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• 151.
Linnaeus University.
The Riesz-Herz equivalence for capacitary maximal functions2012Inngår i: REVISTA MATEMATICA COMPLUTENSE, ISSN 1139-1138, Vol. 25, nr 1, s. 43-59Artikkel i tidsskrift (Fagfellevurdert)

We prove a Riesz-Herz estimate for the maximal function associated to a capacity C on a"e (n) , M (C) f(x)=sup (Qa andlt; x) C(Q)(-1)a andlt;andlt; (Q) |f|, which extends the equivalence (Mf)(au)(t)a parts per thousand integral f (auau)(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadic cubes. As a byproduct we obtain a description of the norm of the interpolation space (L(1), L(1,C))(1/p,p), where L(1), C denotes the Morrey space based on a capacity.

• 152.
Interpolation of Closed Subspaces and Invertibility of Operators2015Inngår i: Journal of Analysis and its Applications, ISSN 0232-2064, Vol. 34, nr 2015, s. 1-15Artikkel i tidsskrift (Fagfellevurdert)

Let (Y0,Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj, (j = 0,1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0,X1)θ,q is a closed subspace of (Y0,Y1)θ,q. In particular, we establish conditions which are necessary and sufficient for the equality (X0,X1)θ,q = (Y0,Y1)θ,q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0.

• 153.
One-sided invertibility of discrete operators and their applications2018Inngår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 92, nr 1, s. 39-73Artikkel i tidsskrift (Fagfellevurdert)

For p is an element of [1, infinity], we establish criteria for the one-sided invertibility of binomial discrete difference operators A = aI - bV on the space l(p) = l(p)(Z), where a, b is an element of l(infinity), I is the identity operator and the isometric shift operator V is given on functions f. lp by (Vf)(n) = f (n+ 1) for all n is an element of Z. Applying these criteria, we obtain criteria for the one-sided invertibility of binomial functional operators A = aI - bU(alpha) on the Lebesgue space L-p(R+) for every p is an element of [1, infinity], where a, b is an element of L-infinity (R+), a is an orientation-preserving bi-Lipschitz homeomorphism of [0, +infinity] onto itself with only two fixed points 0 and infinity, and U-alpha is the isometric weighted shift operator on L-p(R+) given by U(alpha)f = (alpha)(1/p)(f circle alpha). Applications of binomial discrete operators to interpolation theory are given.

• 154.
Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation2013Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, nr 1, s. 207-245Artikkel i tidsskrift (Fagfellevurdert)

Let A be a bounded linear operator from a couple (X-0, X-1) to a couple (Y-0, Y-1) such that the restrictions of A on the end spaces X-0 and X-1 have bounded inverses defined on Y-0 and Y-1, respectively. We are interested in the problem of how to determine if the restriction of A on the space (X-0, XI)(theta,q) has a bounded inverse defined on the space (Y-0, Y-1)(theta,q). In this paper, we show that a solution to this problem can be given in terms of indices of two subspaces of the kernel of the operator A on the space X-0 + X-1.

• 155.
Växjö University.
The Besicovitch covering theorem and near-minimizers for the couple (L-2, BV)2010Inngår i: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, nr 1, s. 29-33Artikkel i tidsskrift (Fagfellevurdert)

Let Omega be a rectangle in R-2. A new algorithm for the construction of a near-minimizer for the couple (L-2 (Omega); BV(Omega)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f is an element of L-2 (Omega).

• 156.
Interpolation of Fredholm Operators2016Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 295, s. 421-496Artikkel i tidsskrift (Fagfellevurdert)
• 157.
Recognizing texts in undergraduate mathematics2012Inngår i: Proceedings 36th Conference of the International Group for the Psychology of Mathematics Education: Opportunities to Learn in Mathematics Education, Taipei-Taiwan, July 18-22, 2012. / [ed] Tso, T.Y., Department of Mathematics, National Taiwan Normal University; Taiwan Association of Mathematics Education , 2012, s. 4-245-Konferansepaper (Fagfellevurdert)

Findings from interviews investigating how Swedish first year engineering students recognize undergraduate mathematics texts as being more or less “mathematical”. The results indicate a relation between the students’ understanding of the principles for knowledge classification and their success in their mathematics studies.

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PME36_4-245_Ashjari
• 158.
A note on transformations of edge colorings of bipartite graphs2009Inngår i: JOURNAL OF COMBINATORIAL THEORY SERIES B, ISSN 0095-8956 , Vol. 99, nr 5, s. 814-818Artikkel i tidsskrift (Fagfellevurdert)

The author and A. Mirumian proved the following theorem: Let G be a bipartite graph with maximum degree Delta and let t, n be integers, t andgt;= n andgt;= Delta. Then it is possible to obtain, from one proper edge t-coloring of G, any proper edge n-coloring of G using only transformations of 2-colored and 3-colored subgraphs such that the intermediate colorings are also proper. In this note we show that if t andgt; Delta then we can transform f to g using only transformations of 2-colored subgraphs. We also correct the algorithm suggested in [A.S. Asratian, Short solution of Kotzigs problem for bipartite graphs, J. Combin. Theory Set. B 74 (1998) 160-168] for transformation of f to g in the case when t = n = Delta and G is regular.

• 159.
A new local condition for a graph to be hamiltonian2004Inngår i: CTW04 Workshop on graph theory and combinatorial optimization,2004, 2004, s. 47-49Konferansepaper (Annet vitenskapelig)
• 160.
Interval edge colorings of graphs and related problems2008Inngår i: Operations research symposium in the honour of T. Liebling and D. de Werra,2008, 2008Konferansepaper (Annet vitenskapelig)
• 161.
New local conditions for a graph to be hamiltonian2006Inngår i: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 22, nr 2, s. 153-160Artikkel i tidsskrift (Fagfellevurdert)

For a vertex w of a graph G the ball of radius 2 centered at w is the subgraph of G induced by the set M 2(w) of all vertices whose distance from w does not exceed 2. We prove the following theorem: Let G be a connected graph where every ball of radius 2 is 2-connected and d(u)+d(v)|M 2(w)|-1 for every induced path uwv. Then either G is hamiltonian or [InlineMediaObject not available: see fulltext.] for some p2 where denotes join. As a corollary we obtain the following local analogue of a theorem of Nash-Williams: A connected r-regular graph G is hamiltonian if every ball of radius 2 is 2-connected and [InlineMediaObject not available: see fulltext.] for each vertex w of G. © Springer-Verlag 2006.

• 162.
New localization theorems on Hamilton cycles2004Inngår i: 8th Nordic Combinatorial conference,2004, 2004Konferansepaper (Annet vitenskapelig)
• 163.
On cyclic properties of some infinite, locally finite graphs2011Konferansepaper (Annet vitenskapelig)
• 164.
Umeå University.
On Path Factors of (3,4)-Biregular Bigraphs2008Inngår i: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 24, nr 5, s. 405-411Artikkel i tidsskrift (Fagfellevurdert)

A (3, 4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose components are nontrivial paths. We prove that a simple (3,4)-biregular bigraph always has a path factor such that the endpoints of each path have degree three. Moreover we suggest a polynomial algorithm for the construction of such a path factor.

• 165.
A sufficient condition for interval edge colorings of (4,3)-biregular bipartite graphs2006Rapport (Annet vitenskapelig)
• 166.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. University of Southern Denmark, Denmark.
Solution of Vizings Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results2016Inngår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 82, nr 4, s. 350-373Artikkel i tidsskrift (Fagfellevurdert)

Let G be a Class 1 graph with maximum degree 4 and let t amp;gt;= 5 be an integer. We show that any proper t-edge coloring of G can be transformed to any proper 4-edge coloring of G using only transformations on 2-colored subgraphs (so-called interchanges). This settles the smallest previously unsolved case of a well-known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5-edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7-edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent. (C) 2015 Wiley Periodicals, Inc.

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• 167.
Some results on interval edge colorings of (a, B)-biregular bipartitie graphs2006Rapport (Annet vitenskapelig)
• 168.
Cyclic deficiency of graphs2019Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 266, s. 171-185Artikkel i tidsskrift (Fagfellevurdert)

A proper edge coloring of a graph G with colors 1, 2, . . . , t is called a cyclic interval t-coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. In this paper we introduce and investigate a new notion, the cyclic deficiency of a graph G, defined as the minimum number of pendant edges whose attachment to G yields a graph admitting a cyclic interval coloring; this number can be considered as a measure of closeness of G of being cyclically interval colorable. We determine or bound the cyclic deficiency of several families of graphs. In particular, we present examples of graphs of bounded maximum degree with arbitrarily large cyclic deficiency, and graphs whose cyclic deficiency approaches the number of vertices. Finally, we conjecture that the cyclic deficiency of any graph does not exceed the number of vertices, and we present several results supporting this conjecture. (C) 2018 Elsevier B.V. All rights reserved.

Fulltekst tilgjengelig fra 2020-12-31 15:04
• 169.
Some results on cyclic interval edge colorings of graphs2018Inngår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 87, nr 2, s. 239-252Artikkel i tidsskrift (Fagfellevurdert)

A proper edge coloring of a graph G with colors 1,2,,t is called a cyclic interval t-coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. We prove that a bipartite graph G of even maximum degree (G)4 admits a cyclic interval (G)-coloring if for every vertex v the degree dG(v) satisfies either dG(v)(G)-2 or dG(v)2. We also prove that every Eulerian bipartite graph G with maximum degree at most eight has a cyclic interval coloring. Some results are obtained for (a,b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b; it has been conjectured that all these have cyclic interval colorings. We show that all (4, 7)-biregular graphs as well as all (2r-2,2r)-biregular (r2) graphs have cyclic interval colorings. Finally, we prove that all complete multipartite graphs admit cyclic interval colorings; this proves a conjecture of Petrosyan and Mkhitaryan.

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• 170.
Umeå University. Polytech State University, Marietta, GA. University of Illinois.
Proper Path-Factors and Interval Edge-Coloring of (3,4)-Biregular Bigraphs2009Inngår i: JOURNAL OF GRAPH THEORY, ISSN 0364-9024 , Vol. 61, nr 2, s. 88-97Artikkel i tidsskrift (Fagfellevurdert)

An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.

• 171.
Department of Mathematics, UmeÅ University, SE-901 87 UmeÅ, Sweden.
On interval edge colorings of (a, ß)-biregular bipartite graphs2007Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 307, nr 15, s. 1951-1956Artikkel i tidsskrift (Fagfellevurdert)

A bipartite graph G is called (a, ß)-biregular if all vertices in one part of G have degree a and all vertices in the other part have degree ß. An edge coloring of a graph G with colors 1, 2, 3, ..., t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored i, for i = 1, ..., t. We show that the problem to determine whether an (a, ß)-biregular bipartite graph G has an interval t-coloring is NP-complete in the case when a = 6, ß = 3 and t = 6. It is known that if an (a, ß)-biregular bipartite graph G on m vertices has an interval t-coloring then a + ß - gcd (a, ß) = t = m - 1, where gcd (a, ß) is the greatest common divisor of a and ß. We prove that if an (a, ß)-biregular bipartite graph has m = 2 (a + ß) vertices then the upper bound can be improved to m - 3. © 2006 Elsevier B.V. All rights reserved.

• 172.
On Local Nature of Some Classical Theorems on Hamilton Cycles2005Rapport (Annet vitenskapelig)
• 173.
On the local nature of some classical theorems on Hamilton cycles2007Inngår i: Australasian journal of combinatorics, ISSN 1034-4942, Vol. 38, s. 77-86Artikkel i tidsskrift (Fagfellevurdert)

The following result gives a flavour of what is in this paper. Ore's theorem is that if $d(u)+d(v)\ge|G|$ for all non-adjacent $u,v\in G$ then $G$ is Hamiltonian. The authors show that this is equivalent to specifying that $d(u)+d(v)\ge |B(x)|$ for every $x\in G$ and all non-adjacent $u,v\in B(x)$, where $B(x)$ is the ball of radius three centred at $x$. The reason is that the condition implies $G$ has diameter at most two, and so $B(x)=G$.

• 174.
Institute for System Programming Russian Acad. Sci..
Analysis of randomized rounding for integer programs2004Inngår i: Discrete mathematics and applications, ISSN 0924-9265, Vol. 14, nr 6Artikkel i tidsskrift (Fagfellevurdert)
• 175.
Institute for System Programming Russian Acad. Sci..
Two sensitivity theorems in fuzzy integer programming2004Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 134, nr 1-3, s. 129-140Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of estimating optima of covering integer linear programs with 0-1 variables under the following conditions: we do not know exact values of elements in the constraint matrix A but we know what elements of A are zero and what are nonzero, and also know minimal and maximal values of nonzero elements. We find bounds for variation of the optima of such programs in the worst and average cases. We also find some conditions guaranteeing that the variation of the optimum of such programs in the average case is close to 1 as the number of variables tends to infinity. This means that the values of nonzero elements in A can vary without significantly affecting the value of the optimum of the integer program.

• 176.
Pk+1- decomposition of eulerian graphs: complexity and some solvable cases2003Rapport (Annet vitenskapelig)
• 177.
Pk+1-Decompositions of Eulerian Graphs: Complexity and Some Solvable Cases2003Inngår i: Electronic Notes in Discrete Mathematics, ISSN 1571-0653, E-ISSN 1571-0653, Vol. 13Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of PMk+1-decomposition of a simple eulerian graph G, that is, decomposition of G into edge disjoint paths of length k. We show that the problem of deciding whether there exists a Pk+1 - decomposition of an eulerian simple graph is NP-complete, for every k = 3. However we find some new classes of graphs where the problem of P4-decomposition can be solved polynomially. We show that an eulerian simple graph G on 3m = 6 edges admits a P4-decomposition if G has no cut vertex v such that exactly one of the components in the graph G - ? has two vertices. In particular, this implies that a 2-connected eulerian simple graph G on 3m = 6 edges admits a P4 -decomposition. © 2003.

• 178.
Technical University of Darmstadt, Germany .
University of Münster, Germany . Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. St. Petersburg State University, Russia.
Persistence probabilities for a Bridge of an integrated simple random walk2014Inngår i: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 34, nr 1, s. 1-22Artikkel i tidsskrift (Fagfellevurdert)

We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability n(-1/2) to stay positive. This question is motivated by random polymer models and proves a conjecture by Caravenna and Deuschel.

• 179.
Université Paris-Sud 11, France.
Remarks on maximal regularity2011Inngår i: Parabolic Problems: The Herbert Amann Festschrift / [ed] Joachim Escher, Patrick Guidotti, Matthias Hieber, Piotr Mucha, Jan W. Prüss, Yoshihiro Shibata, Gieri Simonett, Christoph Walker, Wojciech Zajaczkowski, Springer, 2011, s. 45-56Kapittel i bok, del av antologi (Annet vitenskapelig)

We prove weighted estimates for the maximal regularity operator. Such estimates were motivated by boundary value problems. We take this opportunity to study a class of weak solutions to the abstract Cauchy problem. We also give  a new proof of maximal regularity for closed and maximal accretive operators following from Kato's inequality for fractional powers and almost orthogonality arguments.

• 180.
Université Paris-Sud.
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I2011Inngår i: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 184, nr 1, s. 47-115Artikkel i tidsskrift (Fagfellevurdert)

We develop new solvability methods for divergence form second order, real and complex, elliptic systems  above Lipschitz graphs, with $L_2$ boundary data.    The coefficients $A$ may depend on all variables, but are assumed to be close to coefficients $A_0$ that are independent of the coordinate transversal to the boundary, in the Carleson sense $\|A-A_0\|_C$ defined by Dahlberg.  We obtain a number of {\em a priori} estimates and boundary behaviour results under finiteness of $\|A-A_0\|_C$.  Our methods yield full characterization of weak solutions, whose gradients have $L_2$ estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a singular operator-valued kernel.   Also, the non-tangential maximal function of a weak solution is controlled in $L_2$ by the square function of its   gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension $3$  or higher. The existence of a proof {\em a priori} to well-posedness, is also a new fact.  As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under   smallness of $\|A-A_0\|_C$ and well-posedness for $A_0$, improving earlier results for real symmetric equations.  Our methods build on an algebraic reduction to a first order system first made for coefficients $A_0$ by the two authors   and A. McIntosh in order to use functional calculus related to the Kato conjecture solution,   and the main analytic tool for coefficients $A$ is an operational calculus to prove weighted maximal regularity estimates.

• 181.
Département de Mathématiques d’Orsay, Université Paris-Sud et UMR 8628 du CNRS, Orsay Cedex, France.
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems, II2012Inngår i: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 5, nr 5, s. 983-1061Artikkel i tidsskrift (Fagfellevurdert)

We continue the development, by reduction to a first-order system for the conormal gradient, of L2a priori estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence-form second-order complex elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning a priori almost everywhere nontangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying a posteriori a separate work on bounded domains.

• 182.
Université Paris-Sud, France.
Boundary value problems for degenerate elliptic equations and systems2015Inngår i: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 48, nr 4, s. 951-1000Artikkel i tidsskrift (Fagfellevurdert)
• 183.
Deparrment of Biological Sciences Heriot-Watt University.
Lab. of Microbiology University of Ghent. Dept. of mathematics University of Turku. Nokia Mobile Phones. Lab. of microbiology Univesrity of Ghent. Lab. of microbiology University of Ghent. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
Sliding window discretization: A new method for multiple band matching of bacterial genotyping fingerprints2004Inngår i: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 66, nr 6, s. 1575-1596Artikkel i tidsskrift (Fagfellevurdert)

Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods - such as the minimization of stochastic complexity - for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.

• 184.
Iterative methods for solving a nonlinear boundary inverse problem in glaciology2009Inngår i: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, ISSN 0928-0219 , Vol. 17, nr 3, s. 239-258Artikkel i tidsskrift (Fagfellevurdert)

We address a Cauchy problem for a nonlinear elliptic PDE arising in glaciology. After recasting the Cauchy problem as an ill-posed operator equation, we prove (for values of a certain parameter allowing Hilbert space techniques) differentiability properties of the associated operator. We also suggest iterative methods which can be applied to solve the operator problem.

• 185.
Stability estimate for an inverse problem in glaciology2012Inngår i: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 2, nr 4, s. 367-387Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of reconstruction of the basal velocity of a glacier by measurements of the velocity on glacier’s surface. The main result is a stability estimate in a near-surface region, which represents a multiplicative inequality and shows that small errors in measurements produce small errors in the velocity in this region.

• 186.
Stockholms University.
Stockholms University. University of Seville. Stockholms University. Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
Pentagrams and Paradoxes2011Inngår i: FOUNDATIONS OF PHYSICS, ISSN 0015-9018, Vol. 41, nr 3, s. 414-423Artikkel i tidsskrift (Fagfellevurdert)

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.

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FULLTEXT01
• 187.
Implementering av programmering i matematik åk 7-9: En litteraturstudie om tre olika programmeringsspråks lämplighet i olika matematikområden2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

Hösten 2018 inrättas det en ny version av läroplanen från 2011 med mer fokus på programmering. Syftet med denna litteraturstudie är att sammanställa forskningslitteraturens resultat om olika programmeringsspråks lämplighet för högstadiets matematikundervisning, samt lämpliga matematikområden. Frågeställningarna jämför tre programmeringsspråk med avseende på deras lämplighet och för- och nackdelar i matematikundervisningen. Programmeringsspråken, som jämförs, är Scratch, Python och VBA (Visual Basics of Application, programmering i Microsofts kalkylprogram Excel). Litteraturstudiens resultat visar att Scratch och Python anses vara lämpliga för nybörjare och är utvecklade för att de ska vara lätta att lära sig och förstå medan VBA är det programmeringsspråk som är utvecklat för att utföra matematiska beräkningar med.

Programmeringsspråken kan användas i matematikundervisningen på likvärdiga sätt och i de flesta matematikområdena beroende på elevernas kompetens och lärarens val av uppgifter och tillvägagångssätt. Vidare är det möjligt att eleverna kan bli mer motiverade till att lära sig matematik om de har tillgång till digitala hjälpmedel eller programmering inom matematikundervisningen

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• 188.
Är Python pyton?: Erfarenheter vid användning av programmering i matematikundervisning i grundskolans senaste år2019Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

Hösten 2018 inrättades en reviderad läroplan för grundskolan och gymnasiet. Den största förändringen var att programmering har lagts till i matematik- och teknikämnena. Med detta kommer frågor om hur programmering ska användas i matematikundervisningen och samtidigt inte försämra elevernas kunskaper och resultat. I denna pilotstudie undersöks elever i årskurs 9 och deras kunskapsutveckling och attitydförändring när programmering används för att räkna på aritmetiska talföljder. För denna studie användes programmeringsspråket Python som är ett lämpligt nybörjarspråk i programmering. I resultatet finns det inte några större skillnader i kunskapsutvecklingen varken hos kontrollgruppen som endast fick grundläggande programmering, eller hos de andra klasserna som hade totalt 6 lektioner med programmering med matematisk inriktning. Det fanns inte heller några tydliga förändringar i elevernas attityd mot matematik och programmering.  I studiens slutsats belyses många förbättringar som kan göras för framtida studier samt hur verksamma lärare kan använda programmeringen i matematikundervisningen.

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Coherent functors and asymptotic properties2019Doktoravhandling, med artikler (Annet vitenskapelig)

In this thesis we study properties of the so called coherent functors. Coherent functors were first introduced by Auslander in 1966 in a general setting. Coherent functors have been used since then as powerful tools for different purposes: to describe infinitesimal deformation theory, to describe algebraicity of a stack or to study properties of Rees algebras.

In 1998, Hartshorne proved that half exact coherent functors over a discrete valuation ring 𝐴 are direct sums of the identity functor, Hom-functors of quotient modules of 𝐴 and tensor products of quotient modules of 𝐴. In our first article (Paper A), we obtain a similar characterization for half exact coherent functors over a much wider class of rings: Dedekind domains. This fact allows us to classify half exact coherent functors over Dedekind domains.

In our second article (Paper B), coherent functors over noetherian rings are considered. We study asymptotic properties of sets of prime ideals connected with coherent functors applied to artinian modules or finitely generated modules. Also considering quotient modules M /anM, where an is the nthpower of an ideal 𝑎, one obtains that the Betti and Bass numbers of the images under a coherent functor of the quotient modules above are polynomials in n for large n. Furthermore, the lengths of these image modules are polynomial in 𝑛, for large 𝑛, under the condition that the image modules have finite length.

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Coherent functors and asymptotic properties
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• 190.
Half-exact coherent functors over Dedekind domains2019Inngår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 18, nr 5, artikkel-id 1950099Artikkel i tidsskrift (Fagfellevurdert)

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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• 191.
Half–Exact Coherent Functors over PIDs and Dedekind Domains2016Licentiatavhandling, med artikler (Annet vitenskapelig)

The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.

We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−)  on the category on A–modules, where A is a commutative ring and M is an A–module.

With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.

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• 192.
Univ Zambia, Zambia.
Coherent functors and asymptotic stability2019Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 522Artikkel i tidsskrift (Fagfellevurdert)

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.

• 193.
University of Southern Denmark, Denmark.
Restricted cycle factors and arc-decompositions of digraphs2015Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 193, s. 80-93Artikkel i tidsskrift (Fagfellevurdert)

We study the complexity of finding 2-factors with various restrictions as well as edge-decompositions in (the underlying graphs of) digraphs. In particular we show that it is N P-complete to decide whether the underlying undirected graph of a digraph D has a 2-factor with cycles C-1, C-2, ..., C-k such that at least one of the cycles C-i is a directed cycle in D (while the others may violate the orientation back in D). This solves an open problem from J. Bang-Jensen et al., Vertex-disjoint directed and undirected cycles in general digraphs, JCT B 106 (2014), 1-14. Our other main result is that it is also N P-complete to decide whether a 2-edge-colored bipartite graph has two edge-disjoint perfect matchings such that one of these is monochromatic (while the other does not have to be). We also study the complexity of a number of related problems. In particular we prove that for every even k greater than= 2, the problem of deciding whether a bipartite digraph of girth k has a k-cycle-free cycle factor is N P-complete. Some of our reductions are based on connections to Latin squares and so-called avoidable arrays.

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• 194.
University of Mediterranea Reggio Calabria, Italy.
University of Florence, Italy. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN University, Russia.
Quasilinear elliptic equations on noncompact Riemannian manifolds2017Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 273, nr 11, s. 3426-3462Artikkel i tidsskrift (Fagfellevurdert)

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided. (C) 2017 Elsevier Inc. All rights reserved.

• 195.
Department of Computer Science and Engineering, The Pennsylvania State University, USA.
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan. Department of Statistics, University of Bologna, Italy.
Editorial Material: 3rd Special issue on matrix computations and statistics2010Inngår i: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 54, nr 12, s. 3379-3380Artikkel i tidsskrift (Annet vitenskapelig)

n/a

• 196.
On Poicarés Uniformization Theorem2006Independent thesis Basic level (professional degree), 20 poäng / 30 hpOppgave

A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$.

For each $\Gamma$ acting on $\mathcal{H}$ we have a polygon $P$ such that $\mathcal{H}$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal{H}$ under $\Gamma$.

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• 197.
On the Branch Loci of Moduli Spaces of Riemann Surfaces2012Doktoravhandling, med artikler (Annet vitenskapelig)

The spaces of conformally equivalent Riemann surfaces, Mg where g ≥ 1, are not manifolds. However the spaces of the weaker Teichmüller equivalence, Tg are known to be manifolds. The Teichmüller space Tg is the universal covering of Mg and Mg is the quotient space by the action of the modular group. This gives Mg an orbifold structure with a branch locus Bg. The branch loci Bg can be identified with Riemann surfaces admitting non-trivial automorphisms for surfaces of genus g ≥ 3. In this thesis we consider the topological structure of Bg. We study the connectedness of the branch loci in general by considering families of isolated strata and we we establish that connectedness is a phenomenon for low genera. Further, we give the orbifold structure of the branch locus of surfaces of genus 4 and genus 5 in particular, by studying the equisymmetric stratification of the branch locus.

Paper 1. In this paper we show that the strata corresponding to actions of order 2 and 3 belong to the same connected component for arbitrary genera. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

Paper 2. This paper contains a collection of results regarding components of the branch loci, some of them proved in detail in other papers. It is shown that for any integer d if p is a prime such that p > (d + 2)2, there there exist isolated strata of dimension d in the moduli space of Riemann surfaces of genus (d + 1)(p − 1)/2. It is also shown that if we consider Riemann surfaces as Klein surfaces, the branch loci are connected for every genera due to reflections.

Paper 3. Here we consider surfaces of genus 4 and 5. Here we study the automorphism groups of Riemann surfaces of genus 4 and 5 up to topological equivalence and determine the complete structure of the equisymmetric stratification of the branch locus.

Paper 4. In this paper we establish that the connectedness of the branch loci is a phenomenon for low genera. More precisely we prove that the only genera g where Bg is connected are g = 3, 4, 13, 17, 19, 59.

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• 198.
On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera2009Licentiatavhandling, med artikler (Annet vitenskapelig)

Compact Riemann surfaces of genus greater than 1 can be realized as quotient spaces of the hyperbolic plane by the action of Fuchsian groups. The Teichmüller space is the set of all complex structures of Riemann surfaces and the moduli space the set of conformal equivalence classes of Riemann surfaces. For genus greater than two the branch locus of the covering of the moduli space by the Teichmüller space can be identified wi the set of Riemann surfaces admitting non-trivial automorphisms. Here we give the orbifold structure of the branch locus of surfaces of genus 5 by studying the equisymmetric stratification of the branch locus. This gives the orbifold structure of the moduli space.

We also show that the strata corresponding to surfaces with automorphisms of order 2 and 3 belong to the same connected component for every genus. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

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On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera
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• 199.
On the connected branch loci of moduli spacesManuskript (preprint) (Annet vitenskapelig)

The moduli space Mg of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of such orbifold is the branch locus Bg. In this article we show that Bg is connected exactly for genera three, four, thirteen, seventeen, nineteen and fitfynine by the use automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

• 200.
On automorphisms groups of cyclic p-gonal Riemann surfaces2013Inngår i: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 57, s. 61-69Artikkel i tidsskrift (Fagfellevurdert)

In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p⩾3p⩾3 is a prime integer and the genus of the surfaces is at least (p−1)2+1(p−1)2+1. We use Fuchsian and NEC groups, and cohomology of finite groups.

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