Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Loop closure detection in visual appearance-based SLAM using deep autoencoders117135549910.22060/ajmc.2024.23054.1224ENAmirZarringhalamDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranAliMohades KhorasaniDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-6118-2245SaeedShiry GhidaryStaffordshire University, School of Digital, Technologies and Arts, College Rd, Stoke-on-Trent ST4 2DE, United KingdomJournal Article20240313Abstract: Loop closure detection (LCD) and trajectory generation are critical components of visual simultaneous localization and mapping (vSLAM). In this paper, we aim to solve the LCD and trajectory generation problem in vSLAM using a newly devised vector quantization (VQ) algorithm. The proposed new VQ algorithm is constructed based on a self-supervised deep convolutional autoencoder (AE). The new VQ step is then incorporated into the two famous SLAM algorithms fast appearancebased mapping (FABMAP) and ORB-SLAM, which we now call AE-FABMAP and AE-ORB-SLAM, respectively. Experiments show that using self-supervised autoencoders in the VQ step is far more efficient in terms of speed and memory consumption with respect to other methods such as graph convolutional neural networks. Furthermore, the newly presented algorithms, AE-ORB-SLAM and AE-FABMAP outperform the standard FABMAP2 and ORB SLAM, and in large-scale SLAM, the new approaches improve the accuracy and recall of the LCD.https://ajmc.aut.ac.ir/article_5499_d149231f39b05ae135fa763edb358064.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Numerical solution of fraction Fokker-Planck equation with hybrid method of solution137149561010.22060/ajmc.2024.23176.1238ENOludapo OmotolaOlubanwoDepartment of Mathematical Sciences, Faculty of Science, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria0000-0003-2557-365XSunday SenayonIdowuDepartment of Mathematical Sciences, Faculty of Science, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, NigeriaJulius TemitayoAdepojuDepartment of Mathematical Sciences, Faculty of Science, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria0009-0007-4399-5887Abiodun SufiatAjaniDepartment of Mathematical Sciences, Faculty of Science, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, NigeriaJournal Article20240510The work employs a numerical method for the solution of Fractional Fokker-Planck Equation (FFPE) using the Homotopy Perturbation and Aboodh Transform Method (HPATM). Fractional derivatives issues are successfully solved using the hybrid approach, which yields rapidly convergent solutions. By resolving two cases and contrasting estimated outcomes with exact solutions for various fractional orders, the correctness of the technique was proven. The accuracy of the technique is demonstrated by the good match between the precise and approximation solutions at $\alpha=1$. The findings indicate that fractional differential equations may be solved with a strong and dependable approach using HPATM, which can also be used to describe anomalous diffusion and other intricate physical phenomena.https://ajmc.aut.ac.ir/article_5610_049671e28a386427e432b3370a22aae4.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Exact double domination in the generalized Sierpinski graphs151162561910.22060/ajmc.2024.23345.1251ENMahsaKhatibiDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranAliBehtoeiDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranJournal Article20240714A subset $D$ of vertices of a simple graph $G$ is an exact double dominating set if each vertex $v$ of $G$ is dominated by exactly two vertices of $D$, i.e. $|N_G[v]\cap D|=2$, in which $N_G[v]$ is the closed neighborhood of $v$ in $G$. The generalized Sierpi\'{n}ski graph $S(G,t)$ is a fractal-like graph that uses $G$ as a building block and can be constructed recursively in $t$ steps from the base graph $G$. In this paper we study and determine the existence of exact double dominating sets in generalized Sierpi\'nski graphs $S(P_n,t)$, $S(C_n,t)$, $S(K_{1,n},t)$ and $S(K_n,t)$.https://ajmc.aut.ac.ir/article_5619_1a4ab15f37a1d2341d947a9996ddfbf7.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401The character table of a subgroup $2^7{:}G_2 (2)$ of $Sp_8(2)$163174560510.22060/ajmc.2024.23464.1258ENAbraham LovePrinsDepartment of Pure and Applied Mathematics, University of Fort Hare, Alice, 5700, South Africa0000-0002-4070-7399Jacinta MurungaSikoliaDepartment of Mathematics and Actuarial Science, Kibabii University, PO Box 1699 - 50200, Bungoma, KenyaLucyChikamaiDepartment of Mathematics and Actuarial Science, Kibabii University, PO Box 1699 - 50200, Bungoma, KenyaJournal Article20240824In this paper, the ordinary character table of a finite extension of structure $\overline{G}=2^7{:}G_2(2)$ is computed via the Fischer-Clifford matrices technique. The group $\overline{G}$ sits maximally in the affine subgroup $2^7{:}Sp_6(2)$ of the symplectic group $Sp_8(2)$.https://ajmc.aut.ac.ir/article_5605_7abdfbd11b37a9f822fb1ffefb860a31.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Quasi-multipliers and quasi Jordan multipliers175181563210.22060/ajmc.2025.23476.1260ENAbbasZivari-KazempourDepartment of Mathematics, Faculty of Basic Science, Ayatollah Boroujerdi University, Boroujerd, IranJournal Article20240923We show that every quasi-multiplier $\phi:L^1(G)\times L^1(G)\longrightarrow L^1(G)$, where $G$ is a locally compact group, is of the form $$\phi(f,g)=f\star \mu\star g,\ \ \ \ \ f,g\in L^1(G),$$ for a unique measure $\mu\in M(G)$. As a consequence, we obtain a well-known result due to Wendel. We also prove the analogues result for $C^*$-algebras. Moreover, we introduce the notion of quasi Jordan multipliers and prove that each such map on a $C^*$-algebra, as well as group algebra $L^1(G)$, is a quasi-multiplier.https://ajmc.aut.ac.ir/article_5632_a2232b5b6b17429cdff8ddc2f14ea8c9.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Almost complex structure over almost contact metric structures183188561810.22060/ajmc.2024.23677.1285ENAkbarSadighiDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran0000-0002-9992-2958Seyyed MohammadZamanzadehDepartment of Mathematics,
Bijar Branch, Islamic Azad University,
Bijar, IranJournal Article20241115In this paper, we investigate the conditions under which a lifted almost complex structure $J$ on the tangent bundle $TM$ of a manifold $M$ exhibits various Kählerian properties. We establish several characterizations relating the geometry of $(TM, J)$ to the cosymplectic structure on $M$. Specifically, we show that $(TM, J)$ is Kählerian if and only if $(M, \eta, \xi, \varphi)$ is cosymplectic and $R = 0$. Similarly, we prove that $(TM, J)$ is nearly Kählerian under the same conditions on $M$. Furthermore, we present an alternative criterion for $(TM, J)$ to be Kählerian, involving a nearly cosymplectic condition on $M$ alongside a specific curvature relation. Finally, we demonstrate that $(TM, J)$ is semi-Kählerian if and only if $(M, \eta, \xi, \varphi)$ is semi-cosymplectic with $R(X, Y) \varphi Z = 0$. These results reveal intricate connections between cosymplectic structures on $M$ and Kählerian-type structures on $TM$, contributing to the broader understanding of almost complex geometry on tangent bundles.https://ajmc.aut.ac.ir/article_5618_98fb202278940504d75b5a97b1476be4.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401New general location models for mixed response189200565910.22060/ajmc.2025.23674.1284ENEhsanBahrami SamaniDepartment of Statistics, Faculty of Mathematical Science, Shahid Beheshti University,
Tehran, 1983963113, IranJournal Article20241114In this paper, we introduce new general location model for mixed responses including correlated nominal, ordinal and continuous outcomes by using latent variable approach. We discuss regression methods for jointly analysis of continuous and categorical (nominal and ordinal) responses. After presenting the Leon and Carri\`ere \' general location model (2007), new general location model is introduced. A full likelihood-based approach is used to obtain maximum likelihood estimations of the models parameters. The proposed model is applied to BMI, Steatosis and Osteoporosis data.https://ajmc.aut.ac.ir/article_5659_94b087da83ceb5fe6f1a13150f8c0471.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401A proof for a general form of the Serre-Swan theorem201203563710.22060/ajmc.2025.23797.1308ENMohammad BagherAsadiSchool of Mathematics,
Statistics and Computer Science,
College of Science,
University of Tehran,
Tehran, IranZahraHassanpour-YakhdaniSchool of Mathematics,
Statistics and Computer Science,
College of Science,
University of Tehran,
Tehran, IranJournal Article20250102In this brief note, we present a proof for a general form of the Serre-Swan theorem.https://ajmc.aut.ac.ir/article_5637_71d2d6ccac82f8a334937ff0fcdc0d8a.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Multivalued interpolative type contractions on partial metric spaces205212562410.22060/ajmc.2024.23449.1257ENSirajoYahayaDepartment of Mathematics and Statistics, American University of Nigeria, Yola, Nigeria0000-0002-9602-9451MohammedShehu ShagariDepartment of Mathematics,
Ahmadu Bello University Zaria,
Kaduna, NigeriaJournal Article20240827This article presents the interpolative fixed point theorem with reference to complete partial metric spaces, by taking the multi-valued contraction into account. In particular, the idea of multivalued interpolative Reich–Rus–\'{C}iri\'{c} type contractions is introduced and criteria for the existence of fixed points' of such operators are established. A nontrivial example is provided to support the validity of the obtained results.https://ajmc.aut.ac.ir/article_5624_c460dc0f18fc309ac07306a4a55d2fd6.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497220260401Numerical methods for the time-fractional diffusion equation: A review213269598010.22060/ajmc.2026.24592.1441ENAminGhoreyshiDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran0009-0001-7239-5342MostafaAbbaszadehDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran0000-0001-6954-3896MehdiDehghanDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran0000-0002-2573-9755Journal Article20250818This review paper focuses on the numerical solution of the time-fractional diffusion equation using various discretization techniques. For the time-fractional derivative, we consider methods such as L-type approximations and Grunwald-Letnikov-based formulas, while for the spatial diffusion term, we utilize the compact finite difference method, finite element method, spectral element method, meshless method, Chebyshev spectral method, and finite block method. In addition, stability and convergence theorems are presented, accompanied by numerical examples that confirm the theoretical results.https://ajmc.aut.ac.ir/article_5980_63dfdeb1ff9ff09ecc3f05d2d7221ffa.pdf