Cayley–Klein Lie Bialgebras: Noncommutative Spaces, Drinfel’d Doubles and Kinematical Applications

The Cayley–Klein (CK) formalism is applied to the real algebra so(5) by making use of four graded contraction parameters describing, in a unified setting, 81 Lie algebras, which cover the (anti-)de Sitter, Poincaré, Newtonian and Carrollian algebras. Starting with the Drinfel’d–Jimbo real Lie bialgebra for so(5) together with its Drinfel’d double structure, we obtain the corresponding CK bialgebra and the CK r-matrix coming from a Drinfel’d double. As a novelty, we construct the (first-order) noncommutative CK spaces of points, lines, 2-planes and 3-hyperplanes, studying their structural properties. By requiring dealing with real structures, we found that there exist 63 specific real Lie bialgebras together with their sets of four noncommutative spaces. Furthermore, we found 14 classical r-matrices coming from Drinfel’d doubles, obtaining new results for the de Sitter so(4,1) and anti-de Sitter so(3,2) as well as for some of their contractions. These geometric results were exhaustively applied onto the (3 + 1)D kinematical algebras, considering not only the usual (3 + 1)D spacetime but also the 6D space of lines. We established different assignations between the geometrical CK generators and the kinematical ones, which convey physical identifications for the CK contraction parameters in terms of the cosmological constant/curvature Λ and the speed of light c. We, finally, obtained four classes of kinematical r-matrices together with their noncommutative spacetimes and spaces of lines, comprising all κ-deformations as particular cases.

ONE MORE TIME ON DOUBLE STRUCTURE OF “THE SHOT” OF A.S. PUSHKIN

We reveal a number of structural elements of "The Shot" overlooked before. Mainly, they are presented by a set of oppositions or realize the motif of doubling directly. This motif is related to confrontation between adversaries and peculiarities of an abnormal duel, including the situation “bullet in bullet”. As a result, the life of Silvio appears as a united plot, details of which are expressed in terms of weapon that was exploited by him or remained without application. In particular, this includes the rule of card play in bank in which Silvio was involved. Among artistically relevant oppositions are those between blade and bullet, heat and cold, fire and water, morning and evening. These categories also apply to the count and the narrator. We point to some hidden elements in the brief mentioning the death of Silvio.

K3 carpets on minimal rational surfaces and their smoothings

In this paper, we study K3 double structures on minimal rational surfaces [Formula: see text]. The results show there are infinitely many non-split abstract K3 double structures on [Formula: see text] parametrized by [Formula: see text], countably many of which are projective. For [Formula: see text] there exists a unique non-split abstract K3 double structure which is non-projective (see [J.-M. Drézet, Primitive multiple schemes, preprint (2020), arXiv:2004.04921 , to appear in Eur. J. Math.]). We show that all projective K3 carpets can be smoothed to a smooth K3 surface. One of the byproducts of the proof shows that unless [Formula: see text] is embedded as a variety of minimal degree, there are infinitely many embedded K3 carpet structures on [Formula: see text]. Moreover, we show any embedded projective K3 carpet on [Formula: see text] with [Formula: see text] arises as a flat limit of embeddings degenerating to 2:1 morphism. The rest do not, but we still prove the smoothing result. We further show that the Hilbert points corresponding to the projective K3 carpets supported on [Formula: see text], embedded by a complete linear series are smooth points if and only if [Formula: see text]. In contrast, Hilbert points corresponding to projective (split) K3 carpets supported on [Formula: see text] and embedded by a complete linear series are always smooth. The results in [P. Bangere, F. J. Gallego and M. González, Deformations of hyperelliptic and generalized hyperelliptic polarized varieties, preprint (2020), arXiv:2005.00342 ] show that there are no higher dimensional analogues of the results in this paper.

Outline of a Brain Model for Self-Observing Agents

Brain-inspired models for conscious robots should refer to the cellular double structure of the brain, consisting of the neuronal system and the glial system, embodying two ontological realms. Therefore, a purely neurobiological approach to machine consciousness is biased by an ontological fault in exclusively referring to the neuronal system. The brain model for self-observing agents outlined in this paper focuses on the glial-neuronal synaptic units (tripartite synapses). Whereas the neuronal component of the synapse embodies objective subjectivity processing sensory information, the glial component (astrocyte) embodies subjective subjectivity generating subjective behavior (intentions, consciousness) in its interactions with the neuronal part of the synapse. The elementary principle of the implementation of self-observing agents is this: a brain is capable of self-observation, if the concept of intention to observe something and the concept of the observed are located in different places. Based on a formalism of qualitative information processing, the architecture of self-observation is described in increasing complexity, building networks. It is suggested that if a robot brain is equipped with a network of modules for self-observation, the robot may generate subjective perspectives of self-observation indicating self-consciousness.

MiniPINS - Miniature Planetary In-situ Sensors

<p>MiniPINS (Miniature Planetary IN-situ Sensors) is an ESA study led by the Finnish Meteorological Institute to develop and prototype miniaturised surface sensor packages for Mars and the Moon. The study aims at miniaturising the scientific sensors and subsystems, as well as identifying and utilizing commonalities of the packages, allowing to optimise the design, cut costs and reduce the development time. This presentation includes the main results from Phase A study and Preliminary Requirements Review of MiniPINS.</p><div><span><span>Mars In-Situ Sensors (MINS) is a concept based on the strong heritage of the MetNet lander. MINS mission consists of 4 scientific observation posts on the Martian surface, about 25 kg each. The MINS landers will travel to Mars aboard the carrier spacecraft provided by another mission. Several concepts for MINS penetrators were studied in Phase 0, and finally 2 concepts were chosen for the final selection. </span></span>The concept selection was driven by the target penetration depth, as this parameter is deeply influenced by the penetrator design.</div><div> </div><div> <p>The MINS concept of 0.5 m penetration depth was selected by means of a trade-off. The selected concept is a rigid probe concept, similar to MetNet penetrator.  Its development level is quite high, and its scope is compatible with MINS mission. This concept is limited from the scientific point of view, as it does not allow to penetrate so far in Martian subsoil; but its more advantageous from the criticality point of view as it has a higher development level and is less complex. The concept allows to perform majority of the scientific measurements, as all science goals except <span>the heat flow measurement, can be accomplished also in shallow depth. </span></p> </div><div><span><span>Lunar In-Situ Sensors (LINS) is a new concept of a scientific mission package to investigate the Lunar surface and environment. LINS missions consist of 4 surface stations, 7 kg each, deployed on the Moon by a rover. </span></span>In the case of LINS thermal and power design are the major drivers of the LINS architecture definition because of the Moon extreme environment, owed in part to the long lunar night period. The most relevant decision with regard to the LINS package is whether to include a RHU or not. In the absence of an RHU, the thermal and power subsystems become strongly compromised. Incorporation of an RHU offers many advantages. Consequently, the incorporation of the RHU is the selected concept for LINS.</div><div> </div><div><span><span>The two main concepts for mechanical structure of the LINS were evaluated: m</span></span>onocoque structure with legs and double structure without legs. A design concept was chosen that consists of a double structure, so that there is an internal and an external one. The external one acts as an exoskeleton for the internal and is separated from it by blocks. The separation between the two structures provides some space to accommodate additional thermal insulation if necessary.</div><p> </p><p><strong>Acknowledgements</strong></p><p>The MiniPINS (Miniaturized Sensor Packages and Delivery Systems for In-situ Exploration) Contract is carried out and funded by the European Space Agency activity no. 1000025265 in the “ESA-Star” System. </p>