A note on free divergence-free vector fields

We exhibit an orthonormal basis of cyclic gradients and a (non-orthogonal) basis of the homogeneous free divergence-free vector field on the full Fock space and determine the dimension of Voiculescu's free divergence-free vector field of degree k or less. Moreover, we also give a concrete formula for the orthogonal projection onto the space of cyclic gradients as well as the free Leray projection.Comment: 8 pages. We improved the introduction and added one remark in the last part. We also added examples of vectors in the free divergence-free vector field, inspired by the classical cas

Artificial Extracellular Matrix Proteins Containing Phenylalanine Analogues Biosynthesized in Bacteria Using T7 Expression System and the PEGylation

In vivo incorporation of phenylalanine (Phe) analogues into an artificial extracellular matrix protein (aECM-CS5-ELF) was accomplished using a bacterial expression host that harbors the mutant phenylalanyl-tRNA synthetase (PheRS) with an enlarged binding pocket. Although the Ala294Gly/Thr251Gly mutant PheRS (PheRS**) under the control of T5 promoter allows incorporation of some Phe analogues into a protein, the T5 system is not suitable for material science studies because the amount of materials produced is not sufficient due to the moderate strength of the T5 promoter. This limitation can be overcome by using a pair of T7 promoter and T7 RNA polymerase instead. In the T7 expression system, it is difficult, however, to achieve a high incorporation level of Phe analogues, due to competition of Phe analogues for incorporation with the residual Phe that is required for synthesis of active T7 RNA polymerase. In this study, we prepared the PheRS** under T7 promoter and optimized culture condition to improve both the incorporation level of recombinant aECM protein and the incorporation level of Phe analogues. Incorporation and expression levels tend to increase in the case of p-azidophenylalanine, p-iodophenylalanine, and p-acetylphenylalanine. We evaluated the lower critical transition temperature, which is dependent on the incorporation ratio and the turbidity decreased when the incorporation level increased. Circular dichromism measurement indicated that this tendency is based on conformational change from random coil to β-turn structure. We demonstrated that polyethylene glycol (PEG) can be conjugated at reaction site of Phe analogues incorporated. We also demonstrated that the increased hydrophilicity of elastin-like sequences in the aECM-CS5-ELF made by PEG conjugation could suppress nonspecific adhesion of human umbilical vein endothelial cells (HUVEC)

Economic effects analysis of public investment in road improvement works in Hokkaido. Simulation analysis based on a macro-econometric model of Hokkaido

The objective of this study is to clarify how public investment in road improvement projects over a given analytical period of time has affected Hokkaido`s economic structure on the whole in relation to the industrial economy, prefectural income, household consumption, and commodity prices, through a simulation analysis based on a macro-econometric model. More specifically, our goal is to model both the direct effects achieved through the use of improved roads including the reduction of time-distance coefficients, the reduction of transportation costs and market expansion, and the indirect effects such as enhancement of lifestyles and convenience and influence on other public projects including living area improvement and promotion of regional areas, and to identify these effects quantitatively. Taking data availability into consideration, this study covers a 21-year analysis period covering the years 1976 through 1996. In constructing a quantitative model, the effect flow to be modeled was examined from two perspectives: 1) an effect flow showing the effects of road improvement works on production efficiency and market efficiency; and 2) an effect flow showing the effects of road improvement works on living standards considering convenience and lifestyle improvement. Then we attempted building a model that could indicate the occurrence of these effects in both Flow and Stock contexts. As a result of the simulation analysis, it was clarified that application of road improvement works would bring about pronounced positive economic benefits in tertiary industries, particularly in the transportation-service and wholesale/retail sectors, and greatly expand the prefectural net product on the whole. It was also revealed that these expansion effects would stimulate an increase in the prefectural income and in private final consumption expenditure. Furthermore, a simulation analysis on the economic effects that the expansion of the express-highway network would have on Hokkaido`s entire economy revealed that there would be a large effect particularly on investment and production within the transportation/communication industry and also on the commercial output of the wholesale/retail industry.

Potential Antitumor Activity of 2-O-α-D-Glucopyranosyl-6-O-(2-Pentylheptanoyl)-L-Ascorbic Acid

Intravenous administration of high-dose ascorbic acid (AA) has been reported as a treatment for cancer patients. However, cancer patients with renal failure cannot receive this therapy because high-dose AA infusion can have side effects. To solve this problem, we evaluated the antitumor activity of a lipophilic stable AA derivative, 2-O-α-D-glucopyranosyl-6-O-(2-pentylheptanoyl)-L-ascorbic acid (6-bOcta-AA-2G). Intravenous administration of 6-bOcta-AA-2G suppressed tumor growth in colon-26 tumor-bearing mice more strongly than did AA, even at 1/10 of the molar amount of AA. Experiments on the biodistribution and clearance of 6-bOcta-AA-2G and its metabolites in tumor-bearing mice showed that 6-bOcta-AA-2G was hydrolyzed to 6-O-(2-propylpentanoyl)-L-ascorbic acid (6-bOcta-AA) slowly to yield AA, and the results suggested that this characteristic metabolic pattern is responsible for making the antitumor activity of 6-bOcta-AA-2G stronger than that of AA and that the active form of 6-bOcta-AA-2G showing antitumor activity is 6-bOcta-AA. In in vitro experiments, the oxidized form of 6-bOcta-AA as well as 6-bOcta-AA showed significant cytotoxicity, while the oxidized forms of ascorbic acid showed no cytotoxicity at all, suggesting that the antitumor activity mechanism of 6-bOcta-AA-2G is different from that of AA and that the antitumor activity is due to the reduced and oxidized form of 6-bOcta-AA. The findings suggest that 6-bOcta-AA-2G is a potent candidate as an alternative drug to intravenous high-dose AA

Newton's law in de Sitter brane

Newton potential has been evaluated for the case of dS brane embedded in Minkowski, dS$_5$ and AdS$_5$ bulks. We point out that only the AdS$_5$ bulk might be consistent with the Newton's law from the brane-world viewpoint when we respect a small cosmological constant observed at present universe.Comment: 9 pages, 1 figure, LaTe

<em>Legionella</em> Pneumonia Due to Non-<em>Legionella pneumophila</em> Serogroup 1

Legionella pneumophila is one of the important pathogens in community-acquired (CAP) and hospital-acquired pneumonia that can cause severe pneumonia. Early diagnosis and treatment of Legionella pneumonia (LP) are essential because inappropriate therapy for Legionella pneumonia has been reported to worsen the prognosis. The most frequently identified causative pathogen of Legionella pneumonia is Legionella pneumophila serogroup 1. Legionella pneumonia due to non-Legionella pneumophila serogroup 1 is seen in 20% of cases. In diagnosing Legionella pneumonia caused by non-Legionella pneumophila serogroup 1, the urinary antigen test is usually negative; therefore, we need to suspect Legionella pneumonia by clinical information such as symptoms, vital signs, laboratory findings, and radiological findings. Based on our previous report, Legionella pneumonia due to non-Legionella pneumophila serogroup 1 was a mild to severe pneumonia. In addition, in about half of the patients, we could not suspect Legionella pneumonia using a six-point scoring system, which is one of the diagnostic scoring systems. Recently, a new urinary antigen test kit that could theoretically diagnose Legionella pneumonia due to non-Legionella pneumophila serogroup 1 was released in Japan. This can help in early diagnosis of Legionella pneumonia, including the one caused by non-Legionella pneumophila serogroup 1