bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the relaxation gap for PDE mixed‐integer optimal control problems
Authors: Hante Falk M. 
Published: October 2016

AbstractMixed‐integer optimal control problems require taking discrete and continuous control decisions for the optimization of a dynamical system. We consider dynamics governed by partial differential equations of evolution type and assess the problem by relaxation and rounding strategies. For this solution approach, we present a priori estimates for semilinear evolutions on Banach spaces concerning the optimality gap. The theoretical results show that the gap can be made arbitrary small. We demonstrate the numerical performance of the approach on benchmark problems of parabolic type motivated from thermal manufacturing and of hyperbolic type motivated from traffic flow control. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive fuzzy sliding mode control of the cart‐pole underactuated system
Authors: Bessa Wallace M. , Kreuzer Edwin 
Published: October 2016

AbstractIn this work, an intelligent control scheme is proposed for the stabilization of the cart‐pole underactuated system. The adopted approach is primarily based on a smooth sliding mode controller, but an adaptive fuzzy inference system is embedded within the boundary layer in order to improve the control performance. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Controllability of the powerslide motion of an automobile with different actuation inputs
Authors: Edelmann Johannes , Plöchl Manfred 
Published: October 2016

AbstractBoth human drivers and driver assist systems may apply steering and throttle commands to master several driving situations. In order to study the effectiveness of redundant inputs, modal controllability and observability measures are analysed for both regular steady‐state cornering and, alternatively, inherent unstable powerslide motion. In contrast to regular cornering, both inputs are effective at powerslide motion. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Further Improvements in High Gain Observer Design for Systems with Structured Nonlinearities
Authors: Franke Mirko , Röbenack Klaus 
Published: October 2016

AbstractDue to their simple implementation based on a constant gain matrix, high gain observers are very common in practical applications. We consider systems whose dynamics can be decomposed into a linear and a nonlinear part, where the nonlinear part meets some Lipschitz condition. In many cases there exists a finite bound on the maximum feasible Lipschitz constant for which the error dynamics can be stabilized. Necessary and in some sense sufficient conditions for this maximum Lipschitz constant are given in [1]. These results has been improved in [2,3] by taking the structure of the linear part into account.Having a system with one single nonlinearity, the results given in [2,3] are strict. If multiple nonlinearities occur, even this approach tends to be to conservative. In this case, one could additionally take the internal structure of the nonlinearities into account which leads to a larger set of systems for which convergence of the observer error can be guaranteed.Our new approach is based on an approximation of the structured singular value [4] which yields existence conditions in terms of linear matrix inequalities (LMIs). These LMIs may as well be used for the numerical computation of the observer gain. We demonstrate the advantage of our method on an example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability preserving model reduction for linearly coupled linear time‐invariant systems
Authors: Benner Peter , Grundel Sara , Mlinarić Petar 
Published: October 2016

AbstractWe develop a stability preserving model reduction method for linearly coupled linear time‐invariant (LTI) systems. The method extends the work of Monshizadeh et al. for multi‐agent systems with identical LTI agents. They propose using Bounded Real Balanced Truncation to preserve a sufficient condition for stability of the coupled system. Here, we extend this idea to arbitrary linearly coupled LTI systems using the sufficient condition for stability introduced by Reis and Stykel. The model reduction error bounds for this method also follow from results of Reis and Stykel, which allows the adaptive choice of reduced orders. We demonstrate the method on Reis's and Stykel's coupled string‐beam example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reliability of disturbance rejection control based on the geometrical disturbance decoupling
Authors: Oveisi Atta , Nestorović Tamara 
Published: October 2016

AbstractIn this note, a reliable disturbance decoupled control system based on the geometrical technique is proposed. For this purpose, first, the conditions for nominal disturbance detection and rejection is introduced by using invariant subspaces. Then, the fragility issue of the controller/observer is addressed with appropriate H∞ constraints in the form of some linear matrix inequalities (LMIs). In contrast to conventional pole placement method suitable for systems by neglecting sources of uncertainty, in the presented method, the disturbance rejection problem reduces to a quadratic stability problem. It is observed that the proposed method has a better attenuation performance than classical observer‐based non‐fragile controller. © 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Local Decompositions of Second Order Infinite‐Dimensional Systems
Authors: Rams Hubert , Schöberl Markus , Schlacher Kurt 
Published: October 2016

AbstractThis article deals with the local system decomposition of infinite‐dimensional systems, which are described by second‐order nonlinear partial differential equations. It will be shown that the existence of a certain codistribution allows a local triangular decomposition of the generalized system vector field and the boundary conditions. Based on this triangular decomposition, non‐accessibility follows by a simple structural analysis. Throughout the article differential geometric methods are applied, highlighting the geometric picture behind the system description. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Local steering problem for a class of control‐affine systems with application to continuous crystallization processes
Authors: Zuyev Alexander , Benner Peter 
Published: October 2016

AbstractIn this paper, a nonlinear control‐affine system that describes the dynamics of a continuous crystallizer with fines trap is considered. We study the approximate steering problem for this system, i. e. the problem of constructing an admissible open‐loop control that steers the system from a given initial state to a neighborhood of the target state. This problem is reduced to solving a system of algebraic equations with respect to the control parameters. We show that the resulting algebraic system is locally solvable in a neighborhood of the equilibrium point. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the error behaviour of the filtered back projection
Authors: Beckmann Matthias , Iske Armin 
Published: October 2016

AbstractThe filtered back projection (FBP) formula allows us to reconstruct bivariate functions from given Radon samples. However, the FBP formula is numerically unstable and low‐pass filters with finite bandwidth and a compactly supported window function are employed to make the reconstruction by FBP less sensitive to noise. In this paper we analyse the inherent reconstruction error which is incurred by the application of a low‐pass filter with finite bandwidth. We present L2‐error estimates on Sobolev spaces of fractional order along with asymptotic convergence rates, where the filter's bandwidth goes to infinity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Iterative Phase Retrieval with Sparsity Constraints
Authors: Loock Stefan , Plonka Gerlind 
Published: October 2016

AbstractWe consider the problem of iterative phase retrieval in near‐field X‐ray propagation imaging. Single‐distance measurements ask for strong a priori information about the specimen that are not always accessible, e.g. the specimen's support. We propose to exploit sparsity of real‐valued cartoon‐like images using soft‐thresholding of shearlet coefficients. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive Modelling, Simulation and Optimization of Gas and Water Supply Networks
Authors: Domschke Pia , Kolb Oliver , Lang Jens 
Published: October 2016

AbstractWe consider the simulation and optimisation of transport processes through gas and water supply networks. Using a consistent modeling of the network, adjoint equations for the whole system including initial, coupling and boundary conditions can be derived. These are suitable to compute gradients for optimization tasks but can also be used to estimate the accuracy of models and the discretization with respect to a given cost functional. We show the applicability of an adaptive algorithm that automatically steers the discretization and models while maintaining a given accuracy in an optimisation framework. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An efficient linear solver for the hybridized discontinuous Galerkin method
Authors: Jaust Alexander , Schütz Jochen , Aizinger Vadym 
Published: October 2016

AbstractDiscretizing partial differential equations by an implicit solving technique ultimately leads to a linear system of equations that has to be solved. The number of globally coupled unknowns is especially large for discontinuous Galerkin (DG) methods. It can be reduced by using hybridized discontinuous Galerkin (HDG) methods, but still efficient linear solvers are needed. It has been shown that, if hierarchical basis functions are used, a hierarchical scale separation (HSS) ansatz can be an efficient solver. In this work, we couple the HDG method with an HSS solver to solve a scalar nonlinear problem. It is validated by comparing the results with results obtained by GMRES with ILU(3) preconditioning as linear solver. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An adjoint‐based pressure correction scheme
Authors: Reiss Julius 
Published: October 2016

AbstractIncompressible flows are solenoidal, i. e. the divergence of the flow field is zero. This is an algebraic constraint on the solution in time. The pressure has to be determined, so that the constraint is fulfilled. To calculate the pressure often a Poisson equation is derived, which is then solved by an iterative method. Instead of this the constraint is here formulated as an optimization problem. The objective functional is taken as the square of the norm of the divergence. A gradient based optimization is performed to calculate the pressure in every time step of the simulation. By this an alternative iterative scheme is derived. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation
Authors: Straub Veronika , Ortleb Sigrun , Birken Philipp , Meister Andreas 
Published: October 2016

AbstractWe investigate the adaption of the recently developed exponential integrators called EPIRK in the so‐called domain‐based implicit‐explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A‐ and L‐stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.Here, we introduce the IMEX‐EPIRK method, which consists of coupling an explicit Runge‐Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Limit‐point / limit‐circle classification of second‐order differential operators arising in PT quantum mechanics
Authors: Büttner Florian , Trunk Carsten 
Published: October 2016

AbstractWe consider a second‐order differential equation
−y″ + q(x)y(x) = λy(x)
with complex‐valued potential q and eigenvalue parameter λ ∈ ℂ. In PT quantum mechanics the potential q is given by
q(x) = −(ix)N+2
on a contour Γ ⊂ ℂ. Via a parametrization we obtain two differential equations on [0, ∞) and (−∞, 0]. We give a limit‐point/limit‐circle classification of this problem via WKB‐analysis. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations
Authors: Gernandt Hannes , Trunk Carsten 
Published: October 2016

AbstractWe study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Boundary Damped Inhomogeneous Timoshenko Beams.
Authors: Picard Rainer , Watson Bruce A. 
Published: October 2016

AbstractWe consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations as developed in [1]. The focus is on boundary damping, which is implemented as a dynamic boundary condition. A change of material laws allows to include a large class of cases of boundary damping. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
G‐convergence and the weak operator topology
Authors: Waurick Marcus 
Published: October 2016

AbstractWe show that a bounded sequence (an)n of symmetric d × d‐matrix valued functions is G‐convergent if and only if ((ι∗︁anι)−1 )n converges in the weak operator topology. Here ι: R(grad0) ↪ L2(Ω)d denotes the (canonical) embedding from the range of the weak gradient grad0 defined on H10(Ω) into L2(Ω)d, where Ω ⊆ ℝd is open and bounded. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The mathematics behind Jost Bürgi's method for calculating sine tables
Authors: Ullrich Peter 
Published: October 2016

AbstractJost Bürgi (1552–1632) is not only one of the first persons who set up tables of logarithms for practical use but also invented a method to calculate highly precise tables of the sine function with small increment of the argument, and this with only a modest amount of calculations. Bürgi's manuscript on his method, however, was never published by him and got lost for almost four centuries until Menso Folkerts discovered it, cf. [2]. The article [1] on this manuscript gives a proof for the correctness of this method which, however, relies on the Theorem of Perron‐Frobenius that is over three centuries younger than Bürgi's method. The present contribution discusses how Bürgi may have come to his method and what considerations may have convinced him that it should work. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Where can we really prove instances of the Paris‐Harrington principle?
Authors: Freund Anton 
Published: October 2016

AbstractA fundamental question in mathematical logic asks: What are the minimal assumptions and deduction principles required to prove a particular theorem? Now consider the special case of a theorem that can be established by checking a finite number of decidable cases — think of a single instance of the finite Ramsey theorem. In this particular situation the answer to our question is trivial: The theorem can be demonstrated by an explicit verification, thus without the use of any “strong” proof principles. This answer, however, is not very satisfying: An explicit verification may be unfeasible if there is an enormous number of cases to check. At the same time there might be a short and meaningful proof using stronger proof methods. Such a situation suggests a modified question: What are the minimal assumptions and deduction principles required for a reasonably short proof of the given theorem? Our contribution explores this question for instances of the Paris‐Harrington principle. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Herbrand's theorem revisited
Authors: Afshari Bahareh , Hetzl Stefan , Leigh Graham E. 
Published: October 2016

AbstractWe present recent results on the deepening connection between proof theory and formal language theory. To each first‐order proof with prenex cuts of complexity at most Πn/Σn, we associate a typed (non‐deterministic) tree grammar of order n (equivalently, an order n recursion scheme) that abstracts the computation of Herbrand sets obtained through Gentzen‐style cut elimination. Apart from offering a means to compute Herbrand expansions directly from proofs with cuts, these grammars provide a structural counterpart to Herbrand's theorem that opens the door to tackling a number of questions in proof theory such as proof equivalence, proof compression and proof complexity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Categorical tools for state sum constructions
Authors: Schweigert Christoph , Fuchs Jürgen 
Published: October 2016

AbstractSurface defects in (extended) three‐dimensional topological field theories have important applications, ranging from solid state physics to computations of Brauer‐Picard groups of representation categories. We present some categorical tools that are needed in such a construction, including in particular a category‐valued trace. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical reduction of self‐consistent field models of macromolecular systems
Authors: Disterhoft Alexej , Raasch Thorsten , Schmid Friederike 
Published: October 2016

AbstractWe report on the first application of model reduction techniques to the numerical simulation of self‐consistent field (SCF) models for polymer melts at equilibrium. As a complement to the classical SCF iteration, the parametric reaction‐diffusion equations for the chain propagators are treated by a reduced basis (RB) approximation from spaces of bandlimited functions. Numerical examples in a spatially one‐dimensional, periodic setting show that the approach is feasible, although not all requirements of an orthodox RB scheme are satisfied. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Learning parametrised regularisation functions via quotient minimisation
Authors: Benning Martin , Gilboa Guy , Schönlieb Carola‐Bibiane 
Published: October 2016

AbstractWe propose a novel strategy for the computation of adaptive regularisation functions. The general strategy consists of minimising the ratio of a parametrised regularisation function; the numerator contains the regulariser with a desirable training signal as its argument, whereas the denominator contains the same regulariser but with its argument being a training signal one wants to avoid. The rationale behind this is to adapt parametric regularisations to given training data that contain both wanted and unwanted outcomes. We discuss the numerical implementation of this minimisation problem for a specific parametrisation, and present preliminary numerical results which demonstrate that this approach is able to recover total variation as well as second‐order total variation regularisation from suitable training data. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive first integral preserving methods for PDEs
Authors: Ringholm Torbjørn 
Published: October 2016

AbstractWe present a method for constructing first integral preserving numerical schemes for time‐dependent partial differential equations on non‐uniform grids, using a finite difference approach for spatial discretization and discrete gradients for time stepping. The method is extended to accommodate spatial adaptivity. A numerical experiment is carried out where the method is applied to the Sine‐Gordon equation with moving mesh adaptivity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematical research data
Authors: Koprucki Thomas , Tabelow Karsten , Kleinod Ilka 
Published: October 2016

AbstractThe generation and processing of research data for modeling and simulation is an important part of the scientific work at WIAS. Together with scientific software it plays an essential role for the transfer of mathematical research results to industry or to other scientific disciplines. In the face of the emerging digital science agenda research data is now more and more recognized as an essential foundation for scientific work. The importance of research data is also emphasized by the recent adoption of the “DFG Guidelines on the Handling of Research Data” by the Deutsche Forschungsgemeinschaft and the Open Data Pilot within the EU Horizon 2020 programme. In this contribution we present our definition of research data in mathematical modeling and simulation and requirements for its management. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Synthesis and properties of bromide‐ functionalized poly(isobutylene‐co‐p‐ methylstyrene) random copolymer
Authors: Xie Yi , Chang Jin‐jie , Wu Yi‐bo , Yang Dan , Wang Hao , Zhang Tao , Li Shu‐xin , Guo Wen‐li 
Published: October 2016

AbstractPoly(isobutylene‐co‐p‐methylstyrene) (IB/p‐MS) random copolymer is a new generation of polyisobutylene‐based elastomers. The cationic copolymerization of IB with p‐MS was thoroughly examined by using 2‐chloro‐2,4,4‐trimethylpentane/ethylaluminiumsesquichloride/electron donor as initiating system. IB/p‐MS random copolymers with high molecular weight were obtained at elevated temperature through the addition of ethyl acetate; the reaction proceeded in a mildly exothermic manner. Although the reactivity ratios of comonomer pairs differ by close to an order of magnitude, p‐MS was uniformly distributed in the chains. IB/p‐MS random copolymer can be brominated by adding molecular bromine into the copolymer solution, thereby yielding a completely saturated polymer backbone with a chemically reactive site. The types and selection of appropriate vulcanization systems for bromide‐functionalized IB/p‐MS random copolymers are also discussed. © 2016 Society of Chemical Industry
Protonated Hydrogen Cyanide
Authors: Goetz Nadine R. , Axhausen Joachim A. H. , Soltner Theresa , Rotter Christiane , Kornath Andreas J. 
Published: October 2016

AbstractTrimethylsilylcyanide reacts with superacidic solutions AF/MF5 (A=H, D; M=As, Sb) to form their corresponding salts [ACNA]+[MF6]−, which are protonated forms of hydrogen cyanide and Me3SiF as by‐product. The salts have been characterized by vibrational spectroscopy and a single‐crystal X‐ray structure analysis. [DCND]+[AsF6]− crystallizes in the triclinic space group P‐1 with one formula unit in the unit cell. The disordered cations are linked with two strong hydrogen bonds to [SbF6]− anions to form chains. The crystal structure and the vibrational spectra are compared to the quantum‐chemically calculated (PBE1PBE/6‐311++G(3df,3dp)) [HCNH(HF)2]+ and [DCND(HF)2]+ units which simulate the H⋅⋅⋅F hydrogen bridges found in the solid state. The vibrational modes of the [DCND]+ cation are strongly mixed. For their discussion 13C and 15N isotopomers have been prepared by the reaction of KCN isotopomers with the superacidic solution AF/AsF5.