Rademacher’s reciprocity law for Dedekind sums in function fields

We consider a Dedekind sum \(s(a,c)\) in function fields, defined via the Carlitz module, similar to the classical Dedekind sum \(D(a,c)\) . In this paper, we prove an analog of Pommersheim’s three-term reciprocity law for \(s(a,c)\) .     

Rationality of Dedekind sums in function fields

In the previous paper we introduced the higher dimensional Dedekind sum in a function field (Bayad and Hamahata, Acta Arith. 152:71–80, 2012). The purpose of this paper is to present a criterion for the rationality of our Dedekind sum. To do so, we establish a connection between the field of definition of the Drinfeld module ? and the field of definition of the higher dimensional Dedekind sum s _Λ (a ₀;a ₁,…,a _d ) associated to the A-lattice Λ, which corresponds to ?.     

Supramolecular Adhesives to Hard Surfaces: Adhesion Between Host Hydrogels and Guest Glass Substrates Through Molecular Recognition

Supramolecular materials based on host–guest interactions should exhibit high selectivity and external stimuli‐responsiveness. Among various stimuli, redox and photo stimuli are useful for its wide application. An external stimuli‐responsive adhesive system between CD host‐gels (CD gels) and guest molecules modified glass substrates (guest Sub) is focused. Here, the selective adhesion between host gels and guest substrates where adhesion depends on molecular complementarity is reported. Initially, it is thought that adhesion of a gel material onto a hard material might be difficult unless many guest molecules modified linear polymers immobilize on the surface of hard materials. However, reversible adhesion of the CD gels is observed by dissociating and re‐forming inclusion complex in response to redox and photo stimuli.

     

Broadband dispersion compensation of conventional single mode fibers using microstructure optical fibers

This paper presents a microstructure optical fiber for dispersion compensation in a wide range of wavelengths. The finite-element method with perfectly matched absorbing layers boundary condition is used to investigate the guiding properties. The designed novel dispersion compensating fiber shows that it is possible to obtain a larger negative dispersion coefficient of about −130 to −360 ps/(nm km), better dispersion slope compensation, better compensation ratio, and lower confinement losses less than 10⁻² dB/km in the entire telecommunication (1400–1600 nm) band by using a modest number of design parameters and very simple cladding design.     

Light source design using Kagome-lattice hollow core photonic crystal fibers

Supercontinuum (SC) light source is designed using high pressure Xe-filled hollow core Kagome-lattice photonic crystal fiber. Using finite element method with perfectly matched layer, SC spectra in normal chromatic dispersion region have been generated using picosecond optical pulses from relatively less expensive laser sources.     

On the Phase Transition Behaviour of Binary Systems: Various Non-Nematic Solutes in Nematic Solvent (EBBA)

Phase transition behaviour of the systems of EBBA with methyl alcohol (MeOH), 1.2-dibromo-ethylene (DBE), o-xylene, m-xylene, and p-xylene has been studied. The phase diagrams for each system have been determined by the polarizing microscope. The slopes, β_n and B_i, of the nematic and the isotropic phase boundary lines in each system have been qualitatively described by the molecular field treatment proposed by Humphries. The order parameters for both cis-and trans-DBE in EBBA have been obtained from analyses of ¹H-NMR spectra. In the nematic phase, they decrease with increase in temperature. In the nematic/isotropic coexisting phase (N/I phase), the order parameter for CIS-DBE is almost independent of temperature. The proton spin-lattice relaxation times (T₁) in the MeOH/EBBA system have been measured by a pulse NM R technique. Little temperature dependence of T¹ has been found in the N/1 phase region.c     

π 0 and η Photoproduction on the Deuteron at ELPH, Tohoku University

Baryon spectroscopy is important to understand Quantum Chromodynamics at low energies. In this purpose, a series of π ⁰ and η photoproduction experiments was carried out with an electro-magnetic calorimeter FOREST at Research Center for Electron Photon Science, Tohoku University. The incident tagged bremsstrahlung photon energy ranges from 550 to 1,150 MeV. The differential and total cross sections obtained for π ⁰ and η photoproduction processes on the proton are consistent with the SAID and MAID calculations. The analysis of π ⁰ and η photoproduction on the neutron is underway.     

A Cyclic Hexanuclear Heterometalladithiolene Cluster [{(Cp*Rh)2Mo(μ‐CO)2(CO)}2(S2C6H2S2)2] with Two π‐Conjugated S2C6S2 Bridges: Synthesis,Crystal Structure,and Properties

Two dragons playing ball : Direct metal–metal bond formation using a π‐conjugated dinuclear metalladithiolene complex with two electron‐deficient metal centers as building blocks led to a cyclic double trinuclear heterometalladithiolene cluster with two parallel plane bridges (see structure; Rh pink, Mo green, S yellow, C gray, O red).

     

G protein subtype specificity of rhodopsin intermediates metarhodopsin Ib and metarhodopsin II

Rhodopsin is one of the members of the G protein-coupled receptor family that can catalyze a GDP–GTP exchange reaction on the retinal G protein transducin (Gt) upon photon absorption. There are at least two intermediate states, meta-Ib and meta-II, which exhibit direct interaction with Gt. Meta-Ib binds to GDP-bound Gt, while meta-II forms a complex with Gt having no nucleotide, suggesting that meta-Ib is a state that initially interacts with Gt. Here we investigated whether or not meta-Ib exhibits specific interaction with G protein similar to meta-II, by examining the binding efficiencies of meta-Ib and meta-II to Giα and its mutants whose C-terminal 11 amino acids were replaced with those of Goα, Gqα and Gsα. The affinity of meta-Ib to the C-terminal 11 amino acids of Gtα was similar to those of Giα and its mutant with Goα's C-terminal 11 amino acids, whereas meta-II exhibited affinity to the C-terminal 11 amino acids of Giα mutant with Goα's C-terminal 11 amino acids about half of what was seen for Gtα and Giα. Both intermediates exhibited no affinity to the Giα mutants containing the C-terminal 11 amino acids of Gqα and Gsα. These results suggested that meta-Ib is the state that exhibits specific interaction with G protein as meta-II does, although meta-Ib exhibits a slightly lenient binding selectivity compared to that of meta-II.