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| 2. |
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Algebra, Geometry, and Mathematical Physics 2010
- 2012
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In: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588.
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Editorial collection (other academic/artistic)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. |
- Arnlind, Joakim, et al.
(author)
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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
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In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
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Journal article (peer-reviewed)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 4. |
- Vasilis, Jonatan, 1981
(author)
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Harmonic measures
- 2010
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Doctoral thesis (other academic/artistic)abstract
- This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel. Fix a domain and a boundary point, subject to certain regularity conditions. Consider the part of the boundary that lies within a disc, centered at the fixed boundary point. It is shown that as the radius of the disc tends to zero, the p-harmonic measure of the boundary set decays as an explicitly given power of the radius. The square root of the Poisson kernel is studied in both continuous and discrete settings. In the continuous case the domain is the unit disc, and a Hardy space related to the square root of the Poisson kernel is defined. The main result is that, as opposed to the classical Hardy space, the positive functions do not admit a characterization in terms of an Orlicz space. Similar results are given also in the discrete case, where the domain is instead a regular tree. Further results in the discrete setting include the construction of a nearest neighbor random walk on the tree with exit distribution determined by powers of the Poisson kernel. The minimally thin sets of these random walks are characterized. Finally, we suggest a generalization of a two-dimensional geometric result – the ring lemma – to three dimensions.
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| 5. |
- Hamon, Thierry, et al.
(author)
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Term Ranking Adaptation to the Domain : Genetic Algorithm-Based Optimisation of the C-Value
- 2014
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In: Advances in Natural Language Processing. - Cham : Springer International Publishing. - 9783319108889 ; , s. 71-83
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Conference paper (peer-reviewed)abstract
- Term extraction methods based on linguistic rules have been proposed to help the terminology building from corpora. As they face the difficulty of identifying the relevant terms among the noun phrases extracted, statistical measures have been proposed. However, the term selection results may depend on corpus and strong assumptions reflecting specific terminological practice. We tackle this problem by proposing a parametrised C-Value which optimally considers the length and the syntactic roles of the nested terms thanks to a genetic algorithm. We compare its impact on the ranking of terms extracted from three corpora. Results show average precision increased by 9% above the frequency-based ranking and by 12% above the C-Value-based ranking.
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| 6. |
- Thörnblad, Karin, 1971, et al.
(author)
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Scheduling optimization of a real flexible job shop including side constraints regarding maintenance, fixtures, and night shifts
- 2013
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Other publication (other academic/artistic)abstract
- We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in [35], with an improvement of the iterative solution procedure and the inclusion of constraints regarding night shifts during which only unmanned processing is allowed. The resulting schedules are compared with schedules constructed using two priority dispatching rules. Computational results show that the gain of including the night shifts constraints is significant and that the methodology developed is able to produce near-optimal schedules for industrial data instances for the coming shift within an acceptable practical time frame.
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| 7. |
- Berman, Robert, 1976, et al.
(author)
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Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs
- 2014
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In: Geometric and Functional Analysis. - : Springer Science and Business Media LLC. - 1016-443X .- 1420-8970. ; 24:6, s. 1683-1730
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Journal article (peer-reviewed)abstract
- Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical class KXdefines an ample (Formula presented.)-line bundle, and satisfying the conditions G1and S2. Our main result says that X admits a Kähler–Einstein metric iff X has semi-log canonical singularities i.e. iff X is a stable variety in the sense of Kollár–Shepherd-Barron and Alexeev (whose moduli spaces are known to be compact). By definition a Kähler–Einstein metric in this singular context simply means a Kähler–Einstein on the regular locus of X with volume equal to the algebraic volume of KX, i.e. the top intersection number of KX. We also show that such a metric is uniquely determined and extends to define a canonical positive current in c1(KX). Combined with recent results of Odaka our main result shows that X admits a Kähler–Einstein metric iff X is K-stable, which thus confirms the Yau–Tian–Donaldson conjecture in this general setting of (possibly singular) canonically polarized varieties. More generally, our results are shown to hold in the setting of log minimal varieties and they also generalize some prior results concerning Kähler–Einstein metrics on quasi-projective varieties.
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| 8. |
- Silvestrov, Sergei
(author)
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Interpolation of Normed Abelian Groups and Non-Commutative Integration
- 2012
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In: Analysis for Science, Engineering and Beyond. - Berlin : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 325-341
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Book chapter (peer-reviewed)abstract
- This is a concise review concerned first of all with the two pioneering far reaching and in many ways yet to be fully explored important papers by Gunnar Sparr and Jaak Peetre on interpolation of normed abelian groups and on non-commutative integration. These papers introduced a general framework unifying many previously known interpolation results and methods in the ways applicable for non-commutative integration and non-commutative extensions of the function spaces, the directions of importance for example in non-commutative geometry and applications in quantum physics. Whence some notions and methods from these papers have been applied in various contexts, many other methods and ideas are yet to be discovered and developed further. In addition to the concise review of these important works by Jaak Peetre and Gunnar Sparr, a brief review is presented also of some related works on non-commutative spaces and non-commutative integration in the contexts of the theory of operator algebras and non-commutative geometry
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| 9. |
- Hegarty, Peter, 1971, et al.
(author)
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On the Diameters of Commuting Graphs Arising from Random Skew-Symmetric Matrices
- 2014
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In: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 23:3, s. 449-459
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Journal article (peer-reviewed)abstract
- We present a two-parameter family of finite, non-abelian random groups and propose that, for each fixed k, as m → ∞ the commuting graph of G_{m,k} is almost surely connected and of diameter k. We present heuristic arguments in favour of this conjecture, following the lines of classical arguments for the Erdős–Rényi random graph. As well as being of independent interest, our groups would, if our conjecture is true, provide a large family of counterexamples to the conjecture of Iranmanesh and Jafarzadeh that the commuting graph of a finite group, if connected, must have a bounded diameter. Simulations of our model yielded explicit examples of groups whose commuting graphs have all diameters from 2 up to 10.
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| 10. |
- Hellström, Lars, 1974-
(author)
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Critical Pairs in Network Rewriting
- 2014
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In: IWC 2014. ; , s. 9-13
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Conference paper (peer-reviewed)abstract
- This extended abstract breifly introduces rewriting of networks (directed acyclic graphs with the extra structure needed to serve as expressions for PROducts and Permutations categories) and describes the critical pairs aspects of this theory. The author's interest in these comes from wanting to do equational reasoning in algebraic theories (such as Hopf algebras) that mix ordinary operations with co-operations; networks then serve as a formalism for expressions.The main message is to point out two phenomena that arise in network rewriting. The first is that of non-convexity of rules, wherein the left hand side of a rule need not be syntactically similar to a symbol in any extension of the underlying signature. The second is one of critical pairs potentially arising where two redexes wrap around each other even when they do not intersect.
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