With the above notation and ⇄ indicating interchange, equilibrium equations in stress components are (with 3-D stress components as functions of coordinates x, y, and z) α σ x, x + τ xy, y + τ xz, z = 0 ⇄ x, y Open image in new window (1a) α τ xz, x + τ yz, y + σ z, z = 0 Open image in new window (1b). in which the suffix after ', ' denotes the partial derivative operator.
We studied the borohydride oxidation reaction (BOR) by voltammetry in 0.1 M NaOH/10−3 M BH4− on carbon-supported Pt, Ag and alloyed PtAg nanoparticles (here-after denoted as Pt/C, Ag/C and Pt Ag/C).
After denoting with fd the maximum Doppler frequency, and with τ ̄ rms the root-mean square delay spread of the channel, we define, respectively, the coherence bandwidth ([35], Ch. 4) and coherence time ([36], Ch. 4) of the channel as W C = 1 τ ̄ rms, (28a) T C = 0.423 f d. (28b).
After denoting the 2214 X chromosome as vs, we performed four sets of complementation tests: vs with vs, vs with if, vs with Df(1 Exel6240, and vs with Df(1 Exel6240.
Here and after, ′ denotes the transposition of a vector or a matrix.
For more general problems having the fixed points y ˜ ℓ, ℓ = 1, 2, …, L, such that f ( t, y ˜ ℓ, λ ) = 0, after denoting R ℓ = d f d y | y = y ˜ ℓ. the denominator function ϕ can be chosen as ϕ ( h, R ) = 1 − e − R h R, R = max ℓ = 1, …, L | R ℓ |. to ensure that the steady-state of the discrete model preserves the same stability properties of the original continuous model.
The above ground vegetation was sorted into the live fractions of functional groups (namely: grasses, herbs, Equisetum sp., deciduous shrubs and mosses) and the litter fraction was separated into the non-photosynthesising part of the moss (here after denoted 'brown' moss) and vascular plant litter.
There, we find the fraction of mRNAs in each of the three states after denoting state 0 the state in the middle of the network, state 1 the state on its left side and state 2 the state on the right side (blue circle in Figure 9 and red circle in Figure 11).
Thus b 1, V 1 and S 1 will herein after be denoted as b, V and S, respectively, without loss of generality.
Here and after, (Alesssim B) denotes (Aleq CB) for some constant (C>0); (Asim B) stands for both (Alesssim B) and (Blesssim A).
where and after, I denotes identity matrix.
