Search Results (102)

The recent interest in geometers in the f-structures of K. Yano is motivated by the study of the dynamics of contact foliations, as well as their applications in theoretical physics. Weak metric f-structures on a smooth manifold, recently introduced by the author and R. Wolak, open a new perspective on the theory of classical structures. In this paper, we define structures of this kind, called weak nearly $\mathcal{S}$- and weak nearly $\mathcal{C}$-structures, study their geometry, e.g., their relations to Killing vector fields, and characterize weak nearly $\mathcal{S}$- and weak nearly $\mathcal{C}$-submanifolds in a weak nearly Kähler manifold. Full article

The famous Nyman–Beurling theorem states that the absence of zeroes in the Riemann zeta-function in the half-plane Res > 1/p, p > 1, is equivalent to the circumstance in which the closure of the linear manifold of the functions $f(x)={\displaystyle \sum _{k=1}^n{\alpha }_k\left\{\frac{{\vartheta }_k}{x}\right\}}$, where $0<{\vartheta }_k\le 1$, with the condition ${\displaystyle \sum _{k=1}^n{a}_k{\vartheta }_k}=0$, is dense in L_p(0,1). Here, we show that if the closure of linear manifolds of the same functions but with the conditions ${\displaystyle \sum _{k=1}^n{a}_k{\vartheta }_k^l}=0$ with l = 2, 3, 4 is dense in L_p(0,1), then certain combinations of Riemann zeta-functions are free from zeroes in the half-plane Res > 1/p, p > 1—like, e.g., the function $g_2(s)={\displaystyle \frac{2}{s-1}}\zeta (s-1)+\zeta (s)$ for l = 2. Similar results for larger integer l can be established. The connections between the Riemann zeta-function, including the question concerning the location of its zeroes, with different symmetry aspects of numerous physical systems are well established, and recently they were highlighted also for supersymmetric quantum mechanics. Full article

This paper mainly studies the existence of sign-changing solutions for the following $p\left(x\right)$-biharmonic Kirchhoff-type equations: $-\left(a+b{\int }_{{\mathbb{R}}^N}{\displaystyle \frac{1}{p\left(x\right)}}{|\Delta u|}^{p\left(x\right)}\mathrm{d}x\right){\Delta }_{p\left(x\right)}^{2}u+V\left(x\right){|u|}^{p\left(x\right)-2}u$ = $K\left(x\right)f\left(u\right),x\in {\mathbb{R}}^N$, where ${\Delta }_{p\left(x\right)}^{2}u=\Delta \left({|\Delta u|}^{p\left(x\right)-2}\Delta u\right)$ is the $p\left(x\right)$ biharmonic operator, $a,b>0$ are constants, $N\ge 2$, $V\left(x\right),K\left(x\right)$ are positive continuous functions which vanish at infinity, and the nonlinearity f has subcritical growth. Using the Nehari manifold method, deformation lemma, and other techniques of analysis, it is demonstrated that there are precisely two nodal domains in the problem’s least energy sign-changing solution $u_b$. In addition, the convergence property of $u_b$ as $b\to 0$ is also established. Full article

This study proposes an automatic gear shift classification algorithm in M1 category vehicles using data acquired through the onboard diagnostic system (OBD II) and GPS. The proposed approach is based on the analysis of identification parameters (PIDs), such as manifold absolute pressure (MAP), revolutions per minute (RPM), vehicle speed (VSS), torque, power, stall times, and longitudinal dynamics, to determine the efficiency and behavior of the vehicle in each of its gears. In addition, the unsupervised K-means algorithm was implemented to analyze vehicle gear changes, identify driving patterns, and segment the data into meaningful groups. Machine learning techniques, including K-Nearest Neighbors (KNN), decision trees, logistic regression, and Support Vector Machines (SVMs), were employed to classify gear shifts accurately. After a thorough evaluation, the KNN (Fine KNN) model proved to be the most effective, achieving an accuracy of 99.7%, an error rate of 0.3%, a precision of 99.8%, a recall of 99.7%, and an F1-score of 99.8%, outperforming other models in terms of accuracy, robustness, and balance between metrics. A multiple linear regression model was developed to estimate instantaneous fuel consumption (in L/100 km) using the gear predicted by the KNN algorithm and other relevant variables. The model, built on over 66,000 valid observations, achieved an R² of 0.897 and a root mean square error (RMSE) of 2.06, indicating a strong fit. Results showed that higher gears (3, 4, and 5) are associated with lower fuel consumption. In contrast, a neutral gear presented the highest levels of consumption and variability, especially during prolonged idling periods in heavy traffic conditions. In future work, we propose integrating this algorithm into driver assistance systems (ADAS) and exploring its applicability in autonomous vehicles to enhance real-time decision making. Such integration could optimize gear shift timing based on dynamic factors like road conditions, traffic density, and driver behavior, ultimately contributing to improved fuel efficiency and overall vehicle performance. Full article

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity. Full article

This study aims to analyze electrocardiogram (ECG) data for the classification of five cardiac rhythms: sinus bradycardia (SB), sinus rhythm (SR), atrial fibrillation (AFIB), supraventricular tachycardia (SVT), and sinus tachycardia (ST). While SR is considered normal, the other four represent types of cardiac arrhythmias. A range of methods is utilized, including the supervised learning technique K-Nearest Neighbors (KNNs), combined with dimensionality reduction approaches such as Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP), a modern method based in Riemannian topology. Additionally, logistic regression was applied using both maximum likelihood and Bayesian methods, with two distinct prior distributions: an informative normal prior and a non-informative Jeffreys prior. Performance was assessed using evaluation metrics such as positive predictive value (PPV), negative predictive value (NPV), specificity, sensitivity, accuracy, and F1-score. Ultimately, the UMAP-KNN method demonstrated the best overall performance. Full article

Recent interest among geometers in f-structures of K. Yano is due to the study of topology and dynamics of contact foliations, which generalize the flow of the Reeb vector field on contact manifolds to higher dimensions. Weak metric structures introduced by the author and R. Wolak as a generalization of Hermitian and Kähler structures, as well as f-structures, allow for a fresh perspective on the classical theory. In this paper, we study a new f-structure of this kind, called the weak $\beta$-Kenmotsu f-structure, as a generalization of K. Kenmotsu’s concept. We prove that a weak $\beta$-Kenmotsu f-manifold is a locally twisted product of the Euclidean space and a weak Kähler manifold. Our main results show that such manifolds with $\beta =const$ and equipped with an $\eta$-Ricci soliton structure whose potential vector field satisfies certain conditions are $\eta$-Einstein manifolds of constant scalar curvature. Full article

In this manuscript, we define the $(E,F)$-invex set, $(E,F)$-invex functions, and $(E,F)$-preinvex functions on Euclidean space, i.e., simply vector space. We extend these concepts on the Riemannian manifold. We also detail the fundamental properties of $(E,F)$-preinvex functions and provide some examples that illustrate the concepts well. We have established a relation between $(E,F)$-invex and $(E,F)$-preinvex functions on Riemannian manifolds. We introduce the conditions $\mathcal{A}$ and define the $(E,F)$-proximal sub-gradient. $(E,F)$-preinvex functions are also used to demonstrate their applicability in optimization problems. In the last, we establish the points of extrema of a non-smooth $(E,F)$-preinvex functions on $(E,F)$-invex subset of the Riemannian manifolds by using the $(E,F)$-proximal sub-gradient. Full article

Aphids are significant pests of winter wheat, causing damage by feeding on plant sap and reducing crop yield and quality. This study evaluates the potential of hyperspectral remote sensing (350–2500 nm) and machine learning (ML) models for classifying healthy and aphid-infested wheat canopies. Field-based hyperspectral measurements were conducted at three growth stages—T1 (stem elongation–heading), T2 (flowering), and T3 (milky grain development)—with infestation levels categorized according to established economic thresholds (ET) for each growth stage. Spectral data were analyzed using Uniform Manifold Approximation and Projection (UMAP); vegetation indices; and ML classification models, including Logistic Regression (LR), k-Nearest Neighbors (KNNs), Support vector machines (SVMs), Random Forest (RF), and Light Gradient Boosting Machine (LGBM). The classification models achieved high performance, with F1-scores ranging from 0.88 to 0.99, and SVM and RF consistently outperforming other models across all input datasets. The best classification results were obtained at T2 with an F1-score of 0.98, while models trained on the full spectrum dataset showed the highest overall accuracy. Among vegetation indices, the Modified Triangular Vegetation Index, MTVI (r_pb = −0.77 to −0.82), and Triangular Vegetation Index, TVI (r_pb = −0.66 to −0.75), demonstrated the strongest correlations with canopy condition. These findings underscore the utility of canopy spectra and vegetation indices for detecting aphid infestations above ET levels, allowing for a clear classification of wheat fields into “treatment required” and “no treatment required” categories. This approach provides a precise and timely decision making tool for insecticide application, contributing to sustainable pest management by enabling targeted interventions, reducing unnecessary pesticide use, and supporting effective crop protection practices. Full article

In this paper, we study Einstein doubly warped product Poisson manifolds. First, we provide necessary and sufficient conditions for a doubly warped product manifold $(M={}_{f}B{\times }_{b}F,g,\Pi ),$ equipped with a Poisson structure $\Pi$ to be a contravariant Einstein manifold. Additionally, under certain conditions on the base space B, we prove that if M is an Einstein doubly warped product Poisson manifold with non-positive scalar curvature, then M is simply a singly warped product Poisson manifold. We also investigate the existence and non-existence of the warping function on the base space B associated with constant scalar curvature on M, assuming that the fiber space F has constant scalar curvature. Full article

We explore nonlocal symmetries in a class of Hamiltonian dynamical systems governed by second-order differential equations. Specifically, we establish an algorithm for deriving nonlocal symmetries by utilizing the Jacobi metric and the Eisenhart–Duval lift to geometrize the dynamical systems. The geometrized systems often exhibit additional local symmetries compared to the original systems, some of which correspond to nonlocal symmetries for the original formulation. This novel approach allows us to determine nonlocal symmetries in a systematic way. Within this geometric framework, we demonstrate that the second-order differential equation $\ddot{q}-F\left(q\right)=0$ admits an infinite number of nonlocal symmetries generated by the infinite-dimensional conformal algebra of a two-dimensional Riemannian manifold. Applications to higher-dimensional systems are also discussed. Full article

The exponential growth of patent datasets poses a significant challenge in filtering relevant documents for research and innovation. Traditional semantic search methods based on keywords often fail to capture the complexity and variability in multidisciplinary terminology, leading to inefficiencies. This study addresses the problem by systematically evaluating supervised and unsupervised machine learning (ML) techniques for document relevance filtering across five technology domains: solid-state batteries, electric vehicle chargers, connected vehicles, electric vertical takeoff and landing aircraft, and light detecting and ranging (LiDAR) sensors. The contributions include benchmarking the performance of 10 classical models. These models include extreme gradient boosting, random forest, and support vector machines; a deep artificial neural network; and three natural language processing methods: latent Dirichlet allocation, non-negative matrix factorization, and k-means clustering of a manifold-learned reduced feature dimension. Applying these methods to more than 4200 patents filtered from a database of 9.6 million patents revealed that most supervised ML models outperform the unsupervised methods. An average of seven supervised ML models achieved significantly higher precision, recall, and F1-scores across all technology domains, while unsupervised methods show variability depending on domain characteristics. These results offer a practical framework for optimizing document relevance filtering, enabling researchers and practitioners to efficiently manage large datasets and enhance innovation. Full article

The interest of geometers in f-structures is motivated by the study of the dynamics of contact foliations, as well as their applications in physics. A weak f-structure on a smooth manifold, introduced by the author and R. Wolak, generalizes K. Yano’s f-structure. This generalization allows us to revisit classical theory and discover applications of Killing vector fields, totally geodesic foliations, Ricci-type solitons, and Einstein-type metrics. This article reviews the results regarding weak metric f-manifolds and their distinguished classes. Full article

Background: Alzheimer’s disease is a progressive neurological condition marked by a decline in cognitive abilities. Early diagnosis is crucial but challenging due to overlapping symptoms among impairment stages, necessitating non-invasive, reliable diagnostic tools. Methods: We applied information geometry and manifold learning to analyze grayscale MRI scans classified into No Impairment, Very Mild, Mild, and Moderate Impairment. Preprocessed images were reduced via Principal Component Analysis (retaining 95% variance) and converted into statistical manifolds using estimated mean vectors and covariance matrices. Geodesic distances, computed with the Fisher Information metric, quantified class differences. Graph Neural Networks, including Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and GraphSAGE, were utilized to categorize impairment levels using graph-based representations of the MRI data. Results: Significant differences in covariance structures were observed, with increased variability and stronger feature correlations at higher impairment levels. Geodesic distances between No Impairment and Mild Impairment (58.68, $p<0.001$) and between Mild and Moderate Impairment (58.28, $p<0.001$) are statistically significant. GCN and GraphSAGE achieve perfect classification accuracy (precision, recall, F1-Score: 1.0), correctly identifying all instances across classes. GAT attains an overall accuracy of 59.61%, with variable performance across classes. Conclusions: Integrating information geometry, manifold learning, and GNNs effectively differentiates AD impairment stages from MRI data. The strong performance of GCN and GraphSAGE indicates their potential to assist clinicians in the early identification and tracking of Alzheimer’s disease progression. Full article

The concept of pointwise slant submanifolds of a Kähler manifold was presented by Chen and Garay. This research extends this notion to a more general setting, specifically in a locally conformal Kähler manifold. We study the pointwise pseudo-slant warped products of the form ${\mathsf{\Sigma }}^{\theta }{\times \hspace{0.17em}}_f{\mathsf{\Sigma }}^{\perp }$ in a locally conformal Kähler manifold. Using the concept of pointwise pseudo-slant, we establish the necessary and sufficient condition for it to be characterized as a warped product submanifold. In addition, we derive several results on pointwise pseudo-slant warped products that expand previously proven main ones. Further, some examples of such submanifolds and their warped products are also given. Full article