Superquadratic convergence of DLASQ for computing matrix singular values

DLASQ is a routine in LAPACK for computing the singular values of a real upper bidiagonal matrix with high accuracy. The basic algorithm, the so-called dqds algorithm, was first presented by Fernando-Parlett, and implemented as the DLASQ routine by Parlett-Marques. DLASQ is now recognized as one of the most efficient routines for computing singular values. In this paper, we prove the asymptotic superquadratic convergence of DLASQ in exact arithmetic.     

DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods

In this paper, the theoretical convergence rate of the trapezoidal rule combined with the double-exponential (DE) transformation is given for a class of functions for which the single-exponential (SE) transformation is suitable. It is well known that the DE transformation enables the rule to achieve a much higher rate of convergence than the SE transformation, and the convergence rate has been analyzed and justified theoretically under a proper assumption. Here, it should be emphasized that the assumption is more severe than the one for the SE transformation, and there actually exist some examples such that the trapezoidal rule with the SE transformation achieves its usual rate, whereas the rule with DE does not. Such cases have been observed numerically, but no theoretical analysis has been given thus far. This paper reveals the theoretical rate of convergence in such cases, and it turns out that the DE’s rate is almost the same as, but slightly lower than that of the SE. By using the analysis technique developed here, the theoretical convergence rate of the Sinc approximation with the DE transformation is also given for a class of functions for which the SE transformation is suitable. The result is quite similar to above; the convergence rate in the DE case is slightly lower than in the SE case. Numerical examples which support those two theoretical results are also given.     

Unexpected Macrocyclic Multinuclear Zinc and Nickel Complexes that Function as Multitasking Catalysts for CO2 Fixations

Unique self‐assembled macrocyclic multinuclear Zn^II and Ni^II complexes with binaphthyl‐bipyridyl ligands (L) were synthesized. X‐ray analysis revealed that these complexes consisted of an outer ring (Zn₃L₃ or Ni₃L₃) and an inner core (Zn₂ or Ni). In the Zn^II complex, the inner Zn₂ part rotated rapidly inside the outer ring in solution on an NMR timescale. These complexes exhibited dual catalytic activities for CO₂ fixations: synthesis of cyclic carbonates from epoxides and CO₂ and temperature‐switched N‐formylation/N‐methylation of amines with CO₂ and hydrosilane.     

Chemical Interactions of Cryptic Actinomycete Metabolite 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines through Aggregate Formation

Organisms often produce secondary metabolites as a mixture of biosynthetically related congeners. However, why are metabolites with minor chemical variations produced simultaneously? 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines (5aTHQs) are small, lipophilic metabolites produced by Streptomyces nigrescens HEK616 when cultured with Tsukamurella pulmonis TP‐B0596. A mixture of 5aTHQs forms aggregates that show enhanced membrane affinity and biological activity. The ability to form aggregates and membrane‐binding activity is regulated by the length of the alkyl chains. Aggregates with long alkyl chains were too stable to fuse with lipid membranes. However, if inactive 5aTHQ congener was mixed with active congener, the mixture showed increased membrane affinity, enabling cellular entry and biological activity. Therefore, it is shown that sloppiness in a biosynthetic pathway, by which minor structural variations can be produced, is functionally rational, as the metabolites show synergistic action.     

Novel indoline dye tetrabutylammonium carboxylates attached with a methyl group on the cyclopentane ring for dye-sensitized solar cells

(2R,3aR,8bR)- and (2S,3aS,8bS)-2-Methyl indoline dye tetrabutylammonium carboxylates exhibited the highest conversion efficiency among four regio and stereo isomers. These indoline dyes also showed higher conversion efficiency than DN350.     

Detection of N-nitroso-bile acids at 285 nm in reverse-phase HPLC

In the present study, we developed a novel, simple, and specific detection method using an RP-HPLC at UV 285 nm for the separation and quantification of N-nitroso-bile acids. First, we found that N-nitroso-bile acids have a specific spectrophotometric absorbance at 285 nm. Using this 285 nm detection system, we could especially measure N-nitroso-bile acids, even in co-existence of non-N-nitroso-bile acids. Next, we observed the decomposition of N-nitroso-glychocholate under alkaline, acidic, and neutral conditions. N-nitroso-glychocholate rapidly decomposed under alkaline conditions (pH 9) (t(1/2) = 0.96 h), but remained fairly stable under acidic (pH 2) (t(1/2) = 12.8 h) and neutral (pH 7) (t(1/2) = 7.8 h) conditions. This study is the first report, which simply and specifically analyzes N-nitroso-bile acids using an RP-HPLC system.     

Amplified Chirality Transfer to Aromatic Molecules through Non-specific Inclusion by Amorphous,Hyperbranched Poly(fluorenevinylene) Derivatives

Optically active, hyperbranched, poly(fluorene-2,4,7-triylethene-1,2-diyl) [poly(fluorenevinylene)] derivatives bearing a neomenthyl group and a pentyl group at the 9-position of the fluorene backbone at various ratios acted as a chirality donor (host polymers) efficiently included naphthalene, anthracene, pyrene, 9-phenylanthracene, and 9,10-diphenyanthracene as a chirality acceptor (guest molecules) in their interior space in film as well as in solution, with the guest molecules exhibiting intense circular dichroism through chirality transfer with chirality amplification. The efficiency of the chirality transfer was much higher with higher-molar-mass polymers than lower-molar-mass ones as well as with hyperbranched polymers compared to the analogous linear ones. The hyperbranched polymers include the small molecules in their complex structure without any specific interactions at various stoichiometries. The included molecules may have ordered intermolecular arrangement that may be somewhat similar to those of liquid crystals. Naphthalene, anthracene, and pyrene included in the polymer exhibited efficient circularly polarized luminescence, where the chirality was remarkably amplified in excited states, and anthracene exhibited especially high anisotropies in the emission on the order of 10⁻².     

pH-Dependent catalytic activity and chemoselectivity in transfer hydrogenation catalyzed by iridium complex with 4,4'-dihydroxy-2,2'-bipyridine

Transfer hydrogenation catalyzed by an iridium catalyst with 4,4'-dihydroxy-2,2'-bipyridine (DHBP) in an aqueous formate solution exhibits highly pH-dependent catalytic activity and chemoselectivity. The substantial change in the activity is due to the electronic effect based on the acid-base equilibrium of the phenolic hydroxyl group of DHBP. Under basic conditions, high turnover frequency values of the DHBP complex, which can be more than 1000 times the value of the unsubstituted analogue, are obtained (up to 81 000 h(-1) at 80 degrees C). In addition, the DHBP catalyst exhibits pH-dependent chemoselectivity for alpha,beta-unsaturated carbonyl compounds. Selective reduction of the C=C bond of enone with high activity are observed under basic conditions. The ketone moieties can be reduced with satisfactory activity under acidic conditions. In particular, pH-selective chemoselectivity of the C=O versus C=C bond reduction was observed in the transfer hydrogenation of cinnamaldehyde.     

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.