A separation between the boundary shape and the boundary functions in the parametric integral equation system for the 3D Stokes equation

Numerical Algorithms - The paper introduces the analytical modification of the classic boundary integral equation (BIE) for Stokes equation in 3D. The performed modification allows us to obtain...     

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

The paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions.     

Measurement of ultrasonic exposure with radiation force and thermal methods

It is the purpose of this paper to discuss briefly the factors that influence the interaction of the ultrasonic field and medium being irradiated, and to collect together the various techniques that have been suggested for measuring energetic parameters of the ultrasonic field. The calorimetric and radiation force methods are then discussed in more detail. The former is discussed as a technique whose capabilities have not been fully exploited while the latter demands attention both because of its simplicity and its controversial theoretical basis. Areas in which further work is needed are indicated in the summary and conclusion. It is hoped that the paper will be of practical use to workers in the field.     

Lipase-Catalyzed Synthesis,Antioxidant Activity,Antimicrobial Properties and Molecular Docking Studies of Butyl Dihydrocaffeate

Green chemistry approaches, such as lipase-catalyzed esterification, are promising methods for obtaining valuable chemical compounds. In the case of the use of lipases, unlike in aqueous environments, the processes of the ester bond formations are encountered in organic solvents. The aim of the current research was to carry out the lipase-catalyzed synthesis of an ester of dihydrocaffeic acid. The synthesized compound was then evaluated for antioxidant and antimicrobial activities. However, the vast majority of its antioxidant activity was retained, which was demonstrated by means of DPPH· (2,2-diphenyl-1-picrylhydrazyl) and CUPRAC (cupric ion reducing antioxidant capacity) methods. Regarding its antimicrobial properties, the antifungal activity against Rhizopus oryzae is worth mentioning. The minimum inhibitory and fungicidal concentrations were 1 and 2 mM, respectively. The high antifungal activity prompted the use of molecular docking studies to verify potential protein targets for butyl ester of dihydrocaffeic ester. In the case of one fungal protein, namely 14-α sterol demethylase B, it was observed that the ester had comparable binding energy to the triazole medication, isavuconazole, but the interacted amino acid residues were different.     

Genetic Algorithms Based on a New System of Integral Equations in Identification of Material Constants for Anisotropic Media

A hybrid method for solving inverse boundary problems is presented. The method consists in combining the genetic algorithms with a new system of integral equations. The effectiveness of the general idea of the method and its practical application are tested in the identification of material constants for a two-dimensional anisotropic medium.     

The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries

The paper presents an accelerating of solving potential boundary value problems (BVPs) with curvilinear boundaries by modified parametric integral equations system (PIES). The fast multipole method (FMM) known from the literature was included into modified PIES. To consider complex curvilinear shapes of a boundary, the modification of a binary tree used by the FMM is proposed. The FMM combined with the PIES, called the fast PIES, also allows a significant reduction of random access memory (RAM) utilization. Therefore, it is possible to solve complex engineering problems on a standard personal computer (PC). The proposed algorithm is based on the modified PIES and allows for obtaining accurate solutions of complex BVPs described by the curvilinear boundary at a reasonable time on the PC.