In the present paper, the most important aspects of computer algebra systems applications in complicated calculations for classical queueing theory models and their novel modifications are discussed. We mainly present huge computational possibilities of Mathematica environment and effective methods of obtaining symbolic results connected with most important performance characteristics of queueing systems. First of all, we investigate effective solutions of computational problems appearing in queueing theory such as: finding final probabilities for Markov chains with a huge number of states, calculating derivatives of complicated rational functions of one or many variables with the use of classical and generalized L’Hospital’s rules, obtaining exact formulae of Stieltjes convolutions, calculating chosen integral transforms used often in the above-mentioned theory and possible applications of generalized density function of random variables and vectors in these computations. Some exemplary calculations for practical models belonging both to classical models and their generalizations are attached as well.

Microstructure, mechanical, and corrosion properties of as-cast pure zinc and its binary and ternary alloys with magnesium (Mg), and copper (Cu) additions were investigated. Analysis of microstructure conducted by scanning electron microscopy revealed that alloying additives contributed to decreasing average grain size compared to pure zinc. Corrosion rate was calculated based on immersion and potentiodynamic tests and its value was lower for materials with Cu content. Moreover, it was shown that the intermetallic phase, formed as a result of Mg addition, constitutes a specific place for corrosion. It was observed that a different type of strengthening was obtained depending on the additive used. The presence of the second phase with Mg improved the tensile strength of the Zn-based materials, while Cu dissolved in the solution had a positive effect on their elongation.

The present work investigates the effect of modifying an epoxy resin using two different modifiers. The mechanical and thermal properties were evaluated as a function of modifier type and content. The structure and morphology were also analyzed and related to the measured properties. Polyurethane (PUR) was used as a liquid modifier, while Cloisite Na+ and Nanomer I.28E are solid nanoparticles. Impact strength (IS) of hybrid nanocomposites based on 3.5 wt% PUR and 2 wt% Cloisite or 3.5 wt% PUR and 1 wt% Nanomer was maximally increased by 55% and 30%, respectively, as compared to the virgin epoxy matrix, exceeding that of the two epoxy/nanoparticle binaries but not that of the epoxy/PUR binary. Furthermore, a maximum increase in IS of approximately 20% as compared to the pristine matrix was obtained with the hybrid epoxy nanocomposite containing 0.5 wt% Cloisite and 1 wt% Nanomer, including a synergistic effect, due most likely to specific interactions between the nanoparticles and the epoxy matrix. The addition of polyurethane and nanoclays increased the thermal stability of epoxy composites significantly. However, DSC results showed that the addition of flexible polyurethane chains decreased the glass transition temperatures, while the softening point and the service temperature range of epoxy nanocomposites containing nanofillers were increased. FTIR analysis confirmed the occurrence of interaction between the epoxy matrix and added modifiers. All SEM micrographs showed significant roughness of the fracture surfaces with the formation of elongated platelets, explaining the increase in mechanical properties of the epoxy matrix.

The interpretation of breast magnetic resonance imaging (MRI) in the healthcare field depends on the good knowledge and experience of radiologists. Recent developments in artificial intelligence (AI) have shown advances in the field of radiology. However, the desired levels have not been reached in the field of radiology yet. In this study, a novel model structure is proposed to characterize the diagnostic performance of AI technology for individual breast dynamic contrast material–enhanced (DCE) MRI sequences. In the proposed model structure, Inception-v3, EfficientNet-B3, and DenseNet-201 models were used as hybrids together with the Yolo-v3 algorithm to detect breast and cancer regions. In the proposed model, DCE-MRI sequences (T2, ADC, Diffusion, Non-Contrast Fat Non-Suppressed T1, Non-Contrast Fat Suppressed T1, Contrast Fat Suppressed T1, and Subtraction T1) were evaluated separately and validation was made, thus providing a unique perspective. According to the validation results, the model structure with the best performance was determined as Yolo-v3 + DenseNet-201. With this model structure, 92.41% accuracy, 0.5936 loss, 92.44% sensitivity, and 92.44% specificity rates were obtained. In addition, it was determined that the results obtained without using contrast material in the best model were 91.53% accuracy, 0.9646 loss, 92.19% sensitivity, and 92.19% specificity. Therefore, it is predicted that the need for contrast material use can be reduced with the help of this model structure.