Unitary representations of the quantum group SU q (1, 1): II — Matrix elements of unitary representations and the basic hypergoemetric functions

Some series of unitary representations of the quantum group SU _q (1, 1) are introduced. Their matrix elements are expressed in terms of the basic hypergeometric functions. Operator realization of the coordinate elements of SU _q (1, 1) and aq-analogue of some classical identities are discussed.     

Uniform plasmonic near-field nanopatterning by backward irradiation of femtosecond laser

We present localized optical field distribution properties in the vicinity of gold particles on a silicon substrate by backward and forward irradiation. It is technically difficult to fabricate nanostructures on the surface by a conventional forward laser incident to the substrate because gold nanoparticles easily aggregate to form double-layered particle arrays. We calculated enhanced optical field properties in order to pattern the substrate surface only with a template of the bottom-layered particle arrays in the case that the backward irradiation of a femtosecond laser is used in the system of aggregated double-layered gold nanoparticle arrays. With the backward irradiation, the optical field intensity in the substrate for the double-layered hexagonal arrays is found to be only 30% lower than the mono-layered system. Moreover, a near field cannot be generated with the forward irradiation. As a result, only the backward irradiation scheme is found to be effective for uniform surface nanopatterning at enhanced plasmonic near-field zones.     

High-power diode-pumped mode-locked Yb:YAG ceramic laser

A high-power diode-pumped passively mode-locked Yb:YAG ceramic laser was demonstrated. An average output power of 3.80W with a pulse duration of 433 fs at a repetition rate of 90.9MHz was obtained at a wavelength of 1050 nm using a 2% output coupler. A peak power of 96.5kW was also obtained. To the best of our knowledge, these are the highest reported average power and peak power for a diode-pumped mode-locked Yb:YAG ceramic laser.     

A potential of fuzzy relations with a linear structure: The contractive case

In this paper we develop a potential theory of fuzzy relations on the positive orthant in a Euclidean space. By introducing a linear structure for fuzzy relations, the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness. In the one-dimensional unimodal case, a potential is given explicity. Also, a numerical example is shown to illustrate our approaches.     

Convergent total synthesis of (−)-dactylolide

A convergent total synthesis of (?)-dactylolide is described. Constructing the 2,6-disubstituted exo-methylene THP moiety was achieved by the intramolecular allylation of α-acetoxy ether. The cyclization precursor was prepared from two segments, an alcohol and carboxylic acid derivatives, by esterification followed by reductive acetylation.     

Change in a protein's electronic structure induced by an explicit solvent: an ab initio fragment molecular orbital study of ubiquitin

The effect of solvation on the electronic structure of the ubiquitin protein was analyzed using the ab initio fragment molecular orbital (FMO) method. FMO calculations were performed for the protein in vacuo, and the protein was immersed in an explicit solvent shell as thick as 12 A at the HF or MP2 level by using the 6-31G* basis set. The protein's physical properties examined were the net charge, the dipole moment, the internal energy, and the solvent interaction energy. Comparison of the computational results revealed the following changes in the protein upon solvation. First, the positively charged amino acid residues on the protein surface drew electrons from the solvent, while the negatively charged ones transfer electrons to the solvent. Second, the dipole moment of the protein was enhanced as a result of the polarization. Third, the internal energy of the protein was destabilized, but the destabilization was more than compensated for by the generation of a favorable protein-solvent interaction. Finally, the energetic changes were elicited both by the electron correlation effect of the first solvent shell and by the electrostatic effect of more distant solvent molecules. These findings were consistent with the picture of the solvated protein being a polarizable molecule dissolved in a dielectric media.     

Electron‐Catalyzed Cross‐Coupling of Arylboron Compounds with Aryl Iodides

Arylboroxines in combination with zinc chloride and potassium tert‐butoxide were found to undergo the electron‐catalyzed cross‐coupling with aryl iodides to give the corresponding biaryls without the aid of transition‐metal catalysis.