Die vorliegende Arbeit befasst sich mit Untersuchungen zur Komplexbildung von Cu2+, Zn2+, sowie Sn2+ und B(OMe)3 mit den Schiff-Basen aus 3-Aminopropyl-triethoxysilan (APTES) und 3-(2-Aminoethyl-amino)-propyl-trimethoxysilan (AEPTMS) mit α-Hydroxybenzocarbonylverbindungen. Die Liganden und die Komplexe wurden mit IR-, UV/VIS- und NMR-Spektroskopie charakterisiert. IR-Untersuchungen zeigen die charakteristischen C=N- und C=O-Valenzschwingungen. Sie werden durch die Komplexbildung deutlich verschoben. Die 1H- und 13C-NMR-Messungen indizieren die Komplexbildung mit einer signifikanten Verschiebung in den Signallagen der H- und C-Nachbaratome der Donatoratome. 29Si-NMR-Messungen indizieren keine Hydrolyse- und Kondensationsreaktionen im Verlauf der Synthese. Bei der Komplex-Synthese mit wasserhaltigen Übergangsmetallsalzen wurden Produkte von Sol-Gel-Prozessen gefunden. UV/VIS-spektroskopische Untersuchungen an den Mischungen der Übergangsmetallsalze mit APTES bzw. AEPTMS zeigen die Bildung typischer Aminkomplexe.

In this study a series of novel Fe-based materials derived from a bulk metallic glass-forming composition was investigated to improve the ductility of this high-strength glassy alloy. The interplay between the factors chemistry, structure and resulting mechanical properties was analyzed in detail. It has been recognized that subtle modifications of the chemical composition (carbon addition) lead to appreciable changes in the phase formation, which occurs upon solidification (from a single-phase structure to composite materials). As a consequence, significant differences in the mechanical response of the particular samples have been observed. The materials developed here were fabricated by centrifugal casting. To explore the structure features of the as-cast cylinders, manifold experimental techniques (X-ray diffraction, optical, as well as electron microscopy) were employed. The occurrence of the numerous reflections on the X-ray diffraction patterns has confirmed the crystalline nature of the studied Fe-based alloy systems. The subsequent extensive research on their deformation behavior (Vickers hardness and room temperature compression tests) has revealed that, although the glass-forming ability of the investigated compositions is not high enough to obtain a glassy phase as a product of casting, excellent mechanical characteristics (high strength - comparable to that of the reference bulk metallic glass (BMG) - associated with good ductility) were achieved for the “composite-like” alloys. In contrast, the single phase cylinders, subjected to compressive loading, manifested an amazing capacity for plastic deformation – no failure occurred. The fracture motives developed during deformation of the “composite-structured” samples were studied by scanning electron microscopy. The main emphasis has been put on understanding the mechanisms of crack propagation. Owing to the structural complexity of the deformed samples, it was crucial to elucidate the properties of the individual compounds. Based on the obtained results it was concluded that the coexistence of a soft f.c.c. γ-Fe phase in combination with a hard complex matrix is responsible for the outstanding mechanical response of the tested composites. While the soft particles of an austenite contribute to the ductility (they hinder the crack propagation and hence, cause unequivocal strain-hardening), the hard constituents of the matrix phase yield the strength.

Im Gegensatz zu „festen Säuren“ sind „feste Basen“ wesentlich seltener Untersuchungsgegenstand in ihrer Anwendung als Katalysatoren in der heterogenen Katalyse. In der vorliegenden Promotionsarbeit wurden entgegen diesem Trend die Herstellung, Charakterisierung und Anwendung basischer Oxide sowie modifizierter Oxide in ihrer Eignung als feste Basen in der Katalyse untersucht. Zu diesen Katalysatoren gehören MgO, hergestellt nach unterschiedlichen Methoden, Kalium modifiziertes ZrO2, calcinierte Mg-Al Hydrotalcite und ein neuartiges Katalysatorsystem auf der Basis von Mg(O,F)-Kompositionen, die zum ersten Mal nach einem Sol-Gel-Fluorierungsverfahren hergestellt wurden. Die Katalysatoren wurden mittels N2 Adsorptions/Desorptionsuntersuchungen (BET), XRD, FTIR, XPS, TG-DTA-DTG und MAS NMR untersucht. Die Säure-Basen-Eigenschaften der Katalysatoren wurden durch TPD, FTIR Spektroskopie und Mikrokalorimetrie charakterisiert und mit den katalytischen Eigenschaften korreliert. Calcinierte Mg-Al Hydrotalcite und Mg(O,F) waren in diesem Zusammenhang am stärksten aktiv und auch selektiv wie für die Flüssigphasenreaktion der Michael-Addition von CH aciden Verbindungen mit Methylvinylketon gezeigt wurde. / In contrast to solid acid catalysts, much fewer efforts have been made to study solid base catalysts. In this thesis, preparation, characterization and application of oxides and modified oxide as solid base catalysts were studied. The catalysts include MgO prepared by different methods, potassium-modified ZrO2, calcined Mg-Al hydrotalcites, and a novel catalyst system Mg(O,F), which was prepared by sol-gel method for the first time. The catalysts were studied by N2 adsorption/desorption measurement, XRD, FTIR, XPS, TG-DTA-DTG and NMR. Acid-base properties of the catalysts were investigated by TPD, FTIR spectroscopy and microcalorimetry to correlate with the catalytic behavior. Calcined Mg-Al hydrotalcite and Mg(O,F) are found to be highly active and selective catalysts for liquid-phase Michael additions of CH-acid compounds with methyl vinyl ketone.

The synthesis of five homoleptic transition metal complexes of bis-(phenyl)-diisoindol-aza-methene is described together with the optical, electrochemical and thermal properties of these compounds. Additionally, crystal structures for the Co and the Zn complex are reported. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Aufgrund ihrer Eigenschaften und möglicher Anwendungen werden Siliciumkomplexe mit O,N,O´-Ligandsystemen in der Literatur beschrieben. Jedoch fehlen bisher Untersuchungen zur Strukturaufklärung. Im Rahmen dieser Arbeit wurden zahlreiche Silicium-, Germanium- und Zinnkomplexe mit chiralen O,N,O´-Liganden synthetisiert und strukturanalytisch charakterisiert. Dazu wurden die Liganden durch Kondensationsreaktionen von enantiomerenreinen Aminosäuren mit aromatischen ortho-Hydroxyaldehyden bzw. Acetylaceton hergestellt. Die weitere Umsetzung der Liganden mit Elementhalogeniden der Gruppe 14 führte zu den angestrebten Komplexverbindungen. Alle hergestellten Verbindungen wurden umfassend charakterisiert (NMR-, UV/Vis-, IR-Spektroskopie, Elementaranalyse, Einkristallstrukturanalyse, Drehwert). Quantenchemische Berechnungen an einfachen Modellverbindungen sowie an hergestellten Silicium- und Zinnkomplexen führten zu einem grundlegenden Verständnis der Festkörper-NMR-Parameter dieser Verbindungsklasse.

<p>Велике воде су сложена појава како у погледу фактора који је изазивају, тако и<br />у&nbsp; погледу&nbsp; њеног&nbsp; утицаја&nbsp; на&nbsp; екосистем&nbsp; и друштво.&nbsp; У&nbsp; дисертацији&nbsp; је&nbsp; приказана предност&nbsp; анализе&nbsp; великих&nbsp; вода,&nbsp; са&nbsp; две променљиве&nbsp; (запремине&nbsp; и&nbsp; трајање),&nbsp; у односу&nbsp; на&nbsp; уобичајену&nbsp; анализу&nbsp; са&nbsp; једном вредношћу&nbsp; (најчешће&nbsp; максимални годишњи&nbsp; протицај).&nbsp; Резултати&nbsp; добијени статистичком анализом великих вода, које су издвојене методом&nbsp; прага су показали да имају већу применљивост у водопривреди него&nbsp; методе&nbsp; које&nbsp; користе&nbsp; стандардне вредности,&nbsp; јер&nbsp; дају&nbsp; конкретне&nbsp; вредности могућих&nbsp; количина&nbsp; воде&nbsp; (запремине великих вода)&nbsp; Метода прага је примењена на&nbsp; 22&nbsp; станица&nbsp; на&nbsp; четири&nbsp; највеће&nbsp; реке Панонског&nbsp; басена&nbsp; (Дунав,&nbsp; Сава,&nbsp; Тиса&nbsp; и Драва) за период 1964-2013. година што до сад&nbsp; представља&nbsp; највећи&nbsp; узорак&nbsp; на&nbsp; овако великом&nbsp; географском&nbsp; подручју.&nbsp; Као&nbsp; праг за&nbsp; издвајање&nbsp; великих&nbsp; вода&nbsp; узета&nbsp; је вредност&nbsp; Q10,&nbsp; јер&nbsp; је&nbsp; циљ&nbsp; био&nbsp; анализа просторних&nbsp; и&nbsp; временских&nbsp; карактеристика екстремних&nbsp;&nbsp;&nbsp; великих вода у највећих река Панонског басена. Избор прага утицао је и на&nbsp; избор&nbsp; методе&nbsp; годишњих&nbsp; максимума&nbsp; за статистичку&nbsp; анализу&nbsp; карактеристика великих&nbsp; вода.&nbsp; За&nbsp; одређивање&nbsp; параметра&nbsp; теоријских&nbsp; расподела&nbsp; коришћени&nbsp; су&nbsp; L-моменти&nbsp; који&nbsp; дају&nbsp; поузданије&nbsp; оцене параметара&nbsp; од&nbsp; обичних&nbsp; момената.&nbsp; У досадашњим&nbsp; радовима,&nbsp; који&nbsp; су анализирали&nbsp; карактеристике&nbsp; великих&nbsp; вода методом&nbsp; годишњих&nbsp; максимума,&nbsp; функција расподеле&nbsp; се&nbsp; унапред&nbsp; одабирала,&nbsp; а&nbsp; не&nbsp; на основу&nbsp; тестова&nbsp; сагласности&nbsp; и&nbsp; провере графика вероватноће, као што је урађено у овој&nbsp; дисертацији.&nbsp; За&nbsp; проверу&nbsp; сагласности годишњег максимума запремина и трајања коришћени&nbsp; су&nbsp; тестови&nbsp; Колмогоров-Смирнов&nbsp; и&nbsp; Крамер&nbsp; &ndash;Мизес,&nbsp; на&nbsp; основу којих су изабране меродавне расподеле за прорачун&nbsp; великих&nbsp; вода&nbsp; различитих повратних&nbsp; периода&nbsp; на&nbsp; станицама,&nbsp; и обрнуто.&nbsp; Помоћу&nbsp; L-момент&nbsp; дијаграма&nbsp; (LCs/L-Ck)&nbsp; утврђена&nbsp; је&nbsp; хомогеност&nbsp; региона, у&nbsp; овом&nbsp; случају&nbsp; Панонског&nbsp; басена,&nbsp; као&nbsp; иизабрана&nbsp; регионална&nbsp; расподела&nbsp; (LN)&nbsp; за запремине и трајање велике воде.&nbsp; Кластер анализа коришћена&nbsp; је као друга метода за издвајање&nbsp; хомогених&nbsp; региона.&nbsp; На&nbsp; основу ове&nbsp; анализе&nbsp; у&nbsp; Панонском&nbsp; басену&nbsp; су издвојена&nbsp; три&nbsp; региона&nbsp; која&nbsp; имају&nbsp; исте карактеистике.</p> / <p>Velike vode su složena pojava kako u pogledu faktora koji je izazivaju, tako i<br />u&nbsp; pogledu&nbsp; njenog&nbsp; uticaja&nbsp; na&nbsp; ekosistem&nbsp; i društvo.&nbsp; U&nbsp; disertaciji&nbsp; je&nbsp; prikazana prednost&nbsp; analize&nbsp; velikih&nbsp; voda,&nbsp; sa&nbsp; dve promenljive&nbsp; (zapremine&nbsp; i&nbsp; trajanje),&nbsp; u odnosu&nbsp; na&nbsp; uobičajenu&nbsp; analizu&nbsp; sa&nbsp; jednom vrednošću&nbsp; (najčešće&nbsp; maksimalni godišnji&nbsp; proticaj).&nbsp; Rezultati&nbsp; dobijeni statističkom analizom velikih voda, koje su izdvojene metodom&nbsp; praga su pokazali da imaju veću primenljivost u vodoprivredi nego&nbsp; metode&nbsp; koje&nbsp; koriste&nbsp; standardne vrednosti,&nbsp; jer&nbsp; daju&nbsp; konkretne&nbsp; vrednosti mogućih&nbsp; količina&nbsp; vode&nbsp; (zapremine velikih voda)&nbsp; Metoda praga je primenjena na&nbsp; 22&nbsp; stanica&nbsp; na&nbsp; četiri&nbsp; najveće&nbsp; reke Panonskog&nbsp; basena&nbsp; (Dunav,&nbsp; Sava,&nbsp; Tisa&nbsp; i Drava) za period 1964-2013. godina što do sad&nbsp; predstavlja&nbsp; najveći&nbsp; uzorak&nbsp; na&nbsp; ovako velikom&nbsp; geografskom&nbsp; području.&nbsp; Kao&nbsp; prag za&nbsp; izdvajanje&nbsp; velikih&nbsp; voda&nbsp; uzeta&nbsp; je vrednost&nbsp; Q10,&nbsp; jer&nbsp; je&nbsp; cilj&nbsp; bio&nbsp; analiza prostornih&nbsp; i&nbsp; vremenskih&nbsp; karakteristika ekstremnih&nbsp;&nbsp;&nbsp; velikih voda u najvećih reka Panonskog basena. Izbor praga uticao je i na&nbsp; izbor&nbsp; metode&nbsp; godišnjih&nbsp; maksimuma&nbsp; za statističku&nbsp; analizu&nbsp; karakteristika velikih&nbsp; voda.&nbsp; Za&nbsp; određivanje&nbsp; parametra&nbsp; teorijskih&nbsp; raspodela&nbsp; korišćeni&nbsp; su&nbsp; L-momenti&nbsp; koji&nbsp; daju&nbsp; pouzdanije&nbsp; ocene parametara&nbsp; od&nbsp; običnih&nbsp; momenata.&nbsp; U dosadašnjim&nbsp; radovima,&nbsp; koji&nbsp; su analizirali&nbsp; karakteristike&nbsp; velikih&nbsp; voda metodom&nbsp; godišnjih&nbsp; maksimuma,&nbsp; funkcija raspodele&nbsp; se&nbsp; unapred&nbsp; odabirala,&nbsp; a&nbsp; ne&nbsp; na osnovu&nbsp; testova&nbsp; saglasnosti&nbsp; i&nbsp; provere grafika verovatnoće, kao što je urađeno u ovoj&nbsp; disertaciji.&nbsp; Za&nbsp; proveru&nbsp; saglasnosti godišnjeg maksimuma zapremina i trajanja korišćeni&nbsp; su&nbsp; testovi&nbsp; Kolmogorov-Smirnov&nbsp; i&nbsp; Kramer&nbsp; &ndash;Mizes,&nbsp; na&nbsp; osnovu kojih su izabrane merodavne raspodele za proračun&nbsp; velikih&nbsp; voda&nbsp; različitih povratnih&nbsp; perioda&nbsp; na&nbsp; stanicama,&nbsp; i obrnuto.&nbsp; Pomoću&nbsp; L-moment&nbsp; dijagrama&nbsp; (LCs/L-Ck)&nbsp; utvrđena&nbsp; je&nbsp; homogenost&nbsp; regiona, u&nbsp; ovom&nbsp; slučaju&nbsp; Panonskog&nbsp; basena,&nbsp; kao&nbsp; iizabrana&nbsp; regionalna&nbsp; raspodela&nbsp; (LN)&nbsp; za zapremine i trajanje velike vode.&nbsp; Klaster analiza korišćena&nbsp; je kao druga metoda za izdvajanje&nbsp; homogenih&nbsp; regiona.&nbsp; Na&nbsp; osnovu ove&nbsp; analize&nbsp; u&nbsp; Panonskom&nbsp; basenu&nbsp; su izdvojena&nbsp; tri&nbsp; regiona&nbsp; koja&nbsp; imaju&nbsp; iste karakteistike.</p> / <p>High&nbsp; waters&nbsp; are&nbsp; a&nbsp; complex phenomenon&nbsp; both&nbsp; in&nbsp; terms&nbsp; of&nbsp; the&nbsp; factors&nbsp; that cause it, as well as in terms of its impact on the ecosystem&nbsp; and&nbsp; society.&nbsp; This&nbsp; dissertation presents&nbsp; the&nbsp; advantage&nbsp; of&nbsp; analyzing&nbsp; high waters&nbsp; with&nbsp; two&nbsp; variables&nbsp; (volumes&nbsp; and duration), compared to the usual analysis with one&nbsp; value&nbsp; (usually&nbsp; the&nbsp;&nbsp; maximum&nbsp; annual discharge).&nbsp; The&nbsp; results&nbsp; obtained&nbsp; by&nbsp; the statistical&nbsp; analysis&nbsp; of&nbsp; high&nbsp; waters,&nbsp; which&nbsp; are defined&nbsp; by&nbsp; the&nbsp; threshold&nbsp; method,&nbsp; have&nbsp; shown that&nbsp; they&nbsp; have&nbsp; greater&nbsp; applicability&nbsp; in&nbsp; water management&nbsp; than&nbsp; methods&nbsp; that&nbsp; use&nbsp; standard values&nbsp; because&nbsp; they&nbsp; give&nbsp; concrete&nbsp; values&nbsp; of possible&nbsp; water&nbsp; quantities&nbsp; (volume&nbsp; of&nbsp; highwaters).&nbsp; The&nbsp; threshold&nbsp; method&nbsp; was&nbsp; applied&nbsp; to 22 stations on the four largest rivers Pannonian Basin&nbsp; (Danube,&nbsp; Sava,&nbsp; Tisa&nbsp; and&nbsp; Drava)&nbsp; for the period&nbsp; 1964-2013.&nbsp; This&nbsp; represents&nbsp; the&nbsp; largest sample&nbsp; in&nbsp; such&nbsp; a&nbsp; large&nbsp; geographical&nbsp; area.&nbsp; The value&nbsp; of&nbsp; Q10&nbsp; was&nbsp; taken&nbsp; as&nbsp; the&nbsp; threshold&nbsp; for defining&nbsp; the&nbsp; high&nbsp; waters,&nbsp; as&nbsp; the&nbsp; aim&nbsp; was&nbsp; to analyze the spatial and&nbsp; temporal&nbsp;&nbsp; characteristics of extreme&nbsp; high waters&nbsp; in the&nbsp; largest rivers of the&nbsp; Pannonian&nbsp; Basin.&nbsp; The&nbsp; threshold&nbsp; selection also&nbsp; influenced&nbsp; the&nbsp; selection&nbsp; of&nbsp; the&nbsp; annual maximum method for statistical analysis of the characteristics of high waters. L-moments were<br />used&nbsp; to&nbsp; determine&nbsp; the&nbsp; parameter&nbsp; of&nbsp; the theoretical&nbsp; distributions,&nbsp; which&nbsp; give&nbsp; more reliable&nbsp; estimates&nbsp; of&nbsp; parameters&nbsp; than&nbsp; ordinary moments.&nbsp; In&nbsp; the&nbsp; previous&nbsp; researches,&nbsp; which analyzed&nbsp; the&nbsp; characteristics&nbsp; of&nbsp; high&nbsp; waters&nbsp; by the&nbsp; method&nbsp; of&nbsp; annual&nbsp; maximums,&nbsp; the distribution&nbsp; function&nbsp; was&nbsp; selected&nbsp; in&nbsp; advance, and&nbsp; not&nbsp; on&nbsp; the&nbsp; basis&nbsp; of&nbsp; tests&nbsp; of&nbsp; approval&nbsp; and check&nbsp; of&nbsp; probability&nbsp; graphs,&nbsp; as&nbsp; is&nbsp; done&nbsp; in&nbsp; this dissertation. In order to&nbsp; check the goodness-offit&nbsp; tests&nbsp; of&nbsp; annual&nbsp; maximum &nbsp; volumes&nbsp; and duration,&nbsp; the&nbsp; tests&nbsp; Kolmogorov-Smirnov&nbsp; and Kramer-Mizes&nbsp; were&nbsp; used,&nbsp; and&nbsp; based&nbsp; on&nbsp; their results&nbsp; representative&nbsp; distribution&nbsp; was&nbsp; chosen for&nbsp; calculation&nbsp; of&nbsp; different&nbsp; return&nbsp; periods&nbsp; of high waters on the stations, and vice versa.&nbsp; The L-moment&nbsp; diagram&nbsp; (L-Cs/L-Ck)&nbsp; determined the homogeneity&nbsp;&nbsp; of the region, in this case the Pannonian&nbsp; basin.&nbsp; L-moments&nbsp; were&nbsp; used&nbsp; for selection&nbsp; of&nbsp; regional&nbsp; distribution&nbsp; (LN)&nbsp; forvolumes&nbsp; and&nbsp; duration&nbsp; of&nbsp; high&nbsp; waters.&nbsp; Cluster analysis&nbsp; was&nbsp; used&nbsp; as&nbsp; the&nbsp; second&nbsp; method&nbsp; for separating homogeneous regions.&nbsp; Based on this analysis&nbsp; in the Pannonian&nbsp; Basin, three regions have&nbsp; been&nbsp; identified&nbsp; that&nbsp; have&nbsp; the&nbsp; same hydrological characteristics.</p>

The synthesis of five homoleptic transition metal complexes of bis-(phenyl)-diisoindol-aza-methene is described together with the optical, electrochemical and thermal properties of these compounds. Additionally, crystal structures for the Co and the Zn complex are reported. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

No description available.

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.