Traditionen, Themen, Trends. Pädagogisch-psychologische Forschung aus Sicht einer Zeitzeugin. Ein Interview mit Frau Prof. Dr. Elfriede Höhn anlässlich ihres 80. Geburtstages

Ein Interview wird vorgelegt, das E. Klein-Allermann mit Elfriede Höhn führte. Im Mittelpunkt stehen dabei die Erfahrungen, die Höhn im Zusammenhang mit der Entwicklung der pädagogisch-psychologischen Forschung seit Mitte der sechziger Jahre gesammelt hat

A-Tint: A polymake extension for algorithmic tropical intersection theory

In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of computing certain tropical cycles. The algorithms discussed here have been implemented in an extension for polymake, a software for polyhedral computations.Comment: 32 pages, 5 figures, 4 tables. Second version: Revised version, to be published in European Journal of Combinatoric

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Effects of Salicornia-Based Skin Cream Application on Healthy Humans’ Experimental Model of Pain and Itching

Halophyte plants are salt-tolerant and are acclimated for growth in saline soils such as along coastal areas. Among the halophytes, the Salicornia species have been used as both folk medicine and functional food for many years due to their high levels of bioactive compounds with supposed anti-inflammatory and antioxidative effects. However, the properties of Salicornia bioactive extracts on pain and itching still remain unclear. In this study, 30 healthy volunteers were randomized to treatments with 10% Salicornia-based cream or placebo cream for 24 or 48 h. On day 0, and 24 or 48 h post cream application, cold/heat detection and pain thresholds, mechanical pain thresholds and sensitivity, trans-epidermal water loss, histamine- and cowhage-evoked itch, and micro-vascular reactivity (neurogenic inflammation) were assessed to evaluate the analgesic, anti-pruritogenic and vasomotor effects. Skin permeability was reduced in the Salicornia-treated area for 48 h compared with 24 h application (p-value < 0.05). After 48 h of application, a decrease in mechanical-evoked itching (hyperkinesis) compared with 24 h treatment (p-value < 0.05) and increased warm detection and heat pain thresholds (p-value < 0.05) was found. Histamine-induced neurogenic inflammation showed a significant reduction in the cream-treated areas after 48 h compared with 24 h (p-value < 0.05). The results of this study indicate the overall inhibitory effect of Salicornia on hyperkinesis (mechanically evoked itch), the analgesic effect on thermal sensation, and modulation of the skin barrier architecture. Further studies are needed for the assessment of the long-term effects

Tropical intersection theory

This thesis consists of five chapters: Chapter 1 contains the basics of the theory and is essential for the rest of the thesis. Chapters 2-5 are to a large extent independent of each other and can be read separately. - Chapter 1: Foundations of tropical intersection theory In this first chapter we set up the foundations of a tropical intersection theory covering many concepts and tools of its counterpart in algebraic geometry such as affine tropical cycles, Cartier divisors, morphisms of tropical cycles, pull-backs of Cartier divisors, push-forwards of cycles and an intersection product of Cartier divisors and cycles. Afterwards, we generalize these concepts to abstract tropical cycles and introduce a concept of rational equivalence. Finally, we set up an intersection product of cycles and prove that every cycle is rationally equivalent to some affine cycle in the special case that our ambient cycle is R^n. We use this result to show that rational and numerical equivalence agree in this case and prove a tropical Bézout's theorem. - Chapter 2: Tropical cycles with real slopes and numerical equivalence In this chapter we generalize our definitions of tropical cycles to polyhedral complexes with non-rational slopes. We use this new definition to show that if our ambient cycle is a fan then every subcycle is numerically equivalent to some affine cycle. Finally, we restrict ourselves to cycles in R^n that are "generic" in some sense and study the concept of numerical equivalence in more detail. - Chapter 3: Tropical intersection products on smooth varieties We define an intersection product of tropical cycles on tropical linear spaces L^n_k and on other, related fans. Then, we use this result to obtain an intersection product of cycles on any "smooth" tropical variety. Finally, we use the intersection product to introduce a concept of pull-backs of cycles along morphisms of smooth tropical varieties and prove that this pull-back has all expected properties. - Chapter 4: Weil and Cartier divisors under tropical modifications First, we introduce "modifications" and "contractions" and study their basic properties. After that, we prove that under some further assumptions a one-to-one correspondence of Weil and Cartier divisors is preserved by modifications. In particular we can prove that on any smooth tropical variety we have a one-to-one correspondence of Weil and Cartier divisors. - Chapter 5: Chern classes of tropical vector bundles We give definitions of tropical vector bundles and rational sections of tropical vector bundles. We use these rational sections to define the Chern classes of such a tropical vector bundle. Moreover, we prove that these Chern classes have all expected properties. Finally, we classify all tropical vector bundles on an elliptic curve up to isomorphisms.Tropische Schnitttheori