Bukovinian Mathematical Journal最新文献_第8页

On some generalizations of multiplicative operators on the space h(g) 关于空间h(g)上乘法算子的一些推广

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2019.01.056

Yu. S. Linchuk

引用次数: 0

AVERAGING IN MULTIFREQUENCY SYSTEMS WITH DELAY AND LOCAL INTEGRAL CONDITIONS 具有延迟和局部积分条件的多频系统的平均

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2020.02.02

Ya. I. Bihun, I. Skutar

{"title":"AVERAGING IN MULTIFREQUENCY SYSTEMS WITH DELAY AND LOCAL INTEGRAL CONDITIONS","authors":"Ya. I. Bihun, I. Skutar","doi":"10.31861/bmj2020.02.02","DOIUrl":"https://doi.org/10.31861/bmj2020.02.02","url":null,"abstract":"Multifrequency systems of dierential equations were studied with the help of averaging\u0000method in the works by R.I. Arnold, Ye.O. Grebenikov, Yu.O. Mitropolsky, A.M. Samoilenko\u0000and many other scientists. The complexity of the study of such systems is their inherent resonant\u0000phenomena, which consist in the rational complete or almost complete commensurability of\u0000frequencies. As a result, the solution of the system of equations averaged over fast variables in\u0000the general case may deviate from the solution of the exact problem by the quantity O (1). The\u0000approach to the study of such systems, which was based on the estimation of the corresponding\u0000oscillating integrals, was proposed by A.M. Samoilenko, which allowed to obtain in the works by\u0000A.M. Samoilenko and R.I. Petryshyn a number of important results for multifrequency systems\u0000with initial , boundary and integral conditions.\u0000For multifrequency systems with an argument delay, the averaging method is substantiated\u0000in the works by Ya.Y. Bihun, R.I. Petryshyn, I.V. Krasnokutska and other authors.\u0000In this paper, the averaging method is used to study the solvability of a multifrequency\u0000system with an arbitrary nite number of linearly transformed arguments in slow and fast\u0000variables and integral conditions for slow and fast variables on parts of the interval [0, L] of\u0000the system of equations. An unimproved estimate of the error of the averaging method under\u0000the superimposed conditions is obtained, which clearly depends on the small parameter and\u0000the number of linearly transformed arguments in fast variables.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":"316 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115917190","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}

引用次数: 0

ON SPLITTING AND STABILITY OF LINEAR STATIONARY SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS 线性平稳奇摄动微分方程的分裂与稳定性

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2019.02.076

O. Osypova, I. Cherevko

引用次数: 0

CLUSTERING: MARKOV ALGORITHM 聚类:马尔可夫算法

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2019.02.059

T. Knignitska, I. Malyk, M. Gorbatenko

引用次数: 0

ADVANCED ALGORITHM OF EVOLUTION STRATEGIES OF COVARIATION MATRIX ADAPTATION 协变矩阵自适应进化策略的改进算法

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.02.09

Yu. A. Litvinchuk, I. Malyk

引用次数: 0

THE SET OF INCOMPLETE SUMS OF THE MODIFIED GUTHRIE-NYMANN SERIES 修正guthrie-nymann级数的不完全和集

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.02.15

M. Pratsiovytyi, D. Karvatsky

{"title":"THE SET OF INCOMPLETE SUMS OF THE MODIFIED GUTHRIE-NYMANN SERIES","authors":"M. Pratsiovytyi, D. Karvatsky","doi":"10.31861/bmj2022.02.15","DOIUrl":"https://doi.org/10.31861/bmj2022.02.15","url":null,"abstract":"In this paper we study topological and metric properties of the set of incomplete sums for positive series $sum {a_k}$, where $a_{2n-1}=3/4^n+3/4^{in}$ and $a_{2n}=2/4^n+2/4^{in}$, $n in N$. The series depends on positive integer parameter $i geq 2$ and it is some perturbation of the known Guthrie-Nymann series. We prove that the set of incomplete sums of this series is a Cantorval (which is a specific union of a perfect nowhere dense set of zero Lebesgue measure and an infinite union of intervals), and its Lebesgue measure is given by formula: $lambda(X^+_i)=1+frac{1}{4^i-3}.$ The main idea of ??proving the theorem is based on the well-known Kakey theorem, the closedness of sets of incomplete sums of the series and the density of the set everywhere in a certain segment. The work provides a full justification of the facts for the case $i=2$. To justify the main facts, the ratio between the members and the remainders of the series is used. For $i=2$ we have $r_0=sum {a_k}=2$, $a_{2n}-r_{2n}= frac{1}{3} cdot frac{1}{4^n} + frac{5}{3} cdot frac{1}{16^n}$ $r_{2n-1}-a_{2n-1}= frac{2}{3} cdot frac{ 1}{4^n}-frac{2}{3} cdot frac{1}{16^n}$. The relevance of the study of the object is dictated by the problems of the geometry of numerical series, fractal analysis and fractal geometry of one-dimensional objects and the theory of infinite Bernoulli convolutions, one of the problems of which is the problem of the singularity of the convolution of two singular distributions.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126565689","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}

引用次数: 0

ON SEPARATE ORDER CONTINUITY OF ORTHOGONALLY ADDITIVE OPERATORS 正交加性算子的分离阶连续性

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.01.17

I. Krasikova, O. Fotiy, M. Pliev, M. Popov

引用次数: 0

SINGULARLY FINITE RANK NONSYMMETRIC PERTURBATIONS ${mathcal H}_{-2}$-CLASS OF A SELF-ADJOINT OPERATOR 一类自伴随算子的奇异有限秩非对称微扰

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.01.11

O. Dyuzhenkova, M. Dudkin

引用次数: 0

APPROXIMATION OF BOUNDARY VALUE PROBLEMS FOR INTEGRO-DIFFERENTIAL EQUATIONS WITH DELAY 带时滞的积分-微分方程边值逼近问题

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.01.11

I. Tuzyk, I. Cherevko

{"title":"APPROXIMATION OF BOUNDARY VALUE PROBLEMS FOR INTEGRO-DIFFERENTIAL EQUATIONS WITH DELAY","authors":"I. Tuzyk, I. Cherevko","doi":"10.31861/bmj2022.01.11","DOIUrl":"https://doi.org/10.31861/bmj2022.01.11","url":null,"abstract":"In mathematical modeling of physical and technical processes, the evolution of which\u0000depends on prehistory, we arrive at diﬀerential equations with a delay. With the help of such equations it was possible to identify and describe new eﬀects and phenomena in physics, biology, technology.\u0000An important task for diﬀerential-functional equations is to construct and substantiate\u0000ﬁnding approximate solutions, since there are currently no universal methods for ﬁnding their precise solutions. Of particular interest are studies that allow the use of methods of the theory of ordinary diﬀerential equations for the analysis of delay diﬀerential equations.\u0000Schemes for approximating diﬀerential-diﬀerence equations by special schemes of ordinary diﬀerential equations are proposed in the works N. N. Krasovsky, A. Halanay, I. M. Cherevko, L. A. Piddubna, O. V. Matwiy in various functional spaces.\u0000The purpose of this paper is to apply approximation schemes of diﬀerential-diﬀerence equations to approximation of solutions of boundary-value problems for integro-diﬀerential equations with a delay. The paper presents suﬃcient conditions for the existence of a solution of the boundary value problem for integro-diﬀerential equations with many delays. The scheme of its approximation by a sequence of boundary value problems for ordinary integro-diﬀerential equations is proposed and the conditions of its convergence are investigated. A model example is considered to demonstrate the given approximation scheme.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128783534","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}

引用次数: 0

INVERSOR OF DIGITS OF TWO-BASE G–REPRESENTATION OF REAL NUMBERS AND ITS STRUCTURAL FRACTALITY 实数的二进制g的数的逆表示及其结构分形

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.01.09

M. Pratsiovytyi, V. Drozdenko, I. Lysenko, Y. Maslova

{"title":"INVERSOR OF DIGITS OF TWO-BASE G–REPRESENTATION OF REAL NUMBERS AND ITS STRUCTURAL FRACTALITY","authors":"M. Pratsiovytyi, V. Drozdenko, I. Lysenko, Y. Maslova","doi":"10.31861/bmj2022.01.09","DOIUrl":"https://doi.org/10.31861/bmj2022.01.09","url":null,"abstract":"In the paper, we introduce a new two-symbol system of representation\u0000for numbers from segment $[0;0,5]$ with alphabet (set of digits)\u0000$A={0;1}$ and two bases 2 and $-2$:\u0000[x=dfrac{alpha_1}{2}+dfrac{1}{2}sumlimits^infty_{k=1}dfrac{alpha_{k+1}}{2^{k-(alpha_1+ldots+alpha_k)}(-2)^{alpha_1+ldots+alpha_k}}equiv\u0000Delta^{G}_{alpha_1alpha_2ldotsalpha_kldots},\u0000;;; alpha_kin {0;1}.]\u0000We compare this new system with classic binary system. The function\u0000$I(x=Delta^G_{alpha_1ldots\u0000alpha_nldots})=Delta^G_{1-alpha_1,ldots, 1-alpha_nldots}$,\u0000such that digits of its $G$--representation are inverse (opposite) to\u0000digits of $G$--representation of argument is considered in detail.\u0000This function is well-defined at points having two\u0000$G$--representations provided we use only one of them. We prove that\u0000inversor is a function of unbounded variation, continuous function at\u0000points having a unique $G$--representation, and right- or\u0000left-continuous at points with two representations. The values of all\u0000jumps of the function are calculated. We prove also that the function\u0000does not have monotonicity intervals and its graph has a self-similar\u0000structure.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130669775","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}

引用次数: 0