Wittgenstein's Enigmatic Remarks on Shakespeare

Wittgenstein's occasional remarks on Shakespeare have raised a considerable amount of interest and bewilderment among scholars. They have been read as a harsh critique of the Bard and as the result of a misreading that displays Wittgenstein's feeling of being alien to the culture in which he had chosen to live. On a more benevolent reading they can be taken to shed an interesting light on Wittgenstein himself, though

Company tax coordination cum tax rate competition in the European Union

This paper reviews the recent theoretical literature that analyses the European Union's policy to eliminate preferential corporate tax regimes and the proposal to introduce a consolidated EU tax base with formula apportionment for the taxation of multinational firms. Since neither proposal includes a harmonisation of corporate tax rates, a core issue is how tax competition between member states will be affected by these partial coordination measures. The conclusions from our review are supportive of the EU's ban on preferential tax regimes, but the economic incentive effects of a switch to formula apportionment are found to be ambiguous

The Cameron-Martin Theorem for (p-)Slepian processes

We show a Cameron-Martin theorem for Slepian processes $W_t:=\frac{1}{\sqrt{p}}(B_t-B_{t-p}), t\in [p,1]$, where $p\geq \frac{1}{2}$ and $B_s$ is Brownian motion. More exactly, we determine the class of functions $F$ for which a density of $F(t)+W_t$ with respect to $W_t$ exists. Moreover, we prove an explicit formula for this density. p-Slepian processes are closely related to Slepian processes. p-Slepian processes play a prominent role among others in scan statistics and in testing for parameter constancy when data are taken from a moving window

Boundary crossing probabilities for (q,d)(q,d)-Slepian-processes

For $0<q< d$ fixed let $W^{[q,d]}=(W^{[q,d]}_t)_{t\in {[q,d]}}$ be a $(q,d)$-Slepian-process defined as centered, stationary Gaussian process with continuous sample paths and covariance \begin{align*} C_{W^{[q,d]}}(s,s+t) = (1-\frac{t}{q})^+, \quad q\leq s\leq s+t\leq d. \end{align*} Note that \begin{align*} \frac{1}{\sqrt{q}}(B_t-B_{t-q})_{t\in [q,d]}, \end{align*} where $B_t$ is standard Brownian motion, is a $(q,d)$-Slepian-process. In this paper we prove an analytical formula for the boundary crossing probability $\mathbb{P}\left(W^{[q,d]}_t > g(t) \; \text{for some } t\in[q,d]\right)$, $q< d\leq 2q$, in the case $g$ is a piecewise affine function. This formula can be used as approximation for the boundary crossing probability of an arbitrary boundary by approximating the boundary function by piecewise affine functions

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

Real-valued, time-periodic localized weak solutions for a semilinear wave equation with periodic potentials

We consider the semilinear wave equation $V(x) u_{tt} -u_{xx}+q(x)u = \pm f(x,u)$ for three different classes (P1), (P2), (P3) of periodic potentials $V,q$. (P1) consists of periodically extended delta-distributions, (P2) of periodic step potentials and (P3) contains certain periodic potentials V,q\in H^r_{\per}(\R) for $r\in [1,3/2)$. Among other assumptions we suppose that $|f(x,s)|\leq c(1+ |s|^p)$ for some $c>0$ and $p>1$. In each class we can find suitable potentials that give rise to a critical exponent $p^\ast$ such that for $p\in (1,p^\ast)$ both in the "+" and the "-" case we can use variational methods to prove existence of time-periodic real-valued solutions that are localized in the space direction. The potentials are constructed explicitely in class (P1) and (P2) and are found by a recent result from inverse spectral theory in class (P3). The critical exponent $p^\ast$ depends on the regularity of $V, q$. Our result builds upon a Fourier expansion of the solution and a detailed analysis of the spectrum of the wave operator. In fact, it turns out that by a careful choice of the potentials and the spatial and temporal periods, the spectrum of the wave operator $V(x)\partial_t^2-\partial_x^2+q(x)$ (considered on suitable space of time-periodic functions) is bounded away from $0$. This allows to find weak solutions as critical points of a functional on a suitable Hilbert space and to apply tools for strongly indefinite variational problems

Existence of cylindrically symmetric ground states to a nonlinear curl-curl equation with non-constant coefficients

We consider the nonlinear curl-curl problem $\nabla\times\nabla\times U + V(x) U=f(x,|U|^2)U$ in $\mathbb{R}^3$ related to the nonlinear Maxwell equations with Kerr-type nonlinear material laws. We prove the existence of a symmetric ground-state type solution for a bounded, cylindrically symmetric coefficient $V$ and subcritical cylindrically symmetric nonlinearity $f$. The new existence result extends the class of problems for which ground-state type solutions are known. It is based on compactness properties of symmetric functions due to Lions, new rearrangement type inequalities from Brock and the recent extension of the Nehari-manifold technique by Szulkin and Weth.Comment: 13 page

Analysis of interplanetary solar sail trajectories with attitude dynamics

We present a new approach to the problem of optimal control of solar sails for low-thrust trajectory optimization. The objective was to find the required control torque magnitudes in order to steer a solar sail in interplanetary space. A new steering strategy, controlling the solar sail with generic torques applied about the spacecraft body axes, is integrated into the existing low-thrust trajectory optimization software InTrance. This software combines artificial neural networks and evolutionary algorithms to find steering strategies close to the global optimum without an initial guess. Furthermore, we implement a three rotational degree-of-freedom rigid-body attitude dynamics model to represent the solar sail in space. Two interplanetary transfers to Mars and Neptune are chosen to represent typical future solar sail mission scenarios. The results found with the new steering strategy are compared to the existing reference trajectories without attitude dynamics. The resulting control torques required to accomplish the missions are investigated, as they pose the primary requirements to a real on-board attitude control system

Company Tax Coordination cum Tax Rate Competition in the European Union

This paper reviews the recent theoretical literature that analyses the European Union’spolicy to eliminate preferential corporate tax regimes and the proposal to introduce aconsolidated EU tax base with formula apportionment for the taxation of multinationalfirms. Since neither proposal includes a harmonisation of corporate tax rates, a coreissue is how tax competition between member states will be affected by these partialcoordination measures. The conclusions from our review are supportive of the EU’s banon preferential tax regimes, but the economic incentive effects of a switch to formulaapportionment are found to be ambiguous.Corporate taxation, tax coordination, multinational firms

Company tax coordination cum tax rate competition in the European Union

This paper reviews the recent theoretical literature that analyses the European Union's policy to eliminate preferential corporate tax regimes and the proposal to introduce a consolidated EU tax base with formula apportionment for the taxation of multinational firms. Since neither proposal includes a harmonisation of corporate tax rates, a core issue is how tax competition between member states will be affected by these partial coordination measures. The conclusions from our review are supportive of the EU's ban on preferential tax regimes, but the economic incentive effects of a switch to formula apportionment are found to be ambiguous.corporate taxation; tax coordination; multinational firms