Bukovinian Mathematical Journal最新文献

{"title":"THE LOCALIZATION PRINCIPLE FOR FORMAL FOURIER SERIES SUMMARIZED BY GAUSS-WEIERSTRASS METHOD","authors":"O. Martynyuk, V. Gorodetskyi","doi":"10.31861/bmj2019.02.030","DOIUrl":"https://doi.org/10.31861/bmj2019.02.030","url":null,"abstract":"","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115032071","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":"LOGARITHMIC DERIVATIVE OF THE BLASCHKE PRODUCT WITH SLOWLY INCREASING COUNTING FUNCTION OF ZEROS","authors":"Y. Gal, M. Zabolotskyi, M. Mostova","doi":"10.31861/bmj2021.01.13","DOIUrl":"https://doi.org/10.31861/bmj2021.01.13","url":null,"abstract":"The Blaschke products form an important subclass of analytic functions on the unit disc with bounded Nevanlinna characteristic and also are meromorphic functions on $mathbb{C}$ except for the accumulation points of zeros $B(z)$.\u0000Asymptotics and estimates of the logarithmic derivative of meromorphic functions play an important role in various fields of mathematics. In particular, such problems in Nevanlinna's theory of value distribution were studied by Goldberg A.A., Korenkov N.E., Hayman W.K., Miles J. and in the analytic theory of differential equations -- by Chyzhykov I.E., Strelitz Sh.I.\u0000\u0000Let $z_0=1$ be the only boundary point of zeros $(a_n)$ %=1-r_ne^{ipsi_n},$ $-pi/2+eta<psi_n<pi/2-eta,$ $r_nto0+$ as $nto+infty,$\u0000of the Blaschke product $B(z);$ $Gamma_m=bigcuplimits_{j=1}^{m}{z:|z|<1,mathop{text{arg}}(1-z)=-theta_j}=bigcuplimits_{j=1}^{m}l_{theta_j},$ $-pi/2+eta<theta_1<theta_2<ldots<theta_m<pi/2-eta,$ be a finite system of rays, $0<eta<1$; $upsilon(t)$ be continuous on $[0,1)$, $upsilon(0)=0$, slowly increasing at the point 1 function, that is $upsilon(t)simupsilonleft({(1+t)}/2right),$ $tto1-;$ $n(t,theta_j;B)$ be a number of zeros $a_n=1-r_ne^{itheta_j}$ of the product $B(z)$ on the ray $l_{theta_j}$ such that $1-r_nleq t,$ $0<t<1.$ We found asymptotics of the logarithmic derivative of $B(z)$ as $z=1-re^{-ivarphi}to1,$ $-pi/2<varphi<pi/2,$ $varphineqtheta_j,$ under the condition that zeros of $B(z)$ lay on $Gamma_m$ and $n(t,theta_j;B)sim Delta_jupsilon(t),$ $tto1-,$ for all $j=overline{1,m},$ $0leqDelta_j<+infty.$ We also considered the inverse problem for such $B(z).$","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115782562","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":"MULTIPOINT BY TIME PROBLEM FOR A CLASS OF EVOLUTION EQUATIONS IN S TYPE SPACE","authors":"V. Horodetskii, N. Shevchuk, R. Kolisnyk","doi":"10.31861/bmj2022.02.07","DOIUrl":"https://doi.org/10.31861/bmj2022.02.07","url":null,"abstract":"The goal of this paper is to study evolution equations of the parabolic type with operators $displaystyle varphiBig(i frac{partial}{partial x}Big)$ built according to certain functions (different from polynomials), in particular, with operators of fractional differentiation. It is found that the restriction of such operators to certain $S$-type spaces match with pseudo-differential operators in such spaces constructed by these functions, which are multipliers in spaces that are Fourier transforms of $S$-type spaces. The well-posedness of the nonlocal multipoint by time problem is proved for such equations with initial functions that are elements of spaces of generalized functions of $S$-type. The properties of the fundamental solutions of the specified problem, the behavior of the solution at $tto +infty$ in spaces of $S'$-type (weak stabilization) were studied. We found conditions under which the solution stabilizes to zero uniformly on $mathbb{R}$.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120895590","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":"COMPOSITION OF SLICE ENTIRE FUNCTIONS AND BOUNDED L-INDEX IN DIRECTION","authors":"O. Skaskiv, Andriy Ivanovych Bandura","doi":"10.31861/bmj2021.01.02","DOIUrl":"https://doi.org/10.31861/bmj2021.01.02","url":null,"abstract":"We study the following question: \"Let $f: mathbb{C}to mathbb{C}$ be an entire function of bounded $l$-index, $Phi: mathbb{C}^nto mathbb{C}$ be a slice entire function, $ngeq2,$ $l:mathbb{C}to mathbb{R}_+$ be a continuous function.We study the following question: \"Let $f: mathbb{C}to mathbb{C}$ be an entire function of bounded $l$-index, $Phi: mathbb{C}^nto mathbb{C}$ be a slice entire function, $ngeq2,$ $l:mathbb{C}to mathbb{R}_+$ be a continuous function.What is a  positive continuous function $L:mathbb{C}^nto mathbb{R}_+$ and a direction $mathbf{b}inmathbb{C}^nsetminus{mathbf{0}}$  such that the composite function $f(Phi(z))$ has bounded $L$-index in the direction~$mathbf{b}$?\". In the present paper, early known results on boundedness of $L$-index in direction for the composition of entire functions$f(Phi(z))$ are generalized to the case where  $Phi: mathbb{C}^nto mathbb{C}$ is a slice entire function, i.e.it is an entire function on a complex line ${z^0+tmathbf{b}: tinmathbb{C}}$ for any $z^0inmathbb{C}^n$ andfor a given direction $mathbf{b}inmathbb{C}^nsetminus{mathbf{0}}$.These slice entire functions are not joint holomorphic in the general case. For~example, it allows consideration of functions which are holomorphic in variable $z_1$ and  continuous in variable $z_2.$","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122871229","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":"DEPENDENCE ON COUNTABLE MANY OF COORDINATES OF SEPARATELY CONTINUOUS FUNCTIONS OF THREE VARIABLES","authors":"V. Mykhaylyuk","doi":"10.31861/bmj2022.02.14","DOIUrl":"https://doi.org/10.31861/bmj2022.02.14","url":null,"abstract":"The dependence of continuous mappings on a certain number of coordinates was intensively studied in the works of many mathematicians in the middle of the 20th century. It has become a convenient tool in the study of properties of continuous mappings. The most general results in this direction were obtained in [5], where the necessary and sufficient conditions for the dependence of continuous functions on products from a certain number of coordinates were obtained.\u0000\u0000Starting with [8] the dependence of separately continuous mappings on a certain number of coordinates became the subject of research at the Chernivtsi University. For functions of two variables the most general results were obtained in [10]. The dependence on a certain number of coordinates of separately continuous functions of three or more variables was studied in [7], where the necessary and sufficient conditions were established only in the case of metrizability of all factors, which leaves a lot of room for further research.\u0000\u0000We obtain necessary and sufficient conditions of dependence on countable many of coordinates of functions on the product of three spaces each of which is the product of a family of compact Kempisty spaces.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123163665","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":"TWO-POINT PROBLEM FOR LINEAR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS","authors":"M. Symotiuk","doi":"10.31861/bmj2019.02.086","DOIUrl":"https://doi.org/10.31861/bmj2019.02.086","url":null,"abstract":"The problem with two nodes on the selected variable $t$ and periodicity conditions in other coordinates $x_1,ldots,x_p$ for linear partial differential equations is investigated. The conditions of solvability problem in the spaces of smooth functions with exponential behavior of Fourier coefficients are established. The estimates for characteristic determinants of the problem are proved.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123311509","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":"Inverse problem for a 2d strongly degenerate heat equation with integral overdetermination conditions","authors":"V. Vlasov, M. Ivanchov","doi":"10.31861/bmj2019.01.032","DOIUrl":"https://doi.org/10.31861/bmj2019.01.032","url":null,"abstract":"","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129342599","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":"NONLINEAR MODEL OF THE THREE-COMPONENTS COMPETITIVE ADSORPTION USING LANGMUIR EQUILIBRIUM","authors":"I. Boyko, M. Petryk, M. Shynkaryk, O. Petryk","doi":"10.31861/bmj2021.01.06","DOIUrl":"https://doi.org/10.31861/bmj2021.01.06","url":null,"abstract":"A basis for the mathematical modeling of non-isothermal gas competitive adsorption in a\u0000porous solid using Langmuir equilibrium is given. High-performance analytical solutions of\u0000considered adsorption models based on the Heaviside operating method and Landau’s decom-\u0000position and linearization approach of Langmuir equilibrium by expanding into a convergent\u0000series in the temperature phase transition point are proposed.\u0000Numerical experiments results based on high-speed computations on multicore computers\u0000are presented.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130589632","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":"CONTROLLABILITY OF FREDHOLM’S INTEGRO-DIFFERENTIAL EQUATIONS WITH BY A DEGENERATE KERNEL IN HILBERT SPACES","authors":"V. Zhuravlov, N. Gongalo, I. Slusarenko","doi":"10.31861/bmj2022.01.05","DOIUrl":"https://doi.org/10.31861/bmj2022.01.05","url":null,"abstract":"The work examines integro-differential equations Fredholm with a degenerate kernel with Hilbert control spaces. \u0000\u0000The need to study these equations is related to numerous ones applications of integro-\u0000differential equations in mathematics, physics, technology, economy and other fields. Complexity the study of integro-differential equations is connected with the fact that the integral-differential operator is not solvable everywhere.\u0000\u0000There are different approaches to the solution of not everywhere solvable linear operator\u0000equations: weak perturbation of the right-hand side of this equation with further application of the Vishyk-Lyusternyk method, introduction to system of impulse action, control, etc.\u0000The problem of obtaining coefficient conditions of solvability and analytical presentation\u0000of general solutions of integro-differential equations is a rather difficult problem, so frequent solutions will suffice are obtained by numerical methods.\u0000In this connection, Fredholm’s integro-differential equations with degenerate kernel and\u0000control in Hilbert spaces no were investigated. Therefore, the task of establishing conditions is urgent controllability, construction of general solutions in an analytical form and corresponding general controls of integro-differential equations with a degenerate kernel in abstract Hilbert spaces.\u0000As an intermediate result in the work using the results of pseudoinversion of integral\u0000operators in Hilbert spaces the solvability criterion and the form of general solutions are established integro-differential equations without control in the abstract Hilbert spaces.\u0000To establish the controllability criterion is not solvable everywhere integro-differential equations with Hilbert control spaces, the general theory of research is not applied everywhere solvable operator equations. At the same time, they are used significantly orthoprojectors, pseudo-inverse operators to normally solvable ones operators in Hilbert spaces.\u0000With the use of orthoprojectors, pseudo-inverse operators and pseudoinversion of integraloperators, a criterion is obtained solutions and the general form of solutions of integro-differential equations with a degenerate kernel with control y Hilbert spaces. An image of the general appearance is obtained control under which these solutions exist.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121117101","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":"MYKHAILO KRAWTCHOUK AND COMPUTING DEVICES. ON ETHIC OF INVESTIGATIONS IN HISTORY OF EXACT SCIENCES","authors":"A. Prykarpatsky, A. Plichko","doi":"10.31861/bmj2021.01.22","DOIUrl":"https://doi.org/10.31861/bmj2021.01.22","url":null,"abstract":"In this note, we focus on some aspects of the use of virtual ethics in the study of the\u0000scientific heritage of the outstanding Ukrainian mathematician Mykhailo Krawtchouk and its involvement in the invention of the first electronic computer by Atanasov and Berry. In particular, the biased and clearly propagandistic activity of the Canadian political scientist I. Kachanovsky is analyzed concerning the contrived contribution of Mykhailo Krawtchouk’s mathematical advice to an allegedly substantial solution of the designer G. Atanasov problems of implanting computational algorithms in his designed first electronic computing device. We also noted the ill-considered popularization of these false as well as harmful statements in scientific and popular science Ukrainian literature. Separately, we focused on the openly anti- Ukrainian propaganda activity of I. Kachanovsky, which concerns his clumsy efforts in investi- gating the activities of Ukrainian nationalists during World War II and the last events on the Maidan, and its aggressive dissemination in the press of insinuations, pseudo-historical and pseudo-scientific anti-Ukrainian insults.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114580975","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}