Abstract:
A simple model of random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be both solved analytically and simulated numerically. The analytic solution gives the known Eistein-Smoluchowski diffusion law $ = Dt$ where the diffusion constant $D$ is expressed by the mass and geometry of a particle, the viscosity of a liquid and the average effective time between consecutive collisions of the tracked particle with liquid molecules. The latter allows to make a simulation of the Perrin experiment and verify in detailed study the influence of the statistics on the expected theoretical results. To avoid the problem of small statistics causing departures from the diffusion law we introduce in the second part of the paper the idea of so called Artificially Increased Statistics (AIS) and prove that within this method of experimental data analysis one can confirm the diffusion law and get a good prediction for the diffusion constant even if trajectories of just few particles immersed in a liquid are considered.

Abstract:
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding most intuitive expectations. In particular, the strong qualitative dependence between behaviour of the system, boundary conditions and parameters involved in its description is emphasised. The problem is intended to be discussed in theoretical framework and might be of interest for physics and mechanics students as well as for physics teachers.

Abstract:
We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed. The efficiency and exactness of all three methods towards proper determination of scaling exponent $H$ is discussed, particularly for short series of uncorrelated or persistent data. \end{abstract}

Abstract:
We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of length $L$ of time series and regression line coefficient $R^2$ at various confidence levels. Next, an analysis of artificial short series with long memory is performed. In both cases the scaling range $\lambda$ is found to change linearly -- both with $L$ and $R^2$. We show how this dependence can be generalized to a simple unified model describing the relation $\lambda=\lambda(L, R^2, H)$ where $H$ ($1/2\leq H \leq 1$) stands for the Hurst exponent of long range autocorrelated data. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where enormous number of short time series has to be examined at once, without possibility for preliminary check of the scaling range of each series separately.

Abstract:
We extend our previous study of scaling range properties done for detrended fluctuation analysis (DFA) \cite{former_paper} to other techniques of fluctuation analysis (FA). The new technique called Modified Detrended Moving Average Analysis (MDMA) is introduced and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy $R^2$ of the fit to the considered scaling law imposed by DMA or MDMA schemes. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in e.g., econophysics, finances or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.

Abstract:
Atrophodermia Pasini-Pierini (idiopatyczna progresywna atrophodermia, twardzina zanikowa) jest prawdopodobnie odmian twardziny skórnej ograniczonej. Opisano wiele przypadków wspó istnienia zmian o charakterze atrophodermii z typowymi ogniskami morphea, a tak e przypadki transformacji w kierunku typowej twardziny ograniczonej. Istnieje wiele kontrowersji dotycz cych klasyfikacji i etiologii atrophodermii Pasini-Pierini. Etiologia schorzenia jest nieznana. W niektórych przypadkach o rodzinnym wyst powaniu potwierdzono etiologi genetyczn . Wykazano równie mo liwo istnienia pod o a immunologicznego schorzenia, zaburzeń biochemicznych, zachodz cych w skórze oraz zwi zek z zaka eniem Borrelia burgdorferi. Schorzenie to nierzadko wyst puje u dzieci. Mimo wielu mo liwych sposobów terapii: ogólnych (m.in. PUVA, antybiotyki, tokoferol, piaskledina, penicylina prokainowa, leki immuno-supresyjne), jak i miejscowych (preparaty zmi kczaj ce i kortykosteroidowe) brak jest skutecznej metody leczenia. W pracy opisano przypadek 14-letniej dziewczynki, hospitalizowanej na Oddziale Chorób Skóry Szpitala Wojewódzkiego w Poznaniu z powodu zmian skórnych o charakterze atrophodermia Pasini-Pierini, powoli i systematycznie post puj cych od 3 lat. Zbadano te zwi zek ognisk chorobowych z procesami autoimmunologicznymi i zaka eniem Borrelia burgdorferi.

Abstract:
In humans, the processes of thinking or making decisions are usually based on mental models. Some of these mental models are designed to represent how humans think and decide, while others aim to improve their thinking and decision making. In decision making related to a patient’s health and medical care, high courts aim to protect the patient’s right to be involved in this process, while societal forces attempt to control costs associated with health and medical decision making. This paper examines legal, decision making, and social theories regarding the societal forces that attempt to influence the grounds upon which a patient thinks and decides about his or her health and medical care.

Abstract:
this article is a sort of homage to the literary work of maría salomea wielopolska, author of three works devoted to latin-america. the first section presents the structure and content of the works themselves, foregrounding the author？s erudition as well as her wide knowledge of the nature, history and culture of venezuela, colombia, ecuador and perú. the second part is the etymological, morphological and semantic analysis of the large number of americanisms quoted by wielopolska. the most frequent are those derived from indigenism, but there are cases of mixed indo-spanish lexical items (indigenism with spanish prefixes), or hispanic-indigenous. the semantic changes in the words of a spanish origin are mainly based upon metaphors, permutations, widening or reduction of meaning.

Abstract:
The contribution describes recording of a single dust particle oscillation path inside the electric curtain by a new type of a laser diode apparatus. Visualisation of the particle path trajectory using single pure infrared laser diode, 806 nm, 2 W was analysed. Particle oscillation path was measured from images recorded by CCD monochrome camera. Feasibility of such diode as an efficient light source to illuminate dust particles was verified for experimental investigations in dust technique devices. Particle oscillation paths were recorded throughout changes in the diode beam power and distance. Experimental results were used to determine conditions for the design of a new laser diode apparatus, employing simultaneously several diodes in the laser head. A new type of the laser diode apparatus to record dust trajectory inside electrostatic precipitators and electrostatic separators was developed and tested. A simple high power source of light condensed into a beam proves highly useful in dust technique experiments. Oscillation path and wandering velocity of a single dust particle inside the electric field can be recorded and measured.

Abstract:
We consider an operator $P_N: L_p(I) \to S_n(\Delta_N)$, such that $P_Nf=f$ for $f \in S_n(\Delta_N)$, where $S_n(\Delta_N)$ is the space of splines of degree $n$ with repect to a given partition $\Delta_N$ of the interval $I$. This operator is defined by means of a system of step functions biorthogonal to $B$-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the aproximation of the solution of this equation are given.