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Research Article
Mathematical Modeling of an Intelligent Document Management System Based on Microservice Architecture and BERT Models
Farhod Rahimi*
,
Fayzali Saduiioevich Komiliyon,
Manuchehr Farhodovich Rahimov,
Mehrdod Rahmatullovich Yorov
Issue:
Volume 15, Issue 3, June 2026
Pages:
68-74
Received:
26 March 2026
Accepted:
25 April 2026
Published:
11 May 2026
Abstract: In the context of the ongoing digital transformation of governmental and corporate information systems, the development of intelligent document management solutions capable of efficient processing, structuring, and analysis of textual data has become increasingly important. Particular challenges arise in the processing of multilingual data and low-resource languages, such as Tajik, due to the limited availability of annotated corpora. The aim of this study is to develop and formalize a mathematical model of an intelligent document management system based on microservice architecture and transformer-based natural language processing techniques. The proposed approach integrates a distributed microservice architecture using gRPC with a named entity recognition (NER) model based on multilingual BERT. To address data scarcity, a synthetic data generation mechanism is introduced to augment the training corpus. The NER task is formulated as a probabilistic sequence labeling problem, and the training procedure includes fine-tuning of the transformer model and comparison with baseline approaches, including rule-based methods, Conditional Random Fields (CRF), and BiLSTM-CRF models. Experimental evaluation is conducted on a curated corpus of Tajik-language documents, divided into training, validation, and test subsets. The results demonstrate that the proposed model achieves an F1-score of 0.93, outperforming all baseline methods. In addition, the system exhibits near-linear scalability under horizontal scaling conditions and ensures fault tolerance through a hybrid mechanism that switches to a rule-based extractor in case of service unavailability. The proposed model provides a scalable and robust framework for intelligent document processing systems and can be effectively applied in governmental and corporate environments undergoing digital transformation.
Abstract: In the context of the ongoing digital transformation of governmental and corporate information systems, the development of intelligent document management solutions capable of efficient processing, structuring, and analysis of textual data has become increasingly important. Particular challenges arise in the processing of multilingual data and low-...
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Research Article
Solution of Nonlinear Equations Using the Modified Steffensen’s Type Method
Clement Adaku Nnedinma,
Bazuaye Frank Etin-Osa*
Issue:
Volume 15, Issue 3, June 2026
Pages:
75-88
Received:
7 April 2026
Accepted:
22 April 2026
Published:
16 May 2026
Abstract: The root-finding problem is one of the most important problems in Numerical Analyis. It arises in a wide variety of practical applications in physics, chemistry, biosciences, engineering, etc. As a matter of fact, determination of any unknown appearing implicitly led to the evolution of root-finding problem. Therefore, this paper focuses on the modification and analysis of a high order derivative-free iteration methods for finding roots of nonlinear algebraic equations of the form f (x) = 0. The methods require only one initial approximation. The proposed method is seen as an extension of the second-order Steffensen’s scheme, which is an Iterative method for approximating roots of non-linear equations which often breaks down when the derivative of the function value is zero or near zero at the point of iteration. This work therefore, seeks to introduce a method that overcomes such breakdown. The method herein is a combination of forward difference formula with Simpson’s quadrature in spirit of Steffensen. The idea is to modify the Steffensen’s method, which were recently developed to obtain derivative-free methods. The modified methods are shown to converge. We also describe how to obtain derivative-free methods to find solutions to multiple roots. Several numerical examples are provided to validate the theoretical order of convergence for nonlinear functions with simple roots and results obtained show the comparative advantage the proposed method has over well-known methods.
Abstract: The root-finding problem is one of the most important problems in Numerical Analyis. It arises in a wide variety of practical applications in physics, chemistry, biosciences, engineering, etc. As a matter of fact, determination of any unknown appearing implicitly led to the evolution of root-finding problem. Therefore, this paper focuses on the mod...
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Research Article
Dominant Metric Dimension of Star Fan Graphs
Sali Vadakkethil Mathew,
Venkatajalam Vijayalakshmi*
Issue:
Volume 15, Issue 3, June 2026
Pages:
89-94
Received:
17 April 2026
Accepted:
30 April 2026
Published:
10 June 2026
DOI:
10.11648/j.acm.20261503.13
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Abstract: Abstract: A dominating set of a connected graph G = (V, E) is a subset D of V (G) such that every vertex of G is either in D or adjacent to a vertex in D. A resolving set of a connected graph G is a subset D of V (G) such that each vertex v of G has a unique representation with respect to D. A dominant resolving set of a graph G is a subset D of V (G) that resolves all vertices of G and dominates G. The dominant metric dimension, Ddim(G), is the cardinality of the smallest such set. The dominant metric dimension of a graph combines metric dimension (location identification) with domination (coverage), making it ideal for sensor networks that require both unique positioning and full coverage. Similarly, a dominant edge resolving set of a connected graph G is a vertex subset D of V that resolves all edges and is a covering of G. Star fan graphs are composite graph structures formed by attaching fan graphs to the pendant vertices of a star graph, creating hierarchical networks that are useful for modeling hub-and-spoke systems with additional path structures. This paper computes the dominant metric dimension and dominant edge metric dimension of star fan graphs.
Abstract: Abstract: A dominating set of a connected graph G = (V, E) is a subset D of V (G) such that every vertex of G is either in D or adjacent to a vertex in D. A resolving set of a connected graph G is a subset D of V (G) such that each vertex v of G has a unique representation with respect to D. A dominant resolving set of a graph G is a subset D of V ...
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Research Article
Isogeometric Analysis of the Wave Equation on Curved Domains Using Python: B-spline Parameterization, Stability Analysis and Numerical Validation
Issue:
Volume 15, Issue 3, June 2026
Pages:
95-110
Received:
25 April 2026
Accepted:
7 May 2026
Published:
10 June 2026
DOI:
10.11648/j.acm.20261503.14
Downloads:
Views:
Abstract: Classical finite element methods (FEM) approximate curved boundaries by piecewise polynomials, which introduces geometric errors that degrade the accuracy of wave propagation simulations. Isogeometric analysis (IGA) overcomes this limitation by using the same B-spline basis functions for both exact geometry representation and solution approximation. This paper presents a complete Python implementation of IGA for solving the wave equation on curved domains, extending previous work from rectangular to curved geometries. The methodology includes three main steps. First, we construct exact B-spline parameterizations of a semicircular membrane and a quarter-annular plate, ensuring no geometric approximation error. Second, we discretize the weak Galerkin formulation in space using B-splines and in time using a fourth-order Runge-Kutta scheme. Third, we derive a generalized Courant-Friedrichs-Lewy (CFL) condition that incorporates the effective element size to account for the non-uniform Jacobian of curved mappings. Numerical experiments demonstrate that the method achieves optimal convergence rates. For quadratic B-splines, the observed rate reaches 2.98, very close to the theoretical value of 3. On the quarter-annulus test case, the IGA solution matches the analytical frequency with only 0.3% error, whereas standard FEM with a comparable number of degrees of freedom yields 2.1% error-a sevenfold improvement. The numerical CFL limit is accurately predicted by the generalized condition. The complete open-source Python code is provided in the appendix, enabling full reproducibility. This work lays a foundation for accurate wave propagation simulations on curved geometries in acoustics, elastodynamics, and seismology.
Abstract: Classical finite element methods (FEM) approximate curved boundaries by piecewise polynomials, which introduces geometric errors that degrade the accuracy of wave propagation simulations. Isogeometric analysis (IGA) overcomes this limitation by using the same B-spline basis functions for both exact geometry representation and solution approximation...
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