Latest Research Articles on Math

This article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods is selected as an algorithm for studying this system. The ABMSelkovFracSim 1.0 software package acts as a program, in which a numerical algorithm with the ability to visualize the research results is implemented to build oscillograms and […]

In engineering, physics, and other fields, implicit ordinary differential equations are essential to simulate complex systems. However, because of their intrinsic nonlinearity and difficulty separating higher-order derivatives, implicit ordinary differential equations pose substantial challenges. When applied to these types of equations, traditional numerical methods frequently have problems with convergence or require a significant amount of computing power. In this work, we present the multi-stage differential transform method, a novel semi-analytical approach for effectively solving first- […]

This study introduces a fuzzy interval-valued approach using multi-objective linear programming to optimize passenger–driver matching in ride-hailing systems, addressing uncertainties in waiting times and fare preferences. The model aims to minimize total waiting times, balance job allocations among drivers, and reduce deviations in fare expectations between passengers and drivers. The proposed framework effectively manages operational uncertainties by incorporating interval-valued fuzzy parameters, including traffic variability and fluctuating demand patterns. Numerical experiments […]

Upper-air wind fields play a crucial role in aircraft navigation, directly impacting flight safety and operational efficiency. In this study, we propose an advanced route planning framework that integrates wind field predictions derived from a neural network-based approach. Specifically, we leverage the PredRNN Sequence-to-Sequence algorithm to predict wind fields up to 10 hours in advance. The model is trained on grid-based wind speed data at an altitude of approximately 5500 m, focusing on major airline routes over China. Our approach demonstrates superior accuracy in wind field forecasting […]

In this paper, we investigate the exterior problem of parabolic Hessian quotient equations. By utilizing Perron’s method, we establish the existence of viscosity solutions that exhibit generalized asymptotic behavior at infinity. The main approach we adopt involves constructing sub- and supersolutions to handle the non-constant term on the right-hand side of the equation.

This paper concerns the viscous Boussinesq equations without a dissipation term and their relation to the temperature equation related to the exterior of a ball with a smooth boundary. We first prove the global existence of weak solutions on the bounded domain Ω˜ via the Schauder fixed-point theorem. Then, we derive the uniform estimates to obtain the global existence of weak solutions on the unbounded domain Ω by utilizing the domain expansion method. Finally, we show that the equations have a unique classical solution for H3 initial data by a series of […]

Classifying imbalanced data is a well-known challenge in machine learning. One of the fields inherently affected by imbalanced data is credit datasets in finance. In this study, to address this challenge, we employed one of the most recent methods developed for classifying imbalanced data, CorrOV-CSEn. In addition to the original CorrOV-CSEn approach, which uses AdaBoost as its base learning method, we also applied Multi-Layer Perceptron (MLP), random forest, gradient boosted trees, XGBoost, and CatBoost. Our dataset, sourced from the Iran capital market from 2015 to 2022, utilizes the more […]

Evolutionary inferences from phylogenetic trees can be modeled stochastically using a range of mathematical frameworks. Among these, stochastic differential equations (SDEs) provide a particularly flexible and powerful approach to capturing the continuous-time dynamics of evolutionary processes. This review summarizes advances in stochastic modeling for trait evolution along a phylogenetic tree, with a focus on stochastic differential equations (SDEs), Gaussian and non-Gaussian processes, and time series models that can be expressed as special cases of general stochastic frameworks, depending […]

This paper formalizes the analytic expressions and some properties of the evolution operator that generates the state-trajectory of dynamical systems combining delay-free dynamics with a set of discrete, or point, constant (and not necessarily commensurate) delays, where the parameterizations of both the delay-free and the delayed parts can undergo impulsive changes. Also, particular evolution operators are defined explicitly for the non-impulsive and impulsive time-varying delay-free case, and also for the case of impulsive delayed time-varying systems. In the impulsive cases, in general, […]

Modeling distributed parameter systems (DPSs) is challenging due to their strong nonlinearity and spatiotemporal coupling. In this study, a three-dimensional fuzzy modeling method combining genetic algorithm (GA)-based automatic clustering and hierarchical extreme learning machine (HELM) is proposed for DPS modeling. The method utilizes GA-based automatic clustering to learn the premise part of 3D fuzzy rules, while HELM is employed to learn spatial basis functions and construct a complete fuzzy rule base. This approach effectively captures the spatiotemporal coupling characteristics of the […]

Discontinuities in rock mass are usually considered to be important influencing factors for shear failure. As a type of granular material, the macroscopic mechanical behavior of rock masses is closely related to the anisotropy of the contact network. This paper uses the discrete element method (DEM) to simulate direct shear tests of specimens with different joint inclinations and analyzes the evolution of shear-induced fabric anisotropy and contact force anisotropy during the shear process. Three anisotropic tensors aijc, aijn and aijt are defined to characterize the anisotropic behavior of […]

This paper deals with a two-machine flow shop problem with shortening jobs. A shortening job means that the job’s processing time is a decreasing function of its starting time. The aim is to find a sequence that minimizes the makespan of all the jobs. several dominance properties, some lower bounds, and an initial upper bound are derived, which are applied to propose a branch-and-bound algorithm to solve the problem. We also propose some heuristics and mathematical programming. Computational experiments are conducted to evaluate the performance of the proposed algorithms.