Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Synthesis and cytotoxicity of novel cholesterol–cobalt bis(dicarbollide) conjugates

The novel conjugates of cholesterol with cobalt – bis(dicarbollide) were synthesized by the ring-opening reactions of the cyclic oxonium derivatives of [3,3′-Co(C₂B₉H₁₁)₂]^– with the OH group of cholesterol 2-hydroxyethyl ether. The compounds obtained were tested for toxicity to glioblastoma U-87 MG cells and human embryo fibroblasts FECH-15 cells     

Random Latin squares and 2-dimensional expanders

Expander graphs have been playing an important role in combinatorics and computer science over the last four decades. In recent years a theory of high dimensional expanders is emerging, but as of now all known examples of expanders (random and explicit) have unbounded degrees. The question of existence of bounded degree high dimensional expanders was raised by Gromov and by Dotterrer and Kahle. In this paper we present a new model, based on Latin squares, of 2-dimensional complexes of bounded edge degrees that are expanders with probability tending to 1.     

钚气溶胶环境中惰性气体氪迁移过程研究

放射性气体的安全性问题是涉及反应堆运行中必需研究的重要问题.因此在钚气溶胶环境中,对钚材料裂变产生的放射性气体裂变产物,需要研究其在钚气溶胶环境中的迁移过程.对放射性惰性气体Kr87,Kr88的实验测量数据进行了具体分析.依据它们具有钚材料直接裂变和作为固体裂变产物子体两种来源这一物理特性,在不同的制样时间对Kr87/Kr88比值变化规律进行分析.确立了这两种来源的在钚气溶胶环境中的物理图像和迁移过程的物理模型,并与实验数据进行比较以验证模型的正确性. 关键词： 钚气溶胶 气体裂变产物 放射性Kr87/Kr88 迁移过程     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with8721.gif" alt="sum" align="MIDDLE" BORDER="0"> ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and 8721.gif" alt="sum" align="MIDDLE" BORDER="0"> ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">), or (ii)f is strictly concave on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

The determination and application of 87Sr/86Sr ratio in verifying geographical origin of wheat

As ⁸⁷Sr/⁸⁶Sr ratio plays a significant role in authenticating the geographical origin of foodstuff, it is important to identify where the ⁸⁷Sr/⁸⁶Sr signature in food comes from, and the methods of ⁸⁷Sr/⁸⁶Sr ratio analysis in food and environmental samples. Wheat with three genotypes, soil and groundwater samples were collected from three regions of China during harvest time of 2014. The ⁸⁷Sr/⁸⁶Sr ratios in the samples were determined by thermal ionization mass spectrometer in order to investigate the possible source of ⁸⁷Sr/⁸⁶Sr in wheat, and the concentrations of Rb and Sr in wheat and soils were also detected by inductively coupled plasma mass spectrometry and combined with ⁸⁷Sr/⁸⁶Sr ratio in order to trace the geographical origin of wheat. The ⁸⁷Sr/⁸⁶Sr ratio, the contents Rb and Sr, and Rb/Sr ratio of wheat and soil samples showed significant differences among three regions. The ⁸⁷Sr/⁸⁶Sr ratios and the concentrations of Rb and Sr in soils were higher than those in corresponding wheat. The ⁸⁷Sr/⁸⁶Sr ratio in wheat was identical to that corresponding soil NH₄NO₃ extracts (labile fraction of soil) and groundwater. Wheat uptake more Rb than Sr. 3D distribution of ⁸⁷Sr/⁸⁶Sr, Rb and Sr could identify wheat samples from different regions clearly. The ⁸⁷Sr/⁸⁶Sr ratio of wheat reflects the ⁸⁷Sr/⁸⁶Sr ratio of the associated environment including soil and groundwater. It is expected that the use the parameters of ⁸⁷Sr/⁸⁶Sr ratio, the contents of Rb and Sr will allow to trace geographical origin of wheat. Copyright © 2017 John Wiley & Sons, Ltd.