355 research outputs found

    Arithmetic properties of blocks of consecutive integers

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    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

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

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    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

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

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    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

    Lost in reviews:Looking for the involvement of stakeholders, patients, public and other non-researcher contributors in realist reviews

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    The involvement of non‐researcher contributors (eg, stakeholders, patients and the public, decision and policy makers, experts, lay contributors) has taken a variety of forms within evidence syntheses. Realist reviews are a form of evidence synthesis that involves non‐researcher contributors yet this practice has received little attention. In particular, the role of patient and public involvement (PPI) has not been clearly documented. This review of reviews describes the ways in which contributor involvement, including PPI, is documented within healthcare realist reviews published over the last five years. A total of 448 papers published between 2014 and 2019 were screened, yielding 71 full‐text papers included in this review. Statements about contributor involvement were synthesized across each review using framework analysis. Three themes are described in this article including nomenclature, nature of involvement, and reporting impact.Papers indicate that contributor involvement in realist reviews refers to stakeholders, experts, or advisory groups (ie, professionals, clinicians, or academics). Patients and the public are occasionally subsumed into these groups and in doing so, the nature and impact of their involvement become challenging to identify and at times, is lost completely. Our review findings indicate a need for the realist review community to develop guidance to support researchers in their future collaboration with contributors, including patients and the public
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