Curvature Diffusions in General Relativity

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.Comment: 34 page

Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation

In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation \phi_y+ [\phi^{2}/2]_t=w, where w is a bounded function depending on \phi

Central Limit Theorem for a Class of Relativistic Diffusions

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for a class of Minkowskian diffusions, to which the two above ones belong. As a consequence, we correct a partially wrong guess in [DH1].Comment: 20 page

Variations in the oxygen three-isotope terrestrial fractionation line revealed by an inter-laboratory comparison of silicate mineral analyses

An inter-laboratory comparison of analytical results for the slopes of Terrestrial Fractionation Lines (TFL) measured on a group of quartz and a separate group of garnet samples shows good agreement between laboratories. However, the slopes of the TFL’s for each mineral group differ slightly

Stardust microcrater residue compositional groups

Compositional groups are defined in residue from Stardust craters (1-9 Dc) by qualitative EDS. These compositional groups are being further studied by a FIB-SEM technique to determine representative residue compositions

The experience of Sakhlin in Chekhov’s works

The article was submitted on 27.05.2016.The author maintains that his journey to Sakhalin provided Chekhov with a new perspective on a harsh reality that was little known to the public. This problem concerned Chekhov a lot, and after his trip he wrote a scholarly and statistical work about his experience, thinking he would awaken society’s conscience. In Sakhalin Island, he offers his testimony as a humanist of what he saw, heard and lived through on the island. Even though Chekhov’s trip to Sakhalin Island was an important event in the author’s life, he did not often write about his experiences there in his works of fiction. Except for works where Chekhov mentions Sakhalin directly (The Murder), the author analyses many works that reflect Chekhov’s Sakhalin experience in the representation of the characters, in their way of thinking (The Murder, In Exile), or in their personal understanding of confinement (Ward N° 6). The author argues that Chekhov accentuates many “sore points” of the 20th century. Finally, the author concludes that Chekhov’s writing has a general spirit known as “dead silence”, which can be found in the creative works of many 20th-century artists.Проводится мысль о том, что путешествие Чехова на остров Сахалин через Сибирь открыло ему глаза на суровую реальность, плохо известную русской публике, – жизнь ссыльных и заключенных на каторге. Эта проблема очень волновала Чехова, после путешествия он написал о своем опыте научное и статистическое сочинение, думая, что таким образом он разбудит совесть общества. В книге «Остров Сахалин» он как гуманист свидетельствует о том, что сам видел, слышал и пережил. Хотя чеховское путешествие на Сахалин было важным эпизодом в жизни автора, в художественных произведениях он не часто пишет о своих впечатлениях от пребывания на этом острове, на котором он посетил тюремные лагеря и узнал о жизненных трудностях заключенных, поселенцев, чиновников и других жителей. Рассмотрены не только те произведения Чехова, в которых обнаруживаются буквальные упоминания об острове («Убийство»), но и те, в которых сахалинский опыт отразился либо в изображении действующих лиц, либо в изложении их образа мыслей («Убийство», «В ссылке»), либо в важности темы заключения для них в общественном и личном смысле («Палата № 6»). Отмечено, что в творчестве Чехова акцентируются «больные точки» сознания людей ХХ в. Делается вывод об общем колорите произведений писателя, который определяется как «мертвая тишина» и близость к которому обнаруживается в творчестве ряда художников XX столетия

Melting and differentiation of early-formed asteroids: The perspective from high precision oxygen isotope studies

A number of distinct methodologies are available for determining the oxygen isotope composition of minerals and rocks, these include laser-assisted fluorination, secondary ion mass spectrometry (SIMS)and UV laser ablation. In this review we focus on laser-assisted fluorination, which currently achieves the highest levels of precision available for oxygen isotope analysis. In particular, we examine how results using this method have furthered our understanding of early-formed differentiated meteorites. Due to its rapid reaction times and low blank levels, laser-assisted fluorination has now largely superseded the conventional externally-heated Ni “bomb” technique for bulk analysis. Unlike UV laser ablation and SIMS analysis, laser-assisted fluorination is not capable of focused spot analysis. While laser fluorination is now a mature technology, further analytical improvements are possible via refinements to the construction of sample chambers, clean-up lines and the use of ultra-high resolution mass spectrometers. High-precision oxygen isotope analysis has proved to be a particularly powerful technique for investigating the formation and evolution of early-formed differentiated asteroids and has provided unique insights into the interrelationships between various groups of achondrites. A clear example of this is seenin samples that lie close to the terrestrial fractionation line (TFL). Based on the data from conventional oxygen isotope analysis, it was suggested that the main-group pallasites, the howardite eucrite diogenite suite (HEDs) and mesosiderites could all be derived from a single common parent body. However,high precision analysis demonstrates that main-group pallasites have a Δ17O composition that is fully resolvable from that of the HEDs and mesosiderites, indicating the involvement of at least two parent bodies. The range of Δ17O values exhibited by an achondrite group provides a useful means of assessing the extent to which their parent body underwent melting and isotopic homogenization. Oxygen isotope analysis can also highlight relationships between ungrouped achondrites and the more well-populated groups. A clear example of this is the proposed link between the evolved GRA 06128/9 meteorites and the brachinites. The evidence from oxygen isotopes, in conjunction with that from other techniques, indicates that we have samples from approximately 110 asteroidal parent bodies (∼60 irons, ∼35 achondrites and stony-iron, and ∼15 chondrites) in our global meteorite collection. However, compared to the likely size of the original protoplanetary asteroid population, this is an extremely low value. In addition, almost all of the differentiated samples (achondrites, stony-iron and irons) are derived from parent bodies that were highly disrupted early in their evolution. High-precision oxygen isotope analysis of achondrites provides some important insights into the origin of mass-independent variation in the early Solar System. In particular, the evidence from various primitive achondrite groups indicates that both the slope 1 (Y&R) and CCAM lines are of primordial significance. Δ17O differences between water ice and silicate-rich solids were probably the initial source of the slope 1 anomaly. These phases most likely acquired their isotopic composition as a result of UV photo-dissociation of CO that took place either in the early solar nebula or precursor giant molecular cloud. Such small-scale isotopic heterogeneities were propagated into larger-sized bodies, such as asteroids and planets, as a result of early Solar System processes, including dehydration, aqueous alteration,melting and collisional interactions

Harnack inequality for fractional sub-Laplacians in Carnot groups

In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

Life history and ecological genetics of the colonial ascidian Botryllus schlosseri

The colonial ascidian Botryllus schlosseri is a cosmopolitan, marine filter feeder, introduced as a laboratory research organism in the 1950s. Currently, it is widely used in many laboratories to investigate a variety of biological questions. Recently, it has become a species of concern, as it is an invasive species in many coastal environments. Here, we review studies on the geographical distribution of the species, sexual and asexual reproduction in the field, tolerance to temperature, salinity and anthropogenic activity, polychromatism, enzymatic polymorphism, and the genetic basis of pigmentation. Studying the relationship between genetic polymorphism and the adaptation of B. schlosseri to environmental stress is a challenge of future research and will improve our understanding of its evolutionary success and invasive potential