Journal Staff

The usage of 3D-modeling is expanding rapidly. Modeling from aerial imagery has become very popular due to its increasing number of both civilian and mili- tary applications like urban planning, navigation and target acquisition. This master thesis project was carried out at Vricon Systems at SAAB. The Vricon system produces high resolution geospatial 3D data based on aerial imagery from manned aircrafts, unmanned aerial vehicles (UAV) and satellites. The aim of this work was to investigate to what degree superpixel segmentation and supervised learning can be applied to a terrain classification problem using imagery and digital surface models (dsm). The aim was also to investigate how the height information from the digital surface model may contribute compared to the information from the grayscale values. The goal was to identify buildings, trees and ground. Another task was to evaluate existing methods, and compare results. The approach for solving the stated goal was divided into several parts. The first part was to segment the image using superpixel segmentation, after that features were extracted. Then the classifiers were created and trained and finally the classifiers were evaluated. The classification method that obtained the best results in this thesis had approx- imately 90 % correctly labeled superpixels. The result was equal, if not better, compared to other solutions available on the market.

Distribution of integral values for the ratio of two linear recurrences

Let $F$ and $G$ be linear recurrences over a number field $\mathbb{K}$, and let $\mathfrak{R}$ be a finitely generated subring of $\mathbb{K}$. Furthermore, let $\mathcal{N}$ be the set of positive integers $n$ such that $G(n) \neq 0$ and $F(n) / G(n) \in \mathfrak{R}$. Under mild hypothesis, Corvaja and Zannier proved that $\mathcal{N}$ has zero asymptotic density. We prove that $\#(\mathcal{N} \cap [1, x]) \ll x \cdot (\log\log x / \log x)^h$ for all $x \geq 3$, where $h$ is a positive integer that can be computed in terms of $F$ and $G$. Assuming the Hardy-Littlewood $k$-tuple conjecture, our result is optimal except for the term $\log \log x$

On the sum of digits of the factorial

Let b > 1 be an integer and denote by s_b(m) the sum of the digits of the positive integer m when is written in base b. We prove that s_b(n!) > C_b log n log log log n for each integer n > e, where C_b is a positive constant depending only on b. This improves of a factor log log log n a previous lower bound for s_b(n!) given by Luca. We prove also the same inequality but with n! replaced by the least common multiple of 1,2,...,n.Comment: 4 page

High ionic conductivity in confined heterostructures

The charge transport in oxide thin films could be tuned by the lattice strain engineering resulting in a new class of materials that can be considered fundamental bricks of new generation of devices for energy storage, conversion, and information [1-5]. In particular oxide heterostructures are a very promising type of artificial materials owing to possibility to manipulate the ionic and electronic properties at the interfaces by controlling the properties of the different layers, e.g. epitaxial strain. In these heterostructures, size effects of the layers can lead to enhanced conductivity of the charge carries at the interfaces when, for example, the number of interfaces is increased and/or the thickness of the individual layers decrease. High conductivity in thin heterostructures is often attributed either to the presence of a high density of defects, strain at the interface or space charge effects [1-2]. The latter is the case for heterostructure made of alternate layers of doped Ceria (SDC) and stabilized Zirconia (YSZ) where the ionic conductivity can increase about two order of compared to bulk [2]. However we have demonstrated that the heterostructures could be engineered in order to preserve materials with high ionic conductivity but usually, unstable by confining in more stable materials. This is the case for heterostructures based on bismuth-oxide-based materials. Indeed δ-Bi2O3 with the fluorite structure can be confined at room temperature by depositing alternating layers of bismuth-based oxide material stacked between fluorite materials as Gadolinium-doped Ceria (CGO) or YSZ [4-5]. As consequence, the heterostructures based on bismuth-oxide remain stable without degradation under oxidizing and reducing conditions for a wide range of temperatures, and maintain the high ionic conductivity characteristic of the typical bismuth oxide. References [1] N. Sata, K. Eberl, K. Eberman, J. Maier. Nature, 408 (2000) 946-949. [2] S. Sanna, V. Esposito, A. Tebano, S. Licoccia, E. Traversa, G. Balestrino. Small 6, (2010) 1863-1867. [3] E. Dagotto. Science, 318 (2007) 1076-1077. [4] S. Sanna, V. Esposito, J.W. Andreasen, J. Hjelm,W. Zhang, T. Kasama, S. B. Simonsen, M. Christensen, S. Linderoth, N. Pryds, Nat. Mater. 14, (2015) 500-504. [5] S. Sanna, V. Esposito, Mogens Christensen, Nini Pryds. APL Mater. 4, (2016) 121101 1-5.Universidad de Málaga. Camppus de Excelencia Internacional Andalucía Tec

Covering an arithmetic progression with geometric progressions and vice versa

We show that there exists a positive constant C such that the following holds: Given an infinite arithmetic progression A of real numbers and a sufficiently large integer n (depending on A), there needs at least Cn geometric progressions to cover the first n terms of A. A similar result is presented, with the role of arithmetic and geometric progressions reversed.Comment: 4 page

Survival of Political Leadership

We focus on political violence as a mechanism that allows the political leader to fight off opposition and increase his chances of re-election. In a collusive equilibrium, the leader allocates a bribe to the army, and the latter responds by producing political violence. Such an equilibrium is more likely, the larger are the public resources available to the leader; the lower is army�s potential punishment and salary offered by the opposition regime; the more severe is the incumbent�s potential punishment; and when the political leader is sufficiently patient, but the army is shortsighted enough.

A note on primes in certain residue classes

Given positive integers $a_1,\ldots,a_k$, we prove that the set of primes $p$ such that $p \not\equiv 1 \bmod{a_i}$ for $i=1,\ldots,k$ admits asymptotic density relative to the set of all primes which is at least $\prod_{i=1}^k \left(1-\frac{1}{\varphi(a_i)}\right)$, where $\varphi$ is the Euler's totient function. This result is similar to the one of Heilbronn and Rohrbach, which says that the set of positive integer $n$ such that $n \not\equiv 0 \bmod a_i$ for $i=1,\ldots,k$ admits asymptotic density which is at least $\prod_{i=1}^k \left(1-\frac{1}{a_i}\right)$