Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

A simple and sensitive method for the determination of hydroxylamine in fresh-water samples using hypochlorite followed by gas chromatography.

A new and simple method for the determination of hydroxylamine in environmental water, such as fresh rivers and lakes using hypochlorite, followed by its gas choromatographic detection, has been developed. A glass vial filled with sample water was sealed by a butyl-rubber stopper and aluminum cap without head-space, and then sodium hypochlorite solution was injected into the vial through a syringe to convert hydroxylamine to nitrous oxide. The head-space in the glass vial was prepared with 99.9% grade N2 using a gas-tight syringe. After the glass vial was shaken for a few minutes, nitrous oxide in the gas-phase was measured by a gas chromatograph with an electron-capture detector. The dissolved nitrous oxide in the liquid-phase was calculated according to the solubility formula. The proposed method was applied to the analysis of fresh-water samples taken from Iu river and Hii river, flowing into brackish Lakes Nakaumi and Shinji, respectively.     

Synthesis of well‐defined syndiotactic poly(methyl methacrylate) with low‐temperature atom transfer radical polymerization in fluoroalcohol

The copper‐mediated atom transfer radical polymerization of methyl methacrylate (MMA) in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) was studied to simultaneously control the molecular weight and tacticity. The polymerization using tris[2‐(dimethylamino)ethyl]amine (Me₆TREN) as a ligand was performed even at ?78°C with a number‐average molecular weight (M_n) of 13,400 and a polydispersity (weight‐average molecular weight/number‐average molecular weight) of 1.31, although the measured M_n's were much higher than the theoretical ones. The addition of copper(II) bromide (CuBr₂) apparently affected the early stage of the polymerization; that is, the polymerization could proceed in a controlled manner under the condition of [MMA]₀/[methyl α‐bromoisobutyrate]₀/[CuBr]₀/[CuBr₂]₀/[Me₆TREN]₀ = 200/1/1/0.2/1.2 at ?20°C with an MMA/HFIP ratio of 1/4 (v/v). For the field desorption mass spectrum of Cu^IBr/Me₆TREN in HFIP, there were [Cu(Me₆TREN)Br]⁺ and [Cu(Me₆TREN)OCH(CF₃)₂]⁺, indicating that HFIP should coordinate to the Cu^I/Me₆TREN complex. The syndiotacticity of the obtained poly(methyl methacrylate)s increased with the decreasing polymerization temperature; the racemo content was 84% for ?78°C, 77% for ?30°C, 75% for ?20°C, and 63% for 30°C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1436–1446, 2006     

Design and synthesis of highly sensitive and selective fluorescein-derived magnesium fluorescent probes and application to intracellular 3D Mg2+ imaging

The role of intracellular magnesium ions is of high interest in the fields of pharmacology and cellular biology. To accomplish the dynamic and three-dimensional imaging of intracellular Mg2+, there is a strong desire for the development of optimized Mg2+ fluorescent probes. In this paper we describe the design, synthesis, and cellular application of the three novel Mg2+ fluorescent probes KMG-101, -103, and -104. The compounds of this series feature a charged beta-diketone as a binding site specific for Mg2+ and a fluorescein residue as the fluorophore that can be excited with an Ar+ laser such as is widely used in confocal scanning microscopy. This molecular design leads to an intensive off-on-type fluorescent response toward Mg2+ ions. The two fluorescent probes KMG-103 and -104 showed suitable dissociation constants (Kd,Mg2+ = 2 mM) and nearly a 10-fold fluorescence enhancement over the intracellular magnesium ion concentration range (0.1-6 mM), allowing high-contrast, sensitive, and selective Mg2+ measurements. For intracellular applications, the membrane-permeable probe KMG-104AM was synthesized and successfully incorporated into PC12 cells. Upon application of the mitochondria uncoupler FCCP to the probe-incorporated cells, the resulting increase in the free magnesium ion concentration could be followed over time. By using a confocal microscope, the intracellular 3D magnesium ion concentration distributions were satisfactorily observed.     

Improvement of chemical analysis of antibiotics. X. Determination of eight tetracyclines using thin-layer and high-performance liquid chromatography

Analytical methods for eight tetracyclines (TCs) were established using silica gel high-performance thin-layer chromatography (HPTLC), reversed-phase thin-layer chromatography (RP-TLC) and high-performance liquid chromatography (HPLC). Good separations of eight TCs were obtained using chloroform-methanol-5% disodium ethylenediaminetetraacetate solution (65:20:5) (lower layer) and methanol acetonitrile 0.5 M oxalic acid solution (1:1:4) (pH 3.0) on silica gel HPTLC and C8 TLC plates, respectively. A combination of HPTLC and RP-TLC made possible the identification of the eight TCs. Each calibration graph was linear between 0.1 and 1.0 microgram using UV densitometry except for rolitetracycline. For detection reagents, the diazonium salts including Fast Violet B gave variously coloured spots with the eight TCs and good sensitivities were obtained except with minocycline. In HPLC, the simultaneous analysis of the eight TCs on a C8 column was possible using methanol-acetonitrile-0.01 M oxalic acid solution (1:1.5:7) adjusted to pH 3.0 as the mobile phase. A linear relationship was obtained between 1.0 and 10 ng using the usual sample preparation except for rolitetracycline. The direct determination of rolitetracycline was possible using tetrahydrofuran, dimethyl sulphoxide and the mobile phase as solvents for preparation of the sample. For the determination of residual rolitetracycline, it was effective to measure the amount of rolitetracycline as tetracycline by HPLC, HPTLC and RP-TLC after conversion of rolitetracycline to tetracycline by incubating for 5 min in methanol at 50 degrees C.     

Proof of the generalized expressions for the number of perfect matchings of polycube graphs

The number of perfect rnatchings for the linear 2 × 2 ×n cubic lattice was analytically derived by diagonalizing the skew—symmetric 4n × 4n determinant, whose non—zero off—diagonal elements are either ±1 or ±i (pure imaginary number). The basic formulation invoking the matrix manipulation follows that of Kasteleyn, but the result obtained in this paper is the first example of the analytical solution for a special case of the three-dimensional Ising model.received by the Publisher 20 September 1989