| 1. |
- Byström, Johan, et al.
(författare)
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Some computational aspects of iterated structures
- 2001
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Ingår i: Composites Part B. - 1359-8368 .- 1879-1069. ; 32:6, s. 485-490
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Tidskriftsartikel (refereegranskat)abstract
- We consider some computational aspects of effective properties for some multi-scale structures. In particular, we discuss iterated square honeycombs and another type of square honeycombs containing up to 4000 small discs randomly distributed inside each square. We present some numerical methods for estimating the effective conductivity with good control of the accuracy.
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| 2. |
- Ihre, Johan, 1707-1780
(författare)
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Dissertatio politica, de jure civitatis circa hæreses, quam, ... sub moderamine, ... Johannis Ihre, ... pro gradu publicæ disquisitioni modeste submittit S. R. M. Alumnus. Johannes Helsing, Gothlandus, In Audit. Gustaviano. D. XI. Junii, anni MDCCLV. H. P. M. S.
- 1755
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)
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| 3. |
- Barrett, Jennifer H., et al.
(författare)
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Fine mapping of genetic susceptibility loci for melanoma reveals a mixture of single variant and multiple variant regions
- 2015
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Ingår i: International Journal of Cancer. - : Wiley. - 0020-7136 .- 1097-0215. ; 136:6, s. 1351-1360
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Tidskriftsartikel (refereegranskat)abstract
- At least 17 genomic regions are established as harboring melanoma susceptibility variants, in most instances with genome-wide levels of significance and replication in independent samples. Based on genome-wide single nucleotide polymorphism (SNP) data augmented by imputation to the 1,000 Genomes reference panel, we have fine mapped these regions in over 5,000 individuals with melanoma (mainly from the GenoMEL consortium) and over 7,000 ethnically matched controls. A penalized regression approach was used to discover those SNP markers that most parsimoniously explain the observed association in each genomic region. For the majority of the regions, the signal is best explained by a single SNP, which sometimes, as in the tyrosinase region, is a known functional variant. However in five regions the explanation is more complex. At the CDKN2A locus, for example, there is strong evidence that not only multiple SNPs but also multiple genes are involved. Our results illustrate the variability in the biology underlying genome-wide susceptibility loci and make steps toward accounting for some of the missing heritability. What's new? In genome-wide association studies, researchers identify genetic variants that frequently associate with a particular disease, though the variants identified may not contribute to the molecular cause of the disease. This study took a closer look at 17 regions associated with melanoma, fine mapping the regions both in people with melanoma and in healthy controls. Though single SNPs account for the association in some regions, they found that in a few regions, several SNPs - and possibly multiple genes - contributed to the association signal. These findings illustrate the importance of not overlooking the interaction between multiple genetic markers when conducting such studies.
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| 4. |
- Choi, Doosung, et al.
(författare)
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Inverse Problem for a Planar Conductivity Inclusion*
- 2023
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Ingår i: SIAM Journal on Imaging Sciences. - 1936-4954. ; 16:2, s. 969-995
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous inclusion with arbitrary constant conductivity. The primary outcome of recovering a homogeneous inclusion is an inversion formula in terms of the GPTs for conformal mapping coefficients associated with the inclusion. To prove the formula, we establish matrix factorizations for the GPTs.
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| 5. |
- Choi, Doo Sung, et al.
(författare)
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Corner effects on the perturbation of an electric potential
- 2018
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 78:3, s. 1577-1601
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Tidskriftsartikel (refereegranskat)abstract
- We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coeffcients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, the Nystrom discretization, and recursively compressed inverse preconditioning.
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| 6. |
- Didenko, Victor, et al.
(författare)
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Approximate solution of boundary integral equations for biharmonic problems in non-smooth domains
- 2013
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Ingår i: Proceedings in Applied Mathematics and Mechanics. - : Wiley. - 1617-7061. ; 13:1, s. 435-438
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Konferensbidrag (refereegranskat)abstract
- This paper deals with approximate solutions to integral equations arising in boundary value problems for the biharmonic equation in simply connected piecewise smooth domains. The approximation method considered demonstrates excellent convergence even in the case of boundary conditions discontinuous at corner points. In an application we obtain very accurate approximations for some characteristics of two-dimensional Stokes flow in non-smooth domains.
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| 7. |
- Didenko, Victor D., et al.
(författare)
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On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners
- 2013
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 51:3, s. 1757-1776
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Tidskriftsartikel (refereegranskat)abstract
- The stability of the Nystrom method for the Muskhelishvili equation on piecewise smooth simple contours Gamma is studied. It is shown that in the space L-2 the method is stable if and only if certain operators A tau(j) from an algebra of Toeplitz operators are invertible. The operators A tau(j) depend on the parameters of the equation considered, on the opening angles theta(j) of the corner points t(j) is an element of Gamma, and on parameters of the approximation method mentioned. Numerical experiments show that there are opening angles where the operators A tau(j) are noninvertible. Therefore, for contours with such corners the method under consideration is not stable. Otherwise, the method is always stable. Numerical examples show an excellent convergence of the method.
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| 8. |
- Didenko, Victor, et al.
(författare)
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Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Contours
- 2011
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Ingår i: East Asian Journal on Applied Mathematics. - : Global Science Press. - 2079-7370 .- 2079-7362. ; 1:4, s. 403-414
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Tidskriftsartikel (refereegranskat)abstract
- The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$, it is found that there are $8$ values of $\theta_j$ where the invertibility of the operator $A_{c_j}$ may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification.
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| 9. |
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| 10. |
- Didenko, Victor, et al.
(författare)
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Stability of the Nyström Method for the Sherman–Lauricella Equation
- 2011
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 49:3, s. 1127-1148
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Tidskriftsartikel (refereegranskat)abstract
- The stability of the Nyström method for the Sherman–Lauricella equation on piecewise smooth closed simple contour $\Gamma$ is studied. It is shown that in the space $L_2$ the method is stable if and only if certain operators associated with the corner points of $\Gamma$ are invertible. If $\Gamma$ does not have corner points, the method is always stable. Numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square, and then into various rhombuses. Examples also show an excellent convergence of the method.
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