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- Khrennikov, Andrei
(författare)
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Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals
- 2008
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Ingår i: Izvestiya. Mathematics. - 1064-5632 .- 1468-4810. ; 72:1, s. 127-148
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Tidskriftsartikel (refereegranskat)abstract
- We study the relation between the mathematical structures of statistical mechanics on an infinite-dimensional phase space (denoted by ) and quantum mechanics. It is shown that quantum averages (given by the von Neumann trace formula) can be obtained as the main term of the asymptotic expansion of Gaussian functional integrals with respect to a small parameter . Here is the dispersion of the Gaussian measure. The symplectic structure on the infinite-dimensional phase space plays a crucial role in our considerations. In particular, the Gaussian measures that induce quantum averages must be consistent with the symplectic structure. The equations of Schrödinger, Heisenberg and von Neumann are images of the Hamiltonian dynamics on .
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- Semenov, E. M., et al.
(författare)
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The main classes of invariant Banach limits
- 2019
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Ingår i: Izvestiya Mathematics. - : IOP Publishing. - 1064-5632 .- 1468-4810. ; 83:1, s. 124-150
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Tidskriftsartikel (refereegranskat)abstract
- We study functional characteristics and extreme points of the set of Banach limits on the space of bounded sequences. We also consider Banach limits with additional invariance properties with respect to the dilation operator and the Cesaro operator.
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- Semenov, E. M., et al.
(författare)
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The main classes of invariant Banach limits
- 2019
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Ingår i: Izvestiya Mathematics. - 1468-4810 .- 1064-5632. ; 83:1, s. 124-150
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Tidskriftsartikel (refereegranskat)abstract
- We study functional characteristics and extreme points of the set of Banach limits on the space of bounded sequences. We also consider Banach limits with additional invariance properties with respect to the dilation operator and the Cesaro operator.
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- Yurova, Ekaterina, 1986-, et al.
(författare)
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Subcoordinate Representation of p-adic Functions and Generalization of Hensel's Lemma
- 2018
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Ingår i: Izvestiya. Mathematics. - : Russian Academy of Sciences. - 1064-5632 .- 1468-4810. ; 82:3, s. 632-645
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we describe a new representation of p-adic functions, the so-called subcoordinate representation. The main feature of the subcoordinaterepresentation of a p-adic function is that the values of the function f are given in the canonical form of the representation of p-adic numbers. The function f itself is determined by a tuple of p-valued functions from the set {0, 1,..., p-1} into itself and by the order in which these functions are used to determine the values of f. We also give formulae that enable one to pass from the subcoordinate representation of a 1-Lipschitz function to its van der Put series representation. The effective use of the subcoordinate representation of p-adic functions is illustrated by a study of the feasibility of generalizing Hensel's lemma.
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- Holmström, Gerd, 1951-, et al.
(författare)
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New modifications of Swedish ROP guidelines based on 10-year data from the SWEDROP register
- 2020
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Ingår i: British Journal of Ophthalmology. - : BMJ. - 0007-1161 .- 1468-2079. ; 104:7, s. 943-949
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND/AIMS:During the last decade, improved neonatal care has resulted in increased survival of the most immature infants and improved health of more mature infants. We hypothesise that this has affected incidence and treatment of retinopathy of prematurity (ROP), enabling guidelines for screening to be modified.METHODS: In Sweden, all infants with gestational age (GA) at birth ≤30 weeks are screened for ROP. Results are registered in a web-based register, Swedish National ROP Register, with a coverage rate of 97%. Incidence of ROP and frequency of treatment, aspects on natural course of ROP and number of examinations, are calculated in relation to GA at birth in infants born during 2008-2017.RESULTS: Of 7249 infants, 31.9% (2310) had ROP and 6.1% (440) were treated. No infant with GA 30 weeks was treated. Incidence of ROP remained similar, but frequency of treatment increased (p=0.023). Over time, GA and birth weight were reduced in infants with ROP and with treated ROP. In the most immature infants, postmenstrual age was lower and postnatal age was higher when any ROP and stage 3 ROP were first detected (p<0.001). At treatment, postmenstrual but not postnatal age of the infant was associated with GA (p<0.001). During the 10-year period, 46 038 examinations were performed.CONCLUSION: Modification of Swedish guidelines is proposed, including only infants with a GA of <30 weeks and postponing the first examination with 1 week in infants with GA 26-29 weeks. This would spare many infants from stressful examinations and reduce eye examinations with at least 20%.
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