A (2+ϵ)-approximation for precedence constrained single machine scheduling with release dates and total weighted completion time objective

We give a $(2+?)$-approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture on the approximability of this scheduling problem (Skutella, 2016).     

Dynamic uniqueness for stochastic chains with unbounded memory

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail $\sigma$-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-${?}^2$ summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are ${?}^2$ summable. Finally, if we weaken the condition for DU, asking for coincidence on the future $\sigma$-algebra for almost every pair of pasts, we obtain a condition that is equivalent to $\beta$-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-${?}^2$ summability condition on the kernel is equivalent to the $\beta$-mixing of the compatible stationary chain.     

On Weierstrass semigroups and sets: a review with new results

In this work we present a survey of the main results in the theory of Weierstrass semigroups at several points, with special attention to the determination of bounds for the cardinality of its set of gaps. We also review results on applications to the theory of error correcting codes. We then recall a generalization of the concept of Weierstrass semigroup, which is the Weierstrass set associated to a linear system and several points. We finish by presenting new results on this Weierstrass set, including some on the cardinality of its set of gaps.      

Bounds relating the weakly connected domination number to the total domination number and the matching number

Let G=(V,E) be a connected graph. A dominating set S of G is a weakly connected dominating set of G if the subgraph (V,E∩(S×V)) of G with vertex set V that consists of all edges of G incident with at least one vertex of S is connected. The minimum cardinality of a weakly connected dominating set of G is the weakly connected domination number, denoted . A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γ_t(G) of G. In this paper, we show that . Properties of connected graphs that achieve equality in these bounds are presented. We characterize bipartite graphs as well as the family of graphs of large girth that achieve equality in the lower bound, and we characterize the trees achieving equality in the upper bound. The number of edges in a maximum matching of G is called the matching number of G, denoted α^′(G). We also establish that , and show that for every tree T.     

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.     

超声波法提取迎春花总黄酮含量的工艺研究

研究了超声波法对迎春花中总黄酮的提取条件。其最优提取条件为:料液比1∶40,超声波温度20℃,作用时间20min。在此条件下,用NaNO2-Al(NO3)3-NaOH显色法测定的总黄酮为18.22%,RSD=1.48%(n=5)。     

加拿大一枝黄花总酚超声提取工艺

利用超声提取的方法,通过单因素和正交实验分析了溶液浓度、超声时间、料液比、提取次数4个主要因素对总酚提取率的影响。确立了加拿大一枝黄花总酚的最佳提取工艺条件为:60%甲醇、超声50min、料液比1∶20、提取3次。在此条件下,总酚的提取率为44.61mg/g。     

渐进非对称陀螺分子16O3及同位素16O18O16O的配分函数研究

采用乘积近似法计算了臭氧分子16O3及其同位素16O18O16O在20-6000 K温度范围内的总配分函数。其中转动配分函数用Watson的刚性转子模型,振动配分函数用谐振子模型．总的温度范围被划分为五个温度段。计算的配分函数在这五个温度段分别被拟合到一个温度T的五阶多项式,从而在每个温度段均得到六个拟合系数。由这些拟合系数就可以快速、准确的获得分子在所研究温度范围内任意温度的总配分函数。研究结果为目标特性识别、气动物理的高超声速技术等领域的研究提供了重要的参考信息。     

白簕叶总黄酮的提取和纯化及其抑菌试验初探

观察白簕叶中总黄酮的抑菌作用。采用微波辅助法从白簕叶中提取黄酮化合物,经HPD-600型树脂纯化,通过圆形滤纸片法和二倍稀释法分别对黄酮提取液进行了抑菌试验和最小抑菌浓度(MIC)的测定。HPD-600型树脂纯化后的黄酮纯度达到21.3%,对3种供试菌的抑菌作用为大肠杆菌金色葡萄球菌芽孢杆菌,随着总黄酮浓度的增加,其抑菌作用也增强。白簕叶总黄酮对大肠杆菌、金色葡萄球菌、和芽孢杆菌的MIC分别为原液的1/4、1/2倍和1倍。本方法为白簕的药用价值开发开辟了新途径。     

Optimization of ultrasound-assisted extraction of total monomeric anthocyanin (TMA) and total phenolic content (TPC) from eggplant (Solanum melongena L.) peel

The present study describes the extraction of total monomeric anthocyanin (TMA) and total phenolic content (TPC) from eggplant peel using ultrasonic treatments and methanol and 2-propanol as extraction solvents. The extraction yields were optimized by varying the solvent concentration, ultrasonic frequency, temperature and time of ultrasonic treatment. Box–Behnken design was used to investigate the effect of process variables on the ultrasound-assisted extraction. The results showed that for TPC extraction the optimal condition were obtained with a methanol concentration of 76.6%, 33.88 kHz ultrasonic frequency, a temperature of 69.4 °C and 57.5 min extraction time. For TMA the optimal condition were the following: 54.4% methanol concentration, 37 kHz, 55.1 °C and process time of 44.85 min.