Edge-betweenness centrality measure is an important centrality measure that focuses on the role of edges in a graph. The total edge-betweenness centrality measure (EBCM) of a graph is defined as the sum of the edge-betweenness centrality measures of all its edges. In this work, we derive an explicit expression for the total EBCM of the shadow graph of a graph G in terms of the total EBCM of G. Moreover, we establish an interesting result showing that the total EBCM of a graph is equal to its Wiener index. Furthermore, for certain families of graphs of order n, we identify the graphs that attain the minimum and maximum values of the total EBCM. The results provide deeper insights into network connectivity and structural efficiency, offering mathematical tools that can support the development of more resilient, efficient, and sustainable real-world systems.
Patulin (PAT) is a mycotoxin of regulatory concern in apple-based foods. We evaluated label-free gold screen-printed electrodes (Au/SPEs) against carbon and platinum SPEs for PAT electro-reduction in Britton–Robinson buffer. Au/SPE produced a reproducible cathodic response and was selected for subsequent analytical evaluation. Scan-rate studies demonstrated strongly non-ideal behavior, while the pH study showed a pH-dependent irreversible response. These results did not permit assignment of a specific proton–electron stoichiometry or a diffusion-, adsorption-, or mixed-control mechanism. Under pH 4.0, cyclic-voltammetric (CV) calibration was linear from 1–10 ppb with experimentally determined LOD of 0.42 ppb. The approach showed good repeatability and reproducibility, minimal interference from common sugars/acids/ions, and accurate spike recoveries in commercial apple juice and purée without elaborate pretreatment. The concentration-dependent response demonstrates the feasibility of measurement under the investigated conditions; however, the broad cathodic feature and its partial overlap with the background limit the analytical resolution of direct CV. Accordingly, this configuration is presented as a proof-of-concept evaluation rather than a validated field method.
This study presents a numerical investigation of steady two-dimensional magnetohydrodynamic (MHD) boundary-layer flow and radiative heat transfer of an incompressible Casson fluid over an exponentially stretching sheet with velocity slip, thermal slip, and wall suction/blowing. Thermal radiation is incorporated using the Rosseland diffusion approximation, and similarity transformations reduce the governing nonlinear partial differential equations to a coupled system of ordinary differential equations. The resulting boundary-value problem is solved using the Hermite Wavelet Method (HWM) after transforming the computational domain to a finite interval. The accuracy and convergence of the method are verified through convergence analysis and comparison with benchmark results. The effects of the Casson, magnetic, thermal radiation, Prandtl, velocity slip, thermal slip, and suction/blowing parameters on the velocity and temperature fields are examined. Increasing the Casson, magnetic, velocity slip, and suction parameters suppresses the velocity, whereas thermal radiation enhances the temperature distribution. Higher Prandtl numbers and stronger suction reduce the thermal boundary-layer thickness and improve heat transfer. An increase in the Casson parameter also enhances wall shear stress and slightly increases the local Nusselt number. The HWM demonstrates good accuracy, stability, and computational efficiency for nonlinear boundary-value problems, with potential applications in polymer extrusion, coating, fiber drawing, metallurgical processing, and thermal management.
In this manuscript, we introduce the concept of fuzzy R-contraction and establish the existence of fixed points for fuzzy mappings satisfying the fuzzy R-contraction condition. The results of this study will help researchers develop new methods for investigating fixed point theorems for fuzzy R-contractions in fuzzy set theory. These findings have significant implications for both theoretical research and practical applications in decision-making, fuzzy logic, and fixed point theory.
Rapid growth in municipal solid waste (MSW) generation, limited land availability, and exclusive dependence on the Askar landfill have placed Bahrain’s waste sector under increasing environmental and climate pressure. This study develops an integrated assessment of MSW quantities, landfill methane emissions, and waste-to-energy (WtE) potential using official national datasets, the IPCC 1996 and 2006 First-Order Decay (FOD) methodologies, and US EPA LandGEM modelling with calibrated arid-climate parameters (k = 0.0123 yr⁻¹; L₀ = 90.6 m³ CH₄ Mg⁻¹). Results reveal large methodological divergence: for 2016, estimated emissions range from 3,737 Gg CO₂-eq (IPCC 1996) to 660 Gg CO₂-eq (IPCC, 2006) and ≈280–313 Gg CO₂-eq (LandGEM), demonstrating strong sensitivity to parameterization. LandGEM projections indicate peak emissions of approximately 14,844 Mg CH4 yr−1 in 2020, equivalent to ≈ 371 Gg CO₂-eq. Capturing 75% of landfill gas would reduce emissions by ≈ 75% and generate ≈ 52–57 GWh yr⁻¹, yielding approximately 162 million USD in combined electricity and carbon revenues through 2035. Anaerobic digestion of segregated organics and sewage sludge could further produce ≈ 400–450 GWh yr−1, offering the largest system-level mitigation benefit. Findings indicate that Bahrain’s total waste sector contributed approximately 10%–12% of national GHG emissions in earlier inventories, whereas corrected estimates for solid waste disposal alone indicate a lower landfill-specific contribution of approximately 6.2%. This distinction highlights the importance of clear sectoral bookkeeping when interpreting MSW-related methane emissions.
The sustainable management of dye-contaminated water requires treatment materials that are not only effective but also low-cost, reusable, locally available, and environmental friendly. In this study, agricultural waste biomass derived from Pterospermum acerifolium leaves (PAL) was converted into a bio-based adsorbent for the removal of bromophenol blue from aqueous systems. The work emphasizes the valorization of discarded leaf biomass into a beneficial material, offering a circular and resource-efficient approach for wastewater treatment. The PAL adsorbent was characterized using FT-IR, EDX, SEM, pore-size distribution, and point of zero charge measurements, showing an average pore diameter of 13 nm and a PZC value of 5.40. Batch adsorption studies showed that BPB uptake was influenced by contact time, adsorbent dosage, pH, temperature, particle size, and initial dye concentration, with optimized conditions of pH 4, 1 g PAL dosage, 180 min contact time, 25 °C temperature, and 90–125 μm particle size. The Langmuir isotherm model separately described the equilibrium adsorption behavior, with R2 = 0.9907 and a maximum adsorption capacity of 30.486 mg/g. The pseudo-second-order kinetic model separately described the adsorption kinetics, with R2 = 0. 9958. Thermodynamic analysis confirmed that BPB adsorption onto PAL was spontaneous and exothermic, with reduced randomness at the solid solution interface. Importantly, PAL maintained reusable adsorption capability over five consecutive adsorptions desorption cycles demonstrating its practical relevance beyond synthetic dye solutions. Overall, this study highlights untreated PAL biomass as a sustainable, accessible, and reusable adsorbent for dye-bearing wastewater treatment contributing to agricultural waste valorization and circular environmental management.
One of the main factors challenging the deployment of solar energy technologies in desert-like climates is dust. Most previous studies of soiling have focused on how total PV power output declines with time as dust accumulates. This study takes a different approach by examining how dust affects different cell technologies through the combined analysis of the optical transmittance of the accumulated dust and the spectral response of each cell. Dust was collected on clean glass slides over nine weeks during the summer season (end of June, July, and August) in Bahrain. Four solar cell technologies were considered: two crystalline silicon (c-Si), amorphous silicon (a-Si), copper indium selenide (CIS), and cadmium telluride (CdTe). The short-circuit current (Isc) and open-circuit voltage (Voc) of each cell were calculated for every week using a mathematical model that combines the measured dust optical transmittance with each cell’s spectral response. The results show that dust reduced light transmission to about 50% of the clean-glass value within the first week and to more than 90% by the final week. Among the technologies investigated, crystalline silicon showed the greatest resilience to soiling, while CIS and CdTe experienced a substantial reduction in short circuit current as early as the third week.
This paper develops a novel hybrid numerical method for the [Formula: see text]-uniform approximation of singularly perturbed second-order delay differential equations subject to delay-dependent nonlocal boundary condition. The proposed scheme is constructed by integrating an exponential fitting technique with Gauss-Lobatto quadrature and the composite trapezoidal rule. To accurately resolve the layer behaviour, a hybrid mesh is employed, combining a piecewise-uniform Shishkin mesh with Gauss-Lobatto points. Error estimates for the approximate solution are established on the proposed mesh, and a test problem is presented to validate the effectiveness of the numerical scheme.
This study investigates the steady, laminar, two-dimensional magnetohydrodynamic boundary-layer flow of a chemically reactive Maxwell fluid over a stretching sheet, accounting for Joule heating, viscous dissipation, and Soret diffusion. The flow is assumed incompressible, and the induced magnetic field is neglected. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using similarity transformations and solved numerically using the Taylor wavelet method (TWM). The method’s convergence, accuracy, and stability are verified through matrix order studies and comparisons with previously published results. The effects of key physical parameters, including the magnetic parameter, Maxwell fluid relaxation parameter, Prandtl and Schmidt numbers, Eckert number, Soret number, and chemical reaction parameter, on the velocity, temperature, and concentration profiles, as well as on engineering quantities such as skin-friction, Nusselt, and Sherwood numbers, are systematically analyzed. Results indicate that both magnetic and viscoelastic effects retard fluid motion, while Joule heating and viscous dissipation enhance temperature. Thermal and solutal transport are significantly influenced by the Prandtl, Schmidt, and Soret numbers, with chemical reactions reducing the solute concentration near the surface. The study demonstrates the robustness, computational efficiency, and high accuracy of TWM for solving complex boundary-layer problems in non-Newtonian MHD flows.
The concept of the energy of a graph was introduced by Gutman in 1978, inspired by the Hückel molecular orbital theory, which approximates the total [Formula: see text]-electron energy of a conjugated hydrocarbon molecule using the energy of its molecular graph. Let G be a graph on n vertices with m edges. In this paper, we first present two lower bounds for the energy of a graph. The first bound is based on the order n, the maximum degree [Formula: see text] and the determinant of the adjacency matrix [Formula: see text] The second bound relies on n, the minimum degree [Formula: see text] the independence number [Formula: see text] and [Formula: see text] We also determine extremal graphs for our lower bounds. In addition, we obtain an upper bound for the graph energy in terms of size m, the maximum degree [Formula: see text] and [Formula: see text] Next, we prove that for the general extended adjacency matrix [Formula: see text] with [Formula: see text] being the diagonal entries of [Formula: see text] the expression [Formula: see text] holds if and only if [Formula: see text] where [Formula: see text] Oboudi previously established that [Formula: see text] and proposed the problem of characterizing graphs with the spectrum [Formula: see text] for some non-negative integers [Formula: see text] with [Formula: see text] and [Formula: see text] Here, we provide a generalization of Oboudi’s lower bound for the energy of graphs, and then characterize graphs with the above spectrum when [Formula: see text] We show that [Formula: see text] for all graphs having no eigenvalues in the interval (−1,1), where [Formula: see text] is the largest integer such that the star graph [Formula: see text] is an induced subgraph of G. We also prove that if the general extended matrix [Formula: see text] with [Formula: see text] for vertices [Formula: see text] has exactly one positive eigenvalue, then one of the components of G is a complete multipartite graph, while all other components, if any, are isolated vertices.
The current work focuses on the computational analysis of heat transfer behaviour in sodium alginate-based zirconium oxide nanofluid flowing through a channel formed by parallel squeezing disks under the influence of an external magnetic field. Due to its broad engineering applications, notably in biomedical devices and drug delivery systems, the nanofluid flow through the channel consisting of a moving impermeable top disk and a stationary porous bottom disk through which suction/injection occurs is considered in the study. The fundamental equations governing the momentum and energy are systematically transformed into non-linear ordinary differential equations (ODEs) by employing similarity transformations. Additionally, by applying the power series method, specifically the Homotopy Perturbation Method (HPM), an approximate analytical solution is attained to the problem. This theoretical study mainly emphasizes analyzing the impact of pertinent physical parameters on the velocity and temporal distribution, coefficient of skin friction, and Nusselt number. It is noticed from the results that the temperature distribution elevates with an increment in the Prandtl number in the case of suction as the disks approach each other. It is also noted that the Nusselt number’s magnitude upsurges as the volume of the nanoparticle increases. Furthermore, the tabulated numerical values are compared with those obtained by employing [Formula: see text] order Runge–Kutta method (RK-4), and the results are found to be in harmony with one another.
Dengue fever continues to be a significant global health challenge, influenced by the complex interplay of environmental and human behavioral factors. In this study, we propose a SEIR–SEI mathematical model that integrates human behavioral characteristics and the ecological carrying capacity of mosquitoes. Unlike previous studies, we link carrying capacity to the disease dynamics, where effective interventions in managing waste reduce the availability of breeding sites, directly influencing vector proliferation. The basic reproduction number [Formula: see text] is calculated using the next-generation matrix method, and we discuss the stability analysis incorporating both local and global aspects, conducted using Lyapunov functions and the Hurwitz criterion. The models show that a decrease in carrying capacity simultaneously reduces the vector populations and dramatically changes the disease pattern, driving the system toward stability. Increasing public knowledge about diseases alters people’s behaviors that reduce disease transmission. By combining ecological, mathematical, and public health viewpoints, we show how environmental control should go hand in hand with other strategies for better disease control. This integrated approach helps in sustainable policy development and ensures applicability across related areas.
Integral equations with memory effects and infinite delay arise naturally in applications such as ecology, neuroscience, and viscoelasticity, among others. In this work, we study three classes of equations in the space of functions of locally bounded [Formula: see text]-variation, which accommodates functions with mild singularities whose oscillatory behaviour is controlled in a weaker sense than that provided by classical bounded variation. We analyze a nonlinear Volterra integral equation, a generalization of the Volterra-Hammerstein type equation, and an equation with infinite delay associated with the dynamics of an isolated species. For the first two equations, we establish conditions ensuring existence, uniqueness, and prolongation of solutions, while for the infinite-delay model we additionally derive explicit bounds for the solutions.
This paper proposes a nonlinear mathematical model that describes the dynamics of a 3-species food chain consisting of a prey, an intermediate predator, and a top predator, while explicitly incorporating the effects of refuge and harvesting. Initially, the model’s fundamental qualitative properties, such as positivity, boundedness, and the existence and uniqueness of solutions, are examined. The existence of biologically feasible equilibrium points is derived, and their local stability is investigated using linearization and the Routh–Hurwitz stability criterion. Analytical conditions are obtained to ensure the stability of each equilibrium point. Furthermore, the global stability of the interior equilibrium point is examined by constructing an appropriate Lyapunov function. Numerical simulations are conducted to validate the analytical findings and to demonstrate the impact of key parameters on the system dynamics. Both analytical and numerical results indicate that, under suitable parameter conditions, the prey, intermediate predator, and top predator can coexist in a stable manner. The study highlights the significant role of refuge and harvesting mechanisms in maintaining long-term persistence of all species in the food chain.
This study conducts a numerical analysis of steady, three-dimensional laminar flow and related heat transfer of an incompressible viscous fluid over a stretching surface embedded in a homogeneous porous medium, considering local thermal non-equilibrium (LTNE) conditions. Unlike traditional local thermal equilibrium (LTE) assumptions, the LTNE framework independently models the temperature distributions of the fluid and solid phases, facilitating a more precise depiction of inter-phase heat transfer. The governing partial differential equations, generated using an extended Darcy-Brinkman-Forchheimer technique, are transformed into a set of non-linear ordinary differential equations (ODEs) by similarity transformations. The Keller-box method, recognized for its stability and efficacy in boundary layer flow problems, is employed to solve these equations. The impact of key dimensionless parameters, including the three-dimensional velocity ratio ([Formula: see text]), permeability parameter ([Formula: see text]), Prandtl number ([Formula: see text]), inter-phase heat transfer coefficient ([Formula: see text]), and porosity-scaled conductivity ([Formula: see text]), on the flow and temperature profiles is systematically analyzed. The results reveal the influence of LTNE conditions on thermal and hydrodynamic behavior and demonstrate the conditions under which the system transitions toward LTE.
Let [Formula: see text] and [Formula: see text] Denote by [Formula: see text] the partial transformation semigroup on [Formula: see text] Clearly, the empty set [Formula: see text] is a zero element of [Formula: see text] which is written as 0. Let [Formula: see text] An element [Formula: see text] is called a zero-divisor of [Formula: see text] if there exists [Formula: see text] in which [Formula: see text] The annihilator [Formula: see text] of [Formula: see text] is defined to be the set [Formula: see text] Obviously, [Formula: see text] always contains 0. Further, denote by [Formula: see text] the set of all zero-divisors of [Formula: see text] and [Formula: see text] In this paper, the co-annihilating graph [Formula: see text] of [Formula: see text] is constructed as an undirected simple graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are joined by edge if and only if [Formula: see text] Certain properties of [Formula: see text] are investigated. Moreover, some basic invariants of [Formula: see text] are also determined.
Quercus infectoria (Q. infectoria) is a medicinal plant renowned for its therapeutic benefits. The current study included optimization of microwave-assisted extraction (MAE) and ultrasound-assisted extraction (UAE) for obtaining bioactive compounds from QI galls, identification of its compounds via GC–MS, and isolation of pyrogallol using chromatography, as well as a molecular docking study of pyrogallol and 10 other compounds containing pyrogallol rings against HCV NS3 serine protease using Maestro 12.5. Response surface methodology (RSM) was used for optimization with total phenolic content (TPC), total flavonoid content (TFC), antioxidant activity, and iron chelating activity (Fe-CA) as responses. Well-fitted models were suggested that were supported by validation studies. In MAE, the optimal TPC, TFC, DPPH radical scavenging activity (DRSA), ABTS radical scavenging activity (ARSA), and Fe-CA were 223.25 mg GAE/g DW, 81.28 mg RE/g DW, 79.21%, 89.75% and 46.28%, respectively and in UAE, 202.14 mg GAE/g DW, 74.06 mg RE/g DW, 69.97%, 79.38% and 41%, respectively. MAE and UAE optimal conditions were power 490 W, time 80 s, and 35 mL/g solvent-to-sample ratio (SSR) and amplitude 37%, time 360 s, and solvent-to-sample ratio 15 mL/g, respectively. Isolated pyrogallol was characterized based on spectral data. The highest docking score of −15.177 kcal/mol was shown by eugeniin, followed by casuarinin (−12.76 kcal/mol) and 1,3,6-tri-O-galloyl-β-d-glucose (−12.17 kcal/mol), respectively. The study has important implications for HCV and related antiviral drug discovery and optimal bioactive compounds recovery from Q. infectoria using green techniques.
In the present study, we investigate the (3 + 1)-dimensional Hirota–Satsuma–Ito-Like (HSIL) equation to derive some novel analytical solutions. The HSIL equation arises in various physical phenomena, including fluid dynamics, non-linear optics, and plasma physics. We obtain novel analytical solutions to the HSIL equation by utilizing a relatively new novel analytical technique namely, the generalized exponential rational function (GERF) technique, which offers a systematic approach to solve non-linear partial differential equations. The proposed approach is used to extract various closed form solutions including rational, hyperbolic, trigonometric, and exponential functions solutions. The dynamic behavior of the extracted solutions are presented using 3-D and 2-D plots with help of computational software program like MATHEMATICA. It is observed that some of the obtained solutions are kink and singular periodic type solutions. The derived solutions validate the usefulness and reliability of the suggested method. In addition to providing theoretical insights into the HSIL equation, the discovered solutions have potential applications in a variety of scientific and technical domains, including mathematical physics, wave propagation, and soliton theory. We hold the view that the suggested approach is robust, versatile and capable of generating wave solutions for a diverse area of non-linear evolution equations.
This study evaluated the corrosion mitigation performance of the hydrazide derivative 2-methyl-3-phenylallylidene hydrazinecarbothioamide (MPHT) for mild steel (MS) in 0.5 M HCl and 0.5 M H2SO4 solutions over the temperature range 303–323 K. Electrochemical analysis using potentiodynamic polarization (PDP) and electrochemical impedance spectroscopy (EIS) demonstrated that inhibition efficiency increased progressively with MPHT concentration, achieving maximum efficiencies of 91% in HCl and 89% in H2SO4 at 303 K with 5 mM MPHT. The protective effect diminished at elevated temperatures, indicating predominant physisorption, while adsorption behaviour followed the Temkin isotherm. MPHT acted as a mixed-type inhibitor. Surface characterisation via SEM and AFM confirmed a significant improvement in surface morphology upon inhibitor addition. Complementary theoretical studies, including HOMO–LUMO analysis, Mulliken charges, and Fukui indices, elucidated the electronic properties governing MPHT–metal interactions. Overall, the results establish MPHT as a highly effective corrosion inhibitor for mild steel in acidic media.
