Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
Round 1
Reviewer 1 Report
The problem is kind of interesting, but not well-introduced, more detailed description, particularly the physical background, should be provided to better help potential readers understand the work. The manuscript is not written well (I mean the language), and difficult to follow and understand. It must be further polished and improved. I checked some proofs and calculations, and did not find mistakes. The current form of the manuscript is not ready for Symmetry. I would like the authors to further Polish the work and submit the revised version.
Author Response
First of all, many thanks to the reviewer for his attention to the work.
The comments of the reviewer were taken into account:
1.The introduction has been expanded to indicate possible applications of this study.
2. Potential possible physical applications are given in the introduction.
3.The conclusion of the article is expanded, it indicates the prospects for this research.
4. The text of the article was revised again.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Dear friends ,
Thanks for the great research. Let me make a few comments:
In the References section:
- there are practically no references to studies of recent years ...
- almost all references refer to researchers from the former Soviet Union - is there a good reason for that?
Section Conclusions: very very poor - in my opinion it should be expanded.
Proof of Theorem 4 for s = 2, mistakenly in my opinion, I advise you to double-check the results.
section 29, wrongly in my opinion, I advise you to double-check the results.
The work is written in a very difficult and very incomprehensible language - is there a reason for this?
thank you !
Author Response
First of all, many thanks to the reviewer for his attention to the work.
The comments of the reviewer were taken into account:
- Introduced a link to the book
Ao, S.I; Gelman L .; Electrical Engineering and Applied Computing; Springer Science + Business Media, B.V, 2011,
doi: 10.1007 / 978-94-007-1192-1.
instead of a book
Afanaseva, N.A .; Bulot L.P .; Electrical Engineering and Electronics; St. Petersburg, Russian Federation, 2010. - Introduced a link to the book
Balakrishnan, R .; Ranganathan K .; A Textbook of Graph Theory; Springer Science + Business Media, New York,
2012, doi: 10.1007 / 978-1-4614-4529-6.
instead of a book
Tsoi, S .; Tshai S.M .; Applied graph theory; Alma-Ata, USSR, 1974.
Added links to articles
1. Nurakhmetov D .; Jumabayev S .; Aniyarov A .; Kussainov R .; Symmetric Properties of Eigenvalues ​​and
Eigenfunctions of Uniform Beams. Symmetry 2020, 12:12, 1-13, doi: 10.3390 / sym12122097.
2.Yurko V .; Inverse problems for differential pencils on A-graphs. Journal of Inverse and Ill-Posed Problems 2017,
25: 6, 819-828, doi: 10.1515 / jiip-2016-0065
3. Liu D.-Q .; Yang C.-F .; Inverse spectral problems for Dirac operators on a star graph with mixed boundary
conditions. Mathematical Methods in the Applied Sciences 2021, doi: 10.1002 / mma.7436
2. The conclusion of the article is expanded, it indicates the prospects for this research.
3.The following remark "section 29, wrongly in my opinion, I advise you to double-check the results" could not be answered, since there are no sections 29 in the work.
4.The text of the article was revised again.
5. A more detailed proof of Theorem 4 is given for s = 2.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The manuscript has been improved a lot compared to the first version. Thank the authors for the corresponding response and illustration. I recommend the publication of the work!
Author Response
The introduction has been expanded to indicate possible applications of this study.
It is proved in the work that a finite number of eigenfrequencies is sufficient for uniquely recovering the fixings of the ends of the rods. Moreover, the total number of eigenfrequencies required for unambiguous restoration of boundary restraints does not exceed 2(m + 1)2. In [14], the problem of recovering the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with nonseparated boundary conditions was considered.
The conclusion of the article is expanded, it indicates the prospects for this research.
The total number of eigenvalues required to uniquely recover the boundary coefficients on a
star graph with an (m + 1) edge does not exceed . An interesting question seems to be: to determine the minimum number of eigenvalues for the unambiguous determination of the boundary coefficients.
Author Response File: Author Response.docx
Reviewer 2 Report
Dear friends ,
introduction- Can be improved
conclusions -conclusions
Thank you !
Author Response
The introduction has been expanded to indicate possible applications of this study.
It is proved in the work that a finite number of eigenfrequencies is sufficient for uniquely recovering the fixings of the ends of the rods. Moreover, the total number of eigenfrequencies required for unambiguous restoration of boundary restraints does not exceed 2(m + 1)2. In [14], the problem of recovering the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with nonseparated boundary conditions was considered.
The conclusion of the article is expanded, it indicates the prospects for this research.
The total number of eigenvalues required to uniquely recover the boundary coefficients on a
star graph with an (m + 1) edge does not exceed . An interesting question seems to be: to determine the minimum number of eigenvalues for the unambiguous determination of the boundary coefficients.
Author Response File: Author Response.docx
