The obstacle problem for subelliptic non-divergence form operators on homogeneous groups

The main result established in this paper is the existence and uniqueness of strong solutions to the obstacle problem for a class of subelliptic operators in non-divergence form. The operators considered are structured on a set of smooth vector fields in R^n; X = \{X_0, X_1, ...,X_q\}, q \le n, satisfying H\"ormanders finite rank condition. In this setting, X_0 is a lower order term while {X1, ...,X_q} are building blocks of the subelliptic part of the operator. In order to prove this, we establish an embedding theorem under the assumption that the set {X_0, X_1, ...,X_q} generates a homogeneous Lie group. Furthermore, we prove that any strong solution belongs to a suitable class of H\"older continuous functions

Long-Term Quantitative Microscopy: From Microbial Population Dynamics to Growth of Plant Roots

Quantitative optical measurements at the micron scale have been crucial to the study of multiple biological processes, including bacterial chemotaxis, eukaryotic gene expression and y development. Extending measurements to long time scales allows complete observation of processes that are otherwise studied piecemeal, such as development and evolution. This thesis describes the development of two types of microscope for making long term, quantitative measurements, and the tools for image analysis. The rst device is a digital holographic microscope for measuring microbial population dynamics. It allows three dimensional localization of hundreds of cells within a mm3 sized volume, at micron resolution and an acquisition period of minutes. The technique is simple and inexpensive, which enabled us to construct ten replicate devices for parallel measurements. Each device incorporates precise and programmable control of light and temperature for the microbial ecosystem. Experiments were performed with the green algae Chlamydomonas reinhardtii and the ciliate Tetrahymena reinhardtii, both together and in isolation, and continued for as long as 90 days. The population dynamics exhibited a striking degree of repeatability, despite the presence of added noise in the illumination, spatial gradients of cell density, convection currents and phenotypic changes of both species. The second device is a thin light sheet fluorescence microscope for tracking nuclei in growing roots of the flowering plant Arabidopsis thaliana. The device incorporates a chamber designed to maintain optical quality while providing conditions for root growth. Optical feedback to a translation stage is used to maintain the root tip in the fi eld of view as the root grows by centimeters over several days. Data from a three day experiment is presented to demonstrate the technique. Over 1,000 nuclei were tracked simultaneously, and hundreds of cell divisions were automatically identif ed. The device was also used to image the regeneration of a root tip after surgical excision. The data corroborate earlier investigations at a more detailed level than was previously possible

Pure economic loss from a comparative perspective

English law originally did not provide an action in cases where pure economic loss was caused negligently. From the Middle Ages (i.e. from more or less the 13th century), when there arose a remedy called 'trespass', which was applicable only in cases of direct forcible injury

Generalforsamling i Science Museernes Venner

Torsdag 30. marts 2023 blev der afholdt ordinær generalforsamling på Steno Museet