Sentence examples for in some representation from inspiring English sources

Consider the bilinear form (B :, mathfrak {osp} times mathfrak {osp} rightarrow mathbb {K}) given by the supertrace (in some representation), (B X,Y) : = mathrm {STr}, (XY)).

The character of an operation can be defined in terms of its eigenvalues: begin{aligned} chi ^{Gamma }(R) = displaystyle sum _{k=1}^{dim(Gamma )} lambda _k end{aligned}where (lambda _k) are the eigenvalues of ({hat{R}}) in some representation D R).

Let (mathbf {x}in mathbb {R}^{n}) be a signal that is either s-sparse or compressible in some representation basis Ψ such that x=Ψ α, where (mathbf {alpha } in mathbb {R}^{n} ) is the vector of coefficients having at most s nonzeros values, i.e., ∥α∥0≤s.

are stored in some representation format and potentially decomposed and indexed at some granularity level depending on foreseen major use cases.

As the god of the sun, Shamash was the heroic conqueror of night and death who swept across the heavens on horseback or, in some representations, in a boat or chariot.

While nothing is wrong with the idea that in order to have knowledge we have to take up in some representations some content, what distinguishes knowledge from other kinds of representation must be sought in its form.

For example, a motif may be defined as "L.[RK]"; in this motif, only "L" is allowed at the first motif position, any amino acid is allowed at the second position (""., equivalent to "x" in some representations), and either "R" or "K" is allowed at the third position.

The majority in the High Court decided that although there was no right at common law to have publicly provided legal representation in all cases, in some cases representation is appropriate to ensure a fair trial.

Most NATO countries withdrew their diplomats during the war, but have slowly seen the need for some representation in Belgrade, generally regarding Yugoslavia as too important to ignore.

The constitution of 1946 therefore introduced only mild reforms: the empire was renamed the French Union, within which the colonial peoples would enjoy a narrowly limited local autonomy plus some representation in the French parliament.

Scientific decay got some representation in Krista Jacobsen's speech on cheesemaking, while Levin talked decay in the cosmos.