| 1. |
- Andersson, Fredrik K., et al.
(författare)
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The mathematics of internet search engines
- 2008
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 2. |
- Carlsen, Toke Meier, et al.
(författare)
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On the Exel crossed product of topological covering maps
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 573-583
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Tidskriftsartikel (refereegranskat)abstract
- For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C *-algebras C(X)⋊ α,ℒℕintroduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems.
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| 3. |
- Choquard, Philippe, et al.
(författare)
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A one-dimensional inviscid and compressible fluid in a harmonic potential well
- 2007
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 99:2, s. 161-183
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Tidskriftsartikel (refereegranskat)abstract
- A Hamiltonian model is analyzed for a one-dimensional inviscid compressible fluid. The space-time evolution of the fluid is governed by the following system of the Hamilton-Jacobi and the continuity equations: S-t + 1/2(S-x(2) + omega(2)chi(2)) =0, S(x, 0) = S-0(x); rho(t) + (rho S-x)(x) =0, rho(x, 0) =rho(0)(x).Here S and rho designate the velocity potencial and the mass density, respectively. Unless S-0 is convex, shocks form and the velocity S (x) becomes discontinuous in {0 < omega t < pi/2}. It is demonstrated that there nevertheless exists a unique viscosity-measure solution (S,rho) when S-0 is globally Lipschitz continuous and locally semi-concave while rho(0) is a finite Borel measure. The structure of the velocity and the density is exhibited. For initial data correlated in a certain sense, a class of classical solutions (S,rho) is given. Negative time is also considered, and illustrating examples are given.
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| 4. |
- Ibragimov, Nail H.
(författare)
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Symmetries, Lagrangian and Conservation Laws for the Maxwell Equations
- 2009
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Ingår i: Acta Applicandae Mathematicae. - : Springer. - 0167-8019 .- 1572-9036. ; 105:2, s. 157-187
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Tidskriftsartikel (refereegranskat)abstract
- The evolution equations of Maxwell's equations has a Lagrangian written in terms of the electric E and magnetic H fields, but admit neither Lorentz nor conformal transformations. The additional equations del center dot E=0, del center dot H=0 guarantee the Lorentz and conformal invariance, but the resulting system is overdetermined, and hence does not have a Lagrangian. The aim of the present paper is to attain a harmony between these two contradictory properties and provide a correspondence between symmetries and conservation laws using the Lagrangian for the evolutionary part of Maxwell's equations.
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| 5. |
- Lundquist, Anders, 1978-
(författare)
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On the distance between some πps sampling designs
- 2007
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - Dordrecht : Reidel. - 0167-8019 .- 1572-9036. ; 97:1-3, s. 79-97
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic distances between probability distributions appearing in πps sampling theory are studied. The distributions are Poisson, Conditional Poisson (CP), Sampford, Pareto, Adjusted CP and Adjusted Pareto sampling. We start with the Kullback-Leibler divergence and the Hellinger distance and derive a simpler distance measure using a Taylor expansion of order two. This measure is evaluated first theoretically and then numerically, using small populations. The numerical examples are also illustrated using a multidimensional scaling technique called principal coordinate analysis (PCO). It turns out that Adjusted CP, Sampford, and adjusted Pareto are quite close to each other. Pareto is a bit further away from these, then comes CP and finally Poisson which is rather far from all the others.
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| 6. |
- Silvestrov, Sergei, et al.
(författare)
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Preface
- 2009
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Ingår i: Acta Applicandae Mathematicae. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 108:3, s. 487-488
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 7. |
- Svensson, Christian, et al.
(författare)
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Dynamical systems associated with crossed products
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 547-559
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system.
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| 8. |
- Öinert, Johan, et al.
(författare)
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Commutativity and ideals in pre-crystalline graded rings
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 603-615
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Tidskriftsartikel (refereegranskat)abstract
- Pre-crystalline graded rings constitute a class of rings which share many properties with classical crossed products. Given a pre-crystalline graded ring A, we describe its center, the commutant CA(A0) of the degree zero grading part, and investigate the connection between maximal commutativity of A0 in A and the way in which two-sided ideals intersect A0.
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| 9. |
- Öinert, Johan, et al.
(författare)
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Commutativity and ideals in strongly graded rings
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 585-602
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Tidskriftsartikel (refereegranskat)abstract
- In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A0, the subring in the degree zero component of the grading, is a commutative ring, each non-zero two-sided ideal in A has a non-zero intersection with the commutant CA(A0) of A0 in A. This result has also been generalized to crystalline graded rings; a more general class of graded rings to which algebraic crossed products belong. In this paper we generalize this result in another direction, namely to strongly graded rings (in some literature referred to as generalized crossed products) where the subring A0, the degree zero component of the grading, is a commutative ring. We also give a description of the intersection between arbitrary ideals and commutants to bigger subrings than A0, and this is done both for strongly graded rings and crystalline graded rings.
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| 10. |
- Grill, Kalle, 1976-
(författare)
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The Normative Core of Paternalism
- 2007
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Ingår i: Res Publica. - : Springer. - 1356-4765 .- 1572-8692. ; 13:4, s. 441-458
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Tidskriftsartikel (refereegranskat)abstract
- The philosophical debate on paternalism is conducted as if the property of being paternalistic should be attributed to actions. Actions are typically deemed to be paternalistic if they amount to some kind of interference with a person and if the rationale for the action is the good of the person interfered with. This focus on actions obscures the normative issues involved. In particular, it makes it hard to provide an analysis of the traditional liberal resistance to paternalism. Given the fact that actions most often have mixed rationales, it is not clear how we should categorize and evaluate interfering actions for which only part of the rationale is the good of the person. The preferable solution is to attribute the property of being paternalistic not to actions, but to compounds of reasons and actions. The framework of action–reasons provides the tools for distinguishing where exactly paternalism lies in the complex web of reasons and actions.
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