Functionally Countable Spaces and Baire Functions

The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice

Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

[EN] We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.This second author acknowledges the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals for funding this work through the projects IN151014 and IN141047.Choban, MM.; Berinde, V. (2017). Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance. Applied General Topology. 18(2):317-330. https://doi.org/10.4995/agt.2017.7067SWORD31733018

Spaces with sharp bases and with other special bases of countable order

AbstractWe study spaces with sharp bases and bases of countable order. A characterization of spaces with external bases of countable order is established (Theorem 2.7). Some necessary and sufficient conditions for a space X×S, where S is the convergent sequence, to have a sharp base are given (Theorem 3.2). It follows that a pseudocompact space X is metrizable iff X×S has a sharp base (Corollary 3.3). It is proved that a sharp base of finite rank is a uniform base (Theorem 4.4). Some other new results are also obtained, and some open questions are formulated

Selections, Paracompactness and Compactness

In the present paper, the Lindelof number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.Comment: 23 page

Lepton pair production by high-energy neutrino in an external electromagnetic field

The process of the lepton pair production by a neutrino propagating in an external electromagnetic field is investigated in the framework of the Standard Model. Relatively simple exact expression for the probability as the single integral is obtained, which is suitable for a quantitative analysis.Comment: 9 pages, LATEX, 2 PS figures, submitted to Modern Physics Letters

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Diffuse Inelastic Neutron Scattering from Anharmonic Vibrations in Cuprite

Atomic vibrational dynamics in cuprite, Cu2O, was studied by inelastic neutron scattering and molecular dynamics (MD) simulations from 10 K to 900 K. Above 300 K, a diffuse inelastic intensity (DII) appeared, obscuring the high-energy phonon modes. Classical MD simulations with a machine learning interatomic potential reproduced general features of the DII, especially with a Langevin thermostat. The DII originates from random phase shifts of vibrating O-atoms that have anharmonic interactions with neighboring Cu-atoms

Underweight is independently associated with mortality in post-operative and non-operative patients admitted to the intensive care unit: a retrospective study

BACKGROUND: Low and high body mass index (BMI) have been recently shown to be associated with increased and decreased mortality after ICU admission, respectively. The objective of this study was to determine the impact of BMI on mortality and length of stay in patients admitted to the intensive care unit (ICU). METHODS: In this retrospective cohort study, the Acute Physiology and Chronic Health Evaluation (APACHE) III database of patients admitted to the ICUs of a tertiary academic medical center, from January 1997 to September 2002, was crossed with a Hospital Rule-based Systems database to obtain the height and weight of the patients on admission to the ICU. The cohort was divided in post-operative and non-operative groups. We created the following five subgroups based on the BMI: <18.5, 18.5 to 24.9, 25 to 29.9, 30.0 to 39.9, ≥ 40.0 Kg/m(2). A multiple logistic regression analysis was used to determine the independent impact of BMI on hospital mortality. The ICU length of stay ratio was defined as the ratio of the observed to the predicted LOS. P-value < 0.05 was considered significant. The 95% confidence interval (CI) was calculated for the odds ratio (OR). RESULTS: BMI was available in 19,669 of the 21,790 patients in the APACHE III database; 11,215 (57%) of the patients were admitted post-operatively. BMI < 18.5 was associated with increased mortality in both post-operative (OR = 2.14, 95% CI, 1.39 to 3.28) and non-operative (OR = 1.51, 95% CI, 1.13 to 2.01) patients. Post-operative patients with a BMI between 30.0 to 39.9 had a lower mortality rate (OR = 0.68, 95% CI, 0.49 to 0.94). Post-operative patients with BMI <18.5 or BMI ≥ 40 had an ICU length of stay ratio significantly higher than patients with BMI between 18.5 to 24.9. The addition of BMI < 18.5 did not improve significantly the accuracy of our prognostic model in predicting hospital mortality. CONCLUSIONS: Low BMI is associated with higher mortality in both post- and non-operative patients admitted to the ICU. LOS is increased in post-operative patients with low and high BMIs