-based infrastructure investor I Squared ...
As a second-order differential operator, the Laplace operator maps C k functions to C k−2 functions for k ≥ 2.It is a linear operator Δ : C k (R n) → C k−2 (R n), or more generally, an operator Δ : C k (Ω) → C k−2 (Ω) for any open set Ω ⊆ R n.
Arriva UK Bus is a major bus operator in the United Kingdom based in Sunderland, England. It is a subsidiary of Arriva which runs transport services across Europe, which was a subsidiary of Deutsche Bahn from 2010.
I Squared Capital was founded in 2012 by former senior executives at Morgan Stanley, including Sadek Wahba, Adil Rahmathulla, and Gautam Bhandari. [1] In 2015, the firm closed its first fund, ISQ Global Infrastructure Fund LP, with $3 billion in total commitments with investments from the Rhode Island State Investment Commission, the New Mexico Educational Retirement Board, and Mitsubishi ...
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse: