liu.seSök publikationer i DiVA
Ändra sökning
Avgränsa sökresultatet
1234567 1 - 50 av 3571
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Träffar per sida
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sortering
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
Markera
Maxantalet träffar du kan exportera från sökgränssnittet är 250. Vid större uttag använd dig av utsökningar.
  • 1.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

  • 2.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010Ingår i: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, s. 29-38Artikel i tidskrift (Refereegranskat)
    Ladda ner fulltext (pdf)
    fulltext
  • 3.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008Ingår i: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, s. 52-62Konferensbidrag (Övrigt vetenskapligt)
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009Ingår i: Proc. 19th AIAA CFD Conference, AIAA , 2009Konferensbidrag (Refereegranskat)
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Faculty of Engineering Technology, University of Twente, AE Enschede, The Netherlands.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy Stability of the MUSCL Scheme2010Ingår i: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, s. 65:1-8Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 6.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy stability of the MUSCL scheme2010Ingår i: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, s. 61-68Konferensbidrag (Refereegranskat)
  • 7.
    Abdallah, Nancy
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik.
    Hansson, Mikael
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Hultman, Axel
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Topology of posets with special partial matchings2019Ingår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 348, s. 255-276Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Special partial matchings (SPMs) are a generalisation of Brentis special matchings. Let a pircon be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Mariettis zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic W-sets constitute pircons. Together, these results extend a result of Can, Cherniaysky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.

  • 8.
    Abdallah, Nancy
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Hultman, Axel
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions2018Ingår i: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 47, nr 4, s. 543-560Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    When acts on the flag variety of , the orbits are in bijection with fixed point free involutions in the symmetric group . In this case, the associated Kazhdan-Lusztig-Vogan polynomials can be indexed by pairs of fixed point free involutions , where denotes the Bruhat order on . We prove that these polynomials are combinatorial invariants in the sense that if is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then for all v amp;gt;= u.

    Ladda ner fulltext (pdf)
    fulltext
  • 9.
    Abdulla, Ariyan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Andersson, Erik
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Heuristiska algoritmer för schemaläggning i real-tidssystem med hänsyn till data beroenden2018Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The schedule for the jobs in a real-time system can have a huge impact on how the system behave. Since real-time systems are common in safety applications it is important that the scheduling is done in a valid way. Furthermore, one can enhance the performance of the applications by minimizing data latency and jitter. A challenge is that jobs in real-time systems usually have complex constraints making it too time consuming to minimize data latency and jitter to optimality. The purpose of this report is to investigate the possibility of creating high quality schedules using heuristics, with the goal to keep the computational time under one minute. This will be done by comparing three different algorithms that will be used on real scheduling instances provided by the company Arcticus. The first algorithm is a greedy heuristic, the second one a local search and the third one is a metaheuristic, simulated annealing. The results indicate that the data latency can be reduced whilst keeping the computational time below one minute.

    Ladda ner fulltext (pdf)
    fulltext
  • 10.
    Abdulla, Parosh Aziz
    et al.
    Uppsala Univ, Sweden.
    Atig, Mohamed Faouzi
    Uppsala Univ, Sweden.
    Chen, Yu-Fang
    Acad Sinica, Taiwan.
    Phi Diep, Bui
    Uppsala Univ, Sweden.
    Holik, Lukas
    Brno Univ Technol, Czech Republic.
    Rezine, Ahmed
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Rummer, Philipp
    Uppsala Univ, Sweden.
    TRAU : SMT solver for string constraints2018Ingår i: PROCEEDINGS OF THE 2018 18TH CONFERENCE ON FORMAL METHODS IN COMPUTER AIDED DESIGN (FMCAD), IEEE , 2018, s. 165-169Konferensbidrag (Refereegranskat)
    Abstract [en]

    We introduce TRAU, an SMT solver for an expressive constraint language, including word equations, length constraints, context-free membership queries, and transducer constraints. The satisfiability problem for such a class of constraints is in general undecidable. The key idea behind TRAU is a technique called flattening, which searches for satisfying assignments that follow simple patterns. TRAU implements a Counter-Example Guided Abstraction Refinement (CEGAR) framework which contains both an under- and an over-approximation module. The approximations are refined in an automatic manner by information flow between the two modules. The technique implemented by TRAU can handle a rich class of string constraints and has better performance than state-of-the-art string solvers.

  • 11.
    Abgrall, Remi
    et al.
    Institute of Mathematics, University of Zurich, Switzerland.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten. Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa.
    Öffner, Philipp
    Institute of Mathematics, University of Zurich, Switzerland. Institute of Mathematics, Johannes Gutenberg-Universtiy, Germany.
    Tokareva, Svetlana
    Theoretical Division, Applied Mathematics and Plasma Physics Group (T-5), Los Alamos National Laboratory, USA.
    Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems2020Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 85, nr 2, artikel-id 43Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

    Ladda ner fulltext (pdf)
    fulltext
  • 12.
    Abgrall, Remi
    et al.
    University of Zurich, Switzerland.
    Nordström, Jan
    Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Matematiska institutionen, Tillämpad matematik. University of Johannesburg, South Africa.
    Öffner, Philipp
    University of Zurich, Switzerland.
    Tokareva, Svetlana
    Los Alamos National Laboratory, USA.
    Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability2023Ingår i: Communications on Applied Mathematics and Computation, ISSN 2096-6385, Vol. 5, nr 2, s. 573-595Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly. By applying this technique, the authors demonstrate that a pure continuous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way. In this work, we extend this investigation to the nonlinear case and focus on entropy conservation. By switching to entropy variables, we provide an estimation of the boundary operators also for nonlinear problems, that guarantee conservation. In numerical simulations, we verify our theoretical analysis.

    Ladda ner fulltext (pdf)
    fulltext
  • 13. Beställ onlineKöp publikationen >>
    Abidin, Aysajan
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Weaknesses of Authentication in Quantum Cryptography and Strongly Universal Hash Functions2010Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Authentication is an indispensable part of Quantum Cryptography, which is an unconditionally secure key distribution technique based on the laws of nature. Without proper authentication, Quantum Cryptography is vulnerable to “man-in-the-middle” attacks. Therefore, to guarantee unconditional security of any Quantum Cryptographic protocols, the authentication used must also be unconditionally secure. The standard in Quantum Cryptography is to use theWegman-Carter authentication, which is unconditionally secure and is based on the idea of universal hashing.

    In this thesis, we first investigate properties of a Strongly Universal hash function family to facilitate understanding the properties of (classical) authentication used in Quantum Cryptography. Then, we study vulnerabilities of a recently proposed authentication protocol intended to rule out a "man-in-the-middle" attack on Quantum Cryptography. Here, we point out that the proposed authentication primitive is not secure when used in a generic Quantum Cryptographic protocol. Lastly, we estimate the lifetime of authentication using encrypted tags when the encryption key is partially known. Under simplifying assumptions, we derive that the lifetime is linearly dependent on the length of the authentication key. Experimental results that support the theoretical results are also presented.

    Delarbeten
    1. Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    Öppna denna publikation i ny flik eller fönster >>Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    2009 (Engelska)Ingår i: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, s. 289-293Konferensbidrag, Publicerat paper (Refereegranskat)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

    Ort, förlag, år, upplaga, sidor
    New York: American Institute of Physics, 2009
    Nyckelord
    Quantum cryptography, Quantum theory, Probability
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-18738 (URN)10.1063/1.3109951 (DOI)
    Konferens
    Foundations of Probability and Physics—5, Växjö, augusti 2008
    Projekt
    ICG QC
    Tillgänglig från: 2009-06-03 Skapad: 2009-06-03 Senast uppdaterad: 2016-08-31
    2. Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    Öppna denna publikation i ny flik eller fönster >>Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    2009 (Engelska)Ingår i: International Journal of Quantum Information, ISSN 0219-7499, Vol. 7, nr 5, s. 1047-1052Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    In this paper, we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography" [M. Peev et al., Int. J. Quant. Inf. 3 (2005) 225]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.

    Nyckelord
    Quantum cryptography, quantum key distribution, authentication
    Nationell ämneskategori
    Naturvetenskap
    Identifikatorer
    urn:nbn:se:liu:diva-20405 (URN)10.1142/S0219749909005754 (DOI)
    Projekt
    ICG QC
    Tillgänglig från: 2009-09-08 Skapad: 2009-09-07 Senast uppdaterad: 2019-08-15Bibliografiskt granskad
    Ladda ner fulltext (pdf)
    Weaknesses of Authentication inQuantum Cryptography and Strongly Universal Hash Functions
    Ladda ner (pdf)
    Cover
  • 14.
    Abidin, Aysajan
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Larsson, Jan-Åke
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography2009Ingår i: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, s. 289-293Konferensbidrag (Refereegranskat)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

  • 15.
    Abrahamsson, Olle
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    A Gröbner basis algorithm for fast encoding of Reed-Müller codes2016Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [en]

    In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.

    Ladda ner fulltext (pdf)
    fulltext
  • 16.
    Abrahamsson, Olle
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem.
    Hide and Seek in a Social Network2017Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    In this thesis a known heuristic for decreasing a node's centrality scores while maintaining influence, called ROAM, is compared to a modified version specifically designed to decrease eigenvector centrality. The performances of these heuristics are also tested against the Shapley values of a cooperative game played over the considered network, where the game is such that influential nodes receive higher Shapley values. The modified heuristic performed at least as good as the original ROAM, and in some instances even better (especially when the terrorist network behind the World Trade Center attacks was considered). Both heuristics increased the influence score for a given targeted node when applied consecutively on the WTC network, and consequently the Shapley values increased as well. Therefore the Shapley value of the game considered in this thesis seems to be well suited for discovering individuals that are assumed to actively trying to evade social network analysis.

    Ladda ner fulltext (pdf)
    fulltext
  • 17.
    Abrahamsson, Olle
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    On Aggregation and Dynamics of Opinions in Complex Networks2024Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [sv]

    Avhandlingen studerar två problem definierade på komplexa nätverk, varav det första utforskar en tänkbar utökning av strukturell balansteori och det andra behandlar konvergensfrågor inom opinionsdynamik.

    I avhandlingens första hälft diskuteras möjliga definitioner på villkor för strukturell balans i ett nätverk med preferensordningar som nodattribut. Huvudresultatet är att för fallet med tre alternativ (A, B, C) så kan de (3!)3 = 216 möjliga konfigurationerna av trianglar reduceras till 10 ekvivalensklasser, vilka används som mått på en triangels balans som ett steg mot möjliga utökningar av strukturell balansteori. Vi härleder även en generell formel för antalet ekvivalensklasser för preferensordningar med n alternativ. Slutligen analyseras en empirisk datamängd och dess empiriska sannolikhetsfördelning av triangel-ekvivalensklasser jämförs med en nollhypotes i vilken preferenser tilldelas noderna slumpmässigt.

    Den andra hälften av avhandlingen rör en opinionsdynamikmodell där varje agent agerar slumpmässigt enligt en Bernoullifördelning vars sannolikhet uppdateras vid varje diskret tidssteg, och vi bevisar att denna modell konvergerar nästan säkert till konsensus. Vi ger också en detaljerad kritik av ett påstått bevis av detta resultat i litteraturen. Vi generaliserar resultatet genom att visa att antagandet om irreducibilitet i den ursprungliga modellen inte är nödvändigt. Vidare visar vi, som följdsats av det generaliserade resultatet, att den nästan säkra konvergensen till konsensus även håller om en agent är fullständigt envis och aldrig byter åsikt. I tillägg till detta visar vi att modellen, både i det ursprungliga och i det generaliserade fallet, konvergerar till konsensus även i r:te ordningens moment.  

    Ladda ner fulltext (pdf)
    fulltext
    Ladda ner (png)
    presentationsbild
  • 18.
    Abrahamsson, Olle
    et al.
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Danev, Danyo
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Larsson, Erik G
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Strong Convergence of a Random Actions Model in Opinion Dynamics2024Ingår i: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, ISSN 2373-776X, Vol. 10, s. 147-161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in $r$th mean.

    Ladda ner fulltext (pdf)
    fulltext
  • 19.
    Accardi, Luigi
    et al.
    Università di Roma “Tor Vergata”, Italy.
    Belavkin, V. P.
    University of Nottingham, UK.
    Kent, Johyn T.
    University of Leeds, UK.
    Brody, Dorje C.
    Imperial College, London, UK.
    Bingham, N. H.
    Brunel University, Uxbridge, UK.
    Frey, Jeremy G.
    University of Southampton, UK.
    Helland, Inge S.
    University of Oslo, Norway.
    Larsson, Jan-Åke
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Majumdar, N. K.
    London, UK.
    Minozzo, Marco
    University of Perugia, Italy.
    Thompson, J. W.
    University of Hull, UK.
    Discussion on “On quantum statistical inference” by O. E. Barndorff-Nielsen, R. D. Gill and P.E. Jupp2003Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology, ISSN 1369-7412, E-ISSN 1467-9868, Vol. 65, nr 4, s. 805-816s. 805-816Artikel i tidskrift (Refereegranskat)
    Ladda ner fulltext (pdf)
    Discussion on “On quantum statistical inference” by O. E. Barndorff-Nielsen, R. D. Gill and P.E. Jupp
  • 20. Beställ onlineKöp publikationen >>
    Achieng, Pauline
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains2020Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed.

    We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains.

    We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure.

    In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, μ0 and μ1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, μ0 and μ1 are also chosen appropriately.

    Delarbeten
    1. Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    Öppna denna publikation i ny flik eller fönster >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    2021 (Engelska)Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, s. 1681-1699Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

    Ort, förlag, år, upplaga, sidor
    Springer, 2021
    Nyckelord
    Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
    Nationell ämneskategori
    Matematisk analys
    Identifikatorer
    urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
    Tillgänglig från: 2020-10-26 Skapad: 2020-10-26 Senast uppdaterad: 2024-02-22Bibliografiskt granskad
    Ladda ner fulltext (pdf)
    fulltext
    Ladda ner (png)
    presentationsbild
  • 21. Beställ onlineKöp publikationen >>
    Achieng, Pauline
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten.
    Reconstruction of solutions of Cauchy problems for elliptic equations in bounded and unbounded domains using iterative regularization methods2023Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Cauchy problems for elliptic equations arise in applications in science and engineering. These problems often involve finding important information about an elliptical system from indirect or incomplete measurements. Cauchy problems for elliptic equations are known to be disadvantaged in the sense that a small pertubation in the input can result in a large error in the output. Regularization methods are usually required in order to be able to find stable solutions. In this thesis we study the Cauchy problem for elliptic equations in both bounded and unbounded domains using iterative regularization methods. In Paper I and II, we focus on an iterative regularization technique which involves solving a sequence of mixed boundary value well-posed problems for the same elliptic equation. The original version of the alternating iterative technique is based on iterations alternating between Dirichlet-Neumann and Neumann-Dirichlet boundary value problems. This iterative method is known to possibly work for Helmholtz equation. Instead we study a modified version based on alternating between Dirichlet-Robin and Robin-Dirichlet boundary value problems. First, we study the Cauchy problem for general elliptic equations of second order with variable coefficients in a limited domain. Then we extend to the case of unbounded domains for the Cauchy problem for Helmholtz equation. For the Cauchy problem, in the case of general elliptic equations, we show that the iterative method, based on Dirichlet-Robin, is convergent provided that parameters in the Robin condition are chosen appropriately. In the case of an unbounded domain, we derive necessary, and sufficient, conditions for convergence of the Robin-Dirichlet iterations based on an analysis of the spectrum of the Laplacian operator, with boundary conditions of Dirichlet and Robin types.

    In the numerical tests, we investigate the precise behaviour of the Dirichlet-Robin iterations, for different values of the wave number in the Helmholtz equation, and the results show that the convergence rate depends on the choice of the Robin parameter in the Robin condition. In the case of unbounded domain, the numerical experiments show that an appropriate truncation of the domain and an appropriate choice of Robin parameter in the Robin condition lead to convergence of the Robin-Dirichlet iterations.

    In the presence of noise, additional regularization techniques have to implemented for the alternating iterative procedure to converge. Therefore, in Paper III and IV we focus on iterative regularization methods for solving the Cauchy problem for the Helmholtz equation in a semi-infinite strip, assuming that the data contains measurement noise. In addition, we also reconstruct a radiation condition at infinity from the given Cauchy data. For the reconstruction of the radiation condition, we solve a well-posed problem for the Helmholtz equation in a semi-infinite strip. The remaining solution is obtained by solving an ill-posed problem. In Paper III, we consider the ordinary Helmholtz equation and use seperation of variables to analyze the problem. We show that the radiation condition is described by a non-linear well-posed problem that provides a stable oscillatory solution to the Cauchy problem. Furthermore, we show that the ill–posed problem can be regularized using the Landweber’s iterative method and the discrepancy principle. Numerical tests shows that the approach works well.

    Paper IV is an extension of the theory from Paper III to the case of variable coefficients. Theoretical analysis of this Cauchy problem shows that, with suitable bounds on the coefficients, can iterative regularization methods be used to stabilize the ill-posed Cauchy problem.

    Delarbeten
    1. Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    Öppna denna publikation i ny flik eller fönster >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    2021 (Engelska)Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, s. 1681-1699Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

    Ort, förlag, år, upplaga, sidor
    Springer, 2021
    Nyckelord
    Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
    Nationell ämneskategori
    Matematisk analys
    Identifikatorer
    urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
    Tillgänglig från: 2020-10-26 Skapad: 2020-10-26 Senast uppdaterad: 2024-02-22Bibliografiskt granskad
    2. Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
    Öppna denna publikation i ny flik eller fönster >>Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
    2023 (Engelska)Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 31, nr 5Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

    Ort, förlag, år, upplaga, sidor
    WALTER DE GRUYTER GMBH, 2023
    Nyckelord
    Helmholtz equation; Cauchy problem; inverse problem ill-posed problem
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-192481 (URN)10.1515/jiip-2020-0133 (DOI)000940871600001 ()
    Tillgänglig från: 2023-03-21 Skapad: 2023-03-21 Senast uppdaterad: 2024-03-18Bibliografiskt granskad
    3. Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
    Öppna denna publikation i ny flik eller fönster >>Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
    2023 (Engelska)Ingår i: Computational Methods in Applied Mathematics, ISSN 1609-4840, E-ISSN 1609-9389Artikel i tidskrift (Refereegranskat) Epub ahead of print
    Abstract [en]

    We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip. Homogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary. Additional complexity is that the radiation condition at infinity is unknown. Our aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition. Such problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements. The problem is split into two sub-problems, a well-posed and an ill-posed problem. We analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem. The second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it. Numerical tests show that the approach works well.

    Ort, förlag, år, upplaga, sidor
    WALTER DE GRUYTER GMBH, 2023
    Nyckelord
    Helmholtz Equation; Inverse Problem; Cauchy Problem; Ill-Posed Problem; Well-Posed Problem; Landweber Method
    Nationell ämneskategori
    Strömningsmekanik och akustik
    Identifikatorer
    urn:nbn:se:liu:diva-196637 (URN)10.1515/cmam-2022-0244 (DOI)001035412500001 ()
    Tillgänglig från: 2023-08-17 Skapad: 2023-08-17 Senast uppdaterad: 2023-11-13
    Ladda ner fulltext (pdf)
    fulltext
    Ladda ner (png)
    presentationsbild
  • 22.
    Achieng, Pauline
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Chepkorir, Jennifer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Kozlov, Vladimir
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations2021Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, s. 1681-1699Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

    Ladda ner fulltext (pdf)
    fulltext
  • 23.
    Achieng, Pauline
    et al.
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten. Univ Nairobi, Kenya.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Kozlov, Vladimir
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten.
    Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain2023Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 31, nr 5Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

  • 24.
    Adamowicz, Tomasz
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points2014Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, nr 6, s. 1131-1153Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

    Ladda ner fulltext (pdf)
    fulltext
  • 25.
    Adegboye, Oluwatayomi Rereloluwa
    et al.
    Univ Mediterranean Karpasia, Turkiye.
    Feda, Afi Kekeli
    European Univ Lefke, Turkiye.
    Ojekemi, Opeoluwa Seun
    Univ Mediterranean Karpasia, Turkiye.
    Agyekum, Ephraim Bonah
    Ural Fed Univ, Russia.
    Hussien, Abdelazim
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten. Fayoum Univ, Egypt; Appl Sci Private Univ, Jordan; Middle East Univ, Jordan.
    Kamel, Salah
    Aswan Univ, Egypt.
    Chaotic opposition learning with mirror reflection and worst individual disturbance grey wolf optimizer for continuous global numerical optimization2024Ingår i: Scientific Reports, E-ISSN 2045-2322, Vol. 14, nr 1, artikel-id 4660Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The effective meta-heuristic technique known as the grey wolf optimizer (GWO) has shown its proficiency. However, due to its reliance on the alpha wolf for guiding the position updates of search agents, the risk of being trapped in a local optimal solution is notable. Furthermore, during stagnation, the convergence of other search wolves towards this alpha wolf results in a lack of diversity within the population. Hence, this research introduces an enhanced version of the GWO algorithm designed to tackle numerical optimization challenges. The enhanced GWO incorporates innovative approaches such as Chaotic Opposition Learning (COL), Mirror Reflection Strategy (MRS), and Worst Individual Disturbance (WID), and it's called CMWGWO. MRS, in particular, empowers certain wolves to extend their exploration range, thus enhancing the global search capability. By employing COL, diversification is intensified, leading to reduced solution stagnation, improved search precision, and an overall boost in accuracy. The integration of WID fosters more effective information exchange between the least and most successful wolves, facilitating a successful exit from local optima and significantly enhancing exploration potential. To validate the superiority of CMWGWO, a comprehensive evaluation is conducted. A wide array of 23 benchmark functions, spanning dimensions from 30 to 500, ten CEC19 functions, and three engineering problems are used for experimentation. The empirical findings vividly demonstrate that CMWGWO surpasses the original GWO in terms of convergence accuracy and robust optimization capabilities.

  • 26.
    Adib Yaghmaie, Farnaz
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. Nanyang Technol Univ, Singapore.
    Movric, Kristian Hengster
    Czech Tech Univ, Czech Republic.
    Lewis, Frank L.
    Univ Texas Arlington, TX 76019 USA; Northeastern Univ, Peoples R China.
    Su, Rong
    Nanyang Technol Univ, Singapore.
    Differential graphical games for H-infinity control of linear heterogeneous multiagent systems2019Ingår i: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 29, nr 10, s. 2995-3013Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H-infinity output regulation problems. Our graphical game framework yields coupled Hamilton-Jacobi-Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor-critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall L2-gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.

    Ladda ner fulltext (pdf)
    fulltext
  • 27.
    Adlers, Mikael
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Topics in Sparse Least Squares Problems2000Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    This thesis addresses topics in sparse least squares computation. A stable method for solving the least squares problem, min ||Ax-b||2 is based on the QR factorization.Here we have addressed the difficulty for storing the orthogonal matrix Q. Using traditional methods, the number of nonzero elements in Q makes it in many cases not feasible to store. Using the multifrontal technique when computing the QR factorization,Q may be stored and used more efficiently. A new user friendly Matlab implementation is developed.

    When a row in A is dense the factor R from the QR factorization may be completely dense. Therefore problems with dense rows must be treated by special techniques. The usual way to handle dense rows is to partition the problem into one sparse and one dense subproblem. The drawback with this approach is that the sparse subproblem may be more ill-conditioned than the original problem or even not have a unique solution. Another method, useful for problems with few dense rows, is based on matrix stretching, where the dense rows are split into several less dense rows linked then together with new artificial variables. We give and analyze the conditioning of the matrix obtained by this method and show that no ill-conditioned subproblem arise.

    In many least squares problems upper and lower bounds on the variables have to be satisfied at the solution. This type of problem arises, for example, in reconstruction problems in geodesy and tomography. Here methods based on direct factorization methods for sparse matrix computation are explored. Two completely different approaches for solving the problem are discussed and compared, i.e. active set methods and primal-dual interior-point methods based on Mehrotra's predictor-corrector path following method. An active set block method suitable for sparse problems is developed and a convergence proof is presented. The choice of barrier parameter, multiple corrections and finite termination for the interior-point method are discussed. Numerical comparison is given of the active set method, the interior-point method, together with an trust region method based on the interior-reflective Newton implemented in the optimization toolbox for MATLAB. The numerical tests show that the block active set method is faster and gives better accuracy for both nondegenerate and degenerate problems.

  • 28.
    Adolfsson, Anna
    et al.
    Linköpings universitet, Institutionen för utbildningsvetenskap.
    Hesslid, Anna-Carin
    Linköpings universitet, Institutionen för utbildningsvetenskap.
    Lärarens matematikundervisning: elevens matematikutveckling? En studie om matematiksvårigheter.2002Självständigt arbete på grundnivå (yrkesexamen)Studentuppsats
    Abstract [sv]

    Examensarbetet ger en bild av både lärares och forskares syn på matematiksvårigheter samt deras uppfattning om orsakerna bakom problemen. Vi har undersökt vilka områden i matematiken som elever med matematiksvårigheter har mest problem med samt hur läraren förklarar och underlättar matematiken för dessa elever. Både forskningen och de lärare vi intervjuat är överens om att begreppet matematiksvårigheter är väldigt komplext. Orsakerna kan vara av medicinsk/neurologisk, psykologisk, sociologisk och didaktisk karaktär.

    I våra intervjuer framkommer att positionssystemet, bråk, procent, enheter, multiplikation och division är de områden som kan ställa till mest problem för elever med matematiksvårigheter. Dessa områden nämns även inom forskningen som möjliga problemområden. För att underlätta matematiken för elever med matematiksvårigheter anser forskarna att det är viktigt att undervisningen utgår från elevernas erfarenheter och förkunskaper. De påpekar också vikten av att undervisningen varieras och bör innefatta såväl laborativa som teoretiska arbetssätt där även diskussioner och gruppuppgifter ska förekomma. För att se på vilken nivå lärarna börjar förklara för elever med matematiksvårigheter gav vi dem tre uppgifter som de fick förklara. Svaren placerades in i fyra kategorier:

    1 Erfarenhet/vardag,

    2. Konkret material,

    3. Rita,

    4. Räkna.

    Resultatet visar att lärarna oftast börjar sin förklaring i kategori fyra. Många hamnar i kategori tre och väldigt få hamnar i kategori ett och två.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 29.
    Aerts, Sven
    et al.
    Fundamenten van de Exacte Wetenschappen, Vrije Universiteit Brussel, Brussel, Belgium.
    Kwiat, Paul
    Los Alamos National Laboratory, Los Alamos, New Mexico.
    Larsson, Jan-Åke
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Zukowski, Marek
    Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, Gdańsk, Poland .
    Two-photon Franson-type experiments and local realism1999Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 83, nr 15, s. 2872-2876Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a “Bell test of local realism.” However, it has been suggested that this is incorrect due to the 50% postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.

    Ladda ner fulltext (pdf)
    Two-photon Franson-type experiments and local realism
  • 30.
    Aghapournahr, M
    et al.
    Arak University.
    Melkersson, Leif
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Finiteness properties of minimax and coatomic local cohomology modules2010Ingår i: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 94, nr 6, s. 519-528Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R, and M an R-module. We prove that for a finite module M, if H-alpha(i)(M) is minimax for all i andgt;= r andgt;= 1, then H-alpha(i)(M) is artinian for i andgt;= r. A local-global principle for minimax local cohomology modules is shown. If H-alpha(i)(M) is coatomic for i andlt;= r (M finite) then H-alpha(i)(M) is finite for i andlt;= r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.

  • 31.
    Aghapournahr, Moharram
    et al.
    Arak University.
    Melkersson, Leif
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    A natural map in local cohomology2010Ingår i: ARKIV FOR MATEMATIK, ISSN 0004-2080, Vol. 48, nr 2, s. 243-251Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let R be a Noetherian ring, a an ideal of R, M an R-module and n a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map f: Ext(R)(n) (R/alpha, M) -andgt; Hom(R)(R/alpha, H-alpha(n) (M)), under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.

  • 32.
    Aghapournahr, Moharram
    et al.
    Arak Univ, Arak, Iran.
    Melkersson, Leif
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES2009Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 105, nr 2, s. 161-170Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R such that dim R/alpha = 1 and M a finite R-module. We will study cofiniteness and some other properties of the local cohomology modules H-alpha(i)(M). For an arbitrary ideal alpha and an R-module M (not necessarily finite), we will characterize alpha-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

  • 33.
    Agwa, Mohamed
    et al.
    Department of Mechanical Design and Production Engineering, Faculty of Engineering, Zagazig Egypt.
    Andersson, Lars-Erik
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Pinto da Costa, Ant´onio
    Departamento de Engenharia Civil, Instituto Superior T´ecnico and ICIST, Universidade T´ecnica de Lisboa, Avenida Rovisco Pais, 1049 􀀀 001 Lisboa, Portugal.
    Critical bounds for discrete frictional incremental problems, rateproblems and wedging problems2012Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Summary. Questions of existence and uniqueness for discrete frictional quasi-static incremental problems, rate problems and wedging problems are discussed. Various methods to compute critical bounds for the coefficient of friction which guarantee existence and uniqueness are described, as well as the sharpness of the bounds and their interdependence.

  • 34.
    Ahlinder, Jon
    et al.
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Nordgaard, Anders
    Swedish National Forensic Centre (NFC), Linköping, Sweden.
    Wiklund Lindström, Susanne
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Chemometrics comes to court: evidence evaluation of chem–bio threat agent attacks2015Ingår i: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 29, nr 5, s. 267-276Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Forensic statistics is a well-established scientific field whose purpose is to statistically analyze evidence in order to support legal decisions. It traditionally relies on methods that assume small numbers of independent variables and multiple samples. Unfortunately, such methods are less applicable when dealing with highly correlated multivariate data sets such as those generated by emerging high throughput analytical technologies. Chemometrics is a field that has a wealth of methods for the analysis of such complex data sets, so it would be desirable to combine the two fields in order to identify best practices for forensic statistics in the future. This paper provides a brief introduction to forensic statistics and describes how chemometrics could be integrated with its established methods to improve the evaluation of evidence in court.

    The paper describes how statistics and chemometrics can be integrated, by analyzing a previous know forensic data set composed of bacterial communities from fingerprints. The presented strategy can be applied in cases where chemical and biological threat agents have been illegally disposed.

  • 35.
    Ahlquist, Mari
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    On Knots and DNA2017Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Knot theory is the mathematical study of knots. In this thesis we study knots and one of its applications in DNA. Knot theory sits in the mathematical field of topology and naturally this is where the work begins. Topological concepts such as topological spaces, homeomorphisms, and homology are considered. Thereafter knot theory, and in particular, knot theoretical invariants are examined, aiming to provide insights into why it is difficult to answer the question "How can we tell knots appart?". In knot theory invariants such as the bracket polynomial, the Jones polynomial and tricolorability are considered as well as other helpful results like Seifert surfaces. Lastly knot theory is applied to DNA, where it will shed light on how certain enzymes interact with the genome.

    Ladda ner fulltext (pdf)
    fulltext
  • 36.
    Ahlqvist, Max
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanik och hållfasthetslära. Linköpings universitet, Tekniska fakulteten. Epiroc Rock Drills AB, Sweden.
    Weddfelt, Kenneth
    Epiroc Rock Drills AB, Sweden.
    Norman, Viktor
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Konstruktionsmaterial. Linköpings universitet, Tekniska fakulteten.
    Leidermark, Daniel
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanik och hållfasthetslära. Linköpings universitet, Tekniska fakulteten.
    Probabilistic evaluation of the Step-Stress fatigue testing method considering cumulative damage2023Ingår i: Probabilistic Engineering Mechanics, ISSN 0266-8920, E-ISSN 1878-4275, Vol. 74, artikel-id 103535Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general testing and analysis framework for the Step-Stress fatigue testing method is identified, utilizing interval-censored data and maximum likelihood estimation in an effort to improve estimation of fatigue strength distribution parameters has been performed. The Step-Stress methods limitations are characterized, using a simple material model that considers cumulative damage to evaluate load history effects. In this way, the performance including cumulative damage was evaluated and quantified using a probabilistic approach with Monte-Carlo simulations, benchmarked against the Staircase method throughout the work. It was found that the Step-Stress method, even when cumulative damage occurs to a wide extent, outperforms the Staircase method, especially for small sample sizes. Furthermore, positive results reaches further than the increase performance in estimating fatigue strength distribution parameters, where improvements in secondary information, i.e. S-N data gained from failure specimens, are shown to be distributed more closely to the fatigue life region of interest.

    Ladda ner fulltext (pdf)
    fulltext
  • 37.
    Ahmad, Garmyan
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten.
    Komvuxelever med upplevda matematiksvårigheter: en studie om deras lärandesituation på komvuxkurser i matematik2023Självständigt arbete på grundnivå (yrkesexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Syftet med detta arbete är att undersöka hur komvuxelever beskriver orsaker till sina upplevda matematiksvårigheter och hur de värderar sina lärares strategier för att hjälpa dem. Studien använde sig av semistrukturerade intervjuer för att undersöka matematiksvårigheter hos fem komvuxelever som har haft svårt med ämnet matematik under sin grundskole- eller gymnasietid. En gemensam nämnare visade sig vara att de under sin grundskoletid inte hade motivation för ämnet matematik och det ansåg de flesta av eleverna har haft en negativ inverkan på deras matematiklärande. Bristen på motivation ledde till att de missade väsentliga delar i den grundläggande matematiken trots att de fick hjälp och stöd av sina matematiklärare på grundskolan och gymnasiet. Samtliga elever berättade att deras otillräckliga grundkunskaper i matematik hade betydelse för deras svårigheter idag. Elevers brister från tidigare årskurser gör det svårt för eleverna att tillgodose sig utökade kunskaper. Alla ansåg också att det var svårt med matematikspråket. Med matematikspråk avsåg de begrepp, ord och symboler som har betydelse för att förstå matematik. Informanterna berättade att variation i undervisningen kunde ha påverkat deras motivation och inverkat positivt på deras intresse för matematik.Alla intervjuade elever sade sig idag ha varit missnöjda med den hjälp och det stöd de fick av sina Komvuxlärare, vilket betyder till att de nu hade mer svårigheter i matematik än tidigare.

    Ladda ner fulltext (pdf)
    fulltext
  • 38.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen.
    A note on the (n, p)-asymptotics of ATS for high dimensional multivariate data2010Rapport (Övrigt vetenskapligt)
  • 39.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A two-sample test statistic for high-dimensional multivariate data under non-normality2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Ahmad, Ohlson, and von Rosen (2011a) present asymptotic distribution of a one-sample test statistic under non-normality, when the data are high dimensional, i.e., when the dimension of the vector, p, may exceed the sample size, n. This paper extends the case to a two-sample statistic to test the difference of mean vectors of two independent multivariate distributions, again under high-dimensional set up. Using the asymptotic theory of U-statistics, and under mild assumptions on the traces of the unknown covariance matrices, the statistic is shown to follow an approximate normal distribution when n and p are large. However, no relationship between n and p is assumed. An extension to the paired case is given, which, being essentially a one-sample statistic, supplements the asymptotic results obtained in Ahmad, Ohlson, and von Rosen (2011a).

  • 40.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Robustness of a one-sample statistic for mean testing of high dimensional longitudinal data2010Rapport (Övrigt vetenskapligt)
  • 41.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.

  • 42.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
    Some Tests of Covariance Matrices for High Dimensional Multivariate Data2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

  • 43.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden; University of Munich, Germany.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Swedish University of Agriculture Science, Sweden.
    Tests for high-dimensional covariance matrices using the theory of U-statistics2015Ingår i: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, nr 13, s. 2619-2631Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p and#8811;n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

  • 44.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. Swedish University of Agriculture Science, Sweden.
    Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality2015Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, nr 7, s. 1387-1398Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp greater thangreater than n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.

  • 45.
    Ahmad, M. Rauf
    et al.
    Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A note on mean testing for high dimensional multivariate data under non-normality2013Ingår i: Statistica Neerlandica, ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, nr 1, s. 81-99Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.

    Ladda ner fulltext (pdf)
    fulltext
  • 46.
    Ahnell, Torbjörn
    Linköpings universitet, Institutionen för utbildningsvetenskap.
    Läromedelsanalys matematik A2006Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats
    Abstract [sv]

    Bakgrund: Rapporter från Skolverket, Nationellt Centrum för Matematikutbildning och Utbildnings-departementet visar att dagens matematikundervisning dominerande är traditionell, att eleverna har svårt för problemlösning och att eleverna i hög grad hänvisas till läromedlet. Studier visar också att inslag av undersökande pedagogik (problembaserat lärande, laborativ matematik) påverkar elevernas attityd och resultat positivt. Sedan lpf94 finns också krav i styrdokumenten som syftar till undersökande pedagogik. Mot bakgrund av detta formuleras den här studiens syfte så här:

    Syfte: Att se om inslagen av undersökande pedagogik i läromedlen för gymnasiets kurs Matematik A (eller motsvarande) har förändrat sig under perioden 1980-2006.

    Metod: ·Kvalitativ analys av stil och språkbruk.

    ·Andel uppgifter av undersökande karaktär

    ·Andel intresseväckande bilder som syftar till helhetssyn eller sammanhang.

    Resultat: Det syns tydligt ökade inslag av undersökande pedagogik sedan 80-talets läromedel Gamma Grön. Brytpunkten för denna utveckling var sannolikt början av 90-talet då gymnasiet reformerades. Sedan denna brytpunkt syns också en vidareutveckling, där nya läromedel som Den flygande matten väger in tungt.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 47.
    Aigner, Mats
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Tjatyrko, Vitalij
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda.
    THE ALGEBRA OF SEMIGROUPS OF SETS2015Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, nr 2, s. 161-170Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each n greater than 1 we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of R" without the Baire property.

  • 48.
    Aikawa, Hiroaki
    et al.
    Hokkaido Univ, Japan.
    Björn, Anders
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Björn, Jana
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Shanmugalingam, Nageswari
    Univ Cincinnati, OH 45221 USA.
    Dichotomy of global capacity density in metric measure spaces2018Ingår i: Advances in Calculus of Variations, ISSN 1864-8258, E-ISSN 1864-8266, Vol. 11, nr 4, s. 387-404Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The variational capacity cap(p) in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every E subset of R-n, infx is an element of R(n)cap(p)(E boolean AND B(x, r), B(x, 2r))/cap(p)(B(x, r), B(x, 2r)) is either zero or tends to 1 as r -amp;gt; infinity. We prove that this property still holds in unbounded complete geodesic metric spaces equipped with a doubling measure supporting a p-Poincare inequality, but that it can fail in nongeodesic metric spaces and also for the Sobolev capacity in R-n. It turns out that the shape of balls impacts the validity of the density dichotomy. Even in more general metric spaces, we construct families of sets, such as John domains, for which the density dichotomy holds. Our arguments include an exact formula for the variational capacity of superlevel sets for capacitary potentials and a quantitative approximation from inside of the variational capacity.

  • 49.
    Aitken, Colin
    et al.
    School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom.
    Nordgaard, Anders
    Swedish Police Authority, National Forensic Centre (NFC), Linköping, Sweden.
    Taroni, Franco
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    Biedermann, Alex
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    Commentary: Likelihood Ratio as Weight of Forensic Evidence: A Closer Look: A commentary on Likelihood Ratio as Weight of Forensic Evidence: A Closer Look by Lund, S. P., and Iyer, H. (2017). J. Res. Natl. Inst. Stand. Technol. 122:272018Ingår i: Frontiers in Genetics, E-ISSN 1664-8021, Vol. 9, artikel-id 224Artikel i tidskrift (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 50.
    Al Boraki, Nissren Mohammed
    et al.
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten.
    Jugo, Susana
    Linköpings universitet, Matematiska institutionen, Analys och didaktik. Linköpings universitet, Tekniska fakulteten.
    Ämnesintegrerade matematiklektioner för grundskolans högstadium: En designstudie om samverkan med lärare i teknik, träslöjd och hemkunskap2021Självständigt arbete på grundnivå (yrkesexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Detta arbete utgår från tanken att utveckla undervisningen genom att integrera matematik med  andra ämnen. Projektet har genomförts genom att designa och utvärdera lektioner tillsammans med slöjd- och teknik- och hemkunskapslärare. Studien har utförts i åk 7–9, på en skola i Västmanland och en skola i Östergötland.

    Arbete syftar till att eleverna på högstadiet ska kunna dra nytta av sina matematiska kunskaper i reella situationer. Lektionerna bidrar till att utveckla elevernas tänkande och förmåga att kunna lösa olika problem.

    Vi har observerat lektioner, som de deltagande lärarna har genomfört, och då noterat moment som kan användas för vårt projekt. Efter det har vi intervjuat dem och de har fått bedöma sina kunskaper i den pedagogiska modellen, samt vilka möjligheter de har att genomföra integrering med andra ämnen.

    Enkätundersökning som vi genomfört, har visat deltagarnas intresse och engagemang för denna metod samt att de har motivation, att fortsätta och vidareutveckla sin undervisning enligt denna modell.

    Ladda ner fulltext (pdf)
    fulltext
1234567 1 - 50 av 3571
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf