Sentence examples for obvious identification from inspiring English sources
In the following, we shall make the obvious identification ((mathbf{R}^{n})^{k}=mathbf{R}^{nk}) whenever it is convenient for simpler exposition.
The special case of the Auslander bijection η Λ Y is the obvious identification of both Λ [ → Y 〉 and S Hom ( Λ, Y ) with S Y. First, consider Λ [ → Y 〉 : The determiner formula asserts: a right minimal morphism is right Λ -determined if and only if it is a monomorphism.
Then NI [0]) is by definition the set of its objects of I, and for any object (i in I), we have an obvious identification begin{aligned} mathsf{L}(xi )_i cong (Delta _< NI _i, end{aligned} (6.17 where (mathsf{L}(xi )_i) is the fiber of the cofibration (tau ).
We have used here the Fourier integral for a radial function g in the form that arises from polar integration g ^ = ∫ g ( x ) e - 2 π i ξ · x d x = ∫ 0 ∞ g ( t ) t d - 1 σ ^ ( | ξ | t ) d t, with the obvious identification g ( | x | ) = g ( x ) for a radial function g.
In the light of given information, it is obvious that identification process will be faster than those of 's.
If we have a comonad (varphi ) on a small category I, then for any category (mathcal {C}), (varphi ^*) is a comonad on the category of functors (mathcal {C}^I), and we have an obvious natural identification begin{aligned} {text {Coalg}}(mathcal {C}^I,varphi ^*) cong mathcal {C}^{{text {coalg}}(I,varphi )}.
To simplify notation, denote begin{aligned} {text {DSec}}_{le n}(I,mathcal {C}) = {text {DSec}}left( I_{le n},tau ^*_{le n}mathcal {C}right), end{aligned} (8.6 and notice that since (overline{I}_n) is discrete, we have an obvious natural identification begin{aligned} {text {DSec}}left( overline{I}_n,overline{tau }_n^*mathcal {C}right) cong prod _{i in overline{I}_n}{text {Ho}}(mathcal {C}_i).
Although not an obvious comparison, the identification of Ryan Giggs despite an injunction being in place, in total disregard for the authority of the court, raises all the same issues and concerns in relation to the difficulties in policing what has been to date almost completely unrestrained online dissemination.
Furthermore, the impulse response of every stable finite-dimensional LTI system has a finite representation using the frame we introduce here, with obvious benefits in identification problems.
It is obvious that biomarker identification is equivalent to feature selection if we consider genes or mutations of interest as variables, where the informative genes or mutations are generally picked to discriminate disease samples from normal ones.
The specific 12 kbp genomic island of probable phage origin is of obvious interest for identification purpose, and has already been used for the recovery of B. microti from soil samples [ 6].
