I Have Not Sinned - Tony’s Quest for Wisdom in Bless Me, Ultima by Rudolfo Anaya

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej nauk

Minimal polynomial of an exponential automorphism of C^n

We show that the minimal polynomial of a polynomial exponential automorphism F of C^n (i.e. F=exp(D), where D is a locally nilpotent derivation) is of the form \mu_F(T)=(T-1)^d, d=min{m \in N: D^m(X_i)=0 for i=1,...,n}.Comment: 5 page

Kulturowe uwarunkowania przemocy wobec mniejszości

Autorka swoją pracę poświęciła szerokorozumianemu zjawisku przemocy wobec mniejszości, zarówno w skali globalnej, jak i lokalnej, polskiej. Głównym celem jest uświadomienie, że przemoc jest złożonym zjawiskiem kulturowym i aby je zrozumieć oraz skutecznie przeciw niemu działać, należy pogłębić znajomość uwarunkowań przemocy.Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00

On a Diophantine equation of Erd\H{o}s and Graham

We study solvability of the Diophantine equation \begin{equation*} \frac{n}{2^{n}}=\sum_{i=1}^{k}\frac{a_{i}}{2^{a_{i}}}, \end{equation*} in integers $n, k, a_{1},\ldots, a_{k}$ satisfying the conditions $k\geq 2$ and $a_{i}<a_{i+1}$ for $i=1,\ldots,k-1$. The above Diophantine equation (of polynomial-exponential type) was mentioned in the monograph of Erd\H{o}s and Graham, where several questions were stated. Some of these questions were already answered by Borwein and Loring. We extend their work and investigate other aspects of Erd\H{o}s and Graham equation. First of all, we obtain the upper bound for the value $a_{k}$ given in terms of $k$ only. This mean, that with fixed $k$ our equation has only finitely many solutions in $n, a_{1},\ldots, a_{k}$. Moreover, we construct an infinite set $\cal{K}$, such that for each $k\in\cal{K}$, the considered equation has at least five solutions. As an application of our findings we enumerate all solutions of the equation for $k\leq 8$. Moreover, by applying greedy algorithm, we extend Borwein and Loring calculations and check that for each $n\leq 10^4$ there is a value of $k$ such that the considered equation has a solution in integers $n+1=a_{1}<a_{2}<\ldots <a_{k}$. Based on our numerical calculations we formulate some further questions and conjectures.Comment: 13 pages, to appear in the Journal of Number Theor

On the path sequence of a graph

A subset S of vertices of a graph G = (V;E) is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from S. Denote by k(G) the minimum cardinality of a k-path vertex cover in G and form a sequence (G) = ( 1(G); 2(G); : : : ; jV j(G)), called the path sequence of G. In this paper we prove necessary and sufficient conditions for two integers to appear on fixed positions in (G). A complete list of all possible path sequences (with multiplicities) for small connected graphs is also given

Cultural Particularism and Intercultural Communication: The Case of Chinese Face

In this paper, I argue that the acknowledgement of the particular nature of socio-ethical values and specific modes of communication is a necessary precondition for establishing an effective exchange between members of different cultural circles. For this purposes, I first examine the value of cultural (historical) particularism as a departure from social evolutionism and a unique way of understanding cultures that will serve as a theoretical framework for further deliberation. Following that, I shortly review and evaluate some theories regarding the nature and the functions of the notion of face, that has long been seen as an essential and pervasive element of Chinese culture. Subsequently, I analyse some of the data collected during fieldwork conducted in China and try to show to what degree the phenomenon continues to be present in contemporary Chinese society. In the final section, I argue from a position of cultural particularism that unbiased understanding of cultural characteristics is a sine qua non condition for effective intercultural communication