Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also co
The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network ...
Turan, P.: On the eigenvalues of matrices. Ann. Mat. Pura Appl. (4) 54, 397–401 (1961). MathSciNet MATH Google Scholar Komlós, J., A. Sarközy and E. Szemerédi: On sums of powers of complex numbers. Mat. Lapok 15, 337–347 (1964). MathSciNet MATH Google Scholar Benson...
3a). Eigenvalues for the case of \(\dot{a}(x)\) are shown in Fig. 4b. The largest eigenvalue is negative, indicating that the small perturbations from the steady-state solution decay in time, and the steady-state solution is stable. This is again in agreement with the results of the...
In solving the eigenvalues and eigenstates of AA, AB/BA, and moiré lattices in our silicon-air platform, the calculation regions are selected as hexagonal unit cells with side lengths \(\frac{a}{\sqrt{3}}\), \(\frac{a}{\sqrt{3}}\), and \(\frac{a}{2\sqrt{3}{\rm{sin}}(\...
the distance between thejth largest eigenvalues ofSnandΣiso(p), which tends to 0 asn→∞whenpis of constant order. However, whenpis of the same order withnor of a larger order thann, the bounds of the distances between the eigenvalues ofSnandΣwill blow up. Then,Σcannot be estimated thr...
For the 6R robot, there is no analytical solution for some configurations, so it is necessary to analyse inverse kinematics (IK) by the general solution method, which cannot achieve high precision and high speed as the analytical solution. With the expansion of application fields and the complex...
for a functionon the complex upper half plane,, has a unique solution. The main result of this paper is to establish the local law for Wigner-type matrices, i.e. that for largeNthe resolvent,, with spectral parameter, is close to the diagonal matrix,, as long as. As a consequence, ...
Section 5 delves into the optimal control problem and its optimal solution. Section 6 verifies the theoretical results through numerical simulations and demonstrates the impact of key parameters and control variables on the model. Finally, Sect. 7 summarizes this paper and provides outlooks for ...
3) general solution formula 通解公式 1. By the methods of reducing order and Euler s eigenvalues,we obtain the general solution formula to one kind of systems of three dimensional second order ordinary differential equation with constant coefficients. 采用降阶和特征根 (欧拉 )方法 ,给出了一类...