Determination of molecular weight distribution of nylon 12 by gel permeation chromatography

Molecular weight distribution of Nylon 12 was determined with hexafluoroisopropanol/toluene mixture as eluent by gel permeation chromatography. Calibration curve for Nylon 12 was easily obtained from that of polystyrene because the method of universal calibration was applicable among these polymers. The molecular weight distributions of Nylon 12 were always broader than expected by the theory of polymerization, i.e., most probable distribution. This result was not caused by broadening effect in gel permeation chromatography, but by polymerization itself.     

A Non‐Enzymatic Pathway with Superoxide in Intracellular Terpenoid Synthesis

Non‐C₅‐units terpenoids (norisoprenoids) with an acetonyl group are widely distributed in nature. However, studies on the biosynthesis of norisoprenoids are scarce. Now, the C₃₃ norisoprenoid, (all‐E)‐farnesylfarnesylacetone, was identified from Bacillus spp. and it was elucidated for the first time that superoxide mediates the cleavage of menaquinones (vitamin K) to form norisoprenoids in saponification treatment. From in vivo experiments using gene‐disrupted Bacillus subtilis strains targeted for enzymes responsible for menaquinone biosynthesis and for superoxide dismutase, it was suggested that the non‐enzymatic cleavage (autoxidation) of menaquinone with superoxide resulted in norisoprenoid synthesis in Bacillus cells. Furthermore, the bioactive norisoprenoids, farnesylacetone and phytone, were produced in Bacillus cells by this novel synthesis system.     

Practical synthesis of a 1beta-methylcarbapenem, J-111,225, using 4-mercapto-2-[4-(N-methylaminomethyl)phenyl]pyrrolidine as a precursor

An effective and practical procedure for the synthesis of J-111,225 (1), a new 1beta-methylcarbapenem, was developed using 4-mercapto-2-14-(N-methylaminomethyl)phenyl]pyrrolidine (2a) as a precursor. The coupling reaction of 2a with p-nitrobenzyl (PNB)-protected 1beta-methylcarbapenem enolphosphate 3a and successive removal of PNB group afforded J-111,225 (1) in significantly increased yield compared to the ordinary procedure using a C-2 side-chain thiol with amino-protective groups.     

Decarboxylation of α-keto carboxylic acids by persulfoxide

Photosensitized oxygenation of diethyl sulfide in the presence of α-keto carboxylic acids caused oxidative decarboxylation of the acids by persulfoxide and gave carboxylic acids, carbon dioxide, diethyl sulfoxide and diethyl sulfone.     

A new matrix method based on rigid elements and its application to plane problems

A new matrix is proposed here which is based on rigid elements. The efficiency and usefulness of this method has been demonstrated for plane problems. The purpose of this paper is to formulate the method and to indicate its validity.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

A smoothing property of Schrödinger equations in the critical case

This paper deals with the critical case of the global smoothing estimates for the Schrödinger equation. Although such estimates fail for critical orders of weights and smoothing, it is shown that they are still valid if one works with operators with symbols vanishing on a certain set. The geometric meaning of this set is clarified in terms of the Hamiltonian flow of the Laplacian. The corresponding critical case of the limiting absorption principle for the resolvent is also established. Obtained results are extended to dispersive equations of Schrödinger type, to hyperbolic equations and to equations of other orders.