{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:29:22Z","timestamp":1772252962457,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T00:00:00Z","timestamp":1656806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Sciences Foundation of China","award":["NSFC 11901260"],"award-info":[{"award-number":["NSFC 11901260"]}]},{"name":"National Nature Sciences Foundation of China","award":["[2020]1Y010"],"award-info":[{"award-number":["[2020]1Y010"]}]},{"name":"National Nature Sciences Foundation of China","award":["2017A030303085"],"award-info":[{"award-number":["2017A030303085"]}]},{"name":"Science and Technology Fund for Basic Research of Guizhou Province","award":["NSFC 11901260"],"award-info":[{"award-number":["NSFC 11901260"]}]},{"name":"Science and Technology Fund for Basic Research of Guizhou Province","award":["[2020]1Y010"],"award-info":[{"award-number":["[2020]1Y010"]}]},{"name":"Science and Technology Fund for Basic Research of Guizhou Province","award":["2017A030303085"],"award-info":[{"award-number":["2017A030303085"]}]},{"name":"Science and Technology Planning Projects of Guangdong Province","award":["NSFC 11901260"],"award-info":[{"award-number":["NSFC 11901260"]}]},{"name":"Science and Technology Planning Projects of Guangdong Province","award":["[2020]1Y010"],"award-info":[{"award-number":["[2020]1Y010"]}]},{"name":"Science and Technology Planning Projects of Guangdong Province","award":["2017A030303085"],"award-info":[{"award-number":["2017A030303085"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first propose the partition methods under the lattice point sets and obtain several sub-simplexes without common interior points. Furthermore, we present a method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.<\/jats:p>","DOI":"10.3390\/sym14071371","type":"journal-article","created":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T23:38:55Z","timestamp":1656977935000},"page":"1371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Uniform Test on the Mixture Simplex Region"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6592-6619","authenticated-orcid":false,"given":"Haiqing","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3858-7906","authenticated-orcid":false,"given":"Guanghui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Kaili University, Kaili 556011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junpeng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Kaili University, Kaili 556011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1111\/j.2517-6161.1958.tb00299.x","article-title":"Experiments with mixtures","volume":"20","year":"1958","journal-title":"J. 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Sci."},{"key":"ref_13","first-page":"511","article-title":"Formulation and optimization of floating matrix tablets of clarithromycin using simplex lattice design","volume":"29","author":"Singh","year":"2016","journal-title":"Pak. J. Pharm. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1007\/s11367-020-01738-4","article-title":"Leveraging life cycle assessment and simplex lattice design in optimizing fossil fuel blends for sustainable desalination","volume":"25","author":"Aleisa","year":"2020","journal-title":"Int. J. Life Cycle Assess."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"75","DOI":"10.4028\/p-rj4fmr","article-title":"Formulation and optimization of progesterone microemulsion using simplex lattice mixture design","volume":"914","author":"Aumklad","year":"2022","journal-title":"Key Eng. 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Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1093\/biomet\/asx036","article-title":"Interleaved lattice-based minimax distance designs","volume":"104","author":"He","year":"2017","journal-title":"Biometrika"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1080\/00401706.2018.1458655","article-title":"Sliced rotated sphere packing designs","volume":"61","author":"He","year":"2019","journal-title":"Technometrics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1371\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:42:17Z","timestamp":1760139737000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1371"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,3]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071371"],"URL":"https:\/\/doi.org\/10.3390\/sym14071371","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202206.0342.v1","asserted-by":"object"}]},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,3]]}}}