scholarly journals A note on super Koszul complex and the Berezinian

2021 ◽  
Author(s):  
Simone Noja ◽  
Riccardo Re
Keyword(s):  
Homology Group ◽  
Homology Class ◽  
Koszul Complex ◽  
Single Degree ◽  
Exact Resolution

AbstractWe construct the super Koszul complex of a free supercommutative A-module V of rank p|q and prove that its homology is concentrated in a single degree and it yields an exact resolution of A. We then study the dual of the super Koszul complex and show that its homology is concentrated in a single degree as well and isomorphic to $$\Pi ^{p+q} A$$ Π p + q A , with $$\Pi $$ Π the parity changing functor. Finally, we show that, given an automorphism of V, the induced transformation on the only non-trivial homology class of the dual of the super Koszul complex is given by the multiplication by the Berezinian of the automorphism, thus relating this homology group with the Berezinian module of V.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

scholarly journals A cross-species neural integration of gravity for motor optimization

2021 ◽  
Vol 7 (15) ◽  
pp. eabf7800
Author(s):  
Jeremie Gaveau ◽  
Sidney Grospretre ◽  
Bastien Berret ◽  
Dora E. Angelaki ◽  
Charalambos Papaxanthis
Keyword(s):  
Optimization Strategy ◽  
Motor Patterns ◽  
Activation Patterns ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Neural Integration ◽  
Gravity Effects ◽  
Neural Signature ◽  
Experimental Findings ◽  
Muscular Activation

Recent kinematic results, combined with model simulations, have provided support for the hypothesis that the human brain shapes motor patterns that use gravity effects to minimize muscle effort. Because many different muscular activation patterns can give rise to the same trajectory, here, we specifically investigate gravity-related movement properties by analyzing muscular activation patterns during single-degree-of-freedom arm movements in various directions. Using a well-known decomposition method of tonic and phasic electromyographic activities, we demonstrate that phasic electromyograms (EMGs) present systematic negative phases. This negativity reveals the optimal motor plan’s neural signature, where the motor system harvests the mechanical effects of gravity to accelerate downward and decelerate upward movements, thereby saving muscle effort. We compare experimental findings in humans to monkeys, generalizing the Effort-optimization strategy across species.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait

The Unsteady Aerodynamics of a Finite Supersonic Cascade With Subsonic Axial Flow

1973 ◽  
Vol 40 (3) ◽  
pp. 667-671 ◽  
Author(s):  
J. M. Verdon
Keyword(s):  
Axial Flow ◽  
Unsteady Aerodynamics ◽  
Supersonic Stream ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Combined Use ◽  
Cascade Analysis ◽  
Infinite Array ◽  
Typical Configuration ◽  
Phase Angles

A method is presented for determining the unsteady flow field and the aerodynamic response which occurs when a finite oscillating cascade is placed in a supersonic stream, which has a subsonic velocity component normal to the cascade. Solutions are obtained through the combined use of closed-form and numerical procedures. Computed results indicate that the finite cascade analysis should provide a reasonable indication of the influence of the cascade parameters on the response of the infinite array. A brief parametric study for a typical configuration reveals possible aerodynamic instabilities when the blades perform single-degree-of-freedom pitching oscillations over a broad range of frequencies and interblade phase angles.

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