Boletim da Sociedade Paranaense de Matemática

Advanced Results on Independent and Hinge Domination Numbers of Some Graphs Formed by Performing Certain Graph Operations

2026-04-18T14:30:19+00:00

Variational Physics-Informed Neural Networks for the $p(x)$-Laplacian Problem

2026-04-18T14:37:00+00:00

In this paper, we study a variational physics-informed neural network (VPINN) for solving the p(x)-Laplacian equation with Dirichlet boundary conditions. The proposed method builds a neural network that automatically satis es the boundary values and minimizes the energy of the problem. The loss function is computed using Monte Carlo sampling, and derivatives are obtained with automatic di erentiation. To train the network, we use two steps: rst the Adam optimizer, then the L-BFGS method for faster convergence. We test the approach on several examples in one and two dimensions, where the exponent $p(x)$ changes smoothly or has jumps. The results show that the VPINN gives accurate and stable solutions, even when the coe cients vary strongly in space.

The Wrapped New XLindley Distribution under Right Censoring: Theory, Estimation, and Applications

2026-04-18T14:41:21+00:00

This paper develops a unified likelihood-based framework for modeling right-censored circular
data using the Wrapped New XLindley Distribution (WNXLD), extending Lindley-type life-
time models to periodic domains where directional measurements are incompletely observed.
Starting from the linear New XLindley distribution, we construct its wrapped counterpart,
derive closed-form expressions for the density, survival, and censored likelihood functions,
and obtain score equations for maximum likelihood estimation. Asymptotic properties of the
estimator are discussed under standard regularity conditions, and stable numerical optimiza-
tion strategies are proposed for practical implementation. Extensive Monte Carlo simulations
evaluate bias, efficiency, robustness to censoring, and truncation effects in the infinite-series
representation. Applications to wind direction and animal movement data demonstrate that
the WNXLD provides superior fit compared with commonly used wrapped distributions,
particularly when circular data exhibit asymmetry or multimodality. The proposed model
therefore offers a flexible and computationally tractable tool for circular survival analysis in
environmental, biological, and reliability studies.

Analysis and Control of Hepatitis B Virus Spread with Harmonic Mean Incidence and Vertical Transmission: A Compartmental Modeling Approach

2026-04-18T14:45:40+00:00

Hepatitis B (HBV) is a potentially fatal liver infection that remains a primary widespread disease around the globe, despite the availability of vaccinations, owing to ongoing obstacles such as vertical transmission and delayed treatment. In the present study, a compartmental mathematical model that accounts for the effects of vertical transmission and harmonic mean type incidence is put forward for the analysis of the transmission dynamics of HBV. The model’s threshold behavior is investigated through the basic reproduction number
R0, and the qualitative dynamics around the disease-free and endemic equilibria are examined to establish conditions for their asymptotic local and global stability. To identify key epidemiological drivers, the global sensitivity analysis of the system is performed through the incorporation of Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) methodologies. We formulate the optimal controlproblem using Pontryagin’s maximum principle. Effective strategies for diminishing the prevalence of HBV are emphasized through numerical simulations. Numerical simulations demonstrated that optimized control measures play a significant role in reducing the number of infected individuals and increasing the recovered population. In addition, we have characterized three distinct strategies for reducing infection and observed that each has limitations in eliminating infections. However, the simultaneous administration of treatment and vaccination is useful and effective for the reduction of HBV infection.

Gold Nanoparticles' Effect on MHD Blood Flow via a Stenosed Artery

2026-04-18T14:49:34+00:00

This work employs a rheological model for a theoretical investigation of stress on the walls of the artery and how the enhanced MHD flow of blood circulation through an oblique artery is affected by flow impedance resistance in gold nanoparticles. Blood is designed as a viscous fluid containing a mixture of gold nanoparticles to enhance its thermal and flow characteristics. Analytical solutions are made possible by simplification under low Reynolds number and mild stenosis circumstances. The temperature, velocity profiles, wall shear stress (WSS), and stream resistivity (FR) can all be determined using the current analytical method. In the discussion section, the results are displayed graphically. The analysis indicates that gold nanoparticles significantly reduce resistance and alter wall shear profiles, while an increasing magnetic field tends to elevate flow resistance. These findings can assist in optimizing the use of nanofluids in biomedical applications involving stenosed arteries and catheter-based therapies.

Unified Isomorphism Theory for r-Neutrosophic G- Submodules

2026-04-18T15:01:29+00:00

Neutrosophy is a logical framework that treats uncertainty, truth and falsity as distinct concepts hence better representing ambiguous information. In this paper, we analyze r-neutrosophic G-submodules, where r in [0,1], that bring about the application of known neutrosophic ideas in a more constrained algebraic context. The concept of r-neutrosophic quotient submodules is introduced as an extension of this and some characteristics are recognized and explained. The paper then focuses on the isomorphism properties of r-neutrosophic G-submodules by analysing and proving a version of the isomorphism theorems modified to this limited setting. The results show that the fundamental characteristics of the general neutrosophic G-submodule isomorphism is preserved in this constrained form. This illustrates that r-neutrosophic G-submodules maintain the essential algebraic structure of the extensive framework.

MHD NATURAL CONVECTION IN VERTICAL ANNULUS] {MHD NATURAL CONVECTION WITH RADIAL HEAT AND MASS TRANSFER UNDER HEAT AND MASS ABSORPTION IN A VERTICAL ANNULUS

2026-04-18T15:08:01+00:00

This study presents an analytical investigation of the combined effects of an applied radial magnetic field, an induced magnetic field, and inverse-square heat and mass absorption on fully developed natural convection flow of laminar, viscous incompressible electrically conducting fluid. The governing equations are formulated non-dimensionally and solved analytically under steady-state conditions. Key dimensionless parameters, such as the Hartmann number (Ha), heat absorption parameter (S), chemical reaction parameter ($K^*$) and annular gap ratio ($\lambda$), are systematically varied to examine their effects on velocity, temperature, concentration, magnetic field, and induced current density distributions. The results indicate that increasing Hartmann number suppresses velocity due to Lorentz force effects while enhancing the magnetic field intensity. The annular gap $\lambda$ significantly influences flow dynamics, enhancing heat and mass transfer. Higher heat absorption decreases velocity and temperature, confirming its role in energy extraction, while an increase in ($K^*$) depletes concentration as a result of accelerated species diffusion. Furthermore, isothermal boundary conditions exhibit higher distributions profiles compared to iso-flux conditions, demonstrating improved convective transport. The numerical results indicate that increasing Ha generally decreases skin friction, attributed to the Lorentz force. Under isothermal conditions, higher Ha leads to a decline in $\tau_\lambda$ and Q, while for the iso-flux case, $J_\theta$ shows irregular variations, including negative values suggesting a current reversal. Increasing the annular gap ($\lambda$) raises skin friction. Nusselt number (Nu), decreases with increasing $\lambda$, but increases with higher S, indicating that heat absorption promotes efficient convective transport. Isothermal conditions show more effective heat transfer than iso-flux conditions. The ratio of the mass transfer coefficient (Sh) goes down as $\lambda$ goes up and goes up as ($K^*$) goes up. The iso-flux condition consistently produces lower Sherwood numbers, which means that mass transfer is less effective. These findings offer essential insights for enhancing MHD-driven thermal and mass transport systems, applicable in electromagnetic propulsion, nuclear reactor cooling, and advanced energy conversion technologies.

Squeeze film couplestress lubrication rendered with a porous layer in a sphere-to-sphere configuration - An analytical study.

2026-04-18T15:15:58+00:00

The paper aims to study the role of non- Newtonian couple stresses fluid and porous media on the squeeze film characteristics by considering a sphere-to-sphere geometry. The modified Reynolds equation for the geometry is derived, incorporating the non-Newtonian effects of couple stress fluids and porosity. Closed-form expressions for essential squeeze film characteristics are obtained, including pressure distribution, load-carrying capacity, and squeeze film time. It is observed that as the couple stress parameter value increases, the pressure, load-carrying capacity, and squeeze time also increase. Furthermore, the squeeze film pressure, load, and squeezing time increase with an increase in the radius ratio. Conversely, the introduction of porosity results in lower pressure, load, and squeezing time. These results provide significant insights into the efficacy of bearing lubrication when it is used in porous environments with couple stress fluids.

Magnetohydrodynamic natural convection of water-based SWCNT and MWCNT hybrid nanofluid inside a C-shaped cavity by varying aspect ratios

2026-04-18T15:20:01+00:00

This research article numerically investigates the natural convection and heat transfer analysis of water-based hybrid nanofluid composed of single-walled and multi-walled carbon nanotubes inside a C-shaped cavity under the magnetic field effect. The left vertical wall of the cavity is maintained at a uniform temperature T_h, whereas a specified portion of the right wall is kept at a constant temperature T_c. The remaining sections of the cavity boundaries are assumed to be thermally insulated. The study analyses the impact of parameters such as Rayleigh number (Ra = 10⁴ − 10⁷), the Hartmann number (Ha = 0 − 100), the volume fraction (ϕ_np = 1% - 4%) of the nanoparticles on the heat transfer and fluid fow within the enclosure. Additionally, the influence of aspect ratio variations (AR = 0.25 − 0.75) on heat transfer and fluid fow is analysed. The Galarkin's finite element method is used to solve the governing equations and the numerical solution is represented by plotting streamlines and isotherms. The results show that increasing the Rayleigh number strengthens convective motion, while higher Hartmann numbers suppress convection, causing heat transfer to be dominated by conduction. It is also notable that increasing the aspect ratio reduces the fluid flow rate due to limited space for rotation within the cavity, while smaller aspect ratios enhance thermal performance by promoting stronger fluid circulation.

The Optimizing Innovation and Global Competitiveness: How linguistic Uniformity drives economic performance, The Chakrabartty-Srivastava function approach

2026-04-18T15:24:59+00:00

This paper examines how language acts as a catalyst for economic growth and global competitiveness in advanced economies such as Russia, Japan, Germany, and South Korea. Strong command over national languages, combined with foreign language proficiency, enables effective participation in cross-border trade, technology transfer, and international collaboration. These linguistic capabilities have supported the global success of firms like Mercedes-Benz, BMW, Toyota, Samsung, and Hyundai across key sectors. The study introduces the Chakrabartty–Srivastava Function, a framework linking linguistic diversity with GDP growth by positioning language as a key economic variable. It argues that mother-tongue-based language policies strengthen human capital, improve educational access, and promote long-term socio-economic development. By treating language as a core driver of development rather than a secondary cultural factor, the paper highlights multilingualism as a source of sustained national productivity and economic resilience.

Multi- Objective Green Vehicle Routing Problem with Uncertain Customer Demand and Carbon Emission Reduction

2026-04-18T15:35:52+00:00

Vehicle Routing Problem with Time Windows is a combinatorial optimization problem that deals with the fleet of vehicles to find the optimal set of routes while serving the customers at different nodes in a given geographical region within specific time intervals. In this research article, the objective is to minimize the total operational costs, emissions and fulfilling the fuzzy customer demand. To calculate the optimal results, a mathematical model consisting of all the restricted constraints is presented and genetic algorithm and particle swarm optimization algorithm is preferred to find the solutions. Moreover, alpha- cut method is applied to calculate the crisp interval for the fuzzy demands. To conclude the experimental results, Solomon dataset (R101) is used to compare the outcomes of genetic algorithm and particle swarm optimization algorithm and it is observed that both genetic algorithm and particle swarm optimization algorithm provides satisfactory results but genetic algorithm provides more optimal outcomes as compared to particle swarm optimization algorithm.

$\mathbb{P_{CIF}}$-$Z$-Open Sets in Cubic Intuitionistic Fuzzy Topology with Application to IoT-Enabled Smart Greenhouse Monitoring

2026-04-18T15:42:03+00:00

This paper introduces and investigates the concept of $Z$-open sets in cubic intuitionistic fuzzy topological spaces under $\mathbb{P_{CIF}}$-order. We establish fundamental properties of $\mathbb{P_{CIF}}$-$Z$-open sets and their relationships with other generalized open sets including $\delta$-open, preopen, and $\delta$-semiopen sets. Several characterizations of $\mathbb{P_{CIF}}$-$Z$-open sets are provided through interior and closure operators. We prove that the family of $\mathbb{P_{CIF}}$-$Z$-open sets forms a topology and investigate properties of $\mathbb{P_{CIF}}$-$Z$-interior and $\mathbb{P_{CIF}}$-$Z$-closure operators. The results demonstrate that $\mathbb{P_{CIF}}$-$Z$-open sets provide a unifying framework that generalizes several existing notions of openness in cubic intuitionistic fuzzy topological spaces, with significant implications for modeling hierarchical uncertainty in decision-making systems.

A Binary Tree Interpretation of Shared Key Generation Using Modular Ananta-Graph Paths

2026-04-18T15:47:05+00:00

This paper presents a formally grounded symmetric key agreement scheme based on modular traversal of Ananta-Graphs, reinterpreted 
and visualised through a binary tree model. The underlying encryption protocol is driven by the iterative dynamics of the 
Collatz-like transformation $f(n) = (3n + 1) \bmod m$, applied iteratively over a modular graph structure commencing from a shared 
public base node. Two communicating parties, Alice and Bob, independently traverse the graph using privately selected iteration 
counts, arriving at an identical shared secret without disclosing their private parameters. We introduce the Ananta-Graph Traversal 
Inversion Problem (ATIP) and the Ananta-Graph Traversal Distinguishing Problem (ATDP), and formally argue their hardness by reduction 
from the Discrete Logarithm Problem (DLP) in a cyclic group setting, as well as through the non-linearity and many-to-one nature of 
the modular transformation. The shared traversal endpoint is processed through a hash-based Key Derivation Function (KDF) to obtain 
a cryptographically strong session key, decoupling key agreement from key usage and eliminating structural bias. A binary tree abstraction 
provides intuitive visualisation of the convergence properties of the scheme. Experimental results demonstrate that prime moduli produce 
substantially longer traversal cycles and superior key dispersion, confirming the practical viability of the proposed framework as a 
lightweight symmetric key agreement primitive.