We formulate the Jacobian matrix with arbitrary equation of state and simplify the Jacobian matrix to a simple and structured form with the help of a few auxiliary variables, e.g. isentropic speed of sound.
It is worth noting that for the exact form of P d, it would be useful to refer to the joint distribution of the ordered eigenvalues of non-central uncorrelated Wishart matrix with arbitrary non-centrality matrix rank derived in [36, App. I] and consider rank 1 case.
Unstructured (UNS): R i = [ r jj'] is an m × m covariance matrix with arbitrary structure.
Specifically, the density probability of X, Y localizations of stable binding events was evaluated in a 100 × 100 matrix with arbitrary units.
The proposed architecture is able to process matrices and vectors with arbitrary sizes.
In a recent work, a proximity- and skin-effect aware formulation known as the surface-volume-surface electric field integral equation discretized with 2-D method-of-moments (MoM) was optimized to efficiently extract the frequency dependent series impedance matrix of cables with arbitrary shapes.
The approach favors algorithms for multiplying the sensitivity matrix and its transpose with arbitrary vectors.
To treat the field matter interaction perturbatively, we modify the method developed by Meier and Tannor [C. Meier, D.J. Tannor, J. Chem. Phys. 111 (1999 3365]] and originally designed for propagation of reduced density matrix of systems interacting with arbitrary laser fields.
Matrices A i,X i,Y i,Z i are arbitrary matrices with dimensions of Rr,i×Rs,i, Rr,i×(Nr-Rs,i), (Nr-Rr,i ×Rs,i, (Nr-Rr,i)×(Nr-Rs,i), respectively.
Right column: bit error ratio over signal-to-noise ratio when applying LRA-THP and when applying SLB; top row: SLB with arbitrary additional unimodular matrices; middle row: SLB with additional permutation matrices; bottom row: SLB with additional permutation/phase matrices; insert: zoom into the BER curves; M = 4, D = 512, NC = K = 4, lH = 5.
