The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses

This survey may be seen as an introduction to the use of toric and tropical geometry in the analysis of plane curve singularities, which are germs $(C,o)$ of complex analytic curves contained in a smooth complex analytic surface $S$. The embedded topological type of such a pair $(S, C)$ is usually defined to be that of the oriented link obtained by intersecting $C$ with a sufficiently small oriented Euclidean sphere centered at the point $o$, defined once a system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one works more generally over an arbitrary algebraically closed field of characteristic zero, one speaks instead of the combinatorial type of $(S, C)$. One may define it by looking either at the Newton-Puiseux series associated to $C$ relative to a generic local coordinate system $(x,y)$, or at the set of infinitely near points which have to be blown up in order to get the minimal embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this germ by the resolution. Each point of view leads to a different encoding of the combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques diagram, or a weighted dual graph. The three trees contain the same information, which in the complex setting is equivalent to the knowledge of the embedded topological type. There are known algorithms for transforming one tree into another. In this paper we explain how a special type of two-dimensional simplicial complex called a lotus allows to think geometrically about the relations between the three types of trees. Namely, all of them embed in a natural lotus, their numerical decorations appearing as invariants of it. This lotus is constructed from the finite set of Newton polygons created during any process of resolution of $(C,o)$ by successive toric modifications.Comment: 104 pages, 58 figures. Compared to the previous version, section 2 is new. The historical information, contained before in subsection 6.2, is distributed now throughout the paper in the subsections called "Historical comments''. More details are also added at various places of the paper. To appear in the Handbook of Geometry and Topology of Singularities I, Springer, 202

We are looking for new opportunities for use of pre-stressed structures

Wywiad z dr. inż. Piotrem Gwoździewiczem, pracownikiem naukowym w Zakładzie Konstrukcji Sprężonych Politechniki Krakowskiej, prezesem zarządu ASIS Sp. z o.o.Mariusz Karpiński-Rzepa and Joanna Miciak talk to Piotr Gwoździewicz, Ph.D., Eng., researcher in the Department of Pre-Stressed Constructions of Cracow University of technology

Prestressed structures. Part 2. Prestressing force

Pierwsza część artykułu – Konstrukcje sprężone. Materiały i wykonanie prac – została opublikowana w poprzednim numerze „Nowoczesnego Budownictwa Inżynieryjnego” [2014, nr 5 (56), s. 58–63]. Poza obszernie zreferowanymi i bogato zilustrowanymi zagadnieniami tytułowymi opisano w nim m.in. koncepcję i historię sprężania, czyli celowego wprowadzania naprężeń w materiał, a także rodzaje badań wykonanych konstrukcji. W tej części autor przedstawia metody obliczenia siły sprężającej.The first part of the article "Prestressed structures. Materials and work" was published in the previous issue of NBI [2014, 5 [56], pp. 58-63]. In addition to extensively described and well-illustrated prestressing issues, it also described the concept and history of prestressing, that is intentional introduction of stresses in the material, as well as the types of tests on structures built. In this part, the author presents the methods for calculating prestressing force

Prestressed concrete structures KS2015

16 i 17 kwietnia 2015 r. w Krakowie miały miejsce obrady Konferencji Naukowo-Technicznej Konstrukcje sprężone KS2015. Rozpoczęty trzy lata wcześniej cykl konferencji poświęconych tematyce tej technologii okazał się bardzo potrzebny i zgromadził wielu specjalistów

Prestressed structures. Part 3. Ultimate limit states in prestressed sections

Po omówieniu koncepcji sprężania konstrukcji w pierwszej części opracowania („Nowoczesne Budownictwo Inżynieryjne” 2014, nr 5 [56], s. 58–63) oraz przedstawieniu metod obliczania siły sprężającej w drugiej części („Nowoczesne Budownictwo Inżynieryjne” 2014, nr 6 [57], s. 90–95) w niniejszej części autor opisuje metody obliczania stanów granicznych nośności. Weryfikacja warunków nośności jest warunkiem niezbędnym w projektowaniu elementów konstrukcyjnych z betonu.Having discussed the concept of structure pre-stressing in the first part of the paper (NBI 2014, issue 5 [56], p. 58-63] and having presented methods for calculation of prestressing force in the second part [NBI 2014, issue 6 [57], p. 90-95], the Author in present part describes methods for calculating ultimate limit states. Verification of conditions for load-bearing capacity is a prerequisite in the design of concrete structural elements

Prestressed structures. Part 1. Materials and work

The history of pre-stressing, or intentional introduction of stresses in the material, has many centuries. Today we rarely talk about the fact that a bicycle wheel, oak barrel or stone arch are examples of pre-stressed elements (the latter only as a result of the weight of the material). In civil engineering, the term of prestressing refers to building structures. For the pre-stressing of structural elements primarily steel tensile elements are used (prestressing steel in the form of wires, strands and bars) with strength ranging between 1000 and 2000 MPa

Prestressed structures. Part 4. Serviceability limit states in prestressed elements

Metoda stanów granicznych (SG) w postaci opisanej w normie Eurokod 2 (PN-EN 1992-1-1, [1]), poza omówioną wcześniej grupą stanów granicznych nośności elementów sprężonych („Nowoczesne Budownictwo Inżynieryjne” 2015, nr 1 [58], s. 64–69), wymaga od projektanta sformułowania, a następnie sprawdzenia warunków stanów granicznych użytkowalności (SGU). Warunki te dotyczą cech użytkowych konstrukcji, jej trwałości, estetyki oraz sprawdzenia zgodności przyjętych założeń obliczeniowych z rzeczywistą pracą elementów.The limit state method as described in Eurocode 2 (PN-EN 1992-1-1, [1]), in addition to the previously discussed group of ultimate limit states of prestressed elements (NBI 2015, issue 1 [58], pp. 64-69) requires from a designer to formulate and then check the serviceability limit state conditions. These conditions relate to the functional characteristics of the structure, its durability, aesthetics and checks of the compatibility of the design calculation assumptions with actual work of the elements

Wielopierścieniowe węglowodory aromatyczne (WWA) w wodach opadowych i powierzchniowych w rejonie zakładów koksowniczych w Dąbrowie Górniczej (woj. śląskie)

The paper presents the results of five PAHs contents determination in the surface and gravity-operated water. The samples of gravity-operated water were taken quarterly in 2009 from collectors put in fifteen points in areas located nearby coking plant in Dąbrowa Górnicza (Upper Silesia region, Poland). The results allowed determining the seasonal variability of PAHs concentration in gravity-operated water. Significant differences in concentration of PAHs in the summer and wintertime were observed. Moreover, to check the presence of PAHs contamination in the surface flowing water from selected streams, watercourses and draining system were collected.W pracy przedstawiono wyniki badań zawartości pięciu WWA w próbkach wód opadowych i powierzchniowych. Próbki wód opadowych pobierano kwartalnie w 2009 roku z 15 kolektorów umieszczonych na terenach zlokalizowanych w pobliżu zakładów koksowniczych w Dąbrowie Górniczej (woj. śląskie). Uzyskane wyniki pozwoliły określić zmienność sezonową stężeń WWA w wodach opadowych. Wyraźnie podwyższone stężenia WWA zaobserwowano w sezonie zimowym. Ponadto, w celu sprawdzenia obecności zanieczyszczeń WWA w wodach powierzchniowych, przebadano próbki wód (płynących) powierzchniowych pobranych z wybranych potoków, cieków wodnych oraz rowów melioracyjnych

High efficiency single-phase line start PMSM with number of poles 2p= 4 – experimental results

The paper presents a comparison of selected running properties of a prototype, single-phase synchronous motor with permanent magnets with a corresponding induction motor (the same dimensions and the same number of poles). In experimental studies performed on a specially adapted test bench the mechanical construction of the stator of the series production motor was used

Migration of total petroleum hydrocarbon (TPH) contaminations at boundary of aeration and saturation zones in sandy soils

The paper presents studies results of total petroleum hydrocarbon (TPH) contaminations migration in sandy formations on the post-industrial area in Katowice in aspect their horizontal migration between aeration and saturation zones. In all investigated soil samples were determined mineral oils (>C12), gasoline (C6-C12) and polycyclic aromatic hydrocarbons (PAH) content and were also defined coefficient of filtration. Both mineral oils and gasoline belongs to organic liquids group lighter than water. Researches were supplemented with simulation of ground and underground water contamination state, round investigated area and also migration of petroleum hydrocarbon (TPH) contaminations model in examined grounds. The correlation between seasonal position of underground water level and total petroleum hydrocarbon (TPH) contaminations content in ground vertical profile was also showed. Besides variations of filtration rate in relation to petroleum hydrocarbon (TPH), light non-aqueous phase liquids (LNAPL) contaminations content was presented, as well