Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

Flavor symmetry breaking effects on SU(3) Skyrmion

We study the massive SU(3) Skyrmion model to investigate the flavor symmetry breaking (FSB) effects on the static properties of the strange baryons in the framework of the rigid rotator quantization scheme combined with the improved Dirac quantization one. Both the chiral symmetry breaking pion mass and FSB kinetic terms are shown to improve $c$ the ratio of the strange-light to light-light interaction strengths and $\bar{c}$ that of the strange-strange to light-light.Comment: 12 pages, latex, no figure

Discovery Reach of Charged MSSM Higgs Bosons at CMS

We review the 5 sigma discovery contours for the charged MSSM Higgs boson at the CMS experiment with 30/fb for the two cases M_H+ m_t. In order to analyze the search reach we combine the latest results for the CMS experimental sensitivities based on full simulation studies with state-of-the-art theoretical predictions of MSSM Higgs-boson production and decay properties. Special emphasis is put on the SUSY parameter dependence of the 5 sigma contours. The variation of $\mu$ can shift the prospective discovery reach in tan_beta by up to Delta tan_beta = 40.Comment: 3 pages, 2 figures, talk given at SUSY08, Seoul, Kore

A comparative study of benchmarking approaches for non-domestic buildings: Part 1 – Top-down approach

Benchmarking plays an important role in improving energy efficiency of non-domestic buildings. A review of energy benchmarks that underpin the UK’s Display Energy Certificate (DEC) scheme have prompted necessities to explore the benefits and limitations of using various methods to derive energy benchmarks. The existing methods were reviewed and grouped into top-down and bottom-up approaches based on the granularity of the data used. In the study, two top-down methods, descriptive statistics and artificial neural networks (ANN), were explored for the purpose of benchmarking energy performances of schools. The results were used to understand the benefits of using these benchmarks for assessing energy efficiency of buildings and the limitations that affect the robustness of the derived benchmarks. Compared to the bottom-up approach, top-down approaches were found to be beneficial in gaining insight into how peers perform. The relative rather than absolute feedback on energy efficiency meant that peer pressure was a motivator for improvement. On the other hand, there were limitations with regard to the extent to which the energy efficiency of a building could be accurately assessed using the top-down benchmarks. Moreover, difficulties in acquiring adequate data were identified as a key limitation to using the top-down approach for benchmarking non-domestic buildings. The study suggested that there are benefits in rolling out of DECs to private sector buildings and that there is a need to explore more complex methods to provide more accurate indication of energy efficiency in non-domestic buildings

Selecting Finite Unified Theories with Current Data

Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of low-energy phenomenology observables. Using the restrictions from the top and bottom quark masses, it is possible to discriminate between different models. Including further low-energy constraints such as B-physics observables, the bound on the lightest Higgs boson mass and the cold dark matter density, we derive the predictions for the supersymmetric particle spectrum and the prospects for discoveries at the LHC.Comment: 3 pages, 3 figures, talk given at SUSY08, Seoul, Kore

Straight-line Drawability of a Planar Graph Plus an Edge

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing

Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016). This is an extended abstract. For a full version of this paper, see Hong S-H, Nagamochi H.: Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time, Technical Report TR 2016-002, Department of Applied Mathematics and Physics, Kyoto University (2016

Imaging and burst location with the EXIST high-energy telescope

The primary instrument of the proposed EXIST mission is a coded mask high energy telescope (the HET), that must have a wide field of view and extremely good sensitivity. It will be crucial to minimize systematic errors so that even for very long total integration times the imaging performance is close to the statistical photon limit. There is also a requirement to be able to reconstruct images on-board in near real time in order to detect and localize gamma-ray bursts. This must be done while the spacecraft is scanning the sky. The scanning provides all-sky coverage and is key to reducing systematic errors. The on-board computational problem is made even more challenging for EXIST by the very large number of detector pixels. Numerous alternative designs for the HET have been evaluated. The baseline concept adopted depends on a unique coded mask with two spatial scales. Monte Carlo simulations and analytic analysis techniques have been used to demonstrate the capabilities of the design and of the proposed two-step burst localization procedure