Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.

Arvoja näkyvissä : Kaunokirjallisuuden etiikka Ludwig Wittgensteinin filosofian valossa

The goal of this dissertation was to study whether it is possible and meaningful to apply Ludwig Wittgenstein s distinction between saying (Sagen) and showing (Zeigen) to ethically oriented literary criticism. The following questions were used as the primary guidelines: 1. Is it possible, in the context of literary criticism, to put in practice Wittgenstein s ethical conceptions, which are quite theoretical and metaphysical by nature? 2. If so, what practical literary devices do authors use if they want to demonstrate their ethical values within the frame of a fictional work? 3. Does philosophy offer useful ethical consepts that open us new and interesting readings in fiction? The philosophical background of Wittgenstein s distinction is clarified in chapter I. This clarification is based on his main works, Tractatus logico-philosophicus and Philosophishe Untersuchungen, the published correspondence between Wittgenstein and Paul Engelmann, and selected Wittgenstein research and papers. Analyzing ethics and it s expression in Georg Trakl s poetry further elucidates Wittgenstein s concept of showing. The concept that a literary work is an act of an author was used as a starting point. The presumption was that analyzing this act of an author will reveal how ethical values can be demonstrated in literature. Categorizing an author s act at different levels of literary expression provides the structure of this study. In chapters IV - XIII literary devices useful for demonstrating ethics are examined and explained using examples from the works of Joseph Conrad, Charles Dickens, Nikolay Leskov, Ludwig Uhland, Eino Leino, Pentti Haanpää and Maria Jotuni. The concepts and views of researchers and writers such as Mihail Bahtin, Peter Juhl, E. D. Hirsch, Peter Lamarque and Stein Haugom Olsen are used. The concepts outlined in previous chapters are then applied in three case studies: Aeschylus s Oresteia trilogy, J-L. Runeberg s poem Sven Dufva and Sofi Oksanen s novel Puhdistus (Purge). On the whole, Wittgenstein s idea that ethical values can be demonstrated (shown) by means of literature is revealed as a fruitful point of departure for a more exact ethical reading, offering a new perspective on literary works.