This study was aimed at evaluating the possibility to use the Friedrich-Braun fractional derivative rheological model to assess the viscoelastic properties of xanthan gum with rice starch and sweet potato starch. The Friedrich-Braun fractional derivative rheological model allows to describe viscoelastic properties comprehensively, starting from the behaviour characteristic of purely viscous fluids to the behaviour corresponding to elastic solids. The Friedrich-Braun fractional derivative rheological model has one more virtue which distinguishes it from other models, it allows to determine the relationship between stress and strain and the impact of each of them on viscoelastic properties on the tested material. An analysis of the data described using the Friedrich-Braun fractional derivative rheological model allows to state that all the tested mixtures of starch with xanthan gum form macromolecular gels exhibiting behaviour typical of viscoelastic quasi-solid bodies. The Friedrich-Braun fractional derivative rheological model and 8 rheological parameters of this model allow to determine changes in the structure of the examined starch - xanthan gum mixtures. Similarly important is the possibility to find out the trend and changes going on in this structure as well as their causes.

The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.

Main goal of the paper is to present the algorithm serving to solve the heat conduction inverse problem. Authors consider the heat conduction equation with the Riemann-Liouville fractional derivative and with the second and third kind boundary conditions. This type of model with fractional derivative can be used for modelling the heat conduction in porous media. Authors deal with the heat conduction inverse problem, which, in this case, consists in identifying an unknown thermal conductivity coefficient. Measurements of temperature, in selected point of the region, are the input data for investigated inverse problem. Basing on this information, a functional describing the error of approximate solution is created. Minimizing of this functional is necessary to solve the inverse problem. In the presented approach the Ant Colony Optimization (ACO) algorithm is used for minimization.

In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.

In this paper the way of modeling phenomena occurring during the voltage and current waves passing through a point connection of two lines, with different wave impedance operators, is presented. This connection point is called „the wave transformer”. The analyzes and the resulting formulas concern not the frequency domain, but the time domain. The appropriate transition matrices of waves through the wave transformer are defined. This matrices are the convolution integral-derivative operators of fractional order (the digital filters). For a lossless line the wave transition matrices through the wave transformer become number type instead of operator type. All matrix multiplications occurring in the formulas should be understood in convolution way.

The research focused on the influence of the solution temperature on the structure of precipitation hardening multi-component hypoeutectic aluminium alloys. The AlSi8Cu3 and AlSi6Cu4 alloys were used in the study and were subjected to a thermal-derivative analysis. The chemical composition and crystallization of phases and eutectics shift the characteristic points and the corresponding temperatures to other values, which affect to, for instance, the solution temperature. The alloys were supersaturated at 475°C (according to the determined temperature (TSol) and 505°C for 1.5 hours. Aging was performed at 180°C for 5 hours. The Rockwell hardness measurement, metallographic analysis of alloys by means of light microscopy as well as chemical and phase analysis using scanning electron microscopy and X-ray crystallography were carried out on alloys. The use of computer image analysis enabled the determination of the amount of the current Al2Cu phase in the alloys before and after heat treatment.

Jak powstaje przymiotnik fettleibig (otyły)? Może się on wydawać oczywistym derywatem od fett (gruby) i Leib (ciało), jednak NP fetter Leib jest równie rzadki jak częsty jest przymiotnik: brzmi to paradoksalnie. W tym artykule badany jest nowy sposób wyjaśniania powstawania tego przymiotnika: fettleibig jawi się jako istnienie częstego w dawnych czasach paradygmatu -leibig-. Dlatego też, w ujęciu synchronicznym, przymiotnik ten nie jest tłumaczony jako derywat, choć pozostaje głównie transparentny.

According to the analysis of the current state of the knowledge shows that there is little information on the process of phase transformations

that occur during the cooling Cu-Al-Fe-Ni hypo-eutectoid bronzes with additions of Cr, Mo and/or W, made additions individually

or together, for the determination of: the type of crystallizing phases, crystallizing phases, order and place of their nucleation.

On the basis of recorded using thermal and derivative analysis of thermal effects phases crystallization or their systems, analysis of the

microstructure formed during crystallization - observed on the metallographic specimen casting ATD10-PŁ probe, analysis of the existing

phase equilibrium diagrams forming elements tested Cu-Al-Fe-Ni bronze, with additions of Cr, Mo, W and/or Si developed an original

model of crystallization and phase transformation in the solid state, the casting of high quality Cu-Al-Fe-Ni bronze comprising: crystallizing

type phase, crystallizing phase sequence, place of nucleation.

Water names, using the genetic-motivational criteria, can be divided into two superior groups: deappellative and deproprial hydronyms. Among the hydronyms derived from proper names, one can distinguish between the detoponymic and deanthroponymic. The names of flowing waters from anthroponyms are the subject of this article. Preliminary statistical data regarding deanthroponymic potamonyms in the Vistula river basin, their chronology, naming models, word formation bases and geographical distribution are presented. The results of the analysis show that the deanthroponymic potamonyms account for approximately 6.8% of the names of flowing waters of the Vistula river basin, estimated at more than 13,500. They appear sporadically in documents as early as in the 13th century, with only 12% visible until the 16th century, with most of them not being noticed until the 19th and 20th centuries. Such a statistical distribution is typical for the names of the flowing waters of that basin. Deanthroponymic names of rivers represent a variety of naming models, but most often appear as a part of compound names created with the suffix -ów, one-word formations with the same suffix and derivatives from the suf. -ka. They mainly identify objects located between the Soła River and the Dunajec River, especially in the Dunajec River basin, so in mountainous and submontainous areas, as K. Rymut claimed. The basis of such potamonyms are mainly personal names with different motivations, rarely being ethnonyms and first names.

There is general agreement that primary pyrolysis products of end-of-life tyres should be valorised to improve the economics of pyrolysis. In this work, tyre pyrolysis char (TPC) is produced in a pyrolysis pilot plant designed and built at our home university. The produced TPC was upgraded to tyre-derived activated carbon (TDAC) by activation with CO2, and then characterised using stereological analysis (SA) and nitrogen adsorption at 77 K. SA showed that the grains of TPC and TDAC were quasi- spherical and slightly elongated with a 25% increase in the mean particle cross-section surface area for TDAC. The textural properties of TDAC demonstrated the BET and micropore surface areas of 259 and 70 m2/g, respectively. Micropore volume and micropore surface area were 5.8 and 6.7 times higher for TDAC than TPC at  2 nm, respectively. The n-hexane adsorption was investigated using experiments and modelling. Eight adsorption isotherms along with three error functions were tested to model the adsorption equilibrium. The optimum sets of isotherm parameters were chosen by comparing sum of the normalized errors. The analysis indicated that the Freundlich isotherm gave the best agreement with the equilibrium experiments. In relation to different activated carbons, the adsorption capacity of TDAC for n-hexane is about 16.2 times higher than that of the worst reference material and 4.3 times lower than that of the best reference material. In addition, stereological analysis showed that activation with CO2 did not change the grain’s shape factors. However, a 25% increase in the mean particle cross-section surface area for TDAC was observed.