Faithful Lie algebra modules and quotients of the universal enveloping algebra

We describe a new method to determine faithful representations of small dimension for a finite dimensional nilpotent Lie algebra. We give various applications of this method. In particular we find a new upper bound on the minimal dimension of a faithful module for the Lie algebras being counter examples to a well known conjecture of J. Milnor

TRP Channels in Health and Disease

Almost 25 years ago, the first mammalian transient receptor potential (TRP) channel was cloned and published. TRP channels now represent an extended family of 28 members fulfilling multiple roles in the living organism. Identified functions include control of body temperature, transmitter release, mineral homeostasis, chemical sensing, and survival mechanisms in a challenging environment. The TRP channel superfamily covers six families: TRPC with C for “canonical”, TRPA with A for “ankyrin”, TRPM with M for “melastatin”, TRPML with ML for “mucolipidin”, TRPP with P for “polycystin”, and TRPV with V for “vanilloid”. Over the last few years, new findings on TRP channels have confirmed their exceptional function as cellular sensors and effectors. This Special Book features a collection of 8 reviews and 7 original articles published in “Cells” summarizing the current state-of-the-art on TRP channel research, with a main focus on TRP channel activation, their physiological and pathophysiological function, and their roles as pharmacological targets for future therapeutic options

Towards Next Generation Business Process Model Repositories – A Technical Perspective on Loading and Processing of Process Models

Business process management repositories manage large collections of process models ranging in the thousands. Additionally, they provide management functions like e.g. mining, querying, merging and variants management for process models. However, most current business process management repositories are built on top of relation database management systems (RDBMS) although this leads to performance issues. These issues result from the relational algebra, the mismatch between relational tables and object oriented programming (impedance mismatch) as well as new technological developments in the last 30 years as e.g. more and cheap disk and memory space, clusters and clouds. The goal of this paper is to present current paradigms to overcome the performance problems inherent in RDBMS. Therefore, we have to fuse research about data modeling along database technologies as well as algorithm design and parallelization for the technology paradigms occurring nowadays. Based on these research streams we have shown how the performance of business process management repositories could be improved in terms of loading performance of processes (from e.g. a disk) and the computation of management techniques resulting in even faster application of such a technique. Exemplarily, applications of the compiled paradigms are presented to show their applicability

Sterile neutrino dark matter: impact of active-neutrino opacities

Bödeker D, Klaus A. Sterile neutrino dark matter: impact of active-neutrino opacities. Journal of High Energy Physics. 2020;2020(7): 218.The resonant production of keV sterile-neutrino dark matter mainly takes place during the QCD epoch of the early universe. It has been argued that it could be strongly affected by the opacities (or damping rates) of active neutrinos, which receive non-perturbative QCD-contributions. We find that for lepton asymmetries nL alpha/s below 10(-6) the opacities significantly affect the sterile-neutrino yield, but that for larger asymmetries, which are necessary for producing a significant fraction of the dark matter, the yield is insensitive to changes of the opacities. Thus non-perturbative QCD contributions to the opacities at temperatures around 160 MeV will not affect this dark matter scenario. We obtain larger sterile-neutrino yields than previous studies, and thus weaker lower limits on the active-sterile mixing angle from Big Bang Nucleosynthesis