2-Dimensional complete self-shrinkers in $$\mathbf {R}^3$$

It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for \(\mathcal {L}\)-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \(\mathbb R^3\). Ding and Xin (Trans Am Math Soc 366:5067–5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.     

Synthesis and Applications of (ONO Pincer)Ruthenium‐Complex‐Bound Norvalines

Two (ONO pincer)ruthenium‐complex‐bound norvalines, Boc?[Ru(pydc)(terpy)]Nva?OMe ( 1 ; Boc=tert‐butyloxycarbonyl, terpy=terpyridyl, Nva=norvaline) and Boc?[Ru(pydc)(tBu‐terpy)]Nva?OMe ( 5 ), were successfully synthesized and their molecular structures and absolute configurations were unequivocally determined by single‐crystal X‐ray diffraction. The robustness of the pincer Ru complexes and norvaline scaffolds against acidic/basic, oxidizing, and high‐temperature conditions enabled us to perform selective transformations of the N‐Boc and C?OMe termini into various functional groups, such as alkyl amide, alkyl urea, and polyether groups, without the loss of the Ru center or enantiomeric purity. The resulting dialkylated Ru‐bound norvaline, n‐C₁₁H₂₃CO?l ‐[Ru(pydc)(terpy)]Nva?NH‐n‐C₁₁H₂₃ (l ‐ 4 ) was found to have excellent self‐assembly properties in organic solvents, thereby affording the corresponding supramolecular gels. Ru‐bound norvaline l ‐ 1 exhibited a higher catalytic activity for the oxidation of alcohols by H₂O₂ than parent complex [Ru(pydc)(terpy)] ( 11 a ).     

Silica-supported sodium sulfonate with ionic liquid: a neutral catalyst system for Michael reactions of indoles in water

A neutral catalytic system for Michael reactions of indoles has been developed by combining silica-supported benzenesulfonic acid sodium salt with hydrophobic ionic liquid in water. An efficient hydrophobic environment could be created on the surface of the silica-sodium material under the conditions. Various indole derivatives and alpha,beta-unsaturated carbonyl compounds including some acid-labile substrates were successfully applied to this system with water as the sole solvent to afford the desired Michael adducts in high yields. [structure: see text].     

Molecular aggregates of partially fluorinated quaternary ammonium salt gemini surfactants

The size and shape of novel partially fluorinated gemini surfactant 1,2-bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromide (CnFC3-2-C3CnF, where n=4, 6, and 8) were investigated in aqueous solution by means of light scattering and transmission electron microscopy (TEM). The sizes of these molecular aggregates changed with increasing carbon number of the alkyl chain and concentration. For example, the apparent hydrodynamic radius by dynamic light scattering was 18 nm at a concentration of cmcx5 for n=4, 115 nm at the cmcx15 for n=6, and 62 nm at the cmcx30 for n=8, at 298.2 K. The shapes of CnFC3-2-C3CnF aggregates drastically changed with the alkyl chain length; the aggregates were mainly in the form of large or irregular small aggregates (n=4), string-like aggregates (n=6), and vesicles (n=8). The bromide-ion activity was measured using a bromide-ion-selective electrode to determine the degree of counterion binding to the aggregates. The degree of counterion binding to aggregate was very small compared with that in the typical hydrogenated gemini surfactants. These results indicated that the small curvature of large aggregates was not influenced by an electrostatic repulsion between the cationic head groups in the case of the bulky molecular volume of fluorinated gemini surfactants.     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

Surface-coil-type resonators for in vivo temporal ESR measurements in different organs of nitroxide-treated rats

Three kinds of surface-coil-type resonators (SCRs) operating at 720 MHz were fabricated for in vivo temporal electron spin resonance (ESR) measurements. The inner diameter of the singleturn coil of the SCRs was 3, 4, or 10 mm. ResonatorQ increases and the detection limit decreases with coil diameter. The distance across which the microwave magnetic field can penetrate in the direction facing to the coil was about the same (about 2 mm) for all SCRs. In vivo kinetic studies of intravenously injected 4-hydroxy-2,2,6,6-tetramethylpiperidin-l-oxyl (TEMPOL) were performed at the liver, kidney, stomach, rectum, vein, and skin of rats with SCRs suited to the target areas. The halflife of TEMPOL was estimated from the exponential decay of the ESR signal intensity (the peak-to-peak height). Different sites in the rat showed apparent differences in the half-life of TEMPOL. This suggests that the apparent differences in the reducing ability of TEMPOL are related to the organ or tissue where measurement is taken because no excretion of TEMPOL was observed.     

Characteristics and function of human hemoglobin vesicles as an oxygen carrier

A liposome‐encapsulated human hemoglobin (Neo Red Cell, (NRC) has been developed and evaluated as an artificial oxygen carrier. The NRC is a liposome‐encapsulated highly concentrated (>45%) stroma‐free human hemoglobin with inositol hexaphosphate (IHP as an allosteric effector), a coenzyme and substrates for reducing methemoglobin (metHb). The NRC's surface was coated with polyethylene glycol to prevent aggregation in plasma and to prolong their retention time in the blood stream. The oxygen binding behavior of the NRC in vitro was investigated and it was found that it effectively transports oxygen in vivo as an oxygen carrier. The oxygen binding behavior and kinetics were studied by the stopped‐flow method and the oxygen binding curve of the NRC was determined. The oxygen binding speed and binding coefficient (K_on) of NRC, washed human red blood cells (WRBC) and stroma‐free human hemoglobin (SFHb) were measured by stopped‐flow method. The oxygen binding speed of SFHb was the highest, while that of RBC was the lowest and that of NRC was intermediate. The oxygen binding of NRC ended within 60 msec when deoxy‐NRC was mixed with oxygen. The K_on of NRC was 2.9 × 10⁵, 10 times faster than that of RBC. The oxygen binding curve and P₅₀O₂ of NRC that contained various IHP concentrations were measured. The oxygen‐binding curve of the NRC sequentially shifted to the right as the IHP content was increased. Exchange transfusion of 70% was carried out for rats with NRC containing various concentrations of IHP and of Hb, and investigated the optimum concentration of NRC in vivo. The lactate value after exchange transfusion was three times higher than before exchange transfusion, when rats were subjected to exchange transfused with NRC that did not contain IHP. But the increase of lactate was suppressed when rats were transfused with NRC that contained IHP. When the Hb concentration of NRC was 5 and 6%, exchange transfused rats recovered to normality just like rats transfused with RBC. Copyright © 2000 John Wiley & Sons, Ltd.     

Synthesis of regiocontrolled poly(4,6-di-n-butoxy-1,3-phenylene) by oxidative coupling polymerization

Poly(4,6-di-n-butoxy-1,3-phenylene) ( 6 ) was prepared by oxidative coupling polymerization of 1,3-di-n-butoxybenzene ( 1 ) or 2,2′,4,4′-tetra-n-butoxy biphenyl (3). Polymerizations were conducted in nitrobenzene in the presence of FeCl₃ at room temperature and produced polymers with number-average molecular weights up to 42,000. The effects of various factors, such as amount of FeCl₃ and reaction temperature and time were studied. The structure of polymer 6 was characterized by 270 MHz ¹H- and 68.5 MHz ¹³C-NMR spectroscopies and was estimated to consist of almost completely 1,3-linkage. The regiocontrolled polymer was readily soluble in common organic solvents. Thermogravimetric analysis of polymer 6 showed 10% weight loss at 390°C in nitrogen. © 1997 John Wiley & Sons, Inc. J Polym Chem 35 : 2259–2266, 1997     

Momentum dependence of pseudogap and superconducting gap in variation theory

To consider the origin of a pseudogap and a superconducting (SC) gap found in the high-T_c cuprates, we evaluated the momentum dependence of the singlet gap corresponding to the pseudogap and the SC gap in the t–J model, using an optimization variational Monte Carlo (VMC) method. In the underdoped regime, the singlet gap is significantly modified from the simple d_x²-y²(d)-wave gap (∝ cos k_x − cos k_y) by the contribution of long-range pairings. Its angular dependence at the quasi Fermi surface is qualitatively consistent with those experimentally observed in both hole and electron-doped cuprates. On the other hand, a SC gap is almost unchanged, preserving the original simple d-wave form. Thus, it seems that the incoherent part of the singlet gap mainly influences the forms of observed gaps.