| 1. |
- Pejlare, Johanna, 1976, et al.
(författare)
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On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements
- 2016
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Ingår i: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2909916510 ; , s. 513-523
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Konferensbidrag (refereegranskat)abstract
- In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
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| 2. |
- Bringmann, K., et al.
(författare)
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Almost holomorphic Poincaré series corresponding to products of harmonic Siegel-Maass forms
- 2016
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Ingår i: Research in the Mathematical Sciences. - : Springer Science and Business Media LLC. - 2197-9847 .- 2522-0144. ; 3
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Tidskriftsartikel (refereegranskat)abstract
- We investigate Poincare series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincare series are almost holomorphic as well. In general, this is not the case. The main point of this paper is the study of Siegel-Poincare series of degree 2 attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincare series. We surprisingly discover that these Poincare series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls.
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| 3. |
- Friberg, Jöran, 1934, et al.
(författare)
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More Mathematical Cuneiform Texts of Group 6 from Late Old Babylonian Sippar
- 2016
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Ingår i: Sources and Studies in the History of Mathematics and Physical Sciences. - Cham : Springer International Publishing. ; , s. 371-389
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In Ch. IV of Neugebauer and Sachs, MCT (1945), A. Goetze divided published Old Babylonian mathematical texts without known provenance into 6 different groups with respect to their Akkadian orthography. Goetze’s classification was later refined and extended by J. Høyrup in LWS (2002), Ch. IX. Groups 5 and 6 were classified by Goetze as “northern”.
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| 4. |
- Goffeng, Magnus C H T, 1987, et al.
(författare)
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Clusters of eigenvalues for the magnetic Laplacian with Robin condition
- 2016
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 57:6
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Tidskriftsartikel (refereegranskat)abstract
- We study the Schrodinger operator with a constant magnetic field in the exterior of a compact domain in Euclidean space. Functions in the domain of the operator are subject to a boundary condition of the third type (a magnetic Robin condition). In addition to the Landau levels, we obtain that the spectrum of this operator consists of clusters of eigenvalues around the Landau levels and that they do accumulate to the Landau levels from below. We give a precise asymptotic formula for the rate of accumulation of eigenvalues in these clusters, which is independent of the boundary condition. Published by AIP Publishing.
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| 5. |
- Izzo, Alexander, et al.
(författare)
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Presence or absence of analytic structure in maximal ideal spaces
- 2016
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 366:1-2, s. 459-478
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Tidskriftsartikel (refereegranskat)abstract
- We study extensions of Wermer's maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold.
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| 6. |
- Larson, Simon
(författare)
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A bound for the perimeter of inner parallel bodies
- 2016
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Ingår i: Journal of Functional Analysis. - : Academic Press. - 0022-1236 .- 1096-0783. ; 271:3, s. 610-619
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Tidskriftsartikel (refereegranskat)abstract
- We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that. |∂Ωt|≥(1-tr)+n-1|∂Ω|. In particular the bound is independent of any regularity properties of ∂Ω. As a by-product of the proof we establish precise conditions for equality. The proof, which is straightforward, is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes.
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| 7. |
- Lu, Zhiqin, et al.
(författare)
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One can hear the corners of a drum
- 2016
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Ingår i: Bulletin of the London Mathematical Society. - : Wiley. - 0024-6093 .- 1469-2120. ; 48:1, s. 85-93
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected planar domain with piecewise smooth Lipschitz boundary and at least one corner cannot be isospectral to any connected planar domain, of any genus, that has smooth boundary. Moreover, we prove that amongst all planar domains with Lipschitz, piecewise smooth boundary and fixed genus, the presence or absence of corners is uniquely determined by the spectrum. This means that corners are an elementary geometric spectral invariant; one can hear corners.
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| 8. |
- Lärkäng, Richard, 1985, et al.
(författare)
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Elementary construction of residue currents associated to Cohen-Macaulay ideals
- 2016
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- For a Cohen-Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the theory of linkage, and another using an explicit division formula involving these residue currents to express the ideal membership.
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| 9. |
- Hermansson, Tomas, 1979, et al.
(författare)
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Identification of Material Parameters of Complex Cables from Scanned 3D Shapes
- 2016
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Ingår i: Procedia CIRP: 14th CIRP CAT 2016 - CIRP Conference on Computer Aided Tolerancing. - : Elsevier BV. - 2212-8271. ; 43, s. 280-285
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Konferensbidrag (refereegranskat)abstract
- Simulation of flexible components is becoming an integral part of virtual product design. However, for a simulation model to predict physically correct deformations, it is crucial that the material parameters are authentic. Conventional methods to acquire these parameters involve extensive force-displacement measurements, which may be unpractical or too expensive to perform. We propose an alternative method to identify the material parameters of a flexible one-dimensional component, such as a cable or a hose, from a scanned set of deformed reference shapes. The method finds the model parameters that give the best geometric fit between the model and the reference shapes.
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| 10. |
- Hultman, Axel
(författare)
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Supersolvability and the Koszul property of root ideal arrangements
- 2016
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 144, s. 1401-1413
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Tidskriftsartikel (refereegranskat)abstract
- A root ideal arrangement A_I is the set of reflecting hyperplanes corresponding to the roots in an order ideal I of the root poset on the positive roots of a finite crystallographic root system. A characterisation of supersolvable root ideal arrangements is obtained. Namely, A_I is supersolvable if and only if I is chain peelable, meaning that it is possible to reach the empty poset from I by in each step removing a maximal chain which is also an order filter. In particular, supersolvability is preserved under taking subideals. We identify the maximal ideals that correspond to non-supersolvable arrangements. There are essentially two such ideals, one in type D_4 and one in type F_4. By showing that A_I is not line-closed if I contains one of these, we deduce that the Orlik-Solomon algebra OS(A_I) has the Koszul property if and only if A_I is supersolvable.
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