{"title":"Convergence analysis of feedforward neural networks with backpropagation","authors":"A. Marakhimov, K. Khudaybergenov","doi":"10.56017/2181-1318.1022","DOIUrl":"https://doi.org/10.56017/2181-1318.1022","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124531867","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 work we consider some applications of the Weierstrass preparation theorem and Weierstrass pseudopolynomials to study of behavior of the oscillatory integrals and Fourier transforms with analytic and smooth phases with critical points.
{"title":"Oscillatory integrals and Weierstrass polynomials","authors":"A. Sadullaev, I. Ikromov","doi":"10.56017/2181-1318.1025","DOIUrl":"https://doi.org/10.56017/2181-1318.1025","url":null,"abstract":"In this work we consider some applications of the Weierstrass preparation theorem and Weierstrass pseudopolynomials to study of behavior of the oscillatory integrals and Fourier transforms with analytic and smooth phases with critical points.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132029003","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 consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.
{"title":"On the continuation of the Hartogs series with holomorphic coefficients","authors":"Takhir Tuychiev, Jurabay Tishabaev","doi":"10.56017/2181-1318.1021","DOIUrl":"https://doi.org/10.56017/2181-1318.1021","url":null,"abstract":"In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130140368","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 investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex. It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.
{"title":"Solvable Leibniz superalgebras whose nilradical is a Lie superalgebra of maximal nilindex","authors":"A. Khudoyberdiyev, M. Ladra, Kh. A. Muratova","doi":"10.56017/2181-1318.1019","DOIUrl":"https://doi.org/10.56017/2181-1318.1019","url":null,"abstract":"In this paper, we investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex. It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"368 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122922483","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 waiting time and dynamic partitions","authors":"A. Dzhalilov, M. Khomidov","doi":"10.56017/2181-1318.1018","DOIUrl":"https://doi.org/10.56017/2181-1318.1018","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"435 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116329100","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 the work, it is given the normal functor F acting in the category of compacts and their continuous mappings. This functor does not preserve the Souslin number (or hereditary cellularity), the hereditary density, the hereditary π-weight and the hereditary Shanin number, the hereditary caliber, the hereditary precaliber, the hereditary preshanin number, the hereditary weak density, the hereditary Lindelöf number, and the hereditary extent of a compact. The example of the normal functor and the compact of Aleksandorv’s two arrows are given. We study the action of functors expn, expω, expc and exp on finally compact, hereditarily disconnected, strongly zero-dimensional, extremely disconnected, paracompact spaces.
{"title":"Topological properties of hyperspaces","authors":"R. Beshimov, D. Safarova","doi":"10.56017/2181-1318.1017","DOIUrl":"https://doi.org/10.56017/2181-1318.1017","url":null,"abstract":"In the work, it is given the normal functor F acting in the category of compacts and their continuous mappings. This functor does not preserve the Souslin number (or hereditary cellularity), the hereditary density, the hereditary π-weight and the hereditary Shanin number, the hereditary caliber, the hereditary precaliber, the hereditary preshanin number, the hereditary weak density, the hereditary Lindelöf number, and the hereditary extent of a compact. The example of the normal functor and the compact of Aleksandorv’s two arrows are given. We study the action of functors expn, expω, expc and exp on finally compact, hereditarily disconnected, strongly zero-dimensional, extremely disconnected, paracompact spaces.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123393429","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 a control problem associated with fast heating of a thin rod","authors":"S. Alimov, F. Dekhkonov","doi":"10.56017/2181-1318.1016","DOIUrl":"https://doi.org/10.56017/2181-1318.1016","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129962898","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 work, we study the electronic specific heat Ce(T ) of underdoped to overdoped high-Tc cuprates, and identify the nature of anomalies in Ce(T ) at the superconducting transition temperature Tc and at temperatures above Tc. The doped cuprate superconductor is considered as a multi-carrier model system which is composed of different types of charge carriers. The normal-state electronic specific heat Cn(T ) of high-Tc cuprates below a characteristic pseudogap (PG) temperature T ∗ is calculated taking into account three contributions coming from the excited components of Cooper pairs, the ideal Bose-gas of incoherent Cooper pairs and the unpaired carriers in the impurity band. Above T ∗, two contributions to Cn(T ) coming from the unpaired intrinsic and extrinsic polarons are calculated within the two-component degenerate Fermi-gas model. The total electronic specific heat Ce(T ) = Cn(T ) + Cs(T ) below Tc is calculated by considering the contribution Cn(T ) and the contribution Cs(T ) coming from the superfluid bosonic carriers. We have shown that our theoretical predictions of the behaviors of Ce(T ) near Tc and above Tc are strikingly similar to the behaviors of the electronic specific heat observed below and above Tc in LSCO and YBCO. There is fair quantitative agreement between theoretical predictions about the anomalies in Ce(T ) (i.e. a λ-like anomaly near Tc and a BCS-type anomaly above Tc near T ∗) and experimental data.
{"title":"Electronic specific-heat anomalies in high-Tc cuprates","authors":"S. Dzhumanov, E. Karimboev, B. Yavidov","doi":"10.56017/2181-1318.1012","DOIUrl":"https://doi.org/10.56017/2181-1318.1012","url":null,"abstract":"In this work, we study the electronic specific heat Ce(T ) of underdoped to overdoped high-Tc cuprates, and identify the nature of anomalies in Ce(T ) at the superconducting transition temperature Tc and at temperatures above Tc. The doped cuprate superconductor is considered as a multi-carrier model system which is composed of different types of charge carriers. The normal-state electronic specific heat Cn(T ) of high-Tc cuprates below a characteristic pseudogap (PG) temperature T ∗ is calculated taking into account three contributions coming from the excited components of Cooper pairs, the ideal Bose-gas of incoherent Cooper pairs and the unpaired carriers in the impurity band. Above T ∗, two contributions to Cn(T ) coming from the unpaired intrinsic and extrinsic polarons are calculated within the two-component degenerate Fermi-gas model. The total electronic specific heat Ce(T ) = Cn(T ) + Cs(T ) below Tc is calculated by considering the contribution Cn(T ) and the contribution Cs(T ) coming from the superfluid bosonic carriers. We have shown that our theoretical predictions of the behaviors of Ce(T ) near Tc and above Tc are strikingly similar to the behaviors of the electronic specific heat observed below and above Tc in LSCO and YBCO. There is fair quantitative agreement between theoretical predictions about the anomalies in Ce(T ) (i.e. a λ-like anomaly near Tc and a BCS-type anomaly above Tc near T ∗) and experimental data.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"219 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122852217","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":"Ill-posed boundary value problem for operator-differential equation of fourth order","authors":"K. Fayazov, I. Khajiev, Z. Fayazova","doi":"10.56017/2181-1318.1013","DOIUrl":"https://doi.org/10.56017/2181-1318.1013","url":null,"abstract":"","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116347635","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. Makhmanov, O. Ismailova, A. Kokhkharov, S. Bakhramov
Self-assembling features of molecules of C70 in benzene solution prepared in two various ways – equilibrium and non-equilibrium – has been investigated experimentally by method of high-resolution transmission electron microscopy. It was demonstrated, that the formation of densely packed monomolecular fullerene aggregates with a diameter of not more than 30 nm in solutions prepared by the equilibrium method (without the use of external mechanical influences on solution). In the case of solutions C70, which were prepared by the non-equilibrium method (stirring of solution of C70 by a mechanical rotator), large quasispherical aggregates of nanoporous structure with fractal size D ≈ 2.19 were synthesized.
{"title":"Analysis of clusterization of C70 molecules in benzene solutions prepared by various methods","authors":"U. Makhmanov, O. Ismailova, A. Kokhkharov, S. Bakhramov","doi":"10.56017/2181-1318.1014","DOIUrl":"https://doi.org/10.56017/2181-1318.1014","url":null,"abstract":"Self-assembling features of molecules of C70 in benzene solution prepared in two various ways – equilibrium and non-equilibrium – has been investigated experimentally by method of high-resolution transmission electron microscopy. It was demonstrated, that the formation of densely packed monomolecular fullerene aggregates with a diameter of not more than 30 nm in solutions prepared by the equilibrium method (without the use of external mechanical influences on solution). In the case of solutions C70, which were prepared by the non-equilibrium method (stirring of solution of C70 by a mechanical rotator), large quasispherical aggregates of nanoporous structure with fractal size D ≈ 2.19 were synthesized.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124858339","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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