The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.

The publication presents experimental verification of a mathematical model of silver nanowire (AgNWs) fabrication in a continuous flow process in a helical tubular reactor. Silver nanowires were synthesised with a polyol process, with ethylene glycol as the reductant of the nanomaterial precursor and solvent of the reactants. The observed average diameters and lengths of AgNWs were 98-226 nm and 5-45 μm, respectively. The experimental conversions of the precursor were 0.71-0.90. A comparison of calculated and measured conversions for the investigated range of residence times and temperatures showed that the observed error was less than 20%.