The Probably and the Provable. By Jonathan L. Cohen

  Sight: Långholmen, Stockhomen ”Långholmensmarinstad” består av tre delar. En båtuppställningslada ett bostadsområde och en restaurang. Båtuppställningsladan har även en dubbel funktion som teater under sommar halvåret då Stockholmstads Parkteater får en fast spelplats och båtarna ligger i vattnet. Restarangen ligger i anslutning till båt huset och har en stor glas vägg som öppnar sig in mot Båtarna/teatern som skapar ett tydligt marint tema.   Bostadsområdet består av nio stycken radhus som vilar mot den befintliga Q-märkta fängelsemuren likt små japanskavillor med ljusgård. Det centralt placerade bostadshuset med sina fem våningar är lika högt som de gamla fängelsebyggnaderna. En lugn lummig innergård skapas emellan radhus och bostadshuset. Den lokala segel skolan får även husera i den nedre våningen av bostadshuset.      Sight: Långholmen, Stockhomen ”Långholmensmarinstad” consists of three parts. These are a large boathouse housing complex and a restaurant. The boathouse also has a double function as theatre space during the summer months when the Stockholm Parkteatern needs its seasonal venue. The restaurant is in direct adjacent to the Boathouse/theatre with a large glass wall which gives the restaurant a natural marina vibe. The housing complex consists of nine townhouses adjacent to the old heritage labelled prison wall, with small Japanese courtyards and one housing block. The housing block rises five story’s and has the same metric height as the surrounding historical prison buildings.   This creates a green peaceful inner courtyard in-between the townhouses and the housing block. The locale yachting club is given a natural haven in the ground floor space in the housing block

Minimal multiplicative covers of an integer

AbstractLet |S|=n. The numbers m(n, k)=|{(S1,…,Sk):∪ Si=S and, ∀t∈[1,k], ∪i≠lSi≠S| have been studied previously by Hearne and Wagner. The present paper treats three arrays, m̄(n,k), m̄(n,k), and m̂(n,k), which extend m(n,k) in the sense that m̂(p1⋯ps,k)=m̄(p1⋯ps,k)=m̂(p1⋯ps,k)=m(s,k) for all sequences (p1,…ps) of distinct primes

Partition Statistics and q-Bell Numbers (q = -1

We study three types of q-Bell numbers that arise as generating functions for some well known statistics on the family of partitions of a finite set, evaluating these numbers when q = −1. Among the numbers that arise in this way are (1) Fibonacci numbers and (2) numbers occurring in the study of fermionic oscillators.

On the chromatic roots of generalized theta graphs

The generalized theta graph \Theta_{s_1,...,s_k} consists of a pair of endvertices joined by k internally disjoint paths of lengths s_1,...,s_k \ge 1. We prove that the roots of the chromatic polynomial $pi(\Theta_{s_1,...,s_k},z) of a k-ary generalized theta graph all lie in the disc |z-1| \le [1 + o(1)] k/\log k, uniformly in the path lengths s_i. Moreover, we prove that \Theta_{2,...,2} \simeq K_{2,k} indeed has a chromatic root of modulus [1 + o(1)] k/\log k. Finally, for k \le 8 we prove that the generalized theta graph with a chromatic root that maximizes |z-1| is the one with all path lengths equal to 2; we conjecture that this holds for all k.Comment: LaTex2e, 25 pages including 2 figure

Cloud chamber experiments on the origin of ice crystal complexity in cirrus clouds

This is an open access article, made available under the terms of the Creative Commons attribution license CC BY 3.0 https://creativecommons.org/licenses/by/3.0/This study reports on the origin of ice crystal complexity and its influence on the angular light scattering properties of cirrus clouds. Cloud simulation experiments were conducted at the AIDA (Aerosol Interactions and Dynamics in the Atmosphere) cloud chamber of the Karlsruhe Institute of Technology (KIT). A new experimental procedure was applied to grow and sublimate ice particles at defined super- and subsaturated ice conditions and for temperatures in the −40 to −60 °C range. The experiments were performed for ice clouds generated via homogeneous and heterogeneous initial nucleation. Ice crystal complexity was deduced from measurements of spatially resolved single particle light scattering patterns by the latest version of the Small Ice Detector (SID-3). It was found that a high ice crystal complexity is dominating the microphysics of the simulated clouds and the degree of this complexity is dependent on the available water vapour during the crystal growth. Indications were found that the crystal complexity is influenced by unfrozen H2SO4/H2O residuals in the case of homogeneous initial ice nucleation. Angular light scattering functions of the simulated ice clouds were measured by the two currently available airborne polar nephelometers; the Polar Nephelometer (PN) probe of LaMP and the Particle Habit Imaging and Polar Scattering (PHIPS-HALO) probe of KIT. The measured scattering functions are featureless and flat in the side- and backward scattering directions resulting in low asymmetry parameters g around 0.78. It was found that these functions have a rather low sensitivity to the crystal complexity for ice clouds that were grown under typical atmospheric conditions. These results have implications for the microphysical properties of cirrus clouds and for the radiative transfer through these clouds.Peer reviewedFinal Published versio