| 1. |
- Ivanenko, Yevhen, et al.
(författare)
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Quasi-Herglotz functions and convex optimization
- 2020
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Ingår i: Royal Society Open Science. - : The Royal Society Publishing. - 2054-5703. ; 7:1, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
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| 2. |
- Laksman, Efraim, et al.
(författare)
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Generalized upper bounds on the minimum distance of PSK block codes
- 2015
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Ingår i: IMA Journal of Mathematical Control and Information. - : Oxford Journals. - 0265-0754 .- 1471-6887. ; 32:2, s. 305-327
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Forskningsöversikt (refereegranskat)abstract
- This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK.
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| 3. |
- Agram, Nacira, 1987-, et al.
(författare)
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Optimal control of forward–backward mean-field stochastic delayed systems
- 2018
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Ingår i: Afrika Matematika. - : Springer. - 1012-9405 .- 2190-7668. ; 29:1-2, s. 149-174
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Tidskriftsartikel (refereegranskat)abstract
- We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The resultsare applied to solve a mean-field recursive utility optimal problem.
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| 4. |
- Agram, Nacira, 1987-, et al.
(författare)
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Singular Control Optimal Stopping of Memory Mean-Field Processes
- 2019
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 51:1, s. 450-468
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward stochastic differential equations; and (iii) optimal stopping of mean-field stochastic differential equations. More specifically, we do the following: (1) We prove the existence and uniqueness of the solutions of some reflected advanced memory backward stochastic differential equations; (2) we give sufficient and necessary conditions for an optimal singular control of a memory mean-field stochastic differential equation (MMSDE) with partial information; and (3) we deduce a relation between the optimal singular control of an MMSDE and the optimal stopping of such processes.
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| 5. |
- Djehiche, Boualem, et al.
(författare)
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On the Functional Hodrick-Prescott Filter with Non-compact Operators
- 2016
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Ingår i: Random Operators and Stochastic Equations. - : Walter de Gruyter. - 0926-6364 .- 1569-397X. ; 24:1, s. 33-42
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Tidskriftsartikel (refereegranskat)abstract
- We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associate doptimal smoothing operator preserves the structure obtained in the compact case, when the underlying distribution of the data is Gaussian.
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| 6. |
- Engström, Christian, et al.
(författare)
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Homogenization of the Maxwell equations using Floquet-Bloch decomposition
- 2003
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Ingår i: Mathematical and numerical waves 2003. - Berlin, Heidelberg : Springer. - 9783642558566 - 354040127X ; , s. 412-416
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Konferensbidrag (refereegranskat)abstract
- Using Bloch waves to represent the full solution of the Maxwell equations inperiodic media, we study the limit process where the material's period becomes much smaller than the wavelenght. it is seen that effective material parameters can be extracted and explicity represented in terms of the non-vanishing Bloch waves, providing an alternative means of homogenization.
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| 7. |
- Engström, Christian
(författare)
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Inverse bounds of two-component composites
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:3, s. 666-679
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented for estimating microstructural parameters from permittivity measurements of two-component composites. This structural information is described by a particular positive measure in the Stieltjes integral representation of the effective permittivity. The dependence on the geometrical structure can be reduced to the problem of calculating the moments of the measure. We present a method that uses measurement data at a set of distinct frequencies or temperatures to calculate bounds on several moments. These inverse bounds are improved when the volume fraction is known or the material is isotropic. Composites with known geometrical structure illustrate the method.
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| 8. |
- Engström, Christian, et al.
(författare)
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Numerical methods for homogenization of Maxwell's equations
- 2004
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Ingår i: URSI 2004 International Symposium on Electromagnetic Theory. - : Pisa University Press. - 8884922526 - 9788884922526 ; , s. 987-989
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Konferensbidrag (refereegranskat)abstract
- When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. Two numerical methods for the determination of the homogenized coefficients are compared. Numerical examples, where extreme properties of the effective material are achieved in the two dimensional case, are presented.
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| 9. |
- Engström, Christian
(författare)
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On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals
- 2010
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 20:8, s. 1319-1341
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Tidskriftsartikel (refereegranskat)abstract
- We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational operator-valued function in terms of a polynomial operator pencil and study two-component dispersive and absorptive crystals in detail.
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| 10. |
- Engström, Christian, et al.
(författare)
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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:1, s. 231-247
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Tidskriftsartikel (refereegranskat)abstract
- We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.
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