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Algebra, Geometry, and Mathematical Physics 2010
- 2012
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588.
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- This proceedings volume presents results obtained by the participants of the 6th Baltic–Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25–30, 2010. The Baltic–Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic–Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic–Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers.
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| 3. |
- Bernhoff, Niclas, 1971-
(författare)
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Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
- 2018
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Ingår i: Journal of statistical physics. - New York : Springer. - 0022-4715 .- 1572-9613. ; 172:3, s. 742-761
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Tidskriftsartikel (refereegranskat)abstract
- An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
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| 4. |
- Kavallaris, Nikos I., et al.
(författare)
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On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions
- 2024
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Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 17:3, s. 1222-1268
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study a stochastic parabolic problem involving anonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixtureof a classical Brownian and a fractional Brownian motion with Hurst indexH ∈ (1/2, 1). We first establish local in time existence results and then exploreconditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals ofBrownian motion as well as tail estimates for the fractional Brownian motionwe provide analytic estimates for certain quantities of interest, such as upperbounds for quenching times and the corresponding quenching probabilities.The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analyticalresults demonstrate the non-trivial impact of the noise on the dynamics ofthe system. The analytic results are complemented with a detailed numericalstudy of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of theresults in this context are commented upon.
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| 5. |
- Bernhoff, Niclas, 1971-
(författare)
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Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation
- 2015
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Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 159:2, s. 358-379
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Tidskriftsartikel (refereegranskat)abstract
- We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for a general discrete model of a quantum kinetic equation for excitations in a Bose gas. In the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations. These systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete Boltzmann equation. Then a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete kinetic equation can be made. The number of additional conditions that need to be imposed for well-posedness is given by some characteristic numbers. These characteristic numbers are calculated for discrete models axially symmetric with respect to the x-axis. When the characteristic numbers change is found in the discrete as well as the continuous case. As an illustration explicit solutions are found for a small-sized model.
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| 6. |
- Abramovich, Shoshana, et al.
(författare)
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Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity
- 2020
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Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 23:2, s. 447-458
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss the Hermite-Hadamard and Fejer inequalities vis-a-vis the convexity concept. In particular, we derive some new theorems and examples where Hermite-Hadamard and Fejer type inequalities are satisfied without the assumptions of convexity or concavity on the actual interval [a,b]
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| 7. |
- Aljinovic, Andrea Aglic, et al.
(författare)
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Josip Pecaric- and his life in mathematics and politics
- 2019
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Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 22:4, s. 1067-1080
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Tidskriftsartikel (refereegranskat)abstract
- It is impossible in limited number of pages to give a fair picture of such a remarkable man, great mathematician and human being as Josip Pecaric. Our intention is instead to complement the picture of him in various ways. We hope that our paper will give also someflavor of Josip as family man, fighter, supervisor,international authority, author (also in other subjects than mathematics), fan of the Croatian football team, and not only as his obvious role as our King of Inequalities.
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| 8. |
- Barza, Sorina, 1967-, et al.
(författare)
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Best constants between equivalent norms in Lorentz sequence spaces
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 2012
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Tidskriftsartikel (refereegranskat)abstract
- We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.
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| 9. |
- Barza, Sorina, et al.
(författare)
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Multidimensional rearrangement and Lorentz spaces
- 2004
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Ingår i: Acta Mathematica Hungarica. - 0236-5294 .- 1588-2632. ; 104:3, s. 203-224
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Tidskriftsartikel (refereegranskat)abstract
- We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.
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| 10. |
- Barza, Sorina, et al.
(författare)
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Some multiplicative inequalities for inner products and of the Carlson type
- 2008
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X.
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Tidskriftsartikel (refereegranskat)abstract
- We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.
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