scholarly journals Uniform boundedness for Brauer groups of forms in positive characteristic

2021 ◽  
Vol 28 (2) ◽  
pp. 315-329
Author(s):  
Emiliano Ambrosi
Keyword(s):  
Positive Characteristic ◽  
Uniform Boundedness ◽  
Brauer Groups

A Note on the Height of the Formal Brauer Group of a K3 Surface

2004 ◽  
Vol 47 (1) ◽  
pp. 22-29 ◽  
Author(s):  
Yasuhiro Goto
Keyword(s):  
Positive Characteristic ◽  
Brauer Group ◽  
K3 Surface ◽  
Brauer Groups

AbstractUsing weighted Delsarte surfaces, we give examples of K3 surfaces in positive characteristic whose formal Brauer groups have height equal to 5, 8 or 9. These are among the four values of the height left open in the article of Yui [11].

scholarly journals Brauer groups of moduli of hyperelliptic curves via cohomological invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Di Lorenzo ◽  
Roberto Pirisi
Keyword(s):  
Positive Characteristic ◽  
Hyperelliptic Curves ◽  
Brauer Group ◽  
Base Field ◽  
Brauer Groups ◽  
Algebraic Stacks ◽  
Cohomological Invariants ◽  
Moduli Stack

Abstract Using the theory of cohomological invariants for algebraic stacks, we compute the Brauer group of the moduli stack of hyperelliptic curves ${\mathcal {H}}_g$ over any field of characteristic $0$ . In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of the base field.

scholarly journals A remark on uniform boundedness for Brauer groups

2020 ◽  
pp. 512-522
Author(s):  
Anna Cadoret ◽  
François Charles
Keyword(s):  
Uniform Boundedness ◽  
Brauer Groups

ON THE PRINCIPLE OF UNIFORM BOUNDEDNESS FOR LSC CONVEX PROCESSES IN A STRICTLY N LOCALLY CONVEX SPACES

2008 ◽  
Vol 41 (1) ◽  
Author(s):  
S. Lahrech ◽  
A. Jaddar ◽  
J. Hlal ◽  
A. Ouahab ◽  
A. Mbarki
Keyword(s):  
Uniform Boundedness ◽  
Locally Convex Spaces ◽  
Convex Processes ◽  
Locally Convex ◽  
Convex Spaces

Trajectory following control of lower limb exoskeleton robot based on Udwadia–Kalaba theory

2021 ◽  
pp. 107754632110317
Author(s):  
Jin Tian ◽  
Liang Yuan ◽  
Wendong Xiao ◽  
Teng Ran ◽  
Li He
Keyword(s):  
Lower Limb ◽  
Control Method ◽  
Uniform Boundedness ◽  
Adaptive Robust Control ◽  
Structural Vibration ◽  
Control Approach ◽  
Lower Limb Exoskeleton ◽  
Exoskeleton Robot ◽  
Constraint Problem ◽  
Trajectory Following

The main objective of this article is to solve the trajectory following problem for lower limb exoskeleton robot by using a novel adaptive robust control method. The uncertainties are considered in lower limb exoskeleton robot system which include initial condition offset, joint resistance, structural vibration, and environmental interferences. They are time-varying and have unknown boundaries. We express the trajectory following problem as a servo constraint problem. In contrast to conventional control methods, Udwadia–Kalaba theory does not make any linearization or approximations. Udwadia–Kalaba theory is adopted to derive the closed-form constrained equation of motion and design the proposed control. We also put forward an adaptive law as a performance index whose type is leakage. The proposed control approach ensures the uniform boundedness and uniform ultimate boundedness of the lower limb exoskeleton robot which are demonstrated via the Lyapunov method. Finally, simulation results have shown the tracking effect of the approach presented in this article.

Constraint-oriented integrated longitudinal and lateral robust control for connected and automated vehicle platoons

2021 ◽  
pp. 107754632110026
Author(s):  
Zeyu Yang ◽  
Jin Huang ◽  
Zhanyi Hu ◽  
Diange Yang ◽  
Zhihua Zhong
Keyword(s):  
Robust Control ◽  
Estimation Error ◽  
Uniform Boundedness ◽  
Path Tracking ◽  
Adaptive Robust Control ◽  
Connected Vehicle ◽  
Vehicle Platoon ◽  
Tracking Model ◽  
Vehicle Platoons ◽  
Following Error

The coupling, nonlinearity, and uncertainty characteristics of vehicle dynamics make the accurate longitudinal and lateral control of an automated and connected vehicle platoon a tough task. Little research has been conducted to fully address the characteristics. By using the ideology of constraint-following control this article proposes an integrated longitudinal and lateral adaptive robust control methodology for a vehicle platoon with a bidirectional communication topology. The platoon control objectives contain the path tracking stability, the platoon internal stability, and the string stability. First, we establish the nonlinear kinematics path tracking model and the coupled vehicle longitudinal and lateral dynamical model that contains time-varying uncertainties. Second, we design a series of nonlinear equality constraints that directly guarantee the control objectives based on the kinematic relations. On this basis, an adaptive robust constraint-following control is proposed. It is shown that the control guarantees the uniform boundedness and the uniform ultimate boundedness of the constraint-following error and the uncertainty estimation error. Finally, simulation results are provided to validate the effectiveness of the proposed methodology.

scholarly journals Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

2021 ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Uniform Boundedness ◽  
Metric Structures

AbstractIn this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

Sign in / Sign up

Export Citation Format

Share Document