Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-326-343
A. Kytmanov, Olga V. Khodos
Several types of transcendental systems of equations are considered: the simplest ones, special, and general. Since the number of roots of such systems, as a rule, is infinite, it is necessary to study power sums of the roots of negative degree. Formulas for finding residue integrals, their relation to power sums of a negative degree of roots and their relation to residue integrals (multidimensional analogs of Waring’s formulas) are obtained. Various examples of transcendental systems of equations and calculation of multidimensional numerical series are given
{"title":"On Transcendental Systems of Equations","authors":"A. Kytmanov, Olga V. Khodos","doi":"10.17516/1997-1397-2021-14-3-326-343","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-326-343","url":null,"abstract":"Several types of transcendental systems of equations are considered: the simplest ones, special, and general. Since the number of roots of such systems, as a rule, is infinite, it is necessary to study power sums of the roots of negative degree. Formulas for finding residue integrals, their relation to power sums of a negative degree of roots and their relation to residue integrals (multidimensional analogs of Waring’s formulas) are obtained. Various examples of transcendental systems of equations and calculation of multidimensional numerical series are given","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"50 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85054127","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-369-375
S. Imomkulov, Sultanbay M. Abdikadirov
Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.
{"title":"Removable Singularities of Separately Harmonic Functions","authors":"S. Imomkulov, Sultanbay M. Abdikadirov","doi":"10.17516/1997-1397-2021-14-3-369-375","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-369-375","url":null,"abstract":"Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"13 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80422033","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-344-350
E. B. Durakov
In this paper we study sharply 3-transitive groups. The local finiteness of sharply triply transitive permutation groups of characteristic p > 3 containing a finite element of order p is proved. Keywords: group, sharply k-transitive group, sharply 3-transitive group, locally finite group, neardomain, near-field
{"title":"Sharply 3-transitive Groups with Finite Element","authors":"E. B. Durakov","doi":"10.17516/1997-1397-2021-14-3-344-350","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-344-350","url":null,"abstract":"In this paper we study sharply 3-transitive groups. The local finiteness of sharply triply transitive permutation groups of characteristic p > 3 containing a finite element of order p is proved. Keywords: group, sharply k-transitive group, sharply 3-transitive group, locally finite group, neardomain, near-field","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"112 35","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72376819","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}
Initial boundary value problem for the time-fractional Airy equation on a graph with finite bonds is considered in the paper. Properties of potentials for this equation are studied. Using these properties the solutions of the considered problem were found. The uniqueness theorem is proved using the analogue of Gr¨onwall-Bellman inequality and a-priory estimate
{"title":"The Time-fractional Airy Equation on the Metric Graph","authors":"Rakhimov Kamoladdin, Sobirov Zarifboy, Jabborov Nasridin","doi":"10.17516/1997-1397-2021-14-3-376-388","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-376-388","url":null,"abstract":"Initial boundary value problem for the time-fractional Airy equation on a graph with finite bonds is considered in the paper. Properties of potentials for this equation are studied. Using these properties the solutions of the considered problem were found. The uniqueness theorem is proved using the analogue of Gr¨onwall-Bellman inequality and a-priory estimate","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83299509","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-273-286
Khanssa Ben Dahmane, F. Benatia, B. Brahimi
Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator
{"title":"Estimating the Mean of Heavy-tailed Distribution under Random Truncation","authors":"Khanssa Ben Dahmane, F. Benatia, B. Brahimi","doi":"10.17516/1997-1397-2021-14-3-273-286","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-273-286","url":null,"abstract":"Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"37 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81942692","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-389-398
Nurbek Narzillaev
The article is devoted to properties of a weighted Green function. We study the (δ, ψ)- extremal Green function V ∗ δ (z,K, ψ) defined by the class Lδ = { u(z) ∈ psh(Cn) : u(z) 6 Cu + δ ln+ |z|, z ∈ Cn} , δ > 0. We see that the notion of regularity of points with respect to different numbers δ differ from each other. Nevertheless, we prove that if a compact set K ⊂ Cn is regular, then δ-extremal function is continuous in the whole space Cn
{"title":"Delta-extremal Functions in Cn","authors":"Nurbek Narzillaev","doi":"10.17516/1997-1397-2021-14-3-389-398","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-389-398","url":null,"abstract":"The article is devoted to properties of a weighted Green function. We study the (δ, ψ)- extremal Green function V ∗ δ (z,K, ψ) defined by the class Lδ = { u(z) ∈ psh(Cn) : u(z) 6 Cu + δ ln+ |z|, z ∈ Cn} , δ > 0. We see that the notion of regularity of points with respect to different numbers δ differ from each other. Nevertheless, we prove that if a compact set K ⊂ Cn is regular, then δ-extremal function is continuous in the whole space Cn","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"182 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90767286","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 study the estimation of a multivariate normal mean under the balanced loss function. We present here a class of shrinkage estimators which generalizes the James-Stein estimator and we are interested to establish the asymptotic behaviour of risks ratios of these estimators to the maximum likelihood estimators (MLE). Thus, in the case where the dimension of the parameter space and the sample size are large, we determine the sufficient conditions for that the estimators cited previously are minimax
{"title":"Limits of Risks Ratios of Shrinkage Estimators under the Balanced Loss Function","authors":"Terbeche Mekki, Benkhaled Abdelkader, Hamdaoui Abdenour","doi":"10.17516/1997-1397-2021-14-3-301-312","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-301-312","url":null,"abstract":"In this paper we study the estimation of a multivariate normal mean under the balanced loss function. We present here a class of shrinkage estimators which generalizes the James-Stein estimator and we are interested to establish the asymptotic behaviour of risks ratios of these estimators to the maximum likelihood estimators (MLE). Thus, in the case where the dimension of the parameter space and the sample size are large, we determine the sufficient conditions for that the estimators cited previously are minimax","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"19 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73413367","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-265-272
B. D. Bair, A. Victoria, V. Andrey, I. P. Maxim
The rheological properties of polyvinylidene fluoride (PVDF) solutions in Nmethylpyrrolidone were studied using the rheometric method. It was shown that the viscosity of polymer solutions decreases non-linearly with increasing temperature. The viscosity of the N-methylpyrrolidone used as solvent remains practically unchanged. It was shown that solutions exhibit Newtonian behaviour at concentrations less than 7 wt.%. At higher concentrations, solutions exhibit properties of pseudoplastic fluid
{"title":"Rheological Properties of PVDF Solutions","authors":"B. D. Bair, A. Victoria, V. Andrey, I. P. Maxim","doi":"10.17516/1997-1397-2021-14-3-265-272","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-265-272","url":null,"abstract":"The rheological properties of polyvinylidene fluoride (PVDF) solutions in Nmethylpyrrolidone were studied using the rheometric method. It was shown that the viscosity of polymer solutions decreases non-linearly with increasing temperature. The viscosity of the N-methylpyrrolidone used as solvent remains practically unchanged. It was shown that solutions exhibit Newtonian behaviour at concentrations less than 7 wt.%. At higher concentrations, solutions exhibit properties of pseudoplastic fluid","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"14 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88007852","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}
Pub Date : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-351-359
A. Shamaev, V. V. Shumilova
The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by the Kelvin–Voigt model with fractional time derivatives. For this purpose, the theory of two-scale convergence and the Laplace transform with respect to time are used. It is shown that the effective equations are partial integro-differential equations with fractional time derivatives and fractional exponential convolution kernels. In order to find the coefficients and the convolution kernels of these equations, several auxiliary cell problems are formulated and solved
{"title":"Effective Acoustic Equations for a Layered Material Described by the Fractional Kelvin-Voigt Model","authors":"A. Shamaev, V. V. Shumilova","doi":"10.17516/1997-1397-2021-14-3-351-359","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-351-359","url":null,"abstract":"The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by the Kelvin–Voigt model with fractional time derivatives. For this purpose, the theory of two-scale convergence and the Laplace transform with respect to time are used. It is shown that the effective equations are partial integro-differential equations with fractional time derivatives and fractional exponential convolution kernels. In order to find the coefficients and the convolution kernels of these equations, several auxiliary cell problems are formulated and solved","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"18 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88393473","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}
Pub Date : 2021-02-01DOI: 10.17516/1997-1397-2021-14-1-12-20
G. Egorychev, S. Kolesnikov, V. Leontiev
In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall’s collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups
本文通过计算P. Hall集合公式中换向子的指数，证明了一系列组合恒等式。利用Chevalley群的集合公式求解B. a . F. Wehrfritz群的Sylow子群的正则性问题，得到一个封闭形式的和
{"title":"Integral Representation and the Computation of Multiple Combinatorial Sums from Hall’s Commutator Theory","authors":"G. Egorychev, S. Kolesnikov, V. Leontiev","doi":"10.17516/1997-1397-2021-14-1-12-20","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-1-12-20","url":null,"abstract":"In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall’s collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"26 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77360502","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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