Search Results (80)

The fractal extension of the time-dependent Ginzburg–Landau (TDGL) equation, formulated within the framework of Scale Relativity, generalizes superconducting dynamics to non-differentiable space–time. Although analytically well established, its numerical solution remains difficult because of the strong coupling between amplitude and phase curvature. Here we develop two complementary deep learning solvers for the fractal TDGL (FTDGL) system. The Fractal Physics-Informed Neural Network (F-PINN) embeds the Scale-Relativity covariant derivative through automatic differentiation on continuous fields, whereas the Fractal Graph Neural Network (F-GNN) represents the same dynamics on a sparse spatial graph and learns local gauge-covariant interactions via message passing. Both models are trained against finite-difference reference data, and a parametric study over the dimensionless fractality parameter $\mathcal{D}$ quantifies its influence on the coherence length, penetration depth, and peak magnetic field. Across multivortex benchmarks, the F-GNN reduces the relative L₂ error on ${\left|\psi \right|}^2$ from 0.190 to 0.046 and on B_z from approximately 0.62 to 0.36 (averaged over three seeds). This ≈4× improvement in condensate-density accuracy corresponds to a substantial enhancement in vortex-core localization—from tens of pixels of uncertainty to sub-pixel precision—and yields a cleaner reconstruction of the 2π phase winding around each vortex, improving the extraction of experimentally relevant observables such as ξ_eff, λ_eff, and local B_z peaks. The model also preserves flux quantization and remains robust under 2–5% Gaussian noise, demonstrating stable learning under experimentally realistic perturbations. The $\mathcal{D}$—scan reveals broader vortex cores, a non-monotonic variation in the penetration depth, and moderate modulation of the peak magnetic field, while preserving topological structure. These results show that graph-based learning provides a superior inductive bias for modeling non-differentiable, gauge-coupled systems. The proposed F-PINN and F-GNN architectures therefore offer accurate, data-efficient solvers for fractal superconductivity and open pathways toward data-driven inference of fractal parameters from magneto-optical or Hall-probe imaging experiments. Full article

This paper develops the theory of strongly continuous semigroups and abstract evolution equations in modular function spaces. We study the autonomous problem $\dot{u}\left(t\right)=Bu\left(t\right)$ with initial condition $u\left(0\right)=u_0\in L_{\rho }$, where B is the infinitesimal generator of a strongly continuous semigroup ${\left(S\left(t\right)\right)}_{t\ge 0}$ on $L_{\rho }$. Within this framework, we establish modular analogues of classical results from Banach-space semigroup theory, including criteria for $\rho$-boundedness and $\rho$-continuity, a Laplace resolvent representation of the generator, and explicit resolvent bounds in terms of the modular growth function ${\omega }_{\rho }$. Under a ${\Delta }_2$-type condition on the modular, we justify Steklov regularization of semigroup orbits, obtain domain inclusion and the resolvent identity, and derive spectral consequences for classes of operators naturally acting on $L_{\rho }$. The results show that the structural features of the classical semigroup framework persist in the modular topology, providing a unified approach to linear evolution in modular function spaces. Full article

Cooperative and Autonomous Vehicle (CAV) platoons offer significant potential for improving road safety, traffic efficiency, and energy consumption, but maintaining precise inter-vehicle spacing and synchronized velocity under disturbances while ensuring string stability remains challenging. This paper presents a fully decentralized two-layer architecture for homogeneous platoons whose identical vehicle dynamics and information flow produce an inherent symmetrical system structure. Operating under a predecessor-following topology with a constant time headway policy, the upper layer generates a smooth velocity reference based on local spacing and relative-velocity errors, while the lower layer employs a two-degree-of-freedom (2-DOF) digital RST controller designed through discrete-time pole placement and sensitivity-function shaping. The 2-DOF structure enables independent tuning of tracking and disturbance-rejection dynamics and provides a computationally lightweight solution suitable for embedded automotive platforms. The paper develops a stability analysis demonstrating internal stability and $L_2$ string stability within this symmetrical closed-loop architecture. Simulations confirm string-stable behavior with attenuated spacing and velocity errors across the platoon during aggressive leader maneuvers and under input disturbances. The proposed method yields smooth control effort, fast transient recovery, and accurate spacing regulation, offering a robust and scalable control strategy for real-time longitudinal motion control in connected and automated vehicle platoons. Full article

We study thrust production in a single-fluid magnetohydrodynamic (MHD) thruster with Hall-type coaxial geometry and show how velocity–field alignment and magnetic topology set the operating regime. Starting from the momentum equation with anisotropic conductivity, the axial Lorentz force density reduces to $f_z={\sigma }_{\theta z}{E}_z{B}_r(\chi -1)$, with the motional-field ratio $\chi \equiv \left(u{B}_r\right)/E_z$. Hence, net accelerating force ($f_z>0$) is achieved if and only if the motional electric field $E_m=u{B}_r$ exceeds the applied axial bias $E_z$ ($\chi >1$), providing a compact, testable design rule. We separate alignment diagnostics (cross-helicity $h_c=\mathit{u}·\mathit{B}$) from the thrust criterion ($\chi$) and generate equation-only axial profiles for $\chi \left(z\right)$, $j_{\theta }\left(z\right)$, and $f_z\left(z\right)$ for representative parameters. In a baseline case $(E_z=150\mathrm{V}{\mathrm{m}}^{-1},{\sigma }_{\theta z}=50\mathrm{S}{\mathrm{m}}^{-1},u_0=12\mathrm{km}{\mathrm{s}}^{-1},B_{r0}=0.02\mathrm{T},L=0.10\mathrm{m})$, the $\chi >1$ band spans $\approx 21.2\%$ of the channel; a lagged correlation peaks at $\Delta z^{★}\approx 8.82\mathrm{mm}$$(C_{HU}=0.979)$, and ${\int }_0^L{f}_z\mathrm{d}z$ is slightly negative—indicating that enlarging the $\chi >1$ region or raising ${\sigma }_{\theta z}$ are effective levers. We propose a reproducible validation pathway (finite-volume MHD simulations and laboratory measurements: PIV, Hall probes, and thrust stand) to map $f_z$ versus $\chi$ and verify the response length. The framework yields concrete design strategies—$B_r\left(z\right)$ shaping where u is high, conductivity control, and modest $E_z$ tuning—supporting applications from station-keeping to deep-space cruise. Full article

Microwave devices based on microstrip resonators are widely used today in communication, radar, and navigation systems. The requirements to these devices may include specific frequency-selective properties, as well as size and production costs. The design of resonators and filters are mostly performed manually, as the process requires expert knowledge and computationally expensive modeling, so practitioners are usually limited to tuning a chosen example from a set of known, typical topologies. However, the set of possible topologies remains unexplored and may contain specific constructions, which have not been discovered yet. In this study we propose an approach to automatically search the space multimode resonator topologies using a zero-order optimization algorithm and numerous computational experiments. In particular, a family of symmetrical resonators constructed out of four rectangles is considered, and the parameters are tuned by the recently proposed L-SRTDE algorithm. We state the problem of building the topology of a microwave device conductor with specified frequency-selective characteristics as an optimization problem, and the minimized function (target function) in this problem is based on the evaluation of the deviation between the specified frequency-selective characteristics and their values obtained via electrodynamic modeling. The experiments with two target function formulations have shown that the proposed approach allows finding novel topologies and automatically tune them according to the required frequency-selective properties. It is shown that some of the topologies are different from the known ones but still demonstrate high-quality properties. Full article

Magnetron sputtering offers a scalable route to magnetic topological insulators (MTIs) based on Cr-doped Sb₂Te₃. We combine a range of X-ray diffraction (XRD), reciprocal-space mapping (RSM), scanning transmission electron microscopy (STEM), scanning TEM-energy-dispersive X-ray spectroscopy (STEM-EDS), and X-ray absorption spectroscopy, and X-ray magnetic circular dichroism (XAS/XMCD) techniques to study the structure and magnetism of Cr-doped Sb₂Te₃ films. Symmetric $\theta$-2$\theta$ XRD and RSM establish a solubility window. Layered tetradymite order persists up to ∼10 at.-% Cr, while higher doping yields CrTe/Cr₂Te₃ secondary phases. STEM reveals nanocrystalline layered stacking at low Cr and loss of long-range layering at higher Cr concentrations, consistent with XRD/RSM. Magnetometry on a 6% film shows soft ferromagnetism at 5 K. XAS and XMCD at the Cr $L_{2,3}$ edges exhibits a depth dependence: total electron yield (TE; surface sensitive) shows both nominal Cr²⁺ and Cr³⁺, whereas fluorescence yield (FY; bulk sensitive) shows a much higher Cr²⁺ weight. Sum rules applied to TEY give $m_L=(0.20\pm 0.04)$${\mu }_{\mathrm{B}}$/Cr, and $m_S=(1.6\pm 0.2)$${\mu }_{\mathrm{B}}$/Cr, whereby we note that the applied maximum field (3 T) likely underestimates $m_S$. These results define a practical growth window and outline key parameters for MTI films. Full article

Change points caused by extreme events in global economic markets have been widely studied in the literature. However, existing techniques to identify change points rely on subjective judgments and lack robust methodologies. The objective of this paper is to generalize a novel approach that leverages topological data analysis (TDA) to extract topological features from time series data using persistent homology. In this approach, we use Taken’s embedding and sliding window techniques to transform the initial time series data into a high-dimensional topological space. Then, in this topological space, persistent homology is used to extract topological features which can give important information related to change points. As a case study, we analyzed 26 stocks over the last 12 years by using this method and found that there were two financial market volatility indicators derived from our method, denoted as $L_1$ and $L_2$. They serve as effective indicators of long-term and short-term financial market fluctuations, respectively. Moreover, significant differences are observed across markets in different regions and sectors by using these indicators. By setting a significance threshold of 98 % for the two indicators, we found that the detected change points correspond exactly to four major financial extreme events in the past twelve years: the intensification of the European debt crisis in 2011, Brexit in 2016, the outbreak of the COVID-19 pandemic in 2020, and the energy crisis triggered by the Russia–Ukraine war in 2022. Furthermore, benchmark comparisons with established univariate and multivariate CPD methods confirm that the TDA-based indicators consistently achieve superior F1 scores across different tolerance windows, particularly in capturing widely recognized consensus events. Full article

This paper introduces weak variants of level convergence (L-convergence) and epigraph convergence (E-convergence) for nets of level functions on general topological spaces, extending the classical metric and real-valued frameworks to ordered codomains and generalized minima. We show that L-convergence implies E-convergence and that the two notions coincide when the limit function is level-continuous, mirroring the relationship between strong and weak variational convergence. In Hausdorff topological groups, we define robust level functions and prove that every level function can be approximated by robust ones via convolution-type operations, enabling perturbation-resilient modeling. These results both generalize and connect to $\Gamma$-convergence: they recover the classical metric, lower semicontinuous case, and extend the scope for optimization on Lie groups, fuzzy systems, and mechanics in non-Euclidean spaces. An explicit nonmetrizable example demonstrates the relevance of our theory beyond the reach of $\Gamma$-convergence. Full article

This article proposes a unified concept of topological types of convergence for nets of multifunctions between topological spaces. Any kind of convergence is representable by a (2n + 2)-tuple, n = 0, 1, …, of two special functions u and l, such that their compositions $ul$ and $lu$ create the Choquet supremum and infimum operations, respectively, on the filters considered in terms of the upper Vietoris topology on the range hyperspace of the considered multifunctions. Convergence operators are defined by establishing the order of composition of the functions from such (2n + 2) tuples. An allocation of places for the two distinguished functions in a convergence operator reflects the structure of the used (2n + 2)-tuple. A monoid of special three-parameter functions called products describes the set of all possible structures. The monoid of products is the domain space of the convergence operators. The family of all convergence operators forms a finite monoid whose neutral element determines the pointwise convergence and possesses the structure determined by the neutral element of the monoid of products. We demonstrate the construction process of every convergence operator and show that the notions of the presented concept can characterize many well-known classical types of convergence. Of particular importance are the types of convergence derived from the concept of continuous convergence. We establish some general theorems about the necessary and sufficient conditions for the continuity of the limit multifunctions without any assumptions about the type of continuity of the members of the nets. Full article

The thioether-functionalized 2-azabutadienes (ArS)₂C=C(H)-N=CPh₂ (L1 Ar = Ph, L2 Ar = p-Tol) ligate to [Mn(CO)₅Br] to form the octahedral five-membered S, N-chelate complexes fac-[MnBr(CO)₃{(ArS)₂C=C(H)-N=CPh₂] (1 Ar = Ph; 2 Ar = p-Tol), whose crystal structures have been solved by X-ray diffraction. Complex 1 crystallizes in the non-centrosymmetric orthorhombic space group P2₁2₁2₁, whereas 2 crystallizes in the triclinic space group P$\overline{1}$. The secondary interactions occurring in the packing have also been assessed by an Atoms in Molecules (AIM) topological analysis. Full article

This paper introduces and investigates the fundamental properties of L-primals, a generalization of the primal concept within the framework of L-fuzzy sets and complete lattices. Building upon the established theories of L-topological spaces and L-pre-proximity spaces, this research explores the interrelations among these three generalized topological structures. The study establishes novel categorical links, demonstrating the existence of concrete functors between categories of L-primal spaces and L-pre-proximity spaces, as well as between categories of L-pre-proximity spaces and stratified L-primal spaces. Furthermore, the paper clarifies the existence of a concrete functor between the category of stratified L-primal spaces and the category of L-topological spaces, and vice versa, thereby establishing Galois correspondences between these categories. Theoretical findings are supported by illustrative examples, including applications within the contexts of information systems and medicine, demonstrating the practical aspects of the developed theory. Full article

The problem of inadequate object detection accuracy in complex remote sensing scenarios has been identified as a primary concern. Traditional YOLO-series algorithms encounter challenges such as poor robustness in small object detection and significant interference from complex backgrounds. In this paper, a multi-scale feature fusion framework based on an improved version of YOLOv8_L is proposed. The combination of a graph attention network (GAT) and Dilated Encoder network significantly improves the algorithm detection and recognition performance for space remote sensing objects. It mainly includes abandoning the original Feature Pyramid Network (FPN) structure, proposing an adaptive fusion strategy based on multi-level features of backbone network, enhancing the expression ability of multi-scale objects through upsampling and feature stacking, and reconstructing the FPN. The local features extracted by convolutional neural networks are mapped to graph-structured data, and the nodal attention mechanism of GAT is used to capture the global topological association of space objects, which makes up for the deficiency of the convolutional operation in weight allocation and realizes GAT integration. The Dilated Encoder network is introduced to cover different-scale targets by differentiating receptive fields, and the feature weight allocation is optimized by combining it with a Convolutional Block Attention Module (CBAM). According to the characteristics of space missions, an annotated dataset containing 8000 satellite and space station images is constructed, covering a variety of lighting, attitude and scale scenes, and providing benchmark support for model training and verification. Experimental results on the space object dataset reveal that the enhanced algorithm achieves a mean average precision (mAP) of 97.2%, representing a 2.1% improvement over the original YOLOv8_L. Comparative experiments with six other models demonstrate that the proposed algorithm outperforms its counterparts. Ablation studies further validate the synergistic effect between the graph attention network (GAT) and the Dilated Encoder. The results indicate that the model maintains a high detection accuracy under challenging conditions, including strong light interference, multi-scale variations, and low-light environments. Full article

In this paper, an underlying perturbed Ricci flow construction is made within the metric operator space, originating from the Heisenberg dynamical equations, to formulate a method which appears to provide a new geometric approach for the geometric formulation of the quantum mechanical dynamics. A quantum mechanical notion of stability and local instability is introduced within the quantum mechanical theory, based on the quantum mechanical dynamical equations governing the evolution of the tensor metric operator. The stability analysis is conducted in the topology of little $H\ddot{o}lder$ spaces of metrics which the tensor metric operator acts on. Finally, a theorem is introduced in an attempt to characterize the stability properties of the quantum mechanical system such that it brings the quantum mechanical dynamics into the analysis. Full article

We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensional Hilbert spaces. Following Jacobson, I view the background geometry as a hydrodynamic flow, whose connection to an underlying quantum system follows from the Bekenstein–Hawking relation between area and entropy, generalized to arbitrary causal diamonds. The time-like geodesics are equivalent to the nested sequences of causal diamonds, and the area of the holoscreen (The holoscreen is the maximal $d-2$ volume (“area”) leaf of a null foliation of the diamond boundary. I use the term area to refer to its volume.) encodes the entropy of a certain density matrix on a finite-dimensional Hilbert space. I review arguments that the modular Hamiltonian of a diamond is a cutoff version of the Virasoro generator $L_0$ of a $1+1$-dimensional CFT of a large central charge, living on an interval in the longitudinal coordinate on the diamond boundary. The cutoff is chosen so that the von Neumann entropy is $\ln {\mathrm{D}}_{\diamond },$ up to subleading corrections, in the limit of a large-dimension diamond Hilbert space. I also connect those arguments to the derivation of the ’t Hooft commutation relations for horizon fluctuations. I present a tentative connection between the ’t Hooft relations and $U\left(1\right)$ currents in the CFTs on the past and future diamond boundaries. The ’t Hooft relations are related to the Schwinger term in the commutator of the vector and axial currents. The paper in can be read as evidence that the near-horizon dynamics for causal diamonds much larger than the Planck scale is equivalent to a topological field theory of the ’t Hooft CR plus small fluctuations in the transverse geometry. Connes’ demonstration that the Riemannian geometry is encoded in the Dirac operator leads one to a completely finite theory of transverse geometry fluctuations, in which the variables are fermionic generators of a superalgebra, which are the expansion coefficients of the sections of the spinor bundle in Dirac eigenfunctions. A finite cutoff on the Dirac spectrum gives rise to the area law for entropy and makes the geometry both “fuzzy” and quantum. Following the analysis of Carlip and Solodukhin, I model the expansion coefficients as two-dimensional fermionic fields. I argue that the local excitations in the interior of a diamond are constrained states where the spinor variables vanish in the regions of small area on the holoscreen. This leads to an argument that the quantum gravity in asymptotically flat space must be exactly supersymmetric. Full article

The L-space and P-space are two essential representations for studying complex networks that contain different clusters. Existing network models can successfully generate networks in L-space, but generating networks in P-space poses significant challenges. In this study, we present an empirical analysis of the distribution of the number of a line’s nodes and the properties of the networks generated by these data in P-space. To gain insights into the operational mechanisms of the network of these data, we propose an event–link model that incorporates new nodes and links in P-space based on actual data characteristics using real data from marine and public transportation networks. The entire network consists of a series of events that consist of many nodes, and all nodes in an event are connected in the P-space. We conduct simulation experiments to explore the model’s topological features under different parameter conditions, demonstrating that the simulation outcomes are consistent with the theoretical analysis of the model. This model exhibits small-world characteristics, scale-free behavior, and a high clustering coefficient. The event–link model, with its adjustable parameters, effectively generates networks with stable structures that closely resemble the statistical characteristics of real-world networks that share similar growth mechanisms. Moreover, the network’s growth and evolution can be flexibly adjusted by modifying the model parameters. Full article