Lie coalgebras

AbstractA Lie coalgebra is a coalgebra whose comultiplication Δ : M → M ⊗ M satisfies the Lie conditions. Just as any algebra A whose multiplication ϕ : A ⊗ A → A is associative gives rise to an associated Lie algebra L(A), so any coalgebra C whose comultiplication Δ : C → C ⊗ C is associative gives rise to an associated Lie coalgebra Lc(C). The assignment C ↦ Lc(C) is functorial. A universal coenveloping coalgebra Uc(M) is defined for any Lie Lie coalgebra M by asking for a right adjoint Uc to Lc. This is analogous to defining a universal enveloping algebra U(L) for any Lie algebra L by asking for a left adjoint U to the functor L. In the case of Lie algebras, the unit (i.e., front adjunction) 1 → L o U of the adjoint functor pair U ⊣ L is always injective. This follows from the Poincaré-Birkhoff-Witt theorem, and is equivalent to it in characteristic zero (x = 0). It is, therefore, natural to inquire about the counit (i.e., back adjunction) Lc o Uc → 1 of the adjoint functor pair Lc ⊣ Uc.Theorem. For any Lie coalgebra M, the natural mapLc(UcM) → M is surjective if and only if M is locally finite, (i.e., each element of M lies in a finite dimensional sub Lie coalgebra of M).An example is given of a non locally finite Lie coalgebra. The existence of such an example is surprising since any coalgebra C whose diagonal Δ is associative is necessarily locally finite by a result of that theory. The present paper concludes with a development of an analog of the Poincaré-Birkhoff-Witt theorem for Lie algebras which we choose to call the Dual Poincaré-Birkhoff-Witt Theorem and abbreviate by “The Dual PBWθ.” The constraints of the present paper, however, allow only a sketch of this theorem. A complete proof will appear in a subsequent paper. The reader may, however, consult [12], in the meantime, for details. The Dual PBWθ shows for any locally finite Lie coalgebra M the existence (in χ = 0) of a natural isomorphism of the graded Hopf algebras 0E(UcM) and 0E(ScM) associated to UcM and to ScM = Uc(TrivM) when Uc(M) and Sc(M) are given the Lie filtrations. [Just as Uc(M) is the analog of the enveloping algebra U(L) of a Lie algebra L, so Sc(V) is the analog of the symmetric algebra S(V) on a vector space V. Triv(M) denotes the trivial Lie coalgebra structure on the underlying vector space of M obtained by taking the comultiplication to be the zero map.

Optimization of preparation condition of Ce1-xMxOy AND Ni/Ce1-xMxOy (M = Gd, La, Mg) nanomaterials for hydrogen power engineering

Nanomaterials Ce1-xMxOy and Ni/Ce1-xMxOy (M = Gd, La, Mg, x = 0-0,5) were prepared at variation of temperature, medium and duration of thermal treatment. The effects of type (M = Gd, La, Mg) and content (x = 0-0,5) of doping cation (M) on crystal structure and sintering of nanomaterials during calcination were investigated. It was shown that phase composition of materials did not change under rising of calcination temperature up to 800oC. The material stability against the sintering during thermal treatment increases at an increase of La or Mg content in the materials. The comparative study of functional properties of Ni/Ce1-xMxOy materials was carried out in autothermal reforming of ethanol (ATR of C2H5OH). It is demonstrated that Ni/Ce1-xMxOy samples provide high hydrogen yield in ATR of C2H5OH, which indicates their perspective application for hydrogen power engineering

Methane turnover and temperature response of methane-oxidizing bacteria in permafrost-affected soils of northeast Siberia

The abundance, activity, and temperature response of aerobic methane-oxidizing bacteria were studied in permafrost-affected tundra soils of northeast Siberia. The soils were characterized by both a high accumulation of organic matter at the surface and high methane concentrations in the water-saturated soils. The methane oxidation rates of up to 835 nmol CH4 h−1 g−1 in the surface soils were similar to the highest values reported so far for natural wetland soils worldwide. The temperature response of methane oxidation was measured during short incubations and revealed maximum rates between 22 °C and 28 °C. The active methanotrophic community was characterized by its phospholipid fatty acid (PLFA) concentrations and with stable isotope probing (SIP). Concentrations of 16:1ω8 and 18:1ω8 PLFAs, specific to methanotrophic bacteria, correlated significantly with the potential methane oxidation rates. In all soils, distinct 16:1 PLFAs were dominant, indicating a predominance of type I methanotrophs. However, long-term incubation of soil samples at 0 °C and 22 °C demonstrated a shift in the composition of the active community with rising temperatures. At 0 °C, only the concentrations of 16:1 PLFAs increased and those of 18:1 PLFAs decreased, whereas the opposite was true at 22 °C. Similarly, SIP with 13CH4 showed a temperature-dependent pattern. When the soils were incubated at 0 °C, most of the incorporated label (83%) was found in 16:1 PLFAs and only 2% in 18:1 PLFAs. In soils incubated at 22 °C, almost equal amounts of 13C label were incorporated into 16:1 PLFAs and 18:1 PLFAs (33% and 36%, respectively). We concluded that the highly active methane-oxidizing community in cold permafrost-affected soils was dominated by type I methanotrophs under in situ conditions. However, rising temperatures, as predicted for the future, seem to increase the importance of type II methanotrophs, which may affect methane cycling in northern wetlands

Soft-Goods-Dispenser: eine neue Kommissioniertechnik

Ein amerikanischer Konzern vergab den Auftrag über Entwicklung und den Bau eines Mehrlevel-Soft-Goods-Dispenser-Prototyps an ein deutsches lngenieurbüro. Für die konstruktive Ausbildung und die Funktionsweise dieses Kommissionier-Systems für "weich" verpackte, biegeschlaffe Teile entstanden neue Komponenten und Gesamtlösungen mit zukunftsweisender Charakteristik. Nach den gemessenen Leistungsdaten und der getesteten Artikelvielfalt bestehen hinsichtlich der Wirtschaftlichkeit und Einsatzplanung zum ersten Mal günstige Voraussetzungen für die automatische Kommissionierung in Versand und Großhandelsbetrieben

Massive stereo-based DTM production for Mars on cloud computers

Digital Terrain Model (DTM) creation is essential to improving our understanding of the formation processes of the Martian surface. Although there have been previous demonstrations of open-source or commercial planetary 3D reconstruction software, planetary scientists are still struggling with creating good quality DTMs that meet their science needs, especially when there is a requirement to produce a large number of high quality DTMs using "free" software. In this paper, we describe a new open source system to overcome many of these obstacles by demonstrating results in the context of issues found from experience with several planetary DTM pipelines. We introduce a new fully automated multi-resolution DTM processing chain for NASA Mars Reconnaissance Orbiter (MRO) Context Camera (CTX) and High Resolution Imaging Science Experiment (HiRISE) stereo processing, called the Co-registration Ames Stereo Pipeline (ASP) Gotcha Optimised (CASP-GO), based on the open source NASA ASP. CASP-GO employs tie-point based multi-resolution image co-registration, and Gotcha sub-pixel refinement and densification. CASP-GO pipeline is used to produce planet-wide CTX and HiRISE DTMs that guarantee global geo-referencing compliance with respect to High Resolution Stereo Colour imaging (HRSC), and thence to the Mars Orbiter Laser Altimeter (MOLA); providing refined stereo matching completeness and accuracy. All software and good quality products introduced in this paper are being made open-source to the planetary science community through collaboration with NASA Ames, United States Geological Survey (USGS) and the Jet Propulsion Laboratory (JPL), Advanced Multi-Mission Operations System (AMMOS) Planetary Data System (PDS) Pipeline Service (APPS-PDS4), as well as browseable and visualisable through the iMars web based Geographic Information System (webGIS) system

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Focus on function: Single molecule RNA enzymology

The ability of RNA to catalyze chemical reactions was first demonstrated 25 years ago with the discovery that group I introns and RNase P function as RNA enzymes (ribozymes). Several additional ribozymes were subsequently identified, most notably the ribosome, followed by intense mechanistic studies. More recently, the introduction of single molecule tools has dissected the kinetic steps of several ribozymes in unprecedented detail and has revealed surprising heterogeneity not evident from ensemble approaches. Still, many fundamental questions of how RNA enzymes work at the molecular level remain unanswered. This review surveys the current status of our understanding of RNA catalysis at the single molecule level and discusses the existing challenges and opportunities in developing suitable assays. © 2007 Wiley Periodicals, Inc. Biopolymers 87: 302–316, 2007. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at [email protected] Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57325/1/20819_ftp.pd

Infrared Mapper (IRMA) for Support of Comet Sample Return Missions

Comets are remnants from the formation of the Solar System, and contain the most pristine material available today for deciphering the physical and chemical conditions of this process. As such, they are very interesting candidates for sample return missions, as indicated for example by the recent mission proposals CAESAR, CONDOR, and CORSAIR to the NASA New Frontiers 4 call. For maximizing the science return from such a mission the optimum selection of sampling site(s) is crucial. To support this selection we propose a remote sensing instrument working in the thermal infrared (TIR) wavelength range

Experimental Test of Connector Rotation during DNA Packaging into Bacteriophage ϕ29 Capsids

The bacteriophage ϕ29 generates large forces to compact its double-stranded DNA genome into a protein capsid by means of a portal motor complex. Several mechanical models for the generation of these high forces by the motor complex predict coupling of DNA translocation to rotation of the head-tail connector dodecamer. Putative connector rotation is investigated here by combining the methods of single-molecule force spectroscopy with polarization-sensitive single-molecule fluorescence. In our experiment, we observe motor function in several packaging complexes in parallel using video microscopy of bead position in a magnetic trap. At the same time, we follow the orientation of single fluorophores attached to the portal motor connector. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question