Comparing the direct normal form and multiple scales methods through frequency detuning

Comparing the direct normal form method with harmonic balance and the method of multiple scales

Approximate analytical methods have been used extensively for finding approximate solutions to nonlinear ordinary differential equations. In this paper we compare the recently developed direct normal form transformation with two other very well known and long standing methods, harmonic balance and the method of multiple scales. We will show that the direct normal form method combines some of th...

Laser frequency locking by direct measurement of detuning.

We present a new method of laser frequency locking in which the feedback signal is directly proportional to the detuning from an atomic transition, even at detunings many times the natural linewidth of the transition. Our method is a form of sub-Doppler polarization spectroscopy, based on measuring two Stokes parameters (I2 and I3) of light transmitted through a vapor cell. It extends the linea...

comparing the frequency of mycobacterium tuberculosis with direct microscopy and culture methods

specialized methods to teach spelling: comparing three methods

چکیده: بررسی ادبیات مربوطه در کشور در زمینه یادگیری زبان انگلیسی نشان می‎دهد که علی‎رغم اهمیت املا در فرآیند یادگیری به طور عام و یادگیری زبان انگلیسی به طور خاص، این مولفه از جایگاهی متناسب با اهمیت آن برخوردار نیست و عمدتاً نادیده گرفته شده است. تحقیقات گسترده‎ای در خارج از کشور در مورد ماهیت این مولفه صورت گرفته است، در حالی که به جرأت می‎توان گفت در داخل کشور گامی در مورد درک ماهیت آن و فرآی...

Convergent Multiple-times-scales Reinforcement Learning Algorithms in Normal Form Games

We consider reinforcement learning algorithms in normal form games. Using two-time-scales stochastic approximation, we introduce a modelfree algorithm which is asymptotically equivalent to the smooth fictitious play algorithm, in that both result in asymptotic pseudotrajectories to the flow defined by the smooth best response dynamics. Both of these algorithms are shown to converge almost surel...