Mathematics, Volume 13, Issue 8

Deep neural networks (DNNs) have achieved high accuracy in various applications, but with the rapid growth of AI and the increasing scale and complexity of datasets, their computational cost and power consumption have become even more significant cha...

This paper presents a Finite Element Method (FEM) framework for solving the screened Poisson equation with a Dirac delta function as the forcing term. The singularity introduced by the delta function poses challenges for standard numerical methods, p...

The calibration of ultrasound probes is essential for three-dimensional ultrasound reconstruction and navigation. However, the existing calibration methods are often cumbersome and inadequate in accuracy. In this paper, a hybrid mathematical model, D...

The nonlinear deformation and vibrations of elastic plates represent a fundamental problem in structural vibration analysis, frequently encountered in engineering applications and classical mathematical studies. In the field of studying the nonlinear...

Bi-Frobenius algebras are a class of Frobenius algebras and Frobenius coalgebras with some compatible conditions. In this paper, we construct a class of bi-Frobenius algebras generated by n elements on graded algebra $A.$ The comultiplication and couni...

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a long-standing open problem from convex and discrete geometry, the construction of $\epsilon$-nets for the space of convex bodies endowed with the Banach&ndash...

The increasing complexity of cloud service composition demands innovative approaches that can efficiently optimize both functional requirements and quality of service (QoS) parameters. While several methods exist, they struggle to simultaneously mini...

This article discusses the problem of numerically solving the Navier–Stokes equations, the heat conduction equation, and the transport equation in the orthogonal coordinates of a free curve. Since the numerical solution domain is complex, the c...

In this study, we propose a new nonlinear polarization model that modifies the polarization equation to account for the material’s nonlinear response. Specifically, the nonlinear restoring force in our model is reformulated as an electric field...

The computational prediction of RNA three-dimensional (3D) structures remains a significant challenge, largely due to the limited understanding of RNA folding pathways. Although the scarcity of resolved native RNA structures has hindered the effectiv...

With the continuous integration of globalization and financial markets, the linkage of global financial risks has increased significantly. This study examines the risk spillover effects and transmission dynamics among the financial markets in G20 cou...

This paper studies the data-driven attitude tracking control issue for an unmanned underwater vehicle (UUV) with disturbances. First, a new polynomial finite-time prescribed performance function (FTPF) is introduced to avoid the problem of the comput...

This paper introduces a dual-strategy model based on temporal transformation and fuzzy theory, and designs a partitioned mining algorithm for periodic frequent patterns in large-scale event data (3P-TFT). The model reconstructs original event data th...

To improve the stability of rolling bearing fault signal denoising under different working conditions, this study proposes a multi-condition rolling bearing fault denoising method based on RIME-VMD. According to the characteristics of rolling bearing...

In steel production, the blast furnace is a critical element. In this process, precisely controlling the temperature of the molten iron is indispensable for attaining efficient operations and high-grade products. This temperature is often indirectly...

The analysis of commodity markets—particularly in the energy and metals sectors—is essential for understanding economic dynamics and guiding decision-making. Financial and economic uncertainty indices provide valuable insights that help r...

Geographically and Temporally Weighted Elastic Net Ordinal Logistic Regression is a parsimonious ordinal logistic regression with consideration of the existence of spatial and temporal effects. This model has been developed with the following three c...

We study the thermodynamic properties of the generalized non-convex multispecies Curie–Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior dist...

This study presents a novel finite-time robust control framework for quadrotor systems subjected to model uncertainties and unknown external disturbances. A fast terminal sliding mode (FTSM) manifold is first constructed to achieve finite-time conver...

In this paper, we tackle the challenge of optimizing resource utilization and demand-driven allocation in dynamic, multi-dimensional heterogeneous environments. Traditional containerized task scheduling systems, like Kubernetes, typically rely on def...

This study proposes a rotational speed measurement machine based on the flux-switching principle with a 6-stator-slot/19-rotor-pole (6s/19p) topology. With a rotor shape similar to a variable reluctance sensor (VRS), the proposed machine features a s...

This paper presents a comprehensive time-series analysis framework leveraging the Temporal Fusion Transformer (TFT) architecture to address the challenge of multi-horizon forecasting in complex ecological systems, specifically focusing on global fish...

Recently, causal models have gained significant attention in natural language processing (NLP) and computer vision (CV) due to their capability of capturing features with causal relationships. This study addresses Fine-Grained Visual Categorization (...

The increasing reliance on and remote accessibility of automated industrial systems have shifted SCADA networks from being strictly isolated to becoming highly interconnected systems. The growing interconnectivity among systems enhances operational e...

We prove that chordal graphs are chromatic-choosable and present a decomposition theorem to help estimate the choice numbers for certain classes of chordless and non-chordal graphs.

This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order $\alpha +2n$, where $\alpha \in (m-1,m]$ with $m\ge 3$ and $m,n\in \mathbb{N}$. The con...

In this paper, we focus on the internal structural characteristics of permutation tableaux and their correspondence with linked partitions. We begin by introducing new statistics for permutation tableaux, designed to thoroughly describe various posit...

The study of the equitorsion biholomorphically projective mappings between two generalized Riemannian spaces in the sense of Eisenhart’s definition is continued. Some new invariant geometric objects of an equitorsion canonical biholomorphically...

Large-volume parenterals (LVPs), as essential medical products, are widely used in healthcare settings, making their safety inspection crucial. Current methods for detecting foreign particles in LVP solutions through image analysis primarily rely on...

This paper aims to find optimal feedback policies for the tracking control of Markovian jump Boolean control networks (MJBCNs) over a finite horizon. The tracking objective is a predetermined time-varying trajectory with a finite length. To minimize...

In this paper, by employing the Euler–Maclaurin summation formula and real analysis techniques, an improved version of the parameterized Hardy–Hilbert inequality involving two partial sums is established. Based on the obtained inequality,...

This study proposes a novel nonlinear adaptive fuzzy hybrid sliding mode (AFHSM) control strategy for the precise trajectory tracking of autonomous mobile robots (AMRs) equipped with four Mecanum wheels. The control design addresses the inherent comp...

This paper investigates a backward stochastic linear quadratic control problem with an expected-type equality constraint on the initial state. By using the Lagrange multiplier method, the problem with a uniformly convex cost functional is first trans...

With the development of society and the Internet, images have become an important medium for information exchange. To improve the security of image encryption and transmission, a new image encryption algorithm based on bit-plane decomposition, DNA en...

In the present study, abilities of various macroscopic models (Navier–Stokes–Fourier, Burnett, original and regularized Grad’s 13-moment equations) in predicting the nonequilibrium molecular velocity distribution are examined. The r...

This work considers the Minkowski sum of an N-dimensional ellipsoid and hyperrectangle, a combination that is extremely relevant due to the usage of ellipsoid-adjacent primitives in computer graphics for work such as 3D Gaussian splatting. While para...

This paper considers difference equations with continuous time, piecewise linear delay functions, and oscillatory coefficients. We present new conditions on the coefficients that provide the oscillatory property of the solutions of the considered dif...

In this paper, we consider the Neumann elliptic problem $\left({\mathcal{I}}_{\epsilon }\right)$: $-\Delta u+V\left(x\right)u=u^{p-\epsilon }$, $u>0$ in $\mathsf{\Omega }$, $\partial u/\partial \nu =0$ on $\partial \mathsf{\Omega }$, where $\mathsf{\Omega }$ is a bounded smooth domain in ${\mathbb{R}}^n$, $n\ge 3$, $p+1=2n/(n-2)$ is th...

We study the use of a homogeneous fleet of drones to design an unattended persistent drone-based patrolling system for vast circular areas. The drones follow flight missions supported by auxiliary on-ground charging stations, whose location and numbe...

This study investigates the impact of cyber threats on the clean energy (CE) market, which is increasingly dependent on digital technologies and interconnected infrastructure. The sector’s growing digitalization makes it more susceptible to cyb...

In engineering, the study of the dynamic response of structures subjected to non-deterministically variable loads is particularly important, especially when considering the damage that such loads can cause due to fatigue phenomena. This is the case,...

This study investigates extremal solutions for fractional-order delayed difference equations, utilizing the Caputo nabla operator to establish mild lower and upper approximations via discrete fractional calculus. A new approach is employed to demonst...

In machine learning, when the labeled portion of data needs to be processed, a semi-supervised learning algorithm is used. A dataset with missing attribute values or labels is referred to as an incomplete information system. Addressing incomplete inf...

High-order methods are particularly crucial for achieving highly accurate solutions or satisfying high-order optimality conditions. However, most existing high-order methods require solving complex high-order Taylor polynomial models, which pose sign...

This study presents an advanced adaptive trading framework that integrates Deep Reinforcement Learning (DRL) with the Iterative Model Combining Algorithm (IMCA) to overcome the critical limitations of static ensemble methods in global portfolio optim...

The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological sy...

For scenarios where the type of structural break in a time series is unknown, this paper proposes a modified ratio-type test statistic to enable effective online monitoring of structural breaks, while circumventing the estimation of long-term varianc...

It is vital to study the stability of power systems under small perturbations to prevent blackouts. This study presents a load-shedding strategy that has been incorporated within the swing equation to reduce instability and delay the onset of chaotic...

Traffic and transportation engineering involves the application of scientific principles to the planning, design, and operation of facilities for any mode of transportation and to human resource management in industry, which are required to enable th...

As the primary public source of satellite trajectory data, the Two-Line Element (TLE) dataset offers fundamental orbital parameters for space missions. However, for satellites with poor data quality, traditional neural network models often underperfo...