Visible and near-infrared optics are widely used for non-destructive egg inspection, including detection of internal defects and assessment of freshness, fertility, and sex prediction during incubation. However, our insight in the measured signals remains limited because photons are strongly scattered in the egg shell and yolk and no quantitative data is available on the bulk optical properties (BOPs) of yolk and albumen. Therefore, wavelengthdependent BOPs of yolk (500-1000 nm) and albumen (600-1000 nm) were quantified in this study using double integrating sphere measurements combined with inverse adding doubling analysis. At 800 nm, yolk showed high attenuation (& micro; a = 0.014 mm - 1 , & micro; s = 5.350 mm -1 , g = 0.92), resulting from its high turbidity, whereas albumen remained weakly absorbing and weakly scattering (& micro; a = 0.006 mm -1 , & micro; s = 0.069 mm -1 , g = 0.90). Subsequently, the photon paths in intact eggs were revealed using Monte Carlo simulations in voxelized media (MCVM) combining the measured BOP of yolk and albumen with eggshell parameters at 800 nm obtained from literature. Simulated spatially resolved diffuse reflectance profiles agreed well with laser scatter measurements (R 2 = 0.91), supporting light-transport modeling in intact eggs. The simulations further indicated that photons interact with the yolk primarily near its surface, with negligible penetration to the yolk center. By linking measurable reflectance profiles to tissue-specific interaction depths, this framework provides a physically grounded interpretation of the photon distribution in intact eggs. Measurement of the wavelength-dependent BOP of eggshell beyond 800 nm is recommended to extend this work.
Given a family of graphs ℱ, a graph G is ℱ-saturated if it is ℱ-free but the addition of any missing edge creates a copy of some F ∈ℱ. The study of the minimum number of edges in ℱ-saturated graphs is a central topic in extremal graph theory. Let (p+1)K_2 denote a matching of size p+1. Determining the minimum number of edges in a (p+1)K_2-saturated graph is a fundamental question in this area, explicitly posed as Problem 9 in the survey by Faudree et al. (2011). In this paper, we refine the structural analysis of (p+1)K_2-saturated graphs and derive an explicit formula for the number of edges in terms of a single integer parameter. By minimizing this formula we determine sat(n,(p+1)K_2) for all n>2p, thereby resolving Problem 9 in full generality and extending earlier results of Kászonyi–Tuza (1986) and Zhang–Lu–Yu (2024). Moreover, by maximizing the same formula we recover the classical Erdős–Gallai (1959) upper bound on the number of edges in such graphs.
We determine the image force on an edge dislocation near a smooth closed cavity by combining traction-free boundary collocation with a displacement-circulation condition that selects the Volterra-cut sector. A circular-cavity benchmark reproduces independent analytical glide-force expressions for both bulk approach and release from the cavity: the largest absolute difference in normalized force at four tested positions in each sector is 3.3×10−6. For an equal-area family of rounded-square cavities, changing the corner-radius ratio from 0.05 to 0.35 gives median symmetric differences of 2.1% and 10.1% in the approach force along side- and corner-directed paths. The two cut sectors exert different forces at the same nominal cavity shape, dislocation position, and Burgers vector; the cavity-connected sector is more attractive in the cases examined. The same solution supplies direction-dependent continuum release thresholds under remote shear. A cutoff sweep from s0/R=0.10 to 0.20 preserves the opposing shape trends for the two paths while changing the threshold magnitudes. These results provide a benchmarked outer elastic force law and identify how cavity shape and cut connectivity enter reduced dislocation models.
Watercore is a physiological disorder that reduces fruit quality in durian, yet its underlying mechanism remains poorly understood. This study compared the tolerant cultivar ‘Monthong’ (MT) and the susceptible cultivar ‘Chanee’ (CN) to identify structural, physiological, biochemical, and molecular traits associated with watercore development. CN developed watercore symptoms earlier and reached nearly 100% incidence at the overripe stage, whereas MT exhibited only mild symptoms. These differences were not associated with fruit maturity, transpiration, fruit surface water uptake, or vascular structure. Instead, CN exhibited higher specific gravity and lower intercellular gas content in both the whole fruit and central axis, indicating smaller intercellular air spaces. Ripening was accompanied by greater accumulation of glucose, fructose, and total sugars in the central axis of CN than in MT, although these changes were not consistently associated with the expression of DzSUC2, DzN3, or DzCWINV1. Osmotically driven water uptake was evident following vacuum infiltration, whereas apoplastic soluble solids concentration did not differ between cultivars in healthy fruit. During watercore progression, only apoplastic fructose increased significantly with symptom severity. Membrane deterioration occurred only during advanced ripening. Collectively, these findings suggest that limited intercellular air space is the primary factor associated with watercore susceptibility, while ripening-associated changes in sugar composition may contribute to symptom development.
