Mathematical Models in Engineering: Table of Contents

Assessing environmental influences on radon levels: analysis of independent variables

Pawade, Anil — 2024-06-30T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 3, 2024, p. 168-192.
Anil Pawade, Shrikant Charhate
Regression analysis is essential for prediction analysis and variable identification since air pollution studies are complicated by competing suggestions and require careful interpretation. In the existing predictive analysis, estimating indoor radon levels is challenging due to multicollinearity issues and the existing algorithm's assumption of independent predictor variables, making it difficult to accurately assess individual effects. Hence a novel Unsupervised Bayesian Multiple Regression Analysis is used to correctly offer the specific impacts of each predictor variable by taking the complex interactions between factors in the estimation of indoor radon levels. Furthermore, in the variable identification, indoor radon levels are influenced by complex residual distributions, with existing algorithms failing to predict non-Gaussian residuals due to outlier-sensitive least squares estimation. So a novel Quadratic Discriminant Extreme Learning Machine is implemented to overcome this issue, which creates models that are better able to reliably detect the factors driving indoor radon levels and are more robust to non-Gaussian residual distributions. The proposed method demonstrates excellence in predictive analysis and variable identification achieving high coefficient of relation and low MAE.

Secure metric dimension of new classes of graphs

Batiha, Iqbal M. — 2024-07-15T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 3, 2024, p. 161-167.
Iqbal M. Batiha, Basma Mohamed, Iqbal H. Jebril
The metric representation of a vertex v of a graph G is a finite vector representing distances of v with respect to vertices of some ordered subset S⊆V (G). If no suitable subset of S provides separate representations for each vertex of V(G), then the set S is referred to as a minimal resolving set. The metric dimension of G is the cardinality of the smallest (with respect to its cardinality) minimal resolving set. A resolving set S is secure if for any v∈V–S, there exists x∈S such that (S–{x})∪{v} is a resolving set. For various classes of graphs, the value of the secure resolving number is determined and defined. The secure metric dimension of the graph classes is being studied in this work. The results show that different graph families have different metric dimensions.

Common fixed-point theorem for commuting maps on a metric space

Sahani, Suresh Kumar — 2024-07-20T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 3, 2024, p. 152-160.
Suresh Kumar Sahani, Vijay Vir Singh, Krishnapal Singh Sisodia, Kusum Sharma
Several novel uses of theorems for fixed points in commuting mapping in a fully metric domain are presented. Several conclusions from full metric fixed point theory are improved and extended by our work. Our proofs are inspired by the study of commuting mappings [B. Fisher and S. Sessa, on a fixed point theorem of Gregus, 1986] and [P. Sumati Kumari, Fixed and periodic point theory in certain spaces, 2013].

Finding the domination number of triangular belt networks

Almotairi, Sultan — 2024-07-31T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 234-240.
Sultan Almotairi, Olayan Alharbi, Zaid Alzaid, M. Yasser Hausawi, Jaber Almutairi, Basma Mohamed
Domination in graphs has been an extensively researched branch of graph theory. A set S⊆V is said to be the dominating set of graph G if for every v∈V-S there exists a vertex u∈S such that uv∈E. The minimum cardinality of vertices among the dominating set of G is called the domination number of G denoted by γ(G). The main object of this paper is to study the domination number of some networks such as triangular belt networks TBn, alternate triangular belt networks ATBn and restricted square of bistar networks Bn,n.

A special graph for the connected metric dimension of graphs

Batiha, Iqbal M. — 2024-07-31T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 3, 2024, p. 193-201.
Iqbal M. Batiha, Nidal Anakira, Amal Hashim, Basma Mohamed
Given a connected graph G=(V, E), let d(x, y) represent the separation between x and y at its vertices. If each vertex in a collection B is uniquely identified by its vector of distances to the vertices in B, then that set of vertices resolves a graph G. A metric dimension of G is represented by dim(G) and is the smallest cardinality of a resolving set of G. If the subgraph B- induced by B is a nontrivial connected subgraph of G, then a resolving set B of G is connected. The metric dimension of G is the cardinality of the minimal resolving set, while the connected metric dimension of G is the cardinality of the smallest connected resolving set. The connected metric dimension of the knots graph, whitehead link graph and jewel graph are determined in this study. Finally, we derive the explicit formulas for the triangular book graph, quadrilateral book graph and crystal planar map.

A new mathematical model for optimizing laser cutting parameters to improve fabric quality

Samura, Lisa — 2024-07-31T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 202-216.
Lisa Samura, Muhamad Danil Pratama, Valentinus Galih Vidia Putra, Fandi Achmad, Yusril Yusuf, Fadil Abdullah
We present a model for optimizing laser-cutting process parameters to improve fabric-cutting quality in the textile industry. We use two methods to predict fabric-cutting quality based on customized laser-cutting parameters, Response Surface Methodology (RSM) and Artificial Neural Network (ANN). RSM had an R-squared (R2) value of 0.952, showing high accuracy. As a result of varying iterations and nodes, the results of the ANN models were different. As a result of 10,000 iterations on an architecture with six nodes and one hidden layer, the ANN model with an R-squared of 0.998 was the best optimization model. The novelty of this study found that ANNs with six nodes and 10,000 iterations optimize the laser cutting process for fabrics more effectively than models with fewer nodes and fewer iterations. RSM and ANNs are effective tools for improving fabric-cutting quality in specific applications, as well as providing theoretical contributions through this research.

Landslide susceptibility mapping of Phewa Watershed, Kaski, Nepal

Kunwar, Bimal Bahadur — 2024-08-22T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 217-233.
Bimal Bahadur Kunwar, Nantakan Muensit, Kuaanan Techato, Saroj Gyawali
Heavy and incessant rainfall in Nepal, particularly during the monsoon season, leads to water-induced risks like landslides, necessitating the use of Landslide Susceptibility Mapping (LSM) for the prediction of landslide risks. We aim to determine the degrees of connection and connective factors among landslide incidents to generate an updated landslide susceptibility map of the Phewa watershed in Kaski District, Nepal. The most dependable and popular statistical approach for determining LSMs is the frequency ratio model, which was created in ArcGIS 10.7.1 by identifying 46 landslides in the area and analyzing eight causal factors. The LSM categorized the area into five classes, with the low class representing a large percentage (43.27 %) and the high class a small percentage (0.63 %). In FR techniques, slope, proximity to a stream or road, land use/cover, and precipitation were assigned greater weight than aspect, profile curvature, and plan curvature. Using the area under the curve approach, the applied model’s accuracy revealed a good performance value of 0.717. Taken together, the mapping information provides a crucial understanding of risks posed by landslides, ultimately reducing the impacts in the protected watershed of the Phewa Lake area.

Generalised Poisson-new linear-exponential distribution

Sah, Binod Kumar — 2024-09-08T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 241-250.
Binod Kumar Sah, Suresh Kumar Sahani
It is a compound discrete probability distribution which has two parameters and whose particular case is Poisson-New Linear-Exponential Distribution (PNLED) [1]. The statistical characteristics required for this distribution such as probability mass function (pmf), statistical moments, estimation of parameters and goodness of fit have been derived and explained nicely. To test theoretical reliability of this distribution, goodness of fit has been applied to some over-dispersed data which were used by other researchers and further, we found that this distribution looks more appropriate for statistical modelling than PNLED, generalised Poisson-Lindley distribution (GPLD) [1, 2] and Poisson-Lindley distribution (PLD) [3].

A Comprehensive examination of utilizing neutrosophic parameters in manufacturing industry through queueing approach

B, Logapriya — 2024-09-17T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 251-263.
Logapriya B, Vidhya D, Shobana A, Nirmala V, Gayathri P
Queueing theory plays a pivotal role in analyzing the dynamics of manufacturing systems subject to random arrivals and service times. The M/G/1 queueing model, which represents a single-server queue with general distributions for inter-arrival and service times, is fundamental in this regard. However, traditional queueing models often fail to account for the inherent uncertainties encountered in real-world manufacturing scenarios. Neutrosophic theory provides a robust framework for modeling indeterminacy, ambiguity, and inconsistency in queueing parameters, thereby offering a more adaptable and precise depiction of system behavior. This research investigates the utilization of Neutrosophic sets in defining arrival rates, service times, and queue length distributions within the M/G/1 framework tailored to manufacturing settings. By employing numerical examples and comparative analyses, the study explores the effects of Neutrosophic parameters on key performance indicators such as mean waiting time, queue length distribution, and server utilization, considering distributions like Exponential, Erlang, and Deterministic. Additionally, it delves into the implications of integrating Neutrosophic parameters into queueing theory, providing valuable insights into improved decision-making and system optimization across various manufacturing operational contexts.

A sandwich-type Winkler-Pasternak double elastic foundation beam model for analysis of nut column load transfer systems of shiplifts

Liao, Lekang — 2024-09-25T00:00:00Z

Mathematical Models in Engineering, Vol. 10, Issue 4, 2024, p. 264-280.
Lekang Liao
The rack and pinion shiflifts feature its capability of fortification against extreme accidents of unbalance of ship chamber. This requires the load transfer systems of nut columns to be able to transfer the huge and centralized loads from the safety mechanisms to the tower columns in a distributive bearing way. Aiming at exploring a design-oriented computation method for the nut column load transfer systems (NCLTSs), a sandwich-type semi-infinite coupling Winkler-Pasternak double elastic foundation beam model (DEFBM) has been established, with a distributive assumption of the axial constrain force on the interfaces between the nut columns, mortar beds, adjusting beams and the second stage concrete based on the physical model test, has been proposed. A set of formulars for describing the distribution of deflections, internal forces and stress of nut columns and adjusting beams have been derived. A case study of the Three-Gorges shiplift has been conducted to demonstrate the approach of calculation of internal forces and stress by applying the formulas based on sandwich-type Winkler-Pasternak DEFBM, showing the convenience and rationality of the method to parametric layout design of the nut columns and adjusting beams in NCLTSs. Not only to NCLTSs and rack load transfer systems of shiplifts, the sandwich-type Winkler-Pasternak DEFBM also supplies the reference to the modeling and analysis of the rail-embedment structural systems broadly applied in hydraulic engineering.

More on micro semi – pre-operators in micro topological spaces

Sathishmohan, P. — 2024-10-26T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 1, 2025, p. 1-7.
P. Sathishmohan, G. Poongothai, K. Rajalakshmi, S. Stanley Roshan
The basic objective of this paper is to introduce and investigate the properties of micro semi pre border, micro semi pre kernel and micro semi pre derived set and obtain relation between some of the existing sets.

A novel problem and algorithm for solving permuted cordial labeling of corona product between two graphs

A. Alsatami, Khalid — 2025-01-01T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 1, 2025, p. 23-34.
Khalid A. Alsatami, Yasmin Algrawani, Atef Abd El-hay
This study has come up with a new application of permuted cordial labeling initiated by two graphs based on their corona product, furthering the cause of a better comprehension of and research into specific types of graphs. The Permuted cordial labeling construction for the corona product of graphs consisting of paths, cycles, second power of a path and second power of cycle graphs may facilitate the consideration of the properties and structures of the graphs. It helps us to study its topological properties, connectivity images, symmetries and other properties.

A cost model analysis in the process of refining petroleum using supplementary variable technique

S, Palaniammal — 2025-03-09T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 1, 2025, p. 35-46.
Palaniammal S, Kumar K
This paper presents a cost model analysis for refining petroleum using an MX/G(a , b)/1.MX/G(a , b)/1 queuing system with two stages of heterogeneous services under steady-state conditions. The study derives the total average cost per unit time for two distinct service phases: Phase I and Phase II. In the first case, the analysis focuses on the total average cost of the system when the server operates in Phase I with a probability of π1 at any given time, and in Phase II with a probability of π2. Additionally, the model incorporates holding costs, operating costs, renovation costs for both phases, and closure time costs. Finally, numerical tables and graphical representations are provided to illustrate the observations regarding the total average cost, renovation rate, and arrival rate.

Towards explainable artificial intelligence with potential games

Spyrou, Evangelos — 2025-03-09T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 1, 2025, p. 8-22.
Evangelos Spyrou, Vassilios Kappatos, Afroditi Anagnostopoulou, Evangelos Bekiaris
Explainable Artificial Intelligence (XAI) emerged when researchers attempted to identify methods that would interpret the models that are used to perform classification and predictions, in order to avoid having a black box just informing about the result. Methods of XAI are crucial to determine details of the model feature contribution towards the result. One of these methods is attributed to cooperative game theory and especially Shapley values. With this method the features are considered as players and the marginal contribution of the features are employed. In this paper, we take onboard the Potential Game paradigm to show the interconnection between them and the Shapley values. We show that the Shapley values are interlinked with the potential function. Moreover, we setup a game with the marginal contribution of the players as their utility functions and we prove that the game is a potential game. Finally, we show that the price of stability of this game is 1. We utilise the Simulated Annealing (SA) method to find the optimal solution.

3-D wheel/rail contact modeling method and temperature analyses

Wang, Zexin — 2025-05-05T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 2, 2025, p. 47-55.
Zexin Wang, Tao Yang, Yunpeng Wei
According to the wheel/rail actual dimensions, the modeling process of a 3-D full-size wheel/rail sliding contact finite element model is introduced in detail. During modeling process, the partitioning strategy method and MPC method are adopted. The temperature characteristics of the contact region during sliding contact are researched. The research results show the contact patch shape is close to an ellipse. The stress in the contact area is very concentrated, and the maximum von Mises stress appears in the subsurface at a distance of 2 mm from the contact interface. During the sliding contact, the maximum temperature appears at the contact center. The temperature on wheel contact surface ascends continuously and is significantly greater than the rail surface temperature. High temperatures of contact region are mainly distributed in the contact surface and subsurface, and the influence depth of temperature does not exceed 3 mm.

Rainfall forecast and potential flooding of agricultural land in Serang Regency, Banten, Indonesia

Ruhiat, Yayat — 2025-06-30T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 2, 2025, p. 56-67.
Yayat Ruhiat, John Chaidir, Halim Akbar, Yudi Guntara
Serang Regency has a sub-tropical climate and is classified as lowland, generally consisting of rice fields, fields, and gardens. These three lands have the potential to flood during the rainy season, which has implications for a decrease in agricultural production. Flood forecasts are carried out on agricultural land to avoid decreased production. The data used included rainfall, harvest area, and agricultural production. Estimates of farmland flooding and agricultural production changes are overlayed with Geographic Information Systems (GIS) and production percentages. The results of rainfall analysis show that the monthly average rainfall in Serang Regency is categorized as low to high. Meanwhile, heavy rain has the potential to occur in January and February. After being coated with GIS, it is spatially predicted that six sub-districts with an altitude below 10 meters above sea level have the potential to flood. Of the six sub-districts, 2,902.80 ha of agricultural land is estimated to have the potential to be flooded. Flooding in the area has implications for decreasing the production of seasonal crops, vegetables and fruits. Food crop production decreased by 0.42 %, while seasonal vegetables and fruits decreased by 48.04 %. There are five types of food crops and 12 types of vegetables and fruits that have the potential to be developed in Serang Regency. The food crop with the most significant production is rice, while the seasonal production of vegetables and fruits is cucumbers. In the event of a flood, rice production in Serang Regency is predicted to decrease by 1.23 % and cucumber production is expected to decrease by 0.48 %. It is necessary to adopt a planting pattern with a climate approach to minimize the decline in production.

Stodola-Vianello iteration method for the free flexural vibration frequencies of Shimpi’s single variable shear deformable beams

Ike, Charles Chinwuba — 2025-07-02T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 3, 2025, p. 97-116.
Charles Chinwuba Ike
The natural vibration frequency analysis of beams is vital for their design against resonance failures because such failures occur when the excitation load frequencies of vibration coincide with such natural frequencies. This work presents a single variable shear deformable beam equation formulated using Shimpi’s displacement field assumptions. This results in a quadratic shear stress profile over the depth and a satisfaction of the transverse shear stress-free boundary conditions. The governing equation is obtained using a first principles consideration and equilibrium method as a partial differential equation (PDE) which is non-homogenous for forced vibrations and homogeneous for free vibrations. The study then used the Stodola-Vianello iteration method to solve the resulting homogeneous PDE for simply supported boundary conditions and harmonic response. The problem reduced to an iterative problem of algebra involving the computation of an (n+1)th vibratory modal shape function from an nth shape function that satisfies the boundary conditions. This work used a sinusoidal shape function which is exact for the simply supported boundary condition investigated. The use of boundary conditions solved the integration constants involved. Application of the convergence rule led to the eigenequation from which the eigenvalues were found. The eigenvalues were presented for the first four modes of vibration and for a rectangular beam. It was found that for l/h varying from 5 to 100, the natural vibration frequencies were identical with the ωn values obtained using Navier method for other thick beam vibration problems. It was also found that ωnwas close to the exact values for all vibration modes and for all values of l/h between 5 and 100. For all vibration modes and all considered l/h values negligible differences, were observed between the ωn obtained using SVIM and the exact values obtained by previous researchers.

Performance assessment of network system network comprising four subsystems via multi failure and multi repair methodology

Sharma, Shailly — 2025-08-16T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 3, 2025, p. 117-135.
Shailly Sharma, V. V. Singh, Priyavada Parihar, Padam Lal Neupane
A multi-dimensional repair approach is the most effective policy for restoring repairable systems. This research study analyzes a complex repairable system that consists of four subsystems with different configurations. The system consists of four subsystems: Subsystem 1 contains a single unit, Subsystem 2 includes n identical units operating under a k-out-of-n: G policy, Subsystem 3 features two identical load balancers responsible for distributing the load (with at least one required for operation), and Subsystem 4 consists of four identical units functioning under a 3-out-of-4: G policy. It is assumed that all subsystems have constant failure rates that are distributed exponentially. General repair, which is utilized while the system continues to function in accordance with the established operating policy, and copula-based repair, which is employed when the system stops completely, are the two types of repair techniques that are put into practice. A supplementary variable approach is incorporated to analyses system performance. Various reliability measures are computed using Maple 18, software, and future behaviour of system have been predicted in long run operation. By means of illustrations in the tables and graph it clearly shown how the copula repair is beneficial over ordinary repair.

Optimizing concrete block properties through the use of coconut shell and coconut shell ash: a multilayer perceptron approach

Okeke, T. E. — 2025-08-28T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 3, 2025, p. 155-175.
T. E. Okeke, F. O. Okafor, M. E. Onyia
This research utilized a multilayer perceptron model based on an artificial neural network (ANN) to improve concrete blocks by partially replacing stone dust and cement with coconut shell and coconut shell ash. From 35 experimental data points, 68.6 % were used for training and 31.4 % for testing. Chemical analyses showed that coconut shell ash, rich in silicon and other oxides, enhanced pozzolanic reactions as a cement substitute. Results indicated that higher proportions of coconut shell ash and shells reduced density, making the mixture lighter but potentially affecting structural integrity. However, increased replacement levels improved workability, shown by higher slump values. The curing period significantly impacted strength, with longer times leading to increased strength due to continued hydration. An optimal compressive strength of 14.17 N/mm2 was achieved with a 5 % replacement after 70 days. The ANN model demonstrated a sum square error of 0.198 and a high correlation coefficient of 0.983 when predicting strength. Optimal conditions for achieving a compressive strength of 33.4 N/mm2 were identified, underscoring the cost-effectiveness of using coconut byproducts instead of traditional materials.

Single universal dimensionless specific energy curves for trapezoidal and circular shaped open channels

Tiruneh, Ababu T. — 2025-09-29T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 3, 2025, p. 68-96.
Ababu T. Tiruneh
Trapezoidal and circular channels are commonly employed as conveyances of open channel flow in irrigation canals, for storm and wastewater drainage and at times for transporting raw water. Open channel flow problems in such cross sections typically involve determination of alternate depths, critical depths and specific energy that require solving equations for which explicit solutions are difficult to obtain. This paper demonstrates the development of a solution for such problems through the use of single universal dimensionless specific energy-depth curves for each of the trapezoidal and circular shaped channels. The dimensionless curves are demonstrated to be simple to develop and use and can be adapted for wide range of user environments. Simulation of the graphical solution over broader range of flows and dimensionless depths of flow shows that the solution is reasonably accurate with percentage error of estimation of depth varying between 0 and 4 % with mean percentage error of 1.1 % for trapezoidal shaped channels and 1.2 % for circular shaped channels. Further application examples have been provided that show that the proposed graphical procedure can achieve results that are within close range of the precision of results obtained using numerical methods.

Research on fault diagnosis of electric motor rolling bearings based on CMFSE-SVM

Chen, Linlin — 2025-09-29T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 3, 2025, p. 136-154.
Linlin Chen, Celso Co
Rolling bearings are key components of rotating machinery such as electric motors, and their health status directly affects the reliability and safety of the equipment. In order to improve the fault classification accuracy of electric motor rolling bearing, this paper proposes a diagnostic method based on CMFSE-SVM. Firstly, the composite multi-scale fuzzy slope entropy (CMFSE) method proposed in this paper is used to extract the characteristics of the vibration signal of the motor rolling bearings. Finally, the obtained feature vectors are sent to the support vector machine (SVM) for fault classification. This paper verifies the classification accuracy of the method proposed in this paper on two publicly available datasets of electric motor rolling bearing faults. The experimental results show that the method proposed in this paper achieves average classification accuracies of 100 % and 99.6 % respectively on all working conditions corresponding to these two datasets. And the classification accuracies were 2.4 % and 2.8 % higher respectively than those of the compared methods.

Artificial intelligence-based stock market price prediction, a review

H N, Vishwas — 2025-11-12T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 4, 2025, p. 204-229.
Vishwas H N, Usha B A, Sangeetha K N
The stock market, a cornerstone of the global financial system, is characterized by its dynamic and volatile nature, which makes accurate price-trend prediction challenging. However, traditional statistical models often fail to capture this complexity. Recent advancements in Artificial Intelligence (AI), particularly Machine Learning (ML) and Deep Learning (DL), have transformed stock market forecasting by using diverse datasets and algorithms. This review examines recent studies on AI methodologies for stock market price trend prediction models by analyzing architectures, datasets, performance metrics, and limitations, with a focus on hybrid models, sentiment analysis, and dataset diversity. Hybrid approaches, including the Multi-Model Generative Adversarial Network Hybrid Prediction Algorithm (MMGAN-HPA), K-means long short-term memory (LSTM), and LSTM autoregressive output (LSTM-ARO), improve predictive accuracy by combining statistical methods with deep learning. Sentiment analysis models such as Stock Senti WordNet (SSWN) and Hybrid Quantum Neural Network (HQNN) integrate social media sentiment to capture market dynamics. Real-time frameworks that use stream processing show promise for high-frequency trading applications. This review addresses key challenges including data noise, nonstationarity, overfitting risks, and black-box model interpretability. Solutions include GAN-based synthetic data generation, transformer-based architectures such as SpectralGPT, and optimization techniques for computational efficiency. This review provides a taxonomy of AI-based approaches, while identifying gaps for future research. These findings highlight the potential of AI in financial forecasting while emphasizing the need for interdisciplinary collaboration to address its limitations in data quality, methodology, interpretability, and ethics.

Effect of parametric modulation on the stability of a periodic oscillator: a study with Airy functions

Ayala-Figueroa, Rafael Ivan — 2025-12-22T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 4, 2025, p. 176-186.
Rafael Ivan Ayala-Figueroa, Arturo Alejandro Chávez-Murga, Jesus Elias Miranda-Vega, Ruben Castro-Contreras, Guillermo Prieto-Avalos
This work investigates the stability of a linear oscillator with a periodically varying stiffness composed of constant and linearly time-dependent segments. By combining Floquet theory with an analytical formulation in terms of Airy functions, the monodromy matrix is obtained in closed form and the characteristic multipliers that determine the stability regime are calculated. Unlike the classical literature on Hill or Mathieu systems, where the stiffness profile is assumed to switch instantaneously or vary sinusoidally, the present model explicitly incorporates finite transition times through linear ramps. This allows us to quantify how the duration of these transitions affects the onset of parametric resonance. The resulting stability map reveals alternating bands of stable and unstable regions reminiscent of Arnold tongues, and shows that the proportion of the cycle spent in the linear-ramp stage plays a decisive role in either promoting or suppressing instability. Overall, the study provides a compact analytical and numerical framework for assessing stability in periodically driven parametric systems of practical relevance in physics and engineering.

Numerical study of heat and mass transfer in a relief pipeline with variable diameter

Khujaev, Ismatulla — 2025-12-31T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 4, 2025, p. 243-258.
Ismatulla Khujaev, Muzaffar Hamdamov, Shohjaxon Ravshanov
In this work, a comprehensive numerical and analytical investigation of hydrodynamic and thermal processes in closed pipelines of variable diameter is carried out, taking into account the terrain profile and external temperature effects. The scientific novelty of the study lies in the development of an improved quasi-one-dimensional model that allows for an integral assessment of the influence of geometric parameters (diameter, inclination angle, internal surface roughness) and thermophysical properties (material thermal conductivity, ambient temperature) on the distribution of pressure and temperature along the pipeline. The developed model was validated by comparing it with numerical simulations based on the SST turbulence model and calculations using the Darcy-Weisbach equation. The maximum deviation between the results did not exceed 2 %, confirming the high accuracy of the proposed method. It was established that hydraulic losses are predominantly determined by the pipe diameter and flow velocity, whereas thermal losses depend mainly on the thermal conductivity of the material and the spatial orientation of the pipeline. The proposed approach provides a reliable and computationally efficient foundation for predicting the energy characteristics of liquid transportation systems, optimizing structural parameters, and improving the energy efficiency of industrial, municipal, and thermal networks.

Methods to increase the throughput and carrying capacity of the “Angren-Pop” railway section in line with expected transit freight flows from the “China-Uzbekistan-Kyrgyzstan” railway project

Khusenov, Utkir — 2025-12-31T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 4, 2025, p. 187-203.
Utkir Khusenov, Ma’sud Masharipov, Shinpolat Suyunbayev, Jamshid Toychiyev
The development of the “China-Kyrgyzstan-Uzbekistan” railway (hereinafter referred to as the CKU) can be cited as a promising project to increase transit cargo flows in our country. In organizing the uninterrupted transportation of transit freight flows planned to pass through the territory of our country as a result of the implementation of this project, the “Angren-Pop” railway section, which includes the 19.2 km long “Kamchik” tunnel, is of great importance. This article analyzes the impact of the development of the CKU railway on the throughput and carrying capacities of the “Angren-Pop” railway section. The current maximum freight capacity of the “Angren-Pop” railway section has been studied. The results show that this section is not capable of handling the expected volume of transit cargo. This substantiated the need to find solutions for effectively increasing the carrying capacity of the section while ensuring an economically rational balance. Methods for effectively increasing the carrying capacity of the section are recommended, including the systematic implementation of measures such as increasing the standard weight of freight trains, raising the operating speed on the section, and using electric locomotives with high tractive power.

Kinematic and force analysis of a scissor lift mechanism

Gurskyi, Volodymyr — 2025-12-31T00:00:00Z

Mathematical Models in Engineering, Vol. 11, Issue 4, 2025, p. 230-242.
Volodymyr Gurskyi, Volodymyr Kuzo, Nadiia Maherus, Pavlo Krot
A scissor lift design was developed with a load capacity of 100 kg and a lifting height of 1 m. The platform lifting mechanism is actuated by a traction electric motor via rollers moving along the guides. A calculation model of the scissor lift was created, resulting in a statically indeterminate system. Support reactions and an actuating force were determined depending on the platform lifting height. The analytical results showed that the actuating force increases nonlinearly during platform lifting, ranging from 1.674 kN to 6.45 kN, while the actuator rod stroke is 441 mm. Similarly, the simulation conducted using SolidWorks Motion yielded the actuating force in the range of 1.62 kN-6.5 kN and the rod stroke of 443.5 mm. The study established the patterns of variation of the main kinematic and force parameters of the scissor lift, which exhibit nonlinear characteristics. A piecewise linear variation of the actuating force was synthesized to ensure a trapezoidal motion profile of the platform. This type of motion profile was selected to provide comfortable and safe movement for people, particularly those with disabilities. The strength of the main structural elements of the scissor lift, namely levers, traction crossbar, guides and rollers, was ensured.

The effectiveness of the PI-PSO controller for cylindrical pipe system identification model in NARX system

Ali Jasim, Firas — 2026-02-08T00:00:00Z

Mathematical Models in Engineering, Vol. 12, Issue 1, 2026, p. 37-55.
Firas Ali Jasim, Mohammed Jawad Mohammed, Hatam Kareem Kadhom
One of the main issues in the pipes’ structure that could be affected by wind that led to the failure of the cylinder pipe structure is vortex-induced vibration (VIV). Therefore, there is a need to control the wind that is going through the pipe to avoid vibration. This phenomenon leads to the failure of the structure due to the resonance phenomenon when the natural frequency of the structure is equal to the vortex frequency. The main contributions of this work are mathematical modeling of the system using NARX and suppressing the vibration caused by wind currents through simulation and experiment ways. PI-PSO control employed to reduce the unwanted vibration as a simulation work. Then, an experimental study implemented on the structure as an open and closed loop control techniques to decrease the vibration with disturbance vibrations of 5 and 10 m/s. Open loop active vibration control (OLAVC) is proposed in this work using dual control rods made from hollow stainless steel and driven by dual DC motors in two positions at 6, 8, 10, and 12 DCV. The control rods are located beside the main cylinder pipe (CRBCP) and from the upper and lower of the hollow cylinder pipe. The effectiveness of the passive control strategy was confirmed before supplying electricity to the two DC motors on both sides. The PI controller tuned by the PSO method was developed to control unwanted model vibration. Based on the control results, the best values of KP and KI were 35.78 and 50 respectively at the lowest MSE of 1.3557×10-4, and the frequency magnitude was reduced by 81.17 %. The findings also showed that the cylinder pipe vibration could not be sufficiently suppressed by the passive control method. While OLAVC succeeded in reducing the vibration when the motor voltage was at 12 V. Finally, the closed-loop control technique decreased the vibration up to 61.24 % and 58.65% for disturbance wind speeds of 5 and 10 m/s, respectively.

Numerical simulation of a modified sculla hydrocyclone using the GEKO k-ω turbulence model

Madaliev, Murodil — 2026-02-15T00:00:00Z

Mathematical Models in Engineering, Vol. 12, Issue 1, 2026, p. 56-71.
Murodil Madaliev, Zokhidjon Abdulkhaev, Dilbar Abduraimova, Hasan Ochilov, Tursunoy Apakhodjaeva, Eldorbek Umronov
This study presents a computational fluid dynamics (CFD) simulation of a modified hydrocyclone featuring a redesigned volute (inlet) geometry aimed at enhancing separation efficiency. The numerical investigation was conducted using the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ω GEKO turbulence model under steady-state conditions. The modification primarily improved the tangential velocity distribution and reduced pressure losses in the separation zone. Compared to the standard configuration, the modified design achieved approximately 5 % higher particle separation efficiency and more uniform pressure contours. The study also provides a detailed analysis of flow fields and vortex structures to explain the mechanism behind performance enhancement. The findings demonstrate that the proposed volute modification can substantially improve flow stability and solid-liquid separation, offering a cost-effective design improvement for industrial hydrocyclones.

Organization of empty wagon delivery technology in the logistics network

Barotov, Jamshid — 2026-02-17T00:00:00Z

Mathematical Models in Engineering, Vol. 12, Issue 1, 2026, p. 26-36.
Jamshid Barotov, Jamshid Kobulov
A station-level analysis was conducted to improve customer service at loading and unloading fronts for cargo flows. According to the results of the analysis in 2025, it was found that at the Tashkent Regional Railway Junction, the allocation of wagons at the client's request takes an average of 3-6 days, and this situation is associated with a shortage of wagons and uneven supply due to the different organization of cargo flows. To eliminate this problem, a new technology has been developed based on an optimization model aimed at the rational distribution of empty cars; lease and contract mechanisms with private car owners are also taken into account. The software developed on the basis of the model operatively recalculates orders and forms decisions on the allocation of wagons to customers in real time (practical tests showed a reduction in the delivery time of empty wagons by ~25 % and a reduction in downtime by > 20 %).

A new perspective on shear deformation in a simply supported isotropic plates: static bending and critical load determination

Onyeka, F. C. — 2026-02-27T00:00:00Z

Mathematical Models in Engineering, Vol. 12, Issue 1, 2026, p. 1-25.
F. C. Onyeka, T. E. Okeke, Uzor Onyia
This study advances the analysis of rectangular plates under transverse loading by employing a third-order shear deformation theory and a direct energy method. To address limitations of prior models, exact displacement fields were derived from a general variation of total potential energy, yielding closed-form expressions for deflection and transverse shear in the x and y directions via variational calculus. Subsequently, new formulas for critical lateral loads – applicable before excessive deflection or elastic yield – were developed. Numerical evaluations were conducted for aspect ratios 1 ≤ba≤ 2, spans of L= 1000, 3000, and 5000 mm, and thicknesses t= 5, 10, 12.5, and 15 mm. The results show that increasing thickness markedly enhances load capacity and safety margins, while larger aspect ratios and longer spans reduce stability. For example, a 15 mm plate with a 1000 mm span attains elastic-limit loads qiw> 74.7 N/mm at aspect ratio 1, decreasing to ~29.2 N/mm at aspect ratio 2, with yield loads qip> 77.8 N/mm. In contrast, a 5 mm plate under the same spans has qiw values lowering from ~2.77 N/mm to ~1.08 N/mm as aspect ratio increases, while qip remains in the range 8.39-12.53 N/mm. These trends indicate that thicker plates withstand higher elastic and plastic limits, expanding safe operating margins, whereas slender (high aspect ratio) configurations exhibit reduced capacity and greater susceptibility to instability. Under large-span/large-deflection conditions, negative or near-zero capacity values reveal potential instability modes such as buckling in slender plates. In sum, the proposed model enhances design effectiveness by integrating geometric, material, and reinforcement considerations to ensure safety and serviceability without relying on post hoc deflection or shear assessments. The framework provides reliable, accurate predictions of flexural and shear responses, supporting efficient, safe, and cost-effective structural design.