Invariance of the stability of meissner's equation under a permutation of its intervals

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Shapiroʼs Theorem for subspaces

AbstractIn the previous paper (Almira and Oikhberg, 2010 [4]), the authors investigated the existence of an element x of a quasi-Banach space X whose errors of best approximation by a given approximation scheme (An) (defined by E(x,An)=infa∈An‖x−an‖) decay arbitrarily slowly. In this work, we consider the question of whether x witnessing the slowness rate of approximation can be selected in a prescribed subspace of X. In many particular cases, the answer turns out to be positive

Burden and risk factors for Pseudomonas aeruginosa community-acquired pneumonia:a Multinational Point Prevalence Study of Hospitalised Patients

Pseudornonas aeruginosa is a challenging bacterium to treat due to its intrinsic resistance to the antibiotics used most frequently in patients with community-acquired pneumonia (CAP). Data about the global burden and risk factors associated with P. aeruginosa-CAP are limited. We assessed the multinational burden and specific risk factors associated with P. aeruginosa-CAP. We enrolled 3193 patients in 54 countries with confirmed diagnosis of CAP who underwent microbiological testing at admission. Prevalence was calculated according to the identification of P. aeruginosa. Logistic regression analysis was used to identify risk factors for antibiotic-susceptible and antibiotic-resistant P. aeruginosa-CAP. The prevalence of P. aeruginosa and antibiotic-resistant P. aeruginosa-CAP was 4.2% and 2.0%, respectively. The rate of P. aeruginosa CAP in patients with prior infection/colonisation due to P. aeruginosa and at least one of the three independently associated chronic lung diseases (i.e. tracheostomy, bronchiectasis and/or very severe chronic obstructive pulmonary disease) was 67%. In contrast, the rate of P. aeruginosa-CAP was 2% in patients without prior P. aeruginosa infection/colonisation and none of the selected chronic lung diseases. The multinational prevalence of P. aeruginosa-CAP is low. The risk factors identified in this study may guide healthcare professionals in deciding empirical antibiotic coverage for CAP patients

A constructive proof of a homomorphism between P3 and SO(3)

The paper gives a very elementary proof of the well-known result that the projective space P3 is homeomorphic to the special orthogonal Lie group SO(3). The proof uses only linear algebra, elementary topology and elementary affine geometry. One of its motivations is the theory developed in the classical book of M. L. Curtis [Matrix groups, Springer, New York, 1979; MR0550439 (81c:22001)]. The paper is also very useful for young students in mathematics to become initiated in Lie theory and its applications.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu