Minkowski decompositions for generalized associahedra of acyclic type

We give an explicit subword complex description of the generators of the type cone of the g-vector fan of a finite type cluster algebra with acyclic initial seed. This yields in particular a description of the Newton polytopes of the F-polynomials in terms of subword complexes as conjectured by S. Brodsky and the third author. We then show that the cluster complex is combinatorially isomorphic to the totally positive part of the tropicalization of the cluster variety as conjectured by D. Speyer and L. Williams.Comment: 17 pages. v2: updated and extended examples, added footnote that Theorem 1.4 also follows from [AHL20, Theorems 4.1 & 4.2

The Newton polytope of the discriminant of a quaternary cubic form

We determine the 166104 extremal monomials of the discriminant of a quaternary cubic form. These are in bijection with D-equivalence classes of regular triangulations of the 3-dilated tetrahedron. We describe how to compute these triangulations and their D-equivalence classes in order to arrive at our main result. The computation poses several challenges, such as dealing with the sheer number of triangulations effectively, as well as devising a suitably fast algorithm for computation of a D-equivalence class

Poly(ionic liquid) Based Composite Electrolytes for Lithium Ion Batteries

Polymerized ionic liquids (PIL) are an interesting substance class, which is discussed to transfer the outstanding properties and tunability of ionic liquids into a solid material. In this study we extend our previous research on ammonium based PIL and discuss the influence of additives and their usability as polymer electrolyte membranes for lithium ion batteries. The polymer electrolyte is thereby used as replacement for the commercially widespread system of a separator that is soaked with liquid electrolyte. The influence of the material composition on the ionic conductivity (via electrochemical impedance spectroscopy) and the diffusion coefficients (via pulsed-field-gradient nuclear magnetic resonance spectroscopy) were studied and cell tests with adapted membrane materials were performed. High amounts of the additional ionic liquid (IL) MPPyrr-TFSI (1-methyl-1-propylpyrrolidinium bis(trifluoromethylsulfonyl)imide) increased the ionic conductivity of the materials up to 1.3·10−4 S·cm−1 but made the usage of a cross-linker necessary to obtain mechanically stable membranes. The application of liquid electrolyte mixtures with ethylene carbonate (EC) and MPPyrr-TFSI decreased ionic conductivity values down to the 10−9 S·cm−1 range, but increased 7Li diffusion coefficients with increasing amounts of EC up to 1.7·10−10 m2·s−1. Cell tests with two membrane mixtures proofed that it is possible to build electrolyte membranes on basis of the polymerized ionic liquids, but also showed that further research is necessary to ensure stable and efficient cell cycling

Structure–Property Relationship of Polymerized Ionic Liquids for Solid-State Electrolyte Membranes

Eight new polymerized ammonium‐based ionic liquids were prepared as thin membrane films and evaluated within the scope of their usage in lithium‐ion batteries. The focus of this work is to get a better understanding of the influence of structural modifications of the monomers on the polymerized materials. Further, different concentrations of a lithium‐ion conducting salt were applied in order to receive an optimized combination of monomer structure and lithium salt concentration. It was found that an increased side chain length of the studied ammonium‐based polymerized ionic liquids leads to a reduction in glass transition temperatures and increased ionic conductivity values. As a result of the addition of conducting salt to the PIL membranes, the glass transition temperatures and the ionic conductivity values decreases. Nevertheless, PFG‐NMR reveals a higher lithium‐ion mobility for a sample with higher conducting salt content

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Constructing illoyal algebra-valued models of set theory

AbstractAn algebra-valued model of set theory is called loyal to its algebra if the model and its algebra have the same propositional logic; it is called faithful if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: tail stretches, transposition twists, and maximal twists.</jats:p

GRASS GIS, Star Trek and old Video Tape

This paper discusses the need for the preservation of audiovisual content in the OSGeo communities beyond the established software repositories. Audiovisual content related to OSGeo projects such as training videos can be preserved by multimedia archiving and retrieval services which are currently developed by the library community. This is demonstrated by the reference case of a newly discovered version of the GRASS GIS 1987 promotional video which is being included into the AV-portal of the German National Library of Science and Technology (TIB). Access to the video will be provided upon the release of the web-based portal, allowing for extended search capabilities based on enhanced metadata derived by automated video analysis. This is a reference case for future preservation activities regarding semanticenhanced Web2.0 content from OSGeo project

GRASS GIS, Star Trek and old Video Tape

This paper discusses the need for the preservation of audiovisual content in the OSGeo communities beyond the established software repositories. Audiovisual content related to OSGeo projects such as training videos can be preserved by multimedia archiving and retrieval services which are currently developed by the library community. This is demonstrated by the reference case of a newly discovered version of the GRASS GIS 1987 promotional video which is being included into the AV-portal of the German National Library of Science and Technology (TIB). Access to the video will be provided upon the release of the web-based portal, allowing for extended search capabilities based on enhanced metadata derived by automated video analysis. This is a reference case for future preservation activities regarding semantic-enhanced Web2.0 content from OSGeo projects