| 1. |
- Aikawa, Hiroaki, 1956, et al.
(author)
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MARTIN BOUNDARY FOR UNION OF CONVEX SETS
- 2002
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In: 京都大学数理解析研究所, Potential Theory and Related Topics. ; 1293, s. 1-14
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Journal article (peer-reviewed)abstract
- We study Martin boundary points of aproper subdomain in $\mathbb{R}^{n}$ , where $n$ $\geq 2$ , that can be represented as the union of open convex sets. Especially, we give acertain sufficient condition for aboundary point to have exactly one (minimal) Martin boundary point.
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| 2. |
- Aikawa, Hiroaki, 1956, et al.
(author)
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Martin boundary of a fractal domain
- 2003
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In: Potential Analysis. - : Springer Science and Business Media LLC. - 0926-2601 .- 1572-929X. ; 18:4, s. 311-357
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Journal article (peer-reviewed)abstract
- A uniformly John domain is a domain intermediate between a John domain and a uniform domain. We determine the Martin boundary of a uniformly John domain D as an application of a boundary Harnack principle. We show that a certain self-similar fractal has its complement as a uniformly John domain. In particular, the complement of the 3-dimensional Sierpinacuteski gasket is a uniform domain and its Martin boundary is homeomorphic to the Sierpinacuteski gasket itself.
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| 3. |
- Aikawa, Hiroaki, 1956, et al.
(author)
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Martin boundary points of a John domain and unions of convex sets
- 2006
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In: J. Math. Soc. Japan. - 0025-5645 .- 1881-1167. ; 58:1, s. 247-274
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Journal article (peer-reviewed)abstract
- We show that a John domain has finitely many minimal Martin boundary points at each Euclidean boundary point. The number of minimal Martin boundary points is estimated in terms of the John constant. In particular, if the John constant is bigger than $\sqrt3/2$ , then there are at most two minimal Martin boundary points at each Euclidean boundary point. For a class of John domains represented as the union of convex sets we give a sufficient condition for the Martin boundary and the Euclidean boundary to coincide.
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| 4. |
- Aikawa, Hiroaki, 1956, et al.
(author)
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The 3G inequality for a uniformly John domain
- 2005
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In: Kodai Mathematical Journal. ; 28:2, s. 209-219
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Journal article (peer-reviewed)abstract
- Let G be the Green function for a domain D $\subset$ Rd with d ≥ 3. The Martin boundary of D and the 3G inequality: $\frac{G(x,y)G(y,z)}{G(x,z)} \le A(|x-y|^{2-d}+|y-z|^{2-d})$ for x,y,z $\in$ D are studied. We give the 3G inequality for a bounded uniformly John domain D, although the Martin boundary of D need not coincide with the Euclidean boundary. On the other hand, we construct a bounded domain such that the Martin boundary coincides with the Euclidean boundary and yet the 3G inequality does not hold.
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| 5. |
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| 6. |
- Bengmark, Samuel, 1965, et al.
(author)
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Chalmersutbildning kan ge högre lärarstatus
- 2009
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In: Göteborgs Posten, Debatt, nätupplagan.
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Journal article (other academic/artistic)abstract
- Läraryrket behöver en uppvärdering och stora pensionsavgångar samt svårigheter att konkurrera om studenter till lärarutbildningen kräver åtgärder och nytänkande. Chalmers vill därför starta ämneslärarutbildning i data, fysik, kemi, matematik och teknik så att studenten kan få både en lärarexamen och en ingenjörsexamen, skriver bland andra Samuel Bengmark, programansvarig för Chalmers lärarutbildning.
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| 7. |
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| 8. |
- Bondesson, Johan, 1991, et al.
(author)
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Automated Quantification of Diseased Thoracic Aortic Longitudinal Centerline and Surface Curvatures
- 2020
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In: Journal of Biomechanical Engineering-Transactions of the Asme. - : ASME International. - 0148-0731 .- 1528-8951. ; 142:4
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Journal article (peer-reviewed)abstract
- Precise description of vascular morphometry is crucial to support medical device manufacturers and clinicians for improving device development and interventional outcomes. A compact and intuitive method is presented to automatically characterize the surface geometry of tubular anatomic structures and quantify surface curvatures starting from generic stereolithographic (STL) surfaces. The method was validated with software phantoms and used to quantify the longitudinal surface curvatures of 37 human thoracic aortas with aneurysm or dissection. The quantification of surface curvatures showed good agreement with analytic solutions from the software phantoms, and demonstrated better agreement as compared to estimation methods using only centerline geometry and cross-sectional radii. For the human thoracic aortas, longitudinal inner surface curvature was significantly higher than centerline curvature (0.33 +/- 0.06 versus 0.16 +/- 0.02cm(-1) for mean; 1.38 +/- 0.48 versus 0.45 +/- 0.11cm(-1) for peak; both p<0.001). These findings show the importance of quantifying surface curvatures in order to better describe the geometry and biomechanical behavior of the thoracic aorta, which can assist in treatment planning and supplying device manufactures with more precise boundary conditions for mechanical evaluation.
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| 9. |
- Bondesson, Johan, 1991, et al.
(author)
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Definition of Tubular Anatomic Structures from Arbitrary Stereo Lithographic Surface
- 2017
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In: Initiative Seminar Engineering Health, 8-9 November 2017, Chalmers.
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Conference paper (other academic/artistic)abstract
- An accurate description of anatomies and dynamics of vessels is crucial to understand their characteristics and improve surgical techniques, thus it is the basis, in addition to surgeon experience, on which stent design and operation procedures rely. The process of producing this description is user intensive, and recent improvement in image processing of medical3D imaging allows for a more automated workflow. However, there is a need to bridge the gap from a processed geometry to a robust mathematical computational grid. By sequentially segmenting a tubular anatomic structure, here defined by a stereo lithographic (STL) surface, an initial centerline is formed by connecting centroids of orthogonal cross-sectional contours along the length of the structure. Relying on the initial centerline, a set of non-overlapping 2D cross sectional contours are defined along the centerline, a centerline which is updated after the 2D contours are produced. After a second iteration of producing 2D contours and updating the centerline, a full description of the structure is created. Our method for describing vessel geometry shows good coherence to existing method. The main advantages of our method include the possibility of having arbitrary triangulated STL surface input, automated centerline definition, safety against intersecting cross-sectional contours and automatic clean-up of local kinks and wrinkles.
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| 10. |
- Cardilin, Tim, 1989, et al.
(author)
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Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures
- 2021
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In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 338
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Journal article (peer-reviewed)abstract
- Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.
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