Pub Date : 2024-06-12DOI: 10.52737/18291163-2024.16.6-1-13
Raksha Sharma
In this paper, we consider a perturbation of operator-valued frames (OPV-frames) and obtain conditions for their stability in terms of operators associated with the OPV-frames. Also, some duality relations of OPV-frames are discussed. Finally, some properties of the duals of OPV-frames are proven.
{"title":"Some Results on Perturbation of Duality of OPV-Frames","authors":"Raksha Sharma","doi":"10.52737/18291163-2024.16.6-1-13","DOIUrl":"https://doi.org/10.52737/18291163-2024.16.6-1-13","url":null,"abstract":"In this paper, we consider a perturbation of operator-valued frames (OPV-frames) and obtain conditions for their stability in terms of operators associated with the OPV-frames. Also, some duality relations of OPV-frames are discussed. Finally, some properties of the duals of OPV-frames are proven.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141354078","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 : 2024-02-13DOI: 10.52737/18291163-2024.16.2-1-28
Andrey Osipov
We consider semi-infinite and finite Bogoyavlensky lattices$$oversetcdot a_i =a_ileft(prod_{j=1}^{p}a_{i+j}-prod_{j=1}^{p}a_{i-j}right),$$$$oversetcdot b_i = b_ileft(sum_{j=1}^{p}b_{i+j}-sum_{j=1}^{p}b_{i-j}right),$$for some $pge 1$, and Miura-like transformations between these systems, defined for $pge 2$. Both lattices are integrable (via Lax pair formalism) by the inverse spectral problem method for band operators, i.e., operators generated by band matrices. The key role in this method is played by the moments of the Weyl matrix of the corresponding band operator and their evolution in time. We find a description of the above-mentioned transformations in terms of these moments and apply this result to study finite Bogoyavlensky lattices and, in particular, their first integrals.
{"title":"On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators","authors":"Andrey Osipov","doi":"10.52737/18291163-2024.16.2-1-28","DOIUrl":"https://doi.org/10.52737/18291163-2024.16.2-1-28","url":null,"abstract":"We consider semi-infinite and finite Bogoyavlensky lattices$$oversetcdot a_i =a_ileft(prod_{j=1}^{p}a_{i+j}-prod_{j=1}^{p}a_{i-j}right),$$$$oversetcdot b_i = b_ileft(sum_{j=1}^{p}b_{i+j}-sum_{j=1}^{p}b_{i-j}right),$$for some $pge 1$, and Miura-like transformations between these systems, defined for $pge 2$. Both lattices are integrable (via Lax pair formalism) by the inverse spectral problem method for band operators, i.e., operators generated by band matrices. The key role in this method is played by the moments of the Weyl matrix of the corresponding band operator and their evolution in time. We find a description of the above-mentioned transformations in terms of these moments and apply this result to study finite Bogoyavlensky lattices and, in particular, their first integrals.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139839600","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 : 2024-01-11DOI: 10.52737/18291163-2024.16.1-1-28
D. Biswas, Ipsita Rajwar
In this paper, we have investigated the projective action of the Lie group $text{SL}(3,mathbb{R})$ on the homogeneous space $mathbb{RP}^2$. In particular, we have studied the action of the subgroups of $text{SL}(3,mathbb{R})$ on the non-degenerate conics in the space $mathbb{RP}^2$. Using the Iwasawa decomposition of $text{SL}(2,mathbb{R})$, we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to $text{PSL}(2,mathbb{R})$ under certain conditions.
{"title":"The Geometry of the Projective Action of $text{SL}(3,mathbb{R})$ from the Erlangen Perspective","authors":"D. Biswas, Ipsita Rajwar","doi":"10.52737/18291163-2024.16.1-1-28","DOIUrl":"https://doi.org/10.52737/18291163-2024.16.1-1-28","url":null,"abstract":"In this paper, we have investigated the projective action of the Lie group $text{SL}(3,mathbb{R})$ on the homogeneous space $mathbb{RP}^2$. In particular, we have studied the action of the subgroups of $text{SL}(3,mathbb{R})$ on the non-degenerate conics in the space $mathbb{RP}^2$. Using the Iwasawa decomposition of $text{SL}(2,mathbb{R})$, we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to $text{PSL}(2,mathbb{R})$ under certain conditions.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438515","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 : 2023-12-14DOI: 10.52737/18291163-2023.15.12-1-9
Mohamed Ben Farah
In this paper, we prove a characterization of three-variate inverted Dirichlet distributions by an independence property. The main technical challenge was a problem involving the solution of a related functional equation.
{"title":"Characterization of the Three-Variate Inverted Dirichlet Distributions","authors":"Mohamed Ben Farah","doi":"10.52737/18291163-2023.15.12-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.12-1-9","url":null,"abstract":"In this paper, we prove a characterization of three-variate inverted Dirichlet distributions by an independence property. The main technical challenge was a problem involving the solution of a related functional equation.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002151","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 : 2023-11-28DOI: 10.52737/18291163-2023.15.11-1-9
Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino
We investigate a combinatorial interpretation of the Padovan polynomial sequence, also addressing its polynomial extensions. We thus include the Tridovan polynomial sequence, Tetradovan polynomial sequences, leading up to the Z-dovan polynomial generalization.
{"title":"A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence","authors":"Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino","doi":"10.52737/18291163-2023.15.11-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.11-1-9","url":null,"abstract":"We investigate a combinatorial interpretation of the Padovan polynomial sequence, also addressing its polynomial extensions. We thus include the Tridovan polynomial sequence, Tetradovan polynomial sequences, leading up to the Z-dovan polynomial generalization.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139222302","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 : 2023-10-10DOI: 10.52737/18291163-2023.15.10-1-16
T. Haritha, A.V. Chithra
In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C triangleright (G_{n_2}^Vcup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C triangleright (G_{n_2}^Vcup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane $(C_5H_{10})$ and Spirohexane $(C_6H_{10})$.
{"title":"On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs","authors":"T. Haritha, A.V. Chithra","doi":"10.52737/18291163-2023.15.10-1-16","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.10-1-16","url":null,"abstract":"In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C triangleright (G_{n_2}^Vcup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C triangleright (G_{n_2}^Vcup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane $(C_5H_{10})$ and Spirohexane $(C_6H_{10})$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294018","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 : 2023-09-05DOI: 10.52737/18291163-2023.15.9-1-6
J. Gatsinzi
We use a model of mapping spaces to compute the generalized rational Gottlieb groups of the inclusion $i_{n,k}: mathbb{C}P^n hookrightarrow mathbb{C}P^{n+k}$ between complex projective spaces.
{"title":"Generalized Rational Evaluation Subgroups of the Inclusion between Complex Projective Spaces","authors":"J. Gatsinzi","doi":"10.52737/18291163-2023.15.9-1-6","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.9-1-6","url":null,"abstract":"We use a model of mapping spaces to compute the generalized rational Gottlieb groups of the inclusion $i_{n,k}: mathbb{C}P^n hookrightarrow mathbb{C}P^{n+k}$ between complex projective spaces.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48575017","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 : 2023-05-20DOI: 10.52737/18291163-2023.15.8-1-11
K. Atifi
The main purpose of this work is to propose a new network architecture model for deep learning applied to solve an inverse source problem for a two-dimensional degenerate parabolic equation from final observations with degeneracy occurring anywhere in the spatial domain.
{"title":"A Mesh-Free Algorithm to Solve an Inverse Source Problem for Degenerate Two-Dimensional Parabolic Equation from Final Observations","authors":"K. Atifi","doi":"10.52737/18291163-2023.15.8-1-11","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.8-1-11","url":null,"abstract":"The main purpose of this work is to propose a new network architecture model for deep learning applied to solve an inverse source problem for a two-dimensional degenerate parabolic equation from final observations with degeneracy occurring anywhere in the spatial domain.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42233066","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 : 2023-04-27DOI: 10.52737/10.52737/18291163-2023.15.7-1-12
I. A. Wani, A. Hussain
The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results previously reported in the relevant literature.
{"title":"A Note on Location of the Zeros of Quaternionic Polynomials","authors":"I. A. Wani, A. Hussain","doi":"10.52737/10.52737/18291163-2023.15.7-1-12","DOIUrl":"https://doi.org/10.52737/10.52737/18291163-2023.15.7-1-12","url":null,"abstract":"The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results previously reported in the relevant literature.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45649973","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 : 2023-04-13DOI: 10.52737/18291163-2023.15.6-1-13
Hasan Gökbaş
In this study, we define a new type of number sequence called Leonardo-Alwyn sequence. We obtain the Binet formula, generating function and some relations for these numbers. Moreover, we give the matrix representation of the Leonardo-Alwyn numbers.
{"title":"A New Family of Number Sequences: Leonardo-Alwyn Numbers","authors":"Hasan Gökbaş","doi":"10.52737/18291163-2023.15.6-1-13","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.6-1-13","url":null,"abstract":"In this study, we define a new type of number sequence called Leonardo-Alwyn sequence. We obtain the Binet formula, generating function and some relations for these numbers. Moreover, we give the matrix representation of the Leonardo-Alwyn numbers.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42997037","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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