Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

A new application of statistical moment theory to evaluate the swelling behavior of thermo-responsive gels

The loosely cross-linked poly(acryloyl-L -proline methyl ester) gel, which is known as one of the typical thermo-responsive gels, shows a volume transition around approximately 14°C in pure water. This volume transition is shifted to higher temperature by treatment in aqueous sodium dodecyl sulfate (SDS). The analysis of the swelling-temperature curve (frequency distribution) was performed according to a moment analysis, in which the area under the swelling-temperature curve (AUC), mean swelling transition temperature (MSTT) and variance of swelling transition temperature (VSTT) were calculated. It is shown that the apparent volume transition temperature can be estimated from MSTT and that VSTT can be used to characterize the shape of the corresponding curves.     

Structure Revision of Caesalpinistas A and B and Isolation of a New Furanoditerpenoid from the Cotyledons of Caesalpinia decapetala var. japonica

A known cassane‐type furanoditerpenoid, caesalpinista B ( 1 ), and a new diterpenoid, deoxycaesaljaponin A ( 2 ), were isolated from the cotyledons of Caesalpinia decapetala var. japonica. The previously reported configurational assignments of 1 and the related diterpenoid caesalpinista A ( 3 ) were revised on the basis of X‐ray crystallography and chemical conversion. The structure of 2 was elucidated by spectroscopic data and chemical conversion into 3 .     

Rhodium-catalyzed allyl transfer from homoallyl alcohols to aldehydes via retro-allylation followed by isomerization into ketones

Retro-allylation of homoallyl alcohol by rhodium catalysis occurs to generate allylrhodium species. This allylrhodium reacts with aldehydes to give the corresponding secondary alcohols in situ. Isomerization of these alcohols proceeds in the same pots to furnish the corresponding saturated ketones in good yields. [reaction: see text]     

Gaussian Estimates of Order α and L p -Spectral Independence of Generators of C 0-Semigroups

We prove L^p-spectral independence for generators of C₀-semigroups estimated by the positive C₀-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C₀-semigroup .     

Syntheses, structures, and coordination chemistry of phosphole-containing hybrid calixphyrins: promising macrocyclic P,N2,X-mixed donor ligands for designing reactive transition-metal complexes

The syntheses, structures, and coordination chemistry of phosphole-containing hybrid calixphyrins (P,N2,X-hybrid calixphyrins) and the catalytic activities of their transition-metal complexes are reported. The 5,10-porphodimethene type 14pi-P,(NH)2,X- and 16pi-P,N2,X-hybrid calixphyrins (X = O, S, NH) are prepared via acid-promoted dehydrative condensation between a sigma4-phosphatripyrrane and the corresponding 2,5-bis[hydroxy(phenyl)methyl]heteroles followed by DDQ oxidation. Both spectroscopic and crystallographic data of the hybrid calixphyrins have revealed that the conformation and size of the macrocyclic platforms as well as the oxidation state of the -conjugated pyrrole-heterole-pyrrole (N-X-N) units vary considerably depending on the combination of heteroles. The sigma3-P,(NH)2,S- and sigma3-P,N2,S-hybrids react with Pd(OAc)2 and Pd(dba)2, respectively, to afford the same Pd(II)-P,N2,S-hybrid complex, in which the calixphyrin platform is regarded as a dianionic ligand. In the complexation with [RhCl(CO)2]2 in dichloromethane, the sigma3-P,N2,S-hybrid behaves as a neutral ligand to afford an ionic Rh(I)-P,N2,S-hybrid complex, whereas the sigma3-P,N2,NH-hybrid behaves as an anionic ligand to produce Rh(III)-P,N3-hybrid complexes. In the latter reaction, it is likely that a neutral Rh(I)-P,N3-hybrid complex, generated as a highly nucleophilic intermediate, undergoes C-Cl bond activation of the solvent. The complexation of AuCl(SMe2) with the sigma3-P,N2,X-hybrids (X = S, NH) leads to the formation of the corresponding Au(I)-monophosphine complexes. The spectral data and crystal structures of these metal complexes exhibit the hemilabile nature of the phosphole-containing hybrid calixphyrin platforms derived from the flexible phosphole unit and the redox active N-X-N units. The hybrid calixphyrin-palladium and -rhodium complexes catalyze the Heck reaction and hydrosilylations, respectively, implying that the metal center in the core is capable of activating the substrates under appropriate reaction conditions. The present results demonstrate the potential utility of the phosphole-containing hybrid calixphyrins as a new class of macrocyclic P,N2,X-mixed donor ligands for designing highly reactive transition-metal complexes.     

Caesaljaponins A and B: New Cassane‐Type Furanoditerpenoids from the Seeds of Caesalpinia decapetala var. japonica

Two new cassane‐type furanoditerpenoids, designated caesaljaponin A and caesaljaponin B ( 1 and 2 , resp.), were isolated from seeds of Caesalpinia decapetala var. japonica. The structures were elucidated by spectroscopic data, and the absolute configuration of 1 was determined by X‐ray crystallographic analysis using the anomalous scattering of CuK_α radiation.