Mathematics, Volume 13, Issue 17

In the present work, we consider three branching random walk $S_n\mathsf{Z}\left(\mathsf{t}\right),$$\mathsf{Z}\in \{\mathsf{X},\mathsf{Y},\Phi \}$ on a supercritical random Galton–Watson tree $\partial \mathsf{T}$. We compute the Hausdorff and packing dimensions of the level set ${\mathrm{E}}_{\chi }(\alpha ,\beta )=\left\{\mathsf{t}\in \partial \mathsf{T}:\right\}$...

Convolutional Neural Networks (CNNs) are a highly used machine learning architecture in various fields. Typical descriptions of CNNs are based on low-dimension and tensor representations in the feature extraction part. In this article, we extend the...

Two hybrid, entropy-guided node metrics are proposed for the k-hop environment: Entropy-Weighted Redundancy (EWR) and Normalized Entropy Density (NED). The central idea is to couple local Shannon entropy with neighborhood density/redundancy so that s...

Recent research and instances have demonstrated that most real-world systems can be effectively schematized by multiplex networks. Moreover, the interactions within systems often emerge among triadic or tetradic interactions, or even interactions wit...

The pressing global transition to sustainable energy has intensified interest in overcoming the efficiency bottlenecks of conventional solar technologies. Hybrid photovoltaic–thermoelectric generator (PV–TEG) systems have recently emerged...

Accurate identification of weed species is a fundamental task for promoting efficient farmland management. Existing recognition approaches are typically based on either conventional Convolutional Neural Networks (CNNs) or the more recent Vision Trans...

Mathematical modeling is indispensable in oncology for unraveling the interplay between tumor growth, vascular remodeling, and therapeutic resistance. We present a hybrid modeling framework (continuum-discrete) and present its hybrid mathematical for...

This work presents an extragradient-type iterative process combined with the viscosity method to find a common solution to a split generalized variational-like inequality, a variational inequality, and a fixed point problem associated with a family o...

The first Zagreb index of a graph G is defined as the sum of the squares of the degrees of all the vertices in G. The Laplacian spectral radius of a graph G is defined as the largest eigenvalue of the Laplacian matrix of the graph G. In this paper, w...

Training a machine learning (ML) model always needs many computing resources, and cloud-based outsourced training is a good solution to address the issue of a computing resources shortage. However, the cloud may be untrustworthy, and it may pose a pr...

Graph Neural Networks (GNNs) face significant challenges in node classification across diverse graph structures. Traditional message passing mechanisms often fail to adaptively weight node relationships, thereby limiting performance in both homophili...

Bayesian Optimization (BO) provides an efficient framework for optimizing expensive black-box functions by employing a surrogate model (typically a Gaussian Process) to approximate the objective function and an acquisition function to guide the searc...

The term with ${\mathsf{\Gamma }}_{\nu \mu }^{\mu }$ was omitted in the version of Ref [...]

Few-shot instance segmentation (FSIS) is devised to address the intricate challenge of instance segmentation when labeled data for novel classes is scant. Nevertheless, existing methodologies encounter notable constraints in the agile expansion of no...

This study provides new equivalent descriptions of the Bounded Lower Oscillation ($\mathrm{BLO}$) space through Luxemburg-type $L^{\phi }$ integrability conditions, where $\phi$ is a nonnegative function with either convexity or concavity. The framework accommodates...

This paper develops a unified analytical framework for implicit fractional differential equations subject to anti-periodic boundary conditions. The study considers two main cases: fractional derivatives of order $\alpha \in (0,1)$ and $\alpha \in (1$...

Artificial protozoa optimizer (APO), as a newly proposed meta-heuristic algorithm, is inspired by the foraging, dormancy, and reproduction behaviors of protozoa in nature. Compared with traditional optimization algorithms, APO demonstrates strong com...

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to $1+\mathrm{s}\mathrm{i}\mathrm{n}z$. Coefficient bounds are obtained for the initial Taylor–Maclaurin coeffici...

Mixed-smoothness splines facilitate localized control over smoothness; however, the issue of dimensional instability in mixed-smoothness spline spaces remains unstudied in the existing literature. This paper studies such instabilities over T-meshes,...

This paper investigates the nonlinear dynamics of the wheel-side planetary reducer, considering the tooth wear effect. The tooth wear model based on the Archard adhesion wear theory is established, and the impact of tooth wear on meshing stiffness an...

Penalized regression estimators have become widely adopted alternatives to ordinary least squares while analyzing collinear data, despite introducing some bias. However, existing penalized methods lack universal superiority across diverse data condit...

In this paper, we address the problem of increasing the number of regenerations in the simulation of the workload process in a single-server queueing system. To this end, we extend the splitting technique developed for the Markov workload process in...

The influence of polar ice-covered environments on the corrosion-related static electric field (CRSE) of underwater vehicles is critical for understanding and applying the characteristics of underwater electric fields in polar regions. This study uti...

To address the challenges of unbalanced demand and high operational costs in highway port logistics, this study investigates the scheduling of tractors and semitrailers under time window constraints in a networked environment, where geographically di...

This paper explores some frame bundles and physical implications of Killing vector fields on the two-sphere ${\mathbb{S}}^2$, culminating in a novel application to Maxwell’s equations in free space. Initially, we investigate the Killing vector fields on ${\mathbb{S}}^2$ (...

This paper develops a belief-based dynamic optimisation framework to explain career continuation decisions in settings characterised by monopsonistic employment and asymmetric performance evaluation. Extending Holmström’s career concerns m...

As vision and mission statements embody the directions set forth by an organization, their connection to the Sustainable Development Goals (SDGs) must be made explicit to guide overall decision-making in taking strides toward the sustainability agend...

In this article, we conduct a statistical analysis of the autocorrelation functions (ACF) of multi-scale logarithmic returns computed over maximal monotonic uninterrupted trends (runs) in financial indices’ daily data. We analyze the Dow Jones...

The problem of the integral representation over a bounded surface of a regular field satisfying the Helmholtz equation in all space is investigated. This problem is equivalent to local splitting into an incoming field and an outgoing field. This spli...

We study the line graphs of bipartite multigraphs, which naturally arise in combinatorics, game theory, and applications such as scheduling and motion planning. We introduce a new characterization of these graphs via valid partial assignments of the...

This paper presents new integral inequalities for differentiable generalized convex functions in the second sense, with a focus on improving the accuracy of Weddle’s formula for numerical integration. The study is motivated by the following thr...

This study investigates the dynamic behavior of a discrete epidemic model as affected by media coverage through integrated analytical and numerical methods. The main objective is to quantitatively assess the impact of media coverage on disease outbre...

Atrial fibrillation (AF) is a common arrhythmia associated with major adverse cardiovascular events. Early detection and short-horizon risk prediction are therefore clinically critical. Prior attention-based electrocardiogram (ECG) models typically t...

We consider cooperative non-orthogonal multiple access (CNOMA) transmission through a full-duplex (FD) amplify-and-forward (AF) relay. Two CNOMA users are served by an access point (AP) through the FD-AF relay. FD relaying can be spectrally efficient...

This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity and no manua...

Pansharpening is a method of image fusion that combines a panchromatic (PAN) image with high spatial resolution and multispectral (MS) images which possess different spectral characteristics and are frequently obtained from satellite sensors. Despite...

Necrotizing fasciitis (NF) is a rare but aggressive soft tissue infection with high rates of mortality and amputation, making early identification of key prognostic biomarkers essential for clinical management. However, the rarity and heterogeneity o...

As the demand for air transportation continues to grow, airspace congestion, flight delays, operational costs, and safety have become important and challenging issues. There are various optimization problems in air transportation, which involve large...

The acceptance of generalized distributions has significantly improved over the past two decades. In this paper, we introduce a new generalized distribution: Topp–Leone odd Weibull flexible-G family of distributions (FoD). The new FoD is a comb...

The security of video data requires cryptographic techniques that are resilient to both classical and quantum threats. This study presents an encryption framework based on association schemes and algebraic combinatorial tools that enable systematic a...

Tunnel portal rocks in southern China, which are exposed to intense solar radiation and temperature fluctuations, are susceptible to thermal stress, which directly or indirectly affects the safety, stability, and normal use of a tunnel and its periph...

As supply chains rapidly digitize, platform-driven models have become central to global commerce, requiring sophisticated mathematical modeling for optimization. This systematic review comprehensively analyzes research across six critical technologic...

A review of the development of grid technologies and corresponding numerical approaches based on the lattice Boltzmann method (LBM) is performed in the present study. The history of the algorithmic development and practical applications is presented...

This paper presents a novel non-uniform, non-stationary Loop subdivision that directly interpolates arbitrary initial triangular meshes. This subdivision is derived by assigning distinct parameters for “vertex-point” and “edge-point...

This paper explores a class of analytic functions defined in the open unit disk by means of a symmetric q-differential operator. In the first part, we derive sufficient conditions for functions to belong to a subclass associated with this operator, u...

Broken or loose strands in high-voltage transmission conductors constitute critical defects that jeopardize grid reliability. Unmanned aerial vehicle (UAV) inspection has become indispensable for their timely discovery; however, conventional detector...

A qubit is an exhibition of quantum entanglement and a key element in the quantum teleportation process. In this paper, we review the role of qubits in quantum entanglement and quantum teleportation.

This paper presents the design of a permanent-magnet-assisted synchronous reluctance motor (PMa-SynRM) for compressor applications using Sm-series injection-molded magnets that eliminate heavy rare-earth elements. The high shape flexibility of the in...

Accurate prediction of a robot’s dynamic parameters, including mass and moment of inertia, is essential for adequate motion planning and control in autonomous systems. Traditional methods often depend on manual computation or physics-based mode...

A new macroscopic traffic model is proposed based on visibility distance and the time to collision (TTC) in foggy conditions. The TTC is obtained from real traffic data. It is shown that the proposed model is hyperbolic and has a well-posed solution....