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  • 301.
    Herviou, Loic
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Bardarson, Jens H.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori. KTH Royal Inst Technol, Dept Phys, S-10691 Stockholm, Sweden..
    Regnault, Nicolas
    Univ Paris Diderot, Sorbonne Paris Cite, Sorbonne Univ, ENS,Univ PSL,CNRS,Lab Phys Ecole Normale Super, Paris, France..
    Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition2019Inngår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 99, nr 5, artikkel-id 052118Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular-value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.

  • 302.
    Hidalgo, Ruben A.
    et al.
    University of La Frontera, Chile.
    Jiménez, Leslie
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Quispe, Saul
    University of La Frontera, Chile.
    Reyes-Carocca, Sebastian
    University of La Frontera, Chile.
    Quasiplatonic curves with symmetry group Z(2)(2) x Z(m) are definable over Q2017Inngår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 49, nr 1, s. 165-183Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is well known that every closed Riemann surface S of genus g amp;gt;= 2, admitting a group G of conformal automorphisms so that S/G has triangular signature, can be defined over a finite extension of Q. It is interesting to know, in terms of the algebraic structure of G, if S can in fact be defined over Q. This is the situation if G is either abelian or isomorphic to A x Z(2), where A is an abelian group. On the other hand, as shown by Streit and Wolfart, if G congruent to Z(p) x Z(q), where p, q amp;gt; 3 are prime integers, then S is not necessarily definable over Q. In this paper, we observe that if G congruent to Z(2)(2) x Z(m) with m amp;gt;= 3, then S can be defined over Q. Moreover, we describe explicit models for S, the corresponding groups of automorphisms, and an isogenous decomposition of their Jacobian varieties as product of Jacobians of hyperelliptic Riemann surfaces.

  • 303.
    Hindlycke, Christoffer
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Irreducible representations of finite monoids2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 304.
    Hindlycke, Christoffer
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    The relative consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with the Zermelo-Fraenkel axioms: The constructible sets L2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 305. Hou, Kuen-Bang (Favonia)
    et al.
    Finster, Eric
    Licata, Daniel R.
    Lumsdaine, Peter LeFanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory2016Inngår i: LICS '16 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, New York, USA: Association for Computing Machinery (ACM), 2016, s. 565-574Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper continues investigations in “synthetic homotopy theory”: the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory.

    We present a mechanized proof of the Blakers-Massey connectivity theorem, a result relating the higher-dimensional homotopy groups of a pushout type (roughly, a space constructed by gluing two spaces along a shared subspace) to those of the components of the pushout. This theorem gives important information about the pushout type, and has a number of useful corollaries, including the Freudenthal suspension theorem, which has been studied in previous formalizations.

    The new proof is more elementary than existing ones in abstract homotopy-theoretic settings, and the mechanization is concise and high-level, thanks to novel combinations of ideas from homotopy theory and type theory.

  • 306.
    Husain, Aban Zehra
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Verma Modules, The Weyl Character Formula and Embedding Theorems2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 307.
    Husin, Axel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Gromov-Witten invariants for ℂPn2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 308.
    Höglund, Joel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Lie-algebror2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 309.
    Ibragimov, Nail
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Integration of dynamical systems admitting nonlinear superposition2016Inngår i: JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS, ISSN 2330-152X, Vol. 4, nr 2, s. 91-106Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    A method of integration of non-stationary dynamical systems admitting nonlinear superpositions is presented. The method does not require knowledge of symmetries of the differential equations under consideration. The integration procedure is based on classification of Vessiot-Guldberg-Lie algebras associated with nonlinear superpositions. It is shown that the systems associated with one-and two-dimensional Lie algebras can be integrated by quadrature upon introducing Lie's canonical variables. It is not necessary to know symmetries of a system in question in this approach. Two-dimensional non-stationary dynamical systems with three-dimensional Vessiot-Guldberg-Lie algebras are classified into thirteen standard forms. Ten of them are integrable by quadrature. The remaining three standard forms lead to the Riccati equations. Integration of perturbed dynamical systems possessing approximate nonlinear superposition is discussed.

  • 310.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, A. A.
    Ufa State Aviat Tech Univ, Rus.
    Three-dimensional dynamical systems admitting nonlinear superposition with three-dimensional Vessiot-Guldberg-Lie algebras2016Inngår i: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 52, s. 126-131Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The recent method of integration of non-stationary dynamical systems admitting nonlinear superpositions is applied to the three-dimensional dynamical systems associated with three-dimensional Vessiot-Guldberg-Lie algebras L-3. The investigation is based on Bianchi's classification of real three-dimensional Lie algebras and realizations of these algebras in the three-dimensional space. Enumeration of the Vessiot-Guldberg-Lie algebras L-3 allows to classify three-dimensional dynamical systems admitting nonlinear superpositions into thirty one standard types by introducing canonical variables. Twenty four of them are associated with solvable Vessiot-Guldberg-Lie algebras and can be reduced to systems of first-order linear equations. The remaining seven standard types are nonlinear. Integration of the latter types is an open problem. (C) 2015 Elsevier Ltd. All rights reserved.

  • 311.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, Aliya
    Ufimskij Gosudarstvennyj Aviacionnyj Tehniceskij Universitet, RUS.
    Three-dimensional dynamical systems with four-dimensional vessiot-guldberg-lie algebras2017Inngår i: The Journal of Applied Analysis and Computation, ISSN 2156-907X, E-ISSN 2158-5644, Vol. 7, nr 3, s. 872-883Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    - Dynamical systems attract much attention due to their wide applications. Many significant results have been obtained in this field from various points of view. The present paper is devoted to an algebraic method of integration of three-dimensional nonlinear time dependent dynamical systems admitting nonlinear superposition with four-dimensional Vessiot-Guldberg-Lie algebras L4. The invariance of the relation between a dynamical system admitting nonlinear superposition and its Vessiot-Guldberg-Lie algebra is the core of the integration method. It allows to simplify the dynamical systems in question by reducing them to standard forms. We reduce the three-dimensional dynamical systems with four-dimensional Vessiot-Guldberg-Lie algebras to 98 standard types and show that 86 of them are integrable by quadratures.

  • 312.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, Aliya. A.
    Ufa State Aviation Technical University, RUS.
    Classification and integration of four-dimensional dynamical systems admitting non-linear superposition2017Inngår i: International Journal of Non-Linear Mechanics, ISSN 0020-7462, Vol. 90, s. 50-71Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The method of integration of dynamical systems admitting non-linear superpositions is applied to four-dimensional non-linear dynamical systems. All four-dimensional dynamical systems admitting non-linear superpositions with four-dimensional Vessiot-Guldberg-Lie algebras are classified into 160 standard forms. The integration method is described and illustrated.

  • 313. Ishihara, Hajime
    et al.
    Palmgren, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Quotient topologies in constructive set theory and type theory2006Inngår i: Annals of Pure and Applied Logic, Vol. 141, s. 257-265Artikkel i tidsskrift (Fagfellevurdert)
  • 314.
    Iurato, Giuseppe
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    A possible p-adic Weber-Fechner law2018Inngår i: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 10, nr 4, s. 299-304Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    From a simple extension of a previous formal pattern of unconscious-conscious interconnection based on the representation of mental entities by m-adic numbers through hysteresis phenomenology, a pattern which has been then used to work out a possible psychoanalytic model of human consciousness, we now argue on related simple derivations of p-adic Weber-Fechner laws of psychophysics.

  • 315.
    Iurato, Giuseppe
    et al.
    University of Palermo, Italy.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Hysteresis model of unconscious-conscious interconnection: Exploring dynamics on m-adic trees2015Inngår i: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 7, nr 4, s. 312-321Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers.

  • 316.
    Izquierdo, Milagros
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Ying, Daniel
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    On the space of cyclic trigonal Riemann surfaces of genus 42007Inngår i: Groups St Andrews 2005 Volume 2 / [ed] C. M. Campbell, M. R. Quick, E. F. Robertson, G. C. Smith, Cambridge, UK: Cambridge University Press, 2007, 1, s. 504-516Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

        'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&M, USA).  Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

  • 317.
    Jahrl, Timmy
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ringar, Euklides och polynom: Från ring till polynom2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Heltalen och polynom tycks ha flera gemensamma egenskaper. En av heltalens egenskaper är aritmetikens fundamentalsats som säger att alla heltal kan skrivas som en produkt av primtal. Polynomen har en motsvarande egenskap, faktorsatsen, som innebär att varje polynom kan skrivas som en produkt av rotfaktorer. Denna och flera andra egenskaper som heltal och polynom har som motsvarar varandra beror inte på en slump utan på att de är besläktade. Egenskaper hos många välanvända mängder, de reella talen, de rationella talen samt heltalen kan beskrivas med gruppteori. Dessa egenskaper gäller endast över en binär operation men många intressanta och användbara egenskaper kräver två operationer. Inom denna uppsats undersöks den algebraiska strukturen ringar där många egenskaper som tas för givet beror på speciella egenskaper och därmed inte alltid finns närvarande. Efteråt studeras en speciell typ av ring kallad Euklidiska domän. Där många egenskaper som tillhör heltalen existerar i generaliserade former inom denna ring. Detta kapitel innehåller bevis som har generaliserats. Även polynomens struktur studeras och visar sig vara en Euklidisk domän. I studien används ett annat tillvägagångsätt än den traditionella där det bevisas genom idealer och PID. Uppsatsen avslutas med en kort studie av flervariabelpolynom där de egna bevisen finns varvid det ses att flervariabelpolynom med samma mängdvariabler är isomorfa.

  • 318.
    Jarl, Timmy
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On Completion of Modules and the Abelian Group Formed from Extension of Modules2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 319.
    Jasso, Gustavo
    et al.
    Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany.
    Külshammer, Julian
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Kvamme, Sondre ()
    Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France.
    Higher Nakayama algebras I: Construction2019Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 351, s. 1139-1200Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander–Reiten theory. More precisely, for each Nakayama algebra A and each positive integer d, we construct a finite dimensional algebra A(d) having a distinguished d-cluster-tilting A(d)-module whose endomorphism algebra is a higher dimensional analogue of the Auslander algebra of A. We also construct higher dimensional analogues of the mesh category of type ZΑ∞ and the tubes.

    Fulltekst tilgjengelig fra 2021-06-05 10:25
  • 320. Jiang, Zhi
    et al.
    Lahoz, Martí
    Tirabassi, Sofia
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the Iitaka Fibration of Varieties of MaximalAlbanese Dimension2012Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that the tetracanonical map of a variety X of maximal Albanese dimensioninduces the Iitaka fibration. Moreover, if X is of general type, then the tricanonical mapis birational.

  • 321.
    Jimenez, Leslie
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. University of Chile, Chile.
    On the group algebra decomposition of a Jacobian variety2016Inngår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 110, nr 1, s. 185-199Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a compact Riemann surface X with an action of a finite group G, the group algebra provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely build a decomposition of this kind. Our method allows us to study the geometry of the decomposition. For instance, we build several decompositions in order to determine which one has kernel of smallest order. We apply this method to families of trigonal curves up to genus 10.

  • 322.
    Johan, Johansson
    et al.
    Linköpings universitet, Institutionen för beteendevetenskap och lärande.
    Fredrik, Magnusson
    Linköpings universitet, Institutionen för beteendevetenskap och lärande.
    Olika aspekter av bråk: En litteraturstudie om elevers svårigheter och hur lärare kan underlätta elevers förståelse för bråk i årskurs 4-6.2017Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna litteraturstudie var att granska och analysera vad forskning visar beträffande elevers svårigheter för området bråk, samt hur lärare kan underlätta elevers förståelse för bråk i årskurs 4-6. I litteraturstudien har databassökningar gjorts via UniSearch, ERIC, MathEduc och Google Scholar. Även manuella sökningar har använts. Bråk tonas ned i dagens undervisning och resultat från TIMSS och PISA visar att bråk är ett, för elever såväl som lärare, problematiskt område i matematiken. Forskare framhåller bland annat elevers svårigheter för täljaren och nämnarens innebörd, samt jämförelse och beräkning av bråkuttryck. Vidare framhäver forskare att lärare med bland annat diskussioner i klassrummet, praktiskt material, samt en verklighetsanknuten och elevcentrerad bråkundervisning främjar elevers inlärning. Resultaten visar dock att forskare inte är eniga vad gäller de svårigheter elever har på området bråk.

  • 323.
    Johansson, Emelie
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Vad kom först – matrisen eller determinanten?: Om axiomatiseringen av den linjära algebran2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 324.
    Johansson, Jenny
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, geometri och logik.
    Asymptotiska egenskaper hos vissa kombinatoriska strukturer2011Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 325.
    Johansson, Lovisa
    et al.
    Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Skolnära forskning, Matematikdidaktik.
    Jonsson, Josefine
    Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Skolnära forskning, Matematikdidaktik.
    Structure sense: Ett matematikdidaktiskt begrepp som håller på att formas2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Structure sense är ett begrepp som nyligen har börjat användas inom matematikdidaktik föratt beskriva elevers förståelse för matematiska strukturer. Syftet med det härexamensarbetet är att utforska begreppet structure sense genom att jämföra olikadefinitioner av begreppet. Vidare är syftet också att jämföra structure sense med tre andraliknande begrepp: symbol sense, personal structure och awareness of mathematical pattern and structure. Litteraturstudien bygger på 13 vetenskapliga publikationer som samlades in ochanalyserades. Samtliga publikationer är skrivna av internationella forskare. I resultatetpresenteras och jämförs structure sense utifrån fyra olika definitioner. De olikadefinitionerna av begreppet är riktade mot olika nivåer av matematik men gemensamt förbeskrivningarna är att structure sense uppfattas som en eller flera förmågor som innefattarett mångfacetterat sätt att uppfatta matematisk struktur.

  • 326.
    Johansson, Mikael
    Friedrich-Schiller-Univesität, JGermany.
    Computation of Poincare-Betti series for monomial rings2005Inngår i: Rendiconti dell'Istituto di Matematica dell'Università di Trieste, ISSN 0049-4704, E-ISSN 2464-8728, Vol. 37, nr 1-2, s. 85-94Artikkel i tidsskrift (Fagfellevurdert)
  • 327.
    Jonasson, Henrik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Uncountable categoricity2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 328.
    Jonsson, Helena
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Bimodules over dual numbers2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 329.
    Jonsson, Helena
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Ordnade kroppar och Artin-Schreiers teorem2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 330.
    Ju, Fengkui
    et al.
    School of Philosophy, Beijing Normal University.
    Grilletti, Gianluca
    Institute for Logic, Language and Computation, University of Amsterdam.
    A logic for temporal conditionals and a solution to the Sea Battle Puzzle2018Inngår i: Proceedings of the 12th International Conference on Advances in Modal Logic (AiML'2018), London, 2018, s. 379---398Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle’s famous “Sea Battle Tomorrow” puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL∗ , with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the ‘Sea Battle’ argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

  • 331. Ju, Fengkui
    et al.
    Grilletti, Gianluca
    Goranko, Valentin
    Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.
    A logic for temporal conditionals and a solution to the Sea Battle Puzzle2018Inngår i: Advances in Modal Logic / [ed] Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer, London: College Publications, 2018, s. 379-398Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle’s famous “Sea Battle Tomorrow” puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL∗ , with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the ‘Sea Battle’ argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

  • 332.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Climer, Sharlee
    Zhang, Weixiong
    The complete parsimony haplotype inference problem and algorithms based on integer programming, branch-and-bound and Boolean satisfiability2016Inngår i: Journal of Discrete Algorithms, ISSN 1570-8667, E-ISSN 1570-8675, Vol. 37, s. 68-83Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Haplotype inference by pure parsimony (HIPP) is a well-known paradigm for haplotype inference. In order to assess the biological significance of this paradigm, we generalize the problem of HIPP to the problem of finding all optimal solutions, which we call CHIPP. We study intrinsic haplotype features, such as backbone haplotypes and fat genotypesas well as equal columns and decomposability. We explicitly exploit these features in three computational approaches that are based on integer linear programming, depth-first branch-and-bound, and Boolean satisfiability. Further we introduce two hybrid algorithms that draw upon the diverse strengths of the approaches. Our experimental analysis shows that our optimized algorithms are significantly superior to the baseline algorithms, often with orders of magnitude faster running time. Finally, our experiments provide some useful insights into the intrinsic features of this important problem.

  • 333.
    Kapulkin, Chris
    et al.
    University of Western Ontario.
    Lumsdaine, Peter LeFanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The homotopy theory of type theoriesManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We construct a left semi-model structure on the category of intensional type theories (precisely, on CxlCat_{Id,1,Σ(,Πext)}). This presents an infinity-category of such type theories; we show moreover that there is an infinity-functor Cl_∞ from there to the infinity-category of suitably structured quasi-categories. This allows a precise formulation of the conjectures that intensional type theory gives internal languages for higher categories, and provides a framework and toolbox for further progress on these conjectures.

  • 334. Katzman, Mordechai
    et al.
    Ma, Linquan
    Smirnov, Ilya
    University of Michigan, USA.
    Zhang, Wenliang
    D-module and F-module length of local cohomology modules2018Inngår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, nr 12, s. 8551-8580Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let R be a polynomial or power series ring over a field k. We study the length of local cohomology modules H-I(j) (R) in the category of D-modules and F-modules. We show that the D-module length of H-I(j) (R) is bounded by a polynomial in the degree of the generators of I. In characteristic p > 0 we obtain upper and lower bounds on the F-module length in terms of the dimensions of Frobenius stable parts and the number of special primes of local cohomology modules of R/I. The obtained upper bound is sharp if R/I is an isolated singularity, and the lower bound is sharp when R/I is Gorenstein and F-pure. We also give an example of a local cohomology module that has different D-module and F-module lengths.

  • 335.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Cognitive processes of the brain: An ultrametric model of information dynamics in unconsciousness2014Inngår i: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 6, nr 4, s. 293-302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We discuss differences in mathematical representations of the physical and mentalworlds. Following Aristotle, we present the mental space as discrete, hierarchic, and totally disconnectedtopological space. One of the basic models of such spaces is given by ultrametricspaces and more specially by m-adic trees. We use dynamical systems in such spaces to modelflows of unconscious information at different level of mental representation hierarchy, for “mentalpoints”, categories, and ideas. Our model can be interpreted as an unconventional computationalmodel: non-algorithmic hierarchic “computations” (identified with the process of thinking at theunconscious level).

  • 336.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Foundations of analysis on superspace — 1: Differential calculus2015Inngår i: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 7, nr 2, s. 96-110Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The recent experimental confirmation of the existence of Higgs boson stimulates theoretical research on supersymmetric models; in particular, mathematics of such modeling. Therefore we plan to present essentials of one special approach to “super-mathematics”, so called functional superanalysis (in the spirit of De Witt, Rogers, Vladimirov and Volovich, and the author of this review) in compact and clear form in series of review-type papers. This first paper is a review on super-differential calculus for the concrete model of the superspace (invented by Vladimirov and Volovich). In the next review we plan to present the integral supercalculus. The main distinguishing feature of functional superanalysis is that this is a real super-extension of analysis of Newton and Leibniz, opposite to algebraic models of Martin and Berezin. Here functions of commuting and anticommuting variables are no simply algebraic elements belonging to Grassmann algebras, but point-wise maps, from superspace into superspace. Finally, we remark that the first non-Archimedean physical model was based on invention by Vladimirov and Volovich of superspaces based on supercommutative Banach superalgebras over non-Archimedean (in particular, p-adic) fields. This model plays the basic role in theory of p-adic superstrings.

  • 337.
    Khrennikov, Andrei
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen. Matematik.
    Logical approach to p-adic probabilities2006Inngår i: Bulletin of the Section of Logic, ISSN 0138-0680, Vol. 35/1, s. 49-57Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study coupling between logic an p-adic probability

  • 338.
    Khrennikov, Andrei
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Kotovich, Nikolay
    Institute of System Analysis of Russian Academy of Science, Russia.
    Towards ultrametric modeling of unconscious creativity2015Inngår i: International Journal of Cognitive Informatics and Natural Intelligence, ISSN 1557-3958, E-ISSN 1557-3966, Vol. 8, nr 4, s. 98-109Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Information processed by complex cognitive systems is characterized by the presence of various closely connected hierarchic structures. The most natural geometry for the representation of such structures is geometry of trees and the corresponding topology is the ultrametric topology of on these trees. And the p-adic trees provide the simplest model for representation of mental hierarchies. Moreover, p-adic trees can be endowed with the natural arithmetic reminding the usual arithmetic of real numbers. Therefore it is natural to start from the p-adic models of brain's functioning. In this note the authors apply this model to demonstrate the ability of the “p-adic brain” to process adequately the objects of the physical Euclidean space in the p-adic tree representation. This study also leads to p-adic modeling of brain's creativity and its ability to create abstract images. The authors' model is about unconscious processing of information by the brain. Therefore the authors can say about elements of coming theory of unconscious creativity.

  • 339.
    Khrennikov, Andrei
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Oleshko, Klaudia
    Univ. Nacional Autónoma de Mexico (UNAM), Mexico.
    de Jesús Correa López, Maria
    Caracterizac Yacimientos Act Prod Maloob Zaap, Mexico.
    Application of p-Adic Wavelets to Model Reaction–Diffusion Dynamics in Random Porous Media2016Inngår i: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, nr 4, s. 809-822Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Fourier and more generally wavelet analysis over the fields of p-adic numbers are widely used in physics, biology and cognitive science, and recently in geophysics. In this note we present a model of the reaction–diffusion dynamics in random porous media, e.g., flow of fluid (oil, water or emulsion) in a a complex network of pores with known topology. Anomalous diffusion in the model is represented by the system of two equations of reaction–diffusion type, for the part of fluid not bound to solid’s interface (e.g., free oil) and for the part bound to solid’s interface (e.g., solids–bound oil). Our model is based on the p-adic (treelike) representation of pore-networks. We present the system of two p-adic reaction–diffusion equations describing propagation of fluid in networks of pores in random media and find its stationary solutions by using theory of p-adic wavelets. The use of p-adic wavelets (generalizing classical wavelet theory) gives a possibility to find the stationary solution in the analytic form which is typically impossible for anomalous diffusion in the standard representation based on the real numbers.

  • 340.
    Kildetoft, Tobias
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Decomposition of Tensor Products Involving a Steinberg Module2017Inngår i: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, nr 4, s. 951-975Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group G and when restricted to either a Frobenius kernel G (r) or a finite Chevalley group . In all three cases, we give formulas reducing this to standard character data for G. Along the way, we use a bilinear form on the characters of finite dimensional G-modules to give formulas for the dimension of homomorphism spaces between certain G-modules when restricted to either G (r) or . Further, this form allows us to give a new proof of the reciprocity between tilting modules and simple modules for G which has slightly weaker assumptions than earlier such proofs. Finally, we prove that in a suitable formulation, this reciprocity is equivalent to Donkin's tilting conjecture.

  • 341.
    Kildetoft, Tobias
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Mackaay, Marco
    Inst Super Tecn, Dept Matemat, Ctr Math Anal Geometry & Dynam Syst, P-1049001 Lisbon, Portugal.;Univ Algarve, FCT, Dept Matemat, Campus Gambelas, P-8005139 Faro, Portugal..
    Mazorchuk, Volodymyr
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Zimmermann, Jakob
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Simple transitive 2-representations of small quotients of Soergel bimodules2019Inngår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 371, nr 8, s. 5551-5590Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In all finite Coxeter types but I2(12), I2(18) and I2(30), we classify simple transitive 2-representations for the quotient of the 2-category of Soergel bimodules over the coinvariant algebra which is associated to the two-sided cell that is the closest one to the two-sided cell  containing the identity element. It turns out that, in most of the cases, simple transitive 2-representations are exhausted by cell 2-representations. However, in Coxeter types I2(2k), where k ≥ 3, there exist simple transitive 2-representations which are not equivalent to cell 2-representations.

  • 342.
    Kildetoft, Tobias
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Mazorchuk, Volodymyr
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Special Modules Over Positively Based Algebras2016Inngår i: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 21, s. 1171-1192Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the Kazhdan-Lusztig basis, this agrees with Lusztig's notion of a special module introduced in [Lu2].

  • 343.
    Kitouni, Abdenour
    et al.
    Univ Haute Alsace, France.
    Makhlouf, Abdenacer
    Univ Haute Alsace, France.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras2016Inngår i: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 23, nr 1, s. 75-95Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to study the relationships between an n-Hom-Lie algebra and its induced (n + 1)-Hom-Lie algebra. We provide an overview of the theory and explore structure properties such as ideals, centers, derived series, solvability, nilpotency, central extensions, and the cohomology.

  • 344.
    Koenig, Steffen
    et al.
    Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
    Külshammer, Julian
    Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
    Ovsienko, Sergiy
    Mechanics and Mathematics Faculty, Kiev National University, 01033 Kiev, Ukraine.
    Quasi-hereditary algebras, exact Borel subalgebras, A∞-categories and boxes2014Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 262, s. 546-592Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category O. An analogue of the PBW theorem will be shown to hold for quasi-hereditary algebras: Up to Morita equivalence each such algebra has an exact Borel subalgebra. The category F(\Delta) of modules with standard (Verma, Weyl, …) filtration, which is exact, but rarely abelian, will be shown to be equivalent to the category of representations of a directed box. This box is constructed as a quotient of a dg algebra associated with the A-infinity-structure on Ext(\Delta,\Delta). Its underlying algebra is an exact Borel subalgebra.

  • 345.
    Koerfer, Filip
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classification of Root Systems2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 346.
    Kolyada, Viktor
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.
    My First Meetings with Konstantin Oskolkov2013Inngår i: Recent Advances in Harmonic Analysis and Applications: In honor of Konstantin Oskolkov / [ed] Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, Brett D. Wick, Springer, 2013, 1, Vol. 25, s. 27-29Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This note tells about our first meetings with Konstatin Oskolkov. We discuss also optimal estimates of the rate of convergence of Fourier series obtained by Oskolkov in 1975.

  • 347.
    Konstantopoulos, Takis
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity2013Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 439, nr 9, s. 2651-2658Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity not involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity.

  • 348.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    A limit law of almost l-partite graphs2013Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 78, nr 3, s. 911-936Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For integers l >= 1, d >= 0 we study (undirected) graphs with vertices 1,..., n such that the vertices can be partitioned into l parts such that every vertex has at most d neighbours in its own part. The set of all such graphs is denoted P-n (l, d). We prove a labelled first-order limitlaw, i.e., for every first-order sentence phi, the proportion of graphs in P-n (l, d) that satisfy phi converges as n -> infinity. By combining this result with a result of Hundack, Promel and Steger [12] we also prove that if 1 <= s(1) <=...<= s(1) are integers, then Forb(A(I),s(1),...,s(l)) has alabelled first-order limit law, where Forb (A(I),s(1),...,s(l)) denotes the set of all graphs with vertices 1,..., n, for some n, in which there is no subgraph isomorphic to the complete (l + 1)-partite graph with parts of sizes 1, S-1,..., S-l. In the course of doing this we also prove that there exists a first-order formula depending only on l and d, such that the proportion of g e P (I, d) with the following property approaches 1 as n ->infinity: there is a unique partition of {1,..., n} into l parts such that every vertex has at most d neighbours in its own part, and this partition, viewed as an equivalence relation, is defined by xi.

  • 349.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Binary primitive homogeneous simple structures2017Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 82, nr 1, s. 183-207Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Suppose that M is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of M is 1 and hence 1-based. It follows that M is a random structure. The conclusion that M is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of omega-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

  • 350.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Binary simple homogeneous structures2018Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 169, nr 12, s. 1335-1368Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe all binary simple homogeneous structures M in terms of ∅-definable equivalence relations on M, which “coordinatize” M and control dividing, and extension properties that respect these equivalence relations.

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