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• 1.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Cincinnati, OH 45221 USA.
Locally p-admissible measures on R2020Ingår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 278, nr 4, artikel-id UNSP 108344Artikel i tidskrift (Refereegranskat)

In this note we show that locally p-admissible measures on R necessarily come from local Muckenhoupt A(p) weights. In the proof we employ the corresponding characterization of global p-admissible measures on R in terms of global A(p) weights due to Bjorn, Buckley and Keith, together with tools from analysis in metric spaces, more specifically preservation of the doubling condition and Poincare inequalities under flattening, due to Durand-Cartagena and Li. As a consequence, the class of locally p-admissible weights on R is invariant under addition and satisfies the lattice property. We also show that measures that are p-admissible on an interval can be partially extended by periodical reflections to global p-admissible measures. Surprisingly, the p-admissibility has to hold on a larger interval than the reflected one, and an example shows that this is necessary. (C) 2019 Elsevier Inc. All rights reserved.

• 2.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Makerere Univ, Uganda.
THE QUASISUPERMINIMIZING CONSTANT FOR THE MINIMUM OF TWO QUASISUPERMINIMIZERS IN R-n2020Ingår i: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 45, s. 215-225Artikel i tidskrift (Refereegranskat)

It was shown in Bjorn-Bjorn-Korte [5] that u := min{u(1), u(2)} is a (Q) over bar -quasisuper-minimizer if u(1) and u(2) are Q-quasisuperminimizers and (Q) over bar = 2Q(2)/(Q+1). Moreover, one-dimensional examples therein show that (Q) over bar is close to optimal. In this paper we give similar examples in higher dimensions. The case when u(1) and u(2) have different quasisuperminimizing constants is considered as well.

• 3. Köp publikationen >>
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Kähler-Poisson Algebras2020Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

I denna avhandling introduceras Kähler-Poisson algebror och deras grundläggande egenskaper studeras. Motivationen till detta kommer från differentialgeometri där man kan visa att den metriska geometrin för en Kählermångfald kan formuleras i termer av Poisson algebran av släta funktioner på mångfalden. Det visar sig att man kan identifiera ett algebraiskt villkor i en Poissonalgebra (med en metrik) som gör det möjligt att formulera de flesta geometriska objekt på ett algebraiskt vis. Detta leder till definitionen av en Kähler-Poisson algebra, vilken utgörs av en Poissonalgebra och en metrik som tillsammans uppfyller ett kompatibilitetsvillkor. Vi visar att för varje Kähler-Poisson algebra så existerar det en Levi-Civita förbindelse på modulen som utgörs av de inre derivationerna, och att den tillhörande krökningsoperatorn har alla de klassiska symmetrierna. Vidare presenteras en konstruktion som associerar en Kähler-Poisson algebra till varje algebra i en stor klass av Poissonalgebror. Ur ett mer algebraiskt perspektiv så introduceras flera grundläggande begrepp, såsom morfier, delalgebror, direkta summor och tensorprodukter. Slutligen påbörjas en studie av modulirum för Kähler-Poisson algebror, det vill säga ekvivalensklasser av metriker som ger upphov till isomorfa Kähler-Poisson strukturer. Det visar sig att även i det enkla fallet med en Poisson algebra genererad av två variabler, så leder detta till ett icke-trivialt klassificeringsproblem.

1. Kahler-Poisson algebras
Öppna denna publikation i ny flik eller fönster >>Kahler-Poisson algebras
2019 (Engelska)Ingår i: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 136, s. 156-172Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

We introduce Kahler-Poisson algebras as analogues of algebras of smooth functions on Kahler manifolds, and prove that they share several properties with their classical counterparts on an algebraic level. For instance, the module of inner derivations of a Kahler-Poisson algebra is a finitely generated projective module, and allows for a unique metric and torsion-free connection whose curvature enjoys all the classical symmetries. Moreover, starting from a large class of Poisson algebras, we show that every algebra has an associated Kahler-Poisson algebra constructed as a localization. At the end, detailed examples are provided in order to illustrate the novel concepts. (C) 2018 Elsevier B.V. All rights reserved.

##### Ort, förlag, år, upplaga, sidor
ELSEVIER SCIENCE BV, 2019
##### Nyckelord
Lie-Rinehart algebra; Kahler manifold; Levi-Civita connection; Curvature
Annan fysik
##### Identifikatorer
urn:nbn:se:liu:diva-154675 (URN)10.1016/j.geomphys.2018.11.001 (DOI)000456763300013 ()
##### Anmärkning

Funding Agencies|Swedish Research Council [621-2013-4538]

Tillgänglig från: 2019-03-01 Skapad: 2019-03-01 Senast uppdaterad: 2020-01-20
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• 4.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Univ Zielona Gora, Poland.
On Dynamics of Jellets Egg. Asymptotic Solutions Revisited2020Ingår i: Regulârnaâ i haoticeskaâ dinamika, ISSN 1560-3547, E-ISSN 1468-4845, Vol. 25, nr 1, s. 40-58Artikel i tidskrift (Refereegranskat)

We study here the asymptotic condition. E = -mu gnv2A = 0 for an eccentric rolling and sliding ellipsoid with axes of principal moments of inertia directed along geometric axes of the ellipsoid, a rigid body which we call here Jelletts egg (JE). It is shown by using dynamic equations expressed in terms of Euler angles that the asymptotic condition is satisfied by stationary solutions. There are 4 types of stationary solutions: tumbling, spinning, inclined rolling and rotating on the side solutions. In the generic situation of tumbling solutions concise explicit formulas for stationary angular velocities.. JE(cos.),.3JE(cos.) as functions of JE parameters a, a,. are given. We distinguish the case 1 - a amp;lt; a2 amp;lt; 1+ a, 1 - a amp;lt; a2. amp;lt; 1+ a when velocities.. JE,.3JE are defined for the whole range of inclination angles.. (0, p). Numerical simulations illustrate how, for a JE launched almost vertically with.(0) = 1 100, 1 10, the inversion of the JE depends on relations between parameters.

• 5.
Ariel Univ, Israel.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Liverpool, England; RUDN Univ, Russia.
Sharp pointwise estimates for the gradients of solutions to linear parabolic second-order equation in the layer2020Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArtikel i tidskrift (Refereegranskat)

We deal with solutions of the Cauchy problem to linear both homogeneous and nonhomogeneous parabolic second-order equations with real constant coefficients in the layer , where and . The homogeneous equation is considered with initial data in , . For the nonhomogeneous equation we suppose that initial function is equal to zero and the function in the right-hand side belongs to , pamp;gt;n + 2 and . Explicit formulas for the sharp coefficients in pointwise estimates for the length of the gradient to solutions to these problems are obtained.

• 6.
Univ Firenze, Italy.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN Univ, Russia.
Sobolev inequalities for the symmetric gradient in arbitrary domains2020Ingår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 194, artikel-id 111515Artikel i tidskrift (Refereegranskat)

A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in Rn. In the relevant inequalities, boundary regularity of domains is replaced with information on boundary traces of trial functions. The inequalities so obtained exhibit the same exponents as in classical inequalities for the full gradient of Sobolev functions, in regular domains. Furthermore, they involve constants independent of the geometry of the domain, and hence yield novel results yet for smooth domains. Our approach relies upon a pointwise estimate for the functions in question via a Riesz potential of their symmetric gradient and an unconventional potential depending on their boundary trace. (C) 2019 Elsevier Ltd. All rights reserved.

• 7.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Univ Rostock, Germany.
On the nonstationary Stokes system in a cone: Asymptotics of solutions at infinity2020Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 486, nr 10, artikel-id 123821Artikel i tidskrift (Refereegranskat)

The paper deals with the Dirichlet problem for the nonstationary Stokes system in a cone. The authors obtain existence and uniqueness results for solutions in weighted Sobolev spaces and study the asymptotics of the solutions at infinity. (C) 2020 Elsevier Inc. All rights reserved.

• 8.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
SPECTRAL PROPERTIES OF NONASSOCIATIVE ALGEBRAS AND BREAKING REGULARITY FOR NONLINEAR ELLIPTIC TYPE PDEs2020Ingår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 31, nr 2, s. 223-240Artikel i tidskrift (Refereegranskat)

In this paper, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? Our aim in the paper is twofold. First, to give a survey of diverse examples on nonregular solutions to elliptic PDEs with emphasis on recent results on nonclassical solutions to fully nonlinear equations. Second, to define an appropriate algebraic formalism, which makes the analytic part of the construction of nonclassical solutions more transparent.

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• 9.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Upper bounds on the star chromatic index for bipartite graphs2020Självständigt arbete på grundnivå (kandidatexamen), 14 hpStudentuppsats (Examensarbete)

An area in graph theory is graph colouring, which essentially is a labeling of the vertices or edges according to certain constraints. In this thesis we consider star edge colouring, which is a variant of proper edge colouring where we additionally require the graph to have no two-coloured paths or cycles with length 4. The smallest number of colours needed to colour a graph G with a star edge colouring is called the star chromatic index of G and is denoted $\chi'_{st}(G)$. This paper proves an upper bound of the star chromatic index of bipartite graphs in terms of the maximum degree; the maximum degree of G is the largest number of edges incident to a single vertex in G. For bipartite graphs Bk with maximum degree $k\geq1$, the star chromatic index is proven to satisfy$\chi'_{st}(B_k) \leq k^2 - k + 1$. For bipartite graphs $B_{k,n}$, where all vertices in one part have degree n, and all vertices in the other part have degree k, it is proven that the star chromatic index satisﬁes $\chi'_{st}(Bk,n) \leq k^2 -2k + n + 1, k \geq n > 1$. We also prove an upper bound for a special case of multipartite graphs, namely $K_{n,1,1,\dots,1}$ with m parts of size one. The star chromatic index of such a graph satisﬁes$\chi'_{st}(K_{n,1,1,\dots,1}) \leq 15\lceil\frac{n}{8}\rceil\cdot\lceil\frac{m}{8}\rceil + \frac{1}{2}m(m-1),\,m \geq 5$. For complete multipartite graphs where m < 5, we prove lower upper bounds than the one above.

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• 10.
Univ Firenze, Italy.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN Univ, Russia.
Second-Order Regularity for Parabolic p-Laplace Problems2020Ingår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 30, nr 2, s. 1565-1583Artikel i tidskrift (Refereegranskat)

Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of p-Laplacian type, with square-integrable right-hand sides and initial data in a Sobolev space. As a consequence, generalized solutions are shown to be strong solutions. Minimal regularity on the boundary of the domain is required, though the results are new even for smooth domains. In particular, they hold in arbitrary bounded convex domains.

• 11.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Umea Univ, Sweden. Umea Univ, Sweden.
Edge precoloring extension of hypercubes2020Ingår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118Artikel i tidskrift (Refereegranskat)

We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d-1 edges of the d-dimensional hypercube Qd can be extended to a proper d-edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d-edge colorings of Qd.

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• 12.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Ehime Univ, Japan.
Automorphism groups of dense subgroups of R-n2020Ingår i: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 275, artikel-id 107000Artikel i tidskrift (Refereegranskat)

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R-n, n &gt;= 1. We show that Aut(G) can be naturally identified with the subgroup Phi(G) ={A is an element of GL(n, R) : G center dot A = G} of the group GL(n, R) of all non-degenerated (n x n)-matrices with real coefficients, where G center dot A ={g center dot A : g is an element of G}. We describe Phi(G) for many dense subgroups G of either R or R-2. We consider also an inverse problem of which symmetric subgroups of GL(n, R) can be realized as Phi(G) for some dense subgroup G of R-n. For n &gt;= 2, we show that any subgroup H of GL(n, R) satisfying SO(n, R) subset of H subset of GL(n, R) cannot be realized in this way. (Here SO(n, R) denotes the special orthogonal group of dimension n.) The realization problem is quite non-trivial even in the one-dimensional case and has deep connections to number theory. (C) 2019 Elsevier B.V. All rights reserved.

• 13.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Ehime Univ, Japan.
Topological groups all continuous automorphisms of which are open2020Ingår i: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 275, artikel-id 107051Artikel i tidskrift (Refereegranskat)

A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topological group G is g-reversible if every continuous automorphism of G (=continuous isomorphism of G onto itself) is open. The class of g-reversible groups contains Polish groups, locally compact a-compact groups, minimal groups, abelian groups with the Bohr topology, and reversible topological groups. We prove that subgroups of R-n are g-reversible, for every positive integer it. An example of a compact (so reversible) metric abelian group having a countable dense non-g-reversible subgroup is given. We also highlight the differences between reversible spaces and g-reversible topological groups. Many open problems are scattered throughout the paper. (C) 2019 Elsevier B.V. All rights reserved.

• 14.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Low Dimensional Matrix Representations for Noncommutative Surfaces of Arbitrary Genus2020Ingår i: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 23, nr 2, artikel-id 12Artikel i tidskrift (Refereegranskat)

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in Double-struck capital R-3.

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• 15.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
New explicit solutions to the p-Laplace equation based on isoparametric foliations2020Ingår i: Differential geometry and its applications (Print), ISSN 0926-2245, E-ISSN 1872-6984, Vol. 70, artikel-id 101629Artikel i tidskrift (Refereegranskat)

In contrast to an infinite family of explicit examples of two-dimensional p-harmonic functions obtained by G. Aronsson in the late 80s, there is very little known about the higher-dimensional case. In this paper, we show how to use isoparametric polynomials to produce diverse examples of p-harmonic and biharmonic functions. Remarkably, for some distinguished values of p and the ambient dimension n this yields first examples of rational and algebraic p-harmonic functions. Moreover, we show that there are no p-harmonic polynomials of the isoparametric type. This supports a negative answer to a question proposed in 1980 by J. Lewis.

• 16.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Univ La Frontera, Chile.
A note on large automorphism groups of compact Riemann surfaces2020Ingår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 547Artikel i tidskrift (Refereegranskat)

Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order lambda(g - 1), for each lambda amp;gt; 6, under the assumption that g - 1 is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting 5(g - 1) and 6(g - 1) automorphisms, with g - 1 a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order 3(g - 1), with g - 1 a prime number. We also provide isogeny decompositions of their Jacobian varieties. (C) 2019 Elsevier Inc. All rights reserved.

Publikationen är tillgänglig i fulltext från 2021-11-26 15:46
• 17.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Umea Univ, Sweden.
Latin cubes of even order with forbidden entries2020Ingår i: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 85, artikel-id 103045Artikel i tidskrift (Refereegranskat)

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant gamma amp;gt; 0 such that if n is even and A is a 3-dimensional n x n x n array where every cell contains at most gamma n symbols, and every symbol occurs at most gamma n times in every line of A, then A is avoidable; that is, there is a Latin cube L of order n such that for every i, j, k is an element of {1, ..., n}, the symbol in position (i, j, k) of L does not appear in the corresponding cell of A. (C) 2019 Elsevier Ltd. All rights reserved.

Publikationen är tillgänglig i fulltext från 2021-11-05 12:25
• 18.
Universitat Autònoma de Barcelona.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Universitat Autònoma de Barcelona. Universitat Autònoma de Barcelona.
Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes2019Ingår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 16, nr 1-2, artikel-id 10Artikel i tidskrift (Refereegranskat)

In this paper, we present a qualitative study in which we analyse the video-recordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students’ problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible.

• 19.
Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
A word property for twisted involutions in Coxeter groups2019Ingår i: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 161, s. 220-235Artikel i tidskrift (Refereegranskat)

Given an involutive automorphism theta of a Coxeter system (W, S), let J(theta) subset of W denote the set of twisted involutions. We provide a minimal set of moves that can be added to the braid moves, in order to connect all reduced S-expressions (also known as admissible sequences, reduced I-theta-expressions, or involution words) for any given w is an element of J(theta). This can be viewed as an analogue of the well-known word property for Coxeter groups. It improves upon a result of Hamaker, Marberg, and Pawlowski, and generalises similar statements valid in certain types due to Hu, Zhang, Wu, and Marberg. (C) 2018 Elsevier Inc. All rights reserved.

• 20.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Poincare inequalities and Newtonian Sobolev functions on noncomplete metric spaces2019Ingår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 266, nr 1, s. 44-69Artikel i tidskrift (Refereegranskat)

Let X be a noncomplete metric measure space satisfying the usual (local) assumptions of a doubling property and a Poincare inequality. We study extensions of Newtonian Sobolev functions to the completion (X) over cap of X and use them to obtain several results on X itself, in particular concerning minimal weak upper gradients, Lebesgue points, quasicontinuity, regularity properties of the capacity and better Poincare inequalities. We also provide a discussion about possible applications of the completions and extension results to p-harmonic functions on noncomplete spaces and show by examples that this is a rather delicate issue opening for various interpretations and new investigations. (C) 2018 Elsevier Inc. All rights reserved.

• 21.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications2019Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, nr 1, s. 40-63Artikel i tidskrift (Refereegranskat)

In this paper, boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is obtained for a large class of compactifications, but also two examples when it fails are given. This study is done for complete metric spaces equipped with doubling measures supporting a p-Poincare inequality, but the results are new also in unweighted Euclidean spaces.

• 22.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Umea Univ, Sweden. Umea Univ, Sweden.
Latin cubes with forbidden entries2019Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, nr 1, artikel-id P1.2Artikel i tidskrift (Refereegranskat)

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant gamma amp;gt; 0 such that if n = 2(t) and A is a 3-dimensional n x n x n array where every cell contains at most gamma n symbols, and every symbol occurs at most gamma n times in every line of A, then A is avoidable; that is, there is a Latin cube L of order n such that for every 1 amp;lt;= i, j, k amp;lt;= n, the symbol in position (i, j, k) of L does not appear in the corresponding cell of A.

• 23.
Sapienza Univ, Italy.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN Univ, Russia. Weierstrass Inst Appl Anal and Stochast, Germany.
A fast solution method for time dependent multidimensional Schrodinger equations2019Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 98, nr 1-2, s. 408-429Artikel i tidskrift (Refereegranskat)

In this paper we propose fast solution methods for the Cauchy problem for the multidimensional Schrodinger equation. Our approach is based on the approximation of the data by the basis functions introduced in the theory of approximate approximations. We obtain high-order approximations also in higher dimensions up to a small saturation error, which is negligible in computations, and we prove error estimates in mixed Lebesgue spaces for the inhomogeneous equation. The proposed method is very efficient in high dimensions if the densities allow separated representations. We illustrate the efficiency of the procedure on different examples, up to approximation order 6 and space dimension 200.

• 24.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Geometri för grundlärare2019 (uppl. 3)Bok (Övrigt vetenskapligt)

Denna bok är skriven för studenter som läser matematik inom Grundlärarprogrammet. Den är baserad på och har en tydlig koppling till det centrala innehåll och de förmågor som finns i grundskolans läroplan (Lgr11). Innehållet är uppdaterat utifrån den reviderade läroplan för grundskolan som kom under 2017 och som gäller för undervisning från 1 juli 2018. I denna utgåva har innehållet utökats med ytterligare ett par avsnitt samt en särskild avdelning med blandade uppgifter. Denna utgåva är också inbunden med hård pärm.

Boken innehåller utförligt förklarad teori och lösta exempel samt rikligt antal övningar med svar och lösningsanvisningar. Även den som till vissa delar är bekant med innehållet ges här tillfälle att träna sin problemlösningsförmåga, procedurförmåga, begreppsförmåga, resonemangsförmåga och kommunikationsförmåga.

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• 25.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik.
Analyzing arterial blood flow by simulation of bifurcation trees2019Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

The flow of blood in the human body is a very important component in un-derstanding a number of different ailments such as atherosclerosis and a falseaneurysm. In this thesis, we have utilized Poiseuille’s solution to Navier-Stokesequations with a Newtonian, incompressible fluid flowing laminar with zero ac-celeration in a pipe with non-flexible walls in order to study blood flow in anarterial tree. In order to study and simulate a larger arterial tree we have uti-lized a primitive building block, a bifurcation with one inlet and two outlets,joined together forming a tree. By prescribing an inlet flow and the pressureat every outlet at the bottom of the tree we have shown that we may solvethe system by fixed-point iteration, the Matlab functionfsolve, and Newton’smethod. This way of using primitive building blocks offers a flexible way to doanalysis as it makes it possible to easily change the shape of the tree as well asadding new building blocks such as a block that represents arteriosclerosis.

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• 26.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs2019Ingår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 31, nr 2, s. 255-278Artikel i tidskrift (Refereegranskat)

In this paper, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? The aim of the paper is twofold. Firstly, to give a survey of diverse examples on nonregular solutions to elliptic PDEs with emphasis on recent results on nonclassical solutions to fully nonlinear equations. Secondly, to define an appropriate algebraic formalism which makes the analytic part of the construction of nonclassical solutions more transparent.

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• 27.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Local Conditions for Cycles in Graphs2019Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

A Hamilton cycle in a graph is a cycle that passes through every vertex of the graph. A graph is called Hamiltonian if it contains such a cycle. The problem of determining if a graph is Hamiltonian has been studied extensively, and there are many known sufficient conditions for Hamiltonicity.

A large portion of these conditions relate the degrees of vertices of the graph to the number of vertices in the entire graph, and thus they can only apply to a limited set of graphs with high edge density. In a series of papers, Asratian and Khachatryan developed local analogues of some of these criteria. These results do not suffer from the same drawbacks as their global counterparts, and apply to wider classes of graphs.

In this thesis we study this approach of creating local conditions for Hamiltonicity, and use it to develop local analogues of some classic results. We also study how local criteria can influence other global properties of graphs. Finally, we will see how these local conditions can allow us to extend theorems on Hamiltonicity to infinite graphs.

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Local Conditions for Cycles in Graphs
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• 28.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Mathematical modelling of flow through thin curved pipes with application to hemodynamics2019Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

The problem of mathematical modelling of incompressible flows with low velocities through narrow curvilinear pipes is addressed in this thesis. The main motivation for this modelling task is to eventually model the human circulatory system in a simple way that can facilitate the medical practitioners to efficiently diagnose any abnormality in the system. The thesis comprises of four articles.

In the first article, a two-dimensional model describing the elastic behaviour of the wall of a thin, curved,  exible pipe is presented. The wall is assumed to have a laminate structure consisting of several anisotropic layers of varying thickness. The width of the channel is allowed to vary along the pipe. The two-dimensional model takes the interactions of the wall with any surrounding material and the  fluid  flow into account and is obtained through a dimension reduction procedure. Examples of canonical shapes of pipes and their walls are provided with explicit systems of differential equations at the end.

In the second article, a one-dimensional model describing the blood flow through a moderately curved, elastic blood vessel is presented. The two-dimensional model presented in the first paper is used to model the vessel wall while linearized Navier-Stokes equations are used to model the  flow through the channel. Surrounding muscle tissues and presence of external forces other than gravity are taken into account. The model is again obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow.

The one-dimensional model described in the second paper is used to derive a simplified one-dimensional model of a false aneurysm which forms the subject of the third article. A false aneurysm is an accumulation of blood outside a blood vessel but confined by the surrounding muscle tissue. Numerical simulations are presented which demonstrate different characteristics associated with a false aneurysm.

In the final article, a modified Reynolds equation, along with its derivation from Stokes equations through asymptotic methods, is presented. The equation governs the steady flow of a fluid with low Reynolds number through a narrow, curvilinear tube. The channel considered may have large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed. These approximations satisfy a modified Poiseuille equation. A justification for the approximations is provided along with a comparison with a simpler case.

1. A TWO-DIMENSIONAL MODEL OF THE THIN LAMINAR WALL OF A CURVILINEAR FLEXIBLE PIPE
Öppna denna publikation i ny flik eller fönster >>A TWO-DIMENSIONAL MODEL OF THE THIN LAMINAR WALL OF A CURVILINEAR FLEXIBLE PIPE
2018 (Engelska)Ingår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 71, nr 3, s. 349-367Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

We present a two-dimensional model describing the elastic behaviour of the wall of a curved flexible pipe. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the channel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with any surrounding or supporting material and the fluid flow into account and is obtained via a dimension reduction procedure. The curvature and twist of the pipes axis as well as the anisotropy of the laminate wall present the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of pipes and their walls are supplied with explicit systems of differential equations at the end.

##### Ort, förlag, år, upplaga, sidor
OXFORD UNIV PRESS, 2018
##### Nationell ämneskategori
Annan elektroteknik och elektronik
##### Identifikatorer
urn:nbn:se:liu:diva-150869 (URN)10.1093/qjmam/hby009 (DOI)000441808700006 ()
##### Anmärkning

Funding Agencies|Russian Foundation of Basic Research [18-01-00325]

Tillgänglig från: 2018-09-06 Skapad: 2018-09-06 Senast uppdaterad: 2019-04-16
2. A one dimensional model of blood flow through a curvilinear artery
Öppna denna publikation i ny flik eller fönster >>A one dimensional model of blood flow through a curvilinear artery
2018 (Engelska)Ingår i: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 63, s. 633-643Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

We present a one-dimensional model describing the blood flow through a moderately curved and elastic blood vessel. We use an existing two dimensional model of the vessel wall along with Navier-Stokes equations to model the flow through the channel while taking factors, namely, surrounding muscle tissue and presence of external forces other than gravity into account. Our model is obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow. (C) 2018 Elsevier Inc. All rights reserved.

##### Ort, förlag, år, upplaga, sidor
ELSEVIER SCIENCE INC, 2018
##### Nyckelord
Blood flow; Curvilinear vessel; Asymptotic analysis; Dimension reduction; Numerical simulation
##### Nationell ämneskategori
Strömningsmekanik och akustik
##### Identifikatorer
urn:nbn:se:liu:diva-151627 (URN)10.1016/j.apm.2018.07.019 (DOI)000444362800034 ()
##### Anmärkning

Funding Agencies|Russian Foundation of Basic Research [18-01-00325]

Tillgänglig från: 2018-10-09 Skapad: 2018-10-09 Senast uppdaterad: 2019-04-16
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• 29.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Sun Yat Sen Univ, Peoples R China.
Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular spaces2019Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 474, nr 2, s. 852-875Artikel i tidskrift (Refereegranskat)

We use sphericalization to study the Dirichlet problem, Perron solutions and boundary regularity for p-harmonic functions on unbounded sets in Ahlfors regular metric spaces. Boundary regularity for the point at infinity is given special attention. In particular, we allow for several "approach directions" towards infinity and take into account the massiveness of their complements. In 2005, Llorente-Manfredi-Wu showed that the p-harmonic measure on the upper half space R-+(n), n amp;gt;= 2, is not subadditive on null sets when p not equal 2. Using their result and spherical inversion, we create similar bounded examples in the unit ball B subset of R-n showing that the n-harmonic measure is not subadditive on null sets when n amp;gt;= 3, and neither are the p-harmonic measures in B generated by certain weights depending on p not equal 2 and n amp;gt;= 2. (C) 2019 Elsevier Inc. All rights reserved.

• 30.
Univ Zambia, Zambia.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Coherent functors and asymptotic stability2019Ingår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 522Artikel i tidskrift (Refereegranskat)

Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att(A) F(0 :(N) a(n)) are the same for n large enough. Also it is shown that for an artinian module N if the modules F(0 :(N) a(n)) have finite length and for a finitely generated module M if the modules F(M/a(n) M) have finite length, their lengths are given by polynomials in n, for large n. When A is local it is shown that, the Betti numbers beta(i)(F(M /a(n) M)) and the Bass numbers mu(i)(F(M / a(n) M)) are given by polynomials in n for large n. (C) 2018 Elsevier Inc. All rights reserved.

• 31.
Universitat Autònoma de Barcelona, Bellaterra, Spain.
Universitat Autònoma de Barcelona, Bellaterra, Spain. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Helsingin Yliopisto, Helsinki, Finland. Oxford Brookes University, Oxford, United Kingdom. Universitat Autònoma de Barcelona, Bellaterra, Spain.
Fundamental Mathematical Knowledge: progressing its specification2019Rapport (Övrigt vetenskapligt)

In this paper, we elaborate on the notion of Fundamental Mathematical Knowledge (FMK) which we understand as the minimum mathematical content knowledge essential to enter a degree in primary teacher education. We propose that FMK can be assessed in terms of competency in different areas of primary mathematics. The aim of this paper is to present our on-going work to specify FMK based on the common content of mathematics as a primary school subject in Catalonia, England, Finland, and Sweden.

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Fundamental Mathematical Knowledge: progressing itsspecification
• 32.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
On an extremal property of Jordan algebras of Clifford type2019Ingår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 47, nr 3, s. 1057-1066Artikel i tidskrift (Refereegranskat)
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• 33.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Russian Acad Sci, Russia.
A COMPARISON THEOREM FOR SUPER- AND SUBSOLUTIONS OF del(2)u + f(u)=0 AND ITS APPLICATION TO WATER WAVES WITH VORTICITY2019Ingår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 30, nr 3, s. 471-483Artikel i tidskrift (Refereegranskat)

A comparison theorem is proved for a pair of solutions that satisfy opposite nonlinear differential inequalities in a weak sense. The nonlinearity is of the form f (u) with f belonging to the class L-loc(p) and the solutions are assumed to have nonvanishing gradients in the domain, where the inequalities are considered. The comparison theorem is applied to the problem describing steady, periodic water waves with vorticity in the case of arbitrary free-surface profiles including overhanging ones. Bounds for these profiles as well as streamfunctions and admissible values of the total head are obtained.

• 34.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Liverpool, England.
SOLVABILITY CRITERIA FOR THE NEUMANN p-LAPLACIAN WITH IRREGULAR DATA2019Ingår i: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 30, nr 3, s. 485-492Artikel i tidskrift (Refereegranskat)

Necessary and sufficient conditions are found for the unique solvability of the Neumann problem for the p-Laplace operator. They characterize both the domain and measures on the right-hand sides.

• 35.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Biologi. Linköpings universitet, Tekniska fakulteten.
Density-Dependent Feedback in Age-Structured Populations2019Ingår i: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 242, nr 1, s. 2-24Artikel i tidskrift (Refereegranskat)

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.

• 36.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik.
Numerical Range of Square Matrices: A Study in Spectral Theory2019Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)

In this thesis, we discuss important results for the numerical range of general square matrices. Especially, we examine analytically the numerical range of complex-valued $2 \times 2$ matrices. Also, we investigate and discuss the Gershgorin region of general square matrices. Lastly, we examine numerically the numerical range and Gershgorin regions for different types of square matrices, both contain the spectrum of the matrix, and compare these regions, using the calculation software Maple.

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• 37.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Topology of posets with special partial matchings2019Ingår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 348, s. 255-276Artikel i tidskrift (Refereegranskat)

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

• 38.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik.
Simuleringar av elliptiska kurvor för elliptisk kryptografi2019Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

Denna rapport går igenom teorin bakom Diffie-Hellmans nyckelutbyte över elliptiska kurvor. Från definitionen av en grupp hela vägen till hur operatorn över en elliptisk kurva utgör en abelsk grupp gås igenom och görs tydligt med konstruktiva exempel. Sedan görs en mindre undersökning av sambandet mellan storleken av den underliggande kroppen, antal punkter på kurvan och ordning av punkterna på kurvan, det vill säga svårigheten att hitta den hemliga nyckeln framtagen med Diffie-Hellmans nyckelutbyte för elliptiska kurvor. Ingen tydlig koppling hittas. Då elliptiska kurvor över utvidgade kroppar har mer beräkningstunga operationer dras slutsatsen att dessa kurvor inte är praktiska inom Diffie-Hellman nyckelutbyte över elliptiska kurvor.

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• 39.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN Univ, Russia.
Univ Missouri, MO 65211 USA.
Accretivity of the General Second Order Linear Differential Operator2019Ingår i: Acta Mathematica Sinica. English series, ISSN 1439-8516, E-ISSN 1439-7617, Vol. 35, nr 6, s. 832-852Artikel i tidskrift (Refereegranskat)

For the general second order linear differential operator with complex-valued distributional coefficients a(j,k), b(j), and c in an open set (n) (n 1), we present conditions which ensure that -L0 is accretive, i.e., Re -L0 phi,phi 0 for all phi C-0(infinity) (Omega).

• 40.
Univ Coll Dublin, Ireland.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
A characterization of annular domains by quadrature identities2019Ingår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 51, nr 3, s. 436-442Artikel i tidskrift (Refereegranskat)

This note verifies a conjecture of Armitage and Goldstein that annular domains may be characterized as quadrature domains for harmonic functions with respect to a uniformly distributed measure on a sphere.

• 41.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Chile, Chile. Univ Chile, Chile.
Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification2019Ingår i: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 35, nr 4, s. 1259-1279Artikel i tidskrift (Refereegranskat)

Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We consider the set of equisymmetric Riemann surfaces M(2n -1, D-2n, theta) for all n amp;gt;= 2. We study the group algebra decomposition of the Jacobian JX of every curve X is an element of M (2n - 1, D-2n, theta) for all admissible actions, and we provide affine models for them. We use the topological equivalence of actions on the curves to obtain facts regarding its Jacobians. We describe some of the factors of JX as Jacobian (or Prym) varieties of intermediate coverings. Finally, we compute the dimension of the corresponding Shimura domains.

• 42.
Royal Inst Technol, Sweden; Inst Hautes Etud Sci, France.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
New construction techniques for minimal surfaces2019Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, nr 9, s. 1546-1563Artikel i tidskrift (Refereegranskat)

It is pointed out that despite the nonlinearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.

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• 43.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Univ Rostock, Germany.
On the behavior of solutions of the nonstationary Stokes system near the vertex of a cone2019Ingår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, artikel-id UNSP e201800305Artikel i tidskrift (Refereegranskat)

The paper deals with the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. The authors study the asymptotics of the solutions near the vertex of the cone. They show that the solutions are sums of singular functions and a regular remainder, where the singular functions depend on the eigenvalues of a certain operator pencil.

• 44.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Ghostpeakons and Characteristic Curves for the Camassa-Holm, Degasperis-Procesi and Novikov Equations2019Ingår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 15, artikel-id 017Artikel i tidskrift (Refereegranskat)

We derive explicit formulas for the characteristic curves associated with the multipeakon solutions of the Camassa-Holm, Degasperis-Procesi and Novikov equations. Such a curve traces the path of a fluid particle whose instantaneous velocity equals the elevation of the wave at that point (or the square of the elevation, in the Novikov case). The peakons themselves follow characteristic curves, and the remaining characteristic curves can be viewed as paths of "ghostpeakons" with zero amplitude; hence, they can be obtained as solutions of the ODEs governing the dynamics of multipeakon solutions. The previously known solution formulas for multipeakons only cover the case when all amplitudes are nonzero, since they are based upon inverse spectral methods unable to detect the ghostpeakons. We show how to overcome this problem by taking a suitable limit in terms of spectral data, in order to force a selected peakon amplitude to become zero. Moreover, we use direct integration to compute the characteristic curves for the solution of the Degasperis-Procesi equation where a shockpeakon forms at a peakon-antipeakon collision. In addition to the theoretical interest in knowing the characteristic curves, they are also useful for plotting multipeakon solutions, as we illustrate in several examples.

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• 45.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Zambia, Zambia.
Half-exact coherent functors over Dedekind domains2019Ingår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 18, nr 5, artikel-id 1950099Artikel i tidskrift (Refereegranskat)

Let A be a principal ideal domain (PID) or more generally a Dedekind domain and let F be a coherent functor from the category of finitely generated A-modules to itself. We classify the half-exact coherent functors F. In particular, we show that if F is a half-exact coherent functor over a Dedekind domain A, then F is a direct sum of functors of the form Hom(A) (P,-), Hom(A) (A/p(s),-) and A/p(s) circle times -, where P is a finitely generated projective A-module, p a nonzero prime ideal in A and s amp;gt;= 1.

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• 46.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Univ Barcelona, Spain. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Barcelona, Spain.
Rearrangement estimates for A(infinity) weights2019Ingår i: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 32, nr 3, s. 731-743Artikel i tidskrift (Refereegranskat)

We find a new characterizations of an A(infinity) weight omega, in terms of the decreasing rearrangement of the restriction of omega to cubes Q.

• 47. Köp publikationen >>
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Dynamics of Coinfection: Complexity and Implications2019Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

Living beings are always on risk from multiple infectious agents in individual or in groups. Though multiple pathogens' interactions have widely been studied in epidemiology. Despite being well known, the co-existence of these pathogens and their coinfection remained a mystery to be uncovered. Coinfection is one of the important and interesting phenomenon in multiple interactions when two infectious agents coexist at a time in a host. The aim of this thesis is to understand the complete dynamics of coinfection and the role of different factors affecting these interactions.

Mathematical modelling is one of the tools to study the coinfection dynamics. Each model has its own limitations and choice of the model depends on the questions to be addressed. There is always a crosstalk between the choice of model and limitation of their solvability. The complexity of the problem defines the restriction in analytical possibilities.

In this thesis we formulate and analyse the mathematical models of coinfection with different level of complexities. Since viral infections are a major class of infectious diseases, in the first three papers we formulated a susceptible, infected, recovered (SIR) model for coinfection of the two viral strains in a single host population introducing carrying capacity as limited growth factor in susceptible class. In the first study, we made some assumptions for the transmission of coinfection in the model. In the following papers, the analysis is expanded by relaxing these assumptions which has generated the complexity in dynamics. We showed that the dynamics of stable equilibrium points depends on the fundamental parameters including carrying capacity K. A parameter dependent transition dynamics exists starting from disease free state to a level where coinfection can persists only with susceptible class. A disease-free equilibrium point is stable only when K is small. With increase in carrying capacity to a level where only single infection can invade and persists. Further increase in carrying capacity becomes large enough for the existence and persistence of coinfection due to the high density of susceptible class. In paper I, we proved the existence of a globally stable equilibrium point for any set of parameter values, revealing persistence of disease in a population. This shows a close relationship between the intensity of infection and carrying capacity as a crucial parameter of the population. So there is always a positive correlation between risk of infection and carrying capacity which leads to destabilization of the population.

In paper IV, we formulated mathematical models using different assumptions and multiple level of complexities to capture the effect of additional phenomena such as partial cross immunity, density dependence in each class and a role of recovered population in the dynamics. We found the basic reproduction number for each model which is the threshold that describes the invasion of disease in population. The basic reproduction number in each model shows that the persistence of disease or strains depends on the carrying capacity K. In the first model of this paper, we have also shown the local stability analysis of the boundary equilibrium points and showed that the recovered population is not uniformly bounded with respect to K.

Paper V uses simulations to analyse the dynamics and specifically studies how temporal variation in the carrying capacity of the population affects its dynamics. The degree of autocorrelation in variability of carrying capacity influences whether the different classes exhibit temporal variation or not. The fact that the different classes respond differently to the variation depends in itself on whether their equilibrium densities show a dependence on the carrying capacity or not. An important result is that at high autocorrelation, the healthy part of the population is not affected by the external variation and at the same time the infected part of the population exhibits high variation. A transition to lower autocorrelation, more randomness, means that the healthy population varies over time and the size of the infected population decreases in variation.

1. Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity
Öppna denna publikation i ny flik eller fönster >>Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity
2019 (Engelska)Ingår i: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 42, nr 17, s. 5805-5826Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

##### Ort, förlag, år, upplaga, sidor
John Wiley & Sons, 2019
##### Nyckelord
carrying capacity, coinfection, global stability, linear complementarity problem, SIR model
##### Nationell ämneskategori
Matematisk analys
##### Identifikatorer
urn:nbn:se:liu:diva-160293 (URN)10.1002/mma.5671 (DOI)000496512900014 ()2-s2.0-85066086382 (Scopus ID)
2. Mathematical analysis of complex SIR model with coinfection and density dependence
Öppna denna publikation i ny flik eller fönster >>Mathematical analysis of complex SIR model with coinfection and density dependence
2019 (Engelska)Ingår i: Computational and Mathematical Methods, ISSN 2577-7408, Vol. 1, nr 4Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed, and several threshold conditions are obtained, which describes the establishment of diseases in the population. We prove that, for small carrying capacity K, there exists a globally stable disease-free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, that is, we prove that, (1) for small values of K, there exists a unique globally stable equilibrium point, and (b) it moves continuously as K is growing (while its face type may change). This indicates that the carrying capacity is the crucial parameter and an increase in resources in terms of carrying capacity promotes the risk of infection.

##### Ort, förlag, år, upplaga, sidor
Wiley-Blackwell Publishing Inc., 2019
##### Nyckelord
carrying capacity, coinfection, global stability, SIR model
##### Nationell ämneskategori
Matematik Immunologi
##### Identifikatorer
urn:nbn:se:liu:diva-160284 (URN)10.1002/cmm4.1042 (DOI)
##### Konferens
2019/09/17
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• 48.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Biologi. Linköpings universitet, Tekniska fakulteten.
Mathematical analysis of complex SIR model with coinfection and density dependence2019Ingår i: Computational and Mathematical Methods, ISSN 2577-7408, Vol. 1, nr 4Artikel i tidskrift (Refereegranskat)

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed, and several threshold conditions are obtained, which describes the establishment of diseases in the population. We prove that, for small carrying capacity K, there exists a globally stable disease-free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, that is, we prove that, (1) for small values of K, there exists a unique globally stable equilibrium point, and (b) it moves continuously as K is growing (while its face type may change). This indicates that the carrying capacity is the crucial parameter and an increase in resources in terms of carrying capacity promotes the risk of infection.

Ladda ner fulltext (pdf)
Mathematical analysis of complex SIR model with coinfection and density dependence
• 49.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Harvard Med Sch, MA 02115 USA. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
Orientationally-averaged diffusion-attenuated magnetic resonance signal for locally-anisotropic diffusion2019Ingår i: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 9, artikel-id 4899Artikel i tidskrift (Refereegranskat)

Diffusion-attenuated MR signal for heterogeneous media has been represented as a sum of signals from anisotropic Gaussian sub-domains to the extent that this approximation is permissible. Any effect of macroscopic (global or ensemble) anisotropy in the signal can be removed by averaging the signal values obtained by differently oriented experimental schemes. The resulting average signal is identical to what one would get if the micro-domains are isotropically (e.g., randomly) distributed with respect to orientation, which is the case for "powdered" specimens. We provide exact expressions for the orientationally-averaged signal obtained via general gradient waveforms when the microdomains are characterized by a general diffusion tensor possibly featuring three distinct eigenvalues. This extends earlier results which covered only axisymmetric diffusion as well as measurement tensors. Our results are expected to be useful in not only multidimensional diffusion MR but also solid-state NMR spectroscopy due to the mathematical similarities in the two fields.

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• 50.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
St Petersburg State Univ, Russia; RAS, Russia. Steklov Math Inst, Russia.
PRESSURE DROP MATRIX FOR A BIFURCATION WITH DEFECTS2019Ingår i: EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, ISSN 2306-6172, Vol. 7, nr 3, s. 33-55Artikel i tidskrift (Refereegranskat)

We consider a bifurcation of an artery. The influence of defects of the vessels wall near the bifurcation point on the pressure drop matrix is analyzed. The elements of this matrix are included in the modified Kirchhoff transmission conditions, which were introduced earlier in [1], [2], and which describe adequately the total pressure loss at the bifurcation point of the flow passed through it.

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