Solutions with time-dependent singular sets for the heat equation with absorption

We consider the heat equation with a superlinear absorption term ${?}_{t}u?\mathrm{\Delta }u=?u^p$ in ${\mathbb{R}}^n$ and study the existence of nonnegative solutions with an m-dimensional time-dependent singular set, where $n?m\ge 3$. We prove that if $1<p<(n?m)/(n?m?2)$, then there are two types of singular solutions. Moreover, we show the uniqueness of the solutions and specify the exact behavior of the solutions near the singular set.     

Triflumizole as a Novel Lead Compound for Strigolactone Biosynthesis Inhibitor

Strigolactones (SLs) are carotenoid-derived plant hormones involved in the development of various plants. SLs also stimulate seed germination of the root parasitic plants, Striga spp. and Orobanche spp., which reduce crop yield. Therefore, regulating SL biosynthesis may lessen the damage of root parasitic plants. Biosynthetic inhibitors effectively control biological processes by targeted regulation of biologically active compounds. In addition, biosynthetic inhibitors regulate endogenous levels in developmental stage- and tissue-specific manners. To date, although some chemicals have been found as SL biosynthesis inhibitor, these are derived from only three lead chemicals. In this study, to find a novel lead chemical for SL biosynthesis inhibitor, 27 nitrogen-containing heterocyclic derivatives were screened for inhibition of SL biosynthesis. Triflumizole most effectively reduced the levels of rice SL, 4-deoxyorobanchol (4DO), in root exudates. In addition, triflumizole inhibited endogenous 4DO biosynthesis in rice roots by inhibiting the enzymatic activity of Os900, a rice enzyme that converts the SL intermediate carlactone to 4DO. A Striga germination assay revealed that triflumizole-treated rice displayed a reduced level of germination stimulation for Striga. These results identify triflumizole as a novel lead compound for inhibition of SL biosynthesis.     

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.     

Benzoin reaction in water as an aqueous medium catalyzed by benzimidazolium salt

Benzoin reactions are catalyzed by N,N-dialkylbenzimidazole to yield α-hydroxy ketones; the reaction proceeds in water as an aqueous medium under mild conditions. The utility of these salts as pre-catalysts in these reactions has been demonstrated.     

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.     

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.