Search Results (20)

This study is dedicated to a separable $\mathbb{F}(\mathbb{R},\mathbb{T})$-gravity related to the bulk viscous string fluid to extract the equation of state for $\mathbb{F}(\mathbb{R},\mathbb{T})$-gravity. In this research, we offer an insight into calculating the density and pressure in terms of string tension in the phantom barrier, stiff fluid, and matter-dominated eras. As demonstrated, if a spacetime in $\mathbb{F}(\mathbb{R},\mathbb{T})$-gravity is full of bulk viscous string fluid matter, it is a generalized quasi-Einstein spacetime. In addition, we determine the equation of state of Ricci semi-symmetric and Ricci pseudo-symmetric spacetime in $\mathbb{F}(\mathbb{R},\mathbb{T})$-gravity filled with bulk viscous string fluid matter. Finally, we try to give the energy constraints in view of Penrose’s singularity theorem of black holes for the spacetime in $\mathbb{F}(\mathbb{R},\mathbb{T})$-gravity attached to bulk viscous string fluid. Full article

The aim of this paper is to characterize a relativistic bulk viscous fluid string spacetime whose energy–momentum tensor satisfying certain geometric symmetries. At first, it is shown that a relativistic bulk viscous fluid string spacetime is a generalized quasi-Einstein manifold. Then, we characterize such a spacetime, satisfying Codazzi type of energy–momentum tensor (denoted by ${\mathcal{T}}^{\oslash }$), covariant constant ${\mathcal{T}}^{\oslash }$, recurrent and generalized recurrent ${\mathcal{T}}^{\oslash }$, and almost pseudo-symmetric and weakly symmetric ${\mathcal{T}}^{\oslash }$, respectively. Next, we consider quadratic Killing ${\mathcal{T}}^{\oslash }$ in such a spacetime. Finally, we provide a concrete example using partial differential equations. Full article

Physical-layer key generation (PLKG) is a technique that produces symmetric encryption keys by exploiting the inherent characteristics of wireless channels. It offers advantages including high physical-layer security, elimination of pre-shared keys, dynamic upgradability, and resistance to quantum attacks, making PLKG a promising security solution for next-generation (6G) networks. However, satellite communication channels exhibit high dynamics and long propagation delays. Characteristics such as large Doppler shifts, short coherence times, and orbital predictability pose severe challenges to PLKG, including reciprocity degradation, low key generation rate (KGR), and susceptibility to channel-prediction attacks. This work proposes a delay-Doppler domain time-hopping key generation scheme (KE-DD-TH) based on Orthogonal Time Frequency Space (OTFS) modulation for high-speed links between Low-Earth-Orbit (LEO)/Medium-Earth-Orbit (MEO) satellites and ground terminals in Ka/Ku bands. The scheme performs non-uniform sampling on the DD domain grid of OTFS symbols using an ephemeris-driven pseudo-random time-hopping sequence generated by cascaded linear feedback shift registers (LFSRs) and a nonlinear matrix transformation. Both legitimate parties estimate the channel only at time-hopping instants and multiply two adjacent estimates to construct an “equivalent channel” matrix, yielding a random source with high entropy, high reciprocity, and low predictability. The eavesdropper’s key disagreement rate (KDR) remains close to 0.5 under all signal-to-noise ratio (SNR) conditions, corresponding to the ideal random-guessing baseline. This indicates that Eve obtains negligible mutual information, i.e., $I(K_A;K_E)\approx 0$. By contrast, the conventional KE-DD scheme allows Eve’s KDR to degrade to 0.014 at 30 dB SNR, indicating near-complete key recovery. The generated keys pass all 12 randomness tests of the NIST SP 800-22 statistical test suite. Full article

This manuscript investigates conformal $\eta$-Ricci–Yamabe solitons of type $(\kappa ,l)$ on Kählerian Norden space-time admitting a Kählerian Norden torse-forming vector field. Necessary conditions are obtained under which the soliton exhibits expanding, steady, or shrinking behavior. The analysis is further extended to several physically relevant fluid models, including dark fluid, dust fluid, stiff matter, and radiational fluid, and the corresponding geometric constraints are derived. In addition, structural results are established for Kählerian Norden space-times with a vanishing space–matter tensor and with a divergence-free matter tensor, highlighting their influence on the curvature geometry. The study also addresses several intrinsic curvature conditions of the space-time, such as conformal flatness, Ricci semi-symmetry, Ricci recurrence, and pseudo-Ricci symmetry, leading to a collection of geometric and physical characterizations. The results obtained provide a unified geometric framework linking Ricci–Yamabe soliton structures, fluid dynamics, and curvature properties within the setting of Kählerian Norden geometry. Full article

The present paper is aimed at studying the convergence of the Yamabe flow in the case of noncompact solitons. The more specified example of locally conformally flat noncompact solitons is addressed with the aim to newly analyse the qualities of the Ricci scalar. The particular case of noncompact pseudo-Riemannian solitons is studied; moreover, in the instances of Schwarzschild and Generalized-Schwarzschild geometries, rescalings of spherically symmetric weights are performed. For this purpose, new results are achieved as far as the considered structures are concerned. The Myers Theorem is upgraded as the new Myers paradigm of spacetime-dimensional manifolds, where the Einstein Field Equations can now be taken into account. In particular, the Myers Theorems are studied here as far as their new implementation in General Relativity Theory is concerned. As a first important result, the Myers mean curvature is found to coincide with the Ricci scalar in General Relativity Theory, where the 4-position of the observer, from which the 4-velocity 4-vector is calculated from, is taken as that of the observer solidal with the reference frame of the photon. The following results are also of relevance. In more detail, the umbilicity conditions are applied. At a further step, the role of the umbilicity conditions in GR after the Myers Theorems are studied for weighted manifolds and specific new implications of weighted manifolds are developed. The description of the weighted Schwarzschild manifolds and that of the weighted Generalized-Schwarzschild manifolds are newly studied as follows: as a new finding, the Birkhoff Theorem is newly reconciled with the rotational ansatz of the metrised solitons, and the comparison with the previous results about the Brendle non-metrised solitons is accomplished with the outcome stressing the new roles of the new rescalings of the metric tensor with respect to the previous known results of the scaling of the metric tensor of the non-metrised solitons. In the present framework, these procedures allow one to prove the reconciliation of the EFEs with the Yamabe flow. The flow on the tipping lightcones is newly written. The umbilicity condition is studied in General Relativity after the upgrade of the Myers Theorems as far as the sectional curvatures are concerned; as a result, the Calabi–Bernstein description is implemented in General Relativity, as well as the Chen–Yau requirements, and the cases of weighted manifolds are taken into account. More specifically, the equal-time 2-dimensional space surfaces are studied analytically, onto which the weighted General-Relativistic solitons which satisfy the Einstein field equations after the Yamabe flow are projected due to the rotational ansatz. As an accessory introductory result, the class of Wu non-metrised solitons are proven to be discarded in several aspects of the Wu description as the conditions provided after the work of Wu are not compatible with metrisation. Full article

This study is dedicated to a separable $F(\mathfrak{R},\mathfrak{T})$-gravity related to the anisotropic matter to extract the equation of state for $F(\mathfrak{R},\mathfrak{T})$-gravity. In this research, we offer insight into calculating the density and pressure in the phantom barrier, stiff fluid, and matter-dominated eras, respectively. As demonstrated, a spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity full of anisotropic matter is a generalized quasi-Einstein spacetime. In addition, we gain the equation of state of Codazzi type, Ricci semi-symmetric and Ricci-pseudo symmetric anisotropic fluid spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity. We prove an anisotropic spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity endowed with Codazzi-type Ricci tensor is a Yang Pure spacetime and Robertson–Walker spacetime. Furthermore, we try to give out the energy constraints of Penrose’s singularity theorem for black holes in an anisotropic fluid spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity. Lastly, we study hyperbolic Ricci solitons on anisotropic fluid spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity endowed with a torse-forming vector field, and for steady hyperbolic Ricci soliton, we deduced the equation of state of anisotropic fluid spacetime in $F(\mathfrak{R},\mathfrak{T})$-gravity. Full article

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. Full article

A two-fluid model can be described by an anisotropic fluid matter, and we introduced the notion of an anisotropic fluid spacetime. The algebraic and differential properties of an anisotropic fluid spacetime equipped with several forms of the stress–energy tensor is the focus of this research. We show that an anisotropic fluid spacetime with a radial pressure $p^{\Vert }$, transverse pressure $p^{\perp }$, and the energy density $\rho$ is a generalized quasi-Einstein spacetime. We prove that a dark matter era or an anisotropic fluid spacetime with vanishing vorticity is represented by an anisotropic fluid spacetime endowed with a covariant constant stress–energy tensor; on the contrary, a dark matter era or the expansion scalar vanishes is represented by an anisotropic fluid spacetime endowed with a Codazzi type of stress–energy tensor, as long as $\mathcal{A}$ stays invariant under the velocity vector field $\zeta$. Furthermore, we use the Killing velocity vector field, parallel vector fields to characterize Ricci Semi-Symmetric, $\mathcal{T}$-recurrent, Pseudo-Ricci symmetric, and $\widehat{\mathbb{R}}$-harmonic anisotropic fluid spacetime. We find that the anisotropic fluid spacetime reflect a stiff matter and a radiation era with these geometric symmetries. Finally, we provide findings for an anisotropic fluid spacetime with a divergence-free matter tensor and the vanishing space-matter tensor and explore the dynamical aspects of cosmological epoch of an anisotropic fluid spacetime coupled with $f\left(\mathcal{R}\right)$-gravity. Full article

This paper investigates pseudo-symmetric space–times within two interrelated frameworks: vacuum $f\left(R\right)$-gravity and Gray’s seven canonical decomposition subspaces. First, it is established that any conformally flat pseudo-symmetric space–time satisfying the vacuum field equations of $f\left(R\right)$-gravity necessarily corresponds to a perfect fluid. Subsequently, a detailed analysis of Gray’s subspaces reveals the following structural results: In the trivial and $\mathsf{𝒜}$ subspaces, pseudo-symmetric space–times are Ricci-simple and Weyl-harmonic, and thus are necessarily generalized Robertson–Walker space–times. In the $\mathcal{B}$ and $\mathsf{𝒜}\oplus \mathcal{B}$ subspaces, the associated time-like vector field ${\xi }^l$ is shown to be an eigenvector of the Ricci tensor with the eigenvalue $-R/2$. Furthermore, for a perfect fluid pseudo-symmetric space–time obeying $f\left(R\right)$-gravity and belonging to the trivial, $\mathsf{𝒜}$, $\mathcal{B}$, or $\mathsf{𝒜}\oplus \mathcal{B}$ subspaces, the isotropic pressure p and energy density $\sigma$ are proven to be constants. Additionally, it is demonstrated that Gray’s $\mathcal{I}$ subspace reduces to the $\mathcal{B}$ subspace in the pseudo-symmetric setting. Finally, under specific geometric conditions, pseudo-symmetric space–times in the $\mathcal{I}\oplus \mathsf{𝒜}$ and $\mathcal{I}\oplus \mathcal{B}$ subspaces are also shown to admit perfect fluid representations. These results collectively clarify the geometric and physical constraints imposed by pseudo-symmetry within $f\left(R\right)$-gravity and Gray’s classification scheme. Full article

Source camera identification relies on sensor noise features to distinguish between different devices, but large-scale sample labeling is time-consuming and labor-intensive, making it difficult to implement in real-world applications. The noise residuals generated by different camera sensors exhibit statistical asymmetry, and the structured patterns within these residuals also show local symmetric relationships. Together, these features form the theoretical foundation for camera source identification. To address the problem of limited labeled data under few-shot conditions, this paper proposes a Cross-correlation Guided Augmentation and Prediction with Hybrid Bidirectional State-Space Model Attention (CGAP-HBSA) framework, based on the aforementioned symmetry-related theoretical foundation. The method extracts symmetric correlation structures from unlabeled samples and converts them into reliable pseudo-labeled samples. Furthermore, the HBSA network jointly models symmetric structures and asymmetric variations in camera fingerprints using a bidirectional SSM module and a hybrid attention mechanism, thereby enhancing long-range spatial modeling capabilities and recognition robustness. In the Dresden dataset, the proposed method achieves an identification accuracy for the 5-shot camera source identification task that is only 0.02% lower than the current best-performing method under few-shot conditions, MDM-CPS, and outperforms other classical few-shot camera source identification methods. In the 10-shot task, the method improves by at least 0.3% compared to MDM-CPS. In the Vision dataset, the method improves the identification accuracy in the 5-shot camera source identification task by at least 6% compared to MDM-CPS, and in the 10-shot task, it improves by at least 3% over the best-performing MDM-CPS method. Experimental results demonstrate that the proposed method achieves competitive or superior performance in both 5-shot and 10-shot settings. Additional robustness experiments further confirm that the HBSA network maintains strong performance even under image compression and noise contamination conditions. Full article

The goal of the article is to examine the behavior of bulk viscous fluid string spacetime with a fluid density of the bulk viscous fluid string $\rho$ and a tension of the bulk viscous fluid string $\lambda$. This is known as relativistic bulk viscous fluid string spacetime. We derive some conclusions for bulk viscous fluid string with a vanishing space–matter tensor and a divergence-free matter tensor. We then focus on certain curvature properties for bulk viscous fluid string spacetime, including conformally flat, Ricci recurrent, Ricci semi-symmetric, and pseudo-Ricci-symmetric. Some physical results that align with the equation of state of Ricci semi-symmetric bulk viscous fluid string spacetime are also obtained. Full article

This paper proposes a free-space time–frequency phase (TFP)-synchronization transmission architecture based on optoelectronic hybrid technology, addressing the high-precision TFP synchronization and high-speed communication requirements between mobile platforms in distributed collaborative positioning and other applications. The proposed scheme utilizes symmetric free-space optical (FSO) links to effectively suppress drift errors, integrating the high bandwidth of optical links and the high stability of microwave links, enabling one-to-many networking synchronization between mobile platforms. The system adopts optical wireless transmission technology based on pseudo-code regenerative ranging, integrating 1.5 Gbps high-speed data transmission with high-precision TFP-synchronization functionality. An experimental system consisting of a main station and two auxiliary stations was established in an outdoor mobile platform scenario. Experimental results show that while achieving high-speed communication, the frequency synchronization precision is 0.0131 ppb, frequency stability is in the order of 10⁻¹⁰@1 s, and phase synchronization precision is approximately 3.56°. The system achieves time synchronization precision at the picosecond level. The proposed technology is highly suitable for high-precision synchronization communication in scenarios lacking fiber-optic infrastructure, effectively fulfilling rigorous requirements in mobile platform applications such as distributed collaborative positioning. Full article

In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds ${\left(PSS\right)}_n$. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example. Full article

The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form $\zeta ={\zeta }_1+{\zeta }_2$ are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse’s problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated. Full article

This paper proposes an approach for pool mining in public blockchain systems based on the employment of a recently reported consensus protocol with the puzzle based on a symmetric encryption that provides an energy–space trade-off and reduces energy consumption. The proposed architecture employs a pseudo-symmetric allocation of the resources for the blockchain consensus protocol and provides protection against certain malicious actions of the pool members, as well as a miner’s opportunity for selecting the resources required for participation in the consensus protocol. Given that the considered consensus protocol employs two resources, the proposed architecture uses this two-dimensional nature to provide resistance against block withholding and selfish mining attacks, as well as a reduction in energy spending as a trade-off with the employment of certain memory resources. The high resistance of the proposed pool mining approach against the considered attacks appears to be a consequence of the success probability of the pool in comparison with the success probability of malicious miners. Assuming appropriate selection of the puzzle hardness, the probability that malicious miners can solve the puzzle without the support of the pool manager can be arbitrarily small. Implementation of the proposed approach on a modified Ethereum platform and experimental evaluation issues have also been reported. The conceptual novelty of the proposed pool mining approach is the following: Instead of separation of the blockchain consensus protocol and control of pool miners honest work, this paper proposes an approach where honest work of miners and pool managers is provided by a dedicated application of the considered consensus protocol. Advantages of the proposal in comparison with the previously reported ones include the following: (i) high resistance against block withholding and selfish mining attacks without an additional security procedure; (ii) reduction in the energy required, and at the same time preservationthe security of the consensus protocol; (iii) flexibility of the pool miners regarding selection of the resources that should be employed providing a trade-off between required energy and memory resources. The proposed architecture was implemented employing a dedicated modification of the Ethereum platform and the performed experiments confirmed the feasibility and effectiveness of the proposal. Full article