Search Results (523)

Nucleobases play diverse structural and functional roles in biological systems. Understanding the fundamental properties of nucleobases is important for their applications as chemical probes of nucleic acid function. As the nucleobases are modified to tune their fluorescence or binding properties, their physical properties such as pK_a may also change. Unlike the canonical nucleobases, modified nucleobases are less well understood in terms of their acid-base properties. Previously, theoretical pK_a values of canonical, naturally modified, and aza-/deaza-modified nucleobases were determined. In this study, the theoretical pK_a values for 25 different fluorescent modified nucleobases (55 total pK_a values) were calculated by using an ab initio quantum mechanical method employing the B3LYP density functional with 6-31+G(d,p) basis set along with an implicit–explicit solvation model. The results of these computations are compared to known experimental pK_a values. The ability to estimate theoretical pK_a values will be beneficial for further development and applications of fluorescent nucleobases. Full article

The availability of accurate models capturing the realistic behaviour of complex systems is critical for the safe operation and optimal management of nuclear installations. However, the dynamic nature of such systems and the resulting dense network of interdependencies existing among their parts are no match for current risk modelling techniques, which rely on oversimplifying premises. Dependencies are often simplified or ignored, with conservative assumptions introduced to compensate, leading to results of uncertain realism. Alternative methods address these limitations but often remain difficult to scale, interpret, or integrate into established Probabilistic Safety Assessment practice. The Dynamic and Dependent Tree Theory ($D^2{T}^2$) offers a bridging framework that preserves the familiar FT/ET structure while enabling dependencies to be represented directly at the basic-event, intermediate, or subsystem level through compact submodels. This paper applies $D^2{T}^2$ to a loss of main feed water accident in a boiling water reactor, capturing dependencies from maintenance strategies to subsystem interactions. Results show that $D^2{T}^2$ improves reliability predictions compared with conventional FT/ET, aligns closely with dynamic benchmarks, and remains computationally tractable. Beyond accuracy, the approach makes modelling assumptions explicit and transparent, promoting deeper system understanding while lowering barriers to adoption in safety-critical applications. Full article

We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic ($\mathrm{sech}/\tanh$), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons (bright and dark) arose as limiting cases of the elliptic solutions. We specified the parameter regimes that produced each profile and illustrated representative solutions with 2D/3D plots to highlight symmetry. The results provide a unified, reproducible procedure for generating solitary and periodic DGH waves and expand the catalog of exact solutions for this model. Full article

The DuFort–Frankel scheme was introduced in the 1950s to solve parabolic equations, and has been widely used ever since due to its stability and explicit nature. However, for over seven decades, its application has been limited to Cartesian grids. In this work, we propose a generalization of the DuFort–Frankel scheme that could be applied to arbitrary unstructured grids. Specifically, we focus on Voronoi grids in both 2D and 3D, and use the finite volume method for spatial discretization. Additionally, we present a proof of its stability based on the analysis of the spectrum of the amplification matrix, along with numerical examples. Full article

In this paper, we investigate the behavior of solutions to a nonlinear system of rational difference equations of order two, defined by $x_{n+1}={\displaystyle \frac{x_n{y}_{n-1}}{y_n(a+b{x}_n{y}_{n-1})}},y_{n+1}={\displaystyle \frac{y_n{z}_{n-1}}{z_n(c+d{y}_n{z}_{n-1})}},z_{n+1}={\displaystyle \frac{z_n{x}_{n-1}}{x_n(e+f{z}_n{x}_{n-1})}},$ where n denotes a nonzero integer; the parameters $a,b,c,d,e,f$ are real constants; and the initial conditions $x_{-1},x_0,y_{-1},y_0,z_{-1},z_0$ are nonzero real numbers. By applying a suitable variable transformation, we reduce the original coupled system to three independent rational difference equations. This allows for separate analysis using established methods for second-order nonlinear recurrence relations. We derive explicit solutions and examine the qualitative behavior, including boundedness and periodicity, under different conditions. Our findings contribute to the theory of rational difference equations and offer insights for higher-order systems in applied sciences. Full article

This study quantifies the influence of soil–structure interaction (SSI) on key parameters of performance-based seismic design (PBSD) for steel moment-resisting frames. Specifically, PBSD is extended as a methodology in which explicit structural performance levels, such as immediate occupancy, damage limitation, life safety, and collapse prevention, serve as the basis for sizing and detailing structural members under specified seismic hazard levels, instead of traditional force-based design. The PBSD framework is further developed to incorporate SSI by adopting a beam on a nonlinear Winkler foundation model. This model captures the nonlinear soil response and its interaction with the structure, enabling a more realistic design framework within a performance-based context. To evaluate and quantify the influence of SSI in the PBSD method, an extensive parametric study is performed using 100 far-field ground motions, categorized into four groups (25 records each) corresponding to EC8 soil types A, B, C, and D. Nonlinear time history analyses reveal consistent trends across the examined frames. When SSI is neglected, the fundamental natural period (T) is systematically underestimated by approximately up to 3.5% on EC8 soil type C and up to 15% on soil type D. As a result, the base shear and the mean values of maximum interstorey drift ratios (IDRs) are overestimated compared to cases accounting for soil flexibility, with the largest drift discrepancies observed in frames with eight or more storeys on soil D. The analyses further reveal that softer soils (e.g., Soil D) lead to significantly higher q values, particularly for moderate-to-long period structures, whereas stiffer soils (e.g., Soil B) cause only minor deviations, remaining close to fixed-base values. A complementary machine learning module, trained on the same dataset, is employed to predict base shear, maximum IDR, and the behavior factor q. It successfully reproduces the deterministic SSI trends, achieving coefficients of determination (R²) ranging from 0.986 to 0.992 for maximum IDR, 0.947 to 0.948 for base shear, and 0.944 to 0.952 for q. Feature importance analysis highlights beam and column ductility, soil class, and performance level as the most influential predictors of structural response. Full article

As vehicle-centric perception struggles with occlusion and dense traffic, vehicle-infrastructure cooperative perception (VICP) offers a viable route to extend sensing coverage and robustness. This study proposes a feature-level VICP framework that fuses vehicle- and roadside-derived visual features via V2X communication. The model integrates four components: regional feature reconstruction (RFR) for transferring region-specific roadside cues, context-driven channel attention (CDCA) for channel recalibration, uncertainty-weighted fusion (UWF) for confidence-guided weighting, and point sampling voxel fusion (PSVF) for efficient alignment. Evaluated on the DAIR-V2X-C benchmark, our method consistently outperforms state-of-the-art feature-level fusion baselines, achieving improved ${AP}_{3D}$ and ${AP}_{BEV}$ (reported settings: 16.31% and 21.49%, respectively). Ablations show RFR provides the largest single-module gain +3.27% ${AP}_{3D}$ and +3.85% ${AP}_{BEV}$, UWF yields substantial robustness gains, and CDCA offers modest calibration benefits. The framework enhances occlusion handling and cross-view detection while reducing dependence on explicit camera calibration, supporting more generalizable cooperative perception. Full article

This paper investigates D-finite discrete generating series and their sections. The concept of D-finiteness is extended to multidimensional discrete generating series and its equivalence to p-recursive sequences is rigorously established. It is further shown that sections of the D-finite series preserve D-finiteness, and that their generating functions satisfy systems of linear difference equations with polynomial coefficients. In the two-dimensional case, explicit difference relations are derived that connect section values with boundary data, while in higher dimensions general constructive methods are developed for obtaining such relations, including cases with variable coefficients. Several worked examples illustrate how the theory applies to solving difference equations and analyzing multidimensional recurrent sequences. The results provide a unified framework linking generating functions and recurrence relations, with applications in combinatorics, number theory, symbolic summation, and the theory of discrete recursive filters in signal processing. Full article

We propose a GPU-parallelized collision-detection and response framework for rigid-body dynamics, designed to efficiently handle densely populated 3D simulations in real time. The method combines explicit Euler time integration with a hierarchical Octree–AABB collision-detection scheme, enabling early pruning and localized refinement of contact checks. To resolve collisions, we employ a two-step response algorithm that integrates non-penetration correction and impulse-based velocity updates, stabilized through smoothing, clamping, and bias mechanisms. The framework is fully implemented within Unity3D using compute shaders and optimized GPU kernels. Experiments across multiple mesh models and increasing object counts demonstrate that the proposed hierarchical configuration significantly improves scalability and frame stability compared to conventional flat AABB methods. In particular, a two-level hierarchy achieves the best trade-off between spatial resolution and computational cost, maintaining interactive frame rates (≥30 fps) under high-density scenarios. These results suggest the practical applicability of our method to real-time simulation systems involving complex collision dynamics. Full article

This study compares enhanced turbulence models in a natural river channel 3D simulation under extreme hydrometeorological conditions. Using ANSYS Fluent 2024 R1 and the Volume of Fluid scheme, five RANS closures were evaluated: realizable k–ε, Renormalization-Group k–ε, Shear Stress Transport k–ω, Generalized k–ω, and Baseline-Explicit Algebraic Reynolds Stress model. A segment of the Santa Catarina River in Monterrey, Mexico, defined the computational domain, which produced high-energy, non-repeatable real-world flow conditions where hydrometric data were not yet available. Empirical validation was conducted using surface velocity estimations obtained through high-resolution video analysis. Systematic bias was minimized through mesh-independent validation (<1% error) and a benchmarked reference closure, ensuring a fair basis for inter-model comparison. All models were realized on a validated polyhedral mesh with consistent boundary conditions, evaluating performance in terms of mean velocity, turbulent viscosity, strain rate, and vorticity. Mean velocity predictions matched the empirical value of 4.43 [m/s]. The Baseline model offered the highest overall fidelity in turbulent viscosity structure (up to 43 [kg/m·s]) and anisotropy representation. Simulation runtimes ranged from 10 to 16 h, reflecting a computational cost that increases with model complexity but justified by improved flow anisotropy representation. Results show that all models yielded similar mean flow predictions within a narrow error margin. However, they differed notably in resolving low-velocity zones, turbulence intensity, and anisotropy within a purely hydrodynamic framework that does not include sediment transport. Full article

The rapid and reliable acquisition of canopy-related metrics is essential for improving decision support in viticultural management, particularly when monitoring individual vines for targeted interventions. This study presents a spatially explicit workflow that integrates Uncrewed Aerial System (UAS) imagery, 3D point-cloud analysis, and Object-Based Image Analysis (OBIA) to detect and monitor individual grapevines throughout the growing season. Vines are identified directly from 3D point clouds without the need for prior training data or predefined row structures, achieving a mean Euclidean distance of 10.7 cm to the reference points. The OBIA framework segments vine vegetation based on spectral and geometric features without requiring pre-clipping or manual masking. All non-vine elements—including soil, grass, and infrastructure—are automatically excluded, and detailed canopy masks are created for each plant. Vegetation indices are computed exclusively from vine canopy objects, ensuring that soil signals and internal canopy gaps do not bias the results. This enables accurate per-vine assessment of vigour. NDRE values were calculated at three phenological stages—flowering, veraison, and harvest—and analyzed using Local Indicators of Spatial Association (LISA) to detect spatial clusters and outliers. In contrast to value-based clustering methods, LISA accounts for spatial continuity and neighborhood effects, allowing the detection of stable low-vigour zones, expanding high-vigour clusters, and early identification of isolated stressed vines. A strong correlation (R² = 0.73) between per-vine NDRE values and actual yield demonstrates that NDRE-derived vigour reliably reflects vine productivity. The method provides a transferable, data-driven framework for site-specific vineyard management, enabling timely interventions at the individual plant level before stress propagates spatially. Full article

Background: Emergency laparotomy (EL) carries high morbidity and mortality relative to elective abdominal surgery. While Enhanced Recovery After Surgery (ERAS) principles improve outcomes in elective care, their translation to emergencies is inconsistent. The emergency department (ED) provides a window for rapid risk stratification and pre-optimization, provided that interventions do not delay definitive surgery. Methods: We conducted a PRISMA-ScR–conformant scoping review to map ED-initiated, ERAS-aligned strategies for EL. PubMed, Scopus, and Cochrane were searched in February 2025. Eligible sources comprised ERAS guidelines, systematic reviews, cohort studies, consensus statements, and programmatic reports. Evidence was charted across five a priori domains: (i) ERAS standards, (ii) comparative effectiveness, (iii) ED-feasible pre-optimization, (iv) risk stratification (Emergency Surgery Score [ESS], frailty, sarcopenia), and (v) oncological emergencies. Results: Thirty-four sources met inclusion. ERAS guidelines codify rapid assessment, multimodal intraoperative care, and early postoperative rehabilitation under a strict no-delay rule. Meta-analysis and cohort data suggest ERAS-aligned pathways reduce complications and length of stay, though heterogeneity persists. ED-feasible measures include multimodal analgesia, goal-directed fluids, early safe nutrition, respiratory preparation, and anemia/micronutrient optimization (IV iron, vitamin B12, folate, vitamin D). Sarcopenia, frailty, and ESS consistently predicted adverse outcomes, supporting targeted bundle activation. Evidence from oncological emergencies indicates feasibility under no-delay governance. Conclusions: A minimal, ED-initiated, ERAS-aligned bundle is feasible, guideline-concordant, and may shorten hospitalization and reduce complications in EL. We propose a practical framework that links rapid risk stratification, opportunistic pre-optimization, and explicit continuity into intra- and postoperative care; future studies should test fidelity, costs, and outcome impact in pragmatic emergency pathways. Full article

This study develops a stochastic SIQR epidemic model with mean-reverting Ornstein–Uhlenbeck (OU) processes for both transmission rate $\beta \left(t\right)$ and quarantine release rate $k\left(t\right)$; this is distinct from existing non-white-noise stochastic epidemic models, most of which focus on single-parameter perturbation or only stability analysis. It synchronously embeds OU dynamics into two core epidemic parameters to capture asynchronous fluctuations between infection spread and control measures. It adopts a rare measure solution framework to derive rigorous infection extinction conditions, linking OU’s ergodicity to long-term ${\beta }^{+}\left(t\right)$ averages. It obtains the explicit probability density function of the four-dimensional SIQR system, filling the gap of lacking quantifiable density dynamics in prior studies. Simulations validate that $R_0^d<1$ ensures almost sure extinction, while $R_0^e>1$ leads to stable stochastic persistence. Full article

According to a clever but rarely quoted or acknowledged work of E. Vessiot that won the prize of the Académie des Sciences in 1904, “Differential Galois Theory” (DGT) has mainly to do with the study of “Principal Homogeneous Spaces” (PHSs) for finite groups (classical Galois theory), algebraic groups (Picard–Vessiot theory) and algebraic pseudogroups (Drach–Vessiot theory). The corresponding automorphic differential extensions are such that $di{m}_K\left(L\right)=\mid L/K\mid <\infty$, the transcendence degree $trd(L/K)<\infty$ and $trd(L/K)=\infty$ with $difftrd(L/K)<\infty$, respectively. The purpose of this paper is to mix differential algebra, differential geometry and algebraic geometry to revisit DGT, pointing out the deep confusion between prime differential ideals (defined by J.-F. Ritt in 1930) and maximal ideals that has been spoiling the works of Vessiot, Drach, Kolchin and all followers. In particular, we utilize Hopf algebras to investigate the structure of the algebraic Lie pseudogroups involved, specifically those defined by systems of algebraic OD or PD equations. Many explicit examples are presented for the first time to illustrate these results, particularly through the study of the Hamilton–Jacobi equation in analytical mechanics. This paper also pays tribute to Prof. A. Bialynicki-Birula (BB) on the occasion of his recent death in April 2021 at the age of 90 years old. His main idea has been to notice that an algebraic group G acting on itself is the simplest example of a PHS. If G is connected and defined over a field K, we may introduce the algebraic extension $L=K\left(G\right)$; then, there is a Galois correspondence between the intermediate fields $K\subset K^{\prime }\subset L$ and the subgroups $e\subset G^{\prime }\subset G$, provided that $K^{\prime }$ is stable under a Lie algebra $\Delta$ of invariant derivations of $L/K$. Our purpose is to extend this result from algebraic groups to algebraic pseudogroups without using group parameters in any way. To the best of the author’s knowledge, algebraic Lie pseudogroups have never been introduced by people dealing with DGT in the spirit of Kolchin; that is, they have only been considered with systems of ordinary differential (OD) equations, but never with systems of partial differential (PD) equations. Full article

Virtual experiments (VE) can be used to assess the measurement uncertainty of complex measurements. The typical calculation procedure implemented in such a VE, called VE-DA in this paper, is based on a Monte Carlo method involving simulating possible measurement errors and possible measurement data based on extensive modeling of the measurement instrument, followed by applying a data analysis function (DA) to evaluate the measurement data. This procedure is similar to the propagation of distributions using a Monte Carlo method (PoD) procedure presented in the written standard JCGM-101, in which the Monte Carlo method is applied to an explicit mathematical model for the measurand involving simulating and applying possible corrections to the observed measurement data. However, in this paper, we show that the uncertainty provided by the VE-DA procedure can be both larger and smaller than the uncertainty evaluated based on applying the PoD to the correct measurement model, when available. This is important to realize by users of the VE-DA procedure when claiming conformity of an uncertainty evaluation with JCGM-101. Full article