A satellite of the grand Furuta inequality and its application

The grand Furuta inequality has the following satellite (SGF;$t\in [0\text{,}1]$), given as a mean theoretic expression:$A?B>0\text{,}t\in [0\text{,}1]?A^{-r+t}{\#}_{\frac{1-t+r}{(p-t)s+r}}(A^t{?}_s{B}^p)?B\text{for}r?t\text{;}p\text{,}s?1\text{,}$where ${\#}_{\alpha }$ is the $\alpha$-geometric mean and ${?}_s$ ($s?[0\text{,}1]$) is a formal extension of ${\#}_{\alpha }$. It is shown that (SGF; $t\in [0\text{,}1]$) has the Löwner–Heinz property, i.e. (SGF; $t=1$) implies (SGF;t) for every $t\in [0\text{,}1]$. Furthermore, we show that a recent further extension of (GFI) by Furuta himself has also the Löwner–Heinz property.     

Third-order aberration analysis of an off-axial optical system

The aberration theory applied to co-axial optical systems is extended to off-axial systems, for which third-order aberration coefficients are considered. The derived aberrations are analyzed using three-dimensional ray bundles, spot diagrams, and image charts, and classified in relation to the system symmetry. This theory is very useful for optical designers, allowing them to clarify the relationship between the structures of off-axial optical systems and the corresponding off-axial aberrations.     

A blow-up theorem for a discrete semilinear wave equation

In this paper, a discretization of a semilinear wave equation whose nonlinear term is a power function is investigated. It is shown that, when a condition on the initial value problem, similar to that governing the existence of blow-up solutions for the original continuous equation is met, the newly introduced difference equation has blow-up solutions with characteristics corresponding to those of the blow-up solutions for the original equation.     

Photoinduced tandem three-component coupling of propanedinitrile, 2,5-dimethylhexa-2,4-diene, and cyanoarenes

A tandem three-component coupling photoreaction proceeds upon photoirradiation of MeCN/H2O solutions containing propanedinitrile (1, malononitrile), 2,5-dimethylhexa-2,4-diene (2), and polycyanoarenes in the presence of phenanthrene and carbonate, leading to selective alpha-monoalkylation of 1. The reaction proceeds via photo-NOCAS (Nucleophile-Olefin Combination, Aromatic Substitution) type mechanism: nucleophilic attack of the anion of 1 to photogenerated 2(*+) is followed by ipso-substitution on the radical anion of the polycyanoarene. It advances under mild, safe, and environmentally friendly conditions such as proceeding at ambient temperature without metals and halogens, and in the presence of weak base. The reaction also represents a novel and metal-free cross-coupling reaction that leads to ipso-substitution on polycyanoarene via aryl-cyano bond cleavage. In addition, the reaction is a rare example of introducing carbon nucleophile in the photoinduced electron transfer reaction, except that of cyanide ion.     

Beta-isocupreidine-catalyzed Baylis-Hillman reaction of chiral N-boc-alpha-amino aldehydes

[Structure: see text] Beta-isocupreidine (beta-ICD)-catalyzed Baylis-Hillman reaction of chiral N-Boc-alpha-amino aldehydes and 1,1,1,3,3,3-hexafluoroisopropyl acrylate (HFIPA) takes place without racemization and exhibits the match-mismatch relationship between the substrate and the catalyst. In the case of acyclic amino aldehydes, L-substrates show excellent syn selectivity and high reactivity in contrast to D-substrates. On the other hand, in the case of cyclic amino aldehydes, D-substrates rather than L-substrates show excellent anti selectivity and high reactivity.     

A full multiple scattering model for the analysis of time-resolved X-ray difference absorption spectra

A full multiple theoretical model (MXAN) is applied to fit picosecond difference X-ray absorption spectra at the ruthenium L(3) edge upon photoexcitation of aqueous [RuII(bpy)3]2+. We show that fitting difference spectra allows an increase in sensitivity, such that slight structural changes can be retrieved, which are not detected in fitting full spectra. The Ru-N bond distances of the excited complex in the (3)MLCT state are in good agreement with recently published values. The implementation of the present approach to L-edge spectra and its high sensitivity opens opportunities for its extension to a large class of experiments where difference X-ray absorption spectra are recorded.     

ZINC TETRAPHENYLPORPHYRIN-SENSITIZED PHOTOREDUCTION OF ANTHRAQUINONESULFONATE IN AQUEOUS MICELLAR SOLUTIONS*

Abstract— Zn-tetraphenylporphyrin (ZnTPP), solubilized in non-ionic surfactant micelles, was found to sensitize photoreductions of some sodium anthraquinonesulfonatesz in the presence of ascorbic acid under anaerobic conditions. The reaction rate was increased by the addition of an anionic surfactant, while retardation was observed with a cationic surfactant. The pH-reaction rate profiles showed maxima located in the order corresponding to pK_a-values for the semiquinone of each anthraquinone-sulfonate. A reaction scheme involving the formation of ZnTPP⁺ at the primary step, followed by back-reduction with ascorbic acid, is proposed. The reaction scheme is in good agreement with the results of flash photolysis. The surfactant micelles are suggested to aid the charge-separation between the ionic species just after the redox reaction involving the photoexcited ZnTPP and anthraquinonesulfonates.     

Synthesis of two osteoclast-forming suppressors,demethylincisterol A3 and chaxine A

The synthesis of two potent osteoclast-forming suppressing agents isolated from the Chinese mushroom Agrocybe chaxingu, demethylincisterol A₃ and chaxine A, was accomplished using ergocalciferol as the starting material. Our methodology for the synthesis of demethylincisterol A₃ and chaxine A featured the construction of a butenolide moiety by the intramolecular Horner–Wadsworth–Emmons reaction under Masamune–Roush conditions. This is the first reported synthesis of chaxine A.