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  • 1.
    Argatov, Ivan I
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM).
    A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study2019In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 118, no 1, p. 29-41Article in journal (Refereed)
    Abstract [en]

    A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a priori unknown domain with overdetermined boundary conditions, the right-hand sides of which depend on the unit normal to the free boundary. A perturbation analysis of the nonstandard free boundary problem that models deep abrasive drilling has been performed under the assumption that the free boundary is close to the surface of a given semi-infinite cylinder, the longitudinal position of which depends on the boundary data, and the leading-order asymptotic solution has been developed.

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  • 2.
    Argatov, Ivan
    et al.
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM). Malmö University, Biofilms Research Center for Biointerfaces. Institut für Mechanik Technische Universität Berlin, Berlin 10623 Germany.
    Jin, Xiaoqing
    College of Aerospace Engineering, Chongqing University, Chongqing, 400030, China.
    Gravitational settling of a cell on a high-aspect-ratio nanostructured substrate: An asymptotic modeling approach2022In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 108, p. 294-307Article in journal (Refereed)
    Abstract [en]

    The problem of contact deformation of an elastic body loaded by gravitational forces and laying on several small rigid supports is considered in the framework of the linear theory of elasticity. Using the method of matched asymptotic expansions, the limit asymptotic model for determining the support reactions and the kinematic parameters of the body settling is derived. The effect of the body surface reinforcement is discussed. The case of a uniform (symmetric) settling is considered in detail.

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  • 3.
    Bah, Maryam
    et al.
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Olsson, Mattias
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Kreativt Tänkande Och Problemlösning2024Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med den här kunskapsöversikten är att undersöka vikten av kreativt tänkande, dess relation till problemlösningsförmågan och den relationella förståelsen. Problemlösningsförmågan är en förmåga som understryks i läroplanen för matematik årskurs 4-6, därmed undersöker vi relationen mellan det kreativa tänkandet och problemlösningsförmågan. Undersökningen har gjorts genom att initialt skapa tre frågeställningar och därefter söka data från olika peer-reviewed forskningsartiklar på engelska mellan årtalen 2019–2023 från databaser som ERC, JSTOR, ERIC från olika delar av världen. Forskningen har granskats och sammanställts för att ge svar på frågeställningarna. Under den systematiska sökningsprocessen har vi stött på nya begrepp som open ended och heuristik som visat sig ha en nära relation till problemlösningsförmågan samt det kreativa tänkandet. Utöver det har Skemps lärandeteorier om instrumentell och relationell förståelse satt grunden för vår systematiska sökprocess. Resultatet påvisar att det kreativa tänkandet utvecklas efter arbete med problemlösningsförmågan samt öppna frågor. Det kreativa tänkandet kan i sin tur relateras till en relationell förståelse. De empiriska studierna påvisar att lärare brister i sin kunskap om hur man kan utforma matematiska problem som utvecklar ett kreativt tänkande hos eleverna. De valda empiriska studierna är genomförda i utlandet och Sverige skulle dra nytta av liknande forskning för att stötta pedagogerna i elevernas utveckling mot ett kreativt tänkande som står emot den snabbt utvecklande värld som väntar efter avslutad skolgång.                      

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  • 4.
    Baravdish, George
    et al.
    Linkoping Univ, Linkoping, Sweden..
    Cheng, Yuanji
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM).
    Svensson, Olof
    Linkoping Univ, Linkoping, Sweden..
    Åström, Freddie
    Heidelberg Univ, Heidelberg, Germany..
    Generalizations of p-Laplace operator for image enhancement: Part 22020In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 19, no 7, p. 3477-3500Article in journal (Refereed)
    Abstract [en]

    We have in a previous study introduced a novel elliptic operator Delta((p,q))u = vertical bar del u vertical bar(q) Delta(1)u + (p - 1) vertical bar del u vertical bar(p-2)Delta(infinity) u, p >= 1, q >= 0, as a generalization of the p-Laplace operator. In this paper, we establish the well-posedness of the parabolic equation u(t) =vertical bar del u vertical bar(1-q) Delta((1+q,q)), where q = q(vertical bar del u vertical bar) is continuous and has range in [0, 1], in the framework of viscosity solutions. We prove the consistency and convergence of the numerical scheme of finite differences of this parabolic equation. Numerical simulations shows the advantage of this operator applied to image enhancement.

  • 5.
    Björklund, Camilla
    et al.
    University of Gothenburg.
    Alkhede, Maria
    Malmö högskola, Faculty of Education and Society (LS), Department of Children, Youth and Society (BUS). University of Gothenburg.
    Sharpening the focus on numbers and counting: Preschool educators differentiating aspects of mathematical knowledge for teaching2017In: Mathematics Teacher Education and Development, ISSN 1442-3901, Vol. 19, no 3, p. 117-134Article in journal (Refereed)
    Abstract [en]

    This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics education practice. The object of learning for the participants is more specifically how numbers and counting are made content for learning in preschool practice. The educators' authentic documentations are reflected upon in focus group meetings and further analysed by the researchers to find out what aspects the educators differentiate during the programme. Results show that educators' learning about content for children's learning in preschool is a complex process. This process involves several aspects necessary to discern for a professional development to occur, but the collaborative approach seems prosperous in that new aspects are brought to the fore, influencing their reflective practice.

  • 6.
    Cheng, Yuanji
    et al.
    Malmö högskola, School of Technology (TS).
    Wang, Lina
    Mathematical Center, Lund University, Box 118, 221 00 Lund, Sweden.
    Remarks on bifurcation in elliptic boundary value problems2003In: International Conference on Differential Equations, World Scientific, 2003, p. 1051-1055Conference paper (Refereed)
    Abstract [en]

    In this paper, we present some observations of biurcation in nonlinear elliptic boundary value problem - ∆u = f(λ, u) in domain Ω, and u = 0 on the boundary ∂Ω. We are interested in how solution(s) depends on the parameter λ. Through examples, we show that multiple solutions appear, when λ cross certain critical value, i.e. bifurcation occurs.

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  • 7.
    de Hoop, Maarten
    et al.
    Rice University, Houston, TX, USA.
    Iantchenko, Alexei
    Malmö högskola, Faculty of Technology and Society (TS).
    Nakamura, Gen
    Hokkaido University, Japan.
    Zhai, Jian
    Rice University, Houston, TX, USA.
    Semiclassical analysis of elastic surface waves2017Manuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdi\`ere on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. Using these Hamiltonians, we obtain pseudodifferential surface wave equations. We then construct a parametrix. Finally, we discuss Weyl's formulas for counting surface modes, and the decoupling into two classes of surface waves, that is, Rayleigh and Love waves, under appropriate symmetry conditions.

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  • 8.
    De Hoop, Maarten V
    et al.
    Simons Chair in Computational and Applied Mathematics and Earth Science, Rice University, Houston, TX 77005, United States of America.
    Garnier, Josselin
    CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France.
    Iantchenko, Alexei
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM).
    Ricaud, Julien
    CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France.
    Inverse problem for Love waves in a layered, elastic half-space2024In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, no 045013, p. 1-44Article in journal (Refereed)
    Abstract [en]

    In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to recover the parameters of the elastic medium from the empirical knowledge of the frequency–wavenumber couples of the Love waves.

  • 9.
    de Hoop, Maarten V.
    et al.
    Simons Chair in Computational and Applied Mathematics and Earth Science, Rice University, Houston TX, USA.
    Iantchenko, Alexei
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM).
    Analysis of wavenumber resonances for the Rayleigh system in a half space2023In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 479, no 2277Article in journal (Refereed)
    Abstract [en]

    We present a comprehensive analysis of wavenumber resonances or leaking modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyse their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the Riemann surface as expected.

  • 10.
    de Hoop, Maarten V.
    et al.
    Rice University, Houston, Texas.
    Iantchenko, Alexei
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM).
    Inverse problem for the Rayleigh system with spectral data2022In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 63, no 3, p. 1-33, article id 031505Article in journal (Refereed)
    Abstract [en]

    We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution, while the data are captured in a Jost function, and we point out parallels with a corresponding problem for the Schrödinger equation. The Jost function can be identified with spectral data. We derive a Gel’fand-Levitan type equation and obtain uniqueness with two distinct frequencies.

  • 11.
    Edbladh, Ellinor
    et al.
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Käller Jens, Emmy
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Representationsformer för begreppet derivata: en läromedelsanalys i gymnasiekursen matematik 3c2021Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna undersökning syftar till att undersöka vilka lärandemöjligheter tre vanliga svenska läroböckers övningsuppgifter erbjuder elever för introduktionen av begreppet derivata. Analysens grund utgår från Michelle Zandiehs ramverk om olika aspekter för att förstå begreppet derivata. Tre vanliga läroböcker, Matematik 5000 3c, Matematik Origo 3c och Matematik M 3c, analyserades utifrån detta ramverk. Analysen hade fokus på tre kontexter från Zandiehs ramverk, den algebraiska kontexten, den grafiska kontexten och den verbala kontexten. Samtliga kontexter granskades utifrån de tre lager som också beskrivs av Zandieh. Vilket fokus läroböckerna lade på deriveringsregler undersöktes också. Resultatet presenterades med anpassade Lorenzkurvor för att redovisa förekomsten av de olika uppgiftskategorierna genom läroböckernas gång. Det undersöktes också om det förekom någon skillnad i vilka kategorier som förekommer i läroböckernas olika uppgiftsnivåer. 

    Analysen visade att läroböckerna erbjuder en begränsad möjlighet för att utveckla förståelse för hela begreppet derivata. Förekomsten av de olika kontexterna och lagren skiljde sig mellan läroböckerna, men ingen lärobok erbjöd en bred variation av alla kategorier. Vidare visade analysen även att förekomsten av de olika uppgiftskategorierna skiljde sig mellan de olika uppgiftsnivåerna för respektive lärobok. 

  • 12.
    Iantchenko, Alexei
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM). Malmö University, Biofilms Research Center for Biointerfaces. Reims Universities.
    Inverse problems in surface-wave tomography with spectral and resonance data2023Conference paper (Other academic)
    Abstract [en]

    Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. In the case of an isotropic medium, the surface wave decouples up to principal parts into Love and Rayleigh waves associated to scalar and matrix spectral problems, respectively. Since the mathematical features (such as spectrum, resonances) of these problems can be extracted from the seismograms, we are interested in recovering the Lam e parameters from these data. We generalize spectral methods for Schrodinger operators to the Rayleigh problem, which is essentially not of Schrodinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.

    This is joint work with Maarten V. de Hoop.

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  • 13.
    Iantchenko, Alexei
    Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM). Malmö University, Biofilms Research Center for Biointerfaces.
    Semiclassical inverse spectral and resonance problems in semiclassical surface-wave tomography: Lectures at l'IHP, Paris, 20-21 june 20222022Other (Other academic)
    Abstract [en]

    Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. The propagation of such waves is governed by effective Hamiltonians on the boundary with a space-adiabatic behavior.

    Effective Hamiltonians of surface waves correspond to eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities.Using these Hamiltonians, we obtain pseudodifferential surface wave equations. Then we carry out the semiclassical construction of general surface waveparametrices. In the process, we introduce locally Schrödinger-like operators in the boundary normal coordinate and their eigenvalues signifying effective Hamiltonians in the boundary(tangential) coordinates describing surface-wave propagation.

    In case of isotropic medium the surface wave decouples up to principal parts into Love and Rayleigh waves associated to scalar and matrix spectral problems, respectively.

    Since the mathematical features (such as spectrum, resonances) of these problems can be extracted from the seismograms, we are interested in recovering the Lamé parameters from these data.  Plan of lectures:

    1) Semiclassical description of surface waves.

    2) Semiclassical inverse spectral problems for Love and Rayleigh waves: conditional recovery of S-wave speed using the semiclassical spectra as the data.

    3) Recovery of S-and P-wave speeds from the discrete and continuous spectra using the exact methods for Sturm-Liouville operators: Gel'fand-Levitan-Marchenko approach.

    4) Leaking modes as analogues of scattering resonances.

    The material of these lectures is result of collaboration with Maarten V. de Hoop at Rice University and his Geo-Mathematical Imaging Group.

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  • 14.
    Iantchenko, Alexei
    et al.
    Malmö högskola, School of Technology (TS).
    Korotyaev, Evgeny
    Periodic Jacobi operator with finitely supported perturbations: The inverse resonance problem2012In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 252, no 3, p. 2823-2844Article in journal (Refereed)
    Abstract [en]

    We consider a periodic Jacobi operator H with finitely supported perturbations on Z. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data, the inverse of the transmission coefficient and the Jost function on the right half-axis, is one-to-one and onto. We consider the problem of reconstruction of the scattering data from all eigenvalues, resonances and the set of zeros of R_(lambda) + 1, where R_ is the reflection coefficient. (C) 2011 Elsevier Inc. All rights reserved.

  • 15. Klonowska, Kamilla
    et al.
    Lennerstad, Håkan
    Lundberg, Lars
    Svahnberg, Charlie
    Optimal recovery schemes in fault tolerant distributed computing2005In: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 41, no 6, p. 341-365Article in journal (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all n computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down, the load on these computers must be redistributed to other computers in the system. The redistribution is determined by the recovery scheme. The recovery scheme is governed by a sequence of integers modulo n. Each sequence guarantees minimal load on the computer that has maximal load even when the most unfavorable combinations of computers go down. We calculate the best possible such recovery schemes for any number of crashed computers by an exhaustive search, where brute force testing is avoided by a mathematical reformulation of the problem and a branch-and-bound algorithm. The search nevertheless has a high complexity. Optimal sequences, and thus a corresponding optimal bound, are presented for a maximum of twenty one computers in the distributed system or cluster.

  • 16. Klonowska, Kamilla
    et al.
    Lundberg, Lars
    Lennerstad, Håkan
    Broberg, Magnus
    Comparing the optimal performance of parallel architectures2004In: Computer journal, ISSN 0010-4620, E-ISSN 1460-2067, Vol. 47, no 5, p. 527-544Article in journal (Refereed)
    Abstract [en]

    Consider a parallel program with n processes and a synchronization granularity z. Consider also two parallel architectures: an SMP with q processors and run-time reallocation of processes to processors, and a distributed system (or cluster) with k processors and no run-time reallocation. There is an inter-processor communication delay of t time units for the system with no run-time reallocation. In this paper we define a function H(n,k,q,t,z) such that the minimum completion time for all programs with n processes and a granularity z is at most H(n,k,q,t,z) times longer using the system with no reallocation and k processors compared to using the system with q processors and run-time reallocation. We assume optimal allocation and scheduling of processes to processors. The function H(n,k,q,t,z)is optimal in the sense that there is at least one program, with n processes and a granularity z, such that the ratio is exactly H(n,k,q,t,z). We also validate our results using measurements on distributed and multiprocessor Sun/Solaris environments. The function H(n,k,q,t,z) provides important insights regarding the performance implications of the fundamental design decision of whether to allow run-time reallocation of processes or not. These insights can be used when doing the proper cost/benefit trade-offs when designing parallel execution platforms.

  • 17.
    Klonowska, Kamilla
    et al.
    School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden.
    Lundberg, Lars
    School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden.
    Lennerstad, Håkan
    School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden.
    Svahnberg, Charlie
    School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden.
    Extended Golomb Rulers as the New Recovery Schemes in Distributed Dependable Computing2005Conference paper (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. We have previously defined recovery schemes that are optimal for some limited cases. In this paper we find a new recovery schemes that are based on so called Golomb rulers. They are optimal for a much larger number of cases than the previous results.

  • 18.
    Overgaard, Niels
    Malmö högskola, School of Technology (TS).
    Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Nonlinear Analysis: Theory, Methods & Applications, Vol. 70, no 10, p. 3658-3664Article in journal (Refereed)
    Abstract [en]

    We consider a moving-boundary problem associated with a limiting case of the fluid model for biofilm growth proposed by J. Dockery and I. Klapper, SIAM J. Appl. Math. 62(3), 2001. Concepts of classical, weak, and variational solutions for this problem are introduced. Classical solutions with radial symmetry are constructed, and estimates for their growth are given. Using a weighted Baiocchi transform it is shown that every classical solution is a weak solution. Every weak solution is in turn equivalent to the solution-set of a family of variational inequalities for an elliptic PDE (the variational solution). This allow us to show that, given arbitrary initial data at time t = 0 (any bounded open set), there exists a weak solution defined for all times t > 0. Upper bounds for the weak solutions are given, and a semi-group property is proved. The background for this problem, and a model derivation is also presented.

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  • 19.
    Schultz, Rasmus
    et al.
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Scherp, Lukas
    Malmö University, Faculty of Education and Society (LS), Department of Natural Science, Mathematics and Society (NMS).
    Hur användandet av samtal och diskussion påverkar mellanstadieelevers förståelse för matematik2024Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This research overview is an evaluation of knowledge and explores the impact of language linked to mathematics. This particularly in the context of conversations and discussions, on the mathematical understanding of students in the ages between ten to twelve years old. The research overview attempts to examine the role a conversation plays in a concept of learning, specifically in mathematics teaching. With this study we want to create an understanding between the relationship of a rewarding conversation and the understanding of mathematical concepts and systems. Through systematic search and analysis of scientific texts a total of 10 articles were used to gain a proper overview of the subject found through systematic searches of sources such as ERIC, EBSCO and LibSearch. The limitations set for the chosen articles were a timeframe between the years 2011 until 2023, as well as being peer-reviewed. All chosen articles and studies are written in English but originate from different places which provides a wider perspective on the subject. The results show that conversation has an essential role in students' understanding of mathematics. Through correct language that develops in mathematical conversations, a deeper understanding of the subject is created. The research overview also shows the importance of language in shaping students' mathematical knowledge, presenting it as a crucial component of their proficiency in the subject. The research overview further describes the importance of classroom conversations, the teacher's role in the classroom, and the impact of home environments on learning. An aspect related to the subject is how sociocultural thoughts about active learning in a social context reflect the present of Swedish school and its design. By delving deep into the functionality of conversation and the connection between discussion and learning, the school will be able to develop the learning offered in the classroom to better meet the students and their needs. Furthermore, our research concludes that for future educators it is a necessity to balance teacher guidance and student participation in classroom discussions. 

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