| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain
- 1992
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In: Mathematical Models and Methods in Applied Science. ; 2:3, s. 317-338
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Journal article (peer-reviewed)abstract
- We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
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| 2. |
- Riise, Gerdt C., 1956, et al.
(author)
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The intrabronchial microbial flora in chronic bronchitis patients: a target for N-acetylcysteine therapy?
- 1994
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In: Eur Respir J. - 0903-1936. ; 7:1, s. 94-101
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Journal article (peer-reviewed)abstract
- Chronic bronchitis is common among smokers, often together with recurrent infectious exacerbations. Streptococcus pneumoniae and Haemophilus influenzae are the pathogens traditionally considered most important. N-acetylcysteine (NAC) treatment has been shown to reduce the number of infectious exacerbations in patients with chronic bronchitis. The mechanism behind this is unknown. We attempted to characterize the intrabronchial bacterial flora in patients with chronic bronchitis in an infection-free interval, and to determine whether pharmacological and immunological factors effected the bacterial occurrence. Twenty two smokers with non-obstructive chronic bronchitis, 19 smokers with chronic bronchitis and chronic obstructive pulmonary disease (COPD) and 14 healthy nonsmokers underwent bronchoscopy. To obtain uncontaminated intrabronchial samples, a protected specimen brush was used. Quantitative bacterial cultures and virus isolations were performed. Significantly positive bacterial cultures (> 1,000 colony-forming units (cfu).ml-1) were found only in the patients. S. pneumoniae and H. influenzae were found in five patients, and only in the patients without NAC treatment. The most common bacterium was alpha-haemolytic streptococcus. Negative cultures were more common in the healthy controls. Of the various factors examined, only NAC medication had an influence on bacterial numbers. Significantly fewer patients with NAC medication had positive cultures (3 out of 16) than in the group of patients without NAC therapy (15 out of 21). Our results confirm that chronic bronchitis in smokers leads to increased intrabronchial bacterial colonization. We could also confirm that 1,000 cfu.ml-1 is an adequate cut-off level for significant bacterial growth when using the protected specimen brush. NAC medication was associated with low bacterial numbers.
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| 5. |
- Adolfsson, Klas, 1972, et al.
(author)
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Discretization of integro-differential equations modeling dynamic fractional order viscoelasticity
- 2006
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In: Lecture Notes in Computer Science, Springer, ''Proceedings of Large-Scale Scientific Computations, 2005, Sozopol, Bulgaria'', I. Lirkov, S. Margenov, and J. Wasniewski (Eds.). - 3540319948 ; 3743, s. 76-83
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Conference paper (peer-reviewed)abstract
- We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integro-differential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equation of motion. These are then used to prove a priori error estimates. A numerical experiment is included.
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| 9. |
- Agapiou, Sergios, et al.
(author)
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Posterior consistency of the Bayesian approach to linear ill-posed inverse problems
- 2012
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In: arXiv:1203.5753v2 [math.ST]. ; :1203.5753, s. 1-30
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Other publication (other academic/artistic)abstract
- We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting, with Gaussian prior and noise distribution. A method of identifying the posterior distribution using its precision operator is presented. Work- ing with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to study posterior con- sistency in a frequentist sense, and in particular to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. We show how these rates may be optimized by a choice of the scale parameter in the prior covariance operator. Our methods assume a relatively weak relation between the prior covariance operator, the forward operator and the noise covariance operator; more precisely, we assume that appropriate powers of these operators induce equivalent norms. We compare our results to known minimax rates of convergence in the case where the forward operator and the prior and noise covariances are all simultaneously diagonaliz- able, and confirm that the PDE method provides the same rates for a wide range of parameters. An elliptic PDE inverse problem is used to illustrate the power of the general theory.
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| 10. |
- Agapiou, Sergios, et al.
(author)
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Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
- 2013
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In: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 123:10, s. 3828-3860
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Journal article (peer-reviewed)abstract
- We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.
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