Visiting a left deep node w, for each r such that there is a deep edge (w, r), and for each q∈ A l l S t a t e(r), we firstly calculate the value P r o b(C′(n, s+1, w, r), q) using (24).
According to Schauder's fixed point theorem, it remains to prove that Q n is compact in W r. Firstly, for any B ⊂ W r, we will show that K n B is equicontinuous on t ∈ [ 0, b ].
In practice, we estimate the covariance matrix R(m) firstly.
The extinction cross-section (ECS) intensity distribution map of the Ag TNP dimer showing variation between the wavelength and R was firstly calculated to investigate effect of the misalignment length on the LSPR. Figure 2 shows the ECS intensity distribution color map of the Ag TNP dimer.
holds for all x, y ≥ 1 if and only if p = − ∞ and r ≥ r 0. Proof Firstly, we prove that inequality (3.11) holds if p = − ∞ and r ≥ r 0. Since the first inequality in (3.11) is true if p = − ∞, thus we only need to prove the second inequality in (3.11).
where r > 0. Firstly, we give a nonexistence result of a positive entire radial large solution of system (1.1).
It is clear that the R a increases firstly from 2.205 to 3.362 nm, then decreases back to 2.553 nm.
In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-III type in the closed first quadrant R + 2. Firstly, the existence and stability of fixed points of the system is discussed.
It was found in the present study that r rhBMP2_108 was firstly able to target the recruitment of progenitor cells by favouring early and rapid recruitment of cells within 24 h (Fig. 1).
For any x ∈ R + + n and φ ∈ B C ( R − ; R + + n ), we firstly list the following conditions for both f and g that we will need.
