M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Furusho, stating that the pentagon equation for grt_1-elements implies the hexagon equation

Grothendieck-Teichm\"uller and Batalin-Vilkovisky

It is proven that, for any affine supermanifold $M$ equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ on the set of quantum BV structures (i. e.\ solutions of the quantum master equation) on $M$

Lower limb joint kinetics during the first stance phase in athletics sprinting: three elite athlete case-studies

This study analysed the first stance phase joint kinetics of three elite sprinters to improve the understanding of technique and investigate how individual differences in technique could influence the resulting levels of performance. Force (1000 Hz) and video (200 Hz) data were collected and resultant moments, power and work at the stance leg metatarsal-phalangeal (MTP), ankle, knee and hip joints were calculated. The MTP and ankle joints both exhibited resultant plantarflexor moments throughout stance. Whilst the ankle joint generated up to four times more energy than it absorbed, the MTP joint was primarily an energy absorber. Knee extensor resultant moments and power were produced throughout the majority of stance, and the best-performing sprinter generated double and four times the amount of knee joint energy compared to the other two sprinters. The hip joint extended throughout stance. Positive hip extensor energy was generated during early stance before energy was absorbed at the hip as the resultant moment became flexor-dominant towards toe-off. The generation of energy at the ankle appears to be of greater importance than in later phases of a sprint, whilst knee joint energy generation may be vital for early acceleration and is potentially facilitated by favourable kinematics at touchdown

Sprint start kinetics of amputee and non-amputee sprinters

The purpose of this study was to explore the relationship between the forces applied to the starting blocks and the start performances (SPs) of amputee sprinters (ASs) and non-amputee sprinters (NASs). SPs of 154 male and female NASs (100-m personal records [PRs], 9.58–14.00 s) and 7 male ASs (3 unilateral above knee, 3 unilateral below knee, 1 bilateral below knee; 100 m PRs, 11.70–12.70 s) with running specific prostheses (RSPs) were analysed during full-effort sprint starts using instrumented starting blocks that measured the applied forces in 3D. Using the NAS dataset and a combination of factor analysis and multiple regression techniques, we explored the relationship between force characteristics and SP (quantified by normalized average horizontal block power). Start kinetics were subsequently compared between ASs and NASs who were matched based on their absolute 100 m PR and their 100 m PR relative to the world record in their starting class. In NASs, 86% of the variance in SP was shared with five latent factors on which measured parameters related to force application to the rear and front blocks and the respective push-off directions in the sagittal plane of motion were loaded. Mediolateral force application had little influence on SP. The SP of ASs was significantly reduced compared to that of NASs matched on the basis of relative 100-m PR (−33.8%; d = 2.11, p < 0.001), while a non-significant performance reduction was observed when absolute 100-m PRs were used (−17.7%; d = 0.79, p = 0.09). These results are at least partially explained by the fact that force application to the rear block was clearly impaired in the affected legs of ASs

Stanzen von Loechern hoher Formtreue und Oberflaechenguete in dickwandigen Bauteilen aus Stahl durch Anwendung der Feinschneidtechnologie

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