Finsler Hardy inequalities

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non-attainability of the constants in the inequalities are also proved.     

Approximating Fixed Points of Infinite Nonexpansive Mappings by the Hybrid Method

In this paper, we introduce an iterative scheme for finding a common fixed point of infinite nonexpansive mappings in a Hilbert space by using the hybrid method. Then, we prove a strong convergence theorem which is connected with the problem of image recovery. Further, using this result, we consider the generalized problem of image recovery and the problem of finding a common fixed point of a family of nonexpansive mappings.     

Palladium(0)-catalyzed Mizoroki-Heck reaction and Rh(I)-catalyzed asymmetric hydrogenation of polymer-supported dehydroalanine system

We have developed a practical route for the synthesis of peptides containing unnatural amino acids. Mizoroki-Heck reaction of polymer-supported dehydroalanine, followed by asymmetric hydrogenation was accomplished using Pd(0) and Rh(I)-DuPHOS catalysts, respectively, leading to 36 dipeptides containing phenylalanine derivatives with high stereocontrol.     

Color change (yellow \documentclass{article}\pagestyle{empty}\begin{document}$\rightleftharpoons$\end{document} orange) of 4,6,7-tri(alkoxy-substituted aryl)-1,2,5-thiadiazolo[3,4-c]pyridines in the solid phase

Reversible color change of 4,6,7-tri(alkoxy-substituted phenyl)-1,2,5-thiadiazolo[3,4-c]pyridines 5 in the solid state was observed: on grinding, yellow crystals of 5 became an orange amorphous solid which, on heating or washing with an appropriate solvent, gave the original yellow crystals.     

5-Lipoxygenase inhibitors isolated from the mushroom Boletopsis leucomelas (Pers.) Fayod.

Terphenyl compounds, tentatively named Bl-I (1), Bl-II (2), Bl-III (3), Bl-IV (4) and Bl-V (5), showing 5-lipoxygenase inhibitory activity have been isolated from the mushroom Boletopsis leucomelas (Pers.) Fayod. On the basis of physico-chemical and spectral evidence, they were concluded to be a series of cycloleucomelone-leucoacetates.     

A novel method to quantize systems of damped motion

A novel method to quantize systems of damped motion is proposed in the frameworks of canonical quantization and path integral quantization. It can be afforded by considering a Lagrangian multiplied by a time-dependent function, which may represent an effective interaction with “environment.”     

Infrared reflection spectra of the one-dimensional ionic conductor K— and RbAl priderites

The reflection spectra of the one-dimensional ionic conductors K_1.6Al_1.6Ti_6.4O₁₆ and Rb_1.49Al_1.65Ti_6.35O_15.92 have been measured for the polarizations E ∥ c (channel direction) and E 6 c in the frequency region 60–2000 cm^-1. The spectra of these two compounds are very similar with their features and have the same number of bands. The vibrational mode frequencies are obtained from a Kramers-Kronig analysis for each polarized reflectivity spectrum. A comparison of the corresponding mode frequencies for both priderites shows that only the lowest frequency mode observed in the E 6 c spectra is strongly associated with the alkali ion, while the others are not. The effect due to the non-stoichiometry is not found in the infrared reflection spectra.     

Endogenous synthesis of N-methylsalsolinol, an analogue of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, in rat brain during in vivo microdialysis with salsolinol, as demonstrated by gas chromatography-mass spectrometry.

N-Methylsalsolinol, an analogue of 1,2,3,6-tetrahydropyridine, is present in the brains of patients with Parkinson's disease. To determine the metabolic pathway for the synthesis of N-Methylsalsolinol in the brain, salsolinol was perfused through the striatum or the substantia nigra of the rat brain by in vivo microdialysis. N-Methylsalsolinol was detected in the brain dialysate samples during microdialysis with salsolinol using gas chromatography-mass spectrometry with selected-ion monitoring. These results demonstrate that endogenous N-methylation of salsolinol into N-methylsalsolinol occurs in the brain in vivo.