The process of obtaining alginate microspheres (AMs) by emulsification method was optimized by applying statistical analysis software. Ten batches of microspheres were prepared using the fractional plan 3 ^(K-p). AMs were obtained with two different methods: an ultrasonic homogenization (UH) process and a rotor-stator mechanical homogenization (MH). The amount of a cross-linking agent (CaCl ₂), calcium chloride rate addition, and the sonication amplitude (UH) or the speed of rotor rotation (MH) were selected as formulation variables. All the batches were evaluated in terms of stability and size of the alginate microspheres. Approximation profiles were developed. As a result of the conducted research, stable alginate microspheres with sizes ranging from 10 to 30 micrometres were obtained. The obtained results showed that the quality of AMs was mainly affected by the concentration and the rate of calcium chloride addition into the system. Therefore, the role of calcium ions in the mechanisms of shell structuring was discussed. Lactobacillus casei bacteria were encapsulated into the batches found to be optimum. The high encapsulation efficiency (EE) of the bacteria (72-94%) depending on the form) and their viability over time were obtained. The model developed in the study can be effectively utilized to achieve the AMs formulations.

The article deals with issues related to the application of statistical methods used in the valuation process. The proposed algorithm for real estate valuation can be used in the statistical market analysis method in the process of mass appraisal. The algorithm uses a multiple linear regression model. Legal considerations indicate the need for such an algorithm for the determination of the value of representative properties. Due to the large size of the database of comparables, the proposed algorithm can be used only to appraise typical properties. A good statistical model is parsimonious, that is, it uses as few mathematical concepts as possible in a given situation. A model should extract what is systematic in the results observed, allowing for the presence of purely random deviations. The article discusses the basic principles of building a good statistical model. Attention is drawn to the number of market attributes that are entered into the model and the range of their values. As few explanatory variables as possible should be entered into the model to explain the phenomenon under study. Explanatory variables are only those characteristics of the property that differentiate prices in a given market defined and adopted by the appraiser as the basis for valuation. The article highlights the importance of taking into account market changes during the period under study.

Titanite, an accessory mineral of pegmatite related to aplogranite, was identified in the Szklarska Poręba Huta quarry within the Karkonosze granite massif in Lower Silesia, Poland. It formed during pegmatitic to hydrothermal stages. Besides the isovalent substitution Sn → Ti, the chemical composition of the mineral is characterized by three coupled substitutions: (1) (Al, Fe, Sc)³⁺ + (OH, F)- → ^YTi + ^ZO, (2) XREE³⁺ + ^Y(Al, Fe, Sc)³⁺ →^X)Ca2+ + ^YTi⁴⁺, and (3) (Al, Fe, Sc)³⁺ + (Nb, Ta)⁵⁺ → 2^YTi. These substitutions are strongly dependent on the composition of the magma in terms of its Al₂O₃/TiO₂ activity ratio, with the first one also influenced by the H₂O/HF fugacity ratio. Fluorine, which induced the most common substitution (1), had its source in high-temperature F-bearing fluids released from rocks of the metamorphic envelope adjacent to the intruding granite. These fluids mobilized and transported various rock components (Sc, REE, Nb, Ta, etc.) among others in the form of fluoride complexes, enriching the aplogranite magma with some metallic elements. The substitution of Sn for Ti developed with decreasing temperature to the extent that in thin ore-mineralized quartz veins cutting aplogranite, titanite reaches Sn-bearing compositions up to the prevalence of Sn corresponding to malayaite.