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Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map

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Georgi Vodev (LMJL)

Analysis of PDEs · Submitted 6 Feb 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide.

how it is stated · asserted 1.00 read the record →

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arXiv ID1802.01857 (version 2)
Pith IDXEJRSMTG, Pith's permanent record of this paper and its review
CitationGeorgi Vodev (LMJL). "Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map." arXiv:1802.01857 (2018). https://pith.science/paper/XEJRSMTG
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,606 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the semi-classical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We build a new, improved parametrix in the glancing region compaired with that one built in [9], [12]. We also study the way in which the parametrix depends on the refraction index. As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the semi-classical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. background 0.53 0.78 0.05 asserted 0.96
s1 We build a new, improved parametrix in the glancing region compaired with that one built in [9], [12]. contribution 0.98 0.95 0.25 asserted 1.00
s2 We also study the way in which the parametrix depends on the refraction index. contribution 1.00 0.92 0.06 asserted 0.99
s3 As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide. result 0.93 0.91 0.57 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study the semi-classical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We build a new, improved parametrix in the glancing region compaired with that one built in [9], [12]. We also study the way in which the parametrix depends on the refraction index. As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide.

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