This work presents a novel investigation of the recently derived relativistic Burgers-FLRW model, a scalar hyperbolic balance law with nontrivial source terms, using the Moving Mesh Method (MMM). Building on an MMM framework originally developed for hyperbolic conservation laws, we examine a range of monitor and smoothing functions to identify effective combinations for accurately resolving key solution features while reducing computational error. Numerical experiments compare the MMM with Adaptive Mesh Refinement (AMR) and uniform mesh discretizations. An L¹-error analysis is used to study the effect of different monitor functions, explore the role of various β parameters, and directly compare the performance of the MMM and AMR strategies. The results show that both adaptive approaches provide higher accuracy and better efficiency than uniform meshes, while also offering a clear comparison between MMM and AMR and practical insight into mesh adaptation for scalar balance laws.

The analysis of the fractional time-derivative model of the Caputo-Fabrizio and Atangana-Baleanu in Caputo sense with the ramped temperature on transient free convection flow in the vertical plates with isothermal boundary conditions has been established. The Laplace transform scheme was adopted in solving the governing equations, and semi-analytical solutions were achieved through the inversion of the solutions from the Laplace purview to the time purview. It found that the temperature and velocity obtained via the CF model are higher than ABC model, and the fractional parameters reduced the temperature and slowed down the movement of the fluid. It is perceived that relaxation time parameters boost the temperature and heighten the fluid’s movement. Also noted that the negative augment in the value of the heat source/sink caused retardation in the movement of the fluid, while the positive increment of the heat source/sink heightened the movement of the fluid. Similarly, it is observable that the temperature produced through a ramped temperature is higher than the constant temperature.

Petroleum and petrochemical resources remain pivotal to the energy and revenue streams of many economies, with drilling operations constituting a fundamental phase in hydrocarbon production. Drilling mud and its associated additives are critical components in the drilling process. The escalating cost, pressure on foreign exchange and ecological footprint of some imported drilling mud additives have spurred interest in sustainable, locally derived alternatives. In this work, a water-based drilling mud (WBM) was formulated using only locally sourced materials from Akwa Ibom State, Nigeria. Key components such as beneficiated local clay, okra-ogbono biopolymer, cassava starch, wood-ash alkalinity agent, and coconut-husk filtrate controller were prepared and blended following API RP 13 B-1 protocols. The rheology (apparent and plastic viscosity, yield point), filtrate loss and cake thickness, pH, density, and thermal/biological stability were determined in the laboratory. Compared to commercial variants used as benchmarks, the local WBM met API rheological and density targets but exhibited elevated fluid loss (17.5 mL vs. ≤ 15 mL) and marginal pH buffering (initial pH 9.2 vs. ≥ 9.5). Thermal aging (90 ^∘C, 24 h) and degradation tests revealed viscosity loss and gel-strength decline, greater than polymer-based commercial variants. On implementation of clay micronization and starch modification, the fluid loss reduced below 15 mL while cake thickness was 2.0 mm. At an estimated 60 % – 65 % cost saving, this WBM demonstrates significant promise for eco-friendly, cost-effective drilling in the Niger Delta.

This paper develops a theory for stability analysis of semigroups of linear operators acting on variable Banach spaces—families of Banach spaces {X(t)}_t ≥ 0 whose norms may depend on time. We establish generation theorems under appropriate resolvent conditions, characterize exponential stability through Lyapunov-type functionals, and analyze spectral properties of evolution families in variable settings. Our approach systematically extends classical semigroup theory to accommodate time-dependent norms by transporting all objects to a fixed reference space. Applications include non-autonomous parabolic equations and reaction-diffusion systems with time-dependent coefficients. All proofs are provided with full mathematical rigor, addressing technical challenges unique to variable Banach spaces.

This study reports the synthesis of a sustainable biopolymer-based coating using cassava starch as the polymeric matrix, oil-palm empty fruit bunch (EFB) lignin as reinforcement, and acid-activated nano-bentonite clay with boric acid as a crosslinker. Coatings were applied to mild-steel substrates and characterized using FTIR, TGA, SEM/TEM, XRD, BET, thermal conductivity measurements, and ASTM E1321 lateral ignition and flame-spread tests. FTIR confirmed hydrogen bonding and strong interfacial adhesion, indicated by O–H and C=O stretching from borate crosslinking, aromatic C=C (lignin), and Si–O–Si (bentonite) vibrations, with an O–H peak shift from 3405 to 3378 cm⁻¹. TGA revealed three-stage decomposition with increased onset degradation temperature (300 ^∘C) and enhanced char yield (27.5%). SEM/TEM showed well-dispersed bentonite nanoparticles (<100 nm) and dense post-burn char morphology, while XRD indicated partial intercalation/exfoliation of clay, and BET confirmed increased surface area and mesoporosity. Optimized formulations (Sample B) exhibited superior fire performance: ignition delay of 126 ± 4 s, flame-spread rate of 1.0 ± 0.1 cm min⁻¹, and char continuity of 92 ± 3%, alongside a 35–45% reduction in thermal conductivity. Mechanical evaluations demonstrated improved adhesion, abrasion resistance, and hydrophobicity. These findings confirm that multi-component, bio-based coatings derived from locally available materials provide a low-cost, eco-friendly strategy for fire retardancy and thermal insulation, supporting sustainable development goals (SDGs 9, 11, and 13).

Classical lifetime models often struggle to accommodate skewed data, tail variation, and non-monotone hazard behaviour observed in engineering and reliability applications. Motivated by this limitation, this study considers the Topp–Leone New Weighted-Weibull (TLNWW) construction obtained by applying the Topp–Leone generator to the New Weighted-Weibull baseline distribution. The resulting model is developed in its original parameterization and, importantly, is also expressed through the composite rate parameter k = 2α(1 + β^θ), which yields an equivalent exponentiated Weibull representation and clarifies the model’s identifiable structure. On this basis, we derive the density, distribution, survival and hazard functions, quantile function, moments, and order statistics, and we discuss maximum likelihood estimation using the identifiable parameters. A Monte Carlo study is reported to examine finite-sample behaviour across several parameter settings. The simulation results show that estimation is satisfactory in some scenarios, although interval performance is uneven in others, indicating that numerical inference should be interpreted with appropriate caution. Two real datasets from materials and engineering applications are used to assess empirical performance and to compare the model with related competitors by means of likelihood-based criteria and goodness-of-fit summaries. Across these examples, the TLNWW model provides competitive fits and attains the best information criteria by small margins, while remaining comparable to closely related alternatives. The paper therefore contributes a careful reparameterized treatment of the TLNWW model, clarifies its connection with existing families, and provides a practically useful distributional form for positively skewed lifetime data.

This study presents the synthesis, application, and dosage optimization of nano-lead chromate as a microstructural modifier for cementitious composites. PbCrO₄ nanoparticles were incorporated into cement-paste specimens at addition levels of 5, 10, 20, 40, 80, and 100%, defined with respect to the stoichiometric SiO₂ content of the cement and also reported for comparison with conventional binder-based formulations. The resulting composites were evaluated by X-ray diffraction, FTIR, UV/Vis., TGA/DTA, SEM, EDX, and TEM in order to relate phase development and microstructural features to mechanical performance. Mechanical response was assessed from replicated loading tests at 7 and 28 days, and the recorded failure loads were used to estimate indirect tensile behavior for the prismatic specimens. The results indicate that nano-PbCrO₄ modifies the texture and compactness of the cementitious matrix and increases the measured load-bearing capacity within the investigated dosage range. The study therefore provides an exploratory assessment of PbCrO₄ as a nano-scale mechanical promoter, while practical implementation would require additional durability and environmental verification.

In the work, by establishing integral representations for a class of specific Maclaurin power series, the authors restate recently-published results related to the normalized remainder of the Maclaurin power series of the exponential function, alternatively prove some of these results, and pose some new problems in terms of the majorizing relations.