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 third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.

The reaction of ilmenite raw materials with sulfuric acid has been investigated to find out the influence of diffusion processes on the course of this reaction. Three different laboratory methods were used to initiate the reaction: mixing ilmenite with 83–85% sulfuric acid at a temperature of 80 °C, mixing ilmenite with 90% sulfuric acid at temperatures of 20–40 °C and adding water, and mixing ilmenite with water and adding 95% sulfuric acid. Changes of thermal power during the process (thermokinetics) were studied with the use of calorimetry. It was found that diffusion processes play an important role when the reaction is initiated by mixing ilmenite with water followed by the addition of sulfuric acid and are less important when the reaction is initiated by mixing ilmenite with concentrated sulfuric acid followed by the addition of water. To explain the influence of diffusion processes on the reaction, the model calculations based on mass and heat balance equations were involved. Model calculations showed that the diffusion and mass transport processes are so fast that the reaction kinetics is mainly influenced by the reaction on the surface of ilmenite particles. The adopted model of calculations showed a very good agreement with experimental results.