Pub Date : 2024-07-19DOI: 10.1134/s1995080224600614
F. Hashemi, M. Alimohammady, C. Cesarano
Abstract
This article focuses on the analysis of quasilinear equations influenced by the two-phase operator, commonly referred to as the ‘‘double-phase operator’’, while also incorporating a non-linear boundary condition. We prove the multiplicity of solutions through the utilization the method of Nehari manifold, complemented through the utilization of comparative techniques and critical point theory. Furthermore, determine the polarity of these solutions, distinctly identifying one as positive, another as negative, and a third as nodal.
{"title":"Two-Phase Robin Problem Incorporating Nonlinear Boundary Condition","authors":"F. Hashemi, M. Alimohammady, C. Cesarano","doi":"10.1134/s1995080224600614","DOIUrl":"https://doi.org/10.1134/s1995080224600614","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This article focuses on the analysis of quasilinear equations influenced by the two-phase operator, commonly referred to as the ‘‘double-phase operator’’, while also incorporating a non-linear boundary condition. We prove the multiplicity of solutions through the utilization the method of Nehari manifold, complemented through the utilization of comparative techniques and critical point theory. Furthermore, determine the polarity of these solutions, distinctly identifying one as positive, another as negative, and a third as nodal.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743913","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 : 2024-07-19DOI: 10.1134/s1995080224600699
A. A. Rogov, N. V. Loukachevitch
Abstract
Neural networks are progressively assuming a larger role in individuals daily routines, as their complexity continues to grow. While the model demonstrates satisfactory performance when evaluated on the test data, it often yields unforeseen outcomes in real-world scenarios. To diagnose the source of these errors, understanding the decision-making process employed by the model becomes crucial. In this paper, we consider various methods of interpreting the BERT model in classification tasks, and also consider methods for evaluating interpretation methods using vector representations fastText, GloVe and Sentence-BERT.
{"title":"Evaluating the Performance of Interpretability Methods in Text Categorization Task","authors":"A. A. Rogov, N. V. Loukachevitch","doi":"10.1134/s1995080224600699","DOIUrl":"https://doi.org/10.1134/s1995080224600699","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Neural networks are progressively assuming a larger role in individuals daily routines, as their complexity continues to grow. While the model demonstrates satisfactory performance when evaluated on the test data, it often yields unforeseen outcomes in real-world scenarios. To diagnose the source of these errors, understanding the decision-making process employed by the model becomes crucial. In this paper, we consider various methods of interpreting the BERT model in classification tasks, and also consider methods for evaluating interpretation methods using vector representations fastText, GloVe and Sentence-BERT.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743922","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 : 2024-07-19DOI: 10.1134/s1995080224600535
K. A. Aralova, U. U. Jamilov
Abstract
In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of extremal Volterra and non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. It is described the set of all periodic and the set of all fixed points of such operators. Further for such operator we showed that for an initial point their trajectory either converges to a periodic trajectory or diverges.
{"title":"On a Superposition of Volterra and Permuted Volterra Quadratic Stochastic Operators","authors":"K. A. Aralova, U. U. Jamilov","doi":"10.1134/s1995080224600535","DOIUrl":"https://doi.org/10.1134/s1995080224600535","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of extremal Volterra and non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. It is described the set of all periodic and the set of all fixed points of such operators. Further for such operator we showed that for an initial point their trajectory either converges to a periodic trajectory or diverges.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743892","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 : 2024-07-19DOI: 10.1134/s1995080224600559
V. Bochkarev, S. Khristoforov, A. Shevlyakova, V. Solovyev
Abstract
The paper analyses the correlation of change in word concreteness ratings with semantic change. To perform the analysis, we apply a neural network to diachronic data to obtain concreteness ratings of English words. As input to the model, we use co-occurrence statistics with the most frequent words extracted from the Google Books Ngram diachronic corpus. It is shown that the model, initially trained on data averaged over a long time interval, predicts the concreteness ratings with high accuracy (based on the word co-occurrence data in a particular year). The impact of lexical semantic change on the change in the concreteness rating is analyzed using 69 words borrowed from previous works. As the considered cases show, the neural network estimate of the word concreteness rating is very sensitive to changes in semantics. Among the factors that influence changes in the concreteness rating, we reveal the emergence of new meanings of a word, the competition of word meanings related to different parts of speech, the use of a word as a proper name, and the use of the word as a part of collocations. It is shown in the paper that changes in the concreteness rating can (along with changes in other word properties) serve as a marker of semantic change.
{"title":"Diachronic Analysis of a Word Concreteness Rating: Impact of Semantic Change","authors":"V. Bochkarev, S. Khristoforov, A. Shevlyakova, V. Solovyev","doi":"10.1134/s1995080224600559","DOIUrl":"https://doi.org/10.1134/s1995080224600559","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper analyses the correlation of change in word concreteness ratings with semantic change. To perform the analysis, we apply a neural network to diachronic data to obtain concreteness ratings of English words. As input to the model, we use co-occurrence statistics with the most frequent words extracted from the Google Books Ngram diachronic corpus. It is shown that the model, initially trained on data averaged over a long time interval, predicts the concreteness ratings with high accuracy (based on the word co-occurrence data in a particular year). The impact of lexical semantic change on the change in the concreteness rating is analyzed using 69 words borrowed from previous works. As the considered cases show, the neural network estimate of the word concreteness rating is very sensitive to changes in semantics. Among the factors that influence changes in the concreteness rating, we reveal the emergence of new meanings of a word, the competition of word meanings related to different parts of speech, the use of a word as a proper name, and the use of the word as a part of collocations. It is shown in the paper that changes in the concreteness rating can (along with changes in other word properties) serve as a marker of semantic change.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743895","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 : 2024-07-19DOI: 10.1134/s1995080224600687
B. Sh. Kulpeshov, S. V. Sudoplatov
Abstract
We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.
摘要 我们研究相当 O 最小理论的常数展开。我们证明了有限凸性阶的相当 O 最小艾伦福赫特理论的任何非本质扩展（由有限多个新常数进行的扩展）都保留了艾伦福赫特性。我们还证明了这种扩展理论的可数谱不会减少。
{"title":"Non-Essential Expansions of Quite o-Minimal Theories","authors":"B. Sh. Kulpeshov, S. V. Sudoplatov","doi":"10.1134/s1995080224600687","DOIUrl":"https://doi.org/10.1134/s1995080224600687","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743917","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 : 2024-07-19DOI: 10.1134/s1995080224600602
Messaoud Guesba, Fuad Kittaneh
Abstract
We prove some new Berezin number inequalities for sums and products of operators acting on a reproducing kernel Hilbert space. Among other applications of our inequalities, we present refinements of the triangle inequality for the Berezin norm.
{"title":"Berezin Number Inequalities for Sums and Products of Operators and Applications","authors":"Messaoud Guesba, Fuad Kittaneh","doi":"10.1134/s1995080224600602","DOIUrl":"https://doi.org/10.1134/s1995080224600602","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We prove some new Berezin number inequalities for sums and\u0000products of operators acting on a reproducing kernel Hilbert\u0000space. Among other applications of our inequalities, we present\u0000refinements of the triangle inequality for the Berezin norm.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743902","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 : 2024-07-19DOI: 10.1134/s1995080224600626
B. I. Islomov, A. A. Abdullayev
Abstract
The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.
{"title":"Bitsadze–Samarsky Type Nonlocal Boundary Value Problem for a Second Kind Mixed Equation with a Conjugation Condition of the Frankl Type","authors":"B. I. Islomov, A. A. Abdullayev","doi":"10.1134/s1995080224600626","DOIUrl":"https://doi.org/10.1134/s1995080224600626","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743914","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 : 2024-07-19DOI: 10.1134/s1995080224600778
R. V. Sulzhenko, B. V. Dobrov
Abstract
The paper studies methods for approximating a user labeled topics by simple representations in a text classification problem. It is assumed that in real information systems the meaning of thematic categories can be approximated by a fairly simple interpreted expression. An algorithm for constructing formulas is considered, which constructs a representation of a text topic in the form of a Boolean formula—in fact, a request to a full-text information system. The algorithm is based on an optimized selection of various logical predicates with words and terms from the thesaurus. The presented algorithm has been compared with modern machine learning techniques on real collections with noisy expert markup. The described method can be used for text classification, expert evaluation of the content of the heading, assessment of the complexity of the description of the topic, and correcting the markup.
{"title":"Approximation of the Meaning for Thematic Subject Headings by Simple Interpretable Representations","authors":"R. V. Sulzhenko, B. V. Dobrov","doi":"10.1134/s1995080224600778","DOIUrl":"https://doi.org/10.1134/s1995080224600778","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper studies methods for approximating a user labeled topics by simple representations in a text classification problem. It is assumed that in real information systems the meaning of thematic categories can be approximated by a fairly simple interpreted expression. An algorithm for constructing formulas is considered, which constructs a representation of a text topic in the form of a Boolean formula—in fact, a request to a full-text information system. The algorithm is based on an optimized selection of various logical predicates with words and terms from the thesaurus. The presented algorithm has been compared with modern machine learning techniques on real collections with noisy expert markup. The described method can be used for text classification, expert evaluation of the content of the heading, assessment of the complexity of the description of the topic, and correcting the markup.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746452","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 : 2024-07-19DOI: 10.1134/s1995080224600833
M. I. Tleubergenov, G. K. Vassilina, D. T. Azhymbaev
Abstract
Given second-order Ito stochastic equations, we construct almost surely equivalent stochastic equations of the Lagrangian structure. We establish the conditions for the direct and indirect analytical representations of the Lagrangian in the presence of random perturbations. The results obtained are illustrated by examples.
{"title":"Stochastic Helmholtz Problem and Convergence Almost Surely","authors":"M. I. Tleubergenov, G. K. Vassilina, D. T. Azhymbaev","doi":"10.1134/s1995080224600833","DOIUrl":"https://doi.org/10.1134/s1995080224600833","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Given second-order Ito stochastic equations, we construct almost surely equivalent stochastic equations of the Lagrangian structure. We establish the conditions for the direct and indirect analytical representations of the Lagrangian in the presence of random perturbations. The results obtained are illustrated by examples.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743887","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 : 2024-07-19DOI: 10.1134/s1995080224600870
S. R. Mironova, A. Yu. Pogodina
Abstract
We consider the singular integral operator acting between two weighted Hölder spaces and give an estimate for its norm.
摘要 我们考虑了作用于两个加权赫尔德空间之间的奇异积分算子，并给出了其规范的估计值。
{"title":"Estimate of the Norm of the Singular Integral Operator in Weighted Hölder Spaces","authors":"S. R. Mironova, A. Yu. Pogodina","doi":"10.1134/s1995080224600870","DOIUrl":"https://doi.org/10.1134/s1995080224600870","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider the singular integral operator acting between two weighted Hölder spaces and give an estimate for its norm.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743919","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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