Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

X-ray-induced persistent photoconductivity in La0.9A0.1MnO3 (A=Sr, Ca)

We observed persistent photoconductivity (PPC) in La-based perovskite manganese oxides, La_0.9Sr_0.1MnO₃ (LSMO) and La_0.9Ca_0.1MnO₃ (LCMO), under X-ray irradiation. The PPC in LSMO was attributed to the collapse of the charge- and orbital-ordered (CO and OO, respectively) states, similar to that reported in previous papers. This PPC effect was different from that observed in a similar compound with a slightly different composition. This difference was explained in terms of doped carriers. This observation of PPC in LCMO is the first result of the PPC in a compound in which the ground state is not the CO phase; it was attributed to the collapse of the OO ground state. We proposed that OO ground state is a prerequisite for the occurrence of PPC in these compounds.     

Acylglycerols (=Glycerides) from the Glandular Trichome Exudate on the Leaves of Paulownia tomentosa

Chemical investigations of the glandular trichome exudates on the leaves of Paulownia tomentosa (Scrophulariaceae) led to the identification of the thirty acylglycerols (=glycerides) 1 – 30 , including five known ones ( 2, 3, 6, 9 , and 15 ) (Fig. 1). Spectroscopic analysis combined with GC/MS studies of the glycerides and the liberated fatty acids, in the form of trimethylsilyl ether derivatives and trimethylsilylated methyl esters, respectively, established that the constituents belonged to 1,3‐di‐O‐acetyl‐2‐O‐(fatty acyl)glycerols, 1‐O‐acetyl‐2‐O‐(fatty acyl)‐sn‐glycerols, and 2‐O‐(fatty acyl)glycerols, wherein the fatty acyl moiety was either an eicosanoyl or an octadecanoyl group bearing OH and/or AcO groups at the 3‐, 3,6‐, 3,7‐, 3,8‐, or 3,9‐positions. The 1‐O‐acetyl‐2‐O‐[(3R,6S)‐3‐(acetyloxy)‐6‐hydroxyeicosanoyl]‐sn‐glycerol ( 12 ; 20% of the total glycerides), 2‐O‐[(3R,8R)‐3,8‐bis(acetyloxy)eicosanoyl]glycerol ( 17 ; 14%), 2‐O‐[(3R,9R)‐3,9‐bis(acetyloxy)eicosanoyl]glycerol ( 18 ; 12%), and 2‐O‐[(3R)‐3‐(acetyloxy)eicosanoyl]glycerol ( 10 ; 12%) were relatively abundant constituents. The configurations of the stereogenic centers of the fatty acyl moieties were determined by ¹H‐NMR analysis of the monoesters obtained from (R)‐ and (S)‐2‐(naphthalen‐2‐yl)‐2‐methoxyacetic acid ((R)‐ and (S)‐2NMA? OH and the hydroxy‐substituted fatty acid methyl esters (Fig. 2). The configuration at C(2) of the glycerol moiety of the 1‐O‐acetyl‐2‐O‐(fatty acyl)glycerols was determined to be (2S) by chemical conversion of, e.g., G‐2 (= 2 / 3 1 : 10) to (+)‐3‐O‐[tert‐butyl)diphenylsilyl]‐sn glycerol of known absolute configuration.     

Stereochemistry of pteriatoxins A, B, and C

The C34 and C2' stereochemistry of pteriatoxins A-C has been established. The availability of all the stereoisomers via total synthesis has played an indispensable role.     

Structures of 1-(arylseleninyl)naphthalenes: O, G, and Y dependences in 8-G-1-[p-YC6H4Se(O)]C10H6

Structures of 8-G-1-[p-YC6H4Se(O)]C10H6 [1 (G = H), 2 (G = F), 3 (G = Cl), and 4 (G = Br): Y = H, OMe, OCH2Ph, t-Bu, Me, Cl, and NO2] and (1-C10H7)2SeO (5) are investigated by the X-ray crystallographic analysis. Structures of 1 are all A with regard to the naphthyl group (1 (A)), where the Se-C(Ar) and Se-O bonds are perpendicular to and parallel to the naphthyl plane, respectively. Those of 2-4 are also A. Since structures of 8-G-1-(p-YC6H4Se)C10H6 [7 (G = F), 8 (G = Cl), and 9 (G = Br)] are all B, the results exhibit that B of 7-9 change dramatically to A of 2-4 with the introduction of O atoms. The factor to determine the A structures of 1-4 by O is called O dependence. The origin of the O dependence is the nonbonded np(O)- - -pi(Nap) interaction, which results in CT from np(O) to pi(Nap) since O in 1-4 is highly electron rich due to the polar Se+=O- bond and pi(Nap) acts as an acceptor. There are two types of np(O)'s, npy(O) and npz(O), if the directions of the Se-O bond and the p-orbitals of pi(Nap) are taken in the x- and z-axes, respectively. Double but independent np(O)- - -pi(Nap) interactions in 5 lead to 5 (AA). The conformation of the p-YC6H4Se group in 1 changes depending on Y (Y dependence), although the effect is not strong. The Y dependence is explained on the basis of the magnitude of CT of the np(O)-->pi(Ar) type in 1, in addition to the np(O)- - -pi(Nap) interaction. The structure around the Se=O group in 1 is close to that of 5 (AA), if the accepting ability of the p-YC6H4Se group is similar to that of the naphthyl group. A of 2-4 are further stabilized by the np(G)- - -sigma(Se-O) 3c-4e interactions, which are called G dependence. QC calculations performed on the methyl analogues of 1-4 (11-14, respectively) reproduced the observed structures, supported the above discussion, and revealed the energy profiles. The energy-lowering effect of the O dependence would be close to the G dependence of the nonbonded n(Br)- - -sigma(Se-O) 3c-4e interaction in 14 if the steric repulsion between Br and Se is contained in the G dependence. The value is roughly predicted as 20 kJ mol(-1). The structures of 1-5 are well explained by O, G, and Y dependences.     

Characterization of pressure dynamics in an axisymmetric separating/reattaching flow using fast-responding pressure-sensitive paint

This collaborative work discusses the results of time-resolved pressure-sensitive paint measurements performed on a model of a generic spacecraft under sub- and transonic test conditions. It is shown that optical pressure measurements using an active layer from platinum?Cporphyrin complexes (PtTFPP) in combination with a polymer-ceramic base layer are able to measure dynamic flow phenomena in the trisonic wind tunnel facility up to sampling rates of 2?kHz. Low amplitude fluctuations in the order of 0.1?kPa were determined by means of this measurement technique. The buffet dynamics, as well as the spatial extent of the recirculation area in the near-wake, compare well with numerical predictions and PIV measurements. Furthermore, characteristic coherent pressure modes on the base were resolved, which were predicted by large-eddy simulations.     

Quasi-superradiant soliton state of matter in quantum metamaterials

Strong interaction of a system of quantum emitters (e.g., two-level atoms) with electromagnetic field induces specific correlations in the system accompanied by a drastic increase of emitted radiation (superradiation or superfluorescence). Despite the fact that since its prediction this phenomenon was subject to a vigorous experimental and theoretical research, there remain open question, in particular, concerning the possibility of a first order phase transition to the superradiant state from the vacuum state. In systems of natural and charge-based artificial atom this transition is prohibited by “no-go” theorems. Here we demonstrate numerically and confirm analytically a similar transition in a one-dimensional quantum metamaterial – a chain of artificial atoms (qubits) strongly interacting with classical electromagnetic fields in a transmission line. The system switches from vacuum state to the quasi-superradiant (QS) phase with one or several magnetic solitons and finite average occupation of qubit excited states along the transmission line. A quantum metamaterial in the QS phase circumvents the “no-go” restrictions by considerably decreasing its total energy relative to the vacuum state by exciting nonlinear electromagnetic solitons.     

Organotin-catalyzed highly regioselective thiocarbonylation of nonprotected carbohydrates and synthesis of deoxy carbohydrates in a minimum number of steps

Nonprotected carbohydrates: The catalytic regioselective thiocarbonylation of carbohydrates by using organotin dichloride under mild conditions was demonstrated. The reaction afforded various deoxy saccharides in high yields and excellent regioselectivity in a minimum number of steps. The regioselectivity of the thiocarbonylation is attributed to the intrinsic character of the carbohydrates based on the stereorelationship of their hydroxy groups (see scheme).     

Liver function assessment with three (13)C breath tests by two-point measurements

In this study, we performed three breath tests - l-[1-(13)C ]phenylalanine breath test (PBT), l-[1-(13)C ] methionine breath test, and [(13)C]methacetin breath test (MethaBT) - in patients with chronic liver disease to determine the optimal timing of expired air collection for diagnosing chronic liver disease and evaluating the grade of fibrosis. The subjects were 61 adults with normal livers, 98 chronic hepatitis patients, and 91 liver cirrhosis patients. We investigated the relationships of breath test results with routine biochemical tests and the Child-Pugh score, as well as the diagnostic capacities of the breath tests for liver dysfunction/cirrhosis and grade of liver fibrosis. For the diagnosis of liver cirrhosis and correlations with liver fibrosis, the accuracy of the PBT at 30 min (PBT30) was similar to that of the MethaBT at 15 min (Metha15). For liver function assessment by two-point measurement with (13)C breath tests, we recommend the PBT30 and the Metha15.