Define a projection-operator (Pi_{N}^{1,0}: Vrightarrow X_{N}) by begin{aligned} abigl w-Pi_{N}^{1,0}w,upsilonbigr)=0, quabigl w-Pi_{N}^{1,0}wlonin X_{N}.
While the SELECT statement defines a projection, the FROM clause specifies the relations the operations are applied on.
We are thus defining a projection operator (mathcal{P}_{ell}: mathbb{L}^{2}(mathbb {S}^{2}) rightarrowmathcal {H}_{ell}) (note that (mathcal{P}_{ell}^{2} = mathcal{P}_{ell})).
We used the anatomically well-defined TC projections from the ventroposteromedial thalamic nucleus (VPM) as anatomical landmarks to define a cortical projection column.
In Section 3, we construct appropriate finite element spaces and define an auxiliary projection and prove its convergence.
We define an elliptic projection operator (R_{h}:Wrightarrow W_{h}) that satisfies begin{aligned} a(R_{h}phi-phi,w_{h})=0, quadforall phiin W,w_{h}in W_{h}, end{aligned} (3.9) and the (L^{2} -orthogonal projection operator (Q_{h}:Urightarrow U_{h}) that satisfies begin{aL^{2} -orthogonali-projection=0, quadfoperatoriin U,v_{h}in U_{h}.
Next, the subproblem (5b) in (3) could be updated via entry-wise hard thresholding of X − L t for fixed L t. Before giving the solution, we define an orthogonal projection operator 𝒫.
We define a standard "TC projection column" based on TC axon projection patterns.
Given the pixel dimensions of the image plane, we define a standard perspective projection whose principal point is represented by the central pixel of the image plane.
For given solutions (uin U), define a generalized Ritz projection (R_{h}: Uto U_{h}) such that (R_{h}u-u,v_{h}) +varepsilon a(R_{h}u-u,v_{h})=0,quad forall v_{h}in U_{h}.
