In this paper we prove that any degree d deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko’s result on Hamiltonian differential equations. The main tools are Picard-Lefschetz theory of a polynomial with complex coefficients in two variables, specially the Gusein-Zade/A’Campo’s theorem ...

We show that the minimal speed for the existence of monotonic fronts of the equation ut = (u )xx + f(u) with f(0) = f(1) = 0, m > 1 and f > 0 in (0, 1), derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for general f . The case m = 1 when f (0) = 0 is included as an extension of the results.

in donation contract, the principle is that donor can refer to given property and to take its possession. this principle has some exceptions. one of these exceptions is “donation to children”, which is irrevocable in accordance with the first paragraph of article 803 of civil law. most of the civil law’s writers believe that judgment about donation to children include the donation to grandchild...

Browser extensions are remarkably popular, with one in three Firefox users running at least one extension. Although well-intentioned, extension developers are often not security experts and write buggy code that can be exploited by malicious web site operators. In the Firefox extension system, these exploits are dangerous because extensions run with the user’s full privileges and can read and w...

The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover’s theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only approximately and limitedly. Though Barron et al. recently succeeded in remov...

To enhance the certainty of the grade block model, it is necessary to increase the number of exploratory drillholes and collect more data from the deposit. The inputs of the process of locating these additional drillholes include the variogram model parameters, locations of the samples taken from the initial drillholes, and the geological block model. The uncertainties of these inputs will lead...