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Fourier Analysis of DG Schemes for Advection‐Diffusion
(2021-01-25)
This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection‐diffusion problems in particular with respect to the discretization of diffusion terms. Extending previous investigations, the advection discretization now additionally varies between the choices of central or upwind fluxes. The results show that a previously recognized better performance of central schemes for well‐resolved problems only hold for even polynomial degrees and that upwind‐type discretizations also ...
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A Study of Extensions of Classical Summation Theorems for the Series ₃F₂ and ₄F₃ with Applications
(2021-03-16)
Very recently, Masjed-Jamei & Koepf [Some summation theorems for generalized hypergeometric functions, Axioms, 2018, 7, 38, 10.3390/axioms 7020038] established some summation theorems for the generalized hypergeometric functions. The aim of this paper is to establish extensions of some of their summation theorems in the most general form. As an application, several Eulerian-type and Laplace-type integrals have also been given. Results earlier obtained by Jun et al. and Koepf et al. follow special cases of our main findings.
Aufsatz
Efficient Solution of Distributed MIP in Control of Networked Systems
(2021-01-25)
Certain classes of optimization‐based control problems stated for networked systems involving hybrid dynamics and logical constraints can be cast into Mixed‐Integer Programming (MIP) problems. Since these belong to the complexity class NP‐hard, the motivation arises to find approximations of the optimal solution by distributed solution efficiently. For the cases that the cost functional is linear or quadratic and the constraints are linear, this paper proposes an alternative to the standard centralized schemes, by ...
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A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations
(2020-06-17)
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination ...
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Control of Jump Markov Uncertain Linear Systems With General Probability Distributions
(2022-02-25)
This paper introduces a method to control a class of jump Markov linear systems with uncertain initialization of the continuous state and affected by disturbances. Both types of uncertainties are modeled as stochastic processes with arbitrarily chosen probability distributions, for which however, the expected values and (co-)variances are known. The paper elaborates on the control task of steering the uncertain system into a target set by use of continuous controls, while chance constraints have to be satisfied for ...
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A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics
(2022-01-03)
Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on ...
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Lie algebra for rotational subsystems of a driven asymmetric top
(2022-05-11)
We present an analytical approach to construct the Lie algebra of finite-dimensional subsystems of the driven asymmetric top rotor. Each rotational level is degenerate due to the isotropy of space, and the degeneracy increases with rotational excitation. For a given rotational excitation, we determine the nested commutators between drift and drive Hamiltonians using a graph representation. We then generate the Lie algebra for subsystems with arbitrary rotational excitation using an inductive argument.
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Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school
(2022-04-19)
This study examined whether learning with heuristic worked examples can improve students’ competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks), worked example condition (students studied worked examples representing a realistic process of problem-solving by fictitious students negotiating solutions to the tasks), and ...
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An 8-bit precision cipher for fast image encryption
(2022-04-21)
Implementing chaos based ciphers usually involves 32-bit floating-point arithmetics that is hardware resources costly. The limitation of the computational precision is hardware imposed and transforms chaotic orbits into limit cycles with short periods, hence alters their randomness. In cryptographic applications, short period dynamics and weak randomness result in security issues. In order to address this concern, we propose an 8-bit precision cipher that can be implemented with low-end microprocessors running 8-bit ...
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30 Years with Vladimir Gerdt
(2022-11-12)
My first meeting with Vladimir was in March 1990. I had started two months before as a Ph.D. student of Jacques Calmet in the computer science department of Karlsruhe University and Vladimir was visiting our computer algebra group for a seminar talk on his research. For him, it was one of his first travels into the west, as under Soviet rule he was not considered as sufficiently politically reliable for travels outside of the eastern block. It turned out that after his visit we were both riding on the same train to ...