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Barium-rich silicates were recently found in the lower Cambrian black shale sequence of Anhui Province, South China. The Ba silicates can be divided into Ba-poor K-feldspar, Ba-rich K-feldspar and cymrite, on the basis of occurrence and composition. The Ba-poor K-feldspar have low BaO contents (<1.00 wt.%) and occur as sporadic grains in mudstone. In contrast, the Ba-rich K-feldspar have higher BaO contents (1.36–20.51 wt.%) and occur mainly as rims around grains of Ba-poor K-feldspar in mudstone, as void fillings in dolostone, and as grains dispersed in chert. The cymrite is observed only in chert and occurs as dispersed euhedral tabular crystals. Analyses of the Ba-poor K-feldspar and Ba-rich K-feldspar provide compositions that total <100 wt.% and show non-stoichiometry characterized by (Na + K + Ba + Ca)apfu less than 1.00 and (Al + Si)apfu slightly higher than 4.00. Raman and infrared (IR) spectroscopy has revealed the presence of 
${\rm NH}_{\rm 4}^{\rm +} $
and H2O in the Ba-rich K-feldspar, which accounts for the unusual composition of these feldspars. We suggest that the formation processes of the Ba-poor K-feldspar, Ba-rich K-feldspar and cymrite were closely associated with multi-stage hydrothermal fluids enriched in Ba and NH4, consistent with an extensional tectonic setting during the early Cambrian. The Ba-poor K-feldspars might have formed through interactions between pre-existing K-feldspars and hydrothermal fluids. The Ba-rich K-feldspars in mudstone and dolostone formed mainly by precipitation from hydrothermal fluids that infiltrated the sediments, and we suggest the Ba-rich K-feldspars and cymrite in the chert are of exhalative hydrothermal origin.
We study a nonpreemptive scheduling on two parallel identical machines with a dedicated loading server and a dedicated unloading server. Each job has to be loaded by the loading server before being processed on one of the machines and unloaded immediately by the unloading server after its processing. The loading and unloading times are both equal to one unit of time. The goal is to minimize the makespan. Since the problem is NP-hard, we apply the classical list scheduling and largest processing time heuristics, and show that they have worst-case ratios,
$8/5$
and
$6/5$
, respectively.
Two transmission curved crystal spectrometers are designed to measure the hard x-ray emission in the laser fusion experiment of Compton radiography of implosion target on ShenGuang-III laser facility in China. Cylindrically curved 
${\it\alpha}$
-quartz (10–11) crystals with curvature radii of 150 and 300 mm are used to cover spectral ranges of 10–56 and 17–100 keV, respectively. The distance between the crystal and the x-ray source can be changed over a broad distance from 200 to 1500 mm. The optical design, including the integral reflectivity of the curved crystal, the sensitivity, and the spectral resolution of the spectrometers, is discussed. We also provide mechanic design details and experimental results using a Mo anode x-ray source. High-quality spectra were obtained. We confirmed that the spectral resolution can be improved by increasing the working distance, which is the distance between the recording medium and the Rowland circle.
Let
$\mathcal{F}$
be a family of r-uniform hypergraphs. The chromatic threshold of
$\mathcal{F}$
is the infimum of all non-negative reals c such that the subfamily of
$\mathcal{F}$
comprising hypergraphs H with minimum degree at least
$c \binom{| V(H) |}{r-1}$
has bounded chromatic number. This parameter has a long history for graphs (r = 2), and in this paper we begin its systematic study for hypergraphs.
Łuczak and Thomassé recently proved that the chromatic threshold of the so-called near bipartite graphs is zero, and our main contribution is to generalize this result to r-uniform hypergraphs. For this class of hypergraphs, we also show that the exact Turán number is achieved uniquely by the complete (r + 1)-partite hypergraph with nearly equal part sizes. This is one of very few infinite families of non-degenerate hypergraphs whose Turán number is determined exactly. In an attempt to generalize Thomassen's result that the chromatic threshold of triangle-free graphs is 1/3, we prove bounds for the chromatic threshold of the family of 3-uniform hypergraphs not containing {abc, abd, cde}, the so-called generalized triangle.
In order to prove upper bounds we introduce the concept of fibre bundles, which can be thought of as a hypergraph analogue of directed graphs. This leads to the notion of fibre bundle dimension, a structural property of fibre bundles that is based on the idea of Vapnik–Chervonenkis dimension in hypergraphs. Our lower bounds follow from explicit constructions, many of which use a hypergraph analogue of the Kneser graph. Using methods from extremal set theory, we prove that these Kneser hypergraphs have unbounded chromatic number. This generalizes a result of Szemerédi for graphs and might be of independent interest. Many open problems remain.
We show that for every sufficiently large n, the number of monotone subsequences of length four in a permutation on n points is at least
Furthermore, we characterize all permutations on [n] that attain this lower bound. The proof uses the flag algebra framework together with some additional stability arguments. This problem is equivalent to some specific type of edge colourings of complete graphs with two colours, where the number of monochromatic K4 is minimized. We show that all the extremal colourings must contain monochromatic K4 only in one of the two colours. This translates back to permutations, where all the monotone subsequences of length four are all either increasing, or decreasing only.
\begin{equation*}
\binom{\lfloor{n/3}\rfloor}{4} + \binom{\lfloor{(n+1)/3}\rfloor}{4} + \binom{\lfloor{(n+2)/3}\rfloor}{4}.
\end{equation*}
