Edge switching transformations of quantum graphs

Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schr\"odinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by $\{ E_n\}_{n=1}^{\infty}$ and $\{\widetilde E_n\}_{n=1}^{\infty}$ correspondingly, are level-2 interlaced, so that $E_{n-2}\le \widetilde E_n\le E_{n+2}$. The proofs are guided by considerations of the quantum graphs' discrete analogs

Schaeffler KG/ Continental AG im Lichte der CSX Corp.-Entscheidung des US District Court for the Southern District of New York: Meldepflichten bei öffentlichen Übernahmen und deren Umgehung durch Einsatz von derivativen Finanzinstrumenten

This report analyses the possibility to outflank disclosure obligations under the German Securities Trading Act as well as the German Takeover Act by using derivative instruments in the context of the attack of Schaeffler KG on Continental AG. Irrespective of a limited knowledge of the complete facts it comes to the conclusion that, under certain conditions, there are good reasons to assume violations of legal obligations that would entitle the Federal Financial Supervisory Authority to fix hefty fines but not to prohibit the offer

Aktionärsschutz in der AG falsch verstanden? Die Leica-Entscheidung des LG Frankfurt am Main

This article analyses the recent Leica judgement of the Higher Regional Court Frankfurt/Main and its consequences. In this judgement, the court has established an infringement of special formal requirements with respect to Leica´s invitation to the Annual General Meeting which, if correct, would bear dire consequences for a variety of listed companies, even in DAX. On the other hand, there is a recent decision of the Higher Regional Court Munich in a similar case concerning Hypovereinsbank, coming to the opposite conclusion. Besides the fact that, in the opinion of the authors, the Leica decision not only is legally unfounded and based on a completely unbalanced evaluation of formalistic requirements, it again proves the formalistic approach of German stock corporation law and leaves companies, especially with a respective regulation in their articles of association, their advisors and investors in a situation of uncertainty that has to be clarified urgently by the legislator

Wertpapierprospekte: Markteinführungspublizität nach EU-Prospektverordnung und Wertpapierprospektgesetz 2005

The legal environment for Securities Prospectuses in Germany has changed dramatically with the implementation of the German Securities Prospectus Act (Wertpapierprospektgesetz - WpPG) and the Commission Regulation (EC) No. 809/2004 of 29 April 2004 (Prospectus Regulation) regulating their content and format and harmonizing the requirements for public offerings and stock exchange listings with effect from 1 July 2005. This working report presents the current situation and describes the experience with BaFin, the German Federal Financial Supervisory Agency that now has sole competence for reviewing and approving prospectuses in accordance with the WpPG

Multi-parametric bifurcations in a piecewise-linear discontinuous map

In this paper a one-dimensional piecewise linear map with discontinuous system function is investigated. This map actually represents the normal form of the discrete-time representation of many practical systems in the neighbourhood of the point of discontinuity. In the 3D parameter space of this system we detect an infinite number of co-dimension one bifurcation planes, which meet along an infinite number of co-dimension two bifurcation curves. Furthermore, these curves meet at a few co-dimension three bifurcation points. Therefore, the investigation of the complete structure of the 3D parameter space can be reduced to the investigation of these co-dimension three bifurcations, which turn out to be of a generic type. Tracking the influence of these bifurcations, we explain a broad spectrum of bifurcation scenarios (like period increment and period adding) which are observed under variation of one control parameter. Additionally, the bifurcation structures which are induced by so-called big bang bifurcations and can be observed by variation of two control parameters can be explained

Wertpapierprospekte: Markteinführungspublizität nach EU-Prospektverordnung und Wertpapierprospektgesetz 2005

The legal environment for Securities Prospectuses in Germany has changed dramatically with the implementation of the German Securities Prospectus Act (Wertpapierprospektgesetz - WpPG) and the Commission Regulation (EC) No. 809/2004 of 29 April 2004 (Prospectus Regulation) regulating their content and format and harmonizing the requirements for public offerings and stock exchange listings with effect from 1 July 2005. This working report presents the current situation and describes the experience with BaFin, the German Federal Financial Supervisory Agency that now has sole competence for reviewing and approving prospectuses in accordance with the WpPG. --IPO,Initial Public Offering,Prospectus,Securities,Stock Exchange Act,Stock Exchange Admission Ordinance,German Financial Supervisory Authority,Prospectus Directive,German Securities Prospectus Act,Wertpapierprospektgesetz,WpPG,Public Offer,Subscription Rights,Employee Incentive Programmes,Stock Exchange,Organised Market,Open Market,Entry Standard,Registration Document,Financial Information,European Passport,Notification,Securities Sales Prospectus Act,Securities Sales Prospectus Ordinance

Unternehmen im Prime Standard staying public oder going private? Nutzenanalyse der Börsennotiz

The dramatic drop in prices on the German stock exchange in the period from 2000 to 2003 was one cause for the rising number of delistings in Germany. This development triggered the study on the aptitude of listed companies to remain listed although the authors were well aware that a negative conclusion would not necessarily imply a company's realistic chance of going private, in particular of obtaining the required financing for such a transaction. The study focused on those companies of the Prime Standard that were not included in one of the indices. Using selected indicators, the authors analyzed the question if and to what extent each of the companies examined had reached the goals normally pursued for an IPO. It was concluded that for the overwhelming majority of those companies studied, a listing on a stock exchange would not make sense (any more): in particular, due to the volume of their market capitalization and the liquidity of their stock, they wouldn't interest the analysts and investors nor would their stock prices adequately reflect their intrinsic values. And, especially during these difficult times, it would be very hard to raise additional capital on the markets

Unternehmen im Prime Standard staying public oder going private? Nutzenanalyse der Börsennotiz

The dramatic drop in prices on the German stock exchange in the period from 2000 to 2003 was one cause for the rising number of delistings in Germany. This development triggered the study on the aptitude of listed companies to remain listed although the authors were well aware that a negative conclusion would not necessarily imply a company's realistic chance of going private, in particular of obtaining the required financing for such a transaction. The study focused on those companies of the Prime Standard that were not included in one of the indices. Using selected indicators, the authors analyzed the question if and to what extent each of the companies examined had reached the goals normally pursued for an IPO. It was concluded that for the overwhelming majority of those companies studied, a listing on a stock exchange would not make sense (any more): in particular, due to the volume of their market capitalization and the liquidity of their stock, they wouldn't interest the analysts and investors nor would their stock prices adequately reflect their intrinsic values. And, especially during these difficult times, it would be very hard to raise additional capital on the markets. --Delisting,going private,market capitalisation,IPO,stock exchange,liquidity,capital raising,stock price

High-Order Variational Calculation for the Frequency of Time-Periodic Solutions

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster/, http://www.physik.fu-berlin.de/~kleinert/ and http://www.informatik.uni-stuttgart.de/ipvr/bv/personen/schanz.htm