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Aim: The aim of our study was to scrutinize diagnostic and treatment factors that may contribute to the low survival rate from anorectal melanoma while adding 17 more cases to the global research database.Method: We carried out a retrospective analysis of 17 cases of anorectal melanoma treated at a single institution from 2000 to 2020. Data on patient age, sex, complaints, treatment and survival as well as tumour size, resection margins, histological and immu-nohistochemical features were assessed.Results: The median age of patients was 72 ± 12.49 (45– 92) years. Most of the patients were women (n = 11, 64.71%). Three (17.65%) patients underwent no radical treatment. Of eight patients treated initially with radical surgery (either total mesorectal excision or abdominoperineal resection), six (75%) were found to have positive lymph nodes. Mean survival was 20 ± 23.46 (1– 84) months. The average diameter of the resected tumours was 5.43 ± 3.02 cm (1.3– 10 cm). Most tumours had epithelioid or spindle cell morphol-ogy and were positive for one or more melanocytic markers (S100, HMB- 45 or MITF). More than half of the tumours contained no or very little melanin pigment. None of the tumours had significant lymphocytic infiltration. Three tumours showed positivity for keratins (PANCK or CAM5.2) and one tumour showed positivity for C- KIT stain.Conclusion: An aggressive surgical approach may have an effect on survival in most early stages while more advanced disease benefits from a more conservative approach. Attention to sentinel lymph nodes and further systemic research into therapy is required. For now, treatment and diagnostic modalities seem to be inconsistent, requiring further investigation to elucidate common points.

This paper focuses on numerical and experimental investigations of a novel design piezoelectric energy harvester. Investigated harvester is based on polygon-shaped cantilever array and employs multifrequency operating principle. It consists of eight cantilevers with irregular design of cross-sectional area. Cantilevers are connected to each other by specific angle to form polygon-shaped structure. Moreover, seven seismic masses with additional lever arms are added in order to create additional rotation moment. Numerical investigation showed that piezoelectric polygon-shaped energy harvester has five natural frequencies in the frequency range from 10 Hz to 240 Hz, where the first and the second bending modes of the cantilevers are dominating. Maximum output voltage density and energy density equal to 50.03 mV/mm3 and 604 μJ/mm3, respectively, were obtained during numerical simulation. Prototype of piezoelectric harvester was made and experimental investigation was performed. Experimental measurements of the electrical characteristics showed that maximum output voltage density, energy density, and output power are 37.5 mV/mm3, 815.16 μJ/mm3, and 65.24 μW, respectively.

In this paper, we derive two strongly consistent Hurst index estimators from the limit behavior of the first-and second-order quadratic variations of the solution of an SDE driven by a fractional Brownian motion. We also show that these estimators retain their properties if the solution is replaced with its Milstein approximation.

In the paper, we present upper bounds of L_p norms Δ_DX,p of order (DX)^-1/2 for all 1≤p≤∞ in the central limit theorem for a standardized random variable [...], where a random variable X is distributed by the Poisson distribution with parameter λ>0 or by the standard gamma distribution Γ(α,0,1) with parameter α>0.

The system of hyperbolic heat conduction problems is solved numerically. The explicit and fully implicit Euler type schemes for the time integration of the nonstationary problem are proposed and investigated. Space derivatives are approximated by using the finite volume method, resulting in conservative and monotonous discrete approximations of the second order of accuracy. The stability analysis is done in the L2 and energy norms for a simplified one-temperature equation and the system of two equations, describing the temperature and the flux. Results of numerical experiments are presented.

We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Qswitching process. We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics. The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that the local stability analysis in the selected neighborhood of the exact solution is sufficient.

We continue our investigations on iterated logarithm laws for additive functions defined on random combinatorial structures called assemblies or abelian partitional structures. Exploiting Feller’s theorem, we obtain sharp upper bounds for a sequence of truncated additive functions. The results imply bounds for the sequence of sizes of components. The main ideas originated from the first author’s number-theoretical papers.

We estimate the difference [...] for bounded functions [...] satisfying the Lipschitz condition, where [...] and [...] with discount factor ν such that 0<ν<1. Here {X_n, n≥0} is a sequence of strongly mixing random variables with EX_n=0, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order O((1−ν)^1/2).

The oxidation of TEMPO (2,2,6,6-tetramethyl-piperidine-1-oxyl radical) has been studied in the presence of recombinant laccases (benzenediol:oxygen oxidoreductase, EC 1.10.3.2) from Polyporus pinsitus (rPpL), Myceliophthora thermophila (rMtL), Coprinus cinereus (rCcL) and Rhizoctonia solani (rRsL) in buffer solution pH 4.5–7.3 and at 25 °C. At pH 5.5 the oxidation constant calculated from the initial rate of TEMPO oxidation was 1.7 × 104, 1.4 × 103, 7.8 × 102 and 5.2 × 102 M−1 s−1 for rPpL, rRsL, rCcL and rMtL, respectively. The maximal activity of rPpL-catalysed TEMPO oxidation was at pH 5.0. The pKa obtained in neutral pH range was 6.2. The reactivity of laccases is in a good agreement with laccases copper type I redox potential. TEMPO oxidation rate increased 541 times in the presence of 10-(3-propylsulfonate) phenoxazine (PSPX). The model of synergistic TEMPO and PSPX oxidation was proposed. Experimentally obtained rate constants for rPpL-catalysed PSPX oxidation were in a good agreement with those calculated from the synergistic model, therefore confirming the feasibility of the model. The acceleration of TEMPO oxidation with high reactive laccase substrates opens new possibilities for TEMPO application as a mediator.