| 1. |
- Foda, O., et al.
(author)
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Overlaps of partial Neel states and Bethe states
- 2016
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In: Journal of Statistical Mechanics. - : IOP Publishing. - 1742-5468 .- 1742-5468.
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Journal article (peer-reviewed)abstract
- Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.
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| 2. |
- Ivanenko, Yevhen, et al.
(author)
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Quasi-Herglotz functions and convex optimization
- 2020
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In: Royal Society Open Science. - : The Royal Society Publishing. - 2054-5703. ; 7:1, s. 1-15
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Journal article (peer-reviewed)abstract
- We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
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| 3. |
- Johansson, Petter, et al.
(author)
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A Ronkin type function for coamoebas
- 2017
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In: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 27:1, s. 643-670
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Journal article (peer-reviewed)abstract
- The Ronkin function plays a fundamental role in the theory of amoebas. We introduce an analogue of the Ronkin function in the setting of coamoebas. It turns out to be closely related to a certain toric arrangement known as the shell of the coamoeba and we use our Ronkin type function to obtain some properties of it.
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| 4. |
- Samuelsson Kalm, Håkan, 1976, et al.
(author)
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Regularizations of residue currents
- 2010
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In: Journal für die Reine und Angewandte Mathematik. - 1435-5345 .- 0075-4102. ; 649, s. 33-54
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Journal article (peer-reviewed)abstract
- Under assumptions about complete intersection, we prove that Coleff-Herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the Coleff-Herrera product of the currents.
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| 5. |
- Lu, Xin, et al.
(author)
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Respondent-driven sampling on directed networks
- 2013
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In: Electronic Journal of Statistics. - 1935-7524. ; 7, s. 292-322
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Journal article (peer-reviewed)abstract
- Respondent-driven sampling (RDS) is a widely used method for generating chain-referral samples from hidden populations. It is an extension of the snowball sampling method and can, given that some assumptions are met, generate unbiased population estimates. One key assumption, not likely to be met, is that the acquaintance network in which the recruitment process takes place is undirected, meaning that all recruiters should have the potential to be recruited by the person they recruit. Using a mean-field approach, we develop an estimator which is based on prior information about the average indegrees of estimated variables. When the indegree is known, such as for RDS studies over internet social networks, the estimator can greatly reduce estimate error and bias as compared with current methods; when the indegree is not known, which is most common for interview-based RDS studies, the estimator can through sensitivity analysis be used as a tool to account for uncertainties of network directedness and error in self-reported degree data. The performance of the new estimator, together with previous RDS estimators, is investigated thoroughly by simulations on networks with varying structures. We have applied the new estimator on an empirical RDS study for injecting drug users in New York City.
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| 6. |
- Albeverino, S., et al.
(author)
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Pseudo-Differential Operators with Point Interactions
- 1997
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In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 41, s. 79-92
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Journal article (peer-reviewed)abstract
- Point interactions for pseudo-differential operators are studied. Necessary and sufficient conditions for a pseudo-differential operator to have nontrivial point perturbations are given. The results are applied to the construction of relativistic spin zero Hamiltonians with point interactions.
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| 7. |
- Albeverio, S., et al.
(author)
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Finite rank perturbations and distribution theory
- 1999
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In: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 127:4, s. 1151-1161
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Journal article (peer-reviewed)abstract
- Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2A) to H-2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.
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| 8. |
- Albeverio, S., et al.
(author)
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Many body problems with "spin"-related contact interactions
- 2001
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In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 47:2, s. 157-166
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Journal article (peer-reviewed)abstract
- We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.
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| 9. |
- Albeverio, S., et al.
(author)
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Rank one perturbations of not semibounded operators
- 1997
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In: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400
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Journal article (peer-reviewed)abstract
- Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension
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| 10. |
- Andersson, Johan, 1971-
(author)
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Disproof of some conjectures of P. Turan
- 2007
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In: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 117:3, s. 245-250
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Journal article (peer-reviewed)abstract
- We disprove some power sum conjectures of Turan that would have implied the density hypothesis of the Riemann zeta-function if true.
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