Distribution of Values of Quadratic Forms at Integral Points

The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m : a<Q[m]<b\}$, which are restricted to rescaled and growing domains $r\;\Omega$, is approximated by the volume. An effective error bound of order $o(r^{d-2})$ for this approximation is proved based on Diophantine approximation properties of the quadratic form $Q$. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dimension $d \geq 9$ to dimension $d \geq 5$. They apply to wide shells when $b-a$ is growing with $r$ and to positive definite forms $Q$. For indefinite forms they provide explicit bounds (depending on the signature or Diophantine properties of $Q$) for the size of non-zero integral points $m$ in dimension $d\geq 5$ solving the Diophantine inequality $|Q[m]| < \varepsilon$ and provide error bounds comparable with those for positive forms up to powers of $\log r$.Comment: Section 4 and 7, also bounds in sections 6 have been revised and greatly extended, e.g. box artifacts for wide hyperbolic shells are removed. Applications to Diophantine lattices are revised and reduced exponents for solutions of Diophantine inequalities depending on signature are proved for large $d$, similar to integral forms. For small $d$ larger exponents are now required in Th.1.

Mythes, poésie et musique (dans les grands mythes-poèmes)

Le présent article explore la relation entre le mythe, la poésie et la musique, en cherchant à identifier leurs points de convergence et de divergence au-delà du critère de traduisibilité communément invoqué. Six grands poèmes portant sur des thèmes mythiques sont analysés en fonction de trois problèmes empiriques : ceux du corps, de la langue et de l’économie politique. L’article offre des réflexions sur la musicalité de la langue et conclut sur la question de la mythopoétique de la mort.This essay explores the relationship among myth, poetry, and music, seeking to identify points of convergence and divergence beyond the commonly cited criterion of translatability. Six major poems, drawing on mythic themes, are considered in terms of three empirical problems: the body, language, and political economy. The essay offers reflections on the musicality of language and concludes on the question of the mythopoesis of death.El presente artículo explora la relación entre el mito, la poesía y la música con el fin de identificar sus puntos de convergencia y divergencia, mas allá del criterio de traducibilidad que comúnmente se invoca. Se analizan seis grandes poemas que tratan de temas míticos, en función de tres problemas empíricos : los del cuerpo, los de la lengua y los de la economía política. El artículo ofrece reflexiones sobre la musicalidad de la lengua y concluye abordando la cuestión del mito poético de la muerte

Lenguaje, ideología y Economía Política.

Sin resume

Whither Germany?

https://stars.library.ucf.edu/prism/1644/thumbnail.jp

Generalized Cylinders in Semi-Riemannian and Spin Geometry

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics.Comment: 29 pages, 2 figure

Topology and Sizes of HII Regions during Cosmic Reionization

We use the results of large-scale simulations of reionization to explore methods for characterizing the topology and sizes of HII regions during reionization. We use four independent methods for characterizing the sizes of ionized regions. Three of them give us a full size distribution: the friends-of-friends (FOF) method, the spherical average method (SPA) and the power spectrum (PS) of the ionized fraction. These latter three methods are complementary: While the FOF method captures the size distribution of the small scale H~II regions, which contribute only a small amount to the total ionization fraction, the spherical average method provides a smoothed measure for the average size of the H~II regions constituting the main contribution to the ionized fraction, and the power spectrum does the same while retaining more details on the size distribution. Our fourth method for characterizing the sizes of the H II regions is the average size which results if we divide the total volume of the H II regions by their total surface area, (i.e. 3V/A), computed in terms of the ratio of the corresponding Minkowski functionals of the ionized fraction field. To characterize the topology of the ionized regions, we calculate the evolution of the Euler Characteristic. We find that the evolution of the topology during the first half of reionization is consistent with inside-out reionization of a Gaussian density field. We use these techniques to investigate the dependence of size and topology on some basic source properties, such as the halo mass-to-light ratio, susceptibility of haloes to negative feedback from reionization, and the minimum halo mass for sources to form. We find that suppression of ionizing sources within ionized regions slows the growth of H~II regions, and also changes their size distribution. Additionally, the topology of simulations including suppression is more complex. (abridged

Herod and Mariamne

Originally published in 1950, this volume contains a vivid English verse translation by Paul H. Curts of one of the most profound and moving tragedies of German literature

3D Visual Perception for Self-Driving Cars using a Multi-Camera System: Calibration, Mapping, Localization, and Obstacle Detection

Cameras are a crucial exteroceptive sensor for self-driving cars as they are low-cost and small, provide appearance information about the environment, and work in various weather conditions. They can be used for multiple purposes such as visual navigation and obstacle detection. We can use a surround multi-camera system to cover the full 360-degree field-of-view around the car. In this way, we avoid blind spots which can otherwise lead to accidents. To minimize the number of cameras needed for surround perception, we utilize fisheye cameras. Consequently, standard vision pipelines for 3D mapping, visual localization, obstacle detection, etc. need to be adapted to take full advantage of the availability of multiple cameras rather than treat each camera individually. In addition, processing of fisheye images has to be supported. In this paper, we describe the camera calibration and subsequent processing pipeline for multi-fisheye-camera systems developed as part of the V-Charge project. This project seeks to enable automated valet parking for self-driving cars. Our pipeline is able to precisely calibrate multi-camera systems, build sparse 3D maps for visual navigation, visually localize the car with respect to these maps, generate accurate dense maps, as well as detect obstacles based on real-time depth map extraction