Multiple Eisenstein series and multiple cotangent functions

We construct the multiple Eisenstein series and we show a relation to the multiple cotangent function. We calculate a limit value of the multiple Eisenstein series.     

Determination of the structural features of a long-lived electron-transfer state of 9-mesityl-10-methylacridinium ion

Extensive efforts have been devoted to developing electron donor-acceptor systems that mimic the utilization of solar energy that occurs in photosynthesis. X-ray crystallographic analysis shows how absorbed photon energy is stabilized in those compounds by structural changes upon photoinduced electron transfer (ET). In this study, structural changes of a simple electron donor-acceptor dyad, 9-mesityl-10-methylacridinium cation (Acr(+)-Mes), upon photoinduced ET were directly observed by laser pump and X-ray probe crystallographic analysis. The N-methyl group in Acr(+) was bent, and a weak electrostatic interaction between Mes and a counteranion in the crystal (ClO(4)) was generated by photoinduced ET. These structural changes correspond to reduction and oxidation due to photoinduced ET and directly elucidate the mechanism in Acr(+)-Mes for mimicking photosynthesis efficiently.     

Direct observation of cooperative protein structural dynamics of homodimeric hemoglobin from 100 ps to 10 ms with pump-probe X-ray solution scattering

Proteins serve as molecular machines in performing their biological functions, but the detailed structural transitions are difficult to observe in their native aqueous environments in real time. For example, despite extensive studies, the solution-phase structures of the intermediates along the allosteric pathways for the transitions between the relaxed (R) and tense (T) forms have been elusive. In this work, we employed picosecond X-ray solution scattering and novel structural analysis to track the details of the structural dynamics of wild-type homodimeric hemoglobin (HbI) from the clam Scapharca inaequivalvis and its F97Y mutant over a wide time range from 100 ps to 56.2 ms. From kinetic analysis of the measured time-resolved X-ray solution scattering data, we identified three structurally distinct intermediates (I(1), I(2), and I(3)) and their kinetic pathways common for both the wild type and the mutant. The data revealed that the singly liganded and unliganded forms of each intermediate share the same structure, providing direct evidence that the ligand photolysis of only a single subunit induces the same structural change as the complete photolysis of both subunits does. In addition, by applying novel structural analysis to the scattering data, we elucidated the detailed structural changes in the protein, including changes in the heme-heme distance, the quaternary rotation angle of subunits, and interfacial water gain/loss. The earliest, R-like I(1) intermediate is generated within 100 ps and transforms to the R-like I(2) intermediate with a time constant of 3.2 ± 0.2 ns. Subsequently, the late, T-like I(3) intermediate is formed via subunit rotation, a decrease in the heme-heme distance, and substantial gain of interfacial water and exhibits ligation-dependent formation kinetics with time constants of 730 ± 120 ns for the fully photolyzed form and 5.6 ± 0.8 μs for the partially photolyzed form. For the mutant, the overall kinetics are accelerated, and the formation of the T-like I(3) intermediate involves interfacial water loss (instead of water entry) and lacks the contraction of the heme-heme distance, thus underscoring the dramatic effect of the F97Y mutation. The ability to keep track of the detailed movements of the protein in aqueous solution in real time provides new insights into the protein structural dynamics.     

On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces

In a Hilbert space, we study the finite termination of iterative methods for solving a monotone variational inequality under a weak sharpness assumption. Most results to date require that the sequence generated by the method converges strongly to a solution. In this paper, we show that the proximal point algorithm for solving the variational inequality terminates at a solution in a finite number of iterations if the solution set is weakly sharp. Consequently, we derive finite convergence results for the gradient projection and extragradient methods. Our results show that the assumption of strong convergence of sequences can be removed in the Hilbert space case.     

Electron-transfer through potential gradient based on a dendrimer architecture

A dendritic nano-shell based on rigid phenylazomethine units can rectify electron transfer. By use of this function, the photo-induced charge separation was significantly enhanced due to the facilitated and stabilized radical ion pair.     

Time-evolution of thermal oxidation on high-index silicon surfaces: Real-time photoemission spectroscopic study with synchrotron radiation

The initial oxidation on high-index silicon surfaces with (113) and (120) orientations at 820 K has been investigated by real-time X-ray photoemission spectroscopy (Si 2p and O 1s) using 687 eV photons. The time evolutions of the Siⁿ⁺ (n = 1–4) components in the Si 2p spectrum indicate that the Si^2 + state is suppressed on high-index surfaces compared with Si(001). The O 1s state consists of two components, a low-binding-energy component (LBC) and a high-binding-energy component (HBC). It is suggested that the O atom in strained SiOSi contributes to the LBC component. The reaction rates are slower on high-index surfaces compared with that on Si(001).     

Photoinduced phase transition of coordinationally unsaturated d9 metal centers within the thermal hysteresis of the spin exchange interaction

Diffraction evidence is presented that the structure of one-dimensional arrays of strained, coordinationally unsaturated d9 pseudo-Jahn-Teller centers is affected by excitation of the LMCT bands within the hysteresis region of the low-temperature ferromagnetic-to-antiferromagnetic phase transition.     

Modulation of luminescence intensity of lanthanide complexes by photoinduced electron transfer and its application to a long-lived protease probe

Luminescent lanthanide complexes (Tb(3+), Eu(3+), etc.) have excellent properties for biological applications, including extraordinarily long lifetimes and large Stokes shifts. However, there have been few reports of lanthanide-based functional probes, because of the difficulty in designing suitable complexes with a luminescent on/off switch. Here, we have synthesized a series of complexes which consist of three moieties: a lanthanide chelate, an antenna, and a luminescence off/on switch. The antenna is an aromatic ring which absorbs light and transmits its energy to the metal, and the switch is a benzene derivative with a different HOMO level. If the HOMO level is higher than a certain threshold, the complex emits no luminescence at all, which indicates that the lanthanide luminescence can be modulated by photoinduced electron transfer (PeT) from the switch to the sensitizer. This approach to control lanthanide luminescence makes possible the rational design of functional lanthanide complexes, in which the luminescence property is altered by a biological reaction. To exemplify the utility of our approach to the design of lanthanide complexes with a switch, we have developed a novel protease probe, which undergoes a significant change in luminescence intensity upon enzymatic cleavage of the substrate peptide. This probe, combined with time-resolved measurements, was confirmed in model experiments to be useful for the screening of inhibitors, as well as for clinical diagnosis.     

Mixed La-Li heterobimetallic complexes for tertiary nitroaldol resolution

A kinetic resolution of tertiary nitroaldols derived from simple ketones is described. Mixed BINOL/biphenol La-Li heterobimetallic complexes gave the best selectivity in retro-nitroaldol reactions of racemic tertiary nitroaldols. By using a mixture of La-Li3-(1a)3 complex (LLB 2a) and La-Li3-(1b)3 (LLB* 2b) complex in a ratio of 2/1, chiral tertiary nitroaldols were obtained in 80-97% ee and 30-47% recovery yield.     

A strong convergence theorem for relatively nonexpansive mappings in a Banach space

In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert space and maximal monotone operators in a Banach space.