A simple and effective algorithm based on Haar wavelet is proposed to the solution of linear stiff problems in this paper. And it can integrate the stiff equation with very accurate results for any length of time. The simulation result shows that the single-term Haar wavelet method (STHW) is better than the classical Runge–Kutta fourth-order method (CRK), while the terms of the both expansions are the same.
Cut-off rate performance for phase modulated coherent states in a noiseless optical channel, using a phase measurement operator is calculated. The results obtained deviate significantly from those given by the upper bound, shown previously to be close to the optimal in several practical cases.
Letωbe a Nike Air Force 1 Mid Canada
prime in the quadratic fieldQ(e2πi/3), and letG3(ω) be the cubic Gauss sum. Matthews [Invent. Math.52(1979), 163–185;54(1979), 23–52] determined the product formula ofG3(ω) using Weierstrass' ℘ function. In this paper, we establish an analogous result for the cubic Gauss sum modulo the product of the primes.
A generalization of the particle-plus-rotor model taking into account essential non-adiabatic effects is considered. Numerical calculations for167,169Yb show that accounting of these effects improves substantially the agreement between the Nike Air Force 1 Price In Canada
theory and the data without introducing Coriolis attenuation factors.