Asia Pacific Academy of Science Pte. Ltd. (APACSCI) specializes in international journal publishing. APACSCI adopts the open access publishing model and provides an important communication bridge for academic groups whose interest fields include engineering, technology, medicine, computer, mathematics, agriculture and forestry, and environment.
If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.
Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.
Mathematics and Systems Science (MSS, eISSN: 3029-2522) is an international, peer-reviewed, open access journal on Mathematics. The journal welcomes submissions relate to mathematics, applied mathematics, computational mathematics, system theory, system control, system engineering, system biology, operations research and management, probability theory, statistics, information processing.
Focus and Scope
Mathematics and Systems Science (MSS, eISSN: 3029-2522) is an international, peer-reviewed, open access journal on Mathematics. The journal welcomes submissions relate to mathematics, applied mathematics, computational mathematics, system theory, system control, system engineering, system biology, operations research and management, probability theory, statistics, information processing.
Engineering Mathematics
Mathematics and Computer Science
Network Science
Dynamical Systems
Computational and Applied Mathematics
Fuzzy Sets, Systems and Decision Making
Difference and Differential Equations
Financial Mathematics
Algebra and Geometry
Probability and Statistics
For Authors
APACSCI upholds the spirit of strict adherence to high ethical standards. This is consistent with APACSCI’s mission of publishing high-quality articles and promoting open scientific exchanges globally. APACSCI follows the Ethical Oversight Guidelines of the Committee on Publication Ethics (COPE) in overseeing the publication process, as well as the activities of APACSCI journals, editors, and reviewers.
APACSCI and all the editors adhere to the following guidelines:
APACSCI is committed to protecting the privacy of its contributors and promises not to disclose personal information to third parties without permission, unless for necessary purposes of the publishing process or required by law.
Complaints and appeals
APACSCI takes allegations of misconduct (refer to the Misconduct Policy for more details) seriously and will launch an immediate investigation by a group of investigation members. Decisions will be made by the investigation group based on clear evidence, and the authors will be informed. If there is any appeal against the decision, it must be made to the publisher within 14 days of the decision date, or else actions will be taken after 14 days. The decision on the appeal is final.
Authors also could express complaints and concerns about delays, extensions, and unreasonable handling procedures during the editing process and the time it takes. The editor-in-chief will be accountable for initiating an investigation into the issue, and the complainant will receive feedback. Reasonable editing procedures will be enhanced.
Any complaints and appeals against APACSCI journals and editors can be directed to the publisher at editorial_office@apacsci.com, and APACSCI follows COPE guidelines in handling all complaints and appeals.
Authors should read the “Author Guidelines” before making a submission, and make sure that the manuscripts were written in accordance to the style and specifications of the journal’s policy.
All manuscripts submitted to Mathematics and Systems Science are subject to rigorous peer review. Prior to the peer review process, the manuscripts will be screened for acceptable English language, novelty and relevance to the Focus and Scope of the journal.
Any manuscripts submitted to Mathematics and Systems Sciencewill be treated as confidential materials. The manuscripts will not be disclosed to anyone except individuals such as editorial staff, reviewers and editors who participate in the initial screening, review, processing and preparation of the manuscript for publication (if accepted).
A manuscript would not be accepted if it has been published or is currently under consideration for publication in any other journals. The authors are required to notify the editorial team if the findings and data in their submissions have been presented in conferences.
Authors are required to declare any potential conflicts of interest (financial or non-financial) during the submission stage. Any agreements with study sponsors (for-profit or non-profit), such as those that interfere with the authors’ access to the study’s data or with the authors’ ability to analyze or interpret the data and to publish manuscripts independently according to their own decision, should be avoided by authors at all costs.
APACSCI also requires reviewers and editors to declare any (potential) non-financial conflicts of interest and declare any unpaid roles or relations that may influence the decision on the manuscript’s publication before acknowledging the assigned request. These include, but are not limited to, unpaid roles in a governmental or non-governmental organization, unpaid roles in an advocacy or lobbying organization, and unpaid advisory positions in a commercial organization.
In addition, reviewers and editors must disclose any association that poses a conflict of interest in connection with the manuscript, including but not limited to those interferes with, or could reasonably be perceived as interfering with, the full and objective presentation, peer review, editorial decision-making, or publication of research or non-research articles submitted to a journal. Examples are personal or work-related relationships with one of the authors or the reviewer is on the authors’ avoidance list.
Following COPE guidelines, APACSCI will not accept any misconduct behaviors that may mislead researchers.
Plagiarism
Plagiarism is not acceptable. Using the content from one’s own previously published articles without proper citation is also considered plagiarism. APACSCI adopts Crossref Similarity Check (powered by iThenticate) for checking the originality of submissions. Manuscripts with a high similarity index may be rejected.
Fabrication and falsification
Fabrication and falsification of data or images will mislead researchers. APACSCI strongly opposes such practices and will reject suspicious submissions.
Duplicate submission
Duplicate submission of a manuscript that has been published or submitted to other journals at the same time will not be considered.
Manipulation
Peer review manipulation is expressly forbidden. In particular, peer review manipulation by editors involves ethical issues, and when detected or complained about, editors are dealt with seriously and are subject to dismissal.
Eliminate excessive manipulative citation included in the peer review process by reviewers. Reviewers are encouraged to suggest that authors add references that are necessary and constructive to the research. Reviewers' own articles that do not contribute to the scholarly content of the author’s work must not be oversold for the sole purpose of inflating the number of citations to the reviewer's own article.
Authors are prohibited from over-citing their own previously published articles. The journal’s editorial board will determine self-citation thresholds, which authors must strictly adhere to in order to eliminate any suspicion of citation manipulation.
Editors will be involved in the journal management process to detect citation manipulations from authors or reviewers.
As behaviors above are illegal academic and very unethical, the Publisher will deal with it seriously. If any misconduct action is verified, authors and their institutions will be informed, and all the journals of the Publisher will not receive any new submission from these authors and their institutions in three years. If the allegations are disputable, their institutes are responsible to cooperate with the journal in investigating allegations.
If there are any suspicious allegations of the processing of articles especially the peer review process, referring to For Reviewers, the Editor-in-Chief will receive the complaint, and an investigation group will be formed to investigate the entire process, including the reviewers, editors, and staff who are involved. The journal will follow the procedures described in COPE and Publishing Ethics for handling allegations of misconduct.
Correction
Authors are responsible for approving the final version of their manuscript and they should avoid any errors prior to publishing. In the case of errors that occur in a published article and have no influence on research results, APACSCI will issue a correction/erratum.
Authors, readers, and editors are encouraged to report any errors found in published papers. Please contact the editorial office of the particular journal.
Retraction
Based on COPE guidelines, the following conditions can lead to the retraction of a published article:
Unreliable findings
Plagiarism
Published elsewhere without proper attribution to previous sources, disclosure to the editor, permission to republish, or justification
Containing material or data without the authorization for use
Infringement of copyright, violation of privacy, or other legal issues
Unethical research
Dubious peer review processes
Failing to disclose a major competing interest
If any of the above misconduct proved to be true, a retraction notice will be issued with the reason, while the PDF of the retracted article will be watermarked with “Retracted”. The journal editors will inform the authors of the retraction.
Paid Article Processing Charges will not be refunded to the authors if retraction occurs.
Withdrawal
Although not encouraged, authors can initiate the withdrawal of their submission before and during the peer review process by providing the reason. However, authors should note that a penalty fee of US$200 will be imposed for the withdrawal of a submission undergoing the peer review process due to the spent efforts on the evaluation of the manuscript by the editors and reviewers. Upon the approval of submission withdrawal, the submission will be removed from the journal’s operation system, and the authors be informed.
Accepted articles and articles in press may also be withdrawn due to infringements of professional ethical codes (similar reasons to those for retraction).
The language of all manuscripts must be English (either British or American) and non-English words should be used sparingly. Poor English may lead to article rejection. Authors are encouraged to seek language polishing by a native English speaker or a professional editing service.
APACSCI allows authors to post preprints of the manuscript of their original research articles (limited to only this type of article) on community preprint servers, such as arXiv, bioRxiv, and PeerJ Preprint, prior to or simultaneous with their manuscript submission to APACSCI journals. Authors retain the copyright of the manuscript posted on a preprint server.
Authors should inform the editors of the preprint version of their submitted manuscript in a cover letter, as well as provide any associated accession numbers or DOIs. Revised versions per the result of the peer review process and accepted versions for publication should not be posted on a preprint server.
Upon publication of the article, APACSCI encourages authors to link the article in the preprint server to the journal site, so as to guide readers to access and refer to the final version of the article.
Contributed substantially to the conception or design of the manuscript or the acquisition, analysis, or interpretation of data for the manuscript; AND
Drafted the manuscript or reviewed it critically for significant intellectual content; AND
Have final approval of the version to be published; AND
Agreed to be responsible for the manuscript in ensuring that problems relating to the accuracy or completeness of any part of the manuscript are appropriately investigated and resolved.
Individuals who do not meet the above four criteria should not be listed as authors but should be acknowledged. All authors are expected to make meaningful contributions to this work. The publisher strictly prohibits false authorships, including those obtained through purchase, and only recognizes genuine contributions. Authors should disclose whether artificial intelligence (AI)-assisted technologies were used in the preparation of their manuscripts and how they used them. Authors should also report the use of AI for writing assistance in the Acknowledgment section. AI tools should not be used in sections that rely on human intellectual analysis, such as data interpretation and conclusion summarization.
A corresponding author should be marked with “*”, and the maximum of corresponding authors is two. A corresponding author serves as a representative of the authors and is responsible for contacting editors and reviewers, e.g., submitting manuscripts, responding to reviews, accepting queries, proofreading galleys, making corrections, etc.
Changes to Authorship
Authorship changes (addition, deletion, or rearrangement of author names) should be made before the acceptance of the manuscript. Confirmation from all authors (including existing authors and author(s) to be added and/or removed) should be provided to the editorial office of the journal, together with the reason for such changes. Changes can be made after the approval of the journal. The publisher will deal with any changes or dispute over authorship following the COPE flowcharts of authorship and contributorship.
The opinions, statements, methods, results, and data in APACSCI's published articles are those of the authors and do not reflect the opinions of APACSCI and its editors. APACSCI disclaims responsibility for any injury to people or property resulting from any ideas, methods, or products referred to in the articles or advertisements.
Authors contributing to APACSCI journals retain the copyright.
All articles published by Mathematics and Systems Scienceare licensed under the Creative Commons International Licenses. Without any explicit request from the corresponding author during the submission stage, a paper will be published under the Creative Commons Attribution 4.0 International License (CC BY 4.0) by default. Authors who would like to publish their work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), they should express their request during the submission stage. Please include the statement below in the "Comments for the Editor column" on the submission page:
The contributors or authors for this submission entitled "[MANUSCRIPT TITLE]", i.e. [NAMES of ALL AUTHORS], have given their consents to alter the Creative Commons License to *CC BY-NC 4.0* under which this submission will be published inMathematics and Systems Science.
It is the responsibility of authors to obtain permission to reuse material previously published under a more restrictive license from the copyright holder before the submission stage. These may include figures, tables, and schemes.
The publisher requests that this journal only consider advertising applications that are relevant to the contents of the journal, if available.
The publisher (APACSCI) reserves the right to accept or refuse advertising. The Journal Editorial Office will evaluate whether to accept the request.
Advertisements must comply with relevant rules and laws in the country where they will appear.
Advertisements should be legible and advertisers identifiable. Sponsors may not arrange or influence editorial decisions including any content in the journal.
Advertisements must not be misleading or deceptive. Advertising content must not contain indecent, offensive, or sensitive information (such as politics, ethnicity, gender, religion, etc.).
APACSCI disclaims responsibility for any damages resulting from advertisements in its journals. The publisher or journal does not accept advertisements for products or services known to be harmful to health/science or contrary to academic principles.
Unless the advertiser requests differently, all advertisements posted by the publisher will be displayed at random. Special requests need to be addressed to the publisher, who will make a final decision on a case-by-case basis within 7 working days.
Advertising is independent, with journal web features and academic content free from all advertising and product interference.
Once an advertisement is posted online, it will be removed from the journal’s website at any time if the Editor-in-Chief or publisher requests that it be removed.
APACSCI’s publishing model is open access. Open access enables readers to freely access and download articles immediately after publication online. APACSCI charges authors article processing charges (APCs) so as to cover operation costs, such as those arising from the evaluation and production processes. APCs should be paid upon the acceptance of articles and ahead of publication.
APCs of Mathematics and Systems Science are US$800.
Waiver and Discount Policy
APACSCI believes there should be no barriers to the dissemination of knowledge, and thus APACSCI offers APC waivers and discounts to authors from low-income countries and authors with special circumstances. Authors should write to the editorial office of the specific journal to apply for waivers and discounts. The decision to approve such applications is made by the editorial office on a case-by-case basis. Publishing fees or waiver status should not influence editorial decision making.
All the articles published online will be archived in Portico for long-term digital preservation.
Authors are encouraged to self-archive the final version of their published articles into institutional repositories (such as those listed in the Directory of Open Access Repositories).
Authors are also encouraged to use the final PDF version published on the website of Mathematics and Systems Science.
Researchers using an Artificial Intelligence (AI) tool/service to directly generate the manuscript text must provide clear disclosures and statements, otherwise it will be considered academic misconduct. The journal allows the use of an AI tool/service for text embellishment and automatic sorting of references, but does not recommend the use of the AI tool/service in the thinking and concluding sessions of human involvement such as data analysis and interpretation, opinion hypothesis and conclusions, and the AI tool/service cannot fulfill the role of a textual author. If any part of the manuscript was written using an AI tool/service, it must be described openly, transparently, and in detail in the Methods or Acknowledgments section, for example:
"In the preparation of this work, the authors used the [name of the specific AI tool/service] to [purpose of use: e.g., literature research/text embellishment, etc.]. After using this tool/service, the authors reviewed and edited the content as needed, and take full responsibility for the content of the publication."
Mathematics and Systems Science adopts and follows the rules of International System of Units (SI) for physical quantities and units of measurement. For example:
Quantities including time, length, mass, electric current, etc., should be written as s (second), m (metre), kg (kilogram), A (ampere) after metric numbers.
Adopt unified format for the same unit of measurement.
According to the data and reproducibility of COPE, APACSCI encourages authors to share associated data, code, and materials, register clinical trials, and use standardized guidelines to achieve greater transparency, replicability, and trust in scientific findings. Thus, authors are encouraged to deposit datasets in a data repository; the premise is that this data is not suitable for submission as online supplementary files. Authors who have deposited raw data in community database repositories are encouraged to include a data availability statement in their manuscript. The statement should provide information about the availability of the research data and any limitations or conditions associated with accessing the data, except for reasonable controls related to human privacy or biosecurity. Reusing scientific data can offer great potential for further scientific and economic development.
Data sharing
For data shared, the FAIR Data Principles should be followed, which guides that (meta)data are assigned a globally unique and eternally persistent identifier. Authors should cite the correct sources. Collaborative practices should be implemented across journals and institutions to monitor and ensure the scientific validity and credibility of overall research practices. Authors are encouraged to prioritize the use of original data from their study and provide supporting data such as accessible data sources as early as possible.
Regarding data involving confidentiality/privacy/personal privacy, etc., authors are advised to do their best to hide identifiable sensitive information and to share data in strict accordance with mandatory guidelines for the discipline.
According to the guidelines of COPE regarding unpublished data, the journal will address concerns to the data provider regarding the scientific rigor of an unpublished dataset. The journal will contact the corresponding author, and request comments on the concerns, supporting documentation as needed, and information about any other affected content. Following the guidelines regarding published data, if there is a manuscript associated with a published dataset whose scientific rigor is in doubt, the journal will contact any implicated journals that have published results from the suspicious dataset, summarizing the issue and actions taken to date. Authors must respond with a satisfactory update. If the issues are major or impact the conclusions of the manuscript, the author(s) should withdraw the manuscript or the journal will reject the submission.
Data citation
Authors are encouraged to cite any datasets deposited in external repositories mentioned in their manuscript in the references. For previously published datasets, authors should cite both the published research article and the source of the dataset itself. Journal editorial staff will check and enforce proper data citation before publication.
Data citations should include the minimum information recommended by DataCite:
1) Author(s)
2) Year of publication/release
3) Title
4) Publisher/repository or archive name
5) Persistent identifier (e.g., DOI)
Data repository
Authors are encouraged to deposit their datasets in the relevant community dataset repository, or a general dataset repository (including any generalist data repository provided by a university, funder or institution for its affiliated researchers) that aligns with the specifications and requirements of their discipline could be selected. The publisher recommends that authors select a repository with a DOI (Digital Object Identifier) to ensure that the referenced dataset can be linked to consistently.
Authors could explore online resources for lists of registered data repositories through FAIRsharing.org and re3data.org.
Here are some examples of generalized dataset repositories:
Before submitting to the journal, authors should read through the author guidelines for preparing their manuscript. Starting in 2024, a new layout style will be applied, so please download the new manuscript template.
Manuscript Format
The manuscript should be in MS Word format. The language of all manuscripts must be English (either British or American) and non-English words should be used sparingly. Poor English may lead to article rejection. Authors are encouraged to seek language polishing by a native English speaker or a professional editing service.
Article Types
Please refer to the Article Types for choosing an appropriate type.
Cover Letter
Authors should attach a cover letter together with the article text. A cover letter should contain a brief explanation of the significance of their work and the intention of doing the work. The cover letter is confidential and will be read only by the editors. It will not be seen by the reviewers.
Article Title
Titles should be no more than 50 words, with significant and attractive information for readers. Titles should not include uncommon jargons, abbreviations, and punctuation.
List of Authors
The list of authors should be arranged based on the level of their contribution, with the major contributor listed first. Corresponding authors should be marked with an asterisk (*). Affiliation information should be provided with the following elements: department, institution, city, postal code (if available), and country. The email address of at least one corresponding author must be provided. All authors must approve the final version of the manuscript and agree with the submission. For more information about authorship, please refer to our Authorship Policy.
Abstract and Keywords
Depending on the article type, an abstract should be provided, which gives a concise summary of the article. It is usually a single paragraph of about 200–250 words maximum. Between 5–8 keywords should be included. Words and phrases in article titles should be avoided as keywords.
Text
The text of manuscripts should be in MS Word format. Original research articles should include the Introduction, Materials and Methods, Results, Discussion, and Conclusion (optional) sections.
Section Headings
Headings are used to indicate the hierarchy of the sections of the text. No more than three levels of headings should be employed. The first level of heading should be numbered as 1., 2., 3., 4. in boldface. Likewise, the second and third levels of headings should also be in boldface, for example, 1.1., 1.2., 1.1.1., 1.1.2.
Introduction
The introduction should provide a background that gives the broad readership an overall outlook on the field and the research performed. It pinpoints a problem and states the significance of the study. The introduction can conclude with a brief statement on the aim of the work and a comment about whether that aim was achieved.
Materials and Methods
This section provides the general experimental design and methodologies used. The aim is to provide enough details for other investigators to fully replicate the experiments. It is also to facilitate a better understanding of the results obtained.
Results
This section can be divided into subheadings. This section focuses on the results of the experiments performed.
Discussion
This section should provide the significance of the results and identify the impact of the research in a broader context. It should not be redundant or similar to the content of the Results section.
Conclusion (Optional)
The conclusion section can only be used for interpretation, and not be used to summarize information already presented in the text or abstract.
Figures and Tables
Figures (photographs, images, graphs, charts, and schematic diagrams) and tables should be referred to within the main text and numbered consecutively as Figure 1, Figure 2, Table 1, Table 2, etc. They should be placed as close as possible to where they are first cited and center-aligned. Both figure captions and table captions should be center-aligned, with figure captions set underneath the figures and table captions above the tables. When captions are longer than one line, they should be left-aligned.
Figures can contain multiple panels. They should be numbered by Latin letters with parentheses, e.g., (a), (b), (c), or (A), (B), (C), placed below the image or within the image.
Tables should be in MS Word/Excel table format. Tables containing too much information can be provided as supplementary material.
In the main text, all figures and tables should be cited, e.g., "Table 1 indicates…", "Figures 1 and 2 shows…", and "Figure 1a,b shows…".
Lists and Equations
Both bulleted lists and numbered lists are acceptable (refer to the template). Equations should be center-aligned and equation numbers should be right-aligned. If cited in the text, equations should be labeled with numbers in parentheses, e.g., Equation (1).
In-Text Citations
All bibliographical references that make an important contribution to the article should be numbered according to the appearance order. When cited in the text, the number should be placed in square brackets, for example:
Negotiation research spans many disciplines [3,4].
This effect has been widely studied [1–5,7].
Appendix (Optional)
An appendix provides information supplementary to an article and is included at the end of the article after the References section and it should start on a new page. For one appendix, it is designated as "Appendix"; for more than one appendix, they are designated "Appendix A", "Appendix B", etc.
An appendix should be cited in the main text. Tables, figures, and equations should be started with the prefix A (i.e., Figure A1, Figure A2, Table A1, etc.).
Back Matter
The sequence of back matter elements in an article is listed below. There is no numeral label for back matter headings. Some of these elements are optional.
Supplementary materials (Optional)
The Supplementary Materials section provides a short description of the supplementary materials. One or more individual supplementary files are allowed and should be submitted in Step 4 during submission. These materials are relevant to the manuscript but remain non-essential to readers' understanding of the article's main content. Please ensure the names of such files contain "suppl. info". Videos may be included in this section.
Author contributions
For original research articles, this section is required, except when there is only one author for the article. The contribution of each co‐author should be reported in this section.
The following statements should be used "Conceptualization, XX and YY; methodology, XX; software, XX; validation, XX, YY and ZZ; formal analysis, XX; investigation, XX; resources, XX; data curation, XX; writing—original draft preparation, XX; writing—review and editing, XX; visualization, XX; supervision, XX; project administration, XX; funding acquisition, YY. All authors have read and agreed to the published version of the manuscript."
Funding (Optional)
Authors can acknowledge financial support in this section, which is NOT mandatory. If authors provide a funding statement, it should be in the same style as the template.
For example:
"This research was funded by [name of funder] grant number [xxx]" and "The APC was funded by [XXX]". Please check carefully that the details given are accurate and that the standard spelling of the funding agency's name in https://search.crossref.org/funding is used, as any errors may affect the authors' future funding.
Acknowledgments (Optional)
Authors can acknowledge any support and contribution that cannot be included in the Author Contributions and Funding sections. This section is NOT mandatory.
Conflict of interest
According to our Conflict of Interest Policy, all authors are required to declare all activities that have the potential to be deemed as a source of competing interest in relation to their submitted manuscript. Examples of such activities include personal or work-related relationships and events. Authors who have nothing to declare should add "No conflict of interest was reported by all authors" or "The authors declare no conflict of interest" in this section.
References
This section is compulsory and should be placed at the end of the manuscript. Footnotes or endnotes should not replace a reference list. The list of references should only include works that are cited in the text and that have been published or accepted for publication. Personal communications should be excluded from this section.
The format of author names should be "Last-Name Initial", e.g., David Smith should be written as Smith D.
Journal
Journals in English:
Author AA, Author BB, Author CC, et al. Title of the article. Journal Name. Year, Volume(Issue) (if available): Firstpage–Lastpage. doi (if available)
Journals in languages other than English:
Author AA, Author BB, Author CC, et al. English title of the article (original language). Journal Name. Year, Volume(Issue) (if available): Firstpage–Lastpage. doi (if available)
Book
A book without editors:
Author AA, Author BB. Chapter (optional). Title of the Book, Edition (if available). Publisher; Year. pp. Page range (optional).
A book with editors:
Author AA, Author BB. Title of the contribution. In: Editor CC, Editor DD (editors). Title of the Book, Edition (if available). Publisher; Year. Volume (optional), pp. Page range (optional).
For a translated book, the translators' names should be placed after the editors' names: "Translator AA (translator)" or "Translator AA, Translator BB (translators)".
If the editors and translators are the same, the format should be as follows:
Author AA, Author BB. Title of the contribution. In: Editor CC, Editor DD (editors and translators). Title of the Book, Edition (if available). Publisher; Year. Volume (optional), pp. Page range (optional).
Conference
Full citations of published abstracts (proceedings):
In most cases, proceedings will be simply called "Proceedings of the Name of the Conference (full name)" without a book title. In this case, please only add the conference name in the proceedings' title and keep that in regular font (i.e., do not italicize):
Author AA, Author BB, Author CC, et al. Title of presentation. In: Proceedings of the Name of the Conference; Date of Conference (Day Month Year) (if available); Location of Conference (City, Country) (if available). Abstract Number (optional), Pagination (optional).
If the proceedings are published as a book with a separate title (i.e., not "Proceedings of the Name of the Conference (full name)" as the title), the book title should be included:
Author AA, Author BB, Author CC. Title of presentation. In: Editor DD, Editor EE (editors) (if available). Title of Collected Work, Proceedings of the Name of the Conference; Date of Conference (Day Month Year) (if available); Location of Conference (City, Country) (if available). Publisher; Year. Abstract Number (optional), Pagination (optional).
Oral presentations without published material:
Author AA, Author BB, Author CC. Title of presentation (if any). Presented at the Name of Conference; Date of Conference (Day Month Year) (if available); Location of Conference (City, Country) (if available); Paper number (if available).
Thesis/Dissertation
Author AA. Title of Thesis [Level of thesis]. Degree‐Granting University; Year.
The level of thesis can be called "XX thesis" or "XX dissertation". Thesis types include but are not limited to the following:
PhD thesis
Master's thesis
Bachelor's thesis
Licentiate thesis
Diploma thesis
Newspaper
Author AA, Author BB, Author CC, et al. Title of article. Title of Periodical, Complete Date, Pagination (if available).
Patent
Patent Owner AA, Patent Owner BB, Patent Owner CC. Title of Patent. Patent Number, Date (Day Month Year, the Application granted date).
Unpublished work
Author AA, Author BB. Title of unpublished work. Journal Title. Year(if available); Phrase Indicating Stage of Publication (submitted, in press, etc.).
Online resources
Author (if available). Title of content (if available). Available online: http://URL (accessed on Day Month Year).
For a homepage, the access date is not required.
Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License (CC BY 4.0), allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit, and that in the event of reuse or distribution, the terms of this license are made clear. With this license, the authors hold the copyright without restrictions and are allowed to retain publishing rights without restrictions as long as this journal is the original publisher of the articles.
Asia Pacific Academy of Science Pte. Ltd. (APACSCI) is devoted to protecting authors' privacy. With APACSCI's privacy policy, authors can rest assured of their privacy in collaborating with APACSCI.
1. Personal information
APACSCI collects personal information when individuals register on a journal site (e.g., as an author), when the editorial office helps them register (e.g., as a reviewer), or when they communicate with APACSCI or subscribe to APACSCI notifications. Information, including name, title, affiliation, country, and e-mail address, will be treated as private and only used for activities involving manuscript processing. APACSCI will not disclose any personal information to third parties. This policy also applies to the information of the co-authors of submissions.
APACSCI collects some other information when individuals visit the APACSCI website, such as log data, device information, IP address, time of visit, and visitor interaction. These data are used for optimizing APACSCI's service, gathering statistics on articles, and promoting the APACSCI website.
Registered individuals can access their accounts or make corrections to their personal information. They also have the right to request APACSCI to delete their information.
2. Third-party links
APACSCI is not responsible for any consequences caused when visitors to the APACSCI website are linked or directed to a third-party website.
3. Contact APACSCI
For any questions regarding APACSCI's privacy policy, please send an email to editorial_office@apacsci.com.
Article Processing Charges (APCs)
APACSCI’s publishing model is open access. Open access enables readers to freely access and download articles immediately after publication online. APACSCI charges authors article processing charges (APCs) so as to cover operation costs, such as those arising from the evaluation and production processes. APCs should be paid upon the acceptance of articles and ahead of publication.
APCs of Mathematics and Systems Science are US$800.
Waiver and Discount Policy
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Abstract
The convergence of technology and education has enabled the creation of instructional programs utilizing digital resources, garnering significant interest from educators in developing mathematical culture curricula. This study investigates these factors by incorporating the perceived importance of policy (PIP) variables into the unified theory of acceptance and use of technology (UTAUT) model. Quantitative analysis was employed to collect online questionnaire data from 873 teachers in Henan Province, which was subsequently analyzed using partial least squares structural equation modeling (PLS-SEM). The findings revealed that (1) performance expectation did not significantly impact teachers’ intentions and behaviors regarding the use of digital resources for developing mathematics culture lessons; (2) effort expectations negatively influenced such use; and (3) social influence, facilitating conditions, and perceived policy importance emerged as key drivers, with social influence exerting the most substantial impact. These insights enhance our understanding of the factors influencing teachers’ integration of digital resources in mathematics culture curriculum development. They can inform strategies to improve teachers’ knowledge of teaching with mathematics technology (KTMT) and to promote technology-enhanced mathematics teaching and learning.
Abstract
If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.
Abstract
We introduce an algorithm which allows us to prove that there exists an infinite number of matrix strong Diophantine -tuples. We show that Diophantine quadruples generate matrix elliptic (or hyperelliptic) curves which have each matrix points.
Abstract
Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.