Abstract:
We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n >= 2 we supply n homotopic maps that each represent the (n-1)!-th power of a suitable generator of pi_2n(U(n)) = Z_{n!}. The product of these n commuting maps is the constant map to the identity matrix.

Abstract:
We performed a statistical analysis of 290-500 keV ion data obtained by IMP-8 during the years 1982-1988 within the earth's magnetosheath and analysed in detail some time periods withdistinct ion bursts. These studies reveal the following characteristics for magnetosheath 290-500 keV energetic ions: (a) the occurrence frequency and the flux of ions increase with increasing geomagnetic activity as indicated by the Kp index; the occurrence frequency was found to be as high as P > 42% for Kp > 2, (b) the occurrence frequency in the dusk magnetosheath was found to be slightly dependent on the local time and ranged between ~30% and ~46% for all Kp values; the highest occurrence frequency was detected near the dusk magnetopause (21 LT), (c) the high energy ion bursts display a dawn-dusk asymmetry in their maximum fluxes, with higher fluxes appearing in the dusk magnetosheath, and (d) the observations in the dusk magnetosheath suggest that there exist intensity gradients of energetic ions from the bow shock toward the magnetopause. The statistical results are consistent with the concept that leakage of magnetospheric ions from the dusk magnetopause is a semi-permanent physical process often providing the magnetosheath with high energy (290-500 keV) ions. Key words. Magnetospheric physics (magnetosheath; planetary magnetospheres). Space plasma physics (shock waves).

Abstract:
The long-term solution to the asthma epidemic is believed to be prevention and not treatment of the established disease. Most cases of asthma begin during the first years of life; thus the early determination of which young children will have asthma later in their life counts as an important priority. Artificial neural networks (ANN) have been already utilized in medicine in order to improve the performance of the clinical decision-making tools. In this study, a new computational intelligence technique for the prediction of persistent asthma in children is presented. By employing partial least square regression, 9 out of 48 prognostic factors correlated to the persistent asthma have been chosen. Multilayer perceptron and probabilistic neural networks topologies have been investigated in order to obtain the best prediction accuracy. Based on the results, it is shown that the proposed system is able to predict the asthma outcome with a success of 96.77%. The ANN, with which these high rates of reliability were obtained, will help the doctors to identify which of the young patients are at a high risk of asthma disease progression. Moreover, this may lead to better treatment opportunities and hopefully better disease outcomes in adulthood. 1. Introduction Artificial neural networks (ANNs) are one of the main constituents of the artificial intelligence (AI) techniques. Besides the different applications in many other areas, neural networks are also used in health and medicine areas, such as biomedical signal processing, diagnosis of diseases, and medical decision [1, 2]. ANNs have an excellent capability of learning the relationship between the input-output mapping from a given dataset without any prior knowledge or assumptions about the statistical distribution of the data [3]. This capability of learning from a certain dataset without any a priori knowledge makes the neural networks suitable for classification and prediction tasks in practical situations. Furthermore, neural networks are inherently nonlinear which makes them more practicable for accurate modeling of complex data patterns, in contrast to many traditional methods based on linear techniques. Due to their performance, they can be applied in a wide range of medical fields such as cardiology, gastroenterology, pulmonology, oncology, neurology, and pediatrics [1]. Several studies have proposed ANN models for the prediction of various diseases. The authors of [4] developed an ANN to determine whether patients had breast cancer or not. If they had, its type could be determined by using ANN and

Abstract:
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

Abstract:
We construct a new infinite family of models of exotic 7-spheres. These models are direct generalizations of the Gromoll-Meyer sphere. From their symmetries, geodesics and submanifolds half of them are closer to the standard 7-sphere than any other known model for an exotic 7-sphere.

Abstract:
Our intention in this work is to show, by using two different methods, that magnetospheric dynamics reveal low dimensional chaos. In the first method we extend the chaotic analysis for the AE index time series by including singular value decomposition (SVD) analysis in combination with Theiler's test in order to discriminate dynamical chaos from self-affinity or "crinkliness". The estimated fractality of the AE index time series which is obtained belongs to a strange attractor structure with close returns in the reconstructed phase space. In the second method we extend the linear equivalent magnetospheric electric circuit to a nonlinear one, the arithmetic solution of which reveals low dimensional chaotic dynamics. Both methods strongly support the existence of low dimensional magnetospheric chaos.

Abstract:
We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial elements in pi_1 Diff(S^5) and pi_1 Diff(S^13) and to provide explicit formulas for non-cancellation phenomena in group actions.

Abstract:
In the first part of the paper we study the geometrical characteristics of the magnetospheric ions’ time series in the reconstructed phase space by using the SVD extended chaotic analysis, and we test the strong null hypothesis supposing that the ions’ time series is caused by a linear stochastic process perturbed by a static nonlinear distortion. The SVD reconstructed spectrum of the ions’ signal reveals a strong component of high dimensional, external coloured noise, as well as an internal low dimensional nonlinear deterministic component. Also, the stochastic Lorenz system produced by coloured noise perturbation of the deterministic Lorenz system was used as an archetype model in comparison with the dynamics of the magnetrospheric ions. Key words. Magnetospheric physics (energetic particles) – Radio science (nonlinear phenomena)

Abstract:
In this study we present theoretical concepts and results concerning the hypothesis test of the magnetospheric chaos. For this reason we compare the observational behavior of the magnetospheric system with results obtained by analysing different types of stochastic and deterministic input-output systems. The results of this comparison indicate that the hypothesis of lowdimensional chaos for the magnetospheric dynamics remains a possible and fruitful concept which must be developed further.