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Geometric Description of Fibre Bundle Surface for Birkhoff System

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Chinese Physics Letters 2009年第3期26卷 3-4页

作者：曹丽梅孙华飞张真宁 Department of Mathematics Beijing Institute of Technology Beijing 100081

A fibre bundle surface for the Birkhoff system is constructed. The metric and the Riemannian connection of the surface are defined and the representation of the Gaussian curvature of this surface is presented. Finally... 详细信息

关键词： DYNAMICS FIBER bundles (Mathematics) RIEMANNIAN geometry CONNECTIONS (Mathematics) GAUSSIAN processes differential geometry

Christoffel Symbols and Chiral Properties of the Space-Time geometry for the Atomic Electron States

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Journal of Modern Physics 2021年第4期12卷 483-512页

作者： Claude Daviau Jacques Bertrand Fondation Louis de Broglie Paris France

Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.

关键词： Quantum Mechanics Clifford Algebra differential geometry Dirac Equation Hydrogen Atom Chirality

On the Defining Equations of Protein’s Shape from a Category Theoretical Point of View

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Applied Mathematics 2020年第9期11卷 890-916页

作者： Naoto Morikawa Genocript Zama Japan

This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins, rather than on the proteins themselves. Knowledge of category theory is not required as mathematical notions are defined concretely. In this paper, proteins are represented as closed trajectories (i.e., loops) of flows of triangles. The relations between proteins are defined using the fusion and fission of loops of triangles, where allostery occurs naturally. The shape of a protein is then described with quantities that are measurable with unity elements called “unit loops”. That is, protein’s shape is described with the loops that are obtained by the fusion of unit loops. Measurable loops are called “integral”. In the approach, the unit loops play a role similar to the role “1” plays in the set Z of integers. In particular, the author considers two categories of loops, the “integral” loops and the “rational” loops. Rational loops are then defined using algebraic equations with “integral loop” coefficients. Because of the approach, our theory has some similarities to quantum mechanics, where only observable quantities are admitted in physical theory. The author believes that this paper not only provides a new perspective on protein engineering, but also promotes further collaboration between biology and other disciplines.

关键词： differential geometry Discrete Mathematics Protein Design Triangular Flow Algebra of Loops

Connections with Symplectic Structures

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American Journal of Computational Mathematics 2016年第4期6卷 313-319页

作者： A. K. M. Nazimuddin Md. Showkat Ali Department of Electronics and Communications Engineering East West University Dhaka Bangladesh Department of Applied Mathematics University of Dhaka Dhaka Bangladesh

A charming feature of symplectic geometry is that it is at the crossroad of many other mathematical disciplines. In this article we review the basic notions with examples of symplectic structures and show the connecti... 详细信息

关键词： Connection differential geometry Symplectic geometry

A Vector Tensor Calculus Description of a Euclidean Space

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Journal of Applied Mathematics and Physics 2023年第3期11卷 705-720页

作者： Pavel Grinfeld Drexel University Philadelphia PA USA

We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.

关键词： Tensor Calculus differential geometry Embedded Surfaces and Curves Scalar Curvature Gaussian Curvature

Application of PID Controller to 2D differential Geometric Guidance and Control Problem

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Application of PID Controller to 2D Differential Geometric G...

differential Flatness Applied to Vehicle Trajectory Tracking

第25届中国控制会议

作者： Li Chaoyong, Jing Wuxing Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001,China

＜正＞This paper presents the application of the proportional-integral- derivative （PID） controller to the development of the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem. In particular, the performance of the designed FCS is investigated. To this end, the commanded angle -of-attack （AOA） is firstly developed in the time domain using the classical DG formulations. Then, the classical PID controller is introduced to develop a FCS so as to form the 2D DG guidance and control system, and the PID controller parameters are determined by the Ziegler-Nichols method as well as the Routh-Hurwitz stability algorithm to guarantee a fast convergence of the system error. The results demonstrate that the designed controller yields a fast responding FCS, and the resulting DG guidance and control system is viable and effective in a realistic missile defense engagement.

关键词： differential geometry PID controller Flight control system Missile guidance

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Differential Flatness Applied to Vehicle Trajectory Tracking

Control for the Traveling Wave Solution to the Degasperis-Procesi Equation

第二十七届中国控制会议

作者： Hsiao Fei-Bin Mora-Camino F. Institute of Aeronautics and Astronautics National Cheng Kung University

differential flatness,a property of some dynamic systems which has been recognized only recently,has made possible the development of new tools to control complex nonlinear dynamic *** dynamics of many different systems have been recognized as being explicitly or implicitly differentially flat as it is the case for flight guidance dynamics of conventional *** this paper,a new control structure is proposed to achieve trajectory tracking for vehicles:a neural network deals with the inversion of nominal guidance dynamics while a linear corrector cope with modelling errors and perturbations so that control directives to conventional autopilot systems can be generated in real *** proposed approach is illustrated in the case of conventional aircraft flight dynamics.

关键词： Nonlinear control differential geometry Neural networks Tracking Flight control

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Control for the Traveling Wave Solution to the Degasperis-Pr...