Search Results (2,989)

In recent years, scientific and technological development has made trade-in programs for innovative electronic products more and more popular. Many of these innovative companies that continue to launch new products offer trade-in and cash-out sales strategies to stimulate purchase. This paper studies when a company launches these two sales strategies and how to ensure optimal pricing that maximizes profits, while taking into account the degree of the consumer’s strategy, the degree of the new product’s innovation, the residual value of the old products, and the cost. We construct a two-period dynamic pricing joint optimization model with four core decision variables and derive the closed-form optimal solution through strict mathematical derivation including Hessian matrix analysis and KKT condition verification. We have adopted a dynamic pricing strategy that conforms to the actual market. The results show that this study provides new mathematical insights for dynamic pricing research, and reveals the substantive rule that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate. Statistics show that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate. Full article

Peen forming is a dieless manufacturing process used to shape large, thin aerospace panels through controlled shot impacts that induce residual stresses and curvature. Despite long-standing industrial use, process monitoring still depends largely on indirect proxies such as Almen intensity and coverage, limiting spatially resolved deformation assessment and hindering closed-loop control. In parallel, vision-based artificial intelligence (AI) has enabled adaptive monitoring and feedback in smart-manufacturing domains such as welding, additive manufacturing, and sheet forming. This review examines how such sensing and learning strategies can be transferred to adaptive peening forming. We compare six vision sensing modalities and assess major AI model families for surface mapping, temporal prediction, robustness, and deployment maturity. The synthesis shows that progress is primarily constrained by limited validated datasets, harsh in-cabinet sensing conditions, scarce closed-loop demonstrations, and weak validation on curved aerospace geometries. We conclude that the sensing and AI foundations for adaptive peen forming are already emerging, but industrial translation now depends on stronger experimental validation, standardized benchmarking, robust multi-sensor integration, and edge-capable feedback pipelines. Full article

This paper derives a closed-form expression for the expected discounted value of aggregate cash flows when arrival times follow a Poisson process but both the time horizon and the number of arrivals are finite. The result provides a tractable analytical formula for the expected discounted sum under simultaneous constraints on time and arrival counts. We show that the expression converges to the well-known infinite-horizon and infinite-arrival results as limiting cases. Numerical illustrations demonstrate the behavior of the formula under different parameter values. The result can be interpreted as the valuation of a discounted compound Poisson process with finite constraints and may be useful in stochastic modeling and risk-analysis applications. The proposed formula provides a simple analytical tool for evaluating discounted losses or revenues in finite risk portfolios. Full article

Mountain orchards in southern China are characterized by fragmented and complex terrain with a wide slope variation range (5~30°), which easily leads to uneven pesticide distribution and pesticide accumulation on gentle slopes. These issues give rise to core technical bottlenecks such as low pesticide utilization rate, poor operational efficiency, and unclear atomization mechanism, hindering the optimization of pesticide application parameters, causing pesticide waste and environmental pollution, and restricting the sustainable development of the mountain fruit industry. To address this problem, this study designed a slope-classified pipeline layout and developed a high-efficiency fixed pipeline system for phytosanitary application in mountain orchards, featuring stable operation, low labor intensity, and easy intelligent transformation. Following the technical route of “theoretical design-atomization mechanism analysis-parameter optimization-laboratory verification-field application”, ruby nozzles with high wear resistance, uniform droplet distribution, and long service life were selected and optimized to meet the demand for long-term fixed pesticide application in mountain orchards. High-speed imaging technology was used to real-time capture the dynamic atomization process of nozzles, providing support for clarifying the atomization mechanism. Advanced methods such as fluorescence tracing were adopted to quantitatively evaluate key indicators including droplet deposition in canopies, and the system performance was verified through laboratory and field tests, laying a scientific foundation for its popularization and application. Field test results showed that the optimal spray pressure should not be less than 8 MPa. The XR9002 nozzle can generate fine droplets to achieve pesticide reduction while forming a stable hollow cone atomization flow. Fluorescence tracing analysis indicated that the droplet deposition on the adaxial leaf surface decreases with increasing altitude (presumably affected by wind speed), while the initial deposition on the abaxial leaf surface is low and shows no significant variation with altitude. Deposition on the adaxial leaf surface decreased with canopy height, while abaxial deposition was much lower (8.9–14.9%). This technology enables high-precision quantitative analysis of droplet deposition. The core innovations of this study are: clarifying the atomization mechanism of ruby high-pressure nozzles under pesticide application conditions in mountain orchards, constructing a slope-classified terrain-adaptive pipeline layout model, and establishing a closed-loop technical system of “atomization mechanism-pipeline layout-parameter optimization-deposition detection”. This study provides theoretical and technical support for green and precision pesticide application in mountain orchards, and has important academic value and broad application prospects for promoting the intelligent upgrading of the fruit industry in southern China. Full article

This paper introduces the Polynomial Perceptron (PP), a structured extension of the classical perceptron that incorporates explicit polynomial feature expansions to model nonlinear interactions while preserving analytical transparency. By expressing feature interactions in closed functional form, PP captures higher-order dependencies through a compact set of learned coefficients, establishing a principled trade-off between expressivity and parameter efficiency. The proposed architecture is evaluated across heterogeneous domains, including text, image, and structured data tasks, under controlled experimental settings with parameter-matched baselines. Performance is assessed using standard metrics such as classification accuracy and model complexity (parameter count). Empirical results demonstrate that low-degree PP models achieve competitive accuracy compared to multilayer perceptrons and convolutional neural networks, while requiring significantly fewer parameters. An ablation study further analyzes the impact of polynomial degree on predictive performance, revealing diminishing returns beyond moderate degrees and highlighting favorable efficiency–accuracy trade-offs. A key advantage of PP lies in its intrinsic interpretability. Unlike conventional deep learning models that rely on post hhoc explanation methods, PP provides direct analytical insight through its explicit polynomial structure, enabling decomposition of predictions into feature-, token-, or patch-level contributions without surrogate approximations. Overall, the results indicate that PP offers a lightweight, interpretable, and computationally efficient alternative to standard neural architectures, particularly well-suited for resource-constrained environments and applications where transparency is critical. Full article

In active debris removal missions in low Earth orbit, the semi-major axis difference between a service platform and its target can be large. Analytical relative dynamics models used in formation-flying applications typically retain only the first-order expansion in the orbital element differences; at large separations, the discarded higher-order terms—particularly the power-law dependence on the semi-major axis—introduce systematic along-track drift that degrades the propagation accuracy. This paper derives the power-law truncation correction, a closed-form additive vector that exactly compensates the truncated semi-major-axis power-law remainder, together with a consistent Jacobian correction for the extended Kalman filter covariance prediction. The state dimension and state transition matrix structure remain unchanged. Propagation tests over semi-major axis differences of 36–146 km yield ten-revolution terminal position errors of 0.008–0.065 km for the corrected models, compared with tens to hundreds of kilometers for the uncorrected first-order models and 0.1–8 km for the second-order state transition tensor. In 500-run Monte Carlo angles-only filtering experiments, the corrected filter reduces the median terminal position error by one to nearly three orders of magnitude relative to the uncorrected model. A process noise sensitivity study confirms robustness to calibration uncertainty across two orders of magnitude at a lower computational cost and with simpler implementation than higher-order tensor methods. Full article

To evaluate the coupled deformation of existing shield tunnels induced by multi-segment excavations with isolation piles, this study develops an integrated analytical framework combining a Kerr three-parameter foundation-plate model with a three-dimensional image-source solution. A closed-form expression for the soil displacement field is first derived by incorporating layered soil conditions, staged excavation, and associated spatial effects. The soil–pile interaction of isolation piles is then modeled using the Kerr foundation, and the flexural response is obtained through variational formulation and finite-difference discretization. These responses are sequentially propagated through the excavation stages, enabling the superposition of multi-pit effects on the final retaining-wall deformation. The image-source method and a volume-equivalent transformation are further used to convert wall deformation into an additional stress field acting on the tunnel, which is ultimately coupled with a tunnel–soil deformation–coordination model to compute horizontal tunnel displacements. This unified workflow establishes a continuous mechanical transfer chain—from excavation-induced soil loss to isolation-pile bending and finally tunnel deformation. Parametric analyses show that lateral displacement of the retaining structure is jointly governed by wall bending and pit-bottom uplift, producing a right-skewed “S-shaped’’ profile. The bending-moment peak shifts toward earlier-excavated zones, indicating a memory effect of excavation sequencing. Two engineering cases verify that the proposed method accurately reproduces the magnitude and depth of measured wall deflections, while predicted tunnel displacements show a near-Gaussian pattern with high accuracy near the peak. The analytical framework provides a robust theoretical basis for optimizing pit segmentation and excavation sequencing adjacent to shield tunnels. Full article

To address severe mine pressure disasters induced by the coupling of mining-induced dynamic stress and impact disturbance during close-distance coal seam mining, this paper takes the No. 8 and No. 9 close-distance coal seams in the 119 mining area of a coal mine in Ningxia, China, as the engineering background. Theoretical analysis and FLAC^3D numerical simulation methods were adopted to systematically study the evolution of overburden structure, the manifestation law of mine pressure caused by mining disturbance, and the dynamic response mechanism of roadway surrounding rock under impact load. The findings demonstrate: ① Based on key block theory and elasticity mechanics theory, the stress transfer mechanism of the complete bearing type overburden rock in close-range coal seams was clarified. The calculation model of floor plastic zone depth and additional stress was derived, and the influence mechanism of the bearing state of interlayer rock strata on the stability of underlying coal seam roadways was revealed. ② Comparative numerical simulations of mining schemes revealed that both schemes formed a “goaf pressure relief-workface-coal pillar” load-bearing configuration with “upward subsidence and downward bulging” basin-shaped settlement. Scheme A exhibited significantly increased stress peaks and interlayer plastic zones due to repeated mining-induced stress, substantially elevating the risk of strong mine pressure manifestation and surrounding rock instability. ③ Under 8 MPa cosine impact load with a vibration frequency of 50 Hz (peak particle vibration velocity of 9.57 m/s), compared with the unsupported roadway, the bolt–cable collaborative support system reduced the peak displacement of surrounding rock by over 35% and decreased the shock wave propagation velocity by more than 40%, effectively suppressing the expansion of plastic zones and the transfer of impact energy, while significantly enhancing the impact resistance of the roadway. This study not only provides a systematic theoretical basis for close-distance coal seam mining and rock burst prevention but also offers scientific guidance and technical reference for surrounding rock control and dynamic disaster prevention of roadways in similar close-distance coal seam mining projects, which is of important engineering value for ensuring the safe and efficient mining of underground coal resources. Full article

Accurate prediction of transient melt pool thermal fields in Laser Powder Bed Fusion (LPBF) is essential for understanding melt pool geometry and defect formation mechanisms, yet conventional finite element methods (FEM) impose prohibitive computational costs for parametric process exploration. A variational physics-informed neural network (VPINN) framework is presented for 3D transient thermal modeling of a GH3536 single-track LPBF scan. The framework incorporates a continuously differentiable Goldak double-ellipsoid moving heat source, temperature-dependent thermophysical property surrogates, and an effective heat-capacity treatment of latent heat associated with solid–liquid phase change and vaporization. These components are embedded in a weak-form residual-minimization scheme with octree-adaptive domain decomposition, hierarchical Legendre test functions, and sequential sliding-window time marching. Effective absorptivity is inferred jointly with the network parameters, using sparse experimental melt pool profiles as supervision. Within a parametric study covering laser powers from 100 to 140 W and scan speeds from 1000 to 1500 mm/s, the predicted melt pool width, depth, and aspect ratio agree closely with FEM benchmarks and cross-sectional optical micrograph measurements across both supervised and held-out interpolation conditions, with total relative L₂ nodal temperature errors ranging from 3.23% to 6.75%. Following a one-time offline training investment of 15,323 s that simultaneously resolves the full parametric space, surrogate inference reduces per-condition query time from 3000–4000 s (FEM) to merely 4–5 s, delivering a speedup of two to three orders of magnitude and making the framework increasingly cost-effective for high-throughput parametric studies and digital-twin integration as the number of queried conditions grows. Full article

Under the background of the Rural Revitalization Strategy, Zhejiang Province is promoting “Zhejiang-style Vernacular Dwellings” as a crucial measure to enhance the rural living environment and architectural appearance. However, traditional stylistic control tools, such as standardized rural housing design atlases, exhibit limitations including weak responsiveness to villagers’ individualized needs and high professional thresholds. Consequently, they struggle to address the bottlenecks in grassroots governance efficiency caused by massive and personalized housing demands. Meanwhile, when applied to architectural design, general generative AI technologies often suffer from “structural hallucinations” and the weakening of regional characteristics due to a lack of physical tectonic constraints. Oriented towards the governance requirements of the Zhejiang Provincial Rural Housing Design Guidelines, this study proposes a compliance evaluation-driven “Contour-Semantic-Image” hierarchical generative control framework. This aims to construct a visual scheme generation and pre-screening workflow that deeply adapts to the logic of rural governance. At the data level, this research aggregates multi-source materials, including official standardized atlases, government stylistic guidelines, and real-world photographs. Through expert screening and standardized processing of 596 schemes, a dataset of 333 high-quality, finely annotated structured samples is constructed. Furthermore, a human-guided, machine-segmented workflow assisted by Segment Anything Model 2 (SAM 2) is employed to establish a semantic label system comprising 4 major categories and 13 subcategories of components, thereby achieving the structural deconstruction of architectural prior knowledge. At the generation level, a two-stage model is trained based on Stable Diffusion and ControlNet: Stage I utilizes contour conditions and “layout prompts” to generate semantic label maps, aiming to strengthen component topology and layout consistency; Stage II employs the semantic label maps and “style prompts” as conditions to generate photorealistic facade images. By utilizing explicit semantic constraints to guide the model from pixel synthesis to logical generation, it achieves the controllable rendering of stylistic details and material expressions. At the evaluation level, an automated verification system featuring “clause translation–metric calculation–comprehensive scoring” is proposed. It conducts scoring, re-ranking, and diagnostic feedback on the generated variants across three dimensions: Design Rationality (Q), General Compliance (G), and Jiangnan water-town Regional Characteristics (P-J), forming a closed-loop “Generation-Evaluation-Feedback” workflow. Overall, this framework provides a “visualizable, evaluable, and explainable” pathway for scheme generation and pre-screening in the digital governance of rural architectural appearance. Full article

The Mittag-Leffler function holds significant importance in fractional calculus due to its extensive applications in addressing challenges across science, engineering, biology, hydrology, and earth sciences. Notably, the closed-form solution of a time-fractional model naturally emerges as the Mittag-Leffler function (MLF), necessitating precise and efficient computations. Consequently, numerical approximations are essential for accurately calculating the Mittag-Leffler function. In this study, we develop a straightforward yet precise real pole rational approximation for the Mittag-Leffler function. We demonstrate first-order convergence and L-acceptability, which aid in mitigating unwanted oscillations. Additionally, we create an effective and precise first-order generalized exponential time differencing scheme to solve the time-fractional reaction–diffusion equations. We obtain and prove the convergence result using Grönwall-type inequality. Several numerical experiments are conducted to confirm the efficiency and accuracy of the proposed numerical scheme compared with exact solutions. The computational efficiency of the proposed method is compared with another existing first-order numerical technique. Furthermore, our proposed scheme is crucial for developing higher-order predictor–corrector schemes for solving time-fractional models. Full article

This paper investigates duopoly competition under both constant and decreasing returns to scale in a market characterized by an isoelastic demand function, where firms adjust their strategies using a gradient adjustment mechanism. To establish the stability conditions of the model, we adopt different analytical approaches depending on the type of returns to scale. Under constant returns to scale, we employ a traditional approach by deriving the closed-form solution of the Nash equilibrium and analyzing the Jacobian matrix to verify whether the moduli of all eigenvalues are less than one. In contrast, under decreasing returns to scale, we analyze the local stability of the Nash equilibrium using symbolic computation methods without deriving a closed-form solution. The results show that when firms have heterogeneous costs, the model can exhibit both period-doubling and Neimark–Sacker bifurcations under both types of returns to scale. However, when costs are homogeneous, only period-doubling bifurcations occur. Numerical simulations support these analytical results and further demonstrate the emergence of complex dynamics, including chaotic behavior. Full article

In this review, the formation of the Oort Cloud is illuminated from several aspects. One is the history of the subject with an outline of the fundamental discoveries by Öpik, Oort and Hills. It is argued that the basic reason for judging Oort as the real discoverer is that he had access to observational data in the form of original orbits of long period comets. Further landmarks are identified, like the exploration of the role of the Galactic tide in the supply of observable comets by Heisler and Tremaine, the clarification of a synergy between tide and stars as the reason for a continued, efficient supply by Rickman et al., the discovery by Kaib and Quinn that inner core comets become observable due to planetary perturbations, disguised as new comets, and the demonstration of how Oort Cloud formation may work in the realm of the Nice Model by Brasser and Morbidelli. Further discussions refer to the possible role of the Grand Tack model in Oort Cloud formation and recent developments like Pan-STARRS in obtaining better data on very distant comets and Gaia in identifying stellar encounters in the close past and future with ensuing, important modifications of the Oort Cloud. It is finally argued that an important Galactic sculpting has occurred since the primordial Oort Cloud was formed by means of global shake-up events resulting from impulses imparted to the Sun by external perturbers like massive stars or Giant Molecular Clouds, and that this may be the real reason for the survival of an outer halo that reveals the existence of the Oort Cloud through the Oort spike. Full article

C. F. Hansen’s NASA TR R-50 published in 1959 remains one of the most widely used analytic approximations for the thermodynamic and transport properties of high-temperature air. Although modern equilibrium and nonequilibrium models extend the temperature range and species sets, Hansen’s expressions continue to provide a transparent, closed-form representation valuable for hypersonic aerothermodynamics, preliminary design, and code verification studies up to 15,000 K. In this work, we reconstruct the full Hansen model from his source equations, implement the formulation in a consistent modern notation, and derive all thermodynamic and transport quantities explicitly. The transport-property model developed by Hansen is discussed in comparison to research by Thompson et al., Gordon and McBride, and D’Angola et al. The resulting implementation provides a clean, analytic 7-species-air model for high-speed/hypersonic applications where rapid evaluations of thermodynamic and transport properties are required. Full article

Colmation phenomena play a critical role in long-term gas flow through porous media, significantly influencing methane migration, mine ventilation efficiency, and emission control in both active and abandoned coal mines. In colmation modeling, three fundamental kinetic types are commonly distinguished, with the third kinetic providing a generalized nonlinear formulation capable of describing state-dependent and spatially variable permeability degradation. However, the strong nonlinearity of the coupled transport–colmation equations prevents the derivation of closed-form solutions, which necessitates the application of linearization techniques. In this study, gas flow with colmation governed by third-kinetics is analyzed with particular emphasis on methane migration in underground mining environments. Linearization of nonlinear kinetic terms is applied at the level of the coupled mass balance and colmation equations, resulting in an approximate form of Darcy’s law and an explicit analytical solution describing the evolution of the porous medium state. The primary objective of the study is to quantify the error introduced by the adopted linearization and to analyze its spatial and temporal propagation with respect to the nonlinear reference solution. A rigorous error estimation based on Taylor series truncation is developed, yielding an explicit criterion that defines the validity range of the linearized solution. The results demonstrate that the approximation remains reliable within the regime of weak colmation, while the associated error is locally generated and propagates through transport mechanisms without exhibiting uncontrolled growth. Full article