Approximate controllability for fractional diffusion equations by interior control

We consider the approximate controllability by interior control of a partial differential equation with time derivatives of non-integer order. First, we prove the well-posedness of the inhomogeneous problem for the controlled system. Next, we study the dual system and show a weak type of unique continuation property. Finally, we prove the approximate controllability.     

Bandwidth selection for a data sharpening estimator in nonparametric regression

This paper is concerned with data-based selection of the bandwidth for a data sharpening estimator in nonparametric regression. Two kinds of bandwidths are considered: a bandwidth vector which has a different bandwidth for each covariate, and a scalar bandwidth that is common for all covariates. A plug-in method is developed and its theoretical performance is fully investigated. The proposed plug-in method works efficiently in our simulation study.     

Application of Protonic Acid-Doped Silica Gels to Electric Double-Layer Capacitors

Silica gels doped with several protonic acids such as HClO₄, H₂SO₄ and H₃PO₄ have been prepared by the sol-gel method and totally solid electric double-layer capacitors have been successfully fabricated using the highly proton-conductive silica gels as an electrolyte and activated carbon powder (ACP) hybridized with the silica gels as a polarizable electrode. It was found that the addition of HClO₄, which had the highest value of acid dissociation constant among these three acids, most effectively increased the proton conductivity of the resultant acid-doped silica gels. Tablets of the HClO₄-doped silica gels exhibited conductivities as high as 10^–5–10^–2 S cm^–1 at room temperature in dry N₂ atmosphere. One of the capacitors fabricated using the protonic acid-doped silica gels had a capacitance of 44 F/(gram of total ACP in the capacitor), which was comparable to those of conventional capacitors using liquid electrolytes.     

High oxygen-reduction activity of silk-derived activated carbon

Activated carbon prepared from silk fibroin, which is free of metal elements, showed a high catalytic activity for the oxygen-reduction reaction (ORR). The activated carbon had a very high onset potential of E_onset = 0.83 V (vs. RHE) in oxygen-saturated 0.5 M H₂SO₄ at 60 °C. The ORR on the activated carbon proceeded by a four-electron process in the high-electrode-potential region; this gradually decreased to a 3.5-electron reaction below about 0.6 V (vs. RHE). Only about 1% of nitrogen atoms (mostly quaternary) remained in the activated carbon by heat-treatment at up to 1200 °C are responsible for the high catalytic activity. The open circuit voltage of a polymer electrolyte fuel cell using the activated carbon as the cathode and a platinum/carbon black anode under pure oxygen and hydrogen gases, respectively, both at one atmosphere, was 0.96 V at 27 °C.     

Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.     

Synthesis of 3‐Acyl‐4‐alkenylpyrrolidines by Platinum‐Catalyzed Hydrative Cyclization of Allenynes

A series of nitrogen‐tethered allenynes (‘5‐aza‐1,2‐dien‐7‐ynes’) 1 were transformed to the corresponding 3‐acyl‐4‐alkenylpyrrolidines 3 when treated with a catalytic amount of PtCl₂ in MeOH at 70°. Initial Pt‐promoted cyclization forms a nonclassical carbocationic intermediate. In contrast to the cycloisomerization in toluene, which produced the bicyclic cyclobutenes 2 , the intermediate is intercepted by addition of an oxygen nucleophile to achieve the formal hydrative cyclization.     

Self-assembly of photochromic diarylethenes with amphiphilic side chains: reversible thermal and photochemical control

Diarylethene derivatives with hexaethylene glycol side chains were synthesized and their self-assembling and photochromic reactivity were investigated. The diarylethenes showed photochromism in organic solvents and even in water. The aqueous solution of the compounds turned turbid quickly upon heating. The clouding behavior was investigated using 1H NMR spectroscopy, dynamic light scattering, and absorption spectroscopy. It was revealed that, in the aqueous solution, the compounds self-assembled into aggregates, and the aggregates were loosened by raising the temperature. The cloud-point temperature of the closed-ring isomer was 5-7 degrees C lower than that of the open-ring isomer. When asymmetric methyl groups were introduced in the amphiphilic side chains, induced circular dichroism (ICD) was observed upon irradiation with UV light in water. This ICD was explained by the difference in the self-assembling behavior between the open- and the closed-ring isomers. It was suggested that the closed-ring isomers assembled into a chiral nanostructure.     

A variety of spin-crossover behaviors depending on the counter anion: two-dimensional complexes constructed by NH...Cl- hydrogen bonds, [FeIIH3LMe]Cl.X (X = PF6 -, AsF6 -, SbF6 -, CF3SO3 -; H3L(Me) = Tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine)

A family of spin-crossover (SC) complexes, [Fe(II)H(3)L(Me)]Cl.X (X(-) = PF(6) (-), AsF(6) (-), SbF(6) (-), CF(3)SO(3) (-)), 1-4, has been synthesized, in which H(3)L(Me) denotes the hexadentate N(6) tripod-like ligand tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine, containing three imidazole groups, with a view to establishing the effect of the counter anion on the SC behavior. These complexes have been found to crystallize in the same monoclinic crystal system with similar cell dimensions. The general crystal structure consists of a two-dimensional (2D) extended network constructed by NH...Cl- hydrogen bonds between Cl- and the imidazole NH groups of three neighboring [Fe(II)H(3)L(Me)]2+ ions, while the anion X exists as an isolated counter anion and occupies the space between the 2D sheets. Magnetic susceptibilities and M?ssbauer spectra have revealed a variety of SC behaviors depending on the counter anion, including a one-step HS<==>(HS + LS)/2 (1, X = PF(6) (-)), a two-step HS<==>(HS + LS)/2<==>LS with a slow thermal relaxation (2, X = AsF(6) (-)), a gradual one-step HS<==>LS (3, X = SbF(6) (-)), and a steep one-step HS<==>LS with hysteresis (4, X = CF(3)SO(3) (-)). The complexes assume the space group P2(1)/n in the HS state, P2(1) in the HS + LS state, and P2(1)/n in the LS state. The Fe-N bond lengths and the N-Fe-N bond angles are indicative of the HS, HS + LS, and LS states. The molecular volumes, V, of the counter anions have been evaluated by quantum-chemical calculations as follows: 53.4 A(3) (BF(4) (-)), 54.4 A(3) (ClO(4) (-)), 73.0 A(3) (PF(6) (-)), 78.5 A(3) (AsF(6) (-)), 88.7 A(3) (SbF(6) (-)), and 86.9 A(3) (CF(3)SO(3) (-)). The size and shape of the counter anion affects the flexible 2D network structure constructed by the hydrogen bonds, leading to modifications of the SC behavior. These estimated relative sizes of the counter anions correlate well with the observed SC behaviors.     

Anti-babesial compounds from Curcuma xanthorrhiza

Anti-babesial ingredients, (12R)- and (12S)-12,13-dihydro-12,13-dihydroxyxanthorrhizols, were isolated from Curcuma xanthorrhiza. The structures were established by the extensive NMR techniques. The assignments of (1)H NMR data of (12R)-12,13-dihydro-12,13-dihydroxyxanthorrhizol was revised, and (12S)-12,13-dihydro-12,13-dihydroxyxanthorrhizol was isolated as a pure form for the first time. The IC(50) of the active compounds were compared with that of commercial drug, diminazene aceturate (Ganaseg). IC(50) values of Ganaseg, (12R)-, and (12S)-12,13-dihydro-12,13-dihydroxyxanthorrhizols were 0.6 microg mL(-1), 8.3 microg mL(-1) and 11.6 microg mL(-1), respectively.