{"title":"On time-optimal control problem associated with parabolic equation","authors":"F. Dekhkonov","doi":"10.56017/2181-1318.1137","DOIUrl":"https://doi.org/10.56017/2181-1318.1137","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129631907","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":"Nonlocal problems for a fractional order mixed parabolic equation","authors":"A. Mamanazarov","doi":"10.56017/2181-1318.1143","DOIUrl":"https://doi.org/10.56017/2181-1318.1143","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115058186","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":"Nonlocal boundary value problem for a system of mixed type equations with a line of degeneration","authors":"K. Fayazov, I. Khajiev","doi":"10.56017/2181-1318.1144","DOIUrl":"https://doi.org/10.56017/2181-1318.1144","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131557154","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}
Let H be an infinite-dimensional complex Hilbert space, let (B(H), ‖ · ‖∞) be the C?-algebra of all bounded linear operators acting in H, and let CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu : B(H) → B(H), u = (u1, . . . , ud) ∈ R+, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C1, then the following versions of individual and mean ergodic theorems are true: For each x ∈ CE the net At(x) = 1 td ∫ [0,t]d Tu(x)du, t > 0, converges to some x̂ ∈ CE with respect to the norm ‖ · ‖∞, as t → ∞; moreover, if E is separable and E 6= l1 (as a sets), then lim t→∞ ‖At(x)− x̂‖CE = 0.
{"title":"Ergodic theorems for d-dimensional flows in ideals of compact operators","authors":"A. Azizov","doi":"10.56017/2181-1318.1150","DOIUrl":"https://doi.org/10.56017/2181-1318.1150","url":null,"abstract":"Let H be an infinite-dimensional complex Hilbert space, let (B(H), ‖ · ‖∞) be the C?-algebra of all bounded linear operators acting in H, and let CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu : B(H) → B(H), u = (u1, . . . , ud) ∈ R+, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C1, then the following versions of individual and mean ergodic theorems are true: For each x ∈ CE the net At(x) = 1 td ∫ [0,t]d Tu(x)du, t > 0, converges to some x̂ ∈ CE with respect to the norm ‖ · ‖∞, as t → ∞; moreover, if E is separable and E 6= l1 (as a sets), then lim t→∞ ‖At(x)− x̂‖CE = 0.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116259257","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}
In this paper we construct some families of three-dimensional evolution algebras which satisfies Chapman-Kolmogorov equation. For all of these chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.
{"title":"Behavior and dynamics of the set of absolute nilpotent and idempotent\u0000elements of chain of evolution algebras depending on the time","authors":"A. Imomkulov","doi":"10.56017/2181-1318.1124","DOIUrl":"https://doi.org/10.56017/2181-1318.1124","url":null,"abstract":"In this paper we construct some families of three-dimensional evolution algebras which satisfies Chapman-Kolmogorov equation. For all of these chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128622030","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":"Some properties of A(z)-subharmonic functions","authors":"S. Khursanov","doi":"10.56017/2181-1318.1141","DOIUrl":"https://doi.org/10.56017/2181-1318.1141","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123240928","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":"The Fokas' unified transformation method for Airy equation on simple open star graph","authors":"Z. Sobirov, M. Eshimbetov","doi":"10.56017/2181-1318.1123","DOIUrl":"https://doi.org/10.56017/2181-1318.1123","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132571115","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}
It is known that, the harmonic measure of a set E, relative to a domain D, is defined by means of subharmonic functions on D. In this article we define a generalization of a harmonic measure and prove some of its properties.
{"title":"The ψ-harmonic measure and its properties","authors":"Nurbek Narzillaev, Kobiljon Kuldoshev","doi":"10.56017/2181-1318.1125","DOIUrl":"https://doi.org/10.56017/2181-1318.1125","url":null,"abstract":"It is known that, the harmonic measure of a set E, relative to a domain D, is defined by means of subharmonic functions on D. In this article we define a generalization of a harmonic measure and prove some of its properties.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125808535","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}
U. Mirkhodjaev, O. Yarishkin, U. Sharafutdinova, U. Toyirov, N. Atamuratova, A. K. Tashmukhamedova, Bekdjan Tashmukhamedov
The use of thermodynamic characteristics in the analysis of data on complexation makes it possible to give the obtained data a definite physical and chemical interpretation. Our studies allow us to evaluate the complex forming abilities of compounds similar in structure to the molecules studied, and will help to analyze the "structure-function". They can replenish the database on the physical and chemical properties of crown ethers, and enable the prediction of only "constructed compounds". We have developed a reliable set of procedures for conductometric analysis of complex forming, membrane active and thermodynamic properties of sulfo derivatives-DB18C6, diacyl derivatives-DB18C6, 4’,4"(5")-dimethylaminoethanolDB18C6 and bis-o-methoxyphenoxy-diethyl ethers.
{"title":"Thermodynamics of complexation and membrane activity of crown ethers","authors":"U. Mirkhodjaev, O. Yarishkin, U. Sharafutdinova, U. Toyirov, N. Atamuratova, A. K. Tashmukhamedova, Bekdjan Tashmukhamedov","doi":"10.56017/2181-1318.1115","DOIUrl":"https://doi.org/10.56017/2181-1318.1115","url":null,"abstract":"The use of thermodynamic characteristics in the analysis of data on complexation makes it possible to give the obtained data a definite physical and chemical interpretation. Our studies allow us to evaluate the complex forming abilities of compounds similar in structure to the molecules studied, and will help to analyze the \"structure-function\". They can replenish the database on the physical and chemical properties of crown ethers, and enable the prediction of only \"constructed compounds\". We have developed a reliable set of procedures for conductometric analysis of complex forming, membrane active and thermodynamic properties of sulfo derivatives-DB18C6, diacyl derivatives-DB18C6, 4’,4\"(5\")-dimethylaminoethanolDB18C6 and bis-o-methoxyphenoxy-diethyl ethers.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131404915","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":"On the solvability of hypersingular equation of peridynamics","authors":"S. Alimov, Shukhrat Sheraliev","doi":"10.56017/2181-1318.1109","DOIUrl":"https://doi.org/10.56017/2181-1318.1109","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126451276","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}
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