Let (H_{n}= operatorname {span}{hat{L}_{j}, j=0,1,ldots,n}) be the sequence of Legendre polynomial subspaces of degree ≤n, and let (Pi_{n}: Hlongrightarrow H_{n}) be the orthogonal projection defined as Pi_{n}h=sum_{j=0}^{n}c_{j}(h) hat{L}_{j},quad hin H. (11) We quote some crucial properties of (Pi_{n}) ([38], pp.283-287 and [39]).
This paper investigated the flame projection distance (defined as the distance from the nozzle exit to the furthest point of the flame in the horizontal direction) of horizontally oriented buoyant turbulent rectangular jet fires.
A cosupport Ŝ l which implies a near-optimal projection is defined as hat{S}_{l} text{textbf{textit{v}}})={underset{varLambdain mathrm{L}_{l}}{text{argmin}}}|v-text{textbf{textit{Q}}}_{varLambda}text{textbf{textit{v}}}|^{2}_{2} (9 where v ∈ ℜ d and ( mathrm{L}_{l}=left{varLambdainleft[1,2,cdots,pright],midvarLambdamidgeq l right} ) l-cosparse cosupports.
(C ) Average cortical profile of cdr2-GFP intensities from maximum intensity projection (distance defined as in cartoon in Figure 1F ).
This projection is defined as follows: s i k = h t i k, where h : {1,..., M} → {1,..., N} is a random hash function.
The World Bank's upbeat projections, defining extreme poverty as the 1.3 billion people living on less than $1.25 per day, come as governments and international institutions prepare to set new targets to update the 15-year Millennium Development Goals set by the United Nations in 2000.
Fracture healing was assessed by standard radiographic projections and union defined as dense callus bringing at least three cortices.
where the projection operator is defined as proj b ( a ) = < a, b > < b, b > b, (3).
The projection matrix was defined as a simple stage-structure model with 3 stages describing California sea lion life history: pups (0 1 year-old), juveniles (1 4 year-old), and adults (>4 year-old).
