Stochastic frontier analysis (SFA) is often used to estimate technical efficiency of entities such as firms, countries or municipalities. A potential dependence between the two components of the error term can be taken into account by a copula function. While estimation of the model is straightforward using the Corrected Ordinary Least Squares (COLS) and Maximum Likelihood (ML) methods, an open...

Let H(x) = ∑ n≤x φ(n) n − 6 π2x. Motivated by a conjecture of Erdös, Lau developed a new method and proved that #{n ≤ T : H(n)H(n + 1) < 0} T. We consider arithmetical functions f(n) = ∑ d|n bd d whose summation can be expressed as ∑ n≤x f(n) = αx+P (log(x))+E(x), where P (x) is a polynomial, E(x) = − ∑ n≤y(x) bn n ψ ( x n ) + o(1) and ψ(x) = x− bxc − 1/2. We generalize Lau’s method and prove r...

Approximations based on dyadic centred intervals are investigated as a means for implementing exact real arithmetic. It is shown that the field operations can be implemented on these approximations with optimal or near optimal results. Bounds for the loss in quality of approximations for each of the field operations are also given. These approximations can be used as a more efficient alternativ...

We have noted that the local minima problem in the backpropagation algorithm is usually caused by update disharmony between weights connected to the hidden layer and the output layer. To solve this problem, we propose a modified error function with added terms. By adding one term to the conventional error function, the modified error function can harmonize the update of weights connected to the...

i.e. limT→+∞ π(T ) ehT /hT = 1. This generalized a result of Margulis for geodesic flows over manifolds of negative sectional curvature [6]. It is an interesting problem to estimate the error terms in such asymptotic formulae. In the particular case of geodesic flows over compact negatively curved manifolds we showed that there was an exponential error term (with a suitable principal term) [10]...