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  • 1.
    Cheng, Xiaoliang
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Lin, Guangliang
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Zhang, Ye
    Örebro University, School of Science and Technology. Department of Mathematics.
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology. Department of Mathematics.
    A modified coupled complex boundary method for an inverse chromatography problem2017In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945Article in journal (Refereed)
    Abstract [en]

    Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

  • 2.
    Gulliksson, Mårten
    et al.
    Örebro University, School of Science and Technology.
    Holmbom, Anders
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Persson, Jens
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Zhang, Ye
    Örebro University, School of Science and Technology.
    A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems2016In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, no 2, 025005Article in journal (Refereed)
    Abstract [en]

    Reconstructing the homogenized coefficient, which is also called the G-limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G-limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G-limit from the weak -limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.

  • 3.
    Gustafsson, Jonas
    et al.
    Örebro University, School of Science and Technology.
    Olofsson, Isac
    Örebro University, School of Science and Technology.
    RSA-kryptografi för gymnasiet2011Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna bok riktar sig till gymnasieelever som vill fördjupa sig i ämnet RSA-kryptografi . RSA-kryptografi är en avancerad metod för att kommunicera med hemliga meddelanden och används flitigt inom t.ex. bankvärlden. När du handlar med ditt kort eller använder din e-legitimation används RSA-kryptogra fi för att allt du gör ska vara skyddat och säkert. Vid stora transaktioner mellan olika banker används också RSA-kryptogra fi för att både den som betalar och den som får betalt ska vara säkra att allt går rätt till.Boken är uppdelad i fyra kapitel. Kapitel 3 och 4 är betydligt mer avancerade än kapitel 1 och 2. Kapitel 1 består mestadels av exempel och övningar som behandlar matematiken som krävs för att kunna utföra RSA-kryptogra fi med små tal. Kapitel 2 använder matematiken i kapitel 1 för att genom exempel och övingar metodiskt lära ut hur RSA-kryptogra fi med små tal går till. Kapitel 3 visar matematiken som ligger till grund för att RSA-kryptografi fungerar. Detta visas med hjälp av exempel, satser, förtydligade bevis samt några enstaka övningar. Kapitel 4 förklarar varför RSA-kryptografi är säkert och enkelt att använda. Primtalstester utgör det viktigaste ämnet i detta sista kapitel. 

  • 4.
    Lin, G.
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Zhang, Ye
    Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Cheng, X.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Forssén, P.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    A regularizing Kohn–Vogelius formulation forthe model-free adsorption isotherm estimationproblem in chromatography2017In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed)
    Abstract [en]

    Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.

  • 5.
    Lockby, Andreas
    et al.
    School of Science and Technology, Örebro University, Örebro, Sweden..
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems2016In: Comsol Conference 2016, 2016Conference paper (Refereed)
    Abstract [en]

    The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol.

  • 6.
    Rahayem, Mohamed R.
    et al.
    Örebro University, School of Science and Technology.
    Kjellander, Johan A. P.
    Örebro University, School of Science and Technology.
    Quadric segmentation and fitting of data captured by a laser profile scanner mounted on an industrial robot2010In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 52, no 1-4, 155-169 p.Article in journal (Refereed)
    Abstract [en]

    Applications like geometric reverse engineering, robot vision and automatic inspection require sets of points to be measured from the surfaces of objects and then processed by segmentation and fitting algorithms to establish shape parameters of interest. In industrial applications where speed, reliability and automatic operation is of interest a measuring system based on a laser profile scanner mounted on an industrial robot can be of interest. In earlier publications we have presented such a system and also a segmentation algorithm for planar surfaces using 2D profile data in combination with robot poses. Due to the data reduction offered by this approach the segmentation algorithm computes faster than algorithms based on 3D point sets alone. Encouraged by the results we have now developed a segmentation algorithm for two different quadric surfaces also based on 2D profiles in combination with robot poses. This paper presents the new algorithm together with test results and also an interesting observation that points to future work.

  • 7.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Smyrnakis, J.
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength2017In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, 012142Article in journal (Refereed)
    Abstract [en]

    Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

  • 8.
    Sjölander, Arvid
    et al.
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Lichtenstein, Paul
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Larsson, Henrik
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden.
    Pawitan, Yudi
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Between-within models for survival analysis.2013In: Statistics in Medicine, ISSN 0277-6715, E-ISSN 1097-0258, Vol. 32, no 18, 3067-3076 p.Article in journal (Refereed)
    Abstract [en]

    A popular way to control for confounding in observational studies is to identify clusters of individuals (e.g., twin pairs), such that a large set of potential confounders are constant (shared) within each cluster. By studying the exposure-outcome association within clusters, we are in effect controlling for the whole set of shared confounders. An increasingly popular analysis tool is the between-within (BW) model, which decomposes the exposure-outcome association into a 'within-cluster effect' and a 'between-cluster effect'. BW models are relatively common for nonsurvival outcomes and have been studied in the theoretical literature. Although it is straightforward to use BW models for survival outcomes, this has rarely been carried out in practice, and such models have not been studied in the theoretical literature. In this paper, we propose a gamma BW model for survival outcomes. We compare the properties of this model with the more standard stratified Cox regression model and use the proposed model to analyze data from a twin study of obesity and mortality. We find the following: (i) the gamma BW model often produces a more powerful test of the 'within-cluster effect' than stratified Cox regression; and (ii) the gamma BW model is robust against model misspecification, although there are situations where it could give biased estimates.

  • 9.
    Sørensen, Mads Peter
    et al.
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Falsig Pedersen, Niels
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    The dynamics of magnetic vortices in type II superconductors with pinning sites studied by the time dependent Ginzburg–Landau model2017In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 533, 40-43 p.Article in journal (Refereed)
    Abstract [en]

    We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg–Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.

  • 10.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Hernandez Bennetts, Victor
    Örebro University, School of Science and Technology.
    Schaffernicht, Erik
    Örebro University, School of Science and Technology.
    Reconstructing gas distribution maps via an adaptive sparse regularization algorithm2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 7, 1186-1204 p.Article in journal (Refereed)
    Abstract [en]

    In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.

  • 11.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Lukyanenko, D. V.
    Physical Faculty, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia.
    Yagola, A. G.
    Physical Faculty, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia.
    Using Lagrange principle for solving two-dimensional integral equation with a positive kernel2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 5, 811-831 p.Article in journal (Refereed)
    Abstract [en]

    This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

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