Viscosity solutions of the augmented K-Hessian equations

Abstract

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

The synthesis of TCNQ-based material with derivative of leucine amino acid

Abstract

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.

An improvement of newton – krylov method for solution of nonlinear equations

Abstract

Information security is always a crucial issue in the continuously developing society. There are many solutions that have been proposed to secure information. In this article, the author discusses the introduction of encryption using knowledge from the Linear Algebra course to first-year students so that they can perceive the application of Linear Algebra. The information encryption process uses the knowledge of matrices, matrix operations, inverse matrices, transposition, Gauss elimination, linear transformation....

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Vol. 2 No. 3 (2023): HPU2.Nat.Sci.Tech
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