where β i are a sequence of independent scalar Wiener processes (cf. [[56], Proposition 2.1.10]).
Charges and radical annotation ( doublet monoradical, ^^ triplet diradical) in i are a result of the PubChem standardization protocols.
That is, the remittances of sibling i are a function of the remittances of other siblings and vice versa.
The visibility of a surface at a given depth is computed as (mathop prod nolimits_{{p_{z} < z_{i} }} (1 - alpha_{i} )), where z i and α i are a depth and an opacity of a surface.
Because of the use of matrix sampling (that refers to a design in which each student is presented only a subset of all available items) in NAEP assessments, the algebra questions administered to student i are a subset (J_{ik}) of the set (J_k) of all available algebra questions on the test.
On the other hand, the concentration increase in one unit of time from re-suspension is expressed as varDelta C/varDelta t=varPhi ={k}_itimes {D}_itimes left varDelta xvarDelta y/varDelta xvarDelta yvarDelta zright), in which k i and D i are a re-suspension factor (/s) and surface contamination (Bq/m2) for individual radionuclides, respectively.
where Σ A 1 = E ( ( 1 − π i z ) / π i z ) Var { S β ( Y i | X i ) | Z i, A i } and Σ A 2 = E ( ( 1 − π i z ) / π i z ) Var S β ( Y i | X i ) | X i, A i. The asymptotic variance of β ̂ A 2 is smaller than the asymptotic variance of β ̂ A 1 if the covariates Z i are a proper subset of X i. Suppose that (Z,A) are discrete taking values (z,a) in a set of finite number of values.
R i and F i are a three-element row indicator vector for the location (in the host gene) category (CDS, 3′UTR, or 5′′UTR) and a nine-element row indicator vector for TE category (Alu, ERV1, ERVL, L1, L2, MaLR, MER1, MER2, or MIR) of the exon, respectively.
To summarize, we have, (1) One way to approach the regression problem is to impose a fixed parametric form on f [such as f(x)=∑ i =1 M β i φ i (x), where the β i are parameters, the φ i are a set of basis functions and M ∈ ℕ], and then to estimate its parameters from a set of experimentally obtained observations using methods such as ordinary least squares.
