The dating of pre-exposure times of lunar rocks and soils

Xenon produced by fission of uranium, thorium and plutonium has repeatedly been observed in lunar rocks and soils. In two basaltic rocks and in two soils Xe was found originating from fission of U-235 induced by neutrons which are due to the interactions of cosmic ray particles with lunar matter. Two facts lead to this conclusion: (1) fission Xe is present in excess of that expected for the U, Th, and Pu concentrations and for the gas retention age of the samples; and (2) the Xe-134/Xe-136 ratio of excess fission Xe is close to 1.25 as expected for neutron induced fission of U-235. Information on the duration of the exposure to cosmic rays was obtained from the Kr-81-Kr systematics whereas the effective shielding conditions were derived from the depth sensitive cosmogenic ratio Xe-131/Xe-126. For the four samples the exposure to cosmic rays in the lunar regolith is described by a two stage exposure model. The history of the four samples was derived in terms of duration and shielding depth of the two stages

Vertex covering with monochromatic pieces of few colours

In 1995, Erd\H{o}s and Gy\'arf\'as proved that in every $2$-colouring of the edges of $K_n$, there is a vertex cover by $2\sqrt{n}$ monochromatic paths of the same colour, which is optimal up to a constant factor. The main goal of this paper is to study the natural multi-colour generalization of this problem: given two positive integers $r,s$, what is the smallest number $\text{pc}_{r,s}(K_n)$ such that in every colouring of the edges of $K_n$ with $r$ colours, there exists a vertex cover of $K_n$ by $\text{pc}_{r,s}(K_n)$ monochromatic paths using altogether at most $s$ different colours? For fixed integers $r>s$ and as $n\to\infty$, we prove that $\text{pc}_{r,s}(K_n) = \Theta(n^{1/\chi})$, where $\chi=\max{\{1,2+2s-r\}}$ is the chromatic number of the Kneser gr aph $\text{KG}(r,r-s)$. More generally, if one replaces $K_n$ by an arbitrary $n$-vertex graph with fixed independence number $\alpha$, then we have $\text{pc}_{r,s}(G) = O(n^{1/\chi})$, where this time around $\chi$ is the chromatic number of the Kneser hypergraph $\text{KG}^{(\alpha+1)}(r,r-s)$. This result is tight in the sense that there exist graphs with independence number $\alpha$ for which $\text{pc}_{r,s}(G) = \Omega(n^{1/\chi})$. This is in sharp contrast to the case $r=s$, where it follows from a result of S\'ark\"ozy (2012) that $\text{pc}_{r,r}(G)$ depends only on $r$ and $\alpha$, but not on the number of vertices. We obtain similar results for the situation where instead of using paths, one wants to cover a graph with bounded independence number by monochromatic cycles, or a complete graph by monochromatic $d$-regular graphs

Plutonium-Xenon systematics of Angrites

Introduction: Angrites are igneous meteorites that crystallized very early in the solar system, ~10 Ma after CAIs, as also implied by the presence of now extinct short-lived radionuclides such as 53Mn, 146Sm and 244Pu [1]. Fission Xe was used to calculate 244Pu-136Xeretention ages of eucrites, relative to that of Angra dos Reis (AdoR) [2]. AdoR has an absolute Pb-Pb age of 4557.8 Ma [see 1 for ref.]. Most eucrites, being as old as angrites, experienced various parent body processes leading to ages ranging from ~20 Ma before, to ~100 Ma after AdoR [2]. Angrites, however, remained largely unaltered after differentiation. Here, we examine whether Xe isotopic characteristics allow determining an age sequence for angrites

The composition of lunar noble gases traped 2.5 AE and 3.5 AE ago

The times when the soils 74001 and 73261 were exposed on the lunar surface were determined by the U-235 - Xe-136 dating method. The isotopic composition of the trapped noble gases in these two soils is compared with that of the surface correlated noble gases in the young soils 12001 and in the present day solar wind. The surface correlated trapped gases are a mixture of implanted solar wind particles and retrapped lunar atmospheric gases. The observed changes are interpreted as a result of decreasing outgassing of radiogenic Ar-40 and perhaps He-4 and of fissiogenic Xe from the lunar crust. The old soils probably also contain surface correlated Kr-80 and Kr-82 produced by secondary cosmic ray neutron capture of adsorbed or retrapped bromine. To some extent the isotopic composition of the trapped gases in old lunar soil may also have been altered due to diffusion loss from material of low retentivity

The trapped heavy noble gases in recently found Martian meteorites

The composition of the trapped Ar, Kr, and Xe in the Martian meteorites Los Angeles, Say Al Uhaymir 005/008, and 094 is discussed and found to be consistent with a mixture of Martian mantle and atmosphere noble gases and terrestrial contamination

Treatment of Girls and Boys with McCune-Albright Syndrome with Precocious Puberty - Update 2017

The most common endocrinopathy associated with McCune-Albright Syndrome (MAS) is peripheral precocious puberty (PP) which occurs far more often in girls than in boys. We will discuss the latest advancements in the treatment of precocious puberty in MAS that have been achieved during the past 10 years. However, due to the rarity of the condition and the heterogeneity of the disease, research in this field is limited particularly in regards to treatment in boys. In girls, a period of watchful waiting is recommended prior to initiating therapy due to extreme variability in the clinical course. This article will review in detail current pharmacologic treatment in girls, which typically consists of either inhibiting estrogen production or blocking estrogen action at the level of the end-organ. The two treatments with the most evidence at this time are Tamoxifen (which is an estrogen receptor modulator) and Letrozole (which is a 3rd generation aromatase inhibitor). This article will also review the current treatment strategies in boys which typically include using an androgen receptor blocker and an aromatase inhibitor. Due to the rarity of the condition, large multicenter collaborative studies are needed to further investigate efficacy and safety with the goal of establishing the gold standard for treatment of PP in children with MAS

Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV-4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9–15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin and Truesdell and Noll has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re-ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline

Exploratory Analysis of Benchmark Experiments -- An Interactive Approach

The analysis of benchmark experiments consists in a large part of exploratory methods, especially visualizations. In Eugster et al. [2008] we presented a comprehensive toolbox including the bench plot. This plot visualizes the behavior of the algorithms on the individual drawn learning and test samples according to specific performance measures. In this paper we show an interactive version of the bench plot can easily uncover details and relations unseen with the static version

The pre-atmospheric size of Martian meteorites

The pre-atmospheric size of martian meteorites was calculated based on 80Kr produced by epithermal secondary cosmic-ray produced neutrons of 30-300 eV energy. For seven meteorites we obtained minimum radii of 22-27 cm, corresponding to 150-270 kg