A variant of Shelah's characterization of Strong Chang's Conjecture

Shelah considered a certain version of Strong Chang's Conjecture which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman‐Krueger poset is semiproper. This strengthens and sharpens results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu.     

On the expectations of the mathematical knowledge of first-year undergraduates

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a ‘probable preparedness’ in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit.     

Hybridorubrins A–D: Azaphilone Heterodimers from Stromata of Hypoxylon fragiforme and Insights into the Biosynthetic Machinery for Azaphilone Diversification

The diversity of azaphilones in stromatal extracts of the fungus Hypoxylon fragiforme was investigated and linked to their biosynthetic machineries by using bioinformatics. Nineteen azaphilone-type compounds were isolated and characterized by NMR spectroscopy and mass spectrometry, and their absolute stereoconfigurations were assigned by using Mosher ester analysis and electronic circular dichroism spectroscopy. Four unprecedented bis-azaphilones, named hybridorubrins A–D, were elucidated, in addition to new fragirubrins F and G and various known mitorubrin derivatives. Only the hybridorubrins, which are composed of mitorubrin and fragirubrin moieties, exhibited strong inhibition of Staphylococcus aureus biofilm formation. Analysis of the genome of H. fragiforme revealed the presence of two separate biosynthetic gene clusters (BGCs) hfaza1 and hfaza2 responsible for azaphilone formation. While the hfaza1 BGC likely encodes the assembly of the backbone and addition of fatty acid moieties to yield the (R)-configured series of fragirubrins, the hfaza2 BGC contains the necessary genes to synthesise the widely distributed (S)-mitorubrins. This study is the first example of two distant cross-acting fungal BGCs collaborating to produce two families of azaphilones and bis-azaphilones derived therefrom.     

The effect of music participation on mathematical achievement and overall academic achievement of high school students

A study was conducted on high school students, comparing those with some music credits to those with none. No statistically significant difference was found in their mean math grade point averages (GPA) or their mean cumulative GPAs. Students were then separated into two groups based on the number of music credits. Students who had earned at least two music credits per grade level were placed into Group A. This category included ninth graders with two or more music credits, tenth graders with four or more music credits, eleventh graders with six or more music credits, and twelfth graders with eight or more music credits. The remaining students were placed into Group B. Group A students performed better than group B students. However, the differences were not statistically significant. Scatter plots indicated a slight upward trend in GPAs as the number of music credits increased. Lower GPAs were nonexistent as the music credits increased.     

Three salts from the reactions of cysteamine and cystamine with L‐(+)‐tartaric acid

Reaction between cysteamine (systematic name: 2‐aminoethanethiol, C₂H₇NS) and L‐(+)‐tartaric acid [systematic name: (2R,3R)‐2,3‐dihydroxybutanedioic acid, C₄H₆O₆] results in a mixture of cysteamine tartrate(1−) monohydrate, C₂H₈NS⁺·C₄H₅O₆⁻·H₂O, (I), and cystamine bis[tartrate(1−)] dihydrate, C₄H₁₄N₂S₂²⁺·2C₄H₅O₆⁻·2H₂O, (III). Cystamine [systematic name: 2,2′‐dithiobis(ethylamine), C₄H₁₂N₂S₂], reacts with L‐(+)‐tartaric acid to produce a mixture of cystamine tartrate(2−), C₄H₁₄N₂S₂²⁺·C₄H₄O₆²⁻, (II), and (III). In each crystal structure, the anions are linked by O—H...O hydrogen bonds that run parallel to the a axis. In addition, hydrogen bonding involving protonated amino groups in all three salts, and water molecules in (I) and (III), leads to extensive three‐dimensional hydrogen‐bonding networks. All three salts crystallize in the orthorhombic space group P2₁2₁2₁.     

Modelling interaction between ammonia and nitric oxide molecules and aquaporins

Aquaporin is a family of small membrane-proteins that are capable of transporting nano-sized materials. In the present paper, we investigate the structure of these channels and provide information about the mechanism of individual molecules being encapsulated into aquaglyceroporin (GlpF) and aquaporin-1 (AQP1) channels by calculating the potential energy. In particular, we presents a mathematical model to determine the total potential energy for the interaction of the ammonia and nitric oxide molecules and different aquaporin channels which we assume to have a symmetrical cylindrical structure. We propose to describe these interactions in two steps. Firstly, we model the nitrogen atom as a discrete point and secondly, we model the three hydrogen atoms on the surface of a sphere of a certain radius. Then, we find the total potential energy by summing these interactions. Next, by considering the nitric oxide molecule as two discrete atoms uniformly distributed interacting with GlpF and AQP1 channels then gathering all pairs of interaction to determine the potential energy. Our results show that the ammonia and nitric oxide molecules can be encapsulated into both GlpF and AQP1 channels.     

Potential infrared liquid crystals

Principles for selecting potential infrared nematic liquid crystals are described. Optical and electro-optic properties of two cyanotolanes, 4-n-alkyl-4′-cyanotolanes and three commercial liquid-crystal mixtures were chosen for evaluation. Their applications for modulating infrared radiation are addressed.     

Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

We compare extensive experimental results for the gravity-driven steady drainage of oil-in-water emulsions with two theoretical predictions, both based on the assumption of Poiseuille flow. The first is from standard foam drainage theory, applicable at low aqueous volume fractions, for which a correction is derived to account for the effects of the confinement of the emulsion. The second arises from considering the permeability of a model porous medium consisting of solid sphere packings, applicable at higher aqueous volume fractions. We find quantitative agreement between experiment and the foam drainage theory at low aqueous volume fractions. At higher aqueous volume fractions, the reduced flow rate calculated from the permeability theory approaches the master curve of the experimental data. Our experimental data demonstrates the analogy between the problem of electrical flow and liquid flow through foams and emulsions.