| 1. |
- Johansson, Anders, et al.
(författare)
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Countable state shifts and uniqueness of g-measures
- 2007
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Ingår i: American Journal of Mathematics. - : Project Muse. - 0002-9327 .- 1080-6377. ; 129:6, s. 1501-1511
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of g ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where g >= 0, relaxing the earlier requirement that inf g > 0.
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| 2. |
- Johansson, Anders, et al.
(författare)
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Square Summability of Variations and Convergence of the Transfer Operator
- 2008
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Ingår i: Ergodic Theory and Dynamical Systems. - 0143-3857 .- 1469-4417. ; 28:4, s. 1145-1151
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [P. Walters. Trans. Amer Math. Soc. 353(l) (2001), 327-347], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in our earlier work [A. Johansson and A. Oberg. Math. Res. Lett. 10(5-6) (2003), 587-601]. We also prove uniqueness of the so-called G-measures, introduced by Brown and Dooley [G. Brown and A. H. Dooley. Ergod. Th. & Dynam. Sys. 11 (1991), 279-307], under square summability of variations.
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| 3. |
- Samokhin, Alexander, et al.
(författare)
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Stationary iteration methods for solving 3D electromagnetic scattering problems
- 2013
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Ingår i: Applied Mathematics and Computation. - : Elsevier BV. - 0096-3003 .- 1873-5649. ; 222, s. 107-122
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Tidskriftsartikel (refereegranskat)abstract
- Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on the complex plane are obtained. A minimax problem for the determination of optimal complex iteration parameters is formulated. An algorithm of finding an optimal iteration parameter in the case of arbitrary location of the operator spectrum on the complex plane is constructed for the generalized simple iteration method. The results are applied to numerical solution of volume singular integral equations (VSIEs) associated with the problems of the mathematical theory of wave diffraction by 3D dielectric bodies. In particular, the domain of the spectrum location is described explicitly for low-frequency scattering problems and in the general case. The obtained results are discussed and recommendations concerning their applications are given. (C) 2013 Elsevier Inc. All rights reserved.
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| 4. |
- Shestopalov, Yuri, 1953-, et al.
(författare)
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Eigenwaves in waveguides with dielectric inclusions : completeness
- 2014
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X. ; 93:9, s. 1824-1845
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Tidskriftsartikel (refereegranskat)abstract
- We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then, we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the mnimality' of this system and show that this system is generally not a Schauder basis. This work is a continuation of the paper Eigenwaves in waveguides with dielectric inclusions: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980 by Y. Smirnov and Y. Shestopalov. Therefore, we omit the problem statements and all necessary basic definitions given in the previous paper.
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| 5. |
- Shestopalov, Yuri, 1953-, et al.
(författare)
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Eigenwaves in waveguides with dielectric inclusions : spectrum
- 2014
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 93:2, s. 408-427
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Tidskriftsartikel (refereegranskat)abstract
- We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a non-empty set of isolated points localized in a strip with at most finitely many real points.
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| 6. |
- Jerez-Hanckes, Carlos, et al.
(författare)
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Multiscale analysis of myelinated axons
- 2021
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Ingår i: SEMA SIMAI Springer Series. - Cham : Springer International Publishing. - 2199-305X .- 2199-3041. ; 10, s. 17-35, s. 17-35
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Konferensbidrag (refereegranskat)abstract
- We consider a three-dimensional model for a myelinated neuron, which includes Hodgkin–Huxley ordinary differential equations to represent membrane dynamics at Ranvier nodes (unmyelinated areas). Assuming a periodic microstructure with alternating myelinated and unmyelinated parts, we use homogenization methods to derive a one-dimensional nonlinear cable equation describing the potential propagation along the neuron. Since the resistivity of intracellular and extracellular domains is much smaller than the myelin resistivity, we assume this last one to be a perfect insulator and impose homogeneous Neumann boundary conditions on the myelin boundary. In contrast to the case when the conductivity of the myelin is nonzero, no additional terms appear in the one-dimensional limit equation, and the model geometry affects the limit solution implicitly through an auxiliary cell problem used to compute the effective coefficient. We present numerical examples revealing the forecasted dependence of the effective coefficient on the size of the Ranvier node.
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| 7. |
- Johansson, Anders, 1960-, et al.
(författare)
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Ergodic Theory of Kusuoka Measures
- 2017
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Ingår i: Journal of Fractal Geometry. - : European Mathematical Society Publishing House. - 2308-1309 .- 2308-1317. ; 4:2, s. 185-214
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Tidskriftsartikel (refereegranskat)abstract
- In the analysis on self-similar fractal sets, the Kusuoka measure plays an important role. Here we investigate the Kusuoka measure from an ergodic theoretic viewpoint, seen as an invariant measure on a symbolic space. Our investigation shows that the Kusuoka measure generalizes Bernoulli measures and their properties to higher dimensions of an underlying finite dimensional vector space. Our main result is that the transfer operator on functions has a spectral gap when restricted to a certain Banach space that contains the Hölder continuous functions, as well as the highly discontinuous g" role="presentation">g-function associated to the Kusuoka measure. As a consequence, we obtain exponential decay of correlations. In addition, we provide some explicit rates of convergence for a family of generalized Sierpinski gaskets.
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| 8. |
- Johansson, Anders, 1960-, et al.
(författare)
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Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
- 2019
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Ingår i: Ergodic Theory and Dynamical Systems. - : Cambridge University Press. - 0143-3857 .- 1469-4417. ; 39:5, s. 1317-1330
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Tidskriftsartikel (refereegranskat)abstract
- We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of g-measures. Indag. Math. (N.S.) 22 (2011), 315-329] to a weaker condition, Berbee's condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a g-measure with a continuous g-function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.
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| 9. |
- Johansson, Anders, 1960-, et al.
(författare)
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Unique Bernoulli g-measures
- 2012
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 14:5, s. 1599-1615
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Tidskriftsartikel (refereegranskat)abstract
- We improve and subsume the conditions of Johansson and O¨ berg [18] and Berbee [2]for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular,we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely manystates under any one of the following additional assumptions.(1)P1n=1(varn log g)2 < 1,(2) For any fixed ✏ > 0,P1n=1 e−(1/2+✏)(var1 log g+···+varn log g) = 1,(3) varn log g = o(1/pn) as n!1.That the measure is Bernoulli in the case of (1) is new. In (2) we have an improved version ofBerbee’s [2] condition (concerning uniqueness and Bernoullicity), allowing the variations of log gto be essentially twice as large. Finally, (3) is an example that our main result is new both foruniqueness and for the Bernoulli property.We also conclude that we have convergence in the Wasserstein metric of the iterates of theadjoint transfer operator to the g-measure.
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| 10. |
- Johansson, Anders, 1960-, et al.
(författare)
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Multifractal analysis of non-uniformly hyperbolic systems
- 2010
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Ingår i: Israel Journal of Mathematics. - : Springer. - 0021-2172 .- 1565-8511. ; 177:1, s. 125-144
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Tidskriftsartikel (refereegranskat)abstract
- We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.
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