Lax-Phillips Scattering for Atomorphic Functions Based on the Eisenstein Transform

We construct a Lax-Phillips scattering system on the arithmetic quotient space of the Poincaré upper half-plane by the full modular group, based on the Eisenstein transform. We identify incoming and outgoing subspaces in the ambient space of all functions with finite energy-form for the non-Euclidean wave equation. The use of the Eisenstein transform along with some properties of the Eisenstein series of two variables enables one to work only on the space corresponding to the continuous spectrum of the Laplace-Beltrami operator. It is shown that the scattering matrix is the complex function appearing in the the functional equation of the Eisenstein series of two variables. We obtain a compression operator constructed from the Laplace-Beltrami operator, whose spectrum consists of eigenvalues that coincide, counted with multiplicities, with the non-trivial zeros of the Riemann zeta-function. For this purpose we construct and use a scattering model on the one-dimensional Euclidean space.      

Polysaccharide‐templated twisted assemble of 2‐anilinonaphthalene‐6‐sulfonic acid

Schizophyllan (SPG) is a natural β‐1,3‐glucan that forms a triple helix (t‐SPG) in neutral aqueous solutions and t‐SPG can be denatured to single chains (s‐SPGs) in DMSO or alkaline solutions. Exchanging the denatured solutions for neutral water leads the renaturation of the triple helix. We have reported that hydrophobic molecules can form a complex with s‐SPG when they are present in the renaturation process. Some of these, for example poly(dA) and polyaniline, were found to have aromatic amino moieties. This report demonstrates whether s‐SPG can interact with other aromatic amino compounds such as anilinonaphthalene sulfonic acid (ANS) derivatives. Enhanced fluorescence intensity and red‐shifted UV absorption spectra were observed in the mixture of s‐SPG and 2,6‐ANS or 2,6‐TNS. In the circular dichroism measurement, the positive Cotton effects appeared after mixing 2, 6‐ANS with s‐SPG. When the amino proton was replaced by the methyl group or used in intramolecular hydrogen bonds, any spectral changes were not observed. These results indicate that amino proton in the ANS derivatives plays a key role in the complexation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1440–1448, 2008     

Dielectric relaxation behavior of poly(methyl methacrylate) under high‐pressure carbon dioxide

An in situ dielectric measurement for atactic poly(methyl methacrylate) (at‐PMMA) was performed under high‐pressure CO₂ under various pressures and temperatures. The at‐PMMA has the acetate side group with a large dipole moment. In the glassy state, a local relaxation process (β‐process) can be observed using dielectric measurement. In the rubbery state, the micro‐Brownian motion of main chain (α‐process) occurs, and the β‐process changes into αβ‐process coordinated with the α‐process. The dielectric loss (ε″) spectrum of at‐PMMA in the glassy state is asymmetric because of the density fluctuation for the amorphous structure. The loss peak frequency shifted to higher frequencies, and the relaxation strength increased with increasing CO₂ pressure. In the glassy state, the shape of ε″ spectrum became more symmetric with increasing CO₂ pressure. These show that the molecular mobility enhanced by the plasticization effect of CO₂ allows the dipolar side groups in the high‐density region to contribute to the relaxation process. We also found that the apparent activation energy decreased under high‐pressure CO₂. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2951–2962, 2005     

Evaluation for the configurational and electronic state of SO3 adsorbed on Pt surface

We evaluate the adsorption of SO₃ molecule on the Pt (1 1 1) surface using the first-principles calculations by a slab model with a periodic boundary condition. We find that there are four stable adsorption configurations on the Pt surface, where SO₃ molecules are adsorbed above the three-fold fcc and hcp sites. In two of these configurations, S and two O atoms are bound to the Pt atoms, and in two other of them, all the three O atoms are bound to Pt surface atoms. Besides, it is found that molecular orbitals of SO₃ and those of Pt surface are hybridized in the active metal d-bands region, that the localized molecular orbitals in SO₃ are stabilized, and that the charge is transferred from Pt to S 3p by SO₃ adsorption on Pt surface though the other interaction of S and O (bound to Pt) component with Pt is little. In addition, the bond between S and O bound to Pt become weak by SO₃ adsorption on Pt surface because the charge polarization to O-Pt bond weakens the bond between S and O bound to Pt. This interaction is assumed to encourage the breakage of S-O bond.     

Photoinduced change in the charge order pattern in the quarter-filled organic conductor (EDO-TTF)2PF6 with a strong electron-phonon interaction

The quasistable state in the photoinduced phase transition for the quasi-one-dimensional quarter-filled organic conductor (EDO-TTF)2PF6 has been examined by ultrafast reflective measurements and time-dependent model calculations incorporating both electron-electron and electron-phonon interactions. The transient optical conductivity spectrum over a wide probe photon-energy range revealed that photoexcitation induced a new type of charge-disproportionate state. Additionally, coherent and incoherent oscillations dependent on probe photon energies were found, as predicted by the calculation.     

Observation of a resonancelike structure in the pi +- psi' mass distribution in exclusive B-->Kpi +- psi' decays

A distinct peak is observed in the pi +/- psi' invariant mass distribution near 4.43 GeV in B-->K pi +/- psi' decays. A fit using a Breit-Wigner resonance shape yields a peak mass and width of M=4433+/-4(stat)+/-2(syst) MeV and Gamma=45-13+18(stat)-13+30(syst) MeV. The product branching fraction is determined to be B(B 0-->K -/+Z+/-(4430)) x B(Z+/-(4430)-->pi+/-psi')=(4.1+/-1.0(stat)+/-1.4(syst)) x 10(-5), where Z+/-(4430) is used to denote the observed structure. The statistical significance of the observed peak is 6.5 sigma. These results are obtained from a 605 fb(-1) data sample that contains 657 x 10(6) BB pairs collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e+ e- collider.     

Search for B+-->D*+pi0 decay

We report on a search for the doubly Cabibbo suppressed decay B+-->D*+pi0, based on a data sample of 657x10(6) BB pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We find no significant signal and set an upper limit of B(B+-->D*+pi0)<3.6x10(-6) at the 90% confidence level. This limit can be used to constrain the ratio between suppressed and favored B-->D*pi decay amplitudes, r<0.051, at the 90% confidence level.     

Time-dependent CP-violating asymmetry in B0-->rho0gamma decays

We report the first measurement of CP-violation parameters in B0-->rho0gamma decays based on a data sample of 657x10(6)BB pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain the time-dependent and direct CP-violating parameters, Srho0gamma=-0.83+/-0.65(stat)+/-0.18(syst) and Arho0gamma=-0.44+/-0.49(stat)+/-0.14(syst), respectively.     

Measurement of time-dependent CP-violating parameters in B(0)-->K_(S)(0)K_(S)(0) decays

We report a measurement of the CP-violating parameters in B;{0}-->K_{S}{0}K_{S}{0} decays based on a data sample of 657x10{6} BB[over ] pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e;{+}e{-} collider. In this Letter, one neutral B meson is fully reconstructed in the B;{0}-->K_{S}{0}K_{S}{0} decay mode, and the flavor of the accompanying B meson is identified by its decay products. The CP-violating parameters are measured from the asymmetry in the distributions of the proper-time interval between the two B decays: S_K_{S}{0}K_{S}{0}}=-0.38_{-0.77}{+0.69}(stat)+/-0.09(syst) and A_{K_{S}{0}K_{S}{0}}=-0.38+/-0.38(stat)+/-0.05(syst).