Search results
Results from the WOW.Com Content Network
The pair (P, η) defines the structure of an affine geometry on M, making it into an affine manifold. The affine Lie algebra aff(n) splits as a semidirect product of R n and gl(n) and so η may be written as a pair (θ, ω) where θ takes values in R n and ω takes values in gl(n).
Concentrated solar power can achieve the high temperatures necessary to split water. Hydrosol-2 is a 100-kilowatt pilot plant at the Plataforma Solar de Almería in Spain which uses sunlight to obtain the required 800 to 1,200 °C (1,070 to 1,470 K; 1,470 to 2,190 °F) to split water. Hydrosol II has been in operation since 2008.
The process of water-splitting is a highly endothermic process (ΔH > 0). Water splitting occurs naturally in photosynthesis when the energy of four photons is absorbed and converted into chemical energy through a complex biochemical pathway (Dolai's or Kok's S-state diagrams). [3] O–H bond homolysis in water requires energy of 6.5 - 6.9 eV ...
where the model translation is [t x t y] T and the affine rotation, scale, and stretch are represented by the parameters m 1, m 2, m 3 and m 4. To solve for the transformation parameters the equation above can be rewritten to gather the unknowns into a column vector.
Here, the electric quadrupole interaction is due to the 14 N-nucleus, the hyperfine nuclear spin-spin splitting is from the magnetic coupling between nitrogen, 14 N (I N = 1), and hydrogen, 1 H (I H = 1 ⁄ 2), and a hydrogen spin-rotation interaction due to the 1 H-nucleus. These contributing interactions to the hyperfine structure in the ...
It is induced, in a canonical manner, from the affine connection. It can also be regarded as the gauge field generated by local Lorentz transformations . In some canonical formulations of general relativity, a spin connection is defined on spatial slices and can also be regarded as the gauge field generated by local rotations .
For a general morphism f : X → Y and a point x in X, f is said to be quasi-finite at x if there exist open affine neighborhoods U of x and V of f(x) such that f(U) is contained in V and such that the restriction f : U → V is quasi-finite. f is locally quasi-finite if it is quasi-finite at every point in X. [2]
If the principal bundle P is the frame bundle, or (more generally) if it has a solder form, then the connection is an example of an affine connection, and the curvature is not the only invariant, since the additional structure of the solder form θ, which is an equivariant R n-valued 1-form on P, should be taken into account.