Are the degrees of best (co)convex and unconstrained polynomial approximation the same?

Let ℂ[−1,1] be the space of continuous functions on [−,1], and denote by Δ² the set of convex functions f ∈ ℂ[−,1]. Also, let E _n (f) and E _n ⁽²⁾ (f) denote the degrees of best unconstrained and convex approximation of f ∈ Δ² by algebraic polynomials of degree < n, respectively. Clearly, En (f) ≦ E _n ⁽²⁾ (f), and Lorentz and Zeller proved that the inverse inequality E _n ⁽²⁾ (f) ≦ cE _n (f) is invalid even with the constant c = c(f) which depends on the function f ∈ Δ². In this paper we prove, for every α > 0 and function f ∈ Δ², that

Simple and efficient classification scheme based on specific vocabulary

Assuming a binomial distribution for word occurrence, we propose computing a standardized Z score to define the specific vocabulary of a subset compared to that of the entire corpus. This approach is applied to weight terms (character n-gram, word, stem, lemma or sequence of them) which characterize a document. We then show how these Z score values can be used to derive a simple and efficient categorization scheme. To evaluate this proposition and demonstrate its effectiveness, we develop two experiments. First, the system must categorize speeches given by B. Obama as being either electoral or presidential speech. In a second experiment, sentences are extracted from these speeches and then categorized under the headings electoral or presidential. Based on these evaluations, the proposed classification scheme tends to perform better than a support vector machine model for both experiments, on the one hand, and on the other, shows a better performance level than a Na?ve Bayes classifier on the first test and a slightly lower performance on the second (10-fold cross validation).     

Colloidal systems containing free radical‐forming particles and composites on their basis

Controlled surface activity and reactivity of new carbon‐chain functional surface‐active oligoperoxides (FSAP) and derived metal complexes (OMC) with side and end di‐tertiary and tert‐alkyl (aryl) peroxidic, respectively, and other active functional groups cause the possibility of their tailored utilization as emulsifiers, surface‐active initiators and modifiers of the phase boundaries of liquid, solid and mixed phases in different colloidal systems in a wide temperature range. New materials can be developed such as water and hydrocarbon polymer dispersions, artificial water dispersions of unsaturated polyesters and alkyd resins, polymer/polymeric blends, active glass and carbon fibers, dispersed fillers, reinfourced and filled polymer composites with the definite special properties. Methods for the obtaining and the application of these materials are described.