In this paper we consider the Sogge-Stein problem related to the damped oscillatory integrals. We show that in three-dimensional Euclidean spaces minimal exponent, which guarantees optimal decaying of the Fourier transform of the surfaces-carried measures with mitigating factor is bounded by 3/2. A proof of the main theorem is based on Weierstrass type results.
{"title":"Damped oscillatory integrals and Weierstrass polynomials","authors":"A. Sadullaev, I. Ikromov, Shaxriddin Muranov","doi":"10.56017/2181-1318.1102","DOIUrl":"https://doi.org/10.56017/2181-1318.1102","url":null,"abstract":"In this paper we consider the Sogge-Stein problem related to the damped oscillatory integrals. We show that in three-dimensional Euclidean spaces minimal exponent, which guarantees optimal decaying of the Fourier transform of the surfaces-carried measures with mitigating factor is bounded by 3/2. A proof of the main theorem is based on Weierstrass type results.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126830712","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}
This paper is devoted to geometric properties of A(z)-harmonic functions and the corresponding Laplace operator ∆Au. It is proved that the generalized A(z)-harmonic function is generated by the usual A(z)harmonic function.
{"title":"Geometric properties of A-harmonic functions","authors":"Shokhrukh Khursanov","doi":"10.56017/2181-1318.1099","DOIUrl":"https://doi.org/10.56017/2181-1318.1099","url":null,"abstract":"This paper is devoted to geometric properties of A(z)-harmonic functions and the corresponding Laplace operator ∆Au. It is proved that the generalized A(z)-harmonic function is generated by the usual A(z)harmonic function.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122839504","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 symmetric form of a poroelasticity system in terms of velocities, stresses and pressure","authors":"Sayyora Tuychieva","doi":"10.56017/2181-1318.1094","DOIUrl":"https://doi.org/10.56017/2181-1318.1094","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":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131000821","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":"Fractional differentiation of the Grunwald-Letnikov-Hadamard type and the difference of the fractional order with a multiplicative step","authors":"M. Yakhshiboev","doi":"10.56017/2181-1318.1089","DOIUrl":"https://doi.org/10.56017/2181-1318.1089","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":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122959148","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}
Paper is devoted to investigating classical normalized empirical process of independence. Processes are investigated by using strong approximation meth-ods with best rate of convergence. We also consider the problems of finding of limit distributions of certain classes of statistics for testing the hypothesis of in-dependence of random variable and event. The application to random censoring model also considered.
{"title":"Test statistics based on independence processes","authors":"Leyla R. Kakadjanova","doi":"10.56017/2181-1318.1093","DOIUrl":"https://doi.org/10.56017/2181-1318.1093","url":null,"abstract":"Paper is devoted to investigating classical normalized empirical process of independence. Processes are investigated by using strong approximation meth-ods with best rate of convergence. We also consider the problems of finding of limit distributions of certain classes of statistics for testing the hypothesis of in-dependence of random variable and event. The application to random censoring model also considered.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127345195","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 method of potentials for the Airy equation of fractional order","authors":"K. Rakhimov","doi":"10.56017/2181-1318.1098","DOIUrl":"https://doi.org/10.56017/2181-1318.1098","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":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116553389","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":"Restoring the function set by integrals for the family of parabolas on the plane","authors":"A. Begmatov, A. Ismoilov","doi":"10.56017/2181-1318.1100","DOIUrl":"https://doi.org/10.56017/2181-1318.1100","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":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128720276","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 application of multidimensional logarithmic residue to systems of non-algebraic equations","authors":"B. Prenov","doi":"10.56017/2181-1318.1060","DOIUrl":"https://doi.org/10.56017/2181-1318.1060","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":"2020-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126027151","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}
Herein we demonstrate brief investigation results of photoelectrochemical performance of TiO2 nanotube (NT) based photoelectrode incorporated with V2O5 nanopaerticles (NP). Photoelectrodes were composed of TiO2 NTs with a diameter of 100 nm and length of 8μm,that were prepared by electrochemical anodization process at 35V in a formamade based electrolyte. The V2O5 nanoparticles were formed on the walls of the TiO2 NTs by deep coating technique with an average size of ∼5-10 nm. The V2O5 NP incorporated TiO2 NTs show superior light absorption properties in the visible light region up to ∼600 nm compared to the pristine TiO2NTs. It was found that V2O5 NPs formed vanadium impurities within TiO2 NTs which in its turn ceated acceptor levels of V3+ ions in the TiO2 NTs located deep in the forbidden band gap and provided additional absorption properties of visible light. These impurity levels also provide fast recombination sites of electrons and holes formed by photon excitation.
{"title":"Photocatalytic performance of V2O5 nanoparticles incorporated TiO2 nanotubes as a visible-light active photoelectrodefor water splitting","authors":"U. Shaislamov, K. Mukimov, T. Akhmadjanov","doi":"10.56017/2181-1318.1059","DOIUrl":"https://doi.org/10.56017/2181-1318.1059","url":null,"abstract":"Herein we demonstrate brief investigation results of photoelectrochemical performance of TiO2 nanotube (NT) based photoelectrode incorporated with V2O5 nanopaerticles (NP). Photoelectrodes were composed of TiO2 NTs with a diameter of 100 nm and length of 8μm,that were prepared by electrochemical anodization process at 35V in a formamade based electrolyte. The V2O5 nanoparticles were formed on the walls of the TiO2 NTs by deep coating technique with an average size of ∼5-10 nm. The V2O5 NP incorporated TiO2 NTs show superior light absorption properties in the visible light region up to ∼600 nm compared to the pristine TiO2NTs. It was found that V2O5 NPs formed vanadium impurities within TiO2 NTs which in its turn ceated acceptor levels of V3+ ions in the TiO2 NTs located deep in the forbidden band gap and provided additional absorption properties of visible light. These impurity levels also provide fast recombination sites of electrons and holes formed by photon excitation.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121831659","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 a sequential interval estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter. Reviewed the asymptotical properties of estimates of functionals of an unknown probability density and the conditions of the asymptotical consistency of a confidence interval of a fixed width and the asymptotical efficiency of the stopping time. The convergence rate of consistency of the fixed width interval for the asymptotic variance of rank estimates of the shift parameter is obtained.
{"title":"Sequential estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter","authors":"G. Rakhimova","doi":"10.56017/2181-1318.1056","DOIUrl":"https://doi.org/10.56017/2181-1318.1056","url":null,"abstract":"In this paper, we consider a sequential interval estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter. Reviewed the asymptotical properties of estimates of functionals of an unknown probability density and the conditions of the asymptotical consistency of a confidence interval of a fixed width and the asymptotical efficiency of the stopping time. The convergence rate of consistency of the fixed width interval for the asymptotic variance of rank estimates of the shift parameter is obtained.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129500509","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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