{"title":"Constructions of Urysohn Universal Ultrametric Spaces","authors":"","doi":"10.1134/s2070046623040027","DOIUrl":"https://doi.org/10.1134/s2070046623040027","url":null,"abstract":"<span> <h3>Abstract</h3> <p> In this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric subspace of the space of all continuous functions whose images contain the zero, from a zero-dimensional compact Hausdorff space without isolated points into the space of non-negative real numbers equipped with the nearly discrete topology. As a consequence, the whole function space is Urysohn universal, which can be considered as a non-Archimedean analog of Banach-Mazur theorem. As a more application, we prove that the space of all continuous pseudo-ultrametrics on a zero-dimensional compact Hausdorff space with an accumulation point is a Urysohn universal ultrametric space. This result can be considered as a variant of Wan’s construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric space. </p> </span>","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Number-Theory Renormalization of Vacuum Energy","authors":"","doi":"10.1134/s2070046623040039","DOIUrl":"https://doi.org/10.1134/s2070046623040039","url":null,"abstract":"<span> <h3>Abstract</h3> <p> For QFT on a lattice of dimension <span> <span>(dgeqslant 3)</span> </span>, the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo <span> <span>(N)</span> </span>. This fact is related to a problem from number theory about the number of ways to represent a number as a sum of <span> <span>(d)</span> </span> squares in the ring of residue classes modulo <span> <span>(N)</span> </span>. </p> </span>","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"36 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich
{"title":"On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923–2012)","authors":"B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich","doi":"10.1134/s2070046623030056","DOIUrl":"https://doi.org/10.1134/s2070046623030056","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135737722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modular Nori Motives","authors":"N. C. Combe, Yu. I Manin, M. Marcolli","doi":"10.1134/s2070046623030020","DOIUrl":"https://doi.org/10.1134/s2070046623030020","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135737059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oscillations in $$p$$-Adic Diffusion Processes and Simulation of the Conformational Dynamics of Protein","authors":"A. Kh. Bikulov, A. P. Zubarev","doi":"10.1134/s2070046623030019","DOIUrl":"https://doi.org/10.1134/s2070046623030019","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135737058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coherent States of the $$p$$-Adic Heisenberg Group and Entropic Uncertainty Relations","authors":"Evgeny Zelenov","doi":"10.1134/s2070046623030032","DOIUrl":"https://doi.org/10.1134/s2070046623030032","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135737721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis on Ultra-Metric Spaces via Heat Kernels","authors":"Alexander Grigor’yan","doi":"10.1134/s2070046623030044","DOIUrl":"https://doi.org/10.1134/s2070046623030044","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135737720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Soft Logic as an Extension of Pascal’s Work","authors":"Moshe Klein, O. Maimon","doi":"10.1134/S207004662302005X","DOIUrl":"https://doi.org/10.1134/S207004662302005X","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"46 1","pages":"119 - 132"},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90775182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}