Flat points of two-dimensional Brownian motion

Summary SupposeZ(·) is a two-dimensional Brownian motion. It is shown that a.s. there existt ₀ and >0 such thatZ(t ₀) is an extremal point of the convex hull of {Z(t)|t ₀–tt₀} and also an extremal point of the convex hull of {Z(t)|t ₀tt₀+} and, moreover, the tangent lines to the convex hulls atZ(t ₀) form a non-zero angle.The result is related to the following unsolved problem of S.J. Taylor. Do there exist a.s.t ₀ and >0 such that the intersection of the convex hulls of {Z(t)|t ₀–tt₀} and {Z(t)|t ₀tt₀+} contains onlyZ(t ₀)?This research was partially supported by Grant-in-Aid for Scientific Research (No. 400101540202), Ministry of Education, Science and Culture     

Acridine derivatives. V. Synthesis and P388 antitumor activity of the novel 9-anilino-2,3-ethylenedioxyacridines

A new class of deoxyribonucleic acid (DNA)-intercalating antitumor agents, novel 9-anilino-2,3-ethylenedioxyacridines (five compounds) have been synthesized and evaluated for activity against P388 leukemia in vivo. A few of them possessed the same potency of antitumor activity as amsacrine (m-AMSA) which is an important antitumor agent in clinical use.     

Nature of nonbonded Se...O interactions characterized by 17O NMR spectroscopy and NBO and AIM analyses

To investigate the nature of nonbonded Se...O interactions, three series of 2-substituted benzeneselenenyl derivatives [2-(CHO)C6H4SeX (1), 2-(CH2OH)C6H4SeX, (2), 2-(CH2OiPr)C6H4SeX (3); X = Cl, Br, CN, SPh, SeAr, Me] were synthesized. The 17O NMR absorption observed for 17O-enriched aldehydes 1 appeared upfield relative to benzaldehyde (PhCHO), while the opposite downfield shifts relative to benzyl alcohol (PhCH2OH) were observed for 17O-enriched alcohols 2 and ethers 3. The magnitude of both the upfield and the downfield shifts became larger as the electron-withdrawing ability of a substituent X increased. Quantum chemical calculations at the B3LYP level revealed that for all model compounds the most stable conformer has an intramolecular nonbonded Se.O interaction. Thus, the relative 17O NMR chemical shifts (DeltadeltaO) for 1-3 would reflect the strengths of the Se...O interactions. The natural bond orbital (NBO) analysis demonstrated that the stabilization energy due to an nO --> sigma Se-X orbital interaction (ESe...O) correlates with the Se...O atomic distance on a single curve irrespective of the type of the O atom. On the other hand, the atoms in molecules (AIM) analysis showed that the nonbonded Se...O interactions can be characterized by the presence of a bond critical point, the total energy density (HSe...O) of which decreases with strengthening of the interaction. The results suggested that Se...O interactions have a dominant covalent character rather than an electrostatic one.     

Probing the semi-macroscopic vacuum by higher-harmonic generation under focused intense laser fields

The invention of the laser immediately enabled the detection of nonlinear photon–matter interactions, as manifested for example by Franken et al.’s detection of second-harmonic generation.     

Modeling Thioredoxin Reductase-Like Activity with Cyclic Selenenyl Sulfides: Participation of an NH⋅⋅⋅Se Hydrogen Bond through Stabilization of the Mixed Se−S Intermediate

At the redox-active center of thioredoxin reductase (TrxR), a selenenyl sulfide (Se−S) bond is formed between Cys497 and Sec498, which is activated into the thiolselenolate state ([SH,Se⁻]) by reacting with a nearby dithiol motif ([SH^Cys59,SH^Cys64]) present in the other subunit. This process is achieved through two reversible steps: an attack of a cysteinyl thiol of Cys59 at the Se atom of the Se−S bond and a subsequent attack of a remaining thiol at the S atom of the generated mixed Se−S intermediate. However, it is not clear how the kinetically unfavorable second step progresses smoothly in the catalytic cycle. A model study that used synthetic selenenyl sulfides, which mimic the active site structure of human TrxR comprising Cys497, Sec498, and His472, suggested that His472 can play a key role by forming a hydrogen bond with the Se atom of the mixed Se−S intermediate to facilitate the second step. In addition, the selenenyl sulfides exhibited a defensive ability against H₂O₂-induced oxidative stress in cultured cells, which suggests the possibility for medicinal applications to control the redox balance in cells.     

Stereoselective analysis of flecainide enantiomers using reversed‐phase liquid chromatography for assessing CYP2D6 activity

Stereoselective analyses of flecainide enantiomers were performed using reversed‐phase high‐performance liquid chromatography (HPLC) equipped with a polysaccharide‐based chiral column (Chiralpak AS‐RH) and fluorescence detector. Excitation and emission wavelengths were set at 300 and 370 nm, respectively. Flecainide enantiomers in serum and urine were extracted using diethyl ether. The mobile phase solution, comprising 0.1 m potassium hexafluorophosphate and acetonitrile (65:35, v/v), was pumped at a flow rate of 0.5 mL/min. The recoveries of flecainide enantiomers were greater than 94%, with the coefficients of variation (CVs) <6%. The calibration curves of flecainide enantiomers in serum and urine were linear in the concentration range 5–500 ng/mL and 0.75–15 µg/mL (r > 0.999), respectively. CVs in intra‐day and inter‐day assays were 1.8–5.8 and 3.4–7.5%, respectively. In a pharmacokinetic study, the ratios of (S)‐ to (R)‐flecainide (S/R ratio) in the area under the curve and the amount of flecainide enantiomers excreted in urine were lower in a subject carrying CYP2D6*10/*10 than in subjects carrying CYP2D6*1/*2. The S/R ratio of trough serum flecainide concentration ranged from 0.79 to 1.16 in patients receiving oral flecainide. The present HPLC method can be used to assess hepatic flecainide metabolism in a pharmacokinetic study and therapeutic drug monitoring. Copyright © 2014 John Wiley & Sons, Ltd.     

Cycloaddition to a C3-ethynylated chlorophyll derivative and self-aggregation of zinc chlorin–pyrazole/triazole conjugates

Several kinds of cycloaddition reactions were applied to C3-ethynylated pyropheophorbide-a methyl ester to develop C3-functionalized chlorophyll derivatives. Its [2+2] cycloaddition with tetracyanoethylene, [2+3] cycloaddition with diazomethane, [2+3] Huisgen reaction with trimethylsilyl azide, and [2+4] Diels–Alder reaction with tetraphenylcyclopentadienone gave the expected products in moderate to high yields. Zinc complex of the resulting 3-pyrazolyl-chlorin was found to show self-aggregation in a less polar solvent, in an aqueous micelle, and in the solid thin films more readily than the corresponding zinc 3-triazolyl-chlorin.     

Effects of carboxyl-group counter-ions on biodegradation behaviors of TEMPO-oxidized cellulose fibers and nanofibril films

The biodegradation behaviors of 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO)-oxidized cellulose fibers (TOCs) and TEMPO-oxidized cellulose nanofibril (TOCN) films containing various carboxyl-group counter-ions were studied. Na⁺, H⁺, Ca²⁺, NH₄ ⁺, Cu²⁺, K⁺, and Cs⁺ were introduced into the TOCs or TOCN films, by ion-exchange treatment, as the carboxyl-group counter-ions. TOCs suspended in distilled water were treated with a commercial crude cellulase, and the TOCN films were subjected to soil burial tests. The crude-cellulase-treated products obtained from the TOCs were separated into water/ethanol-insoluble and -soluble fractions, i.e., high- and low-molecular-weight fractions, respectively. The degradation behaviors of the TOCs were evaluated from the weight recovery ratios of the water/ethanol-insoluble fractions and their viscosity-average degrees of polymerization. The results showed that the degradation behaviors of the TOCs were greatly influenced by the counter ion, and the counter-ion order of degradability was Na⁺ ≈ NH₄ ⁺ ≈ K⁺ ≈ Cs⁺ ? Ca²⁺ > H⁺ > Cu²⁺. These degradability differences were influenced by the swelling behavior of the corresponding TOCs in distilled water; the higher the swelling degree of the TOC, the higher the degradation efficiency of the TOC in the reaction with crude cellulase. Similar biodegradation behaviors were observed in soil burial tests for TOCN films containing various carboxyl-group counter-ions in soil burial test; again the counter ion greatly influenced the resultant biodegradability. The biodegradation behaviors of TOCs and TOCN films can therefore be controlled by selecting an appropriate carboxyl-group counter-ion.