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  • 151.
    Dieterich, Ernst
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Lindberg, Lars
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Dissident maps on the seven-dimensional Euclidean space2003Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 97, s. 251-276Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Our article contributes to the classification of dissident maps on R7, which in turn contributes to the classification of 8-dimensional real division algebras. We study two large classes of dissident maps on R7. The first class is formed by all composed dissident maps, obtained from a vector product on R7 by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures of those 8-dimensional real quadratic division algebras which arise from a 4-dimensional real quadratic division algebra by doubling. For each of these two classes we exhibit a complete (but redundant) classification, given by a 49-parameter family of composed dissident maps and a 9-parameter family of doubled dissident maps respectively. The intersection of these two classes forms one isoclass of dissident maps only, namely the isoclass consisting of all vector products on R7.

  • 152.
    Dieterich, Ernst
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Wiedemann, Alfred
    The Auslander-Reiten quiver of a simple curve singularity1986Inngår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 294, nr 2, s. 455-475Artikkel i tidsskrift (Fagfellevurdert)
  • 153.
    Dieterich, Ernst
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Öhman, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    On the classification of four-dimensional quadratic division algebras over square-ordered fields2002Inngår i: Journal of the London Mathematical Society, Vol. 65, s. 285-302Artikkel i tidsskrift (Fagfellevurdert)
  • 154.
    Djordjevic, Marko
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Finite satisfiability and N-0-categorical structures with trivial dependence2006Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 71, nr 3, s. 810-830Artikkel i tidsskrift (Fagfellevurdert)
  • 155.
    Djordjevic, Marko
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Finite variable logic, stability and finite models2001Inngår i: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 66, nr 2, s. 837-858Artikkel i tidsskrift (Fagfellevurdert)
  • 156.
    Djordjevic, Marko
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    The finite submodel property and ω-categorical expansions of pregeometries2006Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 139, nr 1-3, s. 201-229Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove, by a probabilistic argument, that a class of ω-categorical structures, on which algebraic closure defines a pregeometry, has the finite submodel property. This class includes any expansion of a pure set or of a vector space, projective space or affine space over a finite field such that the new relations are sufficiently independent of each other and over the original structure. In particular, the random graph belongs to this class, since it is a sufficiently independent expansion of an infinite set, with no structure. The class also contains structures for which the pregeometry given by algebraic closure is non-trivial.

  • 157.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Structure preserving stratification of skew-symmetric matrix polynomials2017Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 532, s. 266-286Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study how elementary divisors and minimal indices of a skew-symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coefficients. We investigate these changes qualitatively by constructing the stratifications (closure hierarchy graphs) of orbits and bundles for skew-symmetric linearizations. We also derive the necessary and sufficient conditions for the existence of a skew-symmetric matrix polynomial with prescribed degree, elementary divisors, and minimal indices.

  • 158.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Dopico, Froilán
    Universidad Carlos III de Madrid.
    Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade2018Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 536, s. 1-18Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m×m complex skew-symmetric matrix polynomials of odd grade d and rank at most 2r. In particular, this result includes the case of skew-symmetric matrix pencils (d=1).

  • 159.
    Dubsky, Brendan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Koszulity of some path categories2017Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, nr 9, s. 4084-4092Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.

  • 160.
    Ekdahl, Anna-Lena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Elevers skilda sätt att erfara talmönster - en studie av elever i årskurs 3 och 42012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Matematiken handlar i mångt och mycket om att lösa problem och se mönster. Talmönster är en viktig del inom algebran och aritmetiken och är det fenomen som jag i denna studie vill undersöka elevers uppfattningar av. Syftet med föreliggande kvalitativa studie är att skapa kunskap om elevers skilda sätt att erfara talmönster, såväl talföljder som visuella talmönster. Därutöver syftar studien till att identifiera kritiska aspekter utifrån de skilda sätt som talmönstren erfars av eleverna.

    Nio elever i årskurs 3 och 4 har intervjuats utifrån ett antal talmönster. Fenomenografin och variationsteorin utgör studiens teoretiska utgångspunkter och har använts för att analysera materialet. I analysen har förutom likheter och skillnader mellan sätten att erfara, innehållet i elevutsagorna analyserats utifrån erfarandets referentiella och strukturella aspekt.

    Resultatet av den fenomenografiska analysen har utmynnat i följande sex beskrivningskategorier:

    Jämn förflyttning, Konstant eller icke-konstant skillnad, Kombination av delar, Relation mellan vissa delar, Olika del- och helhetsstrukturer och Utöver angiven helhet. I analysen har de aspekter som eleverna fokuserat på varit vägledande för att skilja kategorierna åt och identifiera sex kritiska aspekter. En av dessa kritiska aspekter handlar om att urskilja att förhållandet mellan delarna i mönstret kan se olika ut. En annan kritisk aspekt är fråga om att kunna urskilja delarnas inbördes relation, relationernas förhållande till helheten och den icke angivna helheten. En tredje innebär att delarna behöver urskiljas samtidigt som helheten. Inte nödvändigtvis samtliga delar, men tillräckligt många för att se en regelbundenhet.

    Studiens resultat har gett didaktiska implikationer om vad eleverna i en undervisningssituation behöver ges möjlighet att urskilja för att utveckla ett mer innehållsrikt och differentierat sätt att erfara talmönster.

    Resultatet diskuteras utifrån tidigare internationella undersökningar. Det förs även en diskussion om vad studiens resultat kan tillföra och de didaktiska implikationer resultatet ger.

  • 161.
    Ekholm, Tomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Kovarik, Hynek
    Laptev, Ari
    Hardy inequalities for p-Laplacians with Robin boundary conditions2015Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 128, s. 365-379Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals ((p-1)/p)(p) whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.

  • 162.
    Ekström, Fredrik
    et al.
    Lund University.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras2014Inngår i: Springer Proceedings in Mathematics and Statistics, Springer, 2014, Vol. 85, s. 37-59Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider a family of associative algebras, defined as the quotient of a free algebra with the ideal generated by a set of multi-parameter deformed commutation relations between four generators consisting of five quantum plane relations between pairs of generators and one sub-quadratic relation inter-linking all four generators. For generic parameter vectors, the center and the commutants of the two of the generators are described and conditions on the parameters for these commutants to be itself commutative or non-commutative are obtained.

  • 163.
    Elchinger, O.
    et al.
    Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, Mulhouse, France.
    Lundengård, Karl
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Makhlouf, A.
    Laboratoire de Mathématiques Informatique et Applications, Université de Haute Alsace, Mulhouse, France.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras2016Inngår i: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 28, nr 4, s. 657-673Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.

  • 164.
    Eliasson, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Ultrapowers as sheaves on a category of ultrafilters2001Licentiatavhandling, monografi (Annet vitenskapelig)
  • 165.
    Eliasson, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Ultrapowers as sheaves on a category of ultrafilters2004Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 43, nr 7, s. 825-843Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the paper we investigate the topos of sheaves on a category of ultrafilters. The category is described with the help of the Rudin-Keisler ordering of ultrafilters. It is shown that the topos is Boolean and two-valued and that the axiom of choice does not hold in it. We prove that the internal logic in the topos does not coincide with that in any of the ultrapowers. We also show that internal set theory, an axiomatic nonstandard set theory, can be modeled in the topos.

  • 166.
    Eliasson, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Ultrasheaves2003Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis treats ultrasheaves, sheaves on the category of ultrafilters.

    In the classical theory of ultrapowers, you start with an ultrafilter and, given a structure, you construct the ultrapower of the structure over the ultrafilter. The fundamental result is Los's theorem for ultrapowers giving the connection between what formulas are satisfied in the ultrapower and in the original structure. In this thesis we instead start with the category of ultrafilters (denoted U). On this category U we build the topos of sheaves on U (the ultrasheaves), which we think of as generalized ultrapowers.

    The theorem for ultrapowers corresponding to Los's theorem is Moerdijk's theorem, first proved by Moerdijk for the topos Sh(F) of sheaves on filters. In the thesis we prove that Los's theorem follows from Moerdijk's theorem. We also investigate the exact relation between the topos of ultrasheaves and Moerdijk's topos Sh(F) and prove that Sh(U) is the double negation subtopos of Sh(F).

    The connection between ultrapowers and ultrasheaves is investigated in detail. We also prove some model theoretic results for ultrasheaves, for instance we prove that they are saturated models. The Rudin-Keisler ordering is a tool used in set theory to study ultrafilters. It has a strong relationship to the category U. Blass has given a model theoretic characterization of this ordering and in the thesis we give a new proof of his result.

    One common use of ultrapowers is to give non-standard models. In the thesis we prove that you can model internal set theory (IST) in the ultrasheaves. IST, introduced by Nelson, is a non-standard set theory, an axiomatic approach to non-standard mathematics.

  • 167.
    Emmenegger, Jacopo
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A category-theoretic version of the identity type weak factorization systemManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Gambino and Garner proved that the syntactic category of a dependent type theory with identity types can be endowed with a weak factorization system structure, called identity type weak factorization system. In this paper we consider an enrichment of Joyal's notion of tribe which allow us to prove a purely category-theoretic version of the identity type weak factorization system, thus generalizing Gambino and Garner's result. We investigate then how it relates with other well-known weak factorization systems, namely those arising from Quillen model structures on the category of topological spaces and on the category of small groupoids.

  • 168.
    Emmenegger, Jacopo
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the local cartesian closure of exact completionsManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    A characterisation of cartesian closure of exact completions as a property of the projective objects was given by Carboni and Rosolini. We show that the argument used to prove that characterisation is equivalent to the projectives being closed under binary products (equivalently, being internally projective). The property in question is the existence of weak simple products (a slight strengthening of weak exponentials) and the argument used relies on two claims: that weak simple products endow the internal logic with universal quantification, and that an exponential is the quotient of a weak exponential. We show that either these claims hold if and only if the projectives are internally projectives, which entails that Carboni and Rosolini's characterisation only applies to ex/lex completions. We then argue that this limitation depends on the universal property of weak simple products, and derive from this observation an alternative notion, which we call generalised weak simple product. We conclude by showing that existence of generalised weak simple products in the subcategory of projectives is equivalent to the cartesian closure of the exact category, thus obtaining a complete characterisation of (local) cartesian closure for exact completions of categories with weak finite limits.

  • 169.
    Emmenegger, Jacopo
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Palmgren, Erik
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Exact completion and constructive theories of setsManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    In the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Loef type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e. objects satisfying the axiom of choice). Because of these intended applications, we deal with categories that lack equalisers and just have weak ones, but whose objects can be regarded as collections of global elements. In this context, we study the internal logic of the categories involved, and employ this analysis to give a sufficient condition for the local cartesian closure of an exact completion. Finally, we apply this result to show when an exact completion produces a model of CETCS.

  • 170.
    Epstein, Melker
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Powers and Products of Monomial Ideals2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 171.
    Eriksson, Anders
    Stockholms universitet.
    Differential operators on some classes of rings2000Doktoravhandling, med artikler (Annet vitenskapelig)
  • 172.
    Ernst, Thomas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    On several q-special matrices, including the q-Bernoulli and q-Euler matrices2018Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 542, s. 422-440Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the spirit of our earlier articles [12,14,11], and our work [13], we define two dual q-Bernoulli polynomials, with corresponding vector and matrix forms. Following Aceto Trigiante [1], the q-L matrix, the indefinite q-integral of the q-Pascal matrix is the link between the q-Cauchy and the q-Bernoulli matrix. The q-analogue of the Bernoulli complementary argument theorem can be expressed in matrix form through the diagonal An matrix. For the q-Euler polynomials corresponding results are obtained. The umbral calculus for generating functions of q-Appell polynomials is shown to be equivalent to a transform method, which maps polynomials to matrices, a true q-analogue of Arponen [6]. This is manifested by the Vein [21] matrix, which occurs as the transform of the q-difference operator. The Aceto Trigiante shifted q-Bernoulli matrix has a simple connection to the q-Bernoulli Arponen matrix through the q-Pascal matrix. We reintroduce certain q-Stirling numbers is an element of 7L(q) from [12], which will be needed for the polynomial matrix definitions.

  • 173.
    Ernst, Thomas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    On the q-Lie group of q-Appell polynomial matrices and related factorizations2018Inngår i: Special Matrices, ISSN 2300-7451, Vol. 6, nr 1, s. 93-109Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the spirit of our earlier paper [10] and Zhang andWang [16], we introduce the matrix of multiplicative q-Appell polynomials of order M is an element of Z. This is the representation of the respective q-Appell polynomials in ke-ke basis. Based on the fact that the q-Appell polynomials form a commutative ring [11], we prove that this set constitutes a q-Lie group with two dual q-multiplications in the sense of [9]. A comparison with earlier results on q-Pascal matrices gives factorizations according to [7], which are specialized to q-Bernoulli and q-Euler polynomials. We also show that the corresponding q-Bernoulli and q-Euler matrices form q-Lie subgroups. In the limit q -> 1 we obtain corresponding formulas for Appell polynomial matrices. We conclude by presenting the commutative ring of generalized q-Pascal functional matrices, which operates on all functions f is an element of C-q(infinity).

  • 174.
    Eshagh, Mehdi
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Samhällsplanering och miljö, Geoinformatik och Geodesi.
    Generalized Least Squares Adjustment of Gauss-Helmert Model2005Konferansepaper (Fagfellevurdert)
  • 175.
    Espíndola, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A short proof of Glivenko theorems for intermediate predicate logics2013Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 52, nr 7-8, s. 823-826Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each one of them provides a strictly weaker intermediate logic, and neither of them is derivable from the other. We show that over every intermediate logic there exists a maximal intermediate logic for which Glivenko’s theorem holds. We deduce as well a characterization of DNS, as the weakest (with respect to derivability) scheme that added to REM derives classical logic.

  • 176.
    Espíndola, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Achieving completeness: from constructive set theory to large cardinals2016Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems.

    The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

  • 177.
    Espíndola, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Semantic Completeness of First-Order Theories in Constructive Reverse Mathematics2016Inngår i: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 57, nr 2, s. 281-286Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce a general notion of semantic structure for first-order theories, covering a variety of constructions such as Tarski and Kripke semantics, and prove that, over Zermelo–Fraenkel set theory (ZF), the completeness of such semantics is equivalent to the Boolean prime ideal theorem (BPI). Using a result of McCarty (2008), we conclude that the completeness of Kripke semantics is equivalent, over intuitionistic Zermelo–Fraenkel set theory (IZF), to the Law of Excluded Middle plus BPI. Along the way, we also prove the equivalence, over ZF, between BPI and the completeness theorem for Kripke semantics for both first-order and propositional theories.

  • 178.
    Everitt, Tom
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Lattimore, Tor
    Hutter, Marcus
    Free Lunch for Optimisation under the Universal Distribution2014Inngår i: 2014 IEEE Congress on Evolutionary Computation (CEC), New York: IEEE Computer Society, 2014, s. 167-174Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We argue against the uniform assumption and suggest a universal prior exists for which there is a free lunch, but where no particular class of functions is favoured over another. We also prove upper and lower boundson the size of the free lunch.

  • 179.
    Ezquiaga, J. M.
    et al.
    nstituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid.
    García-Bellido, J.
    nstituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid.
    Zumalacárregui, Miguel
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Towards the most general scalar-tensor theories of gravity: A unified approach in the language of differential forms2016Inngår i: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 94, nr 2, artikkel-id 024005Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under local Lorentz transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as an arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second-order equations, which can be associated with Horndeski's theory. In this process, we identify a new second-order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second-order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step, we focus on theories with second-order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories.

  • 180.
    Farzaneh, Neda
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Matrisexponentialfunktionen2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 181.
    Fastlund, Niklas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    The subgraph containment problem in random graphs2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 182.
    Fiallo Kaminski, Ricardo
    Linköpings universitet, Institutionen för samhälls- och välfärdsstudier. Linköpings universitet, Institutionen för samhälls- och välfärdsstudier.
    Egendom och Stöld: Den juridiska hegemonins svårigheter med teknikens nya matematik2009Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Genom att analysera domstolsmaterialet från rättegången mot fildelningssiten The Pirat Bay, i relation till en idéhistorisk diskussion om äganderätt, har uppsatsen funnit att den liberala tanketraditionen och dess juridiska institutioner står inför en betydelseglidning vad gället begreppsparet ”Egendom” och ”Stöld”. Det har visat sig att Lockes naturtillstånd, varseblivningen av ”det oändliga” på jorden, har skiftat plats; från ”naturen” ut till ”cyberspace”, vilket har resulterat i att fildelningstekniken skapat en ny matematik som omöjliggör tidigare egendomsdefinition.

  • 183.
    Fjelstad, Jens
    et al.
    Department of Physics, Nanjing University, 22 Hankou Road, Nanjing, 210093, China.
    Fuchs, Jürgen
    Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för fysik och elektroteknik.
    Stigner, Carl
    Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för fysik och elektroteknik.
    RCFT with defects: Factorization and fundamental world sheets2012Inngår i: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 863, s. 213-259Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is known that for any full rational conformal field theory, the correlation functions that are obtained bythe TFT construction satisfy all locality, modular invariance and factorization conditions, and that there isa small set of fundamental correlators to which all others are related via factorization – provided that theworld sheets considered do not contain any non-trivial defect lines. In this paper we generalize both resultsto oriented world sheets with an arbitrary network of topological defect lines.

  • 184.
    Fors, Mikael
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Constructive Sets with Non-binary Inclusion2013Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
  • 185.
    Fors, Mikael
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Elementary Discrete Sets in Martin-Löf Type Theory2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 186.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Effective Representations of Hecke-Kiselman Monoids of type AManuskript (preprint) (Annet vitenskapelig)
  • 187.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Effective representations of Hecke-Kiselman monoids of type A2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 188.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Effective representations of path semigroups2016Inngår i: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 92, nr 2, s. 449-459Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give formulas which determine the effective dimensions of path semigroups over an uncountable field and of truncated path semigroups over a field which is uncountable or of characteristic zero.

  • 189.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Multisemigroups with multiplicities and complete ordered semi-rings2017Inngår i: Beitraege zur Algebra und Geometrie, ISSN 0138-4821, E-ISSN 2191-0383, Vol. 58, nr 2, s. 405-426Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Motivated by the apperance of multisemigroups in the study of additive 2-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better siutable for applications in higher representation theory.

  • 190.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On Effective Representations of Path Semigroups and Multi-Multisemigroups2016Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 191.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Semigroups, multisemigroups and representations2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of four papers about the intersection between semigroup theory, category theory and representation theory. We say that a representation of a semigroup by a matrix semigroup is effective if it is injective and define the effective dimension of a semigroup S as the minimal n such that S has an effective representation by square matrices of size n.

    A multisemigroup is a generalization of a semigroup where the multiplication is set-valued, but still associative.

    A 2-category consists of objects, 1-morphisms and 2-morphisms. A finitary 2-category has finite dimensional vector spaces as objects and linear maps as morphisms. This setting permits the notion of indecomposable 1-morphisms, which turn out to form a multisemigroup.

    Paper I computes the effective dimension Hecke-Kiselman monoids of type A. Hecke-Kiselman monoids are defined by generators and relations, where the generators are vertices and the relations depend on arrows in a given quiver.

    Paper II computes the effective dimension of path semigroups and truncated path semigroups. A path semigroup is defined as the set of all paths in a quiver, with concatenation as multiplication. It is said to be truncated if we introduce the relation that all paths of length N are zero.

    Paper III defines the notion of a multisemigroup with multiplicities and discusses how it better captures the structure of a 2-category, compared to a multisemigroup (without multiplicities).

    Paper IV gives an example of a family of 2-categories in which the multisemigroup with multiplicities is not a semigroup, but where the multiplicities are either 0 or 1. We describe these multisemigroups combinatorially.

  • 192.
    Forsberg, Love
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Sub-bimodules of the identity bimodule for cyclic quiversManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We describe the combinatorics of the multisemigroup with multiplicities for the tensor category of subbimodules of the identity bimodule, foran arbitrary non-uniform orientation of a finite cyclic quiver

  • 193.
    Forssell, Henrik
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. University of Oslo.
    Lumsdaine, Peter LeFanu
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Constructive reflection principles for regular theoriesManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Classically, any structure for a signature Σ may be completed to a model of a desired regular theory T by means of the chase construction or small object argument. Moreover, this exhibits Mod(T) as weakly reflective in Str(Σ).

    We investigate this in the constructive setting. The basic construction is unproblematic, however, it is no longer a weak reflection. Indeed, we show that various reflection principles for models of regular theories are equivalent to choice principles in the ambient set theory. However, the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski (i.e. set) models.

    Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables.

  • 194.
    Forssell, Henrik
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Robbestad Gylterud, Håkon
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Spivak, David I.
    Massachusetts Institute of Technology, USA.
    Type Theoretical DatabasesManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to represent tables in a natural way. Thus the category is a model for databases, a single mathematical structure in which all database schemas and instances (of a suitable, but sufficiently general form) are represented. The type theory then allows for the specification of database schemas and instances, the manipulation of the same with the usual type-theoretic operations, and the posing of queries.

  • 195.
    Fredriksson, Pär
    et al.
    Högskolan i Jönköping.
    Hyltén, Ola
    Högskolan i Jönköping.
    Elever och den explicita formeln: En litteraturöversikt om elevers lärande relaterad till växande geometriska mönster och explicit formel.2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Matematik är ett ämne som elever över hela världen behöver lära sig. I de senare årskurserna bygger ämnet på att elever ska kunna behärska algebra. Vi har valt att fokusera på mönster vilket många anser vara inkörsporten till algebra. För att lärare ska kunna erbjuda elever en rättvis utbildning bör de ha kunskap om elevers svårigheter och lärande. Vår litteraturstudie har riktat in sig på att försöka svara på vad forskning säger om elevers lärande till växande geometriska mönster och explicit formel. I de elva studier som valts ut har vi kommit fram till att några gemensamma slutsatser finns men även sådana som skiljer sig åt. Att elever behöver utveckla sitt språk och få förståelse för innebörden av bokstavssymboler i matematiken är en viktig slutsats för lärande relaterad till mönster. Studierna har dessutom visat en stark relevans i att samordna olika delar till en helhet. Svenska elevers resultat i internationella undersökningar problematiseras och vad som kan tänkas vara orsaken till att de presterar sämre i mönsterrelaterade uppgifter än vad de gör i övriga delar i matematiken. Vårt resultat är till stor del överensstämmande med hur de svenska styrdokumenten förhåller sig till ämnet. Trots det har svenska elever svårigheter med att uttrycka en explicit formel till ett växande geometriskt mönster. Just den explicita formeln är viktig för elevers helhetsförståelse av mönster och tidig algebra.

  • 196.
    Fridenfalk, Mikael
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Historisk-filosofiska fakulteten, Institutionen för speldesign.
    Quantum States in Bivalent Logic2014Inngår i: ICSEA 2014, The Ninth International Conference on Software Engineering Advances, 2014, s. 114-116Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Bivalent or two-valued logic is presently the foundation of logic in mathematics and computer science, and a cornerstone of software development. To address a number of classical logical paradoxes, such as Russell’s, multi-valued logic, such as balanced ternary logic has shown to be useful. Current methods lead however to information loss. Thus, to theoretically improve the robustness of bivalent logic, this paper proposes the use of quantum states, followed by an example, where the proposed method is shown to be successful in the solution of a problem that is not directly solvable using contemporary methods.

  • 197.
    Frisk Dubsky, Brendan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classication of simple complex weight modules with finite-dimensional weight spaces over the Schrödinger algebra2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 198.
    Frisk Dubsky, Brendan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Description and classification of the category oftwo-dimensional real commutative division algebras2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 199.
    Frisk Dubsky, Brendan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Incidence category of the Young lattice, injections between finite sets, and KoszulityArtikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    We study the quadratic quotients of the incidence category of the Young lattice defined using the zero relations corresponding to adding two boxes to the same row, or to the same column or both. We show that the latter quotient corresponds to the Koszul dual of the original incidence category while the first two quotients are, in a natural way, Koszul duals of each other, hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather direct, argument establishing this Morita equivalence.

  • 200.
    Frisk Dubsky, Brendan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Induction and restriction on representations of dihedral groupsInngår i: Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the center, and a decomposition into indecomposables of these algebras.

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