Closure concept for 2-factors in claw-free graphs

We introduce a closure concept for 2-factors in claw-free graphs that generalizes the closure introduced by the first author. The 2-factor closure of a graph is uniquely determined and the closure operation turns a claw-free graph into the line graph of a graph containing no cycles of length at most 5 and no cycles of length 6 satisfying a certain condition. A graph has a 2-factor if and only if its closure has a 2-factor; however, the closure operation preserves neither the minimum number of components of a 2-factor nor the hamiltonicity or nonhamiltonicity of a graph.     

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word problems was found to have only a limited impact. Instead, removing contextual constraints from the problem goal was found to motivate students to validate their problem solving in terms of their everyday experiences. Based on these findings, what determines the authenticity and relevance of a mathematical problem seems to be whether the problem allows students to freely reconstruct the problem situation by making use of their imagination and everyday experiences. In short, the basic principle seems to be “less is more”; that is, fewer constraints in problem goals could function to help students personally associate problem solving with their everyday experiences.     

Molecular dynamics study of solubilization of cyclohexane,benzene, and phenol into mixed micelles composed of sodium dodecyl sulfate and octaethylene glycol monododecyl ether

Molecular dynamics calculations of a mixed micelle composed of sodium dodecyl sulfate (SDS) and octaethylene glycol monododecyl ether (C₁₂E₈) were performed for six compositions (SDS/C₁₂E₈ = 100/0, 80/20, 60/40, 40/60, 20/80, and 0/100) to investigate the composition dependence of the mixed micelle structure and solubilization of cyclohexane, benzene, and phenol molecules by the micelle. The radial density distribution of the hydrophilic polyoxyethylene (POE) group of C₁₂E₈ as a function of distance from the micelle center is very sharp for micelles with high SDS content because the POE group captures a Na⁺ ion in solution and wraps around it to form a compact crown-ether-like complex. The hydrophobic dodecyl groups of SDS and C₁₂E₈ were separately distributed in the mixed micelle core. ΔG(r) evaluated for each solute showed that despite the structural changes of the micelle the binding strength of the solute molecules to the micelle did not change significantly. © 2019 Wiley Periodicals, Inc.     

Reactions of a Silylyne Complex with Aldehydes: Formation of W−Si−O−C Four-Membered Metallacycles and Their Metathesis-Like Fragmentation

A tungsten silylyne complex having a W≡Si triple bond reacted with two molecules of aldehydes at room temperature to give W−Si−O−C four-membered metallacycles by [2+2] cycloaddition and subsequent formyl hydrogen transfer from one aldehyde molecule to another. Upon heating to 70 °C, the four-membered metallacycles underwent metathesis-like fragmentation cleanly to afford carbyne complexes and “silanoic esters,” in a manner similar to that of metallacyclobutadiene, an intermediate of alkyne metathesis reactions, and dimerization of the latter products gave 1,3-cyclodisiloxanes. The “silanoic ester” was also trapped by pivalaldehyde to give a [2+2] cycloaddition product in high yield.     

Biphenyl ether and biphenyl quinolizidine lactone alkaloids from Heimia salicifolia

Three new biphenyl ether quinolizidine lactone alkaloids (1–3) and 13 new biphenyl quinolizidine lactone alkaloids (4–16) were isolated from Heimia salicifolia (Lythraceae) together with seven known alkaloids. Their structures were determined by spectroscopic analyses and chemical conversions.     

Farey Series and the Riemann Hypothesis III

In this paper we shall make a further study on the the equivalence problem, i.e., equivalent conditions to the Riemann hypothesis in terms of Farey series by developing a rather analytical (-arithmetical) method to establish unexpected short interval results, namely results, therewith simultaneously clarifying the underlying reasons for results obtained in Part I.     

Iron-catalyzed enyne cross-coupling reaction

In the presence of 0.5-1 mol % of FeCl(3) with lithium bromide as a crucial additive, alkynyl Grignard reagents, prepared from the corresponding alkynes and methylmagnesium bromide, react with alkenyl bromides or triflates to give the corresponding conjugated enynes in high to excellent yields. The reaction shows wide applicability to various terminal alkynes and alkenyl electrophiles.     

In vitro translation with [<Superscript>34</Superscript>S]-labeled methionine,selenomethionine, and telluromethionine

Heteroisotope and heteroatom tagging with [³⁴S]-enriched methionine (Met), selenomethionine (SeMet), and telluromethionine (TeMet) was applied to in vitro translation. Green fluorescent protein (GFP) and JNK stimulatory phosphatase-1 (JSP-1) genes were translated with wheat germ extract (WGE) in the presence of Met derivatives. GFPs containing Met derivatives were subjected to HPLC coupled with treble detection, i.e., a photodiode array detector, a fluorescence detector, and an inductively coupled plasma mass spectrometer (ICP-MS). The activities of JSP-1-containing Met derivatives were also measured. GFP and JSP-1 containing [³⁴S]-Met and SeMet showed comparable fluorescence intensities and enzyme activities to those containing naturally occurring Met. TeMet was unstable and decomposed in WGE, whereas SeMet was stable throughout the experimental period. Thus, although Te was the most sensitive to ICP-MS detection among S, Se, and Te, TeMet was less incorporated into the proteins than Met and SeMet. Finally, the potential of heteroisotope and heteroatom tagging of desired proteins in in vitro translation followed by ICP-MS detection was discussed. Figure TeMet was less incorporated into GFP than Met and SeMet due to its instability in WGE