Search Results (2,007)

In this article, we establish the existence and uniqueness of coupled coincidence fixed points for rational-type contraction mappings in the framework of metric spaces by employing a binary relation. These results are derived under the assumption of the mixed monotone property. To illustrate the effectiveness of the obtained results, a suitable example is provided. Finally, we give an application of our main results to a fractional differential equation involving the Riemann–Liouville fractional derivatives. These findings extend existing results in the literature and highlight the effectiveness of the proposed approach in the analysis of fractional differential equations. Full article

Food and health are converging across the agrifood value chain, and artificial intelligence (AI) is widely promoted to operationalize the link, yet firms cannot tell which food-as-health opportunities current AI can address. We identify the agrifood industry’s highest-priority food-as-health opportunities in the United States and assess, against the peer-reviewed AI literature, how far current AI can address each. A PRISMA 2020 systematic review of 34 U.S.-focused studies establishes the problem space; a Jobs-to-Be-Done map organizes ninety opportunity areas; a blind discovery forum with 37 senior U.S. practitioners gives an independent reading; a convergence analysis joins the map and the forum; and a separate assessment grades each opportunity against the AI literature. Practitioner priorities converge on twelve opportunities in the two segments that physically determine food’s health attributes, agricultural production and food manufacturing. These resolve into five AI capability families. The evidence is strong for sensing, traceability, design, and personalization, and more qualified for evidence synthesis and regulatory intelligence, where reliability limits require human oversight. One core need lies beyond AI, a preliminary finding of a symmetric long-term-contract gap that appears relational. We grade an agenda by how far current AI reaches, with an explicit boundary on what it cannot address. Full article

Lumpy skin disease (LSD) is a rapidly spreading viral disease of cattle that threatens livestock productivity and agricultural trade across Africa, the Middle East, and Asia. Despite effective vaccines being available, evidence-based guidance on allocating limited veterinary budgets across competing interventions remains lacking, and no LSD study has yet combined dynamic transmission modelling with a hard budget constraint and formal cost-effectiveness analysis. We develop a deterministic $S_h{V}_h{E}_h{I}_h{R}_h$–$S_v{I}_v$ (SVEIRSI) compartmental model for LSD, embedded within a budget-constrained optimal control framework with three time-dependent controls—vaccination ($u_1$), vector control ($u_2$), and movement restriction ($u_3$)—evaluated across all eight strategy combinations. The basic reproduction number is ${\mathcal{R}}_0=2.7899$. Pontryagin’s Maximum Principle characterises the optimality conditions. The resulting two-point boundary value problem is solved via forward–backward sweep with budget bisection over a 180-day horizon at three budget levels (${\mathcal{W}}_L=\mathrm{NAD}5000$, ${\mathcal{W}}_M=\mathrm{NAD}\mathrm{15,000}$, ${\mathcal{W}}_H=\mathrm{NAD}\mathrm{40,000}$). Vaccination dominates the optimal allocation at every budget, reducing peak infectious prevalence by 54–57% and averting 15,645–17,970 animal-days of cumulative burden relative to the uncontrolled baseline (${\mathcal{I}}_0=\mathrm{97,313}$ animal-days). Shadow-price analysis reveals that the budget constraint is non-binding across all three policy budget levels (actual optimal spend ≈ NAD 572), indicating that logistical (rather than financial) barriers are the true bottleneck, with the shadow price dropping to zero at $\mathcal{W}\approx \mathrm{NAD}1862$. Incremental cost-effectiveness analysis places vaccination alone ($S_1$), vaccination plus vector control ($S_{12}$), and the combined strategy ($S_{123}$) on the efficiency frontier, with ICERs of NAD 0.012, 0.015, and 0.166 per animal-day averted, respectively. One-way sensitivity analysis identifies vaccine efficacy $\epsilon$ as the dominant driver of cases averted (swing $\approx \mathrm{85,601}$ animal-days), while global sensitivity analysis via Latin Hypercube Sampling identifies the midge biting rate a as the strongest driver of cumulative infectious burden ($\mathrm{PRCC}=0.926$, $p<0.001$). These results provide actionable, quantitative guidance for LSD outbreak response in Namibia and comparable resource-limited settings. Full article

Cross-border e-commerce platforms increasingly operate under economic-security measures that raise sourcing costs and impair order fulfillment, turning supplier reconfiguration into a joint pricing-and-sourcing problem. We develop a joint pricing-and-sourcing model applied to cross-border platform operations, with a low-cost, high-exposure original supplier and a higher-cost, more reliable alternative supplier. A per-unit tariff-equivalent cost $t$ represents the policy-cost channel, an expected order-level fulfillment-loss rate $q$ represents the fulfillment channel, and convex supply-chain switching costs determine the depth of reconfiguration. The model identifies the trigger for the transition from global sourcing (GS) to partial de-risking (DR) and the boundary between DR and decoupling from the original supply chain (DC). These analytical results are evaluated using a case-informed calibration to SHEIN’s low-value U.S. direct-shipping apparel setting. The results show that, under the baseline calibration, the GS-to-DR trigger is $t=5$ when only the tariff-equivalent cost shock is present and $q\approx 0.282$ when only the fulfillment shock is present. Across the case-informed $t$-$q$ domain, DR accounts for 82.11% of evaluated combinations and DC for 0.023%; lower switching-cost intensity and a smaller alternative-supplier cost premium expand the DC region. Robustness analyses examine alternative demand specifications, sourcing granularity, capacity constraints, switching-cost forms, supplier risk, failed-order cost incidence, and supply-chain structures. By distinguishing the trigger for diversification from the depth and boundary of subsequent reconfiguration, the study clarifies why partial de-risking can emerge as a distinct strategy between global sourcing and decoupling from the original supply chain and provides decision benchmarks for supplier diversification, regional fulfillment, and resilience investment. Full article

We study the extremal behavior of real two-term linear combinations of third-order Zernike modes on the closed unit disk $D^2$. Our primary focus is the classification of interior local extrema; absolute extrema on the boundary circle are treated only where they admit a concise description or as a separate boundary-optimization problem. These modes arise naturally in Zernike expansions of optical wavefront aberrations. For each of the six unordered pairwise linear combinations of third-order modes, we classify the interior local extrema in terms of the two real coefficients. The trefoil–trefoil case is treated more generally through linear combinations of primary n-multifoils; harmonicity and the maximum principle show that no interior local extrema occur and that absolute extrema are attained on the boundary circle. For the remaining pairwise combinations, we give analytic conditions for the existence, uniqueness, location, and values of local extrema, including degenerate exceptional cases. We also compare these local extrema with boundary values and describe the associated absolute-extremum problem on the boundary circle. Symbolic computations are included in the appendix to document several algebraic reductions, and numerical illustrations are provided to visualize the resulting classifications. Full article

In this paper, we study the existence of positive solutions for a nonlinear fifth-order boundary value problem arising from fully developed couple-stress fluid flow through a porous channel. Under a natural restriction relating the couple-stress and permeability parameters, the associated linear operator factorizes into two positive second-order operators; we construct the corresponding Green function, show that it is strictly positive, and obtain it in an explicit closed form. By reformulating the problem as a completely continuous operator on a cone in $C[0,1]$ and applying Krasnosel’skiĭ’s fixed point theorem of cone compression–expansion type, sufficient conditions for the existence of positive solutions are established in terms of the load parameter. The positivity of the velocity further yields a strictly positive cumulative-flow solution on $(0,1]$. Several examples and a numerically calibrated application are given to illustrate the main results. Full article

Let $\psi$ be the Chebyshev prime-counting function and $\pi \left(x\right)$ the number of primes up to x. The Chebyshev-prime condition $K\left(p\right)=\mathrm{li}\left(\psi \right(p\left)\right)-\mathrm{li}\left(\psi \right(p-1\left)\right)<1$ is not equivalent to the sign rule $\psi \left(p\right)-p>0$. We prove that its leading threshold is the midpoint correction $\psi \left(p\right)-p>{\displaystyle \frac{1}{2}}\log p$, with an explicit higher-order boundary, and define false Chebyshev primes through the resulting transition layer. Our main unconditional theorem shows that ordinary prime counting does not equidistribute logarithmic prime phases: for every nonzero integer combination $\tau$ of nontrivial zeta-zero ordinates, $\pi {\left(x\right)}^{-1}{\sum }_{p\le x}{p}^{i\tau }=x^{i\tau }/(1+i\tau )+o\left(1\right)$. By contrast, the logarithmically uniform weight $\log p/p$ restores finite-dimensional Haar equidistribution for rationally independent ordinates. This dichotomy motivates the weighted local-time statistic ${\mathcal{L}}_{+}\left(x\right)=2\sum p^{-1/2}$, summed over the layer primes $p\le x$. We show that the layer is exactly the one-sided slab $-T\left(p\right)<B\left(\log p\right)<0$ of the midpoint-centered field B, where $T\left(p\right)=\log p/\left(2\sqrt{p}\right)$, so that ${\mathcal{L}}_{+}$ is a bona fide occupation density. Assuming the Riemann hypothesis, linear independence, and a shrinking-window local limit hypothesis that we isolate as a separate open problem, we prove the one-directional Cesàro law ${\mathcal{L}}_{+}\left(x\right)/\log x\to f_B\left(0\right)$, where $f_B\left(0\right)$ is the value at the origin of the limiting density of B (numerically $f_B\left(0\right)\approx 1.828$). Independently, we prove shrinking-target occupation laws via coarea formulas: unconditionally for fixed windows, including for the finite zeta-derived field itself, and under uniform transversality for the diagonal window. The remaining obstacles are tangential crossings of that field and transfer to the prime-sampled diagonal window. Full article

We study the linear continuous interior penalty finite element method (CIP-FEM) for the two-dimensional Helmholtz equation on nonconvex polygonal obstacle domains with mixed Dirichlet and impedance boundary conditions. Re-entrant corners reduce the global regularity below $H^2\left(\mathrm{\Omega }\right)$ and require a corner-sensitive treatment of the CIP stabilization term. Using a wavenumber-explicit regular–singular decomposition, we establish exact consistency of the CIP formulation under this reduced regularity. We also prove the critical-order penalty-seminorm estimate $|I_h{S}_j{|}_J \lesssim h^{{\alpha }_j}$ for the Scott–Zhang quasi-interpolant of the cut-off corner singular functions. Combining this estimate with endpoint Scott–Zhang approximation and wavenumber-explicit bounds for the regular and singular components yields ${\inf }_{v_h \in V_h}\parallel u-v_h{\parallel }_{h,k} \lesssim (kh + k^{\alpha -1/2}{h}^{\alpha }){\parallel f\parallel }_{0,\mathrm{\Omega }}$. A Schatz-type duality argument then yields the corresponding quasi-optimal error estimate $\parallel u-u_h{\parallel }_{h,k} \lesssim (kh + k^{\alpha -1/2}{h}^{\alpha }){\parallel f\parallel }_{0,\mathrm{\Omega }}$ under the sufficient resolution condition $k^{2}h \le \delta$, where $\delta$ is independent of k and h. Discrete uniqueness is proved independently of this condition. Numerical experiments support the predicted corner-singularity behavior; for the tested problems with the fixed penalty value $\gamma = 0.1$, they show smaller errors than the standard FEM on some relatively coarse meshes in the high-wavenumber pre-asymptotic regime. The present analysis does not separately identify an additive pollution error term. Full article

Particle swarm optimization (PSO) is a widely used method for solving single-objective optimization problems. However, PSO suffers from diversity loss and premature convergence, leading to suboptimal performance in complex problems. To address these limitations, this paper introduces a novel self-adaptive multi-learning strategy PSO (SMLS-PSO) designed for real-parameter optimization tasks. SMLS-PSO integrates four distinct learning strategy-based PSO variants into a behavior pool and employs a new self-adaptive strategy selection mechanism. This mechanism dynamically chooses the most suitable learning strategy to update the velocities and positions of particles based on fitness information and payoff at different evolutionary stages. To enhance the performance of SMLS-PSO, three key improvements are incorporated: (1) a stagnation counter parameter to minimize wasted fitness evaluations; (2) a boundary symmetry mapping method to manage out-of-range searches; and (3) a Quasi-Newton local search operator to boost local exploitation capabilities. SMLS-PSO is first compared with four component PSO variants on 13 basic benchmark functions. Subsequently, SMLS-PSO is compared with eight state-of-the-art PSO variants on both 30D and 50D CEC2017 test suite problems. Experimental results indicate that SMLS-PSO statistically and significantly outperforms the compared algorithms on the majority of the test problems, showcasing its superior optimization capabilities. Finally, SMLS-PSO was applied to the optimization problem of UWB anchors layout, and it achieved a higher locatable space coverage rate and a better average HDOP value compared to the conventional layout scheme and other PSO variant optimization schemes. Full article

Exceptional points are parameter values at which two eigenvalues and their corresponding eigenfunctions coalesce, rendering the wave operator defective. They arise widely in non-Hermitian wave physics and disrupt the modal expansions on which semi-analytic scattering methods rely. For lined acoustic waveguides, an augmented mode-matching ansatz that restores completeness at such a degeneracy—by adjoining the generalised eigenfunction obtained from the derivative of the parametrised duct mode with respect to its transverse spectral parameter—has been established for junctions between duct sections with discrete modal sets. This article extends that ansatz to an open, radiating configuration: a rigid feed duct communicates through an impedance-lined throat, tuned to an order-two exceptional point, with a half-space bounded by a rigid flange. The radiating mouth replaces the discrete modal closure by a continuous spectrum, so the augmented basis must be matched against an improper spectral integral. The half-space field is generated by the aperture velocity, which builds the rigid-flange condition into the representation exactly, and the resulting improper integrals are rendered analytic by branch-aware substitutions whose cutoff is tied to the retained modal content. The formulation is validated on the matching and boundary conditions themselves: pointwise continuity of pressure and of normal velocity at the internal junction, pointwise pressure continuity at the radiating mouth, the vanishing of the normal velocity on the rigid flange, and the recovery of the classical flanged-duct radiation problem in the rigid limit, cross-checked against an independent implementation. The full lined problem, including the defective case, has been further verified against an independent finite-volume solution of the same boundary-value problem, whose grid-converged fractions agree with the mode-matching values to within $8\times {10}^{-5}$. A conserved-power identity is monitored as a necessary but not sufficient check. Numerical experiments confirm the known breakdown of the standard expansion at the exceptional point and the well-conditioned convergence of the augmented one in this radiating setting, and a scan of the complex admittance plane, refined by local optimisation and repeated across throat lengths and frequencies, shows that flange radiation detunes the absorption optimum away from the exceptional point, by an amount that grows with the radiated share of the power budget and vanishes as the throat lengthens. Full article

The contribution deals with the numerical results for the identification problem for heat-transfer coefficient between the outward surface of the mould and the environment, and for the flux density of the modified mass of the glass coefficients between the glass and the mould, and the glass and the plunger. The continuous problem was formulated in detail at AMEE’49. The numerical results were received by the software FreeFem++ version 4.2.1 for the sample of the real vase from the experiment carried out at the Technical University of Liberec in 1999, which was used as a data source for the identification problem. Identification is realized with respect to the measured temperature values at 10 points of the mould and the plunger. The distribution of the searched coefficients along the respective boundaries in the initial, the 10th, the 20th, the 60th and the 100th iterations together with the distribution of temperature throughout the system in the 100th iteration are presented. Full article

In electric vehicles (EVs), the battery management system (BMS) plays a central role in ensuring safe, efficient, and reliable battery operation under varying driving and environmental conditions. The effectiveness of a BMS largely depends on the availability of an accurate battery model, whose performance is strongly influenced by the precision of its identified parameters. However, estimating these parameters remains a difficult nonlinear optimization problem, especially under low state of charge (SOC) operation. Classical identification approaches often have limited robustness under such conditions, while metaheuristic algorithms provide a promising alternative because of their ability to handle nonlinear and multimodal search spaces. Even so, many existing methods still encounter drawbacks related to convergence speed and susceptibility to local optima. Motivated by these challenges, this study investigates the recently introduced Artificial Lemming Algorithm (ALA) for parameter identification of a second-order equivalent circuit model (2RC-ECM) under EV-oriented low-SOC operating conditions. Experimental validation is conducted using two independent dynamic datasets, namely the High Dynamic Profile (HDP) at 25 °C and the Urban Dynamometer Driving Schedule (UDDS) at −5 °C, involving different lithium-ion cells and operating conditions. ALA is benchmarked against nine competing metaheuristic algorithms under identical search boundaries and computational settings. Performance is assessed using RMSE, MAE, MaxAE, bias, convergence behavior, error distributions, execution time, and sensitivity to the number of independent runs, population size, and maximum number of iterations. The results show that ALA achieves the lowest minimum, mean, and maximum RMSE for both datasets, with minimum RMSE values of $0.01075 \mathrm{V}$ for HDP and $0.03534 \mathrm{V}$ for UDDS. Unseen-data validation further yields RMSE and MAE values of $0.0082$ and $0.0061 \mathrm{V}$, respectively, for HDP, and $0.0416$ and $0.0299 \mathrm{V}$, respectively, for UDDS. In addition, convergence, error-distribution, and sensitivity analyses show that ALA maintains competitive and consistent performance across the investigated configurations. Overall, the results demonstrate that ALA provides a favorable balance between estimation accuracy, robustness, convergence behavior, and computational cost for offline lithium-ion battery parameter identification. Full article

The accuracy of microseismic moment tensor inversion critically depends on the spatial configuration of surface sensor arrays, quantified by the condition number $\kappa \left(\mathit{G}\right)$ of the dynamic response matrix. Existing optimization methods suffer from slow convergence and unreliability due to the fundamental lack of gradient information. In this specific context, the analytical gradient of $\kappa \left(\mathit{G}\right)$ with respect to sensor positions via singular value perturbation theory and the chain rule of direction cosines are derived for the first time in this paper. Based on the analytical gradient, three optimization strategies are established: a BFGS quasi-Newton method with quadratic penalty (BP) for smoothly constrained regions; a sequential quadratic programming method (FMC/SQP) achieving the lowest condition numbers across all shapes with approximately 5000 evaluations; and a center-boundary parameterization method (CB) that exploits the structural regularity of optimal configurations to reduce variables from $2N$ to $N-1$, requiring only approximately 300 evaluations (1/16 of FMC). Systematic experiments on five region shapes and two complex constraint scenarios demonstrate that gradient methods achieve a 15–30% reduction in $\kappa$ across 4 of 5 shapes and a 5–31-fold improvement in robustness, with FMC reducing the average condition number by 25% at 15.4-fold better robustness than the baseline. Synthetic inversion experiments confirm that reducing $\kappa$ from approximately $1.5\times {10}^4$ to approximately 50 reduces moment tensor inversion error by approximately 50-fold. The analytical gradient framework is transferable to sensor placement problems across multiple disciplines, and the three-method toolchain offers a graduated accuracy–efficiency trade-off for practical deployment optimization. Full article

In cryptocurrency markets, credibility may be created before it can be verified. Promotional signals from influencers, online communities, exchanges, and project actors can create an impression of legitimacy before consumers are able to independently assess the quality, risks, or underlying value of the asset. This systematic review examines how promotional activity contributes to this condition and how the literature connects it with ethical concerns, consumer consequences, and governance. Following PRISMA 2020, 54 empirical studies published between 2019 and 2025 were identified through Scopus and analyzed using thematic synthesis. The findings indicate that promotion is distributed across social media, influencers, communities, exchanges, and project actors, making the boundary between marketing, personal opinion, and financial advice difficult to maintain. Ethical problems arise not only from fraud, but also from selective information, hidden incentives, artificial attention, and market signals that give uncertain assets an appearance of legitimacy. Consumer vulnerability is similarly situational. Knowledge and experience may offer some protection, but trust, technological complexity, social influence, and speculative expectations continue to shape judgement. Regulatory and educational responses remain fragmented because responsibility is dispersed across actors and jurisdictions. The review connects these relationships through an ethical marketing cycle that conceptually organizes how ethical concerns may develop across communication, market activity, consumer interpretation, and governance. This perspective extends ethical marketing beyond the accuracy of individual claims and locates responsibility within the structures through which cryptocurrency credibility is produced. The review is limited by its reliance on Scopus and the absence of a formal risk-of-bias assessment of the included studies. Full article

Reliable cropland, forestland, and grassland maps support resource assessment and ecological management in arid and semi-arid Central Asia. Existing land-cover products often delineate these classes differently, vary in reliability across classes and locations, and may share the same errors even when they agree. This study formulates multi-product fusion as a pixel- and class-specific reliability decision problem. To address this problem, we propose a reliability-adaptive fusion framework, the Discrepancy-Aware Reliability-Adaptive Fusion Network (DRAFNet), using 2020 maps from three global 30 m land-cover products—FROM-GLC Plus, GLC-FCS30D, and GlobeLand30—and variables representing aridity, temperature, precipitation, elevation, and slope. Unlike fixed-weight fusion methods and segmentation models that use the source products only as input channels, DRAFNet retains the categorical source decisions and adjusts each contribution according to its estimated reliability for the assigned class and location. Weight removed from an unreliable source is transferred to a residual expert, which provides an alternative prediction when the source products are unreliable or share the same error. Voting entropy and geo-environmental variables provide contextual information for this decision. On independent test samples from the five Central Asian countries, DRAFNet achieved an overall accuracy (OA) of 0.8275, a Kappa coefficient of 0.7698, a mean intersection over union (mIoU) of 0.7046, and a macro-averaged F1 score (Macro F1) of 0.8241. These values were 0.95–1.38 percentage points higher than those of U-Net++, the strongest benchmark. Local comparisons indicated more coherent spatial patterns and clearer boundaries in areas of pronounced disagreement. The mean and median absolute log-ratio deviations from area statistics reported by the Food and Agriculture Organization of the United Nations (FAO) were 0.618 and 0.450, respectively, both lower than those of the source products. These results support land-resource assessment and ecological management in Central Asia. Full article