In this paper, the Dirichlet problem for the augmented k – Hessian equations in the bounded domain with nonsmooth data will be investigated. We introduce the concept of (w,k) – convex function, show that all viscosity subsolutions and supersolutions of the considering Dirichlet problem are (w,k) – convex. Furthermore, we prove some sufficient conditions for the existence and uniqueness of the viscosity solutions of the Dirichlet problem
- Từ khóa:
- Augmented Hessian equations
A new material, Leu(CH3)4-TCNQ, has been successfully synthesized from Tetracyanoquinondimethane (TCNQ) and amino acid ester, N,N,N-Trimethyl-L-Leucine Methyl ester ((Leu(CH3)4+). This material was characterized by modern physicochemical methods such as: X-ray diffraction technique (XRD), Raman, Infrared (FT-IR) and UV-Vis spectroscopy and voltammetric technique. This result will offering a new direction for the synthesis of new materials from TCNQ and other amino acids.
In this study, 5 benzo[d]thiazole (3a-3e) derivatives were successfully synthesized in 2 steps through Suzuki cross-coupling reaction from 2-(4-bromophenyl)benzo[d]thiazole (2) and arylboronic acid derivatives in 80-95%.These compounds’ structure was determined through NMR and mass spectral analysis. Besides, The key compound 2 was synthesized with a domestic microwave oven which helps to save cost and time in the synthesis process.