Irregular primes with respect to Genocchi numbers and Artin's primitive root conjecture

We introduce and study a variant of Kummer's notion of (ir)regularity of primes which we call G-irregularity and it is based on Genocchi numbers $G_n$, rather than Bernoulli number $B_n.$ We say that an odd prime $p$ is G-irregular if it divides at least one of the integers $G_2,G_4,\ldots, G_{p-3}$, and G-regular otherwise. We show that, as in Kummer's case, G-irregularity is related to the divisibility of some class number. Furthermore, we obtain some results on the distribution of G-irregular primes. In particular, we show that each primitive residue class contains infinitely many G-irregular primes and establish non-trivial lower bounds for their number up to a given bound $x$ as $x$ tends to infinity. As a by-product, we obtain some results on the distribution of primes in arithmetic progressions with a prescribed near-primitive root

Jorgensen's inequality for non-Archimedean metric spaces.

Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an application, we give a version of Jørgensen’s inequality for SL(2, ℚ p )

Ramanujan-style congruences for prime level

We establish Ramanujan-style congruences modulo certain primes ℓ between an Eisenstein series of weight k, prime level p and a cuspidal newform in the ε-eigenspace of the Atkin–Lehner operator inside the space of cusp forms of weight k for Γ0(p). Under a mild assumption, this refines a result of Gaba–Popa. We use these congruences and recent work of Ciolan, Languasco and the third author on Euler–Kronecker constants, to quantify the non-divisibility of the Fourier coefficients involved by ℓ. The degree of the number field generated by these coefficients we investigate using recent results on prime factors of shifted prime numbers

Multiple planar coincidences with N-fold symmetry

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.Comment: 13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references update

Binary recurrences for which powers of two are discriminating moduli

Given a sequence of distinct positive integers $w_0 , w_1, w_2, \ldots$ and any positive integer $n$, we define the discriminator function $\mathcal{D}_{\bf w}(n)$ to be the smallest positive integer $m$ such that $w_0,\ldots, w_{n-1}$ are pairwise incongruent modulo $m$. In this paper, we classify all binary recurrent sequences $\{w_n\}_{n\geq 0}$ consisting of different integer terms such that $\mathcal{D}_{\bf w}(2^e)=2^e$ for every $e\geq 1.$ For all of these sequences it is expected that one can actually give a fairly simple description of $\mathcal{D}_{\bf w}(n)$ for every $n\ge 1.$ For two infinite families of such sequences this has been done already in 2019 by Faye, Luca and Moree, respectively Ciolan and Moree

hNuf2 inhibition blocks stable kinetochore–microtubule attachment and induces mitotic cell death in HeLa cells

Identification of proteins that couple kinetochores to spindle microtubules is critical for understanding how accurate chromosome segregation is achieved in mitosis. Here we show that the protein hNuf2 specifically functions at kinetochores for stable microtubule attachment in HeLa cells. When hNuf2 is depleted by RNA interference, spindle formation occurs normally as cells enter mitosis, but kinetochores fail to form their attachments to spindle microtubules and cells block in prometaphase with an active spindle checkpoint. Kinetochores depleted of hNuf2 retain the microtubule motors CENP-E and cytoplasmic dynein, proteins previously implicated in recruiting kinetochore microtubules. Kinetochores also retain detectable levels of the spindle checkpoint proteins Mad2 and BubR1, as expected for activation of the spindle checkpoint by unattached kinetochores. In addition, the cell cycle block produced by hNuf2 depletion induces mitotic cells to undergo cell death. These data highlight a specific role for hNuf2 in kinetochore–microtubule attachment and suggest that hNuf2 is part of a molecular linker between the kinetochore attachment site and tubulin subunits within the lattice of attached plus ends

Geoarchaeological and palaeontological research in the Maasvlakte 2 sand extraction zone and on the artificially created Maasvlakte 2 beach: a synthesis

Zooarchaeolog

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Introduction In November 2011 archaeologists of City of Rotterdam Archaeological Service (BOOR) conducted underwater research in the Yangtze harbour, Rotterdam Maasvlakte, The Netherlands. The research was carried out by order of Port of Rotterdam Authority and supervised by the Cultural Heritage Agency of the Netherlands. The results of geological, botanical, zoological and archaeological analyses of the retrieved material generated new information on the occupation of a relatively high river dune by prehistoric hunter-gatherers, and on the development history of the surrounding landscape ca. 9,000 years ago. Methods Rather than employing divers the underwater investigations were carried out on board a vessel using a wire-operated, horizontal closing grab. Three small trenches (total area ca. 375m²) were excavated in layers in a fairly controlled fashion. Underwater excavations cannot achieve the same level of precision as is possible on land, but the many soil core samples taken in the project’s preliminary phase allowed detailed descriptions of the geomorphological stratigraphy. The excavation resulted in 316 bulk bags of soil. All soil was sieved on land, using sieves with mesh sizes of 10 and 2mm, after which archaeologists and volunteers carefully sorted the residues, documenting a total of ca. 46,000 finds. Results Plenty of Mesolithic occupation remains were retrieved at all three grab locations, from depths ranging between 17 to 21m below modern MSL. The finds span the age range from ca. 8400 to 6500BC, when the site transformed from dryland (an inland dune) to wetland (drowned delta subsurface). At the foot of the inland dune, the depositional conditions allowed for excellent preservation of bone, charcoal and plant material as well as stone artefacts. The site provides an unusually rich and detailed body of evidence on environmental conditions and the Middle Mesolithic palaeo-economy. The landscape ecotones around the site yielded an abundance of food while gradually being transformed, due to rising sea levels, from a valley containing the rivers Rhine and Meuse into the mouth area of those rivers. At 6500 BC, the site was finally transgressed: drowned in an estuary and swallowed up by the sea. Conclusion The Rotterdam Yangtze Harbour research project demonstrates the preservation of Mesolithic sites along the river Rhine, at depths in nowadays coastal and offshore areas. Furthermore, it demonstrates the feasibility of archaeological investigation of such submerged sites, even at depths of 18 to 20 m beneath sea, lake and harbour floors. Never before had such a submerged site been excavated at such a great depth. The scientific report (in English) will appear in the autumn of 2014, providing a full description of all finds as well as their landscape context

Indexing the Pseudomonas specialized metabolome enabled the discovery of poaeamide B and the bananamides

Pseudomonads are cosmopolitan microorganisms able to produce a wide array of specialized metabolites. These molecules allow Pseudomonas to scavenge nutrients, sense population density and enhance or inhibit growth of competing microorganisms. However, these valuable metabolites are typically characterized one-molecule–one-microbe at a time, instead of being inventoried in large numbers. To index and map the diversity of molecules detected from these organisms, 260 strains of ecologically diverse origins were subjected to mass-spectrometry-based molecular networking. Molecular networking not only enables dereplication of molecules, but also sheds light on their structural relationships. Moreover, it accelerates the discovery of new molecules. Here, by indexing the Pseudomonas specialized metabolome, we report the molecular-networking-based discovery of four molecules and their evolutionary relationships: a poaeamide analogue and a molecular subfamily of cyclic lipopeptides, bananamides 1, 2 and 3. Analysis of their biosynthetic gene cluster shows that it constitutes a distinct evolutionary branch of the Pseudomonas cyclic lipopeptides. Through analysis of an additional 370 extracts of wheat-associated Pseudomonas, we demonstrate how the detailed knowledge from our reference index can be efficiently propagated to annotate complex metabolomic data from other studies, akin to the way in which newly generated genomic information can be compared to data from public databases