Search Results (527)

This work provides a structured synthesis of visual cryptography, a secret sharing technique that enables image reconstruction only when a specific number of shares are combined, with decryption performed visually by overlaying the shares. Although conceptually simple and distinctive in its reliance on the human visual system rather than complex computation, this method has been predominantly studied from theoretical and construction-oriented perspectives. The work consolidates fundamental concepts, mathematical foundations, operational principles, and security considerations of selected schemes, providing a common context for analyzing their characteristics. Particular attention is given to known attack vectors, including information leakage from individual shares and integrity violations caused by forged shares, together with corresponding mitigation approaches reported in the literature. In addition to this synthesis, the work presents an experimental investigation of the $\varphi$ correlation coefficient and its behavior for genuine and forged shares. Experiments conducted on a dataset of 100 images show that genuine–genuine share pairs consistently exhibit higher mean $\varphi$ correlation values than genuine–forged pairs, although the observed values depend on the underlying scheme. While these results suggest that $\varphi$ correlation may provide useful information for share authenticity analysis, the experiment used the same forged target image throughout the dataset, limiting the variation of the forged samples and potentially making the observed differences partly dependent on the selected target image. Finally, three Proof-of-Concept application scenarios demonstrate possible integrations of visual cryptography into QR code security, physical document verification, and IoT access control, illustrating its potential use in practical security systems. Full article

Non-rigid image registration is a fundamental problem in medical imaging and a representative example of continuous transformation modeling in image processing. Diffeomorphic registration methods, such as Large Deformation Diffeomorphic Metric Mapping (LDDMM) and its PDE-constrained variants (PDE-LDDMM), provide mathematically grounded formulations with strong geometric guarantees for transformation quality. However, existing approaches face persistent trade-offs between numerical stability, accuracy, and computational efficiency. Recent work has explored implicit neural representations (INRs) and neural ordinary differential equations (NODEs) as flexible neural representations for modeling continuous transformations. Despite their increasing adoption, their practical behavior and limitations in diffeomorphic registration remain insufficiently understood. In this paper, we present a unified formulation of INR- and NODE-based registration methods within LDDMM and PDE-LDDMM, enabling a systematic and controlled comparison across architectures, sampling strategies, and numerical solvers. Our analysis reveals fundamental trade-offs between these approaches. In particular, we show that MLP-based INR formulations introduce significant computational overhead and rely on sampling strategies that can degrade smoothness and lead to the increased occurrence of non-diffeomorphic transformations at higher resolutions. Moreover, these approximations do not fully alleviate the computational cost, with some variants exceeding the costs of expensive classical optimization-based methods. In contrast, NODE-based formulations and downsampling strategies consistently provide transformations with more controlled Jacobian extrema while maintaining competitive computational performance. Among the evaluated methods, the original NODE-LDDMM and NODE-PDE-LDDMM formulations achieve the most favorable trade-offs between registration accuracy, geometric consistency, and computational efficiency. These findings provide clear insights into the design of neural representations for continuous transformation modeling, with practical implications for diffeomorphic registration and computational anatomy applications. Full article

High-speed flow visualization provides imaging data containing quantitative information about cavitating-flow dynamics. Accurate determination of attached-cavity length is essential for characterizing cavitation regimes and validating mathematical models. In this study, an advanced image-processing algorithm for semi-automated analysis of cavitation patterns near hydrofoils is proposed. High-speed visualization data obtained for cavitating flow around a NACA0012 hydrofoil in a slit channel were used as input to the algorithm. The developed approach includes hydrofoil suppression, Otsu-based image binarization with threshold correction, filtering, and automated cavity-boundary detection. The initial search region for the cavity inception point is specified manually, whereas subsequent boundary tracking and cavity-length calculation are performed automatically. A dimensionless threshold correction coefficient was introduced to improve cavity identification, and its optimal range was determined. Additional geometric criteria were proposed to identify the cavity inception and closure locations and to separate attached cavities from detached vapor structures. The analysis showed that the optimal range of the threshold correction coefficient was $0.5$ < $th$ < $0.7$, while a geometric connectivity criterion based on a distance of 7 px between neighboring boundary pixels provided stable detection of the cavity closure location. The developed algorithm enables the determination of both instantaneous and time-averaged attached-cavity lengths, with a total estimated uncertainty not exceeding 3.5%. Comparison with previously published experimental and analytical data demonstrated good agreement and supported the reliability of the proposed approach. The method provides an explainable and training-free computer-vision pipeline that can potentially be adapted to other bluff-body geometries under comparable imaging and contrast conditions. It can also support automated annotation and the generation of reference datasets for the development and validation of future machine-learning methods for cavitation-flow analysis. Full article

Two-objective optimization requires both reliable front approximation and explainable non-dominated extraction. This study develops a theoretical and computational method that maps sampled objective vectors to rasterized objective-space images and processes their Pareto structure through supervised neural approximation, a deterministic convolutional extractor, and exploratory reinforcement search. Network I reconstructs a high-density sampled occupancy image from sparse samples, whereas Network II approximates the sampled Pareto-front boundary. The principal algorithmic contribution is a fixed cross-correlation kernel derived from the two-objective dominance quadrant and coupled with a cell archive that preserves original vectors and resolves raster collisions through exact dominance checks. Under the stated coordinate convention, central inversion relates the dominating and dominated displacement quadrants, translation-equivariant cross-correlation applies the same local relation across the grid, and minimization selects only the improvement-directed boundary. Experiments on SCH, FON, POL, KUR, and ZDT synthetic benchmarks assess front-geometry recovery and deterministic extraction on grids from 127 × 127 to 2048 × 2048; the reinforcement-learning results on SCH are interpreted as exploratory feasibility evidence. The present evidence is therefore confined to synthetic benchmarks. The method provides a benchmark-based methodological foundation for future multi-criterion model-selection and calibration research, including option-pricing model research in financial mathematics and quantitative economic analysis. Full article

Accurate and efficient recognition of tomato leaf diseases and pests is essential for precision agriculture, yet practical deployment remains challenging due to complex backgrounds, domain shifts, and subtle inter-class visual differences. From a broader mathematical perspective, this task can be viewed as token-level representation refinement under noise, ambiguity, and distribution shift. Recent state-space-model-based vision backbones provide favorable efficiency for high-resolution imagery but lack explicit mechanisms for adaptive feature refinement under noisy conditions. To address these issues, we propose EATMamba, an evolution-inspired Vision Mamba framework for tomato leaf disease and pest classification. Rather than being limited to a task-specific classifier, EATMamba is formulated as an evolution-inspired differentiable token-refinement mechanism designed to be compatible with state-space visual recognition backbones. EATMamba introduces two lightweight and fully differentiable modules—Evolutionary Crossover–Interaction and Knowledge-Guided Mutation–Selection—which perform token-level recombination and selective refinement to emphasize discriminative disease cues while suppressing irrelevant background information. These modules are inspired by crossover, mutation, and selection concepts, but are implemented as trainable differentiable operations over visual tokens, forming a generate–recombine–select style mechanism for representation refinement. The scope of this study is low-cost RGB-based visible-symptom disease and pest classification, rather than pre-symptomatic early disease detection. Extensive experiments on two complementary tomato datasets, including a controlled high-resolution dataset and an in-the-wild farm dataset, demonstrate that EATMamba consistently outperforms representative CNN-, Transformer-, and state-space-model-based baselines. Ablation studies and visualization analyses further confirm the complementary contributions of the proposed modules. Overall, EATMamba provides an effective and efficient framework for fine-grained plant disease recognition and illustrates how evolution-inspired principles can be incorporated into modern vision backbones for robust agricultural image analysis. Full article

Modern manufacturing is currently shifting toward highly flexible, high-mix, and low-volume production cycles, requiring small and medium-sized enterprises (SMEs) to adopt reconfigurable automation to remain competitive. However, the adoption of such technologies is often slowed down by the high cost and rigidity of commercial solutions, which typically rely on proprietary toolchains and necessitate specialized expert knowledge for reconfiguration. This study proposes a methodological framework for a modular robotic cell based on an open-architecture approach using ROS2 middleware, designed to be maintained by personnel without deep robotics expertise. The methodology emphasizes the replacement of fixed mechanical fixtures with an AI-driven perception pipeline, utilizing YOLO-based image segmentation to enable the autonomous localization of heterogeneous components. A rigorous tolerance chain analysis defines the design requirements of custom 3D-printed self-aligning fingertips, providing a mathematical and mechanical basis for ensuring assembly feasibility under tight geometric constraints. By adopting a node-based software topology, the framework facilitates rapid task reconfiguration and hardware interoperability. Experimental validation in an industrial-like environment confirms that this integrated approach provides a scalable pathway with the potential to improve cost-effectiveness in high-mix low-volume production scenarios to overcome manual production bottlenecks through intelligent, reconfigurable automation. Full article

Background/Objectives: Positive end-expiratory pressure (PEEP) increases end-expiratory lung volume through the addition of PEEP-induced lung volume (PEEPVol), potentially affecting respiratory mechanics and energy load. However, its physiological impact in patients without lung injury remains poorly characterized. We hypothesized that PEEPVol would be closely associated with respiratory system loading beyond conventional respiratory mechanics variables. Methods: We conducted a secondary analysis of a prospective physiological study including 16 deeply sedated, mechanically ventilated adults without lung disease. A standardized incremental PEEP titration (0–16 cmH₂O, steps of 4 cmH₂O) was performed under volume-controlled ventilation. At each step, respiratory mechanics were assessed, including static compliance (Cstat), driving pressure, plateau pressure, and mechanical power. PEEPVol was estimated as PEEP × Cstat, and strain indices were derived relative to predicted functional residual capacity. Linear mixed-effects models evaluated changes across PEEP levels, and associations were initially explored using Spearman correlation and linear regression. To account for repeated measurements within subjects, confirmatory linear mixed-effects regression models were subsequently performed using patients as a random intercept. Results: Incremental PEEP significantly increased PEEPVol, plateau pressure, mechanical power, and both static and global strain (all p < 0.001), while changes in compliance and driving pressure were minimal and not clinically meaningful. PEEPVol showed moderate-to-strong correlations with plateau pressure (ρ = 0.68) and mechanical power (ρ = 0.76) and explained 43% and 56% of their variance, respectively (all p < 0.001);these associations remained significant in additional linear mixed-effects regression analyses accounting for within-subject correlation. PEEPVol also correlated strongly with static strain (ρ = 0.93) and global strain (ρ = 0.83); however, because static strain is calculated as PEEPVol/FRCt, this association is mathematically expected rather than an independent physiological finding and is reported here only for completeness. Notably, 11.1% of measurements exceeded Pplat > 30 cmH₂O and 61.9% exceeded MP ≥ 17 J/min, even at moderate PEEP levels. Conclusions: In patients without lung injury, PEEP-induced increases in lung volume are strongly associated with higher mechanical load and strain, despite minimal changes in compliance or driving pressure. PEEPVol may represent a promising physiological surrogate of static lung deformation and energy transfer, whose potential to improve bedside detection of occult overdistension warrants validation against direct imaging or physiological measurements in larger prospective studies. Full article

Alzheimer’s disease (AD) is the most prevalent neurodegenerative disorder worldwide, affecting approximately 56.9 million people in 2021 and projected to reach 152 million by 2050. Its defining pathological features, amyloid-beta plaques and neurofibrillary tangles, accumulate for up to two decades before cognitive symptoms emerge, placing the preclinical and mild cognitive impairment (MCI) stages at the centre of the early detection problem. Despite this, current diagnostic practice in routine clinical settings remains unreliable, with post-mortem studies placing the specificity of clinical AD diagnosis between 44.3 and 70.8% even in specialist memory clinics. Machine learning (ML) and deep learning (DL) applied to neuroimaging and electrophysiological data have emerged as candidate tools for closing this diagnostic gap, yet whether the accuracy figures reported in published studies translate into clinically useful performance on independent data remains unresolved. This study presents a structured comparative review of machine learning and deep learning methods reported across four publicly available Alzheimer’s disease datasets, namely the Alzheimer’s Disease Neuroimaging Initiative (ADNI), the Open Access Series of Imaging Studies (OASIS), the OpenNeuro ds004504 electroencephalography (EEG) dataset, and the Kaggle Alzheimer’s magnetic resonance imaging (MRI) dataset. Thirteen model families are examined through the published literature rather than through new experiments, and for each model and dataset combination, the best accuracy reported in the source study is recorded alongside the model’s mathematical formulation. All performance figures reported in this abstract and throughout the paper are taken from the published studies reviewed, not from new experiments conducted by the authors. Across the reviewed studies, deep learning architectures pre-trained on ImageNet and fine-tuned on neuroimaging data are reported to produce the highest accuracy on MRI classification tasks. Residual Network (ResNet)-101 is reported at 98.21 percent on ADNI and 97.45 percent on OASIS, while the IncepRes fusion architecture reaches 98.35% on OASIS by combining multi-scale feature extraction from InceptionV3 with residual connectivity from ResNet152V2. Traditional machine learning classifiers remain competitive on tabular clinical and biomarker data, with Extreme Gradient Boosting (XGBoost) reaching 91% on ADNI multiclass features. Logistic Regression achieves 82 to 85% on binary ADNI classification and is the only classifier in this review that provides explicit per-feature prediction contributions without post hoc tooling. Gaussian Naïve Bayes achieves 80 to 83% on the same task. On the OpenNeuro EEG dataset, K-nearest neighbours (KNN) with singular value decomposition (SVD) entropy features achieves 91% binary accuracy, with feature engineering quality determining performance more reliably than classifier architecture. Eight principal findings emerge from the cross-dataset analysis. Binary classification consistently outperforms multiclass by 10 to 30% across all datasets, reflecting the genuine biological ambiguity of the mild cognitive impairment category. Dataset size and augmentation predict reported accuracy more reliably than model architecture. Ensemble methods outperform individual classifiers by 5 to 8% in nearly every imaging study. Deeper architectures can overfit small clinical cohorts. EEG models trail MRI models by approximately 10 to 15% on comparable binary tasks. Cross-dataset generalisation has not been systematically evaluated in most studies, and the few that have tested it report accuracy drops of 5 to 10% or more when models encounter data from different scanners or cohorts. Eight recurring limitations constrain the clinical utility of these findings. Small sample sizes and limited demographic diversity, severe class imbalance inflating raw accuracy metrics, poor cross-dataset generalisation driven by scanner heterogeneity, limited deep learning interpretability, the dominance of binary over multiclass tasks, the absence of longitudinal modelling despite available datasets, inadequate standardisation of preprocessing and evaluation protocols, and the signal-to-noise ratio constraints specific to EEG recordings of elderly patients collectively define the gap between benchmark performance and clinical readiness. Future work must prioritise multi-centre training cohorts, multimodal fusion architectures, longitudinal progression modelling, and standardised interpretability evaluation as non-optional requirements for any system intended for clinical deployment. Full article

Color Contrast Arrangements constitute one of the systems developed for use in color design. Based on Albert Munsell’s work and the Munsell color system, and later developed by Prof. Dr. Şazi Sirel through the proportioning of hue–value–chroma contrasts, Color Contrast Arrangements are known to evoke affective responses on users compared to environments colored at random. Although numerous studies in the literature examine the effects of color on humans, no research has been identified that investigates the affective responses of Color Contrast Arrangements constructed through a mathematical approach. Therefore, the present study aims to examine Color Contrast Arrangements in terms of harmony, preference, and liking by evaluating their affective responses. In line with this objective, a research method was devised and a two-phase online survey was conducted. In the surveys, a total of twelve color arrangements were generated, consisting of two examples from each of the six Color Contrast Arrangements created by Prof. Dr. Şazi Sirel. The colors of these twelve arrangements were applied to the façades of buildings in a visual representation of a street silhouette. In the first survey, participants were asked to evaluate the visuals in terms of harmony, preference, and liking, and to provide three adjectives describing the color arrangement in each image. In the second survey, adjective pairs were formed based on the most frequently mentioned adjectives and their associations with the concepts of harmony, preference, and liking; the visuals were then evaluated using a semantic differential scale. In line with the survey results, the affective responses of the Color Contrast Arrangements and their associations with the aforementioned concepts were examined. The analysis revealed that the strongest relationship among color harmony, preference and liking concepts was between color preference and color liking, while the weakest was between color harmony and color liking. In this study, the arrangements found to be the most harmonious, preferred, and liked were those based on value contrast, whereas the negatively evaluated arrangements across all three concepts were the equivalent chroma arrangement where hue contrast was dominant. Full article

Digital storytelling is widely used in education as a multimodal design practice that foregrounds creator agency and audience awareness. Generative AI (GenAI) expands the speed and range of story production but also raises questions about how educators retain pedagogical control over generated content. This exploratory qualitative study used cross-case workflow analysis to examine how 27 pre-service early childhood educators in Hong Kong designed GenAI-mediated mathematics storybooks. Data included video-recorded process presentations, records of interactions with ChatGPT (GPT-5) and Krea 2, and completed storybooks. Analysis traced participant decisions across planning, generation, curation, and integration, focusing on GenAI-related affordance uptake, recurring workflow patterns, and tensions among technical innovation, ethical accountability, and cultural impact. Findings show that participants commonly used GenAI to steer generation through pedagogical constraints; expand narrative and visual alternatives; and select, reject, or revise generated materials. Two recurring process patterns were identified: constraint-guided planning-to-generation, in which pedagogical requirements were established early and used to guide subsequent decisions, and exploration-to-selection, in which participants generated and compared alternatives before progressively stabilizing a preferred direction. Across both patterns, tensions were particularly evident during curation and integration, when participants balanced efficiency with sustained oversight, creative variation with pedagogical coherence, and generic outputs with local contextual fit. The findings show that GenAI-mediated storybook creation is not simply a process of generating text and images, but a pedagogical workflow in which pre-service teachers exercise agency through the critical selection, revision, and integration of AI-generated materials. Implications are discussed for teacher education, AI literacy, and the design of scalable support for teachers’ use of GenAI. Full article

We develop a non-Archimedean framework for the representation and analysis of genomic sequences based on the arithmetic and geometric structure of the ring of 5-adic integers. The proposed approach associates RNA sequences with points in a compact ultrametric space through an injective symbolic-to-arithmetic embedding that transforms genomic information into a hierarchical geometric object. We prove that the embedding is a global isometry between a natural symbolic prefix metric and the induced 5-adic metric, and we show that its image forms a compact Cantor-type subset of ${\mathbb{Z}}_5$. Building upon this representation, we formulate a continuous-time evolutionary model governed by a Vladimirov pseudo-differential operator. The resulting non-Archimedean diffusion equation provides a mathematically rigorous mechanism for describing evolutionary transitions across hierarchical genomic scales and admits an explicit fundamental solution obtained through 5-adic Fourier analysis. We further introduce a finite-resolution projection onto quotient rings of ${\mathbb{Z}}_5$ and develop an alignment-free phylogenetic inference framework based directly on the 5-adic valuation. The induced distance function is ultrametric and naturally encodes hierarchical relationships through shared symbolic prefixes. The proposed construction establishes a bridge between p-adic analysis, ultrametric geometry, pseudo-differential operators, and computational phylogenetics. As an illustration, we discuss its application to Hantavirus genomic sequences, demonstrating how hierarchical evolutionary organization can be represented within a unified non-Archimedean mathematical framework. Full article

Autism spectrum disorder (ASD) is a heterogeneous neurodevelopmental condition, and objective identification based on neuroimaging remains challenging due to inter-subject variability, multi-site heterogeneity, and the complex topology of brain functional networks. Resting-state functional magnetic resonance imaging (rs-fMRI) provides a non-invasive way to characterize intrinsic brain activity, but existing functional-connectivity-based methods often rely on single-scale static representations and insufficiently capture high-order topology, temporal evolution, and phenotypic heterogeneity. This study aims to develop a mathematical and AI-based brain-network modeling framework for ASD identification from rs-fMRI. The proposed method integrates low-order functional connectivity, high-order functional connectivity, phenotypic information, dynamic graph sequences, Transformer-based temporal attention, and static–dynamic gated fusion. Experiments were conducted on the ABIDE-I dataset, including 1112 subjects from 17 acquisition sites, with 539 ASD subjects and 573 typical controls. The proposed static multi-channel model achieved an accuracy of 75.8%, while the dynamic extension achieved a mean accuracy of 78.5% ± 0.7% and an AUC of 0.84 ± 0.01 over repeated runs. The results suggest that jointly modeling multi-scale static topology and dynamic temporal evolution may improve rs-fMRI-based ASD identification and offer a computationally interpretable framework for AI-assisted neuroimaging analysis. Full article

Accurate object detection in agricultural environments remains challenging due to illumination variation, background clutter, partial occlusion, and overlapping fruits. Conventional object detection methods mainly rely on deterministic data augmentation strategies or feature-level refinement, which often exhibit limited robustness under complex field conditions. To address this issue, this paper proposes a Diffusion-Regularized Object Detection (DROD) framework for robust pineapple target detection in agricultural imagery. The proposed framework introduces a mathematically grounded forward diffusion and diffusion-guided representation mechanism directly in the image domain, where stochastic perturbations are generated through forward diffusion and semantically meaningful image representations are learned via diffusion-guided representation. A unified optimization framework and theoretical analyses of perturbation propagation, Lipschitz stability, and training convergence are further established to provide mathematical support for the proposed method. Extensive experiments were conducted on a self-constructed dataset containing 1600 real-world pineapple images collected under practical agricultural conditions. Comparative evaluations involving YOLOv8-s, YOLOv8-l, traditional data augmentation, and the recent JTA:GAN method demonstrate that the proposed DROD framework consistently achieves the best detection performance in terms of Precision, Recall, mAP@0.5, and mAP@0.5:0.95 while maintaining computational complexity and inference speed comparable to the original YOLOv8 architecture. Furthermore, ablation studies, diffusion parameter sensitivity analysis, visualization analysis, and experimental validation under different perturbation levels consistently verify the effectiveness and robustness of the proposed diffusion mechanism. These results demonstrate that diffusion-based regularization provides an effective and computationally efficient solution for robust agricultural object detection and offers a practical framework for intelligent precision agriculture applications. Full article

To address the limitations of existing chaotic systems such as complex structure and potential chaotic degradation, this paper proposes a novel four-dimensional discrete chaotic system (4D-DCS) and an image encryption algorithm based on it. The 4D-DCS is constructed by integrating a feedback controller and modulo operation into a linear discrete-time system, featuring a simple structure without the need for intricate matrix reconstruction or memristor circuits. Mathematical analysis confirms its chaos in the sense of Li–Yorke and numerical simulations including Lyapunov exponent (LE) analysis, 0–1 test, and NIST SP 800-22 test demonstrate its hyperchaotic characteristics and excellent pseudorandomness. Based on the 4D-DCS, the proposed encryption algorithm employs SHA-256 to generate initial states for key uniqueness, combines row–column permutation to disrupt pixel correlation, and adopts a reversible neural network for diffusion to enhance confusion capability. Comprehensive security analysis shows that the algorithm achieves an NPCR of ∼99.61% and a UACI of ∼33.46%, a key space of $2^{216}$, information entropy close to 8, and correlation coefficients of encrypted images near 0. It also exhibits strong robustness against differential, cropping, noise, and chosen-plaintext attacks. Comparative analysis with state-of-the-art algorithms validates the 4D-DCS’s advantages in structural simplicity and stability, and the encryption algorithm’s superiority in security and practicality, making it suitable for security-critical applications such as image encryption. Full article

Three-dimensional (3D) particle field reconstruction is a core procedure of tomographic particle image velocimetry (Tomo-PIV). Its reconstruction accuracy and efficiency directly determine the ability of the PIV system to characterize various complex flow fields. Compared with traditional multicamera Tomo-PIV, a single light-field camera offers a compact layout, simple calibration, and strong adaptability, making it widely applicable for 3D flow measurement in confined space. This paper systematically reviews recent advances in 3D particle field reconstruction algorithms that use a single light-field camera, including both traditional iterative reconstruction methods and deep learning techniques. First, the imaging mechanism of different light-field cameras, the fundamental theory of light-field Tomo-PIV, and the mathematical foundation of tomographic reconstruction are elaborated to establish a theoretical framework for subsequent algorithm analysis. Next, the advantages, disadvantages, and limitations of traditional iterative reconstruction methods and deep learning techniques are comprehensively analyzed from key dimensions, including reconstruction quality, computational efficiency, inherent defects such as particle elongation and ghost particles, and applicable scenarios. On this basis, the current technical bottlenecks are concluded, including low computational efficiency under high particle concentration, insufficient research on velocity uncertainty quantification, domain mismatch between simulated and experimental datasets, and poor interpretability of deep learning models. Finally, several promising future research directions are discussed, such as the optimization of multiframe correlation-based high-precision reconstruction algorithms, the development of standardized open-source datasets, the interpretability of deep neural networks, and time-resolved flow measurement. This study aims to provide a comprehensive algorithmic reference for researchers in the field and facilitate the practical application of light-field Tomo-PIV in engineering fluid mechanics and related disciplines. Full article