with μ = b, one notices that the coupling for μ > 0 is noncooperative such that indeed, see [14], the standard maximum principle cannot be used. Nevertheless, by the results in [14] one is able to estimate the value bc(Ω) from below by using the so called 3G-Theorem from [3] which can be rephrased as a positivity preserving property for the auxiliary system:    −∆u = f − λ v in Ω, −∆v = f in...

This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency distribution(s) maximize the diversity? The theorem provides the answer. The chief surprise is that although we are dealing with not just a single entropy, but...

In many practical situations, the Maximum Entropy (MaxEnt) approach leads to reasonable distributions. However, in an important case when all we know is that the value of a random variable is somewhere within the interval, this approach leads to a uniform distribution on this interval – while our intuition says that we should have a distribution whose probability density tends to 0 when we appr...

This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

Long sentence analysis has been a critical problem because of high complexity. This paper addresses the reduction of parsing complexity by intra-sentence segmentation, and presents maximum entropy model for determining segmentation positions. The model features lexical contexts of segmentation positions, giving a probability to each potential position. Segmentation coverage and accuracy of the ...