| 21. |
- Westerholt-Raum, Martin, 1985, et al.
(författare)
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All modular forms of weight 2 can be expressed by Eisenstein series
- 2020
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Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2522-0160 .- 2363-9555. ; 6:3
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Tidskriftsartikel (refereegranskat)abstract
- We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L-values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.
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| 22. |
- Brubaker, B., et al.
(författare)
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Colored five-vertex models and Demazure atoms
- 2021
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Ingår i: Journal of Combinatorial Theory Series A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 178
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Tidskriftsartikel (refereegranskat)abstract
- Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a byproduct, we will construct Demazure atoms on Kashiwara's B-infinity crystal and give new algorithms for computing Lascoux-Schutzenberger keys. (C) 2020 Elsevier Inc. All rights reserved.
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| 23. |
- Hultman, Axel, et al.
(författare)
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From Bruhat intervals to intersection lattices and a conjecture of Postnikov
- 2009
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Ingår i: Journal of combinatorial theory. Series A (Print). - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 116:3, s. 564-580
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Tidskriftsartikel (refereegranskat)abstract
- We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w is an element of (sic)(n). is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns.
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| 24. |
- Brattström, Gudrun
(författare)
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Leonardo da Pisa : Inger Christensen och Fibonacci
- 2008
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Ingår i: Lyrikvännen. - 0460-0762. ; 55:6, s. 33-38
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.
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| 25. |
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| 26. |
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| 27. |
- Aas, Erik, et al.
(författare)
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Limiting directions for random walks in classical affine Weyl groups
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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| 28. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model
- 2024
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Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101
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Tidskriftsartikel (refereegranskat)abstract
- Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
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| 29. |
- Luo, Caihua, 1987
(författare)
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Rodier type theorem for generalized principal series
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 299:1-2, s. 897-918
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Tidskriftsartikel (refereegranskat)abstract
- Given a regular supercuspidal representation ρ of the Levi subgroup M of a standard parabolic subgroup P= MN in a connected reductive group G defined over a non-archimedean local field F, we serve you a Rodier type structure theorem which provides us a geometrical parametrization of the set JH(IndPG(ρ)) of Jordan–Hölder constituents of the Harish-Chandra parabolic induction representation IndPG(ρ), vastly generalizing Rodier structure theorem for P= B= TU Borel subgroup of a connected split reductive group about 40 years ago. Our novel contribution is to overcome the essential difficulty that the relative Weyl group W = N (M) / M is not a coxeter group in general, as opposed to the well-known fact that the Weyl group W = N (T) / T is a coxeter group. Along the way, we sort out all regular discrete series/tempered/generic representations for arbitrary G, generalizing Tadić’s work on regular discrete series representation for split (G) Sp and SO , and also providing a new simple proof of Casselman–Shahidi’s theorem on generalized injectivity conjecture for regular generalized principal series. Indeed, such a beautiful structure theorem also holds for finite central covering groups. M G T G 2 n 2 n + 1
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| 30. |
- Fedosova, K., et al.
(författare)
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High energy asymptotics for the perturbed anharmonic oscillator
- 2021
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941.
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Holder continuous perturbation and investigate how the Holder constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.
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