Optical characteristics of Nd:YAG optics and distortions at high power

The intensity profile and beam caustics of a fiber coupled high power Nd:YAG laser beam through a lens system are studied. The thermal lensing effect and its influence on the beam profile and focal position are discussed. Asymmetry of the intensity profile in planes above and below the focal plane is demonstrated. Also the influence of small pollutions on the protective window is explained. Three different methods are used to measure the occurrence\ud of thermal lensing and quantify these effects

Sacrament of holy communion: a real fellowship

Luther turns to the sacraments into to rewrite the contours of a Christian life (and theology). The sacraments and especially the sacrament of Holy Communion, as a place of proclamation, exercise us in faith. In order to highlight this characteristic, Luther works with the metaphor of the happy exchange - a metaphor that has been sidelined or even forgotten by some current of Lutheran theology. Yet, it is in the happy exchange that for Luther the real significant of this sacrament lies: a true fellowship

Disrupting Worship

Worship is not for some pragmatic or utilitarian purpose. Nor do we offer something in worship in order to receive something in return. Worship is to remember the Christ event, to allow Christ to become “for us” as the gathered Christian assembly

Five Hundred Years of Reformation: A Joint Commemoration

In the sixteenth century, Catholics and Lutherans frequently not only misunderstood but also exaggerated and caricatured their opponents in order to make them look ridiculous. Now, the Lutheran World Federation and the Pontifical Council for Promoting Christian Unity have produced a liturgy for a joint commemoration of the five hundredth anniversary of the Reformation

A Communion That Is Holy: A Gospel Economy

The sacrament of Holy Communion trains us in a gospel economy. Receiving from God, we are taught to give. Freed from an obsessive attraction to temporal things, but also from a pious repulsion of them, we are drawn into a holy communion with God, neighbor, and material goods

Cost optimal control of Piecewise Deterministic Markov Processes under partial observation

This work deals with the optimal control problem for Piecewise Deterministic Markov Processes (PDMP) under Partial Observation (PO). The total expected discounted cost over lifetime shall be minimized while neither the states of the PDMP nor the current or cumulated cost are observable. Only noisy measurements (with known noise distribution) of the post-jump states are observable. The cost function, however, depends on the trajectory of the unobservable PDMP as well as on the observable noisy measurements of the post-jump states. Admissible control strategies are history dependent relaxed piecewise open loop strategies: For each point in time and depending on the observable history up to this time, a probability distribution on the action space is selected. This probability distribution defines an expected control action on the jump rate, the drift and the transition kernel at jump times of the PDMP. We first transform the initial continuous-time optimization problem under PO into an equivalent discrete-time optimization problem under PO. For the latter one, we obtain a recursive formulation for the filter: the probability distribution of the unobservable post-jump state of the PDMP given the observable history. This leads to an equivalent fully observable optimization problem in discrete time. Classical approaches of stochastic dynamic programming in combination with results for measurable selection of optimizers are then applied to prove the existence of optimal control strategies. We derive sufficient conditions for the existence of optimal control strategies for lower semi-continuous cost functions and in the case of finite dimensional filters, i.e. if the set of possible post-jump states of the PDMP is finite. Finally, we apply the theory developed in this work to a concrete example of a three states problem that could arise, e.g., from moving particles facing disturbances of their trajectories at random points in time