A5048450491- Polynomial and algebraic computation
- Advanced Differential Equations and Dynamical Systems
- Advanced Topics in Algebra
- Numerical methods for differential equations
- Advanced Numerical Analysis Techniques
- Numerical Methods and Algorithms
- Algebraic Geometry and Number Theory
- Nonlinear Waves and Solitons
- Commutative Algebra and Its Applications
- Cancer Treatment and Pharmacology
- Formal Methods in Verification
- Advanced Materials and Mechanics
- Logic, programming, and type systems
- Algebraic structures and combinatorial models
- Structural Analysis and Optimization
- Dynamics and Control of Mechanical Systems
- Matrix Theory and Algorithms
- Control and Dynamics of Mobile Robots
- Model Reduction and Neural Networks
- Advanced Optimization Algorithms Research
- Mathematics and Applications
- Homotopy and Cohomology in Algebraic Topology
- Geometric and Algebraic Topology
- Finite Group Theory Research
- Innovations in Concrete and Construction Materials
RWTH Aachen University
2007-2023
University of Plymouth
2014-2021
Gesellschaft Fur Mathematik Und Datenverarbeitung
2005
Similarly to the correspondence between radical ideals of a polynomial ring and varieties in algebraic geometry, differential their analytic solution sets has been established algebra. This tutorial discusses aspects this involving symbolic computation. In particular, an introduction Thomas decomposition method is given. It splits system polynomially nonlinear partial equations into finitely many so-called simple systems whose form partition original set. The power series solutions each can...
The central notion of this work is that a functor between categories finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. paper describes way allowing to realize such functors, e.g. Hom , ⊗ [Formula: see text], as mathematical object computer algebra system. Once achieved, compose and derive functors even iterate process without the need any specific knowledge these functors. These...
In this paper we consider finite difference approximations for numerical solving of systems partial differential equations the form f1 = · fp 0, where F := {f1, ..., fp} is a set linear polynomials over field rational functions with coefficients. For orthogonal and uniform solution grids strengthen generally accepted concept equation-wise consistency (e-consistency) 0 as approximation ones. Instead, introduce notion all consequences polynomial f {f, subset ideal 〈F〉. The last consistency,...
An algebraic approach to the design of resource-efficient carbon-reinforced concrete structures is presented. Interdisciplinary research in fields mathematics and algebra on one hand civil engineering other can lead fruitful interactions contribute development sustainable structures. Textile-reinforced (TRC) using non-crimp fabric carbon reinforcement enables very thin lightweight constructions thus requires new construction strategies manufacturing methods. Algebraic methods applied...
For a wide class of polynomially nonlinear systems partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis their finite difference approximations on Cartesian grids. First apply Thomas decomposition input system, resulting in partition solution set. We consider output simple subsystem that contains interest. Then, for this subsystem, algorithm verification s-consistency its approximation. purpose develop analogue decomposition, both which...
It is well-known that a time-varying controllable ordinary differential linear system flat outside some singularities. In this paper, we prove every projection of system. We give an explicit description which projects onto given one. This phenomenon similar to classical one largely studied in algebraic geometry and called the blowing-up singularity. These results simplify ones obtained [6] generalize them MIMO multidimensional systems. Finally, multi-input with polynomial coefficients flat.