Forks, Noodles and the Burau representation for n=4n=4

\begin{abstract} The reduced Burau representation is a natural action of the braid group $B_n$ on the first homology group $H_1({\tilde{D}}_n;\mathbb{Z})$ of a suitable infinite cyclic covering space ${\tilde{D}}_n$ of the $n$--punctured disc $D_n$. It is known that the Burau representation is faithful for $n\le 3$ and that it is not faithful for $n\ge 5$. We use forks and noodles homological techniques and Bokut--Vesnin generators to analyze the problem for $n=4$. We present a Conjecture implying faithfulness and a Lemma explaining the implication. We give some arguments suggesting why we expect the Conjecture to be true. Also, we give some geometrically calculated examples and information about data gathered using a C\texttt{++} program.Comment: 24 pages, 21 figure

Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows

Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the ow. Number of closures for both breakup and coalescence can be identi ed in the literature and most of them need an estimation of model parameters that can di er even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identi cation allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup and co- alescence models over multiple cases and we propose a correlation based on non-dimensional numbers that is applicable to number of di erent ows over wide range of Reynolds numbers

Search for Z-primes and Randall-Sundrum Gravitons with dimuons in CMS

This paper presents results from studies on observability of Z' particles and Randall-Sundrum gravitons in the dimuon channel in the CMS detector. Full detector simulation and reconstruction were carried out to derive both the discovery potential and results for model discrimination. Effects of systematic uncertainties on the expected reach of the CMS experiment are also presented

Aufsätze über Geldpolitik und internationale Makroökonomik

This dissertation contains three essays on monetary policy, dynamics of the interest rates and spillovers across economies. In the first essay I examine the effects of monetary policy and its interaction with financial regulation within a micro-founded macroeconometric framework for a closed economy with a heterogeneous banking system, facing a period of low interest rates. I analyse the interplay between monetary policy and banking regulation and study the role of agents’ expectations for the effectiveness of unconventional monetary policy tools. In the next essay, I argue that openness is crucial for understanding the dynamics of the term structure. In an empirical application, I show that my model of the term structure fits well the yield curve in-sample and has a sound ability to forecast interest rates out-of-sample. The model accounts for the expectations hypothesis, replicates the forward premium anomaly and reconciles the uncovered interest rate parity implications. The last essay is concerned with the dynamics of co-movement among macroeconomic aggregates and the degree of convergence or decoupling amongst economies. The model includes measures of financial and trade-based interdependencies and incorporates feedback between macroeconomic variables and time-varying weights. The findings point at the importance of asset price movements and financial linkages.In meiner Dissertation beschäftige ich mich mit aktuellen Fragestellungen der internationalen und monetären Makroökonomie. Das erste Kapitel zielt auf die Analyse der Effekte der Geldpolitik und ihrer Wechselwirkung mit der Bankregulierung im Rahmen eines mikroökonomisch fundierten Modells für die geschlossene Wirtschaft mit heterogenem Banksektor ab, die sich in einer Periode von niedrigen Zinsen befindet. Der Originalbeitrag bezieht sich auf die Analyse des Zusammenspiels zwischen Geldpolitik und Bankregulierung, und insbesondere auf die Untersuchung der Rolle von Erwartungsbildung bezüglich der künftigen Politik der Zentralbanken im Hinblick auf Effektivität der nicht konventionellen geldpolitischen Instrumente. Im nächsten Kapitel beschäftige ich mich mit einem der Transmissionsmechanismen für die Geldpolitik, der Zinsstrukturkurve, und belege, dass Offenheit der Wirtschaft von entscheidender Bedeutung für das Verstehen der Dynamik der Zinssätze ist. Insbesondere untersuche ich, wie die von innen und von außen kommenden makroökonomischen Faktoren in einer offenen Wirtschaft die Bewegungen der Zinsstrukturkurve und der Risikoprämien beeinflussen. Das letzte Kapitel beschäftigt sich mit Modellierung der Dynamik der makroökonomischen Größen zwischen verschiedenen Ländern, d.h. mit dem eigentlichen Prozess, der die Dynamik der Makrofaktoren aus dem zweiten Kapitel bestimmt. In diesem Teil meiner Dissertation bearbeite ich die Fragestellung, ob die Länder oder Ländergruppen in wirtschaftlicher Hinsicht dazu tendieren zu entkoppeln oder ob sie aufgrund zunehmender Globalisierung konvergieren

Poland's New Foreign Minister: Orbiting Closer to the Center of Power

Zbigniew Rau, who was appointed foreign minister on August 26, will help align the trajectory of Polish diplomacy with the government's general line. His appointment fits into the logic of a larger government reshuffle, expected this fall, which aims for a greater centralization of power. His higher standing in the governing PiS party may, however, halt the gradual loss of relevance of Poland's Ministry for Foreign Affairs

Knots and algebras

This paper gives a skein-theoretic construction of the Hecke algebras based on oriented tangles and the Homfly relations. A similar approach with unoriented tangles and Kauffman's Dubrovnik relations then gives a construction of the Birman-Wenzl algebra

Search for Randall-Sundrum Graviton Excitations in the CMS Experiment

The ability of the CMS experiment to detect massive Kaluza-Klein excitations of gravitons, predicted by the Randall-Sundrum model, is studied. The search reach is estimated for the channel with the graviton, produced in proton-proton collision, decaying into a pair of electrons or muons.Comment: 13 pages, 13 figure

How Poland's Postponed Election is Boosting Opposition Hopes

What was supposed to be a simple reelection campaign for President Andrzej Duda could be a political turning point for Poland. Contrary to expectations that authoritative leaders would use the pandemic to consolidate power, it exposed the ruling party’s vulnerability. The outcome of the new elections, which are expected to take place in late June or early July 2020, is now uncertain. Europe should pay attention, because a new president could help reconfigure domestic politics and restore Poland’s position as a more constructive EU partner