Search Results (106)

To investigate the effects of freeze–thaw (F-T) action on the mechanical properties, pore structure, internal progressive damage evolution laws, and failure characteristics of initially damaged limestone, intact limestone specimens were subjected to different initial damage states and numbers of F-T cycles. Subsequently, the porosity and T₂ spectrum distribution of the specimens were tested using nuclear magnetic resonance (NMR). Finally, uniaxial compression tests were performed while monitoring the acoustic emission system. The test results showed that, as the number of F-T cycles increased or the initial degree of damage intensified, the peak strength of the limestone decreased, and the porosity increased. The higher the number of F-T cycles of limestone, the wider the distribution range of ringing counts in the middle and later stages of loading. As the number of F-T cycles increased, the proportion of tensile cracks in the limestone interior gradually increased and became dominant. The b-value evolution curves generally showed a sudden drop in the later loading stage. The damage variable of limestone did not show regular changes with an increase in the F-T cycles. This results from the superposition of the initial damage and the F-T cycles. Full article

Building information modeling (BIM)-based interior design automation remains constrained by a semantic mismatch: engineering constraints are explicit and categorical, whereas aesthetic style is implicit, contextual, and difficult to formalize. As a result, existing systems often overfit local visual similarity or rely on rigid rules, producing recommendations that drift stylistically at the scene level or conflict with professional design logic. This paper proposes KsDesign, a neuro-symbolic framework for interpretable, retrieval-based BIM scene completion that unifies visual style perception with explicit design knowledge. Offline, KsDesign mines category-level co-occurrence and compatibility patterns from curated designer-quality interiors and encodes them as a weighted Furniture-Matching Knowledge Graph (FMKG). Online, it learns style representations exclusively from BIM-derived 2D renderings/projections of 3D family models and BIM scenes, and applies a knowledge-guided attention mechanism to weight contextual furniture cues, synthesizing a global scene-style representation for candidate ranking and retrieval. In a Top-3 (K = 3) evaluation on 10 BIM test scenes with a 20-expert consensus ground truth, KsDesign consistently outperforms single-modal baselines, achieving 86.7% precision in complex scenes and improving average precision by 23.5% (up to 40%), with a 15.5% average recall increase. These results suggest that global semantic constraints can serve as a logical regularizer, mitigating the local biases of purely visual matching and yielding configurations that are both aesthetically coherent and logically valid. We further implement in-authoring explainability within Revit, exposing KG-derived influence weights and evidence paths to support rationale inspection and immediate family insertion. Finally, the knowledge priors and traceable intermediate representations provide a robust substrate for integration with LLM-driven conversational design agents, enabling constraint-aware, verifiable generation and interactive iteration. Full article

This work explores late-time gravitational collapse using timelike thin-shell methods in classical general relativity. A junction surface separates a regular de Sitter interior from a Schwarzschild or Schwarzschild–de Sitter exterior in a post-transient regime with fixed exterior mass M (ADM for ${\mathrm{\Lambda }}_{+}=0$), modelling a vacuum–energy core surrounded by an asymptotically classical spacetime. The configuration admits a natural thermodynamic interpretation based on a geometric area functional $S_{\mathrm{shell}}\propto R^2$ and Tolman redshift, both derived from classical junction conditions and used as an entropy-like coarse-grained quantity rather than a fundamental statistical entropy. Key results include (i) identification of a deceleration mechanism at the balance radius $R_{\mathrm{thr}}={(3M/{\mathrm{\Lambda }}_{-})}^{1/3}$ for linear surface equations of state $p=w\sigma$; (ii) classification of the allowable radial domain $V\left(R\right)\le 0$ for outward evolution; (iii) bounded curvature invariants throughout the shell-supported spacetime region; and (iv) a mass-scaled frequency bound $f_c{R}_S\le \xi /\left(3\sqrt{3}\pi \right)$ for persistent near-shell spectral modes. All predictions follow from standard Israel junction techniques and provide concrete observational tests. The framework offers an analytically tractable example of regular thin-shell collapse dynamics within classical general relativity, with implications for alternative compact object scenarios. Full article

The AC Optimal Power Flow (AC-OPF) problem remains a major computational bottleneck for real-time power system operation. Conventional solvers are accurate but time-consuming, while Graph Neural Networks (GNNs) offer faster approximations yet struggle to capture long-range dependencies and handle topological variations. To address these limitations, we propose a Heterogeneous Graph Transformer with bus-centric Local–Global Message Passing (LG-HGNN). The model performs type-specific local message passing over heterogeneous power graphs and applies a global Transformer only on bus nodes to capture system-wide correlations efficiently. Effective-resistance positional encodings and resistance-biased attention enhance electrical awareness, whereas bounded decoders and physics-informed regularization preserve operational feasibility. Experiments on IEEE 14-, 30-, and 118-bus systems show that LG-HGNN achieves near-optimal results within a few percent of the AC-OPF optimum and generalizes to thousands of unseen N-1 contingency topologies without retraining. Compared with interior-point solvers, it attains up to $190\times$ speedup before power-flow correction and over $10\times$ afterward on GOC 2000-bus systems, providing a scalable and physically consistent surrogate for real-time AC-OPF. Full article

This work develops and systematically evaluates a physics-informed neural network (PINN) solver for the fully coupled, time-dependent Muskat–Leverett system with capillarity modeled in the pressure equation. A single shallow–wide multilayer perceptron jointly predicts wetting pressure and water saturation; physical capillary pressure regularizes the saturation front, while a small numerical diffusion term in the saturation residual acts as a training stabilizer rather than a shock-capturing device. To guarantee admissible states in stiff regimes, we introduce a saturation soft-clamping head enforcing $0<{\mathrm{S}}_{\mathrm{w}}<1$ and activate it selectively for stiff mobility ratios. Using IMPES solutions as reference, we perform a sensitivity study over network depth and width, interior collocation and boundary data density, mobility ratio, and injection pressure. Shallow-wide networks (10 layers × 50 neurons) consistently outperform deeper architectures, and increasing interior collocation points from 5000 to 50,000 reduces mean saturation error by about half, whereas additional boundary data have a much weaker effect. Accuracy is highest at an intermediate mobility ratio and improves monotonically with higher injection pressure, which sharpens yet better conditions the front. Across all regimes, pressure trains easily while saturation determines model selection, and the PINN serves as a physics-consistent surrogate for what-if studies in two-phase porous-media flow. Full article

Protein and nucleic acid play central roles in biology and pharmaceuticals. Both share a similar architecture made of a backbone and side chains. Protein has a peptide backbone and various side chains, whereas nucleic acid has a phosphate backbone and aromatic side chains. However, they are significantly different in the chemical properties of the backbone and side chains. The protein backbone is uncharged, while nucleic acid backbone is negatively charged. The protein side chains comprise widely different chemical properties. On the other hand, the nucleic acid side chains comprise a uniform chemical property of aromatic bases. Such differences lead to fundamentally different folding, molecular interactions and co-solvent interactions, which are the focus of this review. In regular protein secondary structures, the peptide groups form polar hydrogen bonds, making the interior hydrophilic. The side chains of different chemical properties are exposed on the outside of the protein secondary structures and participate in molecular and co-solvent interactions. On the other hand, hydrophobic/aromatic nucleobase side chains are located inside the typical double helix or quadruplex structures. The charged phosphate groups of the nucleic acid backbone are located outside, participating in electrostatic interactions. The nucleobases are also involved in molecular interactions, when exposed in breaks, hairpins, kinks and loops. These structural differences between protein and nucleic acid confer different interactions with commonly used co-solvents, such as denaturants, organic solvents and polymers. Full article

We present a head-to-head evaluation of the Improved Inexact–Newton–Smart (INS) algorithm against a primal–dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method converges with roughly one-third fewer iterations and about one-half the computation time relative to INS, while attaining marginally higher accuracy and meeting all primary stopping conditions. By contrast, INS succeeds in fewer cases under default settings but benefits markedly from moderate regularization and step-length control; in tuned regimes, its iteration count and runtime decrease substantially, narrowing yet not closing the gap. A sensitivity study indicates that interior-point performance remains stable across parameter changes, whereas INS is more affected by step length and regularization choice. Collectively, the evidence positions the interior-point method as a reliable baseline and INS as a configurable alternative when problem structure favors adaptive regularization. Full article

We study a finite-horizon optimal consumption and investment problem in a complete continuous-time market where consumption is restricted within fixed upper and lower bounds. Assuming constant relative risk aversion (CRRA) preferences, we employ the dual-martingale approach to reformulate the problem and derive closed-form integral representations for the dual value function and its derivatives. These results yield explicit feedback formulas for the optimal consumption, portfolio allocation, and wealth processes. We establish the duality theorem linking the primal and dual value functions and verify the regularity and convexity properties of the dual solution. Our results show that the upper and lower consumption bounds transform the linear Merton rule into a piecewise policy: consumption equals L when wealth is low, follows the unconstrained Merton ratio in the interior region, and is capped at H when wealth is high. Full article

We study compactness for the complex Green operator ${\mathsf{G}}_q$ associated with the Kohn Laplacian ${\square }_b$ on boundaries of pseudoconvex domains in Stein manifolds. Let $\Omega ⋐X$ be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n with $C^1$ boundary. For $1\le q\le n-2$, we first prove a compactness theorem under weak potential-theoretic hypotheses: if $b\Omega$ satisfies weak $\left({\mathcal{P}}_q\right)$ and weak $\left({\mathcal{P}}_{n-1-q}\right)$, then ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$ are compact on ${\mathsf{L}}_{p,q}^2\left(b\Omega \right)$. This extends known $C^{\infty }$ results in ${\mathbb{C}}^n$ to the minimal regularity $C^1$ and to the Stein setting. On locally convexifiable $C^1$ boundaries, we obtain a full characterization: compactness of ${\mathsf{G}}_q$ is equivalent to simultaneous compactness of ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$, to compactness of the $\overline{\partial }$-Neumann operators ${\mathsf{N}}_q$ and ${\mathsf{N}}_{n-1-q}$ in the interior, to weak $\left({\mathcal{P}}_q\right)$ and $\left({\mathcal{P}}_{n-1-q}\right)$, and to the absence of (germs of) complex varieties of dimensions q and $n-1-q$ on $b\Omega$. A key ingredient is an annulus compactness transfer on ${\Omega }_{+}={\Omega }_2\setminus \overline{{\Omega }_1}$, which yields compactness of ${\mathsf{N}}_q^{{\Omega }_{+}}$ from weak $\left(\mathcal{P}\right)$ near each boundary component and allows us to build compact ${\overline{\partial }}_b$-solution operators via jump formulas. Consequences include the following: compact canonical solution operators for ${\overline{\partial }}_b$, compact resolvent for ${\square }_b$ on the orthogonal complement of its harmonic space (hence discrete spectrum and finite-dimensional harmonic forms), equivalence between compactness and standard compactness estimates, closed range and ${\mathsf{L}}^2$ Hodge decompositions, trace-class heat flow, stability under $C^1$ boundary perturbations, vanishing essential norms, Sobolev mapping (and gains under subellipticity), and compactness of Bergman-type commutators when $q=1$. Full article

Accurate volumetric modeling of indoor spaces is essential for emerging 3D cadastral systems, yet existing workflows often rely on manual intervention or produce surface-only models, limiting precision and scalability. This study proposes and validates an integrated, largely automated workflow (named VERTICAL) that converts classified indoor point clouds into topologically consistent 3D solids served as materials for land surveyor’s cadastral analysis. The approach sequentially combines RANSAC-based plane detection, polygonal mesh reconstruction, mesh optimization stage that merges coplanar faces, repairs non-manifold edges, and regularizes boundaries and planar faces prior to CAD-based solid generation, ensuring closed and geometrically valid solids. These modules are linked through a modular prototype (called P2M) with a web-based interface and parameterized batch processing. The workflow was tested on two condominium datasets representing a range of spatial complexities, from simple orthogonal rooms to irregular interiors with multiple ceiling levels, sloped roofs, and internal columns. Qualitative evaluation ensured visual plausibility, while quantitative assessment against survey-grade reference models measured geometric fidelity. Across eight representative rooms, models meeting qualitative criteria achieved accuracies exceeding 97% for key metrics including surface area, volume, and ceiling geometry, with a height RMSE around 0.01 m. Compared with existing automated modeling solutions, the proposed workflow has the ability of dealing with complex geometries and has comparable accuracy results. These results demonstrate the workflow’s capability to produce topologically consistent solids with high geometric accuracy, supporting both boundary delineation and volume calculation. The modular, interoperable design enables integration with CAD environments, offering a practical pathway toward an automated and reliable core of 3D modeling for cadastre applications. Full article

The paper investigates the regularization of solutions to nonlinear Volterra integral equations of the first kind, under the assumption that a solution exists and belongs to the space of continuous functions. The kernel of the equation is a differentiable function and vanishes on the diagonal at an interior point of the integration interval. By applying an appropriate differential operator (with respect to x), the Volterra integral equation of the first kind is reduced to a Volterra integral equation of the third kind, equivalent with respect to solvability. The subdomain method is employed by partitioning the integration interval into two subintervals. Within the imposed constraints, a compatibility condition for the solutions is satisfied at the junction point of the partial subintervals. A Lavrentiev-type regularizing operator is constructed that preserves the Volterra structure of the equation. The uniform convergence of the regularized solution to the exact solution is proved, and conditions ensuring the uniqueness of the solution in Hölder space are established. Full article

Motivation. Analytic function theory on commutative complex extensions calls for an operator–theoretic calculus that simultaneously sees the algebra-induced coupling among components and supports boundary-to-interior mechanisms. Gap. While Dirac-type frameworks are classical in several complex variables and Clifford analysis, a coherent calculus aligning structural CR systems, a canonical first derivative, and a Cauchy-type boundary identity on the commutative model $\mathbb{C}\left(\mathbb{C}\right)\cong {\mathbb{C}}^4$ has not been systematically developed. Purpose and Aims. This paper develops such a calculus for $\mathcal{O}$-regular mappings on $\mathbb{C}\left(\mathbb{C}\right)$ and establishes three pillars of the theory. Main Results. (i) A fully coupled Cauchy–Riemann system characterizing $\mathcal{O}$-regularity; (ii) identification of a canonical first derivative $g^{\prime }\left(z\right)={\partial }_{x_0}g\left(z\right)$; and (iii) a Stokes-driven boundary annihilation law ${\int }_{\partial \mathrm{\Omega }}\tau g=0$ for a canonical 7-form $\tau$. On (pseudo)convex domains, $\overline{\partial }$-methods yield solvability under natural compatibility and regularity assumptions. Stability (under algebra-preserving maps), Liouville-type, and removability results are also obtained, and function spaces suited to this algebra are outlined. Significance. The results show that a large portion of the classical holomorphic toolkit survives, in algebra-aware form, on $\mathbb{C}\left(\mathbb{C}\right)$. Full article

The hydrodynamic response of closed and semi-closed (open-bottom) rigid cylindrical aquaculture platforms was examined through combined model tests and numerical simulations. Free decay tests in calm water quantified natural periods and damping ratios for heave and pitch motions. Subsequent regular wave testing characterized response amplitude operators (RAOs) and wave elevations at interior and exterior wave gauges. Finally, the motion and wave elevation characteristics of the two types of aquaculture platforms under irregular waves were analyzed under extreme sea conditions. Results demonstrated that bottom openings significantly altered hydrodynamic responses of aquaculture platforms, with a 59% enhancement in heave damping ratio and a 47% reduction in heave natural period. Semi-closed cages exhibited asymmetric internal sloshing profiles along the mid-transverse axis, with lateral sloshing amplitudes increasing by 200–300% at lateral wave gauges. Under irregular wave conditions, compared to closed aquaculture platform, semi-closed aquaculture platform increased the heave, pitch motion, and internal sloshing response but reduced run-up on the outer wave-facing side. Full article

Beyond its renowned gemological value, diamond serves as a vital economic mineral and a unique messenger from Earth’s deep interior, preserving invaluable geological information. Since the Mengyin region is the source of China’s greatest diamond deposits, research on the diamonds there not only adds to our understanding of their origins but also offers an essential glimpse into the development of the North China Craton’s mantle lithosphere. In this article, 50 diamond samples from Mengyin were investigated using gemological microscopy, Fourier-transform infrared (FTIR) spectroscopy, Raman spectroscopy, DiamondView™, and X-ray micro-computed tomography (CT) scanning technologies. The types of Mengyin diamonds are mainly Type IaAB, Type IaB, and Type IIa, and the impurity elements are N and H. Inclusions in diamonds serve as direct indicators of mantle-derived components, providing crucial constraints on the pressure–temperature (P–T) conditions during their crystallization. Mengyin diamonds have both eclogite-type and peridotite-type inclusions. It formed at depths ranging from 147 to 176 km, which corresponds to source pressures of approximately 4.45–5.35 GPa, as determined by the Raman shifts of olivine inclusions. The discovery of coesite provides key mineralogical evidence for subduction of an ancient oceanic plate in the source region. The surface morphology of diamonds varies when they are reabsorbed by melts from the mantle, reflecting distinctive features that record subsequent geological events. Distinctive surface features observed on Mengyin diamonds include fusion pits, tile-like etch patterns, and growth steps. Specifically, regular flat-bottomed negative trigons are mainly formed during diamond resorption in kimberlite melts with a low CO₂ (X_CO2 < ~0.5) and high H₂O content. The samples exhibit varying fluorescence under DiamondView™, displaying blue, green, and a combination of blue and green colors. This diversity indicates that the diamonds have undergone a complex process of non-uniform growth. The nitrogen content of the melt composition also varies significantly throughout the different growth stages. The N3 center is responsible for the blue fluorescence, suggesting that it originated in a long-term, hot, high-nitrogen craton, and the varied ring band structure reveals localized, episodic environmental variations. Radiation and medium-temperature annealing produce H3 centers, which depict stagnation throughout the ascent of kimberlite magma and are responsible for the green fluorescence. Full article

In this paper, we propose a class of elementary plane geometry problems closely related to the title of this paper. Here, a circle is the one-dimensional curve bounding a disk. For any non-negative integer, a circle is called n-enclosing if it contains exactly n lattice points on the $xy$-plane in its interior. In this paper, we are mainly interested in when the largest n-enclosing circle exists and what the largest radius is. We study the small integer cases by hand and extend to all $n<1100$ with the aid of a computer. We find that frequently such a circle does not exist, e.g., when $n=5,6$. We then show a few general results on these circles including some regularities among their radii and an easy criterion to determine exactly when the largest n-enclosing circles exist. Further, from numerical evidence, we conjecture that the set of integers whose largest enclosing circles exist is infinite, and so is its complementary in the set of non-negative integers. Throughout this paper, we present more mysteries/problems/conjectures than answers/solutions/theorems. In particular, we list many conjectures and some unsolved problems including possible higher-dimensional generalizations at the end of the last two sections. Full article