Inverse Problems,Trace Formulae for Discrete Schrödinger Operators

We study discrete Schrödinger operators with compactly supported potentials on Z ^d . Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely reconstructed from the S-matrix of all energies. We also study the spectral shift function \({\xi(\lambda)}\) for the trace class potentials, and estimate the discrete spectrum in terms of the moments of \({\xi(\lambda)}\) and the potential.     

Synthesis and properties of trans-3',4'-bridged nucleic acids having typical S-type sugar conformation

The synthesis of nucleoside analogues with a conformationally restricted sugar moiety is of great interest. The present research describes the synthesis of BNA (bridged nucleic acid) monomers 1 and 2 bearing a 4,7-dioxabicyclo[4.3.0]nonane skeleton and a methoxy group at the C2' position. Conformational analysis showed that the sugar moiety of these monomers is restricted in a typical S-type conformation. It was difficult to synthesize the phosphoramidite derivative of the ribo-type monomer 1, while the phosphoramidite of the arabino-type monomer 2 was successfully prepared and incorporated into oligodeoxynucleotides (ODNs). The hybridization ability of the obtained ODN derivatives containing 2 with complementary strands was evaluated by melting temperature (T(m)) measurements. As a result, the ODN derivatives hybridized with DNA and RNA complements in a sequence-selective manner, though the stability of the duplexes was lower than that of the corresponding natural DNA/DNA or DNA/RNA duplex.     

Stratigraphy of the Middle-Upper Permian and Lowermost Triassic at Chaotian,Sichuan, China: Record of Late Permian double mass extinction event

Precise stratigraphic analysis of Middle-Upper Permian and Lower Triassic sequence at Chaotian in northern Sichuan, China, identified two remarkable mass extinction horizons, one at the Middle-Upper Permian (Guadalupian-Lopingian; G-L) boundary and the other at the Upper Permian-Lower Triassic (P-T) boundary. Across each of the boundaries, biodiversity declined sharply in fusulinid, rugose coral, brachiopod, ammonite, conodont, and radiolaria. Both boundaries are characterized by two biohorizons, i.e., one marked by major extinction of pre-existing fauna and the other by the first appearance of younger fauna. It is noteworthy that a peculiar rhyo-dacitic tuff bed occurs at each of the extinction horizons. Thus the Late Permian biosphere was strongly affected twice by highly explosive, severe volcanism. Regional correlation of the G-L and P-T boundary tuff beds throughout South China, and partly to Japan, positively suggests a cause-effect link between large-scale explosive volcanism and mass extinction.     

Inverse Problems for Time-Dependent Singular Heat Conductivities: Multi-Dimensional Case

We consider an inverse boundary value problem for the heat equation ? _t u = div (γ? _x u) in (0, T) × Ω, u = f on (0, T) × ?Ω, u| _t=0 = u ₀, in a bounded domain Ω ? ? ⁿ , n ≥ 2, where the heat conductivity γ(t, x) is piecewise constant and the surface of discontinuity depends on time: γ(t, x) = k ² (x ∈ D(t)), γ(t, x) = 1 (x ∈ Ω?D(t)). Fix a direction e* ∈ 𝕊 ^n?1 arbitrarily. Assuming that ?D(t) is strictly convex for 0 ≤ t ≤ T, we show that k and sup {e*·x; x ∈ D(t)} (0 ≤ t ≤ T), in particular D(t) itself, are determined from the Dirichlet-to-Neumann map : f → ?_ν u(t, x)|_{(0, T)×?Ω}. The knowledge of the initial data u ₀ is not used in the proof. If we know min_0≤t≤T (sup _x∈D(t) x·e*), we have the same conclusion from the local Dirichlet-to-Neumann map. Numerical examples of stationary and moving circles inside the unit disk are shown. The results have applications to nondestructive testing. Consider a physical body consisting of homogeneous material with constant heat conductivity except for a moving inclusion with different conductivity. Then the location and shape of the inclusion can be monitored from temperature and heat flux measurements performed at the boundary of the body. Such a situation appears for example in blast furnaces used in ironmaking.     

Photoreaction of Ketoprofen with Tryptophan and Tyrosine in Phosphate Buffer Solution

Reaction of excited ketoprofen (KP) with tryptophan (Trp) and tyrosine (Tyr) in a phosphate buffer solution was studied by the transient absorption spectroscopy. Both amino acids, which would interact with KP in bovine serum albumin [Monti, S. [2009] Phys. Chem. Chem. Phys., 11, 9104–9113], accelerated the proton transfer reaction to yield 3‐ethylbenzophenone ketyl biradical (EBPH) from KP carbanion, which was produced by photoexcitation of KP^? through decarboxylation. By means of the actinometry method with benzophenone, the reaction quantum yield was successfully estimated to be fairly large, and Trp, Tyr, DOPA and 4‐methylphenol were found to be a good proton donor for the carbanion. The formation rate constants of EBPH by the amino acids (k_r) were also determined to be (2.7 ± 0.1) × 10⁹ M^?1s^?1 for Trp and (7.8 ± 0.4) × 10⁸ M^?1s^?1 for Tyr, which were larger than those by basic amino acids and dipeptides reported. The reason for the highly efficient proton transfer reaction with Trp and Tyr would be explained by difference of the activation energy for the reaction. These results suggest that the proton transfer should be a key process for an initial photoreaction of KP with a protein, causing photosensitization in vivo.     

Selective Alkene Hydrogenation with Atomic Hydrogen Permeating Through a Pd Sheet Electrode

Chemoselective hydrogenation of olefinic double bonds without concomitant hydrogenolysis of allylic and benzylic C-O linkages was performed successfully by the aid of active hydrogen permeated through a Pd sheet electrode.     

Spectroscopic detection of the most stable carbonic acid, cis-cis H2CO3

Carbonic acid had not been detected by any spectroscopic means for a long period. Recently, we have reported the detection of its second most stable conformer, cis-trans H(2)CO(3), as the first spectroscopic detection of the isolated carbonic acid molecule. In the present work, the most stable conformer of carbonic acid, cis-cis H(2)CO(3), in the gas phase has been successfully produced in a supersonic jet using a pulsed discharge nozzle, and pure rotational transitions of this molecule have been observed by a Fourier-transform microwave spectrometer. In addition to cis-cis H(2)CO(3), its deuterated isotopologue, cis-cis D2CO3, has been observed, yielding the r(0) structure of the cis-cis conformer. Furthermore, hyperfine constants of the deuterated cis-trans conformers were also determined. The two structures for the stable isolated carbonic acid molecule, those of the cis-cis and cis-trans conformers, are considered to provide basic information for the understanding of chemical reactions involving carbonic acid The present result is accurate enough to be used in radio astronomical observations, where the ortho∕para ratio of cis-cis H(2)CO(3) may be used as an important probe of interstellar chemistry.