Strong chromatic index of sparse graphs

A coloring of the edges of a graph $G$ is strong if each color class is an induced matching of $G$. The strong chromatic index of $G$, denoted by $\chi_{s}^{\prime}(G)$, is the least number of colors in a strong edge coloring of $G$. In this note we prove that $\chi_{s}^{\prime}(G)\leq (4k-1)\Delta (G)-k(2k+1)+1$ for every $k$-degenerate graph $G$. This confirms the strong version of conjecture stated recently by Chang and Narayanan [3]. Our approach allows also to improve the upper bound from [3] for chordless graphs. We get that $$ for any chordless graph $G$. Both bounds remain valid for the list version of the strong edge coloring of these graphs

Influence of the Balcony Glazing Construction on Thermal Comfort of Apartments in Retrofitted Large Panel Buildings

AbstractThis paper presents the results of the annual computational simulations conducted for separate flats of a ten-story W70 large-panel building. The calculations were carried out in the Design Builder program which prepares a simulation of the building envelope as well as the separate parts of the building interior. The simulations conducted for the polish climatic conditions allowed the assessment of the thermal comfort of the entire multi-family building and of the particular flats. It is very rare to take into consideration the requirements connected with the overheating effect in the panel buildings. This issue is closely related to the thermal comfort of the building, especially during the summer months. For the last couple of years modernization of large panel buildings has become very popular. Most of the multi-family large panel buildings in Poland have already been insulated, windows were exchanged and in many cases balconies were closed with glazing constructions. Based on conducted simulations authors analyzed the microclimate conditions in different apartments, with different orientation of balconies. Different simulation steps were analyzed which allowed an evaluation of the influence of different windows, loggia glazing framings and night cooling on microclimate in different apartments

Centroidal localization game

One important problem in a network is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations. For instance, the metric dimension of a graph $G$ is the minimum number $k$ of detectors placed in some vertices $\{v_1,\cdots,v_k\}$ such that the vector $(d_1,\cdots,d_k)$ of the distances $d(v_i,r)$ between the detectors and the entity's location $r$ allows to uniquely determine $r \in V(G)$. In a more realistic setting, instead of getting the exact distance information, given devices placed in $\{v_1,\cdots,v_k\}$, we get only relative distances between the entity's location $r$ and the devices (for every $1\leq i,j\leq k$, it is provided whether $d(v_i,r) >$, $<$, or $=$ to $d(v_j,r)$). The centroidal dimension of a graph $G$ is the minimum number of devices required to locate the entity in this setting. We consider the natural generalization of the latter problem, where vertices may be probed sequentially until the moving entity is located. At every turn, a set $\{v_1,\cdots,v_k\}$ of vertices is probed and then the relative distances between the vertices $v_i$ and the current location $r$ of the entity are given. If not located, the moving entity may move along one edge. Let $\zeta^* (G)$ be the minimum $k$ such that the entity is eventually located, whatever it does, in the graph $G$. We prove that $\zeta^* (T)\leq 2$ for every tree $T$ and give an upper bound on $\zeta^*(G\square H)$ in cartesian product of graphs $G$ and $H$. Our main result is that $\zeta^* (G)\leq 3$ for any outerplanar graph $G$. We then prove that $\zeta^* (G)$ is bounded by the pathwidth of $G$ plus 1 and that the optimization problem of determining $\zeta^* (G)$ is NP-hard in general graphs. Finally, we show that approximating (up to any constant distance) the entity's location in the Euclidean plane requires at most two vertices per turn

Localization game on geometric and planar graphs

The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph $G$ we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a pursuit graph game that resembles the famous Cops and Robbers game. It can be considered as a game theoretic variant of the \emph{metric dimension} of a graph. We provide upper bounds on the related graph invariant $\zeta (G)$, defined as the least number of cops needed to localize the robber on a graph $G$, for several classes of graphs (trees, bipartite graphs, etc). Our main result is that, surprisingly, there exists planar graphs of treewidth $2$ and unbounded $\zeta (G)$. On a positive side, we prove that $\zeta (G)$ is bounded by the pathwidth of $G$. We then show that the algorithmic problem of determining $\zeta (G)$ is NP-hard in graphs with diameter at most $2$. Finally, we show that at most one cop can approximate (arbitrary close) the location of the robber in the Euclidean plane

Szkoła wobec wyzwań migracyjnych: uchodźcy w szkole

Opis doświadczeń związanych z aklimatyzacją w szkole edukacja i edukacja dzieci uchodźców i imigrantów w Polsc

The traces of an internal prayer in the personal notes of John Paul II (Karol Wojtyła)

Przedmiotem analiz autorki są modlitewne rozważania Karola Wojtyły – Jana Pawła II zawarte w zbiorze: Jestem bardzo w rękach Bożych. Notatki osobiste 1962–2003. Badane są te fragmenty tekstu, w których nadawca jest tożsamy z odbiorcą, a modlitewne akty o charakterze wewnętrznym – medytacje, kontemplacje i adoracje – tworzą jeden z składników dnia skupienia lub rekolekcji pojmowanych jako makrogatunek (gatunek w formie kolekcji). Ujęzykowione modlitwy wewnętrzne pozwalają na ich ogląd zarówno w aspekcie genologicznym, jak i pod kątem cech stylowych. W rekolekcyjnych rozmyślaniach Karola Wojtyły uwidocznione zostają takie wykładniki stylu religijnego, jak: symboliczne widzenie świata, dążenie do odsłonięcia tego, co trudno wyrażalne w języku dyskursywnym i niedostępne w doświadczeniu potocznym, kontemplacyjna postawa wobec rzeczywistości oraz stylistycznie rozumiana kategoria medytacyjności.The author analyses meditative reflections by Karol Wojtyła – John Paul II, collected in a volume entitled I Am so Much in God’s Hands. Personal Notes, 1962–2003 (Krakow 2014). The author examines the fragments of the text in which the speaker is identical with the addressee, and where internal prayer acts: meditations, contemplations and adorations. They are components of a reflection day or a religious retreat defined as a macro-genre (a collective genre). When expressed through language, internal prayers can be viewed in their text-typological and stylistic aspects. Karol Wojtyła’s retreat-related meditations reflect exponents of the religious style including a symbolic vision of the world, an attempt to unveil the reality that is hard to depict through discursive language and unreachable to common experience, a contemplative attitude towards reality and a stylistic understanding of the category of meditation

Sataniczność kreacji bohatera w Arabie Juliusza Słowackiego

This article attempts to read Juliusz Słowacki’s Arab from the comparative perspective of John Milton’s Paradise Lost. The protagonist of Słowacki’s oriental tale, who is a variation on the Byronic hero, also shows similarities with Milton’s Satan: unceasing motion, obsession of revenge, loneliness, axiological preference of evil. The analysis of those similarities creates a new interpretative context for Arab, which was hitherto regarded as a superficial study of the pathological psyche or a caricature of the Byronic model.This article attempts to read Juliusz Słowacki’s Arab from the comparative perspective of John Milton’s Paradise Lost. The protagonist of Słowacki’s oriental tale, who is a variation on the Byronic hero, also shows similarities with Milton’s Satan: unceasing motion, obsession of revenge, loneliness, axiological preference of evil. The analysis of those similarities creates a new interpretative context for Arab, which was hitherto regarded as a superficial study of the pathological psyche or a caricature of the Byronic model

Nowina wspaniała… Boguryma Polskiego na tle tradycji — skrzydlate frazy biblijne

This study focuses on a rhymed adaptation of the four gospels, Jezusa Chrystusa Zbawiennego Pana Nowina Wspaniała wierszem rozgłaszana [Jesus Christ the Saviour and the Lord’s Gospel Most Magnificent in verse], published in Krakow in 2017 by Antoni Gazda under the pseudonym of Bogurym Polski. Subject to discussion are selected conventionalized constructions representing quotation variants: continuous linguistic units and textual sequences of different text genre status (biblicisms in the broader sense), established in the Polish language and disseminated in social discourse, e.g. like sheep without a shepherd; the harvest is plentiful, but the labourers are few; no one can serve two masters; you cannot serve God and mammon; friend, go up higher; come to me, all you who labour and are heavy laden, and I will give you rest; learn from me; for I am gentle and lowly in heart; my yoke is easy and my burden is light; for all things are possible with God; by their fruits you shall know them; in my Father’s house are many rooms; even now the axe is laid to the root of the trees. The biblical phraseology treated as one of the basic exponents of the Polish biblical style in Bogurym Polski’s work is preserved on a general scale, which can be interpreted as a general indication of compliance with the hieratic translation tradition. Individual modifications of biblicisms are those necessitated by the poetic form of the work. The basic types of change are addition of component(s) and changes in word order

Angielskie strofy i polska lutnia. O przekładach „Melodii hebrajskich” George’a Gordona Byrona pióra Antoniego Edwarda Odyńca

The article discusses the translation of four poems by George Gordon Byron: Vision of Belshezzar, The Wild Gazelle, Oh! Weep for Those, On Jordan’s Banks from the collection Hebrew Melodies published in 1816 as a result of the poet’s cooperation with the composer Isaac Nathan. The Polish translations by Antoni Edward Odyniec were published in his collections in 1826 (Vision of Belshezzar) and 1832 (the remaining ones). The first part of the text is dedicated to the circumstances in which the originals were written. The second part constitutes a detailed analysis of the translation choices of Odyniec, which places them in the context of Polish poetry of the post-partitions period (among others, poems by Jan Paweł Woronicz and Adam Jerzy Czartoryski) and in the context of translation studies (Lawrence Venuti, Stanisław Barańczak, André Lefevere)