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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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

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. The $k$-color bipartite Ramsey number of $ S(n,m)$, denoted by $r_{bip}(S(n,m);k)$, is the smallest integer $N$ such that, in any $k$-coloring of the edges of the complete bipartite graph $K_{N,N}$, there is a monochromatic copy of $S(n,m)$. The study of bipartite Ramsey numbers was initiated in the early 1970s by Faudree and Schelp and, independently, by Gy\'arf\'as and Lehel. The exact value of $r_{bip}(S(n,m);k)$ is only known for $n=m=1$ and all $k\ge2$. Here we prove that if $k=2$ and $n\ge m$, or $k\ge3$ and $n\ge 2m$, then \[ r_{bip}(S(n,m);k)=kn+1.\] For $k \geq 3$ and $m \leq n < 2m$, we prove that, \[\max\{kn + 1, (2k-4)m+1\} \leq r_{bip}(S(n,m) ; k) \leq \max\left\{ kn + 1, \left[2k - 1 - \frac{1}{2k} - O\left(\frac{1}{k^2}\right)\right]m + 1 \right \},\] where the lower bound is due to DeBiasio, Gy\'arf\'as, Krueger, Ruszink\'o, and S\'ark\"ozy in 2019.

Varicella zoster virus (VZV) is a highly contagious DNA virus, which causes varicella (chickenpox). After healing it persists in ganglionic neurons. Herpes zoster can occur in childhood after both wild-type childhood varicella and varicella vaccination. Due to several reasons, the virus can reactivate and cause zoster (shingles), which causes a battery of complications, for example, post-zoster neuralgia and meningoencephalitis including cerebellitis or vasculopathy. Only one case report including two men suffering from olfactory impairment and parosmia with Ramsey Hunt syndrome was published.1 Both suffered from loss of olfactory function and one patient reported additionally about parosmia. One patient reported spontaneous olfactory recovery after weeks, without exact time range. The other one reported olfactory recovery 3 weeks after therapy with chloramphenicol and vitamin B1.1 We report about a 15-year-old girl suffering from Ramsey Hunt syndrome. This patient additionally had olfactory impairment, which lasted for 6 months.

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.