Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians

We investigate the long-time behavior of viscosity solutions of Hamilton–Jacobi equations in \mathbbRⁿ{\mathbb{R}^n} with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.     

Synthesis and anti-tumor activity of a fluorinated analog of medroxyprogesterone acetate (MPA), 9alpha-fluoromedroxyprogesterone acetate (FMPA)

We synthesized 9alpha-fluoromedroxyprogesterone acetate (FMPA) in order to test whether it is a more potent anti-angiogenic agent than medroxyprogesterone acetate (MPA), which has been widely used as a therapeutic agent for breast and endometrium cancers. FMPA was previously synthesized in 10 steps (total yield: 1%). An efficient synthesis of FMPA has been achieved in 6 steps (total yield: 12%). We examined the anti-tumor effect of FMPA, complexed with dimethyl-beta-cyclodextrin (DM-beta-CyD), on rat mammary carcinomas induced by 7,12-dimethylbenz[a]anthracene (DMBA). FMPA showed great anti-tumor effect on DMBA-induced rat mammary carcinomas.     

Differences between the internal energy depositions induced by collisional activation and by electron transfer of W(CO)6(2+) ions on collision with Ar and K targets

Doubly charged tungsten hexacarbonyl W(CO)(6) (2+) ions were made to collide with Ar and K targets to give singly and doubly charged positive ions by collision-induced dissociation (CID). The resulting ions were analyzed and detected by using a spherical electrostatic analyzer. Whereas the doubly charged fragment ions resulting from collisional activation (CA) were dominant with the Ar target, singly charged fragment ions resulting from electron transfer were dominant with the K target. The internal energy deposition in collisionally activated dissociation (CAD) evaluated with the Ar target was broad and decreased with increasing internal energy. The predominant peaks observed with the K target were associated with singly charged W(CO)(2) (+) and W(CO)(3) (+) ions: these ions were not the result of CA, but arose from dissociation induced by electron transfer (DIET). The internal energy deposition resulting from the electron transfer was very narrow and centered at a particular energy, 7.8 eV below the energy level of the W(CO)(6) (2+) ion. This narrow internal energy distribution was explained in terms of electron transfer by Landau-Zener potential crossing at a separation of 5.9 x 10(-8) cm between a W(CO)(6) (2+) ion and a K atom, and the coulombic repulsion between singly charged ions in the exit channel. A large cross section of 1.1 x 10(-14) cm(2) was estimated for electron capture of the doubly charged W(CO)(6) (2+) ion from the alkali metal target, whose ionization energy is very low. The term "collision-induced dissociation," taken literally, includes all dissociation processes induced by collision, and therefore encompasses both CAD and DIET processes in the present work. Although the terms CID and CAD have been defined similarly, we would like to propose that they should not be used interchangeably, on the basis that there are differences in the observed ions and in their intensities with Ar and K targets.     

Quantum optimal control for the full ensemble of randomly oriented molecules having different field-free Hamiltonians

We have presented the optimal control theory formulation to calculate optimal fields that can control the full ensemble of randomly oriented molecules having different field-free Hamiltonians. The theory is applied to the fifty-fifty mixture of randomly oriented (133)CsI and (135)CsI isotopomers and an optimal field is sought to achieve isotope-selective vibrational excitations with high efficiency. Rotational motion is frozen and two total times (T's) of electric field duration, 460,000 and 920,000 a.u. (11.1 and 22.2 ps), are chosen in the present calculation. As a result, the final yields for T = 460,000 and 920,000 a.u. are calculated to be 0.706 and 0.815, respectively. The relatively high final yield obtained for T = 920,000 a.u. strongly suggests that a single laser pulse can control the full ensemble of randomly oriented non-identical molecules. The result is quite encouraging in terms of the application to isotope-separation processes.     

Synthesis of a perpendicular TiO2 nanosheet film with the superhydrophilic property without UV irradiation

A method was developed for preparing perpendicular TiO2 nanosheet films from titanate nanosheet films produced on a titanium metal sheet by hydrothermal treatment with aqueous urea. The method is based on the consideration of some important points relating to the thermodynamics of nucleation and crystal growth. The resulting anatase TiO2 nanosheet films showed a specific superhydrophilicity without the need for any prior UV irradiation.     

Water‐Mediated Recognition of Simple Alkyl Chains by Heart‐Type Fatty‐Acid‐Binding Protein

Long‐chain fatty acids (FAs) with low water solubility require fatty‐acid‐binding proteins (FABPs) to transport them from cytoplasm to the mitochondria for energy production. However, the precise mechanism by which these proteins recognize the various lengths of simple alkyl chains of FAs with similar high affinity remains unknown. To address this question, we employed a newly developed calorimetric method for comprehensively evaluating the affinity of FAs, sub‐Angstrom X‐ray crystallography to accurately determine their 3D structure, and energy calculations of the coexisting water molecules using the computer program WaterMap. Our results clearly showed that the heart‐type FABP (FABP3) preferentially incorporates a U‐shaped FA of C10–C18 using a lipid‐compatible water cluster, and excludes longer FAs using a chain‐length‐limiting water cluster. These mechanisms could help us gain a general understanding of how proteins recognize diverse lipids with different chain lengths.     

High rate performances of hydrogen titanate nanowires electrodes

In this study, H₂Ti₃O₇ nanowires were successfully synthesized via a hydrothermal process and post-treatments. The diameter of the nanowires is found to be about 30 nm and the length up to several micrometers. A lithium battery using H₂Ti₃O₇ nanowires as the active material of the positive electrode exhibits a discharge capacity of 100 mA hg⁻¹ and still keeps stable after 200 cycles at a current density as high as 40 Ag⁻¹, demonstrating excellent high rate performance.     

Stereochemistry of lappaol A and F

The absolute configuration of lappaol A and F was determined by the correlation of the ozonolysis products with 2R,3R-(?)-dicarbomethoxymethyl-γ-butyrolactone and S-(?)-methyl paraconate.