| 1. |
- Akbary, Amir, et al.
(författare)
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On the Lang-Trotter conjecture for two elliptic curves
- 2019
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Ingår i: Ramanujan Journal. - : Springer. - 1382-4090 .- 1572-9303. ; 49:3, s. 585-623
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Tidskriftsartikel (refereegranskat)abstract
- Following Lang and Trotter, we describe a probabilistic model that predicts the distribution of primes p with given Frobenius traces at p for two fixed elliptic curves over Q. In addition, we propose explicit Euler product representations for the constant in the predicted asymptotic formula and describe in detail the universal component of this constant. A new feature is that in some cases the l-adic limits determining the l-factors of the universal constant, unlike the Lang-Trotter conjecture for a single elliptic curve, do not stabilize. We also prove the conjecture on average over a family of elliptic curves, which extends the main results of Fouvry and Murty (Supersingular primes common to two elliptic curves, number theory (Paris, 1992), London Mathematical Society Lecture Note Series, vol 215, Cambridge University Press, Cambridge, 1995) and Akbary et al. (Acta Arith 111(3):239-268, 2004), following the work of David et al. (Math Ann 368(1-2):685-752, 2017).
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| 2. |
- Alladi, Krishnaswami, et al.
(författare)
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Preface
- 2023
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Ingår i: Ramanujan Journal. - 1382-4090 .- 1572-9303. ; 61:1, s. 1-6
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 3. |
- Christiansen, Jacob S., et al.
(författare)
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Asymptotics of Chebyshev polynomials, V. residual polynomials
- 2023
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Ingår i: Ramanujan Journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 61:1, s. 251-278
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Tidskriftsartikel (refereegranskat)abstract
- We study residual polynomials, Rx0,n(e), e⊂ R, x∈ R\ e, which are the degree at most n polynomials with R(x) = 1 that minimize the sup norm on e. New are upper bounds on their norms (that are optimal in some cases) and Szegő–Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case such as root asymptotics, a universal lower bound, and a new characterization of sets saturating this lower bound.
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| 4. |
- Eriksson, Kimmo, et al.
(författare)
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Bentley’s conjecture on popularity toplist turnover under random copying
- 2010
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Ingår i: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
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Tidskriftsartikel (refereegranskat)abstract
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
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| 5. |
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| 6. |
- Lazar, Alexander
(författare)
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Ferrers graphs, D-permutations, and surjective staircases
- 2023
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Ingår i: The Ramanujan journal. - : Springer Nature. - 1382-4090 .- 1572-9303. ; 60:2, s. 391-426
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a new family of hyperplane arrangements inspired by the homogenized Linial arrangement (which was recently introduced by Hetyei), and show that the intersection lattices of these arrangements are isomorphic to the bond lattices of Ferrers graphs. Using recent work of Lazar and Wachs we are able to give combinatorial interpretations of the characteristic polynomials of these arrangements in terms of permutation enumeration. For certain infinite families of these hyperplane arrangements, we are able to give generating function formulas for their characteristic polynomials. To do so, we develop a generalization of Dumont’s surjective staircases, and introduce a polynomial which enumerates these generalized surjective staircases according to several statistics. We prove a recurrence for these polynomials and show that in certain special cases this recurrence can be solved explicitly to yield a generating function. We also prove refined versions of several of these results using the theory of complex hyperplane arrangements.
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| 7. |
- Rosengren, Hjalmar, 1972
(författare)
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Proofs of some partition identities conjectured by Kanade and Russell
- 2023
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Ingår i: Ramanujan Journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 61:1, s. 295-317
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Tidskriftsartikel (refereegranskat)abstract
- Kanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some of which are related to level 2 characters of the affine Lie algebra A9(2). Many of these conjectures have been proved by Bringmann, Jennings-Shaffer and Mahlburg. We give new proofs of five conjectures first proved by those authors, as well as four others that have been open until now. Our proofs for the new cases use quadratic transformations for Askey–Wilson and Rogers polynomials. We also obtain some related results, including a partition identity conjectured by Capparelli and first proved by Andrews.
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| 8. |
- Lim, Jun, et al.
(författare)
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Static and dynamic performance optimisation of a 1.3 mu m GaInNAs ridge waveguide laser
- 2008
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Ingår i: Optical and Quantum Electronics. - : Springer Science and Business Media LLC. - 0306-8919 .- 1572-817X. ; 40:14-15, s. 1181-1186
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we perform a multi-parameter design study to improve the performance of an uncooled directly modulated 1.3 mu m GaInNAs ridge waveguide laser for high speed operation especially at high temperature. The static and dynamic performance of the improved design is analyzed using an accurate in-house 2D electro-opto-thermal laser simulator. The improved structure is shown to have a lower threshold current, higher thermal roll-over limit and higher modulation bandwidth-especially under high temperature operation. The improved structure also has a lower vertical beam divergence compared to a reference structure with a conventional design.
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| 9. |
- Fischer Grönlund, Catarina, et al.
(författare)
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Managing Ethical Difficulties in Healthcare : Communicating in Inter-professional Clinical Ethics Support Sessions
- 2016
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Ingår i: HEC Forum. - : Springer Science and Business Media LLC. - 0956-2737 .- 1572-8498. ; 28:4, s. 321-338
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Tidskriftsartikel (refereegranskat)abstract
- Several studies show that healthcare professionals need to communicate inter-professionally in order to manage ethical difficulties. A model of clinical ethics support (CES) inspired by Habermas' theory of discourse ethics has been developed by our research group. In this version of CES sessions healthcare professionals meet inter-professionally to communicate and reflect on ethical difficulties in a cooperative manner with the aim of reaching communicative agreement or reflective consensus. In order to understand the course of action during CES, the aim of this study was to describe the communication of value conflicts during a series of inter-professional CES sessions. Ten audio- and video-recorded CES sessions were conducted over eight months and were analyzed by using the video analysis tool Transana and qualitative content analysis. The results showed that during the CES sessions the professionals as a group moved through the following five phases: a value conflict expressed as feelings of frustration, sharing disempowerment and helplessness, the revelation of the value conflict, enhancing realistic expectations, seeing opportunities to change the situation instead of obstacles. In the course of CES, the professionals moved from an individual interpretation of the situation to a common, new understanding and then to a change in approach. An open and permissive communication climate meant that the professionals dared to expose themselves, share their feelings, face their own emotions, and eventually arrive at a mutual shared reality. The value conflict was not only revealed but also resolved.
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| 10. |
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