Search Results (27)

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background. Full article

This editorial presents 24 research articles published in the Special Issue entitled Geometry of Manifolds and Applications of the MDPI Mathematics journal, which covers a wide range of topics from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in many branches of theoretical and applied mathematical studies, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as complex space forms, metallic Riemannian space forms, Hessian manifolds of constant Hessian curvature; optimal inequalities for submanifolds, such as generalized Wintgen inequality, inequalities involving $\delta$-invariants; homogeneous spaces and Poisson–Lie groups; the geometry of biharmonic maps; solitons (Ricci solitons, Yamabe solitons, Einstein solitons) in different geometries such as contact and paracontact geometry, complex and metallic Riemannian geometry, statistical and Weyl geometry; perfect fluid spacetimes [...] Full article

In recent decades, few-shot object detection in SAR imagery has gained prominence as a major research focus. The unique imaging mechanism of SAR causes the model to suffer from foreground–background imbalance and inaccurate extraction of class prototypes for novel class instances. Therefore, we propose an innovative few-shot object detection algorithm for SAR images via context-aware and robust Gaussian flow representation. First, we design the Context-Aware Enhancement module to address the foreground–context imbalance problem by refining representative support features into fine-grained prototypes, which are deeply fused with query features based on the prototype matching paradigm. Second, we devise the Manifold Class Distribution Estimation module to address the difficulty of class distribution estimation and the fluctuation of class centers of the sparse novel class. Furthermore, we formulate the Category-Balanced Difference Aggregation module to model the relationship between the base class and the novel class, addressing the sensitivity of the model to the variance of the novel class instances. Finally, we design the Cosine Decoupling Module so that the aggregated features are executed only on the classification branch without affecting the precise localization of the target. Experiments based on SAR-AIRcraft-1.0 and the self-constructed MSAR-AIR dataset indicate that the fine-grained detection and identification performance of the novel class of airplanes can reach 32.90% and 55.26%, respectively, in the 10-shot and 50-shot cases. In addition, our method enables cross-domain detection for different scenarios and sample types and exhibits excellent generalization performance in data-sparse scenarios. Full article

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method. Full article

The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. Axioms 2023, 5, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold $\Omega$, which appeared in theoretical physics, near its 3 singular points and near its one line of singular points. For that we used algorithms of Nonlinear Analysis: extraction of truncated polynomials, using the Newton polyhedron, their power transformations and Formal Generalized Implicit Function Theorem. Here we calculate parametric expansions of the manifold $\Omega$ near its one more singular point, near two curves of singular points and near infinity. Here we use 3 new things: (1) computation in algebraic extension of the field of rational numbers, (2) expansions near a curve of singular points and (3) calculation of branches near infinity. Full article

This paper investigates, as a first step, the four branches of BMS transformations, motivated by the classification into elliptic, parabolic, hyperbolic and loxodromic proposed a few years ago in the literature. We first prove that to each normal elliptic transformation of the complex variable $\zeta$ used in the metric for cuts of null infinity, there is a corresponding BMS supertranslation. We then study the conformal factor in the BMS transformation of the u variable as a function of the squared modulus of $\zeta$. In the loxodromic and hyperbolic cases, this conformal factor is either monotonically increasing or monotonically decreasing as a function of the real variable given by the modulus of $\zeta$. The Killing vector field of the Bondi metric is also studied in correspondence with the four admissible families of BMS transformations. Eventually, all BMS transformations are re-expressed in the homogeneous coordinates suggested by projective geometry. It is then found that BMS transformations are the restriction to a pair of unit circles of a more general set of transformations. Within this broader framework, the geometry of such transformations is studied by means of its Segre manifold. Full article

A scaled-down test section representative of an Outboard Segment manifold of the Water-Cooled Lithium Lead Breeding Blanket for the European DEMO has been designed for installation and test in a high- mass flow branch of the W-HYDRA facility, under construction at the premises of ENEA Brasimone Research Center. The test section should confirm the flow repartition recently computed in the different breeding units on the full-scale manifold, validating at the same time the computational tools used for the design and analysis. The detailed objectives and requirements of the test section, as well as the scaling rationale and procedure adopted for its design, are presented in the paper. The final design of the test section is discussed. The preliminary analyses of the developed design are also presented and show that it is compliant with the initial objectives. Full article

The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who dealt with Chen-Ricci and Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. and Ozel C. came with the study of Casorati inequality for statistical submanifolds in the same ambient space by using algebraic technique. Also, Chen, B.-Y., Mihai, A. and Mihai, I. obtained a Chen first inequality for such submanifolds. In 2020, Mihai, A. and Mihai, I. studied the Chen inequality for $\delta (2,2)$-invariant. In the development of this topic, we establish the generalized Wintgen inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Some examples are also discussed at the end. Full article

Fungi are important sources for the discovery of natural products. During the last decades, technological progress and the increasing number of sequenced genomes facilitated the exploration of new secondary metabolites. Among those, polyketides represent a structurally diverse group with manifold biological activities. In this study, we successfully used genome mining and genetic manipulation for functional proof of a polyketide biosynthetic gene cluster from the filamentous fungus Penicillium crustosum. Gene activation in the native host and heterologous expression in Aspergillus nidulans led to the identification of the xil cluster, being responsible for the formation of the 6-methyl-2-pyrone derivative xylariolide D. Feeding with ¹³C-labeled precursors supported the hypothesis of chain branching during the backbone formation catalyzed by a highly reducing fungal polyketide synthase. A cytochrome P450-catalyzed hydroxylation converts the PKS product to the final metabolite. This proved that just two enzymes are required for the biosynthesis of xylariolide D. Full article

Earth-to-air heat exchangers (EAHEs) can be used in the ventilation systems of various types of buildings. Multipipe structures can be found in large-volume buildings, yet scientific analysis of such systems is rare. Annual energy gains and electricity consumption for equivalent single-pipe and multipipe systems are typically not available. This paper bridges this gap, presenting the results of experimental studies on pressure losses in three-, five- and seven-pipe EAHEs and analysis for the annual energy gains and electric energy consumption as compared to a single-pipe exchanger. The results showed that the multipipe EAHE can be successfully replaced by a single-pipe structure with the same thermal performance and similar pressure losses if a tube with the appropriate diameter is used. However, multipipe heat exchangers can also use pipes of larger diameter (manifolds and/or branches), which improves their energy efficiency and may then make them more advantageous than single-pipe structures. From this reason, ultimately, the final selection of exchanger geometry should take into account economic and environmental issues and also user preferences and their importance in the hierarchy. Full article

The scientific community is paying increasing attention to plant waste valorization, and also to “greener” practices in the agriculture, food and cosmetic sectors. In this context, unused forest biomass (e.g., leaves, seed cones, branches/twigs, bark and sapwood) of Cryptomeria japonica, a commercially important tree throughout Asia and the Azores Archipelago (Portugal), is currently waste/by-products of wood processing that can be converted into eco-friendly and high added-value products, such as essential oils (EOs), with social, environmental and economic impacts. Plant-derived EOs are complex mixtures of metabolites, mostly terpenes and terpenoids, with valuable bioactivities (e.g., antioxidant, anti-inflammatory, anticancer, neuroprotective, antidepressant, antimicrobial, antiviral and pesticide), which can find applications in several industries, such as pharmaceutical, medical, aromatherapy, food, cosmetic, perfumery, household and agrochemical (e.g., biopesticides), with manifold approaches. The EOs components are also of value for taxonomic investigations. It is known that the variation in EOs chemical composition and, consequently, in their biological activities and commercial use, is due to different exogenous and endogenous factors that can lead to ecotypes or chemotypes in the same plant species. The present paper aims to provide an overview of the chemical composition, biological properties and proposals of valorization of C. japonica EO from several countries, and also to indicate gaps in the current knowledge. Full article

Advanced machine learning techniques have been used in remote sensing (RS) applications such as crop mapping and yield prediction, but remain under-utilized for tracking crop progress. In this study, we demonstrate the use of agronomic knowledge of crop growth drivers in a Long Short-Term Memory-based, domain-guided neural network (DgNN) for in-season crop progress estimation. The DgNN uses a branched structure and attention to separate independent crop growth drivers and captures their varying importance throughout the growing season. The DgNN is implemented for corn, using RS data in Iowa, U.S., for the period 2003–2019, with United States Department of Agriculture (USDA) crop progress reports used as ground truth. State-wide DgNN performance shows significant improvement over sequential and dense-only NN structures, and a widely-used Hidden Markov Model method. The DgNN had a 4.0% higher Nash-Sutcliffe efficiency over all growth stages and 39% more weeks with highest cosine similarity than the next best NN during test years. The DgNN and Sequential NN were more robust during periods of abnormal crop progress, though estimating the Silking–Grainfill transition was difficult for all methods. Finally, Uniform Manifold Approximation and Projection visualizations of layer activations showed how LSTM-based NNs separate crop growth time-series differently from a dense-only structure. Results from this study exhibit both the viability of NNs in crop growth stage estimation (CGSE) and the benefits of using domain knowledge. The DgNN methodology presented here can be extended to provide near-real time CGSE of other crops. Full article

The objectives of this study were to measure the flow rate distribution from a header pipe to each module installed in parallel for a water treatment membrane filtration process in operation and to investigate the reason for an uneven distribution of the flow rate via the CFD technique. In addition, this study attempted to propose the ratio of the branch pipe to the header pipe required to equalize the flow distribution for the same membrane filtration process. Finally, the relationship between the Reynolds number in the header pipe and the degree of the manifold flow distribution evenness was investigated. Mobile ultrasonic flow meter was used to measure the flow rate flowing from the membrane module pipe to each module, and the CFD technique was used to verify this. From the results of the actual measurement using ultrasonic flow meter and CFD simulation, it was confirmed that the outflow flow rate from the branch pipe located at the end of the header pipe was three times higher than that of the branch pipe near the inlet. The reason was that the differential pressure generated between each membrane module was higher toward the end of the header pipe. When the ratio of the sum of the cross-sectional area of the branch pipe and the cross-sectional area of the header pipe was reduced by about 30 times, it was confirmed that the flow rate flowing from each branch pipe to the membrane module was almost equal. Also, if the flow in the header pipe is transitional or laminar (Reynolds No. is approximately 4000 or less), the flow rate flowing from each branch pipe to the membrane module can be more even. Full article

The Wasserstein distance, especially among symmetric positive-definite matrices, has broad and deep influences on the development of artificial intelligence (AI) and other branches of computer science. In this paper, by involving the Wasserstein metric on $SPD(n)$, we obtain computationally feasible expressions for some geometric quantities, including geodesics, exponential maps, the Riemannian connection, Jacobi fields and curvatures, particularly the scalar curvature. Furthermore, we discuss the behavior of geodesics and prove that the manifold is globally geodesic convex. Finally, we design algorithms for point cloud denoising and edge detecting of a polluted image based on the Wasserstein curvature on $SPD(n)$. The experimental results show the efficiency and robustness of our curvature-based methods. Full article

Stress intensity factor (SIF) is one of three important parameters in classical linear elastic fracture mechanics (LEFM). The evaluation of SIFs is of great significance in the field of engineering structural and material damage assessment, such as aerospace engineering and automobile industry, etc. In this paper, the SIFs of a central straight crack plate, a slanted single-edge cracked plate under end shearing, the offset double-edge cracks rectangular plate, a branched crack in an infinite plate and a crucifix crack in a square plate under bi-axial tension are extracted by using the p-version finite element method (P-FEM) and contour integral method (CIM). The above single- and multiple-crack problems were investigated, numerical results were compared and analyzed with results using other numerical methods in the literature such as the numerical manifold method (NMM), improved approach using the finite element method, particular weight function method and exponential matrix method (EMM). The effectiveness and accuracy of the present method are verified. Full article