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Interestingly, while the trends of the first three quantities remain similar to the original model, the burst frequency changes its trend and increases with less depolarization for gA = 0 while it decreases in control conditions.
We will first concentrate on the first three quantities, and show 3D image data for SHG intensity, orientation, and phase at each z plane in the sample.
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For the first two quantities, we use the well known sliding-window technique with a window size of 125 samples (about 48 λ according to [14]) to calculate the local mean and standard deviation in each window.
The first two quantities (effectiveness in reducing adverse events, and utilities) are used to calculate health benefit (assuming that this cannot be captured directly through a quality of life measurement – see below).
The first three important global conserved quantities associated with the Camassa-Holm equation are [2, 15, 16] left { textstylebegin{array}{l} H_{0} = int u, mathrm{d}x, H_{1} = frac{1}{2}int (u^{2} + u_{x}^{2}), mathrm{d}x, H_{2} = frac{1}{2}int (u^{3} + uu_{x}^{2}), mathrm{d}x.
In Sections 3 and 4, the first nine singular point quantities at degenerate singular point and the first seven singular point quantities at infinity are deduced.
Theorem 3.3 For system (2.10) δ 1 = δ 2 = 0, all the singular point quantities at the origin are zero if and only if the first nine singular point quantities are zero, i.e., one of the two conditions in Theorem 3.2 holds.
Theorem 3.3 For system (3.1) | A 20 = A 02 = 0, all the singular point quantities at the origin are zero if and only if the first eight singular point quantities are zero, i.e., one of the conditions in Theorem 3.2 holds.
Theorem 4.1 The first seven singular point quantities at infinity of system (2.10) δ 1 = δ 2 = 0 are as follows: (4.8).
Theorem 3.1 The first nine singular point quantities at the origin of system (2.10) δ 1 = δ 2 = 0 are as follows: (3.5).
Theorem 4.2 For system (2.10) δ 1 = δ 2 = 0, the first seven singular point quantities at infinity are zero if and only if condition (I) or (II) is satisfied.
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