For each GO term, we obtained a non-redundant list of protein identifiers, either directly associated with the GO term or one of its descendants, and mapped it to a non-redundant list of Entrez Gene ids, GO terms and their relationships (parent/child) [ 24].
To compare dN/dS values of GO terms between subterranean lineages and their surface counterparts, for each GO term, we obtained the log(ω BMR/ ω Mouse) value by taking the logarithm of the ratio of (dN/dS BMR to (dN/dS Mouse and the log(ω NMR/ ω Guinea pig) values taking the logarithm of the ratio of (dN/dS NMR to (dN/dS Guinea pig.
By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point.
Taking in (Equation 11) m as free electron mass and using only the first term, we obtain the ground state energy EGS = 0.73 eV.
Proof Taking into account Theorems 6, 7 and 8 because the constant function is log-convex, summing term by term, we obtain that all functions P n k are convex.
Analogously, for the third term we obtain begin{aligned} I_{3}& leqvarepsilon^{-2} int_{0}^{T}e^{-varepsilon^{-4}w T-tau )}biglVert B_{s}(psi) (tau)bigrVert _{sigma},dtau & leq Cvarepsilon^{-varepsilon^{-4}w T-taurtpsiVert _{sigma }^{-varepsilon^{-4}w T-tau{-4}wT}e^{-varepsilon^{-4}w T-taulon ^{2-6kappa}biglVert
Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution, respectively.
By using the Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this typical molecular model via the exact quantization rule (EQR).
By dropping this constant term, we obtain L boldsymbol{theta}_{ell}) propto - frac{bigl|(boldsymbol{p} tau_{ell},nu_{ell}))^{mathrm{H}}boldsymbol{W}^{-1}{boldsymbol{hat{x}}}_{ell}^{[i]}bigr|^{2}}{ (boldsymbol{p} tau_{ell},nu_{ell}))^{mathrm{H}}boldsymbol{W}^{-1}boldsymbol{p} tau_{ell},nu_{ell})}.
Applying Jensen's inequality on the third term, we obtain the following capacity lower bound: C l = 1 2 E log 2 γ ~ 1 k + γ I 1 + 1 2 E log 2 γ 2 + γ I 2 - 1 2 log 2 E γ ~ 1 k γ I 2 + E γ 2 γ I 2 + E γ I 1 γ I 2. (70).
Instead, candidates for a facet are generated as follows: for every GO term, we obtain the induced subnetwork in G whose nodes are annotated with or its descendants.
