Cut-elimination is the most important proof transformation in logic. Equality is a central paradigm in mathematics and plays a key role in automated deduction. Therefore its importance awakes the necessity of integrating equality into existing cut-elimination methods. In this paper we extend the resolution-based method of cut-elimination CERES to CERES-e by adding equality (and paramodulation t...

Observing Earth’s radiant energy budget from space is critical to improving our understanding of Earth’s climate system. The Earth Radiation Budget Experiment (ERBE) (Barkstrom 1984; Barkstrom and Smith 1986) was the first initiative to provide simultaneous observations of Earth’s radiant energy with identical instruments flying aboard separate satellites. The design of the ERBE instrument was ...

We have investigated the possibility of main belt asteroids being trapped in the 1:1 resonance with other asteroids. Using contemporary mass estimates for the large asteroids (1) Ceres, (2) Pallas and (4) Vesta, it is found that four asteroids are temporarily trapped in such resonances with Ceres and Vesta during numerical integrations spanning 2 × 106 yr. In particular, the asteroid (1372) Har...

We continue the line of research started in [Vig08] proposing broadword (a.k.a. SWAR—“SIMD Within A Register”) algorithms for finding matching closed parentheses and the k-th far closed parenthesis. Our algorithms work in time O(logw) on a word of w bits, and contain no branch and no test instruction. On 64-bit (and wider) architectures, these algorithms make it possible to avoid costly tabulat...

We consider the full Solar System including (1) Ceres and some of the main asteroids, (2) Pallas, (4) Vesta, (7) Iris, and (324) Bamberga. We show that close encounters among these small bodies induce strong chaotic behavior in their orbits and in those of many asteroids that are much more chaotic than previously thought. Even if space missions will allow very precise measurements of the positi...

Introduction: We consider Ceres as a prototype for planetary evolution [1]. From thermal modeling by McCord and Sotin [2, 3, 4], Ceres was inferred to have differentiated into a rocky core of hydrated silicates, and an icy outer shell. Thomas et al. [5] confirmed such a model from direct observation of Ceres’s shape from Hubble Space Telescope observations, and pervious occultation measurements...

The axiomatization of arithmetical properties in theorem proving creates many straightforward inference steps. In analyzing mathematical proofs with the CERES (Cut-Elimination by Resolution) system, it is convenient to hide these inferences. The central topic of the thesis is the extension of the CERES method to allow reasoning modulo equational theories. For this, the inference systems of Sequ...

Prior to the arrival of the Dawn spacecraft at Ceres, the dwarf planet was anticipated to be ice-rich. Searches for morphological features related to ice have been ongoing during Dawn's mission at Ceres. Here we report the identification of pitted terrains associated with fresh Cerean impact craters. The Cerean pitted terrains exhibit strong morphological similarities to pitted materials previo...