Pub Date : 2024-07-19DOI: 10.1134/s199508022460081x
A. K. Urinov, D. M. Mirsaburova
Abstract
In this work, in an unbounded domain, which consists of a half-plane (y>0) and a characteristic triangle for (y<0), a degenerate equation of elliptic-hyperbolic type with singular coefficients is considered for the lower terms of the equation. The correctness of the Gellerstedt–Moiseev ((GM)) problem is studied for data on the part of the boundary and internal characteristics parallel to it. When studying the (GM) problem in the half-plane (y>0), the integral representation of the solution of the Dirichlet problem is used. In the characteristic triangle the Darboux formula, which gives an integral representation of the solution to the modified Cauchy problem with data on the segment ([-1,1]) of the (y=0) axis, is used. To prove the uniqueness of the solution to the problem, a combined method of the extremum principle (for a specially constructed finite domain (D_{R})) and the passing to the limit from the finite domain (D_{R}) to the unbounded domain (D) are used. Using the Dirichlet and Darboux formulas the existence of the solution to the (GM) problem is equivalently reduced to the study of the system of non-standard singular integral equations, which the non-characteristic parts contain non-Fredholm operators with kernels that have isolated first-order singularities. Using the Carleman’s method, i.e., temporarily assuming the non-characteristic parts of these equations as known functions, the regularization of these equations are carried out. From the obtained two relations, one of the unknown function is explicitly expressed through the second one and this makes it possible to reduce this system to the Wiener–Hopf integral equation, which belongs to the class of singular integral equations. It has been proved that the index of this equation is equal to zero. By solving this equation a second kind Fredholm integral equation is obtained. The uniquely solvability of this equation follows from the uniqueness of the solution of the (GM) problem.
AbstractIn this work, in an unbounded domain, which consists of a half-plane (y>0) and a characteristic triangle for (y<0), is considered a degenerate equation of elliptic-hyperbolic type with singular coefficients for the lower terms of the equation.对于边界部分的数据和与之平行的内部特征，研究了 Gellerstedt-Moiseev （(GM)）问题的正确性。在研究半平面 (y>0)中的(GM)问题时，使用了迪里夏特问题解的积分表示法。在特征三角形中，使用了达尔布公式，它给出了修正考希问题解的积分表示，其数据在（y=0）轴的（[-1,1]）段上。为了证明问题解的唯一性，使用了极值原理（对于一个特殊构造的有限域 (D_{R}））和从有限域 (D_{R})到无界域 (D)的极限传递的组合方法。利用狄利克雷公式和达尔布公式，(GM)问题解的存在性等价地简化为非标准奇异积分方程系统的研究，其中非特征部分包含非弗雷德霍姆算子，其核具有孤立的一阶奇异性。利用卡勒曼方法，即暂时假定这些方程的非特征部分为已知函数，对这些方程进行正则化。从得到的两个关系式中，一个未知函数通过第二个关系式明确表达出来，这使得将该系统简化为维纳-霍普夫积分方程成为可能，而后者属于奇异积分方程。事实证明，该方程的指数等于零。通过求解这个方程，可以得到一个第二类弗雷德霍姆积分方程。该方程的唯一可解性源于 (GM) 问题解的唯一性。
{"title":"Gellerstedt–Moiseev Problem with Data on Parallel Characteristics in the Unbounded Domain for a Mixed Type Equation with Singular Coefficients","authors":"A. K. Urinov, D. M. Mirsaburova","doi":"10.1134/s199508022460081x","DOIUrl":"https://doi.org/10.1134/s199508022460081x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this work, in an unbounded domain, which consists of a half-plane <span>(y>0)</span> and a characteristic triangle for <span>(y<0)</span>, a degenerate equation of elliptic-hyperbolic type with singular coefficients is considered for the lower terms of the equation. The correctness of the Gellerstedt–Moiseev (<span>(GM)</span>) problem is studied for data on the part of the boundary and internal characteristics parallel to it. When studying the <span>(GM)</span> problem in the half-plane <span>(y>0)</span>, the integral representation of the solution of the Dirichlet problem is used. In the characteristic triangle the Darboux formula, which gives an integral representation of the solution to the modified Cauchy problem with data on the segment <span>([-1,1])</span> of the <span>(y=0)</span> axis, is used. To prove the uniqueness of the solution to the problem, a combined method of the extremum principle (for a specially constructed finite domain <span>(D_{R})</span>) and the passing to the limit from the finite domain <span>(D_{R})</span> to the unbounded domain <span>(D)</span> are used. Using the Dirichlet and Darboux formulas the existence of the solution to the <span>(GM)</span> problem is equivalently reduced to the study of the system of non-standard singular integral equations, which the non-characteristic parts contain non-Fredholm operators with kernels that have isolated first-order singularities. Using the Carleman’s method, i.e., temporarily assuming the non-characteristic parts of these equations as known functions, the regularization of these equations are carried out. From the obtained two relations, one of the unknown function is explicitly expressed through the second one and this makes it possible to reduce this system to the Wiener–Hopf integral equation, which belongs to the class of singular integral equations. It has been proved that the index of this equation is equal to zero. By solving this equation a second kind Fredholm integral equation is obtained. The uniquely solvability of this equation follows from the uniqueness of the solution of the <span>(GM)</span> problem.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743888","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/s1995080224600742
T. G. Ergashev, A. Hasanov, T. K. Yuldashev
Abstract
In this article, a new inverse pair of symbolic operators with the multidimensional analogues is introduced. The properties of inverse pair of symbolic operators with the multidimensional analogues are studied. Formulas for the infinite expansion of multiple Lauricella functions are established. The application of some expansions in studying the properties of fundamental solutions of singular elliptic equations is shown.
{"title":"Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation","authors":"T. G. Ergashev, A. Hasanov, T. K. Yuldashev","doi":"10.1134/s1995080224600742","DOIUrl":"https://doi.org/10.1134/s1995080224600742","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, a new inverse pair of symbolic operators with\u0000the multidimensional analogues is introduced. The properties of\u0000inverse pair of symbolic operators with the multidimensional\u0000analogues are studied. Formulas for the infinite expansion of\u0000multiple Lauricella functions are established. The application of\u0000some expansions in studying the properties of fundamental\u0000solutions of singular elliptic equations is shown.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743912","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/s1995080224600675
N. A. Lavrentiev, A. Z. Fazliev
Abstract
The article considers the problem of quality control of scientific plots on the example of published plots characterizing continuum radiation absorption, properties of weakly bound molecular complexes and absorption cross sections used in atmospheric chemistry. The tasks of systematization of graphical resources are formulated, the functionality of the GrafOnto information system containing graphical resources is described, statistical samples characterizing, in particular, the quality of graphical resources in the collection are presented. The analysis of the quality of citing plots and proximity estimates for pairwise comparisons of all plots in the collection is presented as well as the applied ontology of graphical resources.
{"title":"Quality Control of Scientific Plot Collections","authors":"N. A. Lavrentiev, A. Z. Fazliev","doi":"10.1134/s1995080224600675","DOIUrl":"https://doi.org/10.1134/s1995080224600675","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The article considers the problem of quality control of scientific plots on the example of published plots characterizing continuum radiation absorption, properties of weakly bound molecular complexes and absorption cross sections used in atmospheric chemistry. The tasks of systematization of graphical resources are formulated, the functionality of the GrafOnto information system containing graphical resources is described, statistical samples characterizing, in particular, the quality of graphical resources in the collection are presented. The analysis of the quality of citing plots and proximity estimates for pairwise comparisons of all plots in the collection is presented as well as the applied ontology of graphical resources.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743916","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/s1995080224600638
N. Ravshanov, Sh. E. Nazarov, B. Boborakhimov
Abstract
The problems of forecasting the pollutant concentration in the atmosphere by means of mathematical modeling remain one of the most relevant scientific areas. Such a conclusion can be drawn from the analysis of scientific publications related to the problems of mathematical modeling of complex processes of mass transfer in the atmosphere. In this regard, the aim of this study is to develop a mathematical model for the transport and diffusion of emissions of polluting particles of technogenic and natural origin and an effective numerical algorithm for solving the problem with a high-order approximation in time and space variables. A feature of the proposed mathematical apparatus is that, in addition to the main factors, the model takes into account the phenomenon of the capture of aerosol particles by elements of vegetation in the land environment. The solution algorithm is based on the method for splitting the original problem into physical factors: advection, diffusion, and absorption of a substance in the air mass of the atmosphere. Computational experiments were conducted using real meteorological parameters and data on sources of atmospheric pollution. An analysis of the results of numerical calculations showed their good agreement with the data of field measurements and the results obtained by other authors. Thus, the adequacy of the developed mathematical model and the accuracy of the numerical algorithm were sufficiently substantiated. In the course of experiments, the influence of the main factors on the process of transfer and diffusion of particles of harmful substances in the atmosphere was established. Particular attention was paid to the study of how the green cover on the terrain affects the propagation of particle concentration fields; what portion of pollutants can be absorbed by vegetation elements compared to other types of the underlying surface. The practical outcome of the study is the possibility of developing recommendations to support decision-making on maintaining the ecological balance of the environment in industrial regions and protecting it from the possible negative impact of technogenic factors.
{"title":"Modeling the Process of Pollutant Spread in the Atmosphere with Account for the Capture of Particles by Vegetation Elements","authors":"N. Ravshanov, Sh. E. Nazarov, B. Boborakhimov","doi":"10.1134/s1995080224600638","DOIUrl":"https://doi.org/10.1134/s1995080224600638","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problems of forecasting the pollutant concentration in the atmosphere by means of mathematical modeling remain one of the most relevant scientific areas. Such a conclusion can be drawn from the analysis of scientific publications related to the problems of mathematical modeling of complex processes of mass transfer in the atmosphere. In this regard, the aim of this study is to develop a mathematical model for the transport and diffusion of emissions of polluting particles of technogenic and natural origin and an effective numerical algorithm for solving the problem with a high-order approximation in time and space variables. A feature of the proposed mathematical apparatus is that, in addition to the main factors, the model takes into account the phenomenon of the capture of aerosol particles by elements of vegetation in the land environment. The solution algorithm is based on the method for splitting the original problem into physical factors: advection, diffusion, and absorption of a substance in the air mass of the atmosphere. Computational experiments were conducted using real meteorological parameters and data on sources of atmospheric pollution. An analysis of the results of numerical calculations showed their good agreement with the data of field measurements and the results obtained by other authors. Thus, the adequacy of the developed mathematical model and the accuracy of the numerical algorithm were sufficiently substantiated. In the course of experiments, the influence of the main factors on the process of transfer and diffusion of particles of harmful substances in the atmosphere was established. Particular attention was paid to the study of how the green cover on the terrain affects the propagation of particle concentration fields; what portion of pollutants can be absorbed by vegetation elements compared to other types of the underlying surface. The practical outcome of the study is the possibility of developing recommendations to support decision-making on maintaining the ecological balance of the environment in industrial regions and protecting it from the possible negative impact of technogenic factors.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743920","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/s1995080224600821
G. I. Ibragimov, X. Sh. Qo’shaqov, A. A. Muxammadjonov
Abstract
We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space (l_{2}) and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.
{"title":"Optimal Pursuit Differential Game Problem for an Infinite System of Binary Differential Equations","authors":"G. I. Ibragimov, X. Sh. Qo’shaqov, A. A. Muxammadjonov","doi":"10.1134/s1995080224600821","DOIUrl":"https://doi.org/10.1134/s1995080224600821","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space <span>(l_{2})</span> and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"71 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746340","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/s1995080224600869
Hashmy Hassan, Sudheep Elayidom, M. R. Irshad, Christophe Chesneau
Abstract
This paper presents the design and construction of GoKnowGraph, a Knowledge Graph (KG) that is customized exclusively for storing and semantically searching for system documents pertaining to the Government of Kerala (GoK). GoKnowGraph empowers the efficient retrieval of relevant government documents in multiple languages, thus augmenting accessibility and information retrieval within this GoK system. Our contributions encompass the development of a meticulously curated ontology, integrating essential information from GoK, and proposing a robust method for constructing and querying the KG. Moreover, our system supports cross-language document search for queries in English and advanced querying options, including attribute-based filters, to ensure precise information retrieval. Comparative assessments against a state-of-the-art system underscore GoKnowGraph’s pronounced superiority in both relevance and accuracy. The meticulous alignment between user queries and the retrieved documents highlights the platform’s capacity to effectively bridge the gap between unstructured data and the facilitation of informed decision-making within the GoK system.
{"title":"GoKnowGraph: A Multilingual Semantic Search System for Government of Kerala System Documents","authors":"Hashmy Hassan, Sudheep Elayidom, M. R. Irshad, Christophe Chesneau","doi":"10.1134/s1995080224600869","DOIUrl":"https://doi.org/10.1134/s1995080224600869","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper presents the design and construction of GoKnowGraph, a Knowledge Graph (KG) that is customized exclusively for storing and semantically searching for system documents pertaining to the Government of Kerala (GoK). GoKnowGraph empowers the efficient retrieval of relevant government documents in multiple languages, thus augmenting accessibility and information retrieval within this GoK system. Our contributions encompass the development of a meticulously curated ontology, integrating essential information from GoK, and proposing a robust method for constructing and querying the KG. Moreover, our system supports cross-language document search for queries in English and advanced querying options, including attribute-based filters, to ensure precise information retrieval. Comparative assessments against a state-of-the-art system underscore GoKnowGraph’s pronounced superiority in both relevance and accuracy. The meticulous alignment between user queries and the retrieved documents highlights the platform’s capacity to effectively bridge the gap between unstructured data and the facilitation of informed decision-making within the GoK system.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746347","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/s1995080224600663
Ismoil Safarov, Bakhtiyor Nuriddinov, Zhavlon Nuriddinov
Abstract
The paper considers the problem of propagation of natural waves in a viscoelastic cylindrical panel of variable thickness. A mathematical formulation, a solution technique and an algorithm for wave propagation problems in viscoelastic cylindrical panels of variable thickness are formulated. To derive the shell equations, the principle of possible displacements was used (within the framework of the Kirchhoff–Love hypotheses). Using the variational equation and physical equations, a system consisting of eight differential equations is obtained. After some transformations, a spectral boundary value problem on a complex parameter is constructed for a system of eight ordinary differential equations with respect to complex functions of the form. Dispersion relations for the cylindrical panel are obtained, numerical results are obtained and an analysis is made. It is established that in the case of a wedge-shaped cylindrical panel, for each mode, there are limiting propagation velocities with an increase in the wave number that coincide in magnitude with the corresponding velocities of normal waves in a wedge-shaped plate of zero curvature.
{"title":"Propagation of Own Waves in a Viscoelastic Cylindrical Panel of Variable Thickness","authors":"Ismoil Safarov, Bakhtiyor Nuriddinov, Zhavlon Nuriddinov","doi":"10.1134/s1995080224600663","DOIUrl":"https://doi.org/10.1134/s1995080224600663","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers the problem of propagation of natural waves in a viscoelastic cylindrical panel of variable thickness. A mathematical formulation, a solution technique and an algorithm for wave propagation problems in viscoelastic cylindrical panels of variable thickness are formulated. To derive the shell equations, the principle of possible displacements was used (within the framework of the Kirchhoff–Love hypotheses). Using the variational equation and physical equations, a system consisting of eight differential equations is obtained. After some transformations, a spectral boundary value problem on a complex parameter is constructed for a system of eight ordinary differential equations with respect to complex functions of the form. Dispersion relations for the cylindrical panel are obtained, numerical results are obtained and an analysis is made. It is established that in the case of a wedge-shaped cylindrical panel, for each mode, there are limiting propagation velocities with an increase in the wave number that coincide in magnitude with the corresponding velocities of normal waves in a wedge-shaped plate of zero curvature.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743886","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/s1995080224600730
S. Z. Dzhamalov, Sh. Sh. Khudoykulov
Abstract
In this article, we investigated the correctness of a linear two-point inverse problem for a multidimensional wave equation. The unique solvability of a generalized solution to a linear two-point inverse problem for a multidimensional wave equation is proved by methods of a priori estimates, a sequence of approximations, and contracting mappings.
{"title":"On Linear Two-Point Inverse Problem for a Multidimensional Wave Equation with Semi-Nonlocal Boundary Conditions","authors":"S. Z. Dzhamalov, Sh. Sh. Khudoykulov","doi":"10.1134/s1995080224600730","DOIUrl":"https://doi.org/10.1134/s1995080224600730","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, we investigated the correctness of a linear two-point inverse problem for a multidimensional wave equation. The unique solvability of a generalized solution to a linear two-point inverse problem for a multidimensional wave equation is proved by methods of a priori estimates, a sequence of approximations, and contracting mappings.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"99 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743900","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/s1995080224600729
R. R. Ashurov, Yu. E. Fayziev, N. M. Tukhtaeva
Abstract
In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, (D^{alpha,beta}u(t)+Au(t)=f(t)) ((0<alpha<1), (0leqbetaleq 1) and (0<tleq T)), (I^{delta}u(t)=gamma I^{delta}u(+0)+varphi) ((gamma) is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator (A), is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.
{"title":"On the Nonlocal Problem for the Equation with the Hilfer Fractional Derivative","authors":"R. R. Ashurov, Yu. E. Fayziev, N. M. Tukhtaeva","doi":"10.1134/s1995080224600729","DOIUrl":"https://doi.org/10.1134/s1995080224600729","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, <span>(D^{alpha,beta}u(t)+Au(t)=f(t))</span> (<span>(0<alpha<1)</span>, <span>(0leqbetaleq 1)</span> and <span>(0<tleq T)</span>), <span>(I^{delta}u(t)=gamma I^{delta}u(+0)+varphi)</span> (<span>(gamma)</span> is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator <span>(A)</span>, is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"77 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743901","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}
Cryptocurrency is a form of digital currency using cryptographic techniques in a decentralized system for secure peer-to-peer transactions. It is gaining much popularity over traditional methods of payment because it facilitates very fast, easy, and secure transactions. Social media is a significant influence, but it is also very volatile and subject to a variety of other factors. Thus, with over four billion active users on social media, we need to understand its influence on the crypto market and how it can lead to fluctuations in the values of these cryptocurrencies. In our work, we analyze the influence of activities on Twitter, in particular the sentiments of the tweets posted regarding cryptocurrencies and how they influence their prices. In addition, we also collect metadata related to tweets and users. We try to leverage these features to predict the price of cryptocurrency, for which we use some regression-based models and an LSTM-based model.
{"title":"The Future of Cryptocurrency Market Analysis: Social Media Data and User Meta-Data","authors":"Samyak Jain, Sarthak Johari, Radhakrishnan Delhibabu","doi":"10.1134/s1995080224600717","DOIUrl":"https://doi.org/10.1134/s1995080224600717","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Cryptocurrency is a form of digital currency using cryptographic techniques in a decentralized system for secure peer-to-peer transactions. It is gaining much popularity over traditional methods of payment because it facilitates very fast, easy, and secure transactions. Social media is a significant influence, but it is also very volatile and subject to a variety of other factors. Thus, with over four billion active users on social media, we need to understand its influence on the crypto market and how it can lead to fluctuations in the values of these cryptocurrencies. In our work, we analyze the influence of activities on Twitter, in particular the sentiments of the tweets posted regarding cryptocurrencies and how they influence their prices. In addition, we also collect metadata related to tweets and users. We try to leverage these features to predict the price of cryptocurrency, for which we use some regression-based models and an LSTM-based model.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743915","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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