| 1. |
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| 2. |
- Ekström, Erik, 1989-
(författare)
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Growth and thermoelectric properties of CaMnO3-based thin films
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The field of them1oelectrics started in early 19th century. Since the discovery of the Seebeck effect and the Peltier effect, thermoelectric modules have found their way into, mostly, niche applications such as radioisotope thermoelectric generators on space missions. Thermoelectric modules can also be used for cooling, utilizing the Peltier effect.Thermoelectrics are promising materials due to the operation nature of the modules. That is, they have no moving parts, no exhaust, long lifetime without maintenance, features that make them attractive for many applications. Despite these promising properties, thermoelectric modules are mostly used in niche applications. The main reason for this is conventional modules with the highest efficiency are commonly made of expensive and/or rare elements which prevents mass production.To tackle this problem, new materials are investigated to find a module that can be made widely available. Oxides are one possibility, where an added benefit is that they are chemically stable even at elevated temperature. The perovskite CaMnO3 is one of the more promising oxides, with elements that are abundant on earth and cheap. The material does suffer from low electrical conductivity which results in a low electrical conductivity and efficiency. A substantial effort has been put in to increase the efficiency of CaMnO3, hut it still needs improvement.In my thesis, I have investigated the CaMnO3 system. CaMnO3 was synthesized using co-reactive RF-magnetron sputtering and post annealing. The synthesis method is already known hut has not been used for deposition of perovskites. I have also demonstrated that this synthesis method can be used to dope CaMnO3 with niobium at appropriate levels for enhancing the efficiency.
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| 3. |
- Ekström, Mikael, et al.
(författare)
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Antiferromagnetism in Zn-doped La2CuO4 as observed by muon spin resonance spectroscopy
- 2001
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Ingår i: Physical Review B - Condensed Matter and Materials Physics. - 0163-1829. ; 64:18, s. 1845221-1845226
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Tidskriftsartikel (refereegranskat)abstract
- The local fields seen by positive muons implanted in Zn-doped La2CuO4 show a distribution with a main peak attributed to muon sites far from the Zn ions and a satellite structure corresponding to muons residing closer to the Zn. The temperature dependence indicates a strong loss of magnetic order for Cu moments near the Zn atoms. The data can be understood in terms of a model where a Zn ion not only introduces a vacancy in the magnetic Cu lattice but also creates a RKKY-type disturbance. The electron spin polarization around the Zn ions induces a change of the magnetic moments on surrounding Cu ions. The AF lattice is found to be strongly perturbed within a radius of 10 Angstrom around each Zn ion. Possible consequences for the superconductivity of the corresponding Sr-doped materials are discussed.
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| 4. |
- Enquist, Henrik, et al.
(författare)
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FemtoMAX - An X-ray beamline for structural dynamics at the short-pulse facility of MAX IV
- 2018
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Ingår i: Journal of Synchrotron Radiation. - 0909-0495. ; 25:2, s. 570-579
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Tidskriftsartikel (refereegranskat)abstract
- The FemtoMAX beamline facilitates studies of the structural dynamics of materials. Such studies are of fundamental importance for key scientific problems related to programming materials using light, enabling new storage media and new manufacturing techniques, obtaining sustainable energy by mimicking photosynthesis, and gleaning insights into chemical and biological functional dynamics. The FemtoMAX beamline utilizes the MAX IV linear accelerator as an electron source. The photon bursts have a pulse length of 100fs, which is on the timescale of molecular vibrations, and have wavelengths matching interatomic distances (Å). The uniqueness of the beamline has called for special beamline components. This paper presents the beamline design including ultrasensitive X-ray beam-position monitors based on thin Ce:YAG screens, efficient harmonic separators and novel timing tools.The FemtoMAX beamline facilitates studies of the structural dynamics of materials on the femtosecond timescale. The first commissioning results are presented.
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| 5. |
- Moberg, Christina, et al.
(författare)
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De unga gör helt rätt när de stämmer staten
- 2022
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Ingår i: Aftonbladet. - 1103-9000.
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- 1 620 forskare och lärare i forskarvärlden: Vi ställer oss bakom Auroras klimatkrav
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| 6. |
- Ryen, Øyvind, et al.
(författare)
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Strengthening mechanisms in solid solution aluminum alloys
- 2006
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Ingår i: Metallurgical and Materials Transactions. A. - : Springer Science and Business Media LLC. - 1073-5623 .- 1543-1940. ; 37A:6, s. 1999-2006
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Tidskriftsartikel (refereegranskat)abstract
- A number of commercial and high-purity non-heat-treatable aluminum alloys are investigated in this work. It is found that both magnesium and manganese in solid solution give a nearly linear concentration dependence of the strength at a given strain for commercial alloys. This deviates from high-purity AlMg binary alloys, where a parabolic concentration dependence is found. Mn in solid solution is found to give a considerably higher strengthening effect per atom than Mg, both in terms of yield stress and initial work hardening rate. This strengthening effect is stronger comparing commercial grades to high-purity alloys. This enhanced strengthening is believed to be a synergy or clustering effect caused by interaction between Mn atoms and trace elements, probably silicon, in solid solution.
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| 7. |
- Saarela, Svetlana, et al.
(författare)
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Comparing frameworks for biomass prediction for the Global Ecosystem Dynamics Investigation
- 2022
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Ingår i: Remote Sensing of Environment. - : Elsevier. - 0034-4257 .- 1879-0704. ; 278
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Tidskriftsartikel (refereegranskat)abstract
- NASA's Global Ecosystem Dynamics Investigation (GEDI) mission offers data for temperate and pan-tropical estimates of aboveground forest biomass (AGB). The spaceborne, full-waveform LiDAR from GEDI provides sample footprints of canopy structure, expected to cover about 4% of the land area following two years of operation. Several options are available for estimating AGB at different geographical scales. Using GEDI sample data alone, gridded biomass predictions are based on hybrid inference which correctly propagates errors due to the modeling and accounts for sampling variability, but this method requires at least two GEDI tracks in the area of interest. However, there are significant gaps in GEDI coverage and in some areas of interest GEDI data may need to be combined with other wall-to-wall remotely sensed (RS) data, such as those from multispectral or SAR sensors. In these cases, we may employ hierarchical model-based (HMB) inference that correctly considers the additional model errors that result from relating GEDI data to the wall-to-wall data. Where predictions are possible from both hybrid and HMB inference the question arises which framework to choose, and under what circumstances? In this paper, we make progress towards answering these questions by comparing the performance of the two prediction frameworks under conditions relevant for the GEDI mission. Conventional model-based (MB) inference with wall-to-wall TanDEM-X data was applied as a baseline prediction framework, which does not involve GEDI data at all. An important feature of the study was the comparison of AGB predictors in terms of both standard deviation (SD: the square root of variance) and root mean square error (RMSE: the square root of mean square error – MSE). Since, in model-based inference, the true AGB in an area of interest is a random variable, comparisons of the performance of prediction frameworks should preferably be made in terms of their RMSEs. However, in practice only the SD can be estimated based on empirical survey data, and thus it is important also to study whether or not the difference between the two uncertainty measures is small or large under conditions relevant for the GEDI mission. Our main findings were that: (i) hybrid and HMB prediction typically resulted in smaller RMSEs than conventional MB prediction although the difference between the three frameworks in terms of SD often was small; (ii) in most cases the difference between hybrid and HMB inference was small in terms of both RMSE and SD; (iii) the RMSEs for all frameworks was substantially larger than the SDs in small study areas whereas the two uncertainty measures were similar in large study areas, and; (iv) spatial autocorrelation of model residual errors had a large effect on the RMSEs of AGB predictors, especially in small study areas. We conclude that hybrid inference is suitable in most GEDI applications for AGB assessment, due to its simplicity compared to HMB inference. However, where GEDI data are sparse HMB inference should be preferred.
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| 8. |
- Uhlén, Mathias, et al.
(författare)
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A human protein atlas for normal and cancer tissues based on antibody proteomics
- 2005
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Ingår i: Molecular & Cellular Proteomics. - 1535-9476 .- 1535-9484. ; 4:12, s. 1920-1932
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Tidskriftsartikel (refereegranskat)abstract
- Antibody-based proteomics provides a powerful approach for the functional study of the human proteome involving the systematic generation of protein-specific affinity reagents. We used this strategy to construct a comprehensive, antibody-based protein atlas for expression and localization profiles in 48 normal human tissues and 20 different cancers. Here we report a new publicly available database containing, in the first version, similar to 400,000 high resolution images corresponding to more than 700 antibodies toward human proteins. Each image has been annotated by a certified pathologist to provide a knowledge base for functional studies and to allow queries about protein profiles in normal and disease tissues. Our results suggest it should be possible to extend this analysis to the majority of all human proteins thus providing a valuable tool for medical and biological research.
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| 9. |
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| 10. |
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| 11. |
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| 12. |
- Albrektson, Anna, 1966-, et al.
(författare)
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Cool Nature : Utopian Landscapes in Sweden 1780–1840
- 2022
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Ingår i: Sjuttonhundratal. - : UiT The Arctic University of Norway. - 1652-4772 .- 2001-9866. ; 19, s. 94-116
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Tidskriftsartikel (refereegranskat)abstract
- In this essay, an interdisciplinary group of researchers sets out to address the period 1780–1840 in Sweden in a new way, by placing nature at its centre. With the help of ecocritical and transcultural theory, combined with renewed attention to the Swedish fine arts, learned discourses, and practices, we suggest a new approach to these revolutionary decades. The perceived dissonance, the interplay between climatic conditions and cultural template in early modern and modern Sweden, has not been fully addressed in current research, despite the fact that the relationship between humankind and the environment is a central issue in contemporary society and scholarship. Representations of nature situate the nation, they negotiate the relationship between a sensed reality and an ideal, between human and more-than-human beings. We suggest a focus on the unpredictable space created by negotiations of nature in Swedish representations during this crucial period, and, furthermore, on the ways in which this creative space is charged with utopian possibilities in the early Anthropocene. This is the background and the driving force of the planned research project ‘Cool Nature: Utopian Landscapes in Sweden 1780–1840’.
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| 13. |
- Alhamdow, Ayman, et al.
(författare)
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Low-level exposure to polycyclic aromatic hydrocarbons is associated with reduced lung function among Swedish young adults
- 2021
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Ingår i: Environmental Research. - : Elsevier BV. - 0013-9351 .- 1096-0953. ; 197
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Tidskriftsartikel (refereegranskat)abstract
- Background: Exposure to polycyclic aromatic hydrocarbons (PAHs) has been linked to adverse pulmonary effects. However, the impact of low-level environmental PAH exposure on lung function in early adulthood remains uncertain. Objectives: To evaluate the associations between urinary PAH metabolites and lung function parameters in young adults. Methods: Urinary metabolites of pyrene, phenanthrene, and fluorene were analysed in 1000 young adults from Sweden (age 22–25 years) using LC-MS/MS. Lung function and eosinophilic airway inflammation were measured by spirometry and exhaled nitric oxide fraction (FeNO), respectively. Linear regression analysis was used to evaluate associations between PAH metabolites and the outcomes. Results: Median urinary concentrations of 1-OH-pyrene, ∑OH-phenanthrene, and ∑OH-fluorene were 0.066, 0.36, 0.22 μg/L, respectively. We found inverse associations of ∑OH-phenanthrene and ∑OH-fluorene with FEV1 and FVC, as well as between 1-OH-pyrene and FEV1/FVC ratio (adjusted P < 0.05; all participants). An increase of 1% in ∑OH-fluorene was associated with a decrease of 73 mL in FEV1 and 59 mL in FVC. In addition, ∑OH-phenanthrene concentrations were, in a dose-response manner, inversely associated with FEV1 (B from −109 to −48 compared with the lowest quartile of ∑OH-phenanthrene; p trend 0.004) and FVC (B from −159 to −102 compared with lowest quartile; p-trend <0.001). Similar dose-response associations were also observed between ∑OH-fluorene and FEV1 and FVC, as well as between 1-OH-pyrene and FEV1/FVC (p-trend <0.05). There was no association between PAH exposure and FeNO, nor was there an interaction with smoking, sex, or asthma. Conclusion: Low-level PAH exposure was, in a dose-response manner, associated with reduced lung function in young adults. Our findings have public health implications due to i) the widespread occurrence of PAHs in the environment and ii) the clinical relevance of lung function in predicting all-cause and cardiovascular disease mortality.
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| 14. |
- Ali, Sharafat, Associate Professor, 1976-, et al.
(författare)
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Optical and mechanical properties of amorphous Mg-Si-O-N thin films deposited by reactive magnetron sputtering
- 2019
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Ingår i: Surface & Coatings Technology. - : Elsevier. - 0257-8972 .- 1879-3347. ; 372:25, s. 9-15
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Tidskriftsartikel (refereegranskat)abstract
- In this work, amorphous thin films in Mg-Si-O-N system typically containing >15 at.% Mg and 35 at.% N were prepared in order to investigate especially the dependence of optical and mechanical properties on Mg composition. Reactive RF magnetron co-sputtering from magnesium and silicon targets were used for the deposition of Mg-Si-O-N thin films. Films were deposited on float glass, silica wafers and sapphire substrates in an Ar, N2 and O2 gas mixture. X-ray photoelectron spectroscopy, atomic force microscopy, scanning electron microscopy, spectroscopic ellipsometry, and nanoindentation were employed to characterize the composition, surface morphology, and properties of the films. The films consist of N and Mg contents up to 40 at.% and 28 at.%, respectively and have good adhesion to substrates and are chemically inert. The thickness and roughness of the films increased with increasing content of Mg. Both hardness (16–21 GPa) and reduced elastic modulus (120–176 GPa) are strongly correlated with the amount of Mg content. The refractive index up to 2.01 and extinction coefficient up to 0.18 were found to increase with Mg content. The optical band gap (3.1–4.3) decreases with increasing the Mg content. Thin film deposited at substrate temperature of 100 °C shows a lower value of hardness (10 GPa), refractive index (1.75), and higher values of reduced elastic modulus (124 GPa) as compared to the thin film deposited at 310 °C and 510 °C respectively, under identical synthesis parameters.
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| 15. |
- Alijan Farzad Lahiji, Faezeh, et al.
(författare)
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Growth and optical properties of NiO thin films deposited by pulsed dc reactive magnetron sputtering
- 2023
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Ingår i: Journal of Vacuum Science & Technology. A. Vacuum, Surfaces, and Films. - : A V S AMER INST PHYSICS. - 0734-2101 .- 1520-8559. ; 41:6
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Tidskriftsartikel (refereegranskat)abstract
- NiO thin films with varied oxygen contents are grown on Si(100) and c-Al2O3 at a substrate temperature of 300 degrees C using pulsed dc reactive magnetron sputtering. We characterize the structure and optical properties of NiO changes as functions of the oxygen content. NiO with the cubic structure, single phase, and predominant orientation along (111) is found on both substrates. X-ray diffraction and pole figure analysis further show that NiO on the Si(100) substrate exhibits fiber-textured growth, while twin domain epitaxy was achieved on c-Al2O3, with NiO(111) k Al2O3(0001) and NiO[1 (1) over bar0]k Al2O3[10 (1) over bar0] or NiO[(1) over bar 10]k Al2O3[2 (1) over bar(1) over bar0] epitaxial relationship. The oxygen content in NiO films did not have a significant effect on the refractive index, extinction coefficient, and absorption coefficient. This suggests that the optical properties of NiO films remained unaffected by changes in the oxygen content.
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| 16. |
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| 17. |
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| 18. |
- Amnå, Erik, 1950-, et al.
(författare)
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Our kids
- 2016
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 19. |
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| 20. |
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| 21. |
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| 22. |
- Barakitis, Nikos, et al.
(författare)
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Preconditioners for fractional diffusion equations based on the spectral symbol
- 2022
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Ingår i: Numerical Linear Algebra with Applications. - : John Wiley & Sons. - 1070-5325 .- 1099-1506. ; 29:5
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that the discretization of fractional diffusion equations with fractional derivatives , using the so-called weighted and shifted Grünwald formula, leads to linear systems whose coefficient matrices show a Toeplitz-like structure. More precisely, in the case of variable coefficients, the related matrix sequences belong to the so-called generalized locally Toeplitz class. Conversely, when the given FDE has constant coefficients, using a suitable discretization, we encounter a Toeplitz structure associated to a nonnegative function, called the spectral symbol, having a unique zero at zero of real positive order between one and two. For the fast solution of such systems by preconditioned Krylov methods, several preconditioning techniques have been proposed in both the one- and two-dimensional cases. In this article we propose a new preconditioner denoted bywhich belongs to the -algebra and it is based on the spectral symbol. Comparing with some of the previously proposed preconditioners, we show that although the low band structure preserving preconditioners are more effective in the one-dimensional case, the new preconditioner performs better in the more challenging multi-dimensional setting.
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| 23. |
- Barbarino, Giovanni, et al.
(författare)
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Matrix-Less Eigensolver for Large Structured Matrices
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Sequences of structured matrices of increasing size arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume as a working hypothesis that the eigenvalues of a matrix X_n belonging to a sequence of this kind are given by a regular expansion. Based on this working hypothesis, which is illustrated to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of X_n for large n and we provide a theoretical analysis of its convergence. The eigensolver is called matrix-less because it does not operate on the matrix X_n but on a few similar matrices of smaller size combined with an interpolation-extrapolation strategy. Its performance is benchmarked on several numerical examples, with a special focus on matrices arising from the discretization of differential problems.
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| 24. |
- Barbarino, Giovanni, et al.
(författare)
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Matrix-Less Eigensolver for Large Structured Matrices
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Sequences of structured matrices of increasing size arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume as a working hypothesis that the eigenvalues of a matrix X_n belonging to a sequence of this kind are given by a regular expansion. Based on the working hypothesis, which is proved to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of X_n for large n. The performance of the eigensolver—which is called matrix-less because it does not operate on the matrix X_n—is illustrated on several numerical examples, with a special focus on matrices arising from the discretization of differential problems, and turns out to be quite satisfactory in all cases. In a sense, this is an a posteriori proof of the reasonableness of the working hypothesis as well as a testimony of the fact that the spectra of large structured matrices are much more “regular” than one might expect.
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| 25. |
- Bargholtz, Chr., et al.
(författare)
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Measurement of the eta -> pi(+)pi(-)e(+)e(-) decay branching ratio
- 2007
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Ingår i: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 644:5-6, s. 299-303
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Tidskriftsartikel (refereegranskat)abstract
- The reaction pd -> He-3 eta at threshold was used to provide a clean source of eta mesons for decay studies with the WASA detector at CELSIUS. The branching ratio of the decay eta -> pi(+)pi(-)e(+)e(-) is measured to be (4.3 +/- 1.3 +/- 0.4) x 10(-4).
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| 26. |
- Bayraktar, Erhan, et al.
(författare)
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Disorder detection with costly observations
- 2022
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Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:2, s. 338-349
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Tidskriftsartikel (refereegranskat)abstract
- We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fixed point of a certain jump operator, and we determine the optimal strategy.
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| 27. |
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| 28. |
- Berggren, Martin, et al.
(författare)
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A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method
- 2009
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Ingår i: Communications in Computational Physics. - 1815-2406. ; 5:2-4, s. 456-468
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Tidskriftsartikel (refereegranskat)abstract
- The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at lowest order. However, many of today's CFD codes use a vertex-centered FV method in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the method successfully handles shocks. We also discuss how to extend the FV edge-based data structure to support the new scheme. In this way, it will in principle be possible to extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.
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| 29. |
- Berlowski, M., et al.
(författare)
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Measurement of eta meson decays into lepton-antilepton pairs
- 2008
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Ingår i: Physical Review D. Particles and fields. - : American Physical Society. - 0556-2821 .- 1089-4918. ; 77:3, s. 032004-
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Tidskriftsartikel (refereegranskat)abstract
- A search for rare lepton decays of the eta meson was performed using the WASA detector at CELSIUS. Two candidates for double Dalitz decay eta -> e(+)e(-)e(+)e(-) events are reported with a background of 1.3 +/- 0.2 events. This allows to set an upper limit to the branching ratio of 9.7x10(-5) (90% CL). The branching ratio for the decay eta -> e(+)e(-)gamma is determined to (7.8 +/- 0.5(stat)+/- 0.8(syst))x10(-3) in agreement with world average value. An upper limit (90% CL) for the branching ratio for the eta -> e(+)e(-) decay is 2.7x10(-5) and a limit for the sum of the eta ->mu(+)mu(-)mu(+)mu(-) and eta ->pi(+)pi(-)mu(+)mu(-) decays is 3.6x10(-4).
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| 30. |
- Björkander, Sophia, et al.
(författare)
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SARS-CoV-2-specific B- and T-cell immunity in a population-based study of young Swedish adults
- 2022
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Ingår i: Journal of Allergy and Clinical Immunology. - : Elsevier BV. - 0091-6749 .- 1097-6825. ; 149:1, s. 65-75
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Tidskriftsartikel (refereegranskat)abstract
- Background: Young adults are now considered major spreaders of coronavirus disease 2019 (COVID-19) disease. Although most young individuals experience mild to moderate disease, there are concerns of long-term adverse health effects. The impact of COVID-19 disease and to which extent population-level immunity against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) exists in young adults remain unclear.Objective: We conducted a population-based study on humoral and cellular immunity to SARS-CoV-2 and explored COVID-19 disease characteristics in young adults.Methods: We invited participants from the Swedish BAMSE (Barn [Children], Allergy Milieu, Stockholm, Epidemiology) birth cohort (age 24-27 years) to take part in a COVID-19 followup. From 980 participants (October 2020 to June 2021), we here present data on SARS-CoV-2 receptor-binding domain-specific IgM, IgA, and IgG titers measured by ELISA and on symptoms and epidemiologic factors associated with seropositivity. Further, SARS-CoV-2-specific memory B-and T-cell responses were detected for a subpopulation (n 5 108) by ELISpot and FluoroSpot.Results: A total of 28.4% of subjects were seropositive, of whom 18.4% were IgM single positive. One in 7 seropositive subjects was asymptomatic. Seropositivity was associated with use of public transport, but not with sex, asthma, rhinitis, IgE sensitization, smoking, or body mass index. In a subset of representative samples, 20.7% and 35.0% had detectable SARSCoV-2 specific B-and T-cell responses, respectively. B-and T-cell memory responses were clearly associated with seropositivity, but T-cell responses were also detected in 17.2% of seronegative subjects.Conclusions: Assessment of IgM and T-cell responses may improve population-based estimations of SARS-CoV-2 infection. The pronounced surge of both symptomatic and asymptomatic infections among young adults indicates that the large-scale vaccination campaign should be continued. (J Allergy Clin Immunol 2022;149:65-75.)
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| 31. |
- Bogoya, Manuel, et al.
(författare)
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Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory
- 2022
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Ingår i: Numerical Algorithms. - : Springer Nature. - 1017-1398 .- 1572-9265. ; :91, s. 1653-1676
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Tidskriftsartikel (refereegranskat)abstract
- Under appropriate technical assumptions, the simple-loop theory allows to derive various types of asymptotic expansions for the eigenvalues of Toeplitz matrices generated by a function f. Independently and under the milder hypothesis that f is even and monotone over [0,π], matrix-less algorithms have been developed for the fast eigenvalue computation of large Toeplitz matrices, within a linear complexity in the matrix order: behind the high efficiency of such algorithms there are the expansions predicted by the simple-loop theory, combined with the extrapolation idea. Here we focus our attention on a change of variable, followed by the asymptotic expansion of the new variable, and we adapt the matrix-less algorithm to the considered new setting. Numerical experiments show a higher precision (till machine precision) and the same linear computation cost, when compared with the matrix-less procedures already presented in the relevant literature. Among the advantages, we concisely mention the following: (a) when the coefficients of the simple-loop function are analytically known, the algorithm computes them perfectly; (b) while the proposed algorithm is better or at worst comparable to the previous ones for computing the inner eigenvalues, it is vastly better for the computation of the extreme eigenvalues; a mild deterioration in the quality of the numerical experiments is observed when dense Toeplitz matrices are considered, having generating function of low smoothness and not satisfying the simple-loop assumptions.
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| 32. |
- Bogoya, Manuel, et al.
(författare)
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Matrix-less methods for the spectral approximation of large non-Hermitian Toeplitz matrices : A concise theoretical analysis and a numerical study
- 2024
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Ingår i: Numerical Linear Algebra with Applications. - : Wiley. - 1070-5325 .- 1099-1506.
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Tidskriftsartikel (refereegranskat)abstract
- It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non-Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non-Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix-size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects; for example, non-Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high-precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.
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| 33. |
- Bolten, Matthias, et al.
(författare)
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A note on the spectral analysis of matrix sequences via GLT momentary symbols : from all-at-once solution of parabolic problems to distributed fractional order matrices
- 2023
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Ingår i: Electronic Transactions on Numerical Analysis. - : Osterreichische Akademie der Wissenschaften, Verlag. - 1068-9613. ; 58, s. 136-163
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Tidskriftsartikel (refereegranskat)abstract
- The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization of a parabolic diffusion problem using a space-time grid and secondly from the approximation of distributed-order fractional equations. For this purpose we use the classical GLT theory and the new concept of GLT momentary symbols. The first permits us to describe the singular value or eigenvalue asymptotic distribution of the sequence of the coefficient matrices. The latter permits us to derive a function that describes the singular value or eigenvalue distribution of the matrix of the sequence, even for small matrix sizes, but under given assumptions. The paper is concluded with a list of open problems, including the use of our machinery in the study of iteration matrices, especially those concerning multigrid-type techniques.
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| 34. |
- Bolten, Matthias, et al.
(författare)
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Toeplitz momentary symbols : definition, results, and limitations in the spectral analysis of structured matrices
- 2022
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 651, s. 51-82
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Tidskriftsartikel (refereegranskat)abstract
- A powerful tool for analyzing and approximating the singular values and eigenvalues of structured matrices is the theory of Generalized Locally Toeplitz (GLT) sequences. By the GLT theory one can derive a function, called the symbol, which describes the singular value or the eigenvalue distribution of the sequence, the latter under precise assumptions. However, for small values of the matrix-size of the considered sequence, the approximations may not be as good as it is desirable, since in the construction of the GLT symbol one disregards small norm and low-rank perturbations. On the other hand, Local Fourier Analysis (LFA) can be used to construct polynomial symbols in a similar manner for discretizations, where the geometric information is present, but the small norm perturbations are retained. The main focus of this paper is the introduction of the concept of sequence of "Toeplitz momentary symbols", associated with a given sequence of truncated Toeplitz-like matrices. We construct the symbol in the same way as in the GLT theory, but we keep the information of the small norm contributions. The low-rank contributions are still disregarded, and we give an idea on the reason why this is negligible in certain cases and why it is not in other cases, being aware that in presence of high nonnormality the same low-rank perturbation can produce a dramatic change in the eigenvalue distribution. Moreover, a difference with respect to the LFA symbols is that GLT symbols and Toeplitz momentary symbols are more general -just Lebesgue measurable -and are applicable to a larger class of matrices, while in the LFA setting only trigonometric polynomials are considered and more specifically those related to the approximation stencils. We show the applicability of the approach which leads to higher accuracy in some cases, when approximating the singular values and eigenvalues of Toeplitz-like matrices using Toeplitz momentary symbols, compared with the GLT symbol. Finally, since for many applications and their analysis it is often necessary to consider non-square Toeplitz matrices, we formalize and provide some useful definitions, applicable for non-square Toeplitz momentary symbols.
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| 35. |
- Brandström, Josef, et al.
(författare)
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Individually dosed omalizumab facilitates peanut oral immunotherapy in peanut allergic adolescents
- 2019
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Ingår i: Clinical and Experimental Allergy. - : Wiley. - 0954-7894 .- 1365-2222. ; 49:10, s. 1328-1341
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Tidskriftsartikel (refereegranskat)abstract
- Background: Peanut oral immunotherapy (pOIT) has showed good short-term outcomes, but allergic reactions may prevent effective up-dosing and is a major cause of stopping OIT. In placebo-controlled trials, omalizumab has been shown to facilitate allergen immunotherapy and increase tolerance to peanut.Objective: We hypothesized that by combining omalizumab with pOIT, and monitor treatment effects with basophil allergen threshold sensitivity tests (CD-sens), peanut allergic patients could safely initiate pOIT and thereafter slowly withdraw omalizumab.Methods: This is the 2nd part of a one-armed open phase-2 study where peanut allergic adolescents (n = 23) started pOIT after an individualized omalizumab treatment. The pOIT dose was increased from 280 to 2800 mg peanut protein in 8 weeks followed by an individualized step-wise withdrawal of omalizumab, based on clinical symptoms and CD-sens levels. pOIT continued for 12 weeks followed by an open peanut challenge. Peanut CD-sens and allergen-binding activity (ABA) and IgE-ab, IgG-ab and IgG4-ab to peanut and its components were measured during the study.Results: All 23 patients successfully reached the 2800 mg maintenance dose. Moderate/systemic allergic reactions were rare while receiving full-dose omalizumab. Eleven of 23 (48%) successfully continued with pOIT after omalizumab was stopped. Compared to treatment failures, median baseline IgE-ab to peanut components Ara h 1-3 and CD-sens to peanut were significantly lower among successfully treated patients and IgG4-ab to peanut, Ara h 2 and 6 increased significantly more during treatment.Conclusions and clinical relevance: This study indicates that omalizumab is an effective adjunctive therapy for initiation and rapid up-dosing of pOIT; however, adverse events from pOIT become more frequent as omalizumab doses are decreased.
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| 36. |
- Brijs, Jeroen, et al.
(författare)
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Cardiac remodeling and increased central venous pressure underlie elevated stroke volume and cardiac output of seawater-acclimated rainbow trout
- 2017
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Ingår i: American Journal of Physiology - Regulatory Integrative and Comparative Physiology. - : American Physiological Society. - 0363-6119 .- 1522-1490. ; 312:1
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Tidskriftsartikel (refereegranskat)abstract
- © 2017 the American Physiological Society.Substantial increases in cardiac output (CO), stroke volume (SV), and gastrointestinal blood flow are essential for euryhaline rainbow trout (Oncorhyncus mykiss) osmoregulation in seawater. However, the underlying hemodynamic mechanisms responsible for these changes are unknown. By examining a range of circulatory and cardiac morphological variables of seawater-and freshwater-acclimated rainbow trout, the present study revealed a significantly higher central venous pressure (CVP) in seawater-acclimated trout (~0.09 vs. -0.02 kPa). This serves to increase cardiac end-diastolic volume in seawater and explains the elevations in SV (~0.41 vs. 0.27 ml/kg) and CO (~21.5 vs. 14.2 ml·min-1·kg-1) when compared with trout in freshwater. Furthermore, these hemodynamic modifications coincided with a significant increase in the proportion of compact myocardium, which may be necessary to compensate for the increased wall tension associated with a larger stroke volume. Following a temperature increase from 10 to 16.5°C, both acclimation groups exhibited similar increases in heart rate (Q10 of ~2), but SV tended to decrease in seawater-acclimated trout despite the fact that CVP was maintained in both groups. This resulted in CO of seawaterand freshwater-acclimated trout stabilizing at a similar level after warming (~26 ml·min-1·kg-1). The consistently higher CVP of seawater-acclimated trout suggests that factors other than compromised cardiac filling constrained the SV and CO of these individuals at high temperatures. The present study highlights, for the first time, the complex interacting effects of temperature and water salinity on cardiovascular responses in a euryhaline fish species.
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| 37. |
- Brijs, Jeroen, et al.
(författare)
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Cardiorespiratory upregulation during seawater acclimation in rainbow trout: effects on gastrointestinal perfusion and postprandial responses
- 2016
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Ingår i: American Journal of Physiology-Regulatory Integrative and Comparative Physiology. - : American Physiological Society. - 0363-6119 .- 1522-1490. ; 310:9
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Tidskriftsartikel (refereegranskat)abstract
- Increased gastrointestinal blood flow is essential for euryhaline fishes to maintain osmotic homeostasis during the initial phase of a transition from freshwater to seawater. However, the cardiorespiratory responses and hemodynamic changes required for a successful long-term transition to seawater remain largely unknown. In the present study, we simultaneously measured oxygen consumption rate ((M)over dot(O2)), cardiac output (CO), heart rate (HR), and gastrointestinal blood flow (GBF) in rainbow trout (Oncorhynchus mykiss) acclimated to either freshwater or seawater for at least 6 wk. Seawater-acclimated trout displayed significantly elevated ((M)over dot(O2)) (day: 18%, night: 19%), CO (day: 22%, night: 48%), and GBF (day: 96%, night: 147%), demonstrating that an overall cardiorespiratory upregulation occurs during seawater acclimation. The elevated GBF was achieved via a combination of increased CO, mediated through elevated stroke volume (SV), and a redistribution of blood flow to the gastrointestinal tract. Interestingly, virtually all of the increase in CO of seawater-acclimated trout was directed to the gastrointestinal tract. Although unfed seawater-acclimated trout displayed substantially elevated cardiorespiratory activity, the ingestion of a meal resulted in a similar specific dynamic action (SDA) and postprandial GBF response as in freshwater-acclimated fish. This indicates that the capacity for the transportation of absorbed nutrients, gastrointestinal tissue oxygen delivery, and acid-base regulation is maintained during digestion in seawater. The novel findings presented in this study clearly demonstrate that euryhaline fish upregulate cardiovascular function when in seawater, while retaining sufficient capacity for the metabolic and cardiovascular changes associated with the postprandial response.
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| 38. |
- Brijs, Jeroen, et al.
(författare)
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Experimental manipulations of tissue oxygen supply do not affect warming tolerance of European perch
- 2015
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Ingår i: Journal of Experimental Biology. - : The Company of Biologists. - 0022-0949 .- 1477-9145. ; 218, s. 2448-2454
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Tidskriftsartikel (refereegranskat)abstract
- A progressive inability of the cardiorespiratory system to maintain systemic oxygen supply at elevated temperatures has been suggested to reduce aerobic scope and the upper thermal limit of aquatic ectotherms. However, few studies have directly investigated the dependence of thermal limits on oxygen transport capacity. By manipulating oxygen availability (via environmental hyperoxia) and blood oxygen carrying capacity (via experimentally-induced anemia) in European perch (Perca fluviatilis, Linneaus), we investigated the effects of oxygen transport capacity on aerobic scope and the critical thermal maximum (CTmax). Hyperoxia resulted in a two-fold increase in aerobic scope at the control temperature of 23°C, but this did not translate to an elevated CTmax in comparison with control fish (34.6±0.1°C vs. 34.0±0.5°C, respectively). Anemia (∼43% reduction in haemoglobin concentration) did not cause a reduction in aerobic scope nor CTmax (33.8±0.3°C) compared with control fish. Additionally, oxygen consumption rates of anemic perch during thermal ramping increased in a similar exponential manner as in control fish, highlighting that perch have an impressive capacity to compensate for a substantial reduction in blood oxygen carrying capacity. Taken together, these results indicate that oxygen limitation is not a universal mechanism determining the CTmax of fishes.
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| 39. |
- Brijs, Jeroen, et al.
(författare)
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Increased mitochondrial coupling and anaerobic capacity minimizes aerobic costs of trout in the sea
- 2017
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 7
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Tidskriftsartikel (refereegranskat)abstract
- Anadromy is a distinctive life-history strategy in fishes that has evolved independently many times. In an evolutionary context, the benefits of anadromy for a species or population must outweigh the costs and risks associated with the habitat switch. The migration of fish across the freshwater-ocean boundary coincides with potentially energetically costly osmoregulatory modifications occurring at numerous levels of biological organization. By integrating whole animal and sub-cellular metabolic measurements, this study presents significant findings demonstrating how an anadromous salmonid (i.e. rainbow trout, Oncorhynchus mykiss) is able to transform from a hyper- to hypo-osmoregulatory state without incurring significant increases in whole animal oxygen consumption rate. Instead, underlying metabolic mechanisms that fuel the osmoregulatory machinery at the organ level (i.e. intestine) are modulated, as mitochondrial coupling and anaerobic metabolism are increased to satisfy the elevated energetic demands. This may have positive implications for the relative fitness of the migrating individual, as aerobic capacity may be maintained for locomotion (i.e. foraging and predator avoidance) and growth. Furthermore, the ability to modulate mitochondrial metabolism in order to maintain osmotic balance suggests that mitochondria of anadromous fish may have been a key target for natural selection, driving species adaptations to different aquatic environments.
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| 40. |
- Brijs, J., et al.
(författare)
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Prevalence and severity of cardiac abnormalities and arteriosclerosis in farmed rainbow trout (Oncorhynchus mykiss)
- 2020
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Ingår i: Aquaculture. - : Elsevier BV. - 0044-8486 .- 1873-5622. ; 526
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Tidskriftsartikel (refereegranskat)abstract
- Cardiovascular disease may pose a major threat to the health and welfare of farmed fish. By investigating a range of established cardiovascular disease indicators, we aimed to determine the prevalence, severity and consequences of this affliction in farmed rainbow trout (Oncorhynchus mykiss) from an open cage farm in the Baltic Sea, an open cage farm in a freshwater lake, and a land-based recirculating aquaculture system. We also aimed to identify environmental, anthropogenic and physiological factors contributing towards the development of the disease. The majority of trout possessed enlarged hearts with rounded ventricles (mean height:width ratios of 1.0–1.1 c.f. ~1.3 in wild fish) and a high degree of vessel misalignment (mean angles between the longitudinal ventricular axis and the axis of the bulbus arteriosus of 28–31 °c.f. ~23° in wild fish). The prevalence and severity of coronary arteriosclerosis was also high, as 92–100% of fish from the different aquaculture facilities exhibited coronary lesions. Mean lesion incidence and severity indices were 67–95% and 3.1–3.9, respectively, which resulted in mean coronary arterial blockages of 19–32%. To evaluate the functional significance of these findings, we modelled the effects of arterial blockages on coronary blood flow and experimentally tested the effects of coronary occlusion in a sub-sample of fish. The observed coronary blockages were estimated to reduce coronary blood flow by 34–54% while experimental coronary occlusion adversely affected the electrocardiogram of trout. Across a range of environmental (water current, predation), anthropogenic (boat traffic intensity, hatchery of origin, brand of feed pellets) and physiological factors (condition factor, haematological and plasma indices), the hatchery of origin was the main factor contributing towards the observed variation in the development of cardiovascular disease. Therefore, further research on the effects of selective breeding programs and rearing strategies on the development of cardiovascular disease is needed to improve the welfare and health of farmed fish. © 2020 The Authors
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| 41. |
- Chen, Minghua, et al.
(författare)
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A Multigrid method for nonlocal problems : non-diagonally dominant Toeplitz-plus-tridiagonal systems
- 2020
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Ingår i: SIAM Journal on Matrix Analysis and Applications. - 0895-4798 .- 1095-7162. ; 41:4, s. 1546-1570
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Tidskriftsartikel (refereegranskat)abstract
- Nonlocal problems have been used to model very different applied scientific phenomena which involve the fractional Laplacian when one looks at the Lévy processes and stochastic interfaces. This paper deals with the nonlocal problems on a bounded domain where the stiffness matrices of the resulting systems are Toeplitz plus tridiagonal or far from being diagonally dominant as occurs when dealing with linear finite element approximations. By exploiting a weakly diagonally dominant Toeplitz property of the stiffness matrices, the optimal convergence of the two-grid method is well established in [Fiorentino and Serra-Capizzano, SIAM J. Sci. Comput., 17 (1996), pp. 1068–1081; Chen and Deng, SIAM J. Matrix Anal. Appl., 38 (2017), pp. 869–890], and there are still questions about the best ways to define the coarsening and interpolation operators when the stiffness matrix is far from being weakly diagonally dominant [Stüben, J. Comput. Appl. Math., 128 (2001), pp. 281–309]. In this work, using spectral indications from our analysis of the involved matrices, the simple (traditional) restriction operator and prolongation operator are employed in order to handle general algebraic systems which are neither Toeplitz nor weakly diagonally dominant corresponding to the fractional Laplacian kernel and the constant kernel, respectively. We focus our efforts on providing the detailed proof of the convergence of the two-grid method for such situations. Moreover, the convergence of the full multigrid is also discussed with the constant kernel. The numerical experiments are performed to verify the convergence with only O(NlogN) complexity by the fast Fourier transform, where N is the number of the grid points.
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| 42. |
- Coco, Armando, et al.
(författare)
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Spectral and norm estimates for matrix-sequences arising from a finite difference approximation of elliptic operators
- 2023
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 667, s. 10-43
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Tidskriftsartikel (refereegranskat)abstract
- When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for matrix-sequences arising from the approximation of the Laplacian via ad hoc finite differences. The analysis involves several tools from matrix theory and in particular from the setting of Toeplitz operators and Generalized Locally Toeplitz matrix-sequences. Several numerical experiments are conducted, which confirm the correctness of the theoretical findings.
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| 43. |
- Dahl, Viktor, 1979-
(författare)
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Breaking the law : adolescents' involvement in illegal political activitiy
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Illegal political activity has always been part of a democratic society. Despite this, not much is known about young people’s involvement in these political activities. Research portrays political influence attempts of this kind in different terms; as troublesome for the democratic political system, as expressions of conscious decisions vital for humanity’s future, and yet other times as illustrations of a coming-of-age rebellion. Overall there is a lack of collective knowledge on illegal political activity, and especially in adolescence – the age period when these political activities seem to peak.The aim of this dissertation is therefore to enhance knowledge of involvement in illegal political activity in adolescence. This dissertation addresses this task in four empirical studies. Results show that mostly boys engage politically with illegal political means. Adolescents involved are also interested in politics, believe in their own abilities to take part in political activities, have long-term political goals, and approve of violent political tactics. In addition, these activities also seem to associate with a challenge of authority. This could be seen in how political dissatisfaction was translated into illegal political activity, and in the way these activities seemed to be reactions to a non legitimized parental authority. Besides authority challenges, these activities are likely the result of important peer relations; influences from peers with experiences of illegal political activity seem to be a most probable answer to why adolescents adopt these political means. Taken together, the results of this dissertation show that adolescents involved in illegal political activity are well-equipped for political involvement, challenge authorities in most contexts of their lives, and are likely to adopt these political means from already involved peers.
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| 44. |
- Dareiotis, Konstantinos, et al.
(författare)
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Density symmetries for a class of 2-D diffusions with applications to finance
- 2019
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Ingår i: Stochastic Processes and their Applications. - : ELSEVIER SCIENCE BV. - 0304-4149 .- 1879-209X. ; 129:2, s. 452-472
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Tidskriftsartikel (refereegranskat)abstract
- We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding forward Kolmogorov equation problematic. We overcome this by extending a classical symmetry result for densities of one-dimensional diffusions to our case, thereby reducing the study of forward equations with exploding boundary data to the study of a related backward equation with non-exploding boundary data. We also discuss applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models. (C) 2018 Elsevier B.V. All rights reserved.
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| 45. |
- De Angelis, Tiziano, et al.
(författare)
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Dynkin Games with Incomplete and Asymmetric Information
- 2022
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Ingår i: Mathematics of Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0364-765X .- 1526-5471. ; 47:1, s. 560-586
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Tidskriftsartikel (refereegranskat)abstract
- We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian setup, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result that allows us to find the value of the game and players' optimal strategies by solving suitable quasi-variational inequalities with some nonstandard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.
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| 46. |
- De Angelis, Tiziano, et al.
(författare)
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Playing with ghosts in a Dynkin game
- 2020
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Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149 .- 1879-209X. ; 130:10, s. 6133-6156
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of two-player optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that if the underlying process is a R-d-valued, continuous, strong Markov process, and the stopping payoff is a continuous function (with mild integrability properties) there exists a Nash equilibrium in randomised stopping times for the game. Moreover, the equilibrium strategies and the expected payoffs of the two players are computed explicitly in terms of the corresponding one-player game. To the best of our knowledge this is the first paper to address this version of Dynkin games.
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| 47. |
- De Angelis, Tiziano, et al.
(författare)
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The dividend problem with a finite horizon
- 2017
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Ingår i: The Annals of Applied Probability. - : INST MATHEMATICAL STATISTICS. - 1050-5164 .- 2168-8737. ; 27:6, s. 3525-3546
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Tidskriftsartikel (refereegranskat)abstract
- We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0 and created at a rate proportional to its local time.
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| 48. |
- De Angelis, Tiziano, et al.
(författare)
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The maximality principle in singular control with absorption and its applications to the dividend problem
- 2024
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 62:1, s. 91-117
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
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| 49. |
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| 50. |
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