We study the initial value problem for the Majda–McLaughlin–Tabak model i∂tu+−∂x2α/2u=κDxβDxβu2Dxβu,ux,0=u0x, x∈R,t∈R, for α=2 and −1/4<β<1/2 with β≠0, where u≔ux,t is a complex-valued function. We show that the uniform radius of spatial analyticity σt of the solutions at time t is bounded from below by ct−1/2γ for some positive constant c, where γ=3−4β/4 for −1/4<β<0, γ=5−8β/8 for 0<β<1/4, and γ=1−2β/2 for 1/4≤β<1/2. To establish these results, we employ a higher-order almost conservation law in modified Gevrey spaces, Strichartz estimates associated with the free wave, Plancherel’s theorem, Hölder’s inequality, Duhamel’s formula, the contraction mapping principle, and Sobolev embedding.
As global climate anomalies alter aquatic ecosystems, traditional epidemiological models frequently overlook the fundamental thermodynamic laws governing environmental pathogen reservoirs. This study bridges that critical gap by introducing a novel thermo-environmental modeling framework that couples the transmission dynamics of water-borne cholera with macroscopic ecosystem energetics. Utilizing a system of nonlinear differential equations embedded with temperature-dependent biological parameters, we examine the dual impact of thermal warming and metabolic entropy on epidemic intensity. Our numerical and sensitivity analyses reveal that ambient temperature acts as a critical control lever, where elevated thermal baselines concurrently compress the time-to-peak outbreak window and escalate maximum infection prevalence. Crucially, we identify striking temporal synchronization between peak human infection and maximum environmental exergy destruction E˙d within the aquatic reservoir. This energetic signature proves that explosive bacterial proliferation and host-induced pathogen shedding fundamentally destabilize the thermodynamic stability of the ecosystem. From a public health perspective, these findings establish environmental exergy profiles as a viable, nontraditional ecological diagnostic tool to forecast high-risk outbreak windows before clinical spikes occur. Ultimately, our structural sensitivity analysis demonstrates that while clinical scaling is essential for patient recovery, long-term epidemic containment rests heavily on targeted environmental sanitation and water-treatment infrastructure designed to shatter this thermo-biological feedback loop.
Malaria is a vector-borne infectious disease, particularly found in tropical and subtropical regions, where its transmission is driven by the bite of Anopheles mosquitoes. To explore the malaria transmission dynamics between two patches with varying degrees of endemicity, we developed and analyzed a two-patch Atangana-Baleanu fractional-order malaria model that incorporates patch-specific optimal controls: treated mosquito nets, antimalaria drugs, and insecticide. We established nonnegativity and bounded solutions, confirming the model’s mathematical and epidemiological well-posedness. The next-generation matrix technique was employed to calculate the basic reproduction number. The stability analysis indicated that the malaria-free equilibrium is locally and globally asymptotically stable when R0m<1, otherwise unstable when R0m>1. Actual data on the prevalence of malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. Numerical simulations indicate that human mobility significantly influences the geographical spread of malaria, while temperature variability notably affects mosquito biting and mortality rates. Furthermore, as fractional orders decrease from one, the spread of the endemic slows. Hence, by applying optimal control, we examined the effectiveness of patch-specific, time-dependent interventions. Results demonstrate that the combined implementation of treated mosquito nets, antimalaria drugs, and insecticide spraying significantly reduces malaria prevalence in both patches, underscoring the importance of integrated, localized intervention strategies. The main novelty lies in the fusion of fractional-order dynamics, spatial heterogeneity (two patches and temperature variability), real-data validation, and patch-specific optimal controls, which collectively provide a more realistic and policy-relevant framework than traditional malaria models that focus on a single homogeneous population.
We propose a fully unsupervised, convex, and globally convergent framework for multimodal grayscale image fusion based on adaptive weighted nuclear norm minimization (WNNM). By formulating the fusion task as a low-rank matrix recovery problem with data-driven singular value reweighting, the method automatically preserves salient structural features from both source images while effectively suppressing noise and redundancy. We establish global convergence of the proximal gradient algorithm with a Q-linear rate, derive a new perturbation error bound based on weighted Eckart–Young–Mirsky theory, and accelerate convergence using FISTA. Extensive experiments on the TNO, RoadScene, and Harvard Medical imaging datasets, comprising over 100 image pairs, demonstrate that the proposed approach achieves state-of-the-art performance in terms of entropy (EN), edge-based quality index (QAB/F), visual information fidelity (VIF), spatial frequency (SF), and subjective visual quality. The method consistently outperforms classical matrix-based approaches and performs competitively with recent supervised deep learning methods while requiring neither training data nor GPU acceleration.
Considering the importance of food chains in the environment from both biological and economic points of view, the life of a living organism depends on the existence of organisms that precede it. Many predators have also developed their own methods of obtaining food, although there is competition among them. Thus, studying hunting cooperation, which is typical of some predators, and the resulting fear of prey and its impact on food chain dynamics, is essential to understanding and controlling the presence and stability of those food chains. Therefore, the influence of hunting cooperation and the fear effect in a three-species food chain model was investigated in this paper. The feeding process was represented by a Holling Type II functional response at each level of the chain. Intraspecific competition among predator species was also taken into account. The system solution’s features are investigated. The analysis of the system’s equilibria’s local and global stability was explored. The food chain model’s persistence conditions were determined. The necessary conditions for the occurrence of local bifurcation around the equilibria were established. To determine the presence of chaos in the food chain system, bifurcation diagrams were obtained. It is discovered that the system has rich dynamics, including point attractors, periodic attractors, and strange attractors.
In this article, we undertake a comprehensive study of almost Riemann solitons and their gradient counterparts within the framework of relativistic bulk-viscous fluid string (BVFS) geometries. We begin by analyzing the potential vector field. It is shown that, on BVFS backgrounds, this potential vector must coincide with a torse-forming field which is unit timelike. This correspondence allows the scalar curvature to be reformulated explicitly through both the soliton data and the intrinsic geometric invariants of the spacetime. Subsequently, we turn to almost gradient Riemann solitons generated by a potential function ψ, obtaining a relation that links the Laplacian of ψ with the curvature properties of BVFS metrics. A classification result is derived as well, asserting that whenever the soliton vector satisfies the Killing condition, the almost Riemann soliton falls into the shrinking, steady, or expanding categories. Moreover, we establish that any BVFS spacetime admitting a Killing field automatically accommodates an almost Riemann soliton. Finally, we prove that the model behaves like a dark fluid provided the potential vector field is of νRic-type, or if the BVFS structure is W2-flat or pseudoprojectively flat.
In this paper, a complete Lie symmetry analysis of the time-fractional Benjamin–Bona–Mahony (BBM) equation in the Riemann–Liouville sense is presented. We give a full symmetry classification and two infinitesimal generators Q1 and Q2, unlike previous studies concerned with the construction of particular solutions. These symmetries are then used to reduce the governing fractional partial differential equation to a system of ordinary fractional differential equations. The reduced equation is solved analytically by the power series method, and the convergence of the series solution is rigorously proved by the implicit function theorem. Moreover, the systematic derivation of conservation laws is carried out by the nonlinear self-adjointness method. The results offer an analytical method to investigate fractional BBM-type equations, including convergent series representations and related conservation laws. The proposed framework can be applied to the mathematical modelling of systems with nonlinear dispersive and memory effects. A numerical example accompanied by a table and figure is provided to complement the theoretical results.
This study presents new results on resolving edge colorings in graphs, a concept introduced by V. Saenpholphat and P. Zhang in 2003. We determine the resolving edge chromatic number for several well-known families of graphs, including complete graphs, complete bipartite graphs, wheel graphs, sun graphs, and friendship graphs. Additionally, we investigate how this invariant behaves under graph operations such as the corona product, join, and Cartesian product. In this study, we establish several formal results, presented as theorems, by employing the Tabu Search metaheuristic algorithm on certain types of graphs.
This paper investigates the numerical solution of time-fractional Volterra integrodifferential equations that arise in many real-life problems. A higher-order numerical scheme is proposed using the L1-2-3 method for the time-fractional derivative, Simpson’s 1/3 rule approximates the integral part, and the spatial derivatives are approximated using the central finite difference method. The stability and convergence analysis of the proposed method is presented. The method’s efficiency is verified through illustrative examples, and the results are compared with those reported in other works.
This paper establishes new fixed-point and common fixed-point theorems for continuous and asymptotically regular self-maps defined on finite-dimensional normed pre-A∗ vector spaces over σ-complete pre-A∗-algebras. We prove that every continuous and asymptotically regular self-map on such a space has at least one fixed point (Theorem 2). Furthermore, for a pair of continuous, asymptotically regular, and r-weakly commuting self-maps satisfying a generalized contractive condition, we obtain a unique common fixed point (Theorem 3). An application to fractal image compression is presented, demonstrating how the pre-A∗ framework can model uncertainty in pixel values. These results extend classical fixed-point theory to algebraic structures where norms take values in a logical algebra rather than real numbers.
This paper develops a sheaf-theoretic reduction formalism for real-analytic homogeneous CR manifolds realized as orbits in complex homogeneous manifolds. Let M=G0/H0 be such a CR manifold, let M↪X be a complex realization, and let π:X⟶Y be the holomorphic reduction of the ambient complex manifold. For Z=πM and ρ=πM, it is proved that, under a global CR-extension hypothesis, the fibers of ρ are exactly the equivalence classes determined by global CR functions on M. Thus, the set-theoretic CR reduction of M is induced by the ambient holomorphic reduction. The local problem is then separated from the global one: Under a local descent hypothesis, the direct image ρ∗OMCR is canonically identified with the restricted ambient quotient sheaf OZres≔i−1OY/IZ, where IZ is the sheaf of ambient holomorphic germs vanishing on Z. A practical descent criterion is given, showing that local CR extension, together with sheaf-level holomorphic descent along π, implies the required local CR descent. The resulting morphism carries an ordinary Leray spectral sequence E2a,b=HaZ,Rbρ∗OMCR⟹Ha+bM,OMCR, with no use of Kähler identities or Hodge-theoretic assumptions. As a genuinely Levi-flat application, compact Levi-flat CR manifolds with a dense bounded-Liouville Levi leaf are shown to have trivial global CR reduction; in particular, dense Cousin-type leaves force all global CR functions to be constant. A fully explicit Kronecker Levi-flat three-torus illustrates the dense-leaf mechanism. A second product example, built from a Stein homogeneous curve, an Iwasawa factor, and a Kronecker Levi-flat torus, gives a nonpoint CR reduction for which both global extension and local descent are verified directly. Finally, a separated holomorphic suspension model over compact complex curves is worked out: The higher direct images are sheaves of holomorphic sections of flat holomorphic vector bundles associated with monodromy on HqF,OF, giving corrected curve-base dimension formulas. The paper is a conditional reduction framework whose applicability depends on verifying extension and descent hypotheses in concrete homogeneous non-Kähler models.
This study develops a nonlinear thermo–mechanical dynamical model describing the coupled interaction among mechanical motion, heat transfer, viscous dissipation, and melt-layer evolution during thermally induced phase change. The formulation addresses the limited availability of unified mathematical frameworks capable of simultaneously capturing thermal activation, interfacial evolution, and mechanical response within a single system of coupled nonlinear ordinary differential equations. The proposed model incorporates lubrication-based viscous resistance together with a temperature-activated melting mechanism, resulting in a strongly coupled piecewise-smooth dynamical system. A systematic non-dimensionalization is performed to identify the governing dimensionless parameters controlling thermal interaction, viscous dissipation, and phase-change dynamics. The mathematical analysis combines equilibrium analysis, Jacobian linearization, eigenvalue decomposition, Lyapunov energy arguments, and parameter-dependent stability investigation to characterize the qualitative behaviour of the coupled system. Numerical simulations are performed to illustrate the predicted thermo–mechanical evolution, energy dissipation, and regime-transition behaviour under representative parameter conditions. The analysis demonstrates that the coupled thermo–mechanical system possesses a block-structured Jacobian whose eigenvalue spectrum consists of one dissipative mode together with multiple neutral modes, establishing marginal stability of the equilibrium configuration. The results further show that variations in viscous resistance and melt-layer evolution govern continuous transitions between weakly damped, strongly dissipative, and melt-dominated operating regimes without classical eigenvalue crossing. The principal contribution of the present work is the development of a mathematically consistent nonlinear dynamical framework that unifies thermo–mechanical coupling, phase-change dynamics, stability analysis, and regime-transition behaviour within a single analytical formulation. The present model is intentionally formulated as a reduced-order dynamical system and therefore does not incorporate spatial heat conduction, temperature-dependent material properties, or fully distributed phase-interface evolution. Nevertheless, it provides a rigorous analytical foundation for future extensions involving higher-dimensional thermo–mechanical models and more general multiphysics coupling.
This research focuses on studying an incompressible, non-Newtonian fluid within an axisymmetric straight channel in cylindrical coordinates, divided under the influence of two zones, subject to two boundary conditions: one without slip and the other with slip. This is known as a complex problem called the “stick–slip problem.” Navier–Stokes partial differential equations are used to model the fluid flow, while the inelastic power-law model is employed simultaneously to treat the variation of viscosity, involving shear-thinning and shear-thickening situations. To simulate this problem, an efficient algorithm named the Taylor–Galerkin/pressure-correction (TG/PC) method, which is based on the finite element method, is used. The fundamental contribution of this study is in establishing an efficient numerical simulation to simulate thinning and shear-thickening inelastic fluid flow. In addition, a comprehensive analysis of the influence of applying two different boundary conditions on both sticking and slipping zones and the effect of a singular point located in the transitional region between the two zones. Moreover, this study focused on exploring the effect of the power law index (n), the consistency coefficient (k), and the dimensionless Reynolds number (Re) on the principal variables' components, with a comparison of the effect of stick–slip boundary conditions on it. Also, understanding the impact of these factors on the convergence performance of components was investigated. The results indicate that these rates, as well as the corresponding velocity and pressure’s temporal convergence rates, are greatly affected by characteristics of the power-law inelastic model. In summary, the present work observes that shear-thickening flow displays a higher convergence rate as compared to shear-thinning flow.
Results on cycles in flag domains are introduced in the context of a first interesting example, namely the flag domains of SU(2, 1) in flag manifolds of its complexification S L 3 (C).
The Pathway-type Pε-transform technique has been introduced as a versatile binomial transform encompassing various classes, including the classical Laplace transform. In this paper, we apply this technique to derive solutions for fractional Volterra integral equations (FVIEs) and fractional Abel–Volterra integral equations (FAVIEs) that involve Hilfer fractional derivatives. We establish the existence of solutions for several systems, a system of FVIEs, a system of FAVIEs, and a mixed system combining Volterra integral equations with FAVIEs. Additionally, we present a numerical and graphical analysis of these solutions, illustrating their behavior and properties.
For any two vertices u and v in a graph G, u−v geodesic is the shortest path between u and v. A set S of vertices in G is called an edge geodetic cover for G if every edge in G belongs to a geodesic between two vertices of S. The minimum cardinality of an edge geodetic cover is called the edge geodetic number and is denoted by egG. In this paper, we determine the exact edge geodetic number of k-powered paths and k-powered cycles. The proofs rely on a careful characterization of semiextreme vertices and geodesic covering arguments. The obtained results extend previous work on edge geodetic parameters and provide new insights into metric properties of graph powers.
This article is devoted to the estimation and prediction problems on the power-linear hazard rate model using record values. The maximum likelihood technique and the Bayesian technique under the squared error, linear-exponential, and entropy loss functions are used for the point estimation of the parameters of this model. Also, the asymptotic confidence interval, two confidence intervals based on bootstrapping, as well as the highest posterior density confidence region are constructed for the interval estimation of the parameters. The problem of predicting future record values using the observed record data from the power-linear hazard rate distribution is investigated using both the maximum likelihood and Bayesian techniques. A real data set is analyzed in order to explain the estimation and prediction methods. Finally, a Monte Carlo simulation study is implemented to explore and compare the performance of the various discussed procedures. Based on our simulation results, it was observed that the performances of the Bayesian estimators and predictors under an informative prior and their corresponding confidence regions are more suitable in comparison with the other methods for most of the cases.
This paper develops a family of Hermite–Hadamard–Mercer-type inequalities within the framework of generalized conformable fractional calculus. By interpreting generalized conformable fractional integrals as weighted integral means depending on the order parameter, we derive refined two-sided bounds for coordinated convex functions that incorporate Mercer-type improvements inspired by Jensen–Mercer structures. The proposed estimates reduce to the classical Hermite–Hadamard–Mercer inequalities when the fractional order equals one, and they recover several known Hermite–Hadamard-type bounds under suitable parameter choices and assumptions. In addition, we present weighted (Fejér-type) variants by introducing admissible weight functions, which enhances applicability in settings where nonuniform densities naturally arise. Overall, the conformable fractional Hermite–Hadamard–Mercer framework provides a unified and flexible approach for integral estimation problems in coordinated convex analysis.
This paper introduces a rigorous optimal control framework for bioeconomic fisheries management modeled as a nonlinear differential game between two competing firms. The importance of this study lies in the fact that it offers a rigorous and computationally reliable framework for the management of competitive fisheries, a field where nonlinear ecological economic interactions make analytical solutions challenging and policy design highly sensitive to parameter uncertainty. In contrast to the previous works, this paper combines Pontryagin’s maximum principle with a Picard-type forward–backward iteration and derives explicit mathematical conditions that ensure geometric convergence to the unique Nash equilibrium trajectory. In addition, the extensive sensitivity analysis points to the intrinsic growth rate, catchability parameters, and pricing structure as the main factors that determine equilibrium harvesting strategies and payoffs. These results demonstrate that robust optimal strategies should essentially harmonize biological dynamics with economic incentives. The suggested Picard–Pontryagin method is the one that directly accomplishes this, thus offering a computationally efficient framework for strategic decision-making in the case of competitive renewable resource exploitation under parameter uncertainty.
For α∈0,1, the matrix Aα−G=αDG+α−1AG defines a Laplacian–type operator associated with a graph G, interpolating between −AG and DG. In this paper, we develop a systematic study of the Aα−-spectrum under several classical graph products. Complete spectral characterizations are obtained for the Cartesian, lexicographic, and generalized lexicographic products. For the direct and strong products of connected regular graphs, explicit formulas are derived in terms of the Laplacian and signless Laplacian spectra of the factor graphs. The results demonstrate that Aα− exhibits a spectral behavior that is structurally distinct from the classical Aα-matrix, particularly in the presence of product constructions. These findings provide a unified framework for the analysis of Aα− across graph products and contribute to the broader development of parametrized spectral graph theory.
