A formal "small tension" expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite-dimensional coset space E(10)/K(E10), where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible repres...

We review the recently discovered connection between the Belinsky-Khalatnikov-Lifshitz-like “chaotic” structure of generic cosmological singularities in eleven-dimensional supergravity and the “last” hyperbolic Kac-Moody algebra E10. This intriguing connection suggests the existence of a hidden “correspondence” between supergravity (or even M-theory) and null geodesic motion on the infinite-dim...

Pb(ZrxTi1-x)O3 [PZT] thin films of morphotropic phase boundary (MPB) composition having {001}, {110}, and {111}orientations were fabricated on silicon substrates (111)Pt/Ti/SiO2/Si using a metal organic decomposition spin-coating technique. The influence of crystallographic orientation on the transverse piezoelectric coefficient e31 * of the films have been determined. The largest e31 * was fou...

In this work, an internal combustion (IC) engine air-fuel ratio (AFR) control system is presented and evaluated by simulation. The scheme aims to regulate the overall (AFRoverall) in IC fueled with a hydrogen-enriched ethanol-gasoline blend (E10) as fast possible. designed developed work considers two laws, feedback law hydrogen adaptive nonlinear for controlling E10 mass flow injection. main c...

We study the “fermionic billiards”, i.e. the chaotic dynamics of the gravitino, that arise in the near-spacelike-singularity limit of elevendimensional supergravity and of its dimensional truncations (notably fourdimensional simple supergravity). By exploiting the gravity-coset correspondence, we show that the billiard dynamics of the gravitino is described by a ‘spin extension’ of the E10 Weyl...

The conjecture of a hidden E10 symmetry of M-theory is supported by the close connection between the dynamics of D = 11 supergravity near a spacelike singularity and a truncation of an one-dimensional σ-model with E10 symmetry where all representations beyond SL(10) level l = 3 are omitted. If this conjecture is right, higher-level representations should especially capture the dynamics of furth...

The cases of Poland’s 2018-2019 and South Africa’s 2019-2020 terms as elected members (E10) the United Nations Security Council (UNSC) can be used to confront well-known claim that due a prevailing democratic, legitimacy or efficiency deficit(s) in structure and/or working methods Council, there is no significant space for E10 influential. By examining these two representative cases, E10’s capa...

Tits has defined Kac–Moody groups for all root systems, over all commutative rings with unit. A central concept is the idea of a prenilpotent pair of (real) roots. In particular, writing down his group presentation explicitly would require knowing all the Weyl-group orbits of such pairs. We show that for the hyperbolic root system E10 there are so many orbits that any attempt at direct enumerat...

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