Blow-up theorem for semilinear wave equations with non-zero initial position

One of the features of solutions of semilinear wave equations can be found in blow-up results for non-compactly supported data. In spite of finite propagation speed of the linear wave, we have no global in time solution for any power nonlinearity if the spatial decay of the initial data is weak. This was first observed by Asakura (1986) [2] finding out a critical decay to ensure the global existence of the solution. But the blow-up result is available only for zero initial position having positive speed.In this paper the blow-up theorem for non-zero initial position by Uesaka (2009) [22] is extended to higher-dimensional case. And the assumption on the nonlinear term is relaxed to include an example, |u|^p−1u. Moreover the critical decay of the initial position is clarified by example.     

Recent topics of the stereodivergent synthesis of natural products

A variety of natural products, a valuable source of drug lead compounds, coexist with their stereoisomers as congeners. For pursuing the structural elucidation and the structure–activity relationship study of natural products, it is needed to establish the streamlined synthetic route to supply natural products and their stereoisomers. Divergent pathway is one of the synthetic strategies to deliver more than one target compound. In this digest, selected examples of the stereodivergent approach toward the synthesis of natural products are described. Especially, this digest focuses on common synthetic intermediates and stereodiversification steps from the common intermediates to reach the target compounds.     

Total synthesis and absolute configuration of (-)-gummiferol

Stereoselective synthesis of two possible diastereomers of (-)-gummiferol was accomplished by the stepwise epoxidation and Cadiot-Chodkiewicz reaction as the key transformations. Detailed comparison of their (1)H and (13)C NMR data and specific rotation with those of the natural product led to the absolute structural elucidation of (-)-gummiferol.     

Differentiation between sulfoaildenafil and its analogs

An analog of aildenafil, which is a potent and highly selective inhibitor of phosphodiesterase 5, was found in a dietary supplement marketed for enhancement of sexual function. The compound was isolated by silica gel column chromatography, and its structure was identified by means of 13C-NMR spectrometry, 1H-NMR spectrometry, high-resolution MS, and X-ray structure determination. The compound was identified to be sulfoaildenafil (other names: thioaildenafil, dimethyl sildenafil thione, and thiomethisosildenafil). Sulfoaildenafil is very similar to the compound thiohomosildenafil. As it is difficult to distinguish between them by LC-photodiode array detector analysis, ultra-performance LC (UPLC)/MS, ion trap LC/MS/MS (LC/IT-MS/MS), and GC/MS were performed. The mass spectra of thiohomosildenafil by UPLC/MS and LC/IT-MS/MS showed mass fragments of m/z 58, 72, and 355, and the mass spectrum by GC/MS showed mass fragments of m/z 56, 72, and 420. Some of these fragments had low intensities, but they were useful for distinguishing between the two compounds. The relationship between aildenafil (other names: dimethylsildenafil and methisosildenafil) and homosildenafil is similar to that between sulfoaildenafil and thiohomosildenafil. Therefore, these compounds were also examined.     

Structural Identification of DNA Adducts Derived from 3‐Nitrobenzanthrone,a Potent Carcinogen Present in the Atmosphere

3‐Nitrobenzanthrone is a powerful bacterial mutagen and carcinogen to mammals. To obtain precise information on DNA‐adduct formation by 3‐nitrobenzanthrone, a number of DNA adducts, including N‐(2′‐deoxyguanosin‐8‐yl)‐3‐aminobenzanthrone ( 13 a ), 2‐(2′‐deoxyguanosin‐N²‐yl)‐3‐aminobenzanthrone ( 14 a ), N‐(2′‐deoxyadenosin‐8‐yl)‐3‐aminobenzanthrone ( 15 a ), 2‐(2′‐deoxyadenosin‐N⁶‐yl)‐3‐aminobenzanthrone ( 16 a ), and their N‐acetylated counterparts 13 b , 14 b , 15 b , and 16 b were synthesized by palladium‐catalyzed aryl amination of the corresponding nucleoside and bromobenzanthrone derivatives. Among these DNA adducts, DNA adducts 13 a , 13 b , 14 a , 14 b , and 16 a were identified in the reaction mixture of nucleosides (2′‐deoxyguanosine, 2′‐deoxyadenosine, or DNA) with N‐acetoxy‐3‐aminobenzanthrone or N‐acetyl‐N‐acetoxy‐3‐aminobenzanthrone, both of which are recognized as activated metabolites of 3‐nitrobenzanthrone. The formation of these multiple DNA adducts may help explain the potent mutacarcinogenicity of 3‐nitrobenzanthrone.     

Simulation and experiment on detached plasmas in the linear divertor simulator NAGDIS-II

We have performed two dimensional fluid B2 simulations on detached recombining plasmas to compare with experimental observations in a linear divertor plasma simulator. In detached helium plasmas associated with volumetric electron-ion recombination (collisional radiative recombination), an electron-ion energy exchange process followed by ion-neutral charge exchange is found to be a key to reduce the electron temperature along the magnetic field to be less than leV. The structural change of detached plasmas associated with molecular activated recombination has been also discussed in detail.     

Preparation and properties of organic–inorganic hybrid gel films based on polyvinylpolysilsesquioxane synthesized from trimethoxy(vinyl)silane

Polyvinylpolysilsesquioxane (PVPS) organic–inorganic hybrid gel films comprising polyethylene and siloxane backbone linkages were prepared through two routes: trimethoxy(vinyl)silane (VTS) was first subjected to radical polymerization of the vinyl groups, followed by acid‐catalyzed hydrolytic polycondensation of the trimethoxysilyl groups (route A) to afford PVPS; in the second route PVPS was prepared in reverse order (route B). PVPS gel films were transparent and homogeneous. We find that the mechanical and heat‐resisting properties correlate both to the degree of polymerization and the degree of cross‐linking. Copyright © 2003 John Wiley & Sons, Ltd.     

An electrochemical on-field sensor system for the detection of compost maturity

A maturity sensor system was developed, based on the combination of three electrically measured parameters, pH, NH₄⁺ concentration, and phosphatase activity in the water extracts of compost samples. One of these parameters, the apparent phosphatase activity in crude test solutions was determined using screen-printed carbon strips (SPCSs) coated with α-naphthyl phosphate (α-NP) in Nafion film. The phosphatase activity was monitored in connection with differential pulse voltammetry (DPV) with an aliquot (30 μL) of the test solution on SPCS. The phosphatase activity sensor was validated using alkaline phosphatase (ALP) in Tris-HCl buffer (pH 8.0) and acid phosphatase (ACP) in citric acid buffer (pH 5.0). The activity of the spiked enzymes in the water extract of the compost sample could be confirmed with the change of corresponding oxidation peak current signal of the product, α-naphthol. The water extracts of compost samples (n = 24) collected in various composting days were applied to our compost maturity sensor system, and the conventional germination tests. Using multiple regression analysis, the germination index (GI) was expressed by the multi-linear regression equation consisting of pH, NH₄⁺ concentration, and the phosphatase activity. The calculated GI from the regression equation had a good correlation with the measured GI of the corresponding composts (r = 0.873). As a result, we have determined an equation for the determination of the compost stability using our portable sensor system rapidly at the composting site.     

Powers of positive elements in C*‐algebras

In this paper, we show that Ogasawa’s theorem has a proof in Bishop style constructive mathematics (BISH). In 25 , we introduced the elementary constructive theory of C*‐algebras in BISH, but we did not discuss the powers of positive elements there. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Elemental Selenium Generated by the Photobleaching of Seleno-Merocyanine Photosensitizers Forms Conjugates with Serum Macro-Molecules That are Toxic to Tumor Cells

Abstract

Elemental selenium generated by the photobleaching of selenomerocyanine dyes forms conjugates with serum albumin and serum lipoproteins that are toxic to leukemia and selected solid tumor cells but well tolerated by normal CD34-positive hematopoietic stem and progenitor cells. Serum albumin and lipoproteins act as Trojan horses that deliver the cytotoxic entity (elemental selenium) to tumor cells as part of a physiological process. They exploit the fact that many tumors have an increased demand for albumin and/or low-density lipoprotein. Se(0)-protein conjugates are more toxic than selenium dioxide, sodium selenite, selenomethionine, or selenocystine. They are only minimally affected by a drug resistance mechanism, and they potentiate the cytotoxic effect of ionizing radiation and several standard chemotherapeutic agents. The cytotoxic mechanism of Se(0)-protein conjugates is not yet fully understood. Currently available data are consistent with the notion that Se(0)-protein conjugates act as air oxidation catalysts that cause a rapid depletion of intracellular glutathione and induce apoptosis. Drugs modeled after our Se(0)-protein conjugates may prove useful for the local and/or systemic therapy of cancer.