Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65?years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”     

Ensuring robustness in the quality of antibiotic susceptibility test discs for four novel antibiotics

Antibiotic susceptibility test (AST) discs are used as an in-vitro diagnostic tool to select the appropriate antibiotic to treat an infection. Generally, the concentration of the drug loaded on to the AST discs is measured by studying its activity against quality control organisms. This methodology has several limitations—it is time consuming, requires trained manpower, has a wider acceptance criteria of zone of inhibitions—causing ambiguity in judging smaller variations in drug concentration. To overcome these issues, we have developed and validated high-performance liquid chromatographic (HPLC) methods for the determination of strength of AST discs for in-house researched antibiotics, namely Levonadifloxacin/WCK 771, Nafithromycin/WCK 4873, Cefepime-Tazobactam/WCK 4282, and Cefepime-Zidebactam/WCK 5222. The drugs were extracted from the AST discs using an appropriate solvent. The developed methods are simple, accurate, precise, reproducible, rugged, and robust. They are efficient in terms of time, and can be easily conducted in a quality control laboratory during release as well as stability evaluation of AST disc. Application of HPLC methods for the determination of strength of AST discs ensures flawless quality and, consequently, a better selection of drugs to treat bacterial infections in clinics.     

Chemical Composition and Antibacterial Activity of Lippia multiflora Moldenke Essential Oil from Different Regions of Angola

The purpose of the study was to determine the chemical composition and antibacterial activity of Lippia multiflora Moldenke essential oils (EOs) collected in different regions of Angola. Antibacterial activity was evaluated using the agar wells technique and vapour phase test. Analysis of the oils by GC/MS identified thirty-five components representing 67.5 to 100% of the total oils. Monoterpene hydrocarbons were the most prevalent compounds, followed by oxygenated monoterpenes. The content of the compounds varied according to the samples. The main components were Limonene, Piperitenone, Neral, Citral, Elemol, p-cymene, Transtagetone, and Artemisia ketone. Only one of the eleven samples contained Verbenone as the majority compound. In the vapour phase test, a single oil was the most effective against all the pathogens studied. The principal component analysis (PCA) and hierarchical cluster analysis (HCA) of components of the selected EOs and inhibition zone diameter values of agar wells technique allowed us to identify a variability between the plants from the two provinces, but also intraspecific variability between sub-groups within a population. Each group of essential oils constituted a chemotype responsible for their bacterial inhibition capacity. The results presented here suggest that Angolan Lippia multiflora Moldenke has antibacterial properties and could be a potential source of antimicrobial agents for the pharmaceutical and food industry.     

Inverse colloidal crystal membranes for hydrophobic interaction membrane chromatography

A collaborative study on the robustness and portability of a capillary electrophoresis‐mass spectrometry method for peptide mapping was performed by an international team, consisting of 13 independent laboratories from academia and industry. All participants used the same batch of samples, reagents and coated capillaries to run their assays, whereas they utilized the capillary electrophoresis‐mass spectrometry equipment available in their laboratories. The equipment used varied in model, type and instrument manufacturer. Furthermore, different types of sheath‐flow capillary electrophoresis–mass spectrometry interfaces were used. Migration time, peak height and peak area of ten representative target peptides of trypsin‐digested bovine serum albumin were determined by every laboratory on two consecutive days. The data were critically evaluated to identify outliers and final values for means, repeatability (precision within a laboratory) and reproducibility (precision between laboratories) were established. For relative migration time the repeatability was between 0.05 and 0.18% RSD and the reproducibility between 0.14 and 1.3% RSD. For relative peak area repeatability and reproducibility values obtained were 3–12 and 9–29% RSD, respectively. These results demonstrate that capillary electrophoresis‐mass spectrometry is robust enough to allow a method transfer across multiple laboratories and should promote a more widespread use of peptide mapping and other capillary electrophoresis‐mass spectrometry applications in biopharmaceutical analysis and related fields.     

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In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given.     

具有遗传性疾病和性状的遗传位点分析

随着信息技术的进步和发展,现代生物学越来越多地将这些技术用于大规模生物数据的收集、分析、挖掘等过程.大量计算机技术,特别是统计方法被用来进行复杂疾病的分析.大量研究表明,人体的许多表型性状差异以及对药物和疾病的易感性等都可能与某些位点相关联,或和包含有多个位点的基因相关联.因此,定位与性状或疾病相关联的位点在染色体或基因中的位置,能帮助研究人员了解性状和一些疾病的遗传机理,也能使人们对致病位点加以干预,防止一些遗传病的发生.利用随机森林方法、Bootstrap重抽样、logistic回归等大数据分析方法,意在解决优化生物学位点关联性分析中单一致病位点识别、多位点相互作用和多性状位点关联性分析等子问题.     

小样本定数截尾场合下威布尔和对数正态分布的拟合检验

本文给出了小样本定数截尾场合下两参数威布尔分布和对数正态分布的拟合检验方法,该方法还适用于一般的位置-刻度参数族分布,论文还通过实际算例说明方法的可行性。     

石英的顺磁中心在电子自旋共振测年中的特性及应用

沉积物的电子自旋共振测年是利用石英矿物中的顺磁中心浓度确定总辐射能量,进而推定石英矿物的埋藏年代。石英中可用于测年的顺磁中心包括E’心、Al心、Ti心和Ge心。E’心需要经过热活化后才能测年。Al心是一种电子空穴心,在低温下可观测到较强的信号值。光照可以使Al心漂白,但有残留值存在。Ti心、Ge心都是电子中心,Ti心在低温测试中可见,信号微弱。Ge心光晒退最敏感,在常温观测中可见。不同顺磁中心的形成机理不同导致它们具有不同的特性,适用于不同沉积环境中的样品测年,在冰碛物中Ge心测年更具有可行性。电子自旋共振测试时降低温度可使信号增强,Ti心在10 K和15 K时信号强度最大;Al心在20 K时信号最强。Ge心在200 K时信号明显增强。在电子自旋共振测年中可根据不同顺磁中心信号强度的变化调整测试温度获得信号的最优值。在以后的ESR测试中可以选取信号最强时的测试温度进行测试,以增强微弱信号的信噪比,有利于对复杂的信号形态的分辨确定,提高对信号强度定量的准确性。     

A novel lipid droplets-targeting fluorescent probe based on dicyanisophorone and carbazole for Cu2+ and its application

A novel fluorescent probe, LCH , based on dicyanisophorone and carbazole, was prepared for the visual detection of Cu²⁺. The probe LCH could recognize Cu²⁺ by fluorescence quenching in EtOH/H₂O (1/4, v/v) solution, which could be easily identified under the 365 nm UV lamp, and the detection limit was as low as 0.785 μM. The recognition mechanism of probe LCH with Cu²⁺ was determined by combining ¹H NMR titration, MS, and theoretical calculations. Practical application experiments showed that probe LCH could be used to detect Cu²⁺ in the test strip experiments. Cell imaging experiments showed that the probe LCH owned good cell permeability and could be applied to the imaging of Cu²⁺ in HepG2 cells. In addition, fluorescence colocalization experiments showed that LCH could target lipid droplets. These results indicate that the probe LCH will have a good application prospect in environmental detection and clinical medicine.