σk(Fm)=Fn \sigma_k(F_m) = F_n

Let $\sigma_k(n)$ be the sum of the $k$th powers of the divisors of $n$. Here, we prove that if $(F_n)_{n \geq 1}$ is the Fibonacci sequence, then the only solutions of the equation $\sigma_k(F_m) = F_n$ in positive integers $k \geq 2$, $m$ and $n$ have $k=2$ and $m \in \{1,2,3\}$. The proof uses linear forms in two and three logarithms, lattice basis reduction, and some elementary considerations

σk(Fm)=Fn \sigma_k(F_m) = F_n

Let $\sigma_k(n)$ be the sum of the $k$th powers of the divisors of $n$. Here, we prove that if $(F_n)_{n \geq 1}$ is the Fibonacci sequence, then the only solutions of the equation $\sigma_k(F_m) = F_n$ in positive integers $k \geq 2$, $m$ and $n$ have $k=2$ and $m \in \{1,2,3\}$. The proof uses linear forms in two and three logarithms, lattice basis reduction, and some elementary considerations

Arithmetic properties of blocks of consecutive integers

This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for each k>2.Comment: A slightly corrected and extended version of a paper which will appear in January 2017 in the book From Arithmetic to Zeta-functions published by Springe

Late Miocene contourite channel system reveals intermittent overflow behavior

Paleoceanographic information from submarine overflows in the vicinity of oceanic gateways is of major importance for resolving the role of ocean circulation in modulating Earth’s climate. Earth system models are currently the favored way to study the impact of gateways on global-scale processes, but studies on overflow-related deposits are more suitable to understand the detailed changes. Such deposits, however, had not yet been documented in outcrop. Here, we present a unique late Miocene contourite channel system from the Rifian Corridor (Morocco) related to the initiation of Mediterranean Outflow Water (MOW). Two channel branches were identified consisting of three vertically stacked channelized sandstone units encased in muddy deposits. Both branches have different channel-fill characteristics. Our findings provide strong evidence for intermittent behavior of overflow controlled by tectonic processes and regional climatic change. These fluctuations in paleo-MOW intermittently influenced global ocean circulation

До мінералогії сезонних сульфатів мису Фіолент (Південно-Західний Крим)

Комплексом методів вивчено колекцію зразків вторинних мінералів одного з узбережних відслонень зони окиснення сульфідної мінералізації мису Фіолент (Південно-Західний Крим). Установлено, що всі досліджені зразки є полімінеральними утвореннями, в яких одночасно співіснують у різних пропорціях сульфати Mg, Al, Fe²⁺, Fe³⁺, Ca тощо: пікерингіт (найпоширеніший), пікерингіт залізистий, гексагідрит, старкіїт, епсоміт, алуноген, ботріоген, копіапіт, ярозит, гіпс та ін. Старкіїт і ботріоген у Криму виявлено вперше.The collection of secondary minerals from one of littoral occurrences of sulphide zone of oxidation of the Fiolent Cape (South-Western Crimea) is studied by different methods. It was established that all studied samples were polymineral formations which consisted of sulphates of Mg, Al, Fe²⁺, Fe³⁺, Ca, etc. in different proportions: pickeringite (the most wide-spread), ferropickeringite, hexahydrite, starkeyite, epsomite, alunogen, botryogen, copiapite, jarosite, gypsum etc. Starkeyite and botryogen are detected in the Crimea for the first time

Personalized pollen monitoring and symptom scores: a feasibility study in grass pollen allergic patients

Background: Pollen is a major trigger for allergic symptoms in sensitized individuals. Airborne pollen is usually monitored by Hirst type pollen samplers located at rooftop level, providing a general overview of the pollen distribution in the larger surroundings. In this feasibility study, grass pollen-sensitized subjects monitored the pollen in their direct environment using a portable pollen sampler (Pollensniffer) and scored their symptoms, to study the relation between symptom severity and personal grass pollen exposure. For comparison the symptoms were also correlated with pollen collected by the rooftop sampler.Methods: After recruitment 18 participants were screened for grass pollen specific (GP-sIgE) of which 12 were eligible. Nine participants completed the study (May, 2018). They were asked to monitor personal pollen exposure using a Pollensniffer on their way to school, work or other destination, and to score their symptoms via a mobile app on a scale from 0 to 10. Daily pollen concentrations were collected by a Hirst type sampler at rooftop level. Pollen grains were analyzed using a microscope.Results: Three of the four participants with high GP-sIgE (9.6 kU/l) reported high symptom scores (>4) and an analysis showed a significant correlation (CC) between eye, nose, and lung symptoms and the grass pollen counts collected by the Pollensniffer, as well as the daily grass pollen concentrations monitored by the rooftop sampler (CC0.54). In contrast, the participants with low GP-sIgE levels (Conclusion: The results of this feasibility study suggest that correlations between the severity of clinical symptoms of grass pollen allergic patients, and grass pollen counts as determined by the Pollensniffer or a rooftop sampler, is restricted to patients with high GP-sIgE levels, high symptom scores, and no relevant other sensitizations. Based on the low numbers of subjects with severe symptoms included in this feasibility study, no conclusions can be drawn on the performance of the Pollensniffer in relating symptoms and pollen exposure in comparison with the rooftop sampler.</p

Sandy contourite drift in the late Miocene Rifian Corridor (Morocco):Reconstruction of depositional environments in a foreland-basin seaway

The Rifian Corridor was a seaway between the Atlantic Ocean and the Mediterranean Sea during the late Miocene. The seaway progressively closed, leading to the Messinian Salinity Crisis in the Mediterranean Sea. Despite the key palaeogeographic importance of the Rifian Corridor, patterns of sediment transport within the seaway have not been thoroughly studied. In this study, we investigated the upper Miocene sedimentation and bottom current pathways in the South Rifian Corridor. The planktic and benthic foraminifera of the upper Tortonian and lower Messinian successions allow us to constrain the age and palaeo-environment of deposition. Encased in silty marls deposited at 150–300 m depth, there are (i) 5 to 50 m thick, mainly clastic sandstone bodies with unidirectional cross-bedding; and (ii) 50 cm thick, mainly clastic, tabular sandstone beds with bioturbation, mottled silt, lack of clear base or top, and bi-gradational sequences. Furthermore, seismic facies representing elongated mounded drifts and associated moat are present at the western mouth of the seaway. We interpret these facies as contourites: the products of a westward sedimentary drift in the South Rifian Corridor. The contourites are found only on the northern margin of the seaway, thus suggesting a geostrophic current flowing westward along slope and then northward. This geostrophic current may have been modulated by tides. By comparing these fossil examples with the modern Gulf of Cadiz, we interpret these current-dominated deposits as evidence of late Miocene Mediterranean overflow into the Atlantic Ocean, through the Rifian Corridor. This overflow may have affected late Miocene ocean circulation and climate, and the overflow deposits may represent one of the first examples of mainly clastic contourites exposed on land

A new portable sampler to monitor pollen at street level in the environment of patients

Allergic rhinitis caused by pollen exposure is one of the most common allergic diseases. Therefore monitoring pollen levels in ambient air is an important tool in research and health care. Most European monitoring stations collect airborne pollen at rooftop levels for measurements in the larger surrounding of the sampling station, and not in the direct environment of sensitized subjects. Here we present the development and evaluation of a por table pollen sampler, called "Pollensniffer", that was designed to collect pollen in the immediate environment of allergic subjects. Validation of the Pollensniffer against the standard volumetric pollen sampler showed for most pollen types high correlations between the number of pollen collected by those two devices (Spearman's Correlation Coefficient > 0.8); the Pollensniffer appeared to collect on average 5.8 times more pollen per hour than the static sampler. Pollen monitoring was performed using this Pollensniffer at street level at 3 different locations in the city of Leiden during 22 weeks in 2017 and 21 weeks in 2018, during three 15-min periods a day and at one day in the week. The results showed that the pollen levels for birch and grass pollen can significantly differ from location to location and per time of day. Furthermore, the Pollensniffer measurements at street level showed that birch and grass pollen grains were detected 1 1/2 and 2-3 weeks, respectively, before detection at rooftop level. The street measurements show that allergic subjects can encounter varying pollen levels throughout the city and that they can be exposed to grass and birch pollen and may experience hay fever symptoms, even before the sampler at rooftop level registers these pollen. (C) 2020 The Authors. Published by Elsevier B.VPathogenesis and treatment of chronic pulmonary disease

Prognostic value of nonalcoholic fatty liver disease in patients with severe aortic stenosis who underwent transcatheter aortic valve implantation

Nonalcoholic fatty liver disease (NAFLD) is associated with an increased risk of cardiovascular events. Although the association between NAFLD and aortic valve sclerosis has been described, the prevalence and prognostic implications of NAFLD among patients with severe aortic stenosis (AS) have not been described. In addition, the effect of the presence of severe tricuspid regurgitation (TR) on the prevalence of NAFLD remains unexplored. Accordingly, we investigated the prognostic implications of NAFLD among patients with severe AS with and without concomitant significant TR. A total of 538 patients (aged 80 +/- 7 y, 49.6% men) who underwent noncontrast computed tomography before transcatheter aortic valve implantation (TAVI) between 2007 and 2019 were included. NAFLD was defined as a liver-to-spleen attenuation ratio Thoracic Surger