Abstract. The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can not describe correlations between particles. We introduce here an alternative variational approach, based on the correlated Gaussian method, which ...

Abstract—The design problem of Infinite Impulse Response (IIR) digital filters is usually expressed as the minimization problem of the complex magnitude error that includes both the magnitude and phase information. However, the group delay of the filter obtained by solving such design problem may be far from the desired group delay. In this paper, we propose a design method of stable IIR digita...

We study a Newton-like method for the minimization of an objective function φ that is the sum of a smooth convex function and an `1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton method, computes a step by minimizing a piecewise quadratic model qk of the objective function φ. In order to make this approach efficient in practice, it is imp...

A successive approximation time-to-digital converter (TDC) is presented. The proposed TDC is based on the vernier charging method, and characterized with its timing resolution independent of the period of the reference clock. Further by including voltage ratio together with both current and capacitor ratios to enlarge the pulse stretch factor, a higher timing resolution is attained. The circuit...