On the strength of marriage theorems and uniformity

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in , and investigate the sequential and Weihrauch strength of marriage theorems under that condition.     

Regioselectivity Control in Lipase‐Catalyzed Polymerization of Divinyl Sebacate and Triols

Lipase‐catalyzed regioselective polymerization of divinyl sebacate and triols has been performed in bulk. NMR analysis of the product obtained by the polymerization of divinyl sebacate and glycerol using Candida antarctica lipase at 60°C showed that 1,3‐diglyceride was a main unit and a small amount of the branching unit (triglyceride) was contained. The polymerization of divinyl sebacate with 1,2,4‐butanetriol or 1,2,6‐hexanetriol at 60°C produced a branched polymer. In polymerization at a lower temperature, the regioselectivity was perfectly controlled to give a linear polymer consisting of the α,ω‐disubstituted unit exclusively. The lipase origin and feed ratio of monomers greatly affected the microstructure of the polymer; under selected conditions, regiospecific polymerization was achieved.     

Triflumizole as a Novel Lead Compound for Strigolactone Biosynthesis Inhibitor

Strigolactones (SLs) are carotenoid-derived plant hormones involved in the development of various plants. SLs also stimulate seed germination of the root parasitic plants, Striga spp. and Orobanche spp., which reduce crop yield. Therefore, regulating SL biosynthesis may lessen the damage of root parasitic plants. Biosynthetic inhibitors effectively control biological processes by targeted regulation of biologically active compounds. In addition, biosynthetic inhibitors regulate endogenous levels in developmental stage- and tissue-specific manners. To date, although some chemicals have been found as SL biosynthesis inhibitor, these are derived from only three lead chemicals. In this study, to find a novel lead chemical for SL biosynthesis inhibitor, 27 nitrogen-containing heterocyclic derivatives were screened for inhibition of SL biosynthesis. Triflumizole most effectively reduced the levels of rice SL, 4-deoxyorobanchol (4DO), in root exudates. In addition, triflumizole inhibited endogenous 4DO biosynthesis in rice roots by inhibiting the enzymatic activity of Os900, a rice enzyme that converts the SL intermediate carlactone to 4DO. A Striga germination assay revealed that triflumizole-treated rice displayed a reduced level of germination stimulation for Striga. These results identify triflumizole as a novel lead compound for inhibition of SL biosynthesis.     

Shock wave detection in two-dimensional flow based on the theory of characteristics from CFD data

A method to detect the discontinuity of a shock wave from computational fluid dynamics (CFD) data was developed based on the theory of characteristics and was adopted to replace the inaccurate method that involves observation of the location of steep spatial gradient with respect to the primitive variables, such as pressure. A shock wave is mathematically defined as a convergence of characteristics, in which each type of Riemann invariant is conserved within each characteristic. In the vector field of the characteristics, such convergences are interpreted as critical lines of the streamlines, which are easily identified by calculating the eigenvectors of the vector field of propagation velocity of the Riemann invariant. The use of a triangular cell system enables unique determination of the linearized vector field in each cell and enables analytical identification of the critical line within this field. Shock waves can be successfully extracted using this method. The method can be extended to the detection of moving shock waves by considering the coordinate moving with the shock.     

Synthesis of Polycyclic and Cage Siloxanes by Hydrolysis and Intramolecular Condensation of Alkoxysilylated Cyclosiloxanes

The controlled synthesis of oligosiloxanes with well-defined structures is important for the bottom-up design of siloxane-based nanomaterials. This work reports the synthesis of various polycyclic and cage siloxanes by the hydrolysis and intramolecular condensation of monocyclic tetra- and hexasiloxanes functionalized with various alkoxysilyl groups. An investigation of monoalkoxysilylated cyclosiloxanes revealed that intramolecular condensation occurred preferentially between adjacent alkoxysilyl groups to form new tetrasiloxane rings. The study of dialkoxy- and trialkoxysilylated cyclotetrasiloxanes revealed multistep intramolecular condensation reactions to form cubic octasiloxanes in relatively high yields. Unlike conventional methods starting from organosilane monomers, intramolecular condensation enables the introduction of different organic substituents in controlled arrangements. So-called Janus cubes have been successfully obtained, that is, Ph₄R₄Si₈O₁₂, in which R=Me, OSiMe₃, and OSiMe₂Vi (Vi=vinyl). These findings will enable the creation of siloxane-based materials with diverse functions.     

Recognition and one-pot extraction of right- and left-handed semiconducting single-walled carbon nanotube enantiomers using fluorene-binaphthol chiral copolymers

Synthesized single-walled carbon nanotubes (SWNTs) are mixtures of right- and left-handed helicity and their separation is an essential topic in nanocarbon science. In this paper, we describe the separation of right- and left-handed semiconducting SWNTs from as-produced SWNTs. Our strategy for this goal is simple: we designed copolymers composed of polyfluorene and chiral bulky moieties because polyfluorenes with long alkyl-chains are known to dissolve only semiconducting SWNTs and chiral binaphthol is a so-called BINAP family that possesses a powerful enantiomer sorting capability. In this study, we synthesized 12 copolymers, (9,9-dioctylfluorene-2,7-diyl)x((R)- or (S)-2,2'-dimethoxy-1,1'-binaphthalen-6,6-diyl)y, where x and y are copolymer composition ratios. It was found that, by a simple one-pot sonication method, the copolymers are able to extract either right- or left-handed semiconducting SWNT enantiomers with (6,5)- and (7,5)-enriched chirality. The separated materials were confirmed by circular dichroism, vis-near IR and photoluminescence spectroscopies. Interestingly, the copolymer showed inversion of SWNT enantiomer recognition at higher contents of the chiral binaphthol moiety. Molecular mechanics simulations reveal a cooperative effect between the degree of chirality and copolymer conformation to be responsible for these distinct characteristics of the extractions. This is the first example describing the rational design and synthesis of novel compounds for the recognition and simple sorting of right- and left-handed semiconducting SWNTs with a specific chirality.     

The Utility of p-N-Succinimidobenzoyl Isothiocyanate in Synthesis of Benzoxazole,Quinazoline, Pyrimidine, 1,2,4-Triazoline, 1,3-Thiazolidine,and Thiourea Derivatives

Reactions of p-N-succinimidobenzoyl isothiocyanate (1) with different nucleophilic reagents afforded adducts. Simultaneous or subsequent cyclization of these adducts gave access to a variety of different heterocycles, including benzoxazole, quinazoline, pyrimidine, 1,2,4-triazoline, 1,3-thiazolidine and others. The structures of the new products were confirmed by their micro-analytical and spectral data.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Iron-catalyzed δ-selective conjugate addition of methyl and cyclopropyl Grignard reagents to α,β,γ,δ-unsaturated esters and amides

Iron-catalyzed δ-selective conjugate addition of methyl and cyclopropyl Grignard reagents to α,β,γ,δ-unsaturated esters and amides took place in good yields to give products exclusively with cis-β,γ-olefinic bond.     

Global fit of rotational transitions of methyl formate (HCOOCH3) in the ground and first excited torsional states

The microwave spectrum of methyl formate (HCOOCH₃) has been observed in the frequency range from 7 to 200 GHz. New 348 lines were assigned to E-species in the first excited torsional state. By combining these lines with previously reported data, a global analysis of A- and E-species lines of the ground and first excited torsional states were carried out on the basis of the internal axis method. A total of 3862 transitions were fitted to a Hamiltonian model involving 69 molecular parameters to a weighted unitless standard deviation of 1.96.