Article retraction and statement of concern

Expression of Concern
Issued by the editor-in-chief in cases where there is a reasonable suspicion of an ethical violation, but the investigation is still ongoing or the evidence is not conclusive.
Grounds: Serious doubts about the reliability of the data, suspicions of citation manipulation, or a potential conflict of interest that has not been declared.
Purpose: To inform the scientific community that the article is under editorial supervision until all the circumstances have been clarified.
Outcome: After the investigation is complete, the statement may be withdrawn (if the suspicions are not confirmed) or replaced with a notice of retraction.

Retraction of the article (Retraction)
The most severe measure used to identify articles whose results are so erroneous or unreliable that they cannot be trusted. According to the COPE Retraction Guidelines, which the Journal adheres to, an article may be retracted due to:
detection of significant plagiarism or duplication of publication;
fabrication or falsification of data (particularly in mathematical proofs or calculations, fraudulent use of data);
unintentional critical errors that completely nullify the conclusions of the study;
gross violations of publication ethics and conflict of interest.
Article retraction procedure. The EASE Retraction Form is used for the retraction procedure. The article should be withdrawn after the editor-in-chief and editor-in-chief of the journal have carefully considered the appeal received from the editor(s), author(s) or reader(s) (for details on the procedure for considering appeals, see the section "Appeals and Appeals").
If, as a result of considering the appeal, it turns out that:
the conclusions are unreliable or made on the basis of a significant error (in particular, a miscalculation or experimental error), or as a result of falsification (in particular, image manipulation);
the text contains plagiarism; ω the conclusions have already been published previously without proper reference to previous sources or disclosure of information to the editor, without permission for re-publication or justification (i.e., a case of duplication of publications);
the text contains materials or data without obtaining proper permission for use; ω copyright has been violated or another significant violation of rights has been detected (in particular, defamation, violation of confidentiality, etc.);
the research is unethical;
the publication was solely based on a compromised or manipulative review process;
the author(s) did not provide the editorial office with information about a significant conflict of interest that, in the opinion of the editor-in-chief, could have significantly influenced the evaluation of the work or the recommendations of the editors and reviewers;
the original PDF file of the article on the website is marked with a watermark “RETRACTED”, but remains available to maintain the transparency of the scientific record. An official notice of retraction is published separately, indicating the reasons.

Removal of the article (Removal)
Complete removal of the published text of the article from the Journal website and electronic repositories is used only in exceptional cases when keeping the material in the public domain creates direct legal risks or security threats.
Examples of such situations may include:
Violation of intellectual property rights of third parties. If the article contains program code, algorithms or proprietary data, the use of which was not authorized by the owner (for example, disclosure of trade secrets or confidential computational methods).
Data confidentiality breach. If personal or confidential data was used in applied mathematical research (in particular in the field of mathematical biology, statistics or social modeling) without the consent of the subjects, which identifies specific individuals.
Legal requirements – execution of court decisions on defamation, copyright infringement or other legal requirements.
Cybersecurity threat. If the published material contains vulnerabilities or methods, the direct application of which could harm critical digital infrastructure (for example, in the field of applied cryptography).
Violation of legislation. – the presence in the text of calls for violation of territorial integrity, state order or other norms stipulated by the legislation of Ukraine (in particular, clause 2.2.8 of this Policy).
Removal procedure. In the event of removal of the article, the full text (PDF/HTML) is removed from the OJS platform. Instead, it remains page with metadata (title, authors, DOI) and an official message from the Editors explaining the reasons for the deletion. This is necessary to preserve the integrity of the scientific record and to inform readers who may have previously cited this work.

Substitution

In exceptional cases, the Editorial Board may consider replacing a published article with an updated version. This procedure is used only when a serious error is found in the original text that does not invalidate the work, but requires correction to ensure scientific accuracy.

Examples of such precedents in the Journal may include:

Correction of proofs - if the authors have discovered a logical error in the proof of a theorem or lemma, which can be eliminated without changing the formulation of the main result.

Clarification of algorithms - if an error is found in a mathematical model or program code, which leads to incorrect computational data, but the general approach remains correct.

Improvement of visualization - replacement of graphs or diagrams, if the original versions were misleading due to technical failures in rendering complex mathematical objects.

Substitution procedure:

Request. Authors submit a detailed description of the error and a new version of the manuscript.
Peer review. The editor or independent reviewer checks whether the correction actually fixes the problem and is not an attempt to replace the research results with others.
Publication. The original article is replaced by a new version (PDF).
Transparency. A clear note is added on the first page of the new version of the article and in its metadata: “This article replaces the previous version from [date]. A description of the changes is available at [DOI of the replacement note]”.
Archiving. The previous version of the article is removed from open access, but is stored in the publisher’s archive to ensure the transparency of the scientific record.

Integrity of images and graphic data

The Journal’s editorial team adheres to strict standards for the scientific accuracy of graphic materials. Any image (graph, diagram, scheme, result of computer simulation) must be an accurate reflection of the original data.

Acceptability criteria and violations:

Selective retouching, changing the brightness or contrast of individual areas of the graph is unacceptable if this leads to hiding anomalies or artificially emphasizing certain results.
The use of generative artificial intelligence (Generative AI) to create illustrations, function graphs or visualizations of numerical arrays is allowed only if the tool is clearly indicated and the generation algorithm is described. Attempts to present AI-generated graphs as a direct result of real data analysis without proper justification are considered falsification.
Graphs should be constructed with respect for proportions and appropriate axis scales. The use of visual effects (e.g. 3D effects for 2D data) that may mislead the reader about the significance of deviations is not recommended.

Verification procedure:

Editors and reviewers have the right to require authors to provide the source data (point sets, Python/R/MATLAB program codes, LaTeX/PGFPlots files) on the basis of which the image was constructed.
If signs of intentional distortion of data in the graphs are detected after publication, the Editorial Board acts in accordance with clause 2.11.3.
If the error in the image is technical and unintentional, the Correction or Substitution procedure is applied.