The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix with respect to parameters of interest.
The introduction into mixed matrix PU/PHEMA of special fillers, in particular nanosized silica with biologically active compounds (BAC) which immobilized on its surface, allows to create composites with specific pharmacological properties [13].
This matrix corresponds to the Seidel matrix of a special type of strongly regular graphs [6].
Skew-Hadamard matrices are of special interest due to their use, among others, in constructing orthogonal designs.
Skew Hadamard matrices are of special interest due to their use, among others, in constructing D-optimal weighing designs for n≡3 (mod 4).
The resulting optimization problems are addressed using two techniques: (i) nonlinear optimization, where the attitude installation rotation matrix is parameterized by the ZYX Euler angles, and (ii) optimization on Riemannian manifolds, enabling the estimation of the attitude installation matrix on the group of special orthogonal matrices SO(3).
An explicit representation of solutions of (1.6) with the aid of special matrix functions called a delayed matrix sine and a delayed matrix cosine was used to solve this problem.
An explicit representation of solutions with the aid of special matrix functions called a delayed matrix sine and a delayed matrix cosine is used to develop the conditions of relative controllability and to construct a specific control function solving the relative controllability problem of transferring an initial function to a prescribed point in the phase space.
Similarly, let F ~ y be the same type of special matrix obtained by deleting the second row and column of F. Subsequently, (27) can be rewritten as: ε rms 2 = E [ ε 2 ] ≥ [ F − 1 ] 1, 1 + [ F − 1 ] 2, 2 = det F ~ x det ( F ) + det F ~ y det ( F ), (29).
Enormous strength increase of the composite can be attributed to a homogeneous distribution of Ni-GNFs in the Ti matrix coupled with the formation of special interface (Ti/Ti2Ni/nano-TiCX/Ni-GNFs).
