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1. Shard Calculation

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Calculated Shard: 11 (from laksa099)

2. Crawled Status Check

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curl -X POST \
  'http://laksa011.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.ejpam.com/ejpam/article/view/5986\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.ejpam.com/ejpam/article/view/5986\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.ejpam.com\/ejpam\/article\/view\/5986","crawl_time":1775630450,"first_indexed_time":1771788153,"http_code":200,"src_unparsed":"com,ejpam!www,\/ejpam\/article\/view\/5986 s443","src_root_hash":"15298235157264263211","history_drop_reason":null,"meta_title":"Modified Laplace-type Transform and Its Properties | European Journal of Pure and Applied Mathematics","meta_descriptions":[],"attrs_boilerpipe_text":"Authors\nInci Ege\nDepartment of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye\nDOI:\nhttps:\/\/doi.org\/10.29020\/nybg.ejpam.v18i2.5986\nKeywords:\nLaplace transform, \t\t\t\t\t\t\t\t\t\t\tLaplace-type integral transform, \t\t\t\t\t\t\t\t\t\t\tmodified degenerate Gamma function\nAbstract\nIn this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind.\nReferences\nPublished\n2025-05-01\nIssue\nSection\nMathematical Analysis\nLicense\nCopyright (c) 2025 Inci Ege\nThis work is licensed under a\nCreative Commons Attribution-NonCommercial 4.0 International License\n.\nUpon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.\nBy agreeing to this statement, you acknowledge that:\nYou retain full copyright over your work.\nThe European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).\nThis license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.","attrs_markdown":"![](https:\/\/www.facebook.com\/tr?id=696542671375298&ev=PageView&noscript=1) \\>\n\n[Skip to main content](https:\/\/www.ejpam.com\/ejpam\/article\/view\/5986#pkp_content_main) [Skip to main navigation menu](https:\/\/www.ejpam.com\/ejpam\/article\/view\/5986#siteNav) [Skip to site footer](https:\/\/www.ejpam.com\/ejpam\/article\/view\/5986#pkp_content_footer)\n\nOpen Menu\n\n[![ejpam-logo](https:\/\/www.ejpam.com\/public\/journals\/1\/pageHeaderLogoImage_en_US.png)](https:\/\/www.ejpam.com\/ejpam\/article\/view\/%09%09%09%09%09%09https:\/\/www.ejpam.com\/ejpam\/index%0A%09%09%09%09%09)\n\n- [Current](https:\/\/www.ejpam.com\/ejpam\/issue\/current)\n- [Archives](https:\/\/www.ejpam.com\/ejpam\/issue\/archive)\n- [Search](https:\/\/www.ejpam.com\/ejpam\/search)\n- [Announcements](https:\/\/www.ejpam.com\/ejpam\/announcement)\n- [Login](https:\/\/www.ejpam.com\/ejpam\/login)\n- [Register](https:\/\/www.ejpam.com\/ejpam\/user\/register)\n- [About](https:\/\/www.ejpam.com\/ejpam\/about)\n  - [About the Journal](https:\/\/www.ejpam.com\/ejpam\/about)\n  - [Editorial Board](https:\/\/www.ejpam.com\/ejpam\/editorial-board)\n  - [Focus and Scope](https:\/\/www.ejpam.com\/ejpam\/about\/editorialPolicies-focusAndScope)\n  - [Peer Review Process](https:\/\/www.ejpam.com\/ejpam\/about\/editorialPolicies-peerReviewProces)\n  - [Abstracting and Indexing](https:\/\/www.ejpam.com\/ejpam\/about\/editorialPolicies-abstracting)\n  - [Publication Ethics and Publication Malpractice Statement](https:\/\/www.ejpam.com\/ejpam\/about\/editorialPolicies-publicationEthics)\n  - [Citation Policy](https:\/\/www.ejpam.com\/index.php\/ejpam\/about\/citationPolicies)\n  - [Artificial Intelligence (AI) Use Policy](https:\/\/www.ejpam.com\/ejpam\/about\/editorialPolicies-artificialIntelligenceUsePolicy)\n  - [Author Fees](https:\/\/www.ejpam.com\/ejpam\/about\/submissions-authorFees)\n  - [Business Model and Revenue Sources](https:\/\/www.ejpam.com\/ejpam\/about\/businessModel-revenueSources)\n  - [Publishing Schedule](https:\/\/www.ejpam.com\/ejpam\/about\/publishing-schedule)\n  - [Submissions](https:\/\/www.ejpam.com\/ejpam\/about\/submissions)\n  - [Privacy Statement](https:\/\/www.ejpam.com\/ejpam\/about\/privacy)\n  - [Contact](https:\/\/www.ejpam.com\/ejpam\/about\/contact)\n\n[Search](https:\/\/www.ejpam.com\/ejpam\/search)\n\n- [Register](https:\/\/www.ejpam.com\/ejpam\/user\/register)\n- [Login](https:\/\/www.ejpam.com\/ejpam\/login)\n\n1. [Home](https:\/\/www.ejpam.com\/ejpam\/index)  \/\n2. [Archives](https:\/\/www.ejpam.com\/ejpam\/issue\/archive)  \/\n3. [Vol. 18 No. 2: (April 2025)](https:\/\/www.ejpam.com\/ejpam\/issue\/view\/78)  \/\n4. Mathematical Analysis\n\n# Modified Laplace-type Transform and Its Properties\n## Authors\n- Inci Ege   Department of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye\n\n## DOI:\n<https:\/\/doi.org\/10.29020\/nybg.ejpam.v18i2.5986>\n\n## Keywords:\nLaplace transform, Laplace-type integral transform, modified degenerate Gamma function\n\n## Abstract\nIn this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind.\n## References\n\n## Downloads\n- [Full Text](https:\/\/www.ejpam.com\/ejpam\/article\/view\/5986\/1994)\n\n## Published\n2025-05-01\n\n## Issue\n[Vol. 18 No. 2: (April 2025)](https:\/\/www.ejpam.com\/ejpam\/issue\/view\/78)\n\n## Section\nMathematical Analysis\n\n## License\nCopyright (c) 2025 Inci Ege\n\n[![Creative Commons License](https:\/\/i.creativecommons.org\/l\/by-nc\/4.0\/88x31.png)](https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/)\n\nThis work is licensed under a [Creative Commons Attribution-NonCommercial 4.0 International License](https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/).\n\nUpon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.\n\nBy agreeing to this statement, you acknowledge that:\n\n- You retain full copyright over your work.\n- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).\n- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.\n\n## How to Cite\nModified Laplace-type Transform and Its Properties. (2025). *European Journal of Pure and Applied Mathematics*, *18*(2), 5986. <https:\/\/doi.org\/10.29020\/nybg.ejpam.v18i2.5986>\n\nMore Citation Formats\n\n- [ACS](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/acs-nano?submissionId=5986&publicationId=5764&issueId=78)\n- [APA](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/apa?submissionId=5986&publicationId=5764&issueId=78)\n- [ABNT](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/associacao-brasileira-de-normas-tecnicas?submissionId=5986&publicationId=5764&issueId=78)\n- [Harvard](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/harvard-cite-them-right?submissionId=5986&publicationId=5764&issueId=78)\n- [IEEE](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/ieee?submissionId=5986&publicationId=5764&issueId=78)\n- [Turabian](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/turabian-fullnote-bibliography?submissionId=5986&publicationId=5764&issueId=78)\n- [Vancouver](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/vancouver?submissionId=5986&publicationId=5764&issueId=78)\n- [AMA](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/get\/ama?submissionId=5986&publicationId=5764&issueId=78)\n\nDownload Citation\n\n- [Endnote\/Zotero\/Mendeley (RIS)](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/download\/ris?submissionId=5986&publicationId=5764&issueId=78)\n- [BibTeX](https:\/\/www.ejpam.com\/ejpam\/citationstylelanguage\/download\/bibtex?submissionId=5986&publicationId=5764&issueId=78)\n\n## submit a manuscript\n[Submit a Manuscript](https:\/\/ejpam.com\/index.php\/ejpam\/about\/submissions)\n\n## Information\n- [For Readers](https:\/\/www.ejpam.com\/ejpam\/information\/readers)\n- [For Authors](https:\/\/www.ejpam.com\/ejpam\/information\/authors)\n- [For Librarians](https:\/\/www.ejpam.com\/ejpam\/information\/librarians)\n\n## right\\_block\\_image\nEJPAM IN THE NEWS\n\n- [Oxford University announces Nobel Laureate Sir Clive W.J. Granger Special Issue.](http:\/\/www.inet.ox.ac.uk\/news\/new-publication \"EJPAM, Oxford University Granger Special Issue\")\n\n## affiliated\\_journal\\_block\n**OUR **AFFILIATED** JOURNALS**\n\n- - [European Journal of Mathematical Sciences](https:\/\/ejmathsci.org\/index.php\/ejmathsci \"European Journal of Mathematical Sciences\")\n  - [Journal of Analytics](https:\/\/www.journalofanalytics.com\/ \"Journal of Analytics\")\n  - [Journal of Algebraic Statistics](https:\/\/jalgstat.com\/ \"Journal of Algebraic Statistics\")\n\n## formatting\\_package\n**EJPAM FORMATTING PACKAGE**\n\n- [EJPAM Formatting Package](https:\/\/www.ejpam.com\/public\/journals\/1\/EJPAM_formatting_package.zip \"EJPAM Author Formatting Package\")\n\nEuropean Journal of Pure and Applied Mathematics (EJPAM) Published by New York Business Global, Maryland, USA","attrs_readable_markdown":"## Authors\n- Inci Ege   Department of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye\n\n## DOI:\n<https:\/\/doi.org\/10.29020\/nybg.ejpam.v18i2.5986>\n\n## Keywords:\nLaplace transform, Laplace-type integral transform, modified degenerate Gamma function\n\n## Abstract\nIn this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind.\n## References\n\n## Published\n2025-05-01\n\n## Issue\n## Section\nMathematical Analysis\n\n## License\nCopyright (c) 2025 Inci Ege\n\n[![Creative Commons License](https:\/\/i.creativecommons.org\/l\/by-nc\/4.0\/88x31.png)](https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/)\n\nThis work is licensed under a [Creative Commons Attribution-NonCommercial 4.0 International License](https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/).\n\nUpon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.\n\nBy agreeing to this statement, you acknowledge that:\n\n- You retain full copyright over your work.\n- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).\n- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.","meta_canonical":null}

3. Robots.txt Check

Query:

Response:

4. Spam/Ban Check

Query:

Response:

5. Seen Status Check

ℹ️ Skipped - page is already crawled

📄

INDEXABLE

✅

CRAWLED

5 days ago

🤖

ROBOTS ALLOWED

Page Info Filters

Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
Age cutoff	PASS	`download_stamp > now() - 6 MONTH`	0.2 months ago
History drop	PASS	`isNull(history_drop_reason)`	No drop reason
Spam/ban	PASS	`fh_dont_index != 1 AND ml_spam_score = 0`	ml_spam_score=0
Canonical	PASS	`meta_canonical IS NULL OR = '' OR = src_unparsed`	Not set

Page Details

Property	Value
URL	https://www.ejpam.com/ejpam/article/view/5986
Last Crawled	2026-04-08 06:40:50 (5 days ago)
First Indexed	2026-02-22 19:22:33 (1 month ago)
HTTP Status Code	200
Meta Title	Modified Laplace-type Transform and Its Properties \| European Journal of Pure and Applied Mathematics
Meta Description	null
Meta Canonical	null
Boilerpipe Text	Authors Inci Ege Department of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye DOI: https://doi.org/10.29020/nybg.ejpam.v18i2.5986 Keywords: Laplace transform, Laplace-type integral transform, modified degenerate Gamma function Abstract In this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind. References Published 2025-05-01 Issue Section Mathematical Analysis License Copyright (c) 2025 Inci Ege This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License . Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes. By agreeing to this statement, you acknowledge that: You retain full copyright over your work. The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.
Markdown	![](https://www.facebook.com/tr?id=696542671375298&ev=PageView&noscript=1) \> [Skip to main content](https://www.ejpam.com/ejpam/article/view/5986#pkp_content_main) [Skip to main navigation menu](https://www.ejpam.com/ejpam/article/view/5986#siteNav) [Skip to site footer](https://www.ejpam.com/ejpam/article/view/5986#pkp_content_footer) Open Menu [![ejpam-logo](https://www.ejpam.com/public/journals/1/pageHeaderLogoImage_en_US.png)](https://www.ejpam.com/ejpam/article/view/%09%09%09%09%09%09https://www.ejpam.com/ejpam/index%0A%09%09%09%09%09) - [Current](https://www.ejpam.com/ejpam/issue/current) - [Archives](https://www.ejpam.com/ejpam/issue/archive) - [Search](https://www.ejpam.com/ejpam/search) - [Announcements](https://www.ejpam.com/ejpam/announcement) - [Login](https://www.ejpam.com/ejpam/login) - [Register](https://www.ejpam.com/ejpam/user/register) - [About](https://www.ejpam.com/ejpam/about) - [About the Journal](https://www.ejpam.com/ejpam/about) - [Editorial Board](https://www.ejpam.com/ejpam/editorial-board) - [Focus and Scope](https://www.ejpam.com/ejpam/about/editorialPolicies-focusAndScope) - [Peer Review Process](https://www.ejpam.com/ejpam/about/editorialPolicies-peerReviewProces) - [Abstracting and Indexing](https://www.ejpam.com/ejpam/about/editorialPolicies-abstracting) - [Publication Ethics and Publication Malpractice Statement](https://www.ejpam.com/ejpam/about/editorialPolicies-publicationEthics) - [Citation Policy](https://www.ejpam.com/index.php/ejpam/about/citationPolicies) - [Artificial Intelligence (AI) Use Policy](https://www.ejpam.com/ejpam/about/editorialPolicies-artificialIntelligenceUsePolicy) - [Author Fees](https://www.ejpam.com/ejpam/about/submissions-authorFees) - [Business Model and Revenue Sources](https://www.ejpam.com/ejpam/about/businessModel-revenueSources) - [Publishing Schedule](https://www.ejpam.com/ejpam/about/publishing-schedule) - [Submissions](https://www.ejpam.com/ejpam/about/submissions) - [Privacy Statement](https://www.ejpam.com/ejpam/about/privacy) - [Contact](https://www.ejpam.com/ejpam/about/contact) [Search](https://www.ejpam.com/ejpam/search) - [Register](https://www.ejpam.com/ejpam/user/register) - [Login](https://www.ejpam.com/ejpam/login) 1. [Home](https://www.ejpam.com/ejpam/index) / 2. [Archives](https://www.ejpam.com/ejpam/issue/archive) / 3. [Vol. 18 No. 2: (April 2025)](https://www.ejpam.com/ejpam/issue/view/78) / 4. Mathematical Analysis # Modified Laplace-type Transform and Its Properties ## Authors - Inci Ege Department of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye ## DOI: <https://doi.org/10.29020/nybg.ejpam.v18i2.5986> ## Keywords: Laplace transform, Laplace-type integral transform, modified degenerate Gamma function ## Abstract In this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind. ## References ## Downloads - [Full Text](https://www.ejpam.com/ejpam/article/view/5986/1994) ## Published 2025-05-01 ## Issue [Vol. 18 No. 2: (April 2025)](https://www.ejpam.com/ejpam/issue/view/78) ## Section Mathematical Analysis ## License Copyright (c) 2025 Inci Ege [![Creative Commons License](https://i.creativecommons.org/l/by-nc/4.0/88x31.png)](https://creativecommons.org/licenses/by-nc/4.0/) This work is licensed under a [Creative Commons Attribution-NonCommercial 4.0 International License](https://creativecommons.org/licenses/by-nc/4.0/). Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes. By agreeing to this statement, you acknowledge that: - You retain full copyright over your work. - The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). - This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source. ## How to Cite Modified Laplace-type Transform and Its Properties. (2025). 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Readable Markdown	## Authors - Inci Ege Department of Mathematics, Aydın Adnan Menderes University, Aydın, T¨urkiye ## DOI: <https://doi.org/10.29020/nybg.ejpam.v18i2.5986> ## Keywords: Laplace transform, Laplace-type integral transform, modified degenerate Gamma function ## Abstract In this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind. ## References ## Published 2025-05-01 ## Issue ## Section Mathematical Analysis ## License Copyright (c) 2025 Inci Ege [![Creative Commons License](https://i.creativecommons.org/l/by-nc/4.0/88x31.png)](https://creativecommons.org/licenses/by-nc/4.0/) This work is licensed under a [Creative Commons Attribution-NonCommercial 4.0 International License](https://creativecommons.org/licenses/by-nc/4.0/). Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes. By agreeing to this statement, you acknowledge that: - You retain full copyright over your work. - The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). - This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.
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