Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring $R[x,f]$ that are Artinian as $R$-modules and the category of right $R[x,f]$-modules that are Noetherian as $R$-modules.Comment: 16 pages, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society. This revised version includes two additionl references and points out that some of the results have been obtained independently by M. Blickle and G. Boeckl

γ+C 反応による核媒質中における η\u27質量スペクトルの直接測定

Tohoku University大西宏明論

Dihydroxylation of Naphthalene by Molecular Oxygen and Water Using TiO2 Photocatalysts

TiO2-catalyzed photo-reaction of naphthalene was investigated in mixed solutions of acetonitrile and water. The main products were confirmed to be 1,8- and 1,3-dihydroxynaphthalene, without any 1- or 2-naphthol being detected. Both O2 and H2O were essential to yield the products. The quantum efficiency of the 1,8- and 1,3-dihydroxynaphthalene products reached about 10% at 365 nm after irradiated for 1 h

Pulmonary artery injury during mediastinoscopy controlled without gauze packing

The most serious complication that can occur during mediastinoscopy is hemorrhage from large vessels in the mediastinum, whereas there are few articles relating to injury to major vessels. We describe a case of 77-year-old male with mediastinal lymphadenopathy, who underwent a mediastinoscopy procedure. When the pretracheal lymph nodes adjoining the right pulmonary artery were biopsied, a massive amount of bleeding spilled out through the scope. Immediately, the scope was removed from the body and the bleeding was controlled with digital compression at the skin incision. Then we closed the incision in a three-layer manner without any gauze packing in the mediastinum. Although some reports recommended gauze packing for massive bleeding during mediastinoscopy, we believe not all cases need gauze packing because bleeding from a low-pressure circulation system component into closed compartment, such as mediastinum, would cease without resulting in a large hematoma or pseudoaneurysm

PROGNOSTIC IMPLICATIONS OF TYPE 2 MYOCARDIAL INFARCTION IN VASOSPASTIC ANGINA: A HIGH-RISK SUBGROUP

summary:The Golomb space ${\mathbb N}_\tau$ is the set ${\mathbb N}$ of positive integers endowed with the topology $\tau$ generated by the base consisting of arithmetic progressions $\{a+ bn: n\ge 0\}$ with coprime $a,b$. We prove that the Golomb space ${\mathbb N}_\tau$ has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set $\Pi$ of prime numbers is a dense metrizable subspace of ${\mathbb N}_\tau$, and each homeomorphism $h$ of ${\mathbb N}_\tau$ has the following properties: $h(1)=1$, $h(\Pi)=\Pi$, $\Pi_{h(x)}=h(\Pi_x)$, and $h(x^{{\mathbb N}})=h(x)^{\,\mathbb N}$ for all $x\in{\mathbb N}$. Here $x^{\mathbb N}:=\{x^n\colon n\in{\mathbb N}\}$ and $\Pi_x$ denotes the set of prime divisors of $x$

TiO2-Photocatalyzed Epoxidation of 1-Decene by H2O2 under Visible Light

1-Decene was converted to 1,2-epoxydecane on UV-irradiated TiO2 powder using molecular oxygen as the oxygen source. Other main products were nonanal and 2-decanone. For anatase-form TiO2 powders, the reaction rate was hardly affected by addition of hydrogen peroxide to the solution. In contrast, for rutile-form TiO2 powders, the rate of epoxide generation was significantly increased by addition of hydrogen peroxide. In this case, the reaction occurred under visible light as well as UV light. The selectivity of the production of 1,2-epoxydecane was higher under visible light than under UV light. The conversion efficiency of an incident photon to 1,2-epoxydecane was about 2% when irradiated with visible light in the range 440–480 nm. UV–visible diffuse reflection spectroscopy, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy suggested the generation of a Ti–η2-peroxide on rutile TiO2 surface after treatment with hydrogen peroxide. The initial step of the reaction under visible light was attributed to a photochemical reaction of this peroxide with 1-decene

Side-scattered finger-photoplethysmography: experimental investigations toward practical noninvasive measurement of blood glucose

The aim of this study was to discover a simple/convenient geometrical arrangement of radiation sources and detector to acquire finger-photoplethysmograms (PPGs) with wavelength regions of blood glucose (BGL) absorption, toward practical noninvasive BGL measurement. First, we compared PPGs with three wavelengths: 808 nm (without water absorption), 1160 nm (with weak water absorption), and 1600 nm (with nearly peak BGL absorption and strong water absorption), while the source-detector spacing was successively increased circumferentially around a fingertip. In 10 healthy subjects, we observed clear cardiac-related pulsatile components of PPG signals at 808 and 1160 nm in any incident positions with more than 15 dB of signal-to-noise ratio (S/N), but reliable PPG detections at 1600 nm with more than 10 dB of S/N was only possible when the source-detector distance was less than 3mm around the fingertip circumference. Second, with this arrangement, an experiment was performed using six wavelengths to cover glucose absorption bands (from 1550 to 1749 nm), obtaining pulsatile PPG signals with more or less 15 dB of S/N. Through the present experiments, this orthogonal arrangement of the source and detector to detect forward-and side-scattered radiation through the tissue is appropriate for PPG measurements with wavelength regions where there is potential for BGL measurement