La théorie des catégories (ses apports mathématiques et ses implications épistémologiques)

La théorie des catégories (TC) vaut tant par ses applications mathématiques que par les débats philosophiques qu'elle suscite. Elle sert à exprimer en topologie algébrique, à déduire en algèbre homologique et, en tant qu'alternative à la théorie des ensembles, à construire des objets en géométrie algébrique dans la conception de Grothendieck. Des sources non publiées montrent que Grothendieck quitta le groupe Bourbaki à l'issue d'un débat sur la TC relevant en partie de l'épistémologie, notamment quant à la réalisation ensembliste des constructions catégorielles. Nous soutenons que la TC est fondamentale, car elle traite d'opérations typiques de la mathématique de structures : d'après notre position pragmatique, la justification de la connaissance mathématique ne se fait pas par la réduction à des objets de base mais plutôt, à chaque niveau, par rapport au sens commun technique (les théories de niveau ultérieur ont pour objets les théories des objets originaux).Category theory (CT) is important in virtue of its mathematical applications and its power to generate philosophical debate. It is a language for algebraic topology, a deductive system in homological algebra, and, as an alternative to set theory, a means of object construction (in Grothendieck's conception of algebraic geometry). Unpublished sources show that Grothendieck quit the Bourbaki group because of a debate on CT, which was partly epistemological in nature, especially as far as set-theoretical realisation of categorical constructions was concerned. We claim that CT is fundamental because it is a theory of some typical operations of structural mathematics: in our pragmatic perspective, justification of mathematical knowledge is not provided for by the reduction to basic objects but rather by a technical common sense intervening on each level (the theories on the higher level having as their objects the theories of the original objects).NANCY2-BU Lettres (543952103) / SudocSudocFranceF

On/Off solenoid with sensorless position detection

As is generally known, pressure-resistant solenoids for valves are used in hydraulics and pneumatics. These solenoids, for example, consist of a so-called pole tube with an integrated armature and a separate solenoid coil. Suitable displacement measuring systems are used in order to measure the armature´s as well as valve spool´s position constnatly; these ar directly mounted to the solenoid. Exeamples here are Hall Effect sensors or LVDT transducers. In case of lesser requirements, it is also possible to measure the valve spool´s position directly and in simplified manner. Here, partially standard proximity sensors are employed, which use the valve spool directly as measuring object. In these cases, however, only discrete position measurement is possible. A constant displacement measurement is not necessary. By means of the sensorless position-control developed by MSM, the armature´s position can be executed directly by analyzing the solenoid coil, partly replacing the usual sensors, under adapted basic conditions

Electrochemical impedance spectroscopy of Li4Ti5O12 and LiCoO2 based half-cells and Li4Ti5O12/LiCoO2 cells: Internal interfaces and influence of state-of-charge and cycle number

We studied Li/Li4Ti5O12 and Li/LiCoO2 half-cells as well as Li4Ti5O12/LiCoO2 coin-type battery cells at different state-of-charge over several cycles by means of electrochemical impedance spectroscopy. A simple equivalent-circuit model has been applied to probe changes at the internal interfaces of these batteries. The parameters of this model are used to follow the state-of-charge and state-of-health of the cells. Moreover plain empirical relations were introduced to accurately delineate those courses

Nanoscale spinel LiFeTiO4for intercalation pseudocapacitive Li+storage

Intercalation pseudocapacitive Li+ storage has been recognized recently in metal oxide materials, wherein Li+ intercalation into the lattice is not solid-state diffusion-limited. This may bridge the performance gap between electrochemical capacitors and battery materials. To date, only a few materials with desired crystal structure and with well-defined nanoarchitectures have been found to exhibit such attractive behaviour. Herein, we report for the first time that nanoscale spinel LiFeTiO4 as a cathode material for Li-ion batteries exhibits intercalation pseudocapacitive Li+ storage behaviour. Nanoscale LiFeTiO4 nanoparticles with native carbon coating were synthesized by a sol-gel route. A fast and large-amount of Li+ storage (up to 1.6 Li+ per formula unit over cycling) in the nanoscale LiFeTiO4 host has been achieved without compromising kinetics

Local structure transformations promoting high lithium diffusion in defect perovskite type structures

Defect perovskites, AxBO3 such as (Li3xLa2/3-x)TiO3, are attracting attention as high capacity electrodes in lithium-ion batteries. However, the mechanism enabling high lithium storage capacities has not been fully investigated. In this work, the reversible insertion and removal of lithium up to an average A-site cavity occupancy of 1.71 in the defect perovskite (Li0.18Sr0.66)(Ti0.5Nb0.5)O3 is investigated. It was shown that subtle lithium reorganization during lithiation has a significant impact on enabling high capacity. Contrary to previous studies, lithium was coordinated to triangular faces of Ti/Nb oxygen octahedra and offset from O4 windows between A-site cavities in the as-synthesised material. Upon electrochemical lithiation Li-Li repulsion redistributes of all the lithium towards the O4 window position resulting in a loss of lithium mobility. Surprisingly, the mobility is regained during over-lithiation and following multiple electrochemical cycles. It is suggested that lithium reorganisation into the center of the O4 window alleviates the Li-Li repulsion and modifies the diffusion behavior from site percolation to bond percolation. The results obtained provide valuable insight into the chemical drivers enabling higher capacities and enhanced diffusion in defect perovskites. More broadly the study delivers fundamental understanding on the non-equilibrium structural transformations occurring within electrode materials during repeated electrochemical cycles

Reversible Li+Storage in a LiMnTiO4Spinel and Its Structural Transition Mechanisms

In this work, LiMnTiO4 (a structural analogue of classic spinel LiMn2O4) with a disordered cubic spinel structure (Fd (3) over barm) has been synthesized by a low-temperature sol-gel route. The as-obtained LiMnTiO4 exhibits excellent cycling stability in a wide voltage range from 1.5 to 4.8 V with high discharge capacities of 290, 250, and 140 mA h g(-1) at a C/40, C/19, and 1C rate, respectively. Combined long- and short-range structural characterization techniques are used to reveal the correlation between structure and electrochemical behavior. During cycling, the charge/discharge profiles of LiMnTiO4 evolve from initially two well-separated plateaus into sloping regimes. In the early stage of discharge, LiMnTiO4 undergoes phase transitions from an initial spinel phase to mixtures of predominant rock-salt (Fm (3) over barm) and tetragonal (I4(1)/amd) structures along with a decrease in crystallite size from 12 nm to 3 to 4 nm. During further cycling, the spinel/rock-salt phase transition was found to be reversible with the cubic framework remaining intact. The presence of the tetragonal phase after the first discharge suggests that the Mn3+ Jahn-Teller distortion is partially involved during lithiation from Li1-yMn3+yTiO4 to Li1+xMn3-xTiO4 and the fraction of such a tetragonal phase remains at about 30-40% during subsequent cycling

Orientation and location of the cyclotide kalata B1 in lipid bilayers revealed by solid-state NMR

Cyclotides are ultra-stable cyclic disulfide-rich peptides from plants. Their biophysical effects and medically interesting activities are related to their membrane-binding properties, with particularly high affinity for phosphatidylethanolamine lipids. In this study we were interested in understanding the molecular details of cyclotide-membrane interactions, specifically with regard to the spatial orientation of the cyclotide kalata B1 from Oldenlandia affinis when embedded in a lipid bilayer. Our experimental approach was based on the use of solid-state F-NMR of oriented bilayers in conjunction with the conformationally restricted amino acid L-3-(trifluoromethyl)bicyclopent-[1.1.1]-1-ylglycine as an orientation-sensitive F-NMR probe. Its rigid connection to the kalata B1 backbone scaffold, together with the well-defined structure of the cyclotide, allowed us to calculate the protein alignment in the membrane directly from the orientation-sensitive F-NMR signal. The hydrophobic and polar residues on the surface of kalata B1 form well-separated patches, endowing this cyclotide with a pronounced amphipathicity. The peptide orientation, as determined by NMR, showed that this amphipathic structure matches the polar/apolar interface of the lipid bilayer very well. A location in the amphiphilic headgroup region of the bilayer was supported by N-NMR of uniformly labeled protein, and confirmed using solid-state P- and H-NMR. P-NMR relaxation data indicated a change in lipid headgroup dynamics induced by kalata B1. Changes in the H-NMR order parameter profile of the acyl chains suggest membrane thinning, as typically observed for amphiphilic peptides embedded near the polar/apolar bilayer interface. Furthermore, from the F-NMR analysis two important charged residues, E7 and R28, were found to be positioned equatorially. The observed location thus would be favorable for the postulated binding of E7 to phosphatidylethanolamine lipid headgroups. Furthermore, it may be speculated that this pair of side chains could promote oligomerization of kalata B1 through electrostatic intermolecular contacts via their complementary charges

Mechanism of the Delithiation/Lithiation Process in LiFe_0.4Mn_0.6PO₄: in Situ and ex Situ Investigations on Long-Range and Local Structures

LiFe_0.4Mn_0.6PO₄ olivine was prepared by a sol–gel route, using citric acid as a chelating agent and NH₄H₂PO₄ as a phosphorus source. Sucrose was used as the source for the carbon-coating of the particles. The correlation between the physicochemical and the electrochemical properties of this positive electrode material was investigated. The electrochemical tests showed an initial discharge capacity of 121 mAh/g at a C/20 rate with a good reversibility of the lithiation/delithiation reactions. In situ XRD on Li_<i>x</i>Fe_0.4Mn_0.6PO₄ reveals the occurrence of new phases upon cycling, which disappeared again at the end of discharge. The single phase observed after one complete cycle is identical to the pristine one. In situ XAS spectroscopy in combination with ⁵⁷Fe Mössbauer and ⁷Li NMR spectroscopy were used to investigate the changes in the local structure and the oxidation states of the transition metals and thus to complete the overall characterization of the lithiation/delithiation mechanism. All results reveal a high reversibility of the reactions in this electrode material