Isometric embeddings of a class of separable metric spaces into Banach spaces

Let (M, d) be a bounded countable metric space and c > 0 a constant, such that d(x, y) + d(y, z) - d(x, z) ≥ c, for any pairwise distinct points x, y, z of M. For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of ℓ∞. © 2018 Charles University, Faculty of Mathematics and Physics

A study of correlation between seismicity and mental health: Crete, 2008–2010

We compared the number of M > 2 earthquakes in an area, including the island of Crete, Greece, to the number of admissions to the Psychiatric Inpatient Unit of the University of Crete (IPU/UoC), during the period 2008–2010. We found that when earthquakes with M 6.4 occurred in the region examined, the number of monthly admissions to the Acute Care Unit of the IPU/UoC, NAA, reached lowest values, whereas this number increased when the monthly number NE of small (M < 3) earthquakes increased. We also found a positive correlation between the total number of monthly admissions NA and NE (r = 0.601/P = 0.001). When a daily resolution analysis was performed for the month with the highest value of NE, we found that an abrupt increase in the number of small earthquakes was followed by an increase in the number of admissions after ∼2 days (during that month, from a total of 71 patients, 38/10 people were diagnosed with schizophrenia/bipolar disorder). We hypothesize that seismic activity might be a significant contributing factor influencing the frequency of admissions of psychotic disorders in Crete in the period 2008–2010 and that the beneficial/adverse effects are related to the anomalous electric field/extra low frequency–ultra low frequency emissions

Large-scale fields and flows in the magnetosphere-ionosphere system

Advances in our understanding of the large-scale electric and magnetic fields in the coupled magnetosphere-ionosphere system are reviewed. The literature appearing in the period January 1991–June 1993 is sorted into 8 general areas of study. The phenomenon of substorms receives the most attention in this literature, with the location of onset being the single most discussed issue. However, if the magnetic topology in substorm phases was widely debated, less attention was paid to the relationship of convection to the substorm cycle. A significantly new consensus view of substorm expansion and recovery phases emerged, which was termed the ‘Kiruna Conjecture’ after the conference at which it gained widespread acceptance. The second largest area of interest was dayside transient events, both near the magnetopause and the ionosphere. It became apparent that these phenomena include at least two classes of events, probably due to transient reconnection bursts and sudden solar wind dynamic pressure changes. The contribution of both types of event to convection is controversial. The realisation that induction effects decouple electric fields in the magnetosphere and ionosphere, on time scales shorter than several substorm cycles, calls for broadening of the range of measurement techniques in both the ionosphere and at the magnetopause. Several new techniques were introduced including ionospheric observations which yield reconnection rate as a function of time. The magnetospheric and ionospheric behaviour due to various quasi-steady interplanetary conditions was studied using magnetic cloud events. For northward IMF conditions, reverse convection in the polar cap was found to be predominantly a summer hemisphere phenomenon and even for extremely rare prolonged southward IMF conditions, the magnetosphere was observed to oscillate through various substorm cycles rather than forming a steady-state convection bay