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Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning 具有自适应突触和延迟海比学习的随机霍普菲尔德神经网格模型的动力学特性
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02298-8
Xiaoying Han, Peter E. Kloeden
{"title":"Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning","authors":"Xiaoying Han, Peter E. Kloeden","doi":"10.1007/s11253-024-02298-8","DOIUrl":"https://doi.org/10.1007/s11253-024-02298-8","url":null,"abstract":"<p>A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied. The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to changes in the states after a short delay. The lattice system is first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space. Then it is shown that the solution of the system exists and is unique. Furthermore, it is demonstrated that the system of equations generates a continuous random dynamical system. Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ideal Turbulence as a Kind of Disturbed Chaos: Brief Essay 作为一种受扰混沌的理想湍流：简论
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02297-9
Olena Romanenko, Abdyvali Akbergenov
{"title":"Ideal Turbulence as a Kind of Disturbed Chaos: Brief Essay","authors":"Olena Romanenko, Abdyvali Akbergenov","doi":"10.1007/s11253-024-02297-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02297-9","url":null,"abstract":"<p>We outline key points of the concept of ideal turbulence offering novel scenarios for distributed chaos based not on the geometric-dynamical complexity of the attractor but on the extremely complex spatial structure of elements of the attractor. Ideal turbulence is observed in idealized (without internal resistance) models of various processes related to electromagnetic or acoustic oscillations. This idealization significantly simplifies the analysis and, at the same time, in many cases, provides a quite adequate description of real processes.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"40 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Stochastic Interpretation of the Parametrix Method 参数矩阵法的随机解释
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-23 DOI: 10.1007/s11253-024-02287-x
A. Kohatsu-Higa
{"title":"A Stochastic Interpretation of the Parametrix Method","authors":"A. Kohatsu-Higa","doi":"10.1007/s11253-024-02287-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02287-x","url":null,"abstract":"<p>We revisit, in a didactic manner and by using stochastic analysis, the parametrix method and its application to unbiased simulation. We consider, in particular, the case of one-dimensional diffusions without drift.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"2 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Reflected Diffusions in Cones and Cylinders 论锥体和圆柱体中的反射扩散
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02288-w
Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
{"title":"On Reflected Diffusions in Cones and Cylinders","authors":"Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly","doi":"10.1007/s11253-024-02288-w","DOIUrl":"https://doi.org/10.1007/s11253-024-02288-w","url":null,"abstract":"<p>Let <i>X</i> be a diffusion in a cone with oblique reflection at the boundary. We study the question whether <i>X</i> reaches the vertex of the cone for a finite time with positive probability. We propose a new probabilistic method of investigation connected with the long-term behavior of the diffusion reflected in a cylinder.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems 有膜介质中的扩散和一些非局部抛物问题
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02285-z
Bohdan Kopytko, Mykhailo Osypchuk, Roman Shevchuk
{"title":"Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems","authors":"Bohdan Kopytko, Mykhailo Osypchuk, Roman Shevchuk","doi":"10.1007/s11253-024-02285-z","DOIUrl":"https://doi.org/10.1007/s11253-024-02285-z","url":null,"abstract":"<p>We establish the classical solvability of a certain conjugation problem for one-dimensional (with respect to a spatial variable) Kolmogorov backward equation with discontinuous coefficients and some versions of the general nonlocal Feller–Wentzell boundary condition given on nonsmooth boundaries of the considered curvilinear domains. In addition, we prove, that the two-parameter Feller semigroup defined by the solution of this problem describes some inhomogeneous diffusion process with moving membranes on the given region of the real line. We also show the relationship between the constructed process and the generalized diffusion in a sense of M. I. Portenko.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Genetic Contribution of an Advantaged Mutant in the Biparental Moran Model 双亲莫兰模式中优势突变体的遗传贡献
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02286-y
Camille Coron, Yves Le Jan
{"title":"Genetic Contribution of an Advantaged Mutant in the Biparental Moran Model","authors":"Camille Coron, Yves Le Jan","doi":"10.1007/s11253-024-02286-y","DOIUrl":"https://doi.org/10.1007/s11253-024-02286-y","url":null,"abstract":"<p>We consider a large population of haploid sexually reproducing individuals. It is assumed that one individual initially carries a very strongly advantageous mutation at a single locus. We study the long-term contribution of this initial individual to the genome of the population.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pointwise Hemi-Slant Riemannian Submersions 点状半斜黎曼潜流
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-08 DOI: 10.1007/s11253-024-02273-3
Mehmet Akif Akyol, Cem Sayar
{"title":"Pointwise Hemi-Slant Riemannian Submersions","authors":"Mehmet Akif Akyol, Cem Sayar","doi":"10.1007/s11253-024-02273-3","DOIUrl":"https://doi.org/10.1007/s11253-024-02273-3","url":null,"abstract":"<p>We introduce a new type of submersions, which are called <i>pointwise hemi-slant Riemannian submersions,</i> as a generalization of slant Riemannian submersions, hemi-slant submersions, and pointwise slant submersions from Kaehler manifolds onto Riemannian manifolds. We obtain some geometric interpretations of this kind of submersions with respect to the total manifold, base manifold, and fibers. Moreover, we present nontrivial illustrative examples in order to demonstrate the existence of submersions of this kind. Finally, we obtain some curvature equalities and inequalities with respect to a certain basis.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"77 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Sharp Landau–Kolmogorov–Nagy-Type Inequalities in Sobolev Spaces of Multivariate Functions 多变量函数索波列夫空间中的一些尖锐兰道-科尔莫戈罗夫-纳吉不等式
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-06 DOI: 10.1007/s11253-024-02275-1
{"title":"Some Sharp Landau–Kolmogorov–Nagy-Type Inequalities in Sobolev Spaces of Multivariate Functions","authors":"","doi":"10.1007/s11253-024-02275-1","DOIUrl":"https://doi.org/10.1007/s11253-024-02275-1","url":null,"abstract":"<p>For a function <em>f</em> from the Sobolev space <em>W</em><sup>1<em>,p</em></sup>(<em>C</em>)<em>,</em> where <em>C</em> ⊂ ℝ<sup><em>d</em></sup> is an open convex cone, we establish a sharp inequality estimating ∥<em>f</em>∥ <sub><em>L</em>∞</sub> via the <em>L</em><sub><em>p</em></sub>-norm of its gradient and a seminorm of the function. With the help of this inequality, we prove a sharp inequality estimating the <em>L</em><sub>∞</sub>-norm of the Radon–Nikodym derivative of a charge defined on Lebesgue measurable subsets of <em>C</em> via the <em>L</em><sub><em>p</em></sub>-norm of the gradient of this derivative and the seminorm of the charge. In the case where <em>C</em> = ℝ<sub>+</sub><sup><em>m</em></sup>× ℝ<sup><em>d−m</em></sup><em>,</em> 0 ≤ <em>m</em> ≤ <em>d,</em> we obtain inequalities estimating the <em>L</em><sub>∞</sub>-norm of a mixed derivative of the function <em>f</em> : <em>C →</em> ℝ via its <em>L</em><sub>∞</sub>-norm and the <em>L</em><sub><em>p</em></sub>-norm of the gradient of mixed derivative of this function.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"67 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140597439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Sharp Bound of Certain Second Hankel Determinants for the Class of Inverse of Starlike Functions with Respect to Symmetric Points 关于对称点的星形反函数类的某些第二汉克尔决定项的锐界
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-06 DOI: 10.1007/s11253-024-02278-y
{"title":"The Sharp Bound of Certain Second Hankel Determinants for the Class of Inverse of Starlike Functions with Respect to Symmetric Points","authors":"","doi":"10.1007/s11253-024-02278-y","DOIUrl":"https://doi.org/10.1007/s11253-024-02278-y","url":null,"abstract":"<p>We investigate the sharp bound of certain coefficient functionals associated with a Hankel determinant of the second kind for the inverse function when <em>f</em> belongs to the class of starlike functions with respect to symmetric points.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"299 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140597011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and Regularity Results for Degenerate Parabolic Problems in the Presence of Strongly Increasing Regularizing Lower-Order Terms and Lm-Data/Dirac Mass 存在强递增正则化低阶项和 Lm-Data/Dirac 质量的畸变抛物问题的存在性和正则性结果
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-04-06 DOI: 10.1007/s11253-024-02274-2
{"title":"Existence and Regularity Results for Degenerate Parabolic Problems in the Presence of Strongly Increasing Regularizing Lower-Order Terms and Lm-Data/Dirac Mass","authors":"","doi":"10.1007/s11253-024-02274-2","DOIUrl":"https://doi.org/10.1007/s11253-024-02274-2","url":null,"abstract":"<p>We study the existence and regularity results for degenerate parabolic problems in the presence of strongly increasing regularizing lower-order terms and <em>L</em><sup><em>m</em></sup>-data/Dirac mass.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"47 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140597013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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