Fast enclosure for all eigenvalues in generalized eigenvalue problems

A fast method for enclosing all eigenvalues in generalized eigenvalue problems Ax=λBx is proposed. Firstly a theorem for enclosing all eigenvalues, which is applicable even if A is not Hermitian and/or B is not Hermitian positive definite, is presented. Next a theorem for accelerating the enclosure is presented. The proposed method is established based on these theorems. Numerical examples show the performance and property of the proposed method. As an application of the proposed method, an efficient method for enclosing all eigenvalues in polynomial eigenvalue problems is also sketched.     

New aplysiatoxin derivatives from the Okinawan cyanobacterium Moorea producens

The marine cyanobacterium Moorea producens is a rich source of diverse compounds that possess a variety of biological activities. In the present study, eight new aplysiatoxin derivatives, namely 6, 8–13, and 15, along with aplysiatoxin (1), debromoaplysiatoxin (2), 3-methoxyaplysiatoxin (3), anhydroaplysiatoxin (4), anhydrodebromoaplysiatoxin (5), oscillatoxin B2 (7), and 30-methyloscillatoxin D (14) were isolated and identified from the Okinawan M. producens. In cytotoxicity and diatom growth inhibition tests, the fifteen compounds tested (1–15) showed moderate or no activity at a concentration of 10?μg/mL.     

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.     

Control of the Dynamic Motion of a Gel Actuator Driven by the Belousov‐Zhabotinsky Reaction

A novel self‐oscillating gel actuator with gradient structure, which generates a pendulum motion by fixing one edge of the gel without external stimuli was achieved. The gel was synthesized by copolymerizing the ruthenium catalyst for the Belousov‐Zhabotinsky reaction with N‐isopropylacrylamide and 2‐acrylamido‐2‐methylpropane sulfonic acid. Furthermore, we clarified that the period and amplitude for the self‐oscillating behavior of the gel actuator are controllable by changing the composition, temperature, and size of the gel. The maximum amplitude of the novel gel actuator is about a 100 times larger than that of the conventional self‐oscillating gel system.

     

Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point,II — Its relevance to the Mathieu equation and the Legendre equation

We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.     

Concise synthesis of the CDE ring system of tetrahydroisoquinoline alkaloids using carbophilic Lewis acid-catalyzed hydroamidation and oxidative Friedel-Crafts cyclization

A concise synthesis of the CDE ring system of the tetrahydroisoquinoline antitumor alkaloids such as saframycins, renieramycins, and ecteinascidins has been developed. Both Au(I)-catalyzed intramolecular hydroamidation of alkynylamide and NBS-mediated oxidative Friedel-Crafts cyclization of the resulting 2-ketopiperazine were utilized as key reactions.     

Stern-gerlach study of multidecker lanthanide-cyclooctatetraene sandwich clusters

Multilayer lanthanide-cyclooctatetraene organometallic clusters, Lnn(C8H8)m (Ln = Eu, Tb, Ho, Tm; n = 1-7; m = n - 1, n, n + 1) were produced by a laser vaporization synthesis method. The magnetic deflections of these organometallic sandwich clusters were measured by a molecular beam magnetic deflection technique. Most of the sandwich species displayed one-sided deflection, while some of smaller Ln-C8H8 clusters showed symmetric broadening without or with only very small (or absent) net high-field deflection. In general, the total magnetic moments, calculated from the magnitude of the beams deflections, increase with the number of lanthanide atoms (i.e., with increasing sandwich layers); however for Tb-, Ho-, and Tm-C8H8 clusters with n > 3, the suppression of the magnetic moments was observed, possibly through antiferromagnetic interactions. For Eu-C8H8 clusters, we observe a linear increase of the magnetic moments with the number of Eu atoms up to n = 7, with average magnetic moment per Eu atom around 7 muB--similar to that displayed by conventionally synthesized mononuclear EuIIC8H8 complexes, indicating that Eu atoms exist as Eu2+ ions in the full sandwich Eun(C8H8)n+1 clusters. These results suggest that Eun(C8H8)n+1 is a promising candidate for a high-spin, one-dimensional building block in organometallic magnetic materials.     

Comparative study on the structural, optical, and electrochemical properties of bithiophene-fused benzo[c]phospholes

Three types of bithiophene-fused benzo[c]phospholes were successfully prepared by Ti(II)-mediated cyclization of the corresponding dialkynylated bithiophene derivatives as a key step. Each sigma(3)-phosphorus center of the benzo[c]phosphole subunits was readily transformed into sigma(4)-phosphorus center by Au coordination or oxygenation. In addition, the bithiophene subunit was functionalized at the alpha,alpha'-carbon atoms by Pd-catalyzed cross-coupling reactions with heteroarylmetals and by an S(N)Ar reaction with hexafluorobenzene. The experimentally observed results (NMR spectroscopy, X-ray analysis, UV/Vis absorption/fluorescence spectroscopy, and cyclic/differential-pulse voltammetry) have revealed that the structural, optical, and electrochemical properties of the bithiophene-fused benzo[c]phospholes vary considerably depending on the pi-conjugation modes at the bithiophene subunits and the substituents of the heterocyclopentadiene components. The appropriately ring-annulated sigma(3)-P derivatives and sigma(4)-P-AuCl complexes were found to emit fluorescence in the orange-red region, and the sigma(4)-P-oxo derivatives proved to undergo reversible one-electron reduction at -1.4 to -1.8 V (vs ferrocene/ferrocenium). These results indicate that the bithiophene-fused benzo[c]phospholes possess narrow HOMO-LUMO gaps and low-lying LUMOs, which was confirmed by density functional theory calculations of their model compounds. The time-of-flight measurement of an ITO/benzo[c]phosphole/Al device showed that the electron mobility in the P-oxo derivative is one-order higher than that in Alq(3) at low electric fields. The present study demonstrates that the arene-fused benzo[c]phosphole skeleton could be a highly promising platform for the construction of a new class of phosphole-based optoelectrochemical materials.     

Electron transfer activation of chromopyrrolic acid by cytochrome p450 en route to the formation of an antitumor indolocarbazole derivative: theory supports experiment

QM/MM calculations support experiment and show that StaP is a P450 that functions like a peroxidase: its active species is the one-electron-reduced Cpd II species with a radical on CPA, by analogy to cytochrome c peroxidase (CcP), and its reaction with the substrate proceeds by overall proton-coupled electron transfer (PCET), in analogy to the corresponding mechanism in horseradish peroxidase (HRP). The electron transfer is enabled by His250, the presence of carboxylate groups in CPA, and by the H-bonding network that tunes the energetic of the process. Theory supports experiment but reveals some novel aspects of this unusual P450.