Based on a suitable separation method, combined with the Lyapunov stability and the matrix measure theory, the complete synchronization and anti-synchronization for chaotic systems are investigated.
It should be noted that for a completely random surface (white noise), the final number of data measured is twice larger than for a standard matrix measurement (we measure both rows and columns independently).
A common approach to address this problem is to determine the frequency response function (FRF) matrix, measure the structural responses, and calculate the dynamic forces based on least-squares (LS) scheme.
Each frame of the glycan HA MD trajectories was converted from Cartesian coordinates to a distance matrix, measured between the glycan and protein.
(9) K (X, Y ) = F 1 K m × K m + F 1 K c × K c K m and K c represent the kernel matrix measured from the microarray data and the ChIP-seq data, respectively.
By Theorem 1, the matrix norm and the matrix measure are defined as (mu(A)= 2.6591), (Vert B Vert = 0.7353), and (Vert Delta A Vert leq a = 1.2), (Vert Delta B Vert leq b = 0.8).
By Theorem 1, we take the values are (mu(A)= 1.2029), (Vert B Vert = 0.12) and (Vert Delta A Vert leq a = 0), (Vert Delta B Vert leq b = 0), using the matrix norm and the matrix measure.
Further, we use the defined matrix norm and the matrix measure to get (mu(A)= 1.2828 ), (Vert B Vert = 1.7999), (Vert C Vert = 0.8151) and (Vert Delta A Vert leq a = 0.1), (Vert Delta B Vert leq b=0.2), (Vert Delta C Vert leq c=0.3).
Since is controllable, there exists such that is a stability matrix and with prescribed spectrum then with prescribed matrix measure.
The aforementioned rescaling procedure, when applied to the density matrix measured via the probe qubit, gives a modified state correlation of 0.881±0.034.
