As the twentieth century dawned in the western world, there were voices both inside and out of the Christian Church that began to question religion's central place in man's daily life. Had humanity finally progressed to the point where religion was no longer necessary? Had we at long last developed the characteristics and perspectives that religion had attempted to engrain within us? Or were the rules and regulations of religion still needed to ensure the continued advancement of civilization? This is a study of two opposing voices in that debate: theologian Dietrich Bonhoeffer and ethicist Paul Ramsey. What follows is my attempt to examine, explain, and expound upon the philosophies of both men in an endeavor to more fully understand their perspectives and the implications each has for civilization and religion as we move now firmly into the twenty-first century and beyond.

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As soon as Bennett and Gill first demonstrated that, relative to a randomly chosen oracle, P is not equal to NP with probability 1, the random oracle hypothesis began piquing the interest of mathematicians and computer scientists. This was quickly disproven in several ways, most famously in 1992 with the result that IP equals PSPACE, in spite of the classes being shown unequal with probability 1. Here, we propose what could be considered strengthening of the random oracle hypothesis, using a stricter notion of what it means for a set to be 'large'. In particular, we suggest using largeness with respect to the Ramsey forcing notion. In this new context, we demonstrate that the set of oracles separating NP and coNP is 'not small', and obtain similar results for the separation of PSPACE from PH along with the separation of NP from BQP. In a related set of results, we demonstrate that these classes are all of the same descriptive complexity. Finally we demonstrate that this strengthening of the hypothesis turns it into a sufficient condition for unrelativized relationships, at least in the three cases considered here.

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Sjöfartsverkets ställning liknande ett naturligt monopol och dagens politiska läge kräver en farledsavgift utformad på ett sätt som gör att Sjöfartsverket täcker sina kostnader samtidigt som de snedvrider beteendet av sjöfartens aktörer så lite som möjligt. Syftet med denna uppsats är att undersöka elasticiteterna för olika fartygssegment och om Ramseyprissättning utifrån dessa kan användas för att utforma de svenska farledsavgifterna så att dessa krav uppfylls. Genom att kartlägga de avgiftsförändringar som skett mellan 2008–2020 och använda data från Sjöfartsverkets årliga farledsdeklarationer för samma period kan vi skatta elasticiteterna inom svensk sjöfart. Våra resultat indikerar att olika fartygssegment har olika elasticiteter vilket innebär att de har olika känslighet för avgiftsförändringar. Likt tidigare forskning är de elasticiteter vi får fram främst oelastiska och negativa. Vissa icke-signifikanta eller orimliga resultat innebär dock osäkerhet kring hur segmenten skiljer sig åt mellan varandra och över tid. Denna osäkerhet tillsammans med osäkerheten kring beräkningen av marginalkostnader och konkurrensen med andra transportslag gör att vi rekommenderar att Ramseyprissättning inte borde användas som grund för farledsavgifternas utformande i dagens läge. Vår kartläggning av avgiftsförändring kom fram till att endast två av dessa var lämpliga att utföra skattningar på. Detta tillsammans med det endogenitetsproblem som farledsavgifternas nuvarande struktur ger upphov till bidrog troligen till att vi inte kunde få fler signifikanta och rimliga elasticiteter. / The Swedish Maritime Administrations (SMA) position resembling that of a natural monopoly and the current political situation demands a fairway due designed in a way that allows the SMA to cover their costs while at the same time distorts the behaviour of the maritime agents as little as possible. The purpose of this essay is to examine the elasticities of different ship segments and whether Ramsey pricing based on these can be used to design the Swedish fairway dues in a way that meets these demands. By mapping the changes in dues between 2008-2020 and using data from the SMAs yearly fairway declarations during the same period, we can estimate the elasticities within Swedish shipping. Our results indicate that different ship segments have different elasticities which means that they have different sensitivity to changes in dues. Like previous research, the elasticities we find are mainly inelastic and negative. However, some insignificant or unreasonable results imply uncertainty around how the segments differ from each other and over time. This uncertainty together with the uncertainty around the calculations of marginal costs and competition with other modes of transportation makes us recommend not to use Ramsey pricing as a basis for designing the fairway dues in the current situation. Our mapping of changes in dues concluded that only two of these were suitable for making estimations. This, together with the endogeneity problem that the current structure of the fairway dues generates, probably contributed to our resulting elasticities not being more significant and reasonable.

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A bounded and linear operator is said to be hypercyclic if there exists a vector such that its orbit under the action of the operator is dense. The first example of a hypercyclic operator on a Banach space was given in 1969 by Rolewicz who showed that if B is the unweighted unilateral backward shift on l 2 , then λB is hypercyclic if and only if |λ| > 1. Among its features, we can mention for example that finite-dimensional spaces cannot support hypercyclic operators, proved by Kitai. On the other hand, several people have shown in different contexts, in the Hilbert space frame, that the set of hypercyclic vectors for a hypercyclic operator is a Gδ dense set. This thesis is divided into four chapters. In the first one, we give some preliminaries by mentioning some definitions and known results that will be of great help later. In chapter 2, we introduce a refinement of the notion of hypercyclicity, relative to the set N(U, V ) = {n ∈ N : T −nU ∩ V 6= ∅} when belonging to a certain collection F of subsets of N, namely a bounded and linear operator T is called F-operator if N(U, V ) ∈ F, for any pair of non-empty open sets U, V in X. First, we do an analysis of the hierarchy established between F-operators, whenever F covers those families mostly studied in Ramsey theory. Second, we investigate which kind of properties of density can have the sets N(x, U) = {n ∈ N : T nx ∈ U} and N(U, V ) for a given hypercyclic operator, and classify the hypercyclic operators accordingly to these properties. In chapter three, we introduce the following notion: an operator T on X satisfies property PF if for any U non-empty open set in X, there exists x ∈ X such that N(x, U) ∈ F. Let BD the collection of sets in N with positive upper Banach density. We generalize the main result of a paper due to Costakis and Parissis using a strong result of Bergelson and Mccutcheon in the vein of Szemerédi’s theorem, leading us to a characterization of those operators satisfying property PBD. It turns out that operators having property PBD satisfy a kind of recurrence described in terms of essential idempotents of βN (the Stone-Čech compactification of N). We will discuss the case of weighted backward shifts satisfying property PBD. On the other hand, as a consequence we obtain a characterization of reiteratively hypercyclic operators, i.e. operators for which there exists x ∈ X such that for any U non-empty open set in X, the set N(x, U) ∈ BD. The fourth chapter focuses on a refinement of the notion of disjoint hypercyclicity. We extend a result of Bès, Martin, Peris and Shkarin by stating: Bw is F-weighted backward shift if and only if (Bw, . . . , Br w) is d-F, for any r ∈ N, where F runs along some filters containing strictly the family of cofi- nite sets, which are frequently used in Ramsey theory. On the other hand, we point out that this phenomenon does not occur beyond the weighted shift frame by showing a mixing linear operator T on a Hilbert space such that the tuple (T, T2 ) is not d-syndetic. We also, investigate the relationship between reiteratively hypercyclic operators and d-F tuples, for filters F contained in the family of syndetic sets. Finally, we examine conditions to impose in order to get reiterative hypercyclicity from syndeticity in the weighted shift frame. / Puig De Dios, Y. (2014). Recurrence in Linear Dynamics [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48473

Die Regularitätsmethode für Graphen wurde vor über 30 Jahren von Szemerédi, für den Beweis seines Dichteresultates über Teilmengen der natürlichen Zahlen, welche keine arithmetischen Progressionen enthalten, entwickelt. Grob gesprochen besagt das Regularitätslemma, dass die Knotenmenge eines beliebigen Graphen in konstant viele Klassen so zerlegt werden kann, dass fast alle induzierten bipartiten Graphen quasi-zufällig sind, d.h. sie verhalten sich wie zufällige bipartite Graphen mit derselben Dichte. Das Regularitätslemma hatte viele weitere Anwendungen, vor allem in der extremalen Graphentheorie, aber auch in der theoretischen Informatik und der kombinatorischen Zahlentheorie, und gilt mittlerweile als eines der zentralen Hilfsmittel in der modernen Graphentheorie. Vor wenigen Jahren wurden Regularitätslemmata für andere diskrete Strukturen entwickelt. Insbesondere wurde die Regularitätsmethode für uniforme Hypergraphen und dünne Graphen verallgemeinert. Ziel der vorliegenden Arbeit ist die Weiterentwicklung der Regularitätsmethode und deren Anwendung auf Probleme der theoretischen Informatik. Im Besonderen wird gezeigt, dass vererbbare (entscheidbare) Hypergrapheneigenschaften, das sind Familien von Hypergraphen, welche unter Isomorphie und induzierten Untergraphen abgeschlossen sind, testbar sind. D.h. es existiert ein randomisierter Algorithmus, der in konstanter Laufzeit mit hoher Wahrscheinlichkeit zwischen Hypergraphen, welche solche Eigenschaften haben und solchen die „weit“ davon entfernt sind, unterscheidet. / About 30 years ago Szemerédi developed the regularity method for graphs, which was a key ingredient in the proof of his famous density result concerning the upper density of subsets of the integers which contain no arithmetic progression of fixed length. Roughly speaking, the regularity lemma asserts, that the vertex set of every graph can be partitioned into a constant number of classes such that almost all of the induced bipartite graphs are quasi-random, i.e., they mimic the behavior of random bipartite graphs of the same density. The regularity lemma had have many applications mainly in extremal graph theory, but also in theoretical computer science and additive number theory, and it is considered one of the central tools in modern graph theory. A few years ago the regularity method was extended to other discrete structures. In particular extensions for uniform hypergraphs and sparse graphs were obtained. The main goal of this thesis is the further development of the regularity method and its application to problems in theoretical computer science. In particular, we will show that hereditary, decidable properties of hypergraphs, that are properties closed under isomorphism and vertex removal, are testable. I.e., there exists a randomised algorithm with constant running time, which distinguishes between Hypergraphs displaying the property and those which are “far” from it.

本研究利用台灣2001年資料以Ramsey與OLG假設分別建立區分四部門別與八部門別之動態可計算一般均衡模型，進行「提高間接稅（消費稅、環境稅）、降低直接稅（資本、勞動所得稅）」之稅制改革模擬分析。結果發現若以單一時點比較靜態方式分析可能迥異於動態長期分析結果；其次以Ramsey分析所欠缺的代際分配影響結果在OLG分析中可以察見，特別是進行以消費稅或環境稅替代資本所得稅模擬時；再者OLG因代際傳遞效果可能較Ramsey假設下反應緩慢，故也可觀察到Ramsey模型面對衝擊後若干變數增減幅度會較OLG模型陡峭。最後特別在環境稅替代所得稅模擬中經由替代稅率變化發現，活在初期世代雖可享受所得稅下降好處但卻也面臨排放稅課徵，因此福利水準增減變化不大，惟屆至排放稅課徵瀕至臨界點需使用原所得稅來平衡稅收時，此為另一波必須為減量政策付出代價的時點與世代。 / Based on a thorough comparison of the basic assumptions and economic underpinning of the Ramsey and Overlapping generation (OLG) model, this study builds both static and dynamic computable general equilibrium tax policy models to analyze the effect of tax reform on Taiwan’s economy. The new tax structure considers mainly a replacement of some parts of direct tax - labor and capital income taxes by indirect tax- consumption tax or environment tax. The benchmark year of the model is 2001, and the economy is divided into four and eight sectors. The modeling framework is implemented on top of MPSGE, which is a special module within the General Algebraic Modeling System (GAMS).Our simulation results show differential outcomes for static and dynamic models. The slower speed of transition inherent in OLG model has caused variables such as welfare, capital stock, and replacement consumption tax rate change less than that in the Ramsey model when the tax reform policy is imposed. And the intergeneration effects of different tax burden between young and old generations can be found in the OLG model but not in the Ramsey model. Finally, we find as the income tax rate coming lower and the environment tax going up when simulation of tax replacement, causing the welfare does not change much at the beginning of shock, and generations especially born in the near future when environment tax does not grow and revenue neutrality needs to be meet are another cost payers of abatement policy.