The rate of approximation by means of polynomials with restricted coefficients

For a sequenceA = {A_k} _k?1 ^∞ of positive constants letP _A = {p(x): p(x) = Σ _k?1 ⁿ a _k x _k ,n = 1,2, …, ¦a _k ≦ A _k ^k }. We consider the rate of approximation by elements ofP _A , of continuous functions in [0, 1] which vanish at x = 0. Also a classP _A is called “efficient” if globally it guarantees the Jackson rate of approximation. Some necessary conditions for efficiency and some sufficient ones are derived.     

Kolmogorov and Linear Widths of Weighted Sobolev-Type Classes on a Finite Interval, II

Let I be a finite interval, r and ρ(t)=dist{t, ∂I}, tI. Denote by Δ^s₊W^r_p, α, 0α<∞, the class of functions x on I with the seminorm x^(r)ρ^α_Lp1 for which Δ^s_τx, τ>0, is nonnegative on I. We obtain two-sided estimates of the Kolmogorov widths d_n(Δ^s₊W^r_p, α)_Lq and of the linear widths d_n(Δ^s₊W^r_p, α)^lin_Lq, s=0, 1, …, r+1.     

NAIMA as a solution for future GMO diagnostics challenges

In the field of genetically modified organism (GMO) diagnostics, real-time PCR has been the method of choice for target detection and quantification in most laboratories. Despite its numerous advantages, however, the lack of a true multiplexing option may render real-time PCR less practical in the face of future GMO detection challenges such as the multiplicity and increasing complexity of new transgenic events, as well as the repeated occurrence of unauthorized GMOs on the market. In this context, we recently reported the development of a novel multiplex quantitative DNA-based target amplification method, named NASBA implemented microarray analysis (NAIMA), which is suitable for sensitive, specific and quantitative detection of GMOs on a microarray. In this article, the performance of NAIMA is compared with that of real-time PCR, the focus being their performances in view of the upcoming challenge to detect/quantify an increasing number of possible GMOs at a sustainable cost and affordable staff effort. Finally, we present our conclusions concerning the applicability of NAIMA for future use in GMO diagnostics.     

Logic and Colour

In this paper evidence will be provided that Wittgenstein??s intuition about the logic of colour relations is to be taken near-literally. Starting from the Aristotelian oppositions between propositions as represented in the logical square of oppositions on the one hand and oppositions between primary and secondary colors as represented in an octahedron on the other, it will be shown algebraically how definitions for the former carry over to the realm of colour categories and describe very precisely the relations obtaining between the known primary and secondary colours. Linguistic evidence for the reality of the resulting isomorphism will be provided. For example, the vertices that resist natural single-item lexicalization in logic (such as the O-corner, for which there is no natural lexicalization *nall (=not all)) are not naturally lexicalized in the realm of colour terms either. From the perspective of the architecture of cognition, the isomorphism suggests that the foundations of logical oppositions and negation may well be much more deeply rooted in the physiological structure of human cognition than is standardly assumed.     

Evolution of order and chaos across a first-order quantum phase transition

We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.