Der Gleason-Score ist ein wichtiges Kriterium für die prognostische Einteilung des Prostatakarzinoms und sollte auch am positiven Resektionsrand bestimmt werden. Es wurden 1 836 Prostatakarzinomfälle aus den Jahren 2006-2010 analysiert. Dabei wurden Anzahl sowie Lokalisation der R1-Resektionen; der Gleason-Score und die Länge (mm) des positiven Resektionsrand bestimmt. Danach wurden Unterschiede zwischen R0- und R1-resezierten Patienten; Unterschiede innerhalb der R1-Kohorte und die Länge des positiven Resektionsrands ausgewertet. Es erfolgte eine statistisch-explorative Analyse der Überlebenszeit der R1-Kohorte und der Einfluss der klinisch-pathologischen Variablen (Alter, PSA, pT-, pN-Kategorie, EPE, Gleason-Score im Tumor, Gleason-Score am Resektionsrand, Länge des Resektionsrand, Operationsmodus) auf die Prognose des Prostatakarzinoms. Alle Einteilungen wurden anhand der TNM-Klassifikation 7. Auflage, (UICC), Gleason-Grading-System Revision 2015 (ISUP) und dem prognostischen Gruppierungssystem der ISUP 2015 vorgenommen. Nach radikaler Prostatektomie zeigten 242 (13,2 %) Patienten eine R1-Resektion und 166 (9 %) ein biochemisches Rezidiv. Es zeigte sich, dass in der R1-Kohorte gegenüber der R0-Kohorte mehr pT3-/pT3b-/pT4-Kategorien, mehr positive Lymphknoten, Infiltrationen der Perineuralscheiden und Venen, EPE und Samenblaseninfiltrationen auftraten ( p <0,001). In der R0-Kohorte häuften sich die Gleason-Scores 6 und 7a (25,4 % | 47,5 %), in der R1-Kohorte dagegen die Werte 8 und 9-10 (28,5 % | 17,8 %). Von 242 positiven Resektionsrändern unterschieden sich 147 (60,74 %) in ihrem Gleason-Score vom Gleason-Score des Tumors, 103 (42,56 %) hatten einen niedrigeren und 44 (18,18 %) einen höheren Gleason-Score am Resektionsrand. Die Analyse der R1-Kohorte mittels der ISUP-Grade zeigte, dass in Präparaten mit Gleason-Score von 6 und 7a mehr pT2c- und pT3a-Kategorien vorhanden waren, dagegen in solchen mit Gleason-Score 7b, 8 und 9-10 ein Anstieg von pT3b- und pT4-Kategorien zu verzeichnen war. Mit steigendem ISUP-Grad kam es zum Anstieg der pN-Kategorie, der EPE und der Infiltrationen der Samenblase sowie der Anzahl und medianen Länge der positiven Resektionsränder. Nach Kaplan-Meier wurde der Einfluss der o.g. Variablen auf die Überlebenszeit bis zum biochemischen Rezidiv überprüft. Die roboterassistierten Prostatektomien zeigten mit (82 Mon. | CI 70-96) im Vergleich mit den retropubischen (72 Mon. | CI 68–76) und laparoskopischen (53 Mon. | CI 39–67) die höchste Überlebensrate. Nach 85 Mon. hatten 70 % der R1-Resezierten ein Rezidiv vs. 30 % R0-Resezierter. Überraschend ergab sich innerhalb der R1-Kohorte eine prognostisch „gute“ Gruppe aus Gleason-Score 6 und 7a mit Überlebenszeiten von (72 Mon. | (CI 50–95) || 49 Mon.|(CI 30–69)). Die prognostisch „schlechte“ Gruppe bildeten Gleason-Score 7b, 8, 9-10 (27 Mon. | (CI 16–38), 25 Mon. | (CI 14–36) & 24 Mon. | (CI 11–36)). Patienten mit Gleason-Score ≤6 und 7a am Resektionsrand zeigten (53 bzw. 51 Mon. | CI 50–95) im Vergleich zu Gleason-Score 7b, 8 und 9-10 (25; 24 bzw. 26 Mon.|CI 15–36) rezidivfreies Überleben. Patienten mit Gleason-Score 6 zeigten bei R0- (82 Mon. | CI 78–98) und R1-Resektion (72 Mon | CI 51–94) nur einen geringen Unterschied. Positive Resektionsränder ≤3mm vs. ≥3mm zeigten wie nur ein positiver Resektionsrand vs. multiple positive Resektionsränder ein längeres Überleben. Mittels Cox-Regression wurden die o.g. Variablen auf ihr Risiko für die Entstehung eines biochemischen Rezidivs überprüft. In der univariaten Analyse ergaben sich hohe Risiken für die Gleason-Scores 7b, 8 & 9-10 am positiven Resektionsrand (HR 2,5 bis HR 2,3) und für multiple positive Resektionsränder (HR 2,1). Die multivariate Cox-Regression mit Basis pT-Kategorie ergab eine Steigerung des Risikos für ein Rezidiv durch die Gleason-Scores am Resektionsrand 7b und 8 (HR 1,8) sowie für den positiven Resektionsrand ≥3mm (HR 1,4). Wurde der Gleason-Score des Tumors als Basis genutzt, so erhöhte sich das Risiko für ein Rezidiv durch den Gleason-Score des Resektionsrands 9-10 (HR 1,8), den positiven Resektionsrand ≥3mm (HR 1,4) und multiple positive Resektionsränder (HR 1,4). Auf Basis dieser Ergebnisse ist die Bestimmung des Gleason-Scores am Resektionsrand sowie der Länge und Anzahl der positiven Resektionsränder nach R1-Resektionen erforderlich, um eine bessere Risikostratifizierung durchführen und so die angemessene Therapie auswählen zu können.:Inhaltsverzeichnis Abkürzungsverzeichnis Tabellenverzeichnis Abbildungsverzeichnis 1. Einführung 1.1 Klassifikation 1.1.1 TNM-Klassifikation 1.1.2 Gleason-Score 1.2 Forschungsstand zu positiven Resektionsrändern 1.2.1 Forschungsstand zum Gleason-Score am Resektionsrand 1.2.2 Forschungsstand zur Länge des positiven Resektionsrand 2. Ziele der Arbeit 3. Materialien und Methoden 3.1 Studienpopulation 3.2 Vorgehen der Erhebung 3.2.1 Bestimmung des Gleason-Scores am Resektionsrand 3.2.2 Bestimmung der Länge des positiven Resektionsrands 3.3 Pathologische Klassifikationen 3.4 Geräte 3.5 Statistische Methoden 4. Ergebnisse 4.1 Analyse der klinisch-pathologischen Kriterien für Grundgesamtheit, R1- und R0-Kohorte 4.1.1 Subgruppenanalyse der R1-Kohorte nach ISUP-Graden 4.2 Korrelationsanalyse von Gleason-Score und Länge des positiven Resektionsrandes 4.3 Überlebenszeitanalyse der Grundgesamtheit 4.3.1 Überlebenszeitanalyse der R1-Kohorte unter Gruppierung klinisch-pathologischer Variable 4.4 Hazard Ratios der klinisch-pathologischen Variablen 5. Diskussion 5.1 Limitationen 6. Zusammenfassung 7. Literaturverzeichnis Anhang Lebenslauf Danksagung Eigenständigkeitserklärung

Als Ergänzung für die Lehrbriefe des Instituts für Massivbau der TU Dresden zu den Grundlagen des Stahlbetons (Teil 1 und 3 sowie Übungen Teil 1 bis 3) werden hier Bilder von Versuchsreihen vorgestellt, die am Lehrstuhl für Stahlbeton, Spannbeton und Massivbrücken der TH/TU Dresden, aus dem das heutige Institut für Massivbau hervorging, innerhalb verschiedener Forschungsarbeiten von 1956 bis 1965 entstanden. Neben dem Einblick in die damaligen Arbeitsweisen und Möglichkeiten sind vor allem die zahlreichen Bruchbilder geeignet, sich in das Tragverhalten des Stahlbetons hineinzudenken. Diese Überlegungen gaben den Ausschlag dafür, das vorhandene Bildmaterial noch einmal zu ordnen und mit kurzen Erläuterungen zu versehen, um es so nochmals für Lehre und Forschung nutzbar zu machen.

This work refers to ball-intersections bodies as well as covering, packing, and kissing problems related to balls and spheres in normed spaces. A quick introduction to these topics and an overview of our results is given in Section 1.1 of Chapter 1. The needed background knowledge is collected in Section 1.2, also in Chapter 1. In Chapter 2 we define ball-intersection bodies and investigate special classes of them: ball-hulls, ball-intersections, equilateral ball-polyhedra, complete bodies and bodies of constant width. Thus, relations between the ball-hull and the ball-intersection of a set are given. We extend a minimal property of a special class of equilateral ball-polyhedra, known as Theorem of Chakerian, to all normed planes. In order to investigate bodies of constant width, we develop a concept of affine orthogonality, which is new even for the Euclidean subcase. In Chapter 2 we solve kissing, covering, and packing problems. For a given family of circles and lines we find at least one, but for some families even all circles kissing all the members of this family. For that reason we prove that a strictly convex, smooth normed plane is a topological Möbius plane. We give an exact geometric description of the maximal radius of all homothets of the unit disc that can be covered by 3 or 4 translates of it. Also we investigate configurations related to such coverings, namely a regular 4-covering and a Miquelian configuration of circles. We find the concealment number for a packing of translates of the unit ball.

We present several possible forms of mathematical competitions for University students. One of them is Blitz Mathematical Olympiad. It is a team competition, when all teams receive the same problem and are allotted 10-15 minutes to come up with a solution. This cycle is repeated 6-8 times with different problems. Modern Internet technologies allow us to organize Blitz Mathematical Olympiads for the teams which are in different cities and even countries.

Als Ergänzung für die Lehrbriefe des Instituts für Massivbau der TU Dresden zu den Grundlagen des Stahlbetons (Teil 1 und 3 sowie Übungen Teil 1 bis 3) werden hier Bilder von Versuchsreihen vorgestellt, die am Lehrstuhl für Stahlbeton, Spannbeton und Massivbrücken der TH/TU Dresden, aus dem das heutige Institut für Massivbau hervorging, innerhalb verschiedener Forschungsarbeiten von 1956 bis 1965 entstanden. Neben dem Einblick in die damaligen Arbeitsweisen und Möglichkeiten sind vor allem die zahlreichen Bruchbilder geeignet, sich in das Tragverhalten des Stahlbetons hineinzudenken. Diese Überlegungen gaben den Ausschlag dafür, das vorhandene Bildmaterial noch einmal zu ordnen und mit kurzen Erläuterungen zu versehen, um es so nochmals für Lehre und Forschung nutzbar zu machen.

We present several possible forms of mathematical competitions for University students. One of them is Blitz Mathematical Olympiad. It is a team competition, when all teams receive the same problem and are allotted 10-15 minutes to come up with a solution. This cycle is repeated 6-8 times with different problems. Modern Internet technologies allow us to organize Blitz Mathematical Olympiads for the teams which are in different cities and even countries.

This work refers to ball-intersections bodies as well as covering, packing, and kissing problems related to balls and spheres in normed spaces. A quick introduction to these topics and an overview of our results is given in Section 1.1 of Chapter 1. The needed background knowledge is collected in Section 1.2, also in Chapter 1. In Chapter 2 we define ball-intersection bodies and investigate special classes of them: ball-hulls, ball-intersections, equilateral ball-polyhedra, complete bodies and bodies of constant width. Thus, relations between the ball-hull and the ball-intersection of a set are given. We extend a minimal property of a special class of equilateral ball-polyhedra, known as Theorem of Chakerian, to all normed planes. In order to investigate bodies of constant width, we develop a concept of affine orthogonality, which is new even for the Euclidean subcase. In Chapter 2 we solve kissing, covering, and packing problems. For a given family of circles and lines we find at least one, but for some families even all circles kissing all the members of this family. For that reason we prove that a strictly convex, smooth normed plane is a topological Möbius plane. We give an exact geometric description of the maximal radius of all homothets of the unit disc that can be covered by 3 or 4 translates of it. Also we investigate configurations related to such coverings, namely a regular 4-covering and a Miquelian configuration of circles. We find the concealment number for a packing of translates of the unit ball.

We prove that there exist three distinct, comprehensive classes of (formal) contexts with polynomially many concepts. Namely: contexts which are nowhere dense, of bounded breadth or highly convex. Already present in G. Birkhoff's classic monograph is the notion of breadth of a lattice; it equals the number of atoms of a largest boolean suborder. Even though it is natural to define the breadth of a context as being that of its concept lattice, this idea had not been exploited before. We do this and establish many equivalences. Amongst them, it is shown that the breadth of a context equals the size of its largest minimal generator, its largest contranominal-scale subcontext, as well as the Vapnik-Chervonenkis dimension of both its system of extents and of intents. The polynomiality of the aforementioned classes is proven via upper bounds (also known as majorants) for the number of maximal bipartite cliques in bipartite graphs. These are results obtained by various authors in the last decades. The fact that they yield statements about formal contexts is a reward for investigating how two established fields interact, specifically Formal Concept Analysis (FCA) and graph theory. We improve considerably the breadth bound. Such improvement is twofold: besides giving a much tighter expression, we prove that it limits the number of minimal generators. This is strictly more general than upper bounding the quantity of concepts. Indeed, it automatically implies a bound on these, as well as on the number of proper premises. A corollary is that this improved result is a bound for the number of implications in the canonical basis too. With respect to the quantity of concepts, this sharper majorant is shown to be best possible. Such fact is established by constructing contexts whose concept lattices exhibit exactly that many elements. These structures are termed, respectively, extremal contexts and extremal lattices. The usual procedure of taking the standard context allows one to work interchangeably with either one of these two extremal structures. Extremal lattices are equivalently defined as finite lattices which have as many elements as possible, under the condition that they obey two upper limits: one for its number of join-irreducibles, other for its breadth. Subsequently, these structures are characterized in two ways. Our first characterization is done using the lattice perspective. Initially, we construct extremal lattices by the iterated operation of finding smaller, extremal subsemilattices and duplicating their elements. Then, it is shown that every extremal lattice must be obtained through a recursive application of this construction principle. A byproduct of this contribution is that extremal lattices are always meet-distributive. Despite the fact that this approach is revealing, the vicinity of its findings contains unanswered combinatorial questions which are relevant. Most notably, the number of meet-irreducibles of extremal lattices escapes from control when this construction is conducted. Aiming to get a grip on the number of meet-irreducibles, we succeed at proving an alternative characterization of these structures. This second approach is based on implication logic, and exposes an interesting link between number of proper premises, pseudo-extents and concepts. A guiding idea in this scenario is to use implications to construct lattices. It turns out that constructing extremal structures with this method is simpler, in the sense that a recursive application of the construction principle is not needed. Moreover, we obtain with ease a general, explicit formula for the Whitney numbers of extremal lattices. This reveals that they are unimodal, too. Like the first, this second construction method is shown to be characteristic. A particular case of the construction is able to force - with precision - a high number of (in the sense of "exponentially many'') meet-irreducibles. Such occasional explosion of meet-irreducibles motivates a generalization of the notion of extremal lattices. This is done by means of considering a more refined partition of the class of all finite lattices. In this finer-grained setting, each extremal class consists of lattices with bounded breadth, number of join irreducibles and meet-irreducibles as well. The generalized problem of finding the maximum number of concepts reveals itself to be challenging. Instead of attempting to classify these structures completely, we pose questions inspired by Turán's seminal result in extremal combinatorics. Most prominently: do extremal lattices (in this more general sense) have the maximum permitted breadth? We show a general statement in this setting: for every choice of limits (breadth, number of join-irreducibles and meet-irreducibles), we produce some extremal lattice with the maximum permitted breadth. The tools which underpin all the intuitions in this scenario are hypergraphs and exact set covers. In a rather unexpected, but interesting turn of events, we obtain for free a simple and interesting theorem about the general existence of "rich'' subcontexts. Precisely: every context contains an object/attribute pair which, after removed, results in a context with at least half the original number of concepts.

We prove that there exist three distinct, comprehensive classes of (formal) contexts with polynomially many concepts. Namely: contexts which are nowhere dense, of bounded breadth or highly convex. Already present in G. Birkhoff's classic monograph is the notion of breadth of a lattice; it equals the number of atoms of a largest boolean suborder. Even though it is natural to define the breadth of a context as being that of its concept lattice, this idea had not been exploited before. We do this and establish many equivalences. Amongst them, it is shown that the breadth of a context equals the size of its largest minimal generator, its largest contranominal-scale subcontext, as well as the Vapnik-Chervonenkis dimension of both its system of extents and of intents. The polynomiality of the aforementioned classes is proven via upper bounds (also known as majorants) for the number of maximal bipartite cliques in bipartite graphs. These are results obtained by various authors in the last decades. The fact that they yield statements about formal contexts is a reward for investigating how two established fields interact, specifically Formal Concept Analysis (FCA) and graph theory. We improve considerably the breadth bound. Such improvement is twofold: besides giving a much tighter expression, we prove that it limits the number of minimal generators. This is strictly more general than upper bounding the quantity of concepts. Indeed, it automatically implies a bound on these, as well as on the number of proper premises. A corollary is that this improved result is a bound for the number of implications in the canonical basis too. With respect to the quantity of concepts, this sharper majorant is shown to be best possible. Such fact is established by constructing contexts whose concept lattices exhibit exactly that many elements. These structures are termed, respectively, extremal contexts and extremal lattices. The usual procedure of taking the standard context allows one to work interchangeably with either one of these two extremal structures. Extremal lattices are equivalently defined as finite lattices which have as many elements as possible, under the condition that they obey two upper limits: one for its number of join-irreducibles, other for its breadth. Subsequently, these structures are characterized in two ways. Our first characterization is done using the lattice perspective. Initially, we construct extremal lattices by the iterated operation of finding smaller, extremal subsemilattices and duplicating their elements. Then, it is shown that every extremal lattice must be obtained through a recursive application of this construction principle. A byproduct of this contribution is that extremal lattices are always meet-distributive. Despite the fact that this approach is revealing, the vicinity of its findings contains unanswered combinatorial questions which are relevant. Most notably, the number of meet-irreducibles of extremal lattices escapes from control when this construction is conducted. Aiming to get a grip on the number of meet-irreducibles, we succeed at proving an alternative characterization of these structures. This second approach is based on implication logic, and exposes an interesting link between number of proper premises, pseudo-extents and concepts. A guiding idea in this scenario is to use implications to construct lattices. It turns out that constructing extremal structures with this method is simpler, in the sense that a recursive application of the construction principle is not needed. Moreover, we obtain with ease a general, explicit formula for the Whitney numbers of extremal lattices. This reveals that they are unimodal, too. Like the first, this second construction method is shown to be characteristic. A particular case of the construction is able to force - with precision - a high number of (in the sense of "exponentially many'') meet-irreducibles. Such occasional explosion of meet-irreducibles motivates a generalization of the notion of extremal lattices. This is done by means of considering a more refined partition of the class of all finite lattices. In this finer-grained setting, each extremal class consists of lattices with bounded breadth, number of join irreducibles and meet-irreducibles as well. The generalized problem of finding the maximum number of concepts reveals itself to be challenging. Instead of attempting to classify these structures completely, we pose questions inspired by Turán's seminal result in extremal combinatorics. Most prominently: do extremal lattices (in this more general sense) have the maximum permitted breadth? We show a general statement in this setting: for every choice of limits (breadth, number of join-irreducibles and meet-irreducibles), we produce some extremal lattice with the maximum permitted breadth. The tools which underpin all the intuitions in this scenario are hypergraphs and exact set covers. In a rather unexpected, but interesting turn of events, we obtain for free a simple and interesting theorem about the general existence of "rich'' subcontexts. Precisely: every context contains an object/attribute pair which, after removed, results in a context with at least half the original number of concepts.