| 1. |
- Andrist B., Rafael, et al.
(författare)
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Holomorphic Automorphisms of Danielewski Surfaces II: Structure of the Overshear Group
- 2015
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Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 25:3, s. 1859-1889
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Tidskriftsartikel (refereegranskat)abstract
- We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group, which is known to be dense in the identity component of the holomorphic automorphism group, is a free product.
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| 2. |
- Flodén, Lotta, et al.
(författare)
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A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
- 2017
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Ingår i: ICNPAA 2016 World Congress. - Melville, USA : American Institute of Physics (AIP). - 9780735414648
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Konferensbidrag (refereegranskat)abstract
- We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ε → 0.We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ε−1∂tuε as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.
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| 3. |
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| 4. |
- Holmbom, Anders
(författare)
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Some modes of convergence and their application to homogenization and optimal composites design
- 1996
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we develop, extend, apply, and discuss a number of methods for the study of limits of sequences of functions and operators. The connection between the notion of two-scale convergence and more general concepts of convergence is investigated and some alternative classes of admissible test functions are characterized. These techniques are extended into compactness results suitable to prove homogenization and corrector results for linear parabolic equations. A further refinement of these methods, together with a characterization of the limits of certain sequences of parameter-dependent functions which has been subject to extension from a quite general class of periodic domains, is introduced. This provides an efficient tool for the homogenization of e.g. nonlinear evolution heat conduction in heterogeneous materials which vibrate with high frequencies or are perforated by periodically arranged nonconducting holes. Moreover, we prove compactness and homogenization for sequences of solutions of linear elliptic and monotone parabolic equations defined in some classes of nonperiodic domains and derive a Darcy's law for a type of nonperiodic porous media. In the linear elliptic case the convergence is strengthened by means of correctors. Finally, we present some numerical results for homogenized stiffness of fibre composites and demonstrate how homogenization techniques for elasticity in composite materials and for liquid flow in porous media can be combined with recent optimization techniques to obtain optimal layout of composite materials.
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| 5. |
- Wikström, Frank
(författare)
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The Dirichlet problem for maximal plurisubharmonic functions on analytic varieties in C^n
- 2009
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 20:4, s. 521-528
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function , we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on .
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| 6. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Nonsearch paradigm for large-scale parameter-identification problems in dynamical systems related to oncogenic hyperplasia
- 2006
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Ingår i: Systems, Control, Modeling and Optimization. IFIP International Federation for Information Processing. - : Springer US. - 1571-5736. - 9780387338811 - 0387338810 ; 202, s. 269-278
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Konferensbidrag (refereegranskat)abstract
- In many engineering and biomedical problems there is a need to identify parameters of the systems from experimental data. A typical example is the biochemical-kinetics systems describing oncogenic hyperplasia where the dynamical model is nonlinear and the number of the parameters to be identified can reach a few hundreds. Solving these large-scale identification problems by the local- or global-search methods can not be practical because of the complexity and prohibitive computing time. These difficulties can be overcome by application of the non-search techniques which are much less computation- demanding. The present work proposes key components of the corresponding mathematical formulation of the nonsearch paradigm. This new framework for the nonlinear large-scale parameter identification specifies and further develops the ideas of the well-known approach of A. Krasovskii. The issues are illustrated with a concise analytical example. The new results and a few directions for future research are summarized in a dedicated section.
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| 7. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Stochastic mechanics in the context of the properties of living systems
- 2006
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177 .- 1872-9479. ; 44:7-8, s. 595-607
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Tidskriftsartikel (refereegranskat)abstract
- Many features of living systems prevent the application of fundamental statistical mechanics (FSM) to study such systems. The present work focuses on some of these features. After discussing all the basic approaches of FSM, the work formulates an extension of the kinetic theory paradigm (based on the reduced one-particle distribution function) that exhibits all of the living-system properties considered. This extension appears to be a model within the generalized kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. A mathematical formulation of homeorhesis is also derived. An example discussed in the work is a generalized kinetic equation coupled with a probability-density equation representing the varying component content of a living system. The work also suggests a few directions for future research. [All rights reserved Elsevier]
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| 8. |
- Mamontov, Eugen, 1955, et al.
(författare)
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The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
- 2006
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Ingår i: Acta Biotheoretica. - : Springer Science and Business Media LLC. - 0001-5342 .- 1572-8358. ; 54:2, s. 61-101
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Tidskriftsartikel (refereegranskat)abstract
- Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
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| 9. |
- Mamontov, Eugen, 1955, et al.
(författare)
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What stochastic mechanics are relevant to the study of living systems?
- 2005
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Ingår i: Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences. - Riga, Latvia : Latvian Academy of Sciences. - 1407-009X. ; 59:6, s. 255-262
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Tidskriftsartikel (refereegranskat)abstract
- Biologists have identified many features of living systems which cannot be studied by application of fundamental statistical mechanics (FSM). The present work focuses on some of these features. By discussing all the basic approaches of FSM, the work formulates the extension of the kinetic-theory paradigm (based on the reduced one-particle distribution function) that possesses all the considered properties of the living systems. This extension appears to be a model within the generalized-kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. An example is discussed, which is a generalized kinetic equation coupled with the probability-density equation which represents the varying component content of a living system. The work also suggests directions for future research.
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| 10. |
- Boggess, Al, et al.
(författare)
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On The Hartogs Extension Theorem For Unbounded Domains In Cn
- 2022
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Ingår i: Annales de l'Institut Fourier. - : Cellule MathDoc/CEDRAM. - 0373-0956 .- 1777-5310. ; 72:3, s. 1185-1206
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω ⊂ Cn, n > 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of Cn \ Ω is Cn. It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in Cn for which the Hartogs phenomenon holds. Comparing this to earlier work by the first two authors and Z. Słodkowski, one observes that the extension problem changes in character if one restricts to CR functions of higher regularity.
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