Search Results (153)

In this review, we begin with a historical survey of some singular solutions in the theory of gravitation, as well as a very brief discussion of how black holes could physically form. Some possible scenarios which could perhaps eliminate these singularities are then reviewed and discussed. Due to the vastness of the field, its coverage is not exhaustive; instead, the concentration is on a small subset of topics such as possible quantum gravity effects, non-commutative geometry, and gravastars. A simple singularity theorem is also reviewed. Although parts of the manuscript assume some familiarity with relativistic gravitation or differential geometry, the aim is for the broad picture to be accessible to non-specialists of other physical sciences and mathematics. Full article

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation $AXB=C$ has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation $AXB=C$ over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation $AXB=C$. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions. Full article

A nontrivial conformal vector field $\omega$ on an m-dimensional connected Riemannian manifold $\left(M^m,g\right)$ has naturally associated with it the conformal potential $\theta$, a smooth function on $M^m$, and a skew-symmetric tensor T of type $(1,1)$ called the associated tensor. There is a third entity, namely the vector field $T\omega$, called the orthogonal reflection field, and in this article, we study the impact of the condition that commutator $\left[\omega ,T\omega \right]=0$; this condition that we refer to as the orthogonal reflection field is commutative. As a natural impact of this condition, we see the existence of a smooth function $\rho$ on $M^m$ such that $\nabla \theta =\rho \omega$; this function $\rho$ is called the proportionality function. First, we show that an m-dimensional compact and connected Riemannian manifold $\left(M^m,g\right)$ admits a nontrivial conformal vector field $\omega$ with a commuting orthogonal reflection $T\omega$ and constant proportionality function $\rho$ if and only if $\left(M^m,g\right)$ is isometric to the sphere $S^m\left(c\right)$ of constant curvature c. Secondly, we find three more characterizations of the sphere and two characterizations of a Euclidean space using these ideas. Finally, we provide a condition for a conformal vector field on a compact Riemannian manifold to be closed. Full article

The ability of the cross-city commuting labor force to obtain housing has a profound impact on the development of the housing market and the enhancement of social welfare, but whether cross-city commuting has facilitated housing purchases remains to be verified However, the research on whether cross-city commuting behavior promotes labor force housing purchase in metropolitan areas is still lacking, especially in China, where the culture of buying houses is relatively special. This article used field survey data from the 2023 China Metropolitan Area Occupation and Housing Status Sampling Survey to empirically analyze whether cross-city commuting has facilitated housing purchases within metropolitan areas. The analysis was conducted by constructing a baseline model, a mediation effect model, and a subsample regression model. The results show that the cross-city commuting facilitated housing purchase within metropolitan areas, and the location preference is to purchase a house with a distance of 20–40 km from the workplace, but the contribution of the cross-city commuting to multi-suite purchases is relatively low. Mechanism analysis shows that compared to the workers who work and live in peripheral areas or the workers who work and live in cores, intercity commuters are promoted to purchase housing by relatively higher income and inducement of the housing price gap. The above conclusions still hold after controlling potential endogeneity issues and in robustness tests. The research of this paper can provide a new perspective for alleviating the housing inequality in the metropolitan area. Full article

Understanding the travel patterns of university campus visitors is crucial for developing effective transportation strategies. Existing research predominantly focuses on student commuting within specific regions, often overlooking the diverse needs of faculty and staff and varying campus contexts. This study addresses a significant gap in the literature by investigating travel behaviors at Beirut Arab University (BAU), which has not been previously studied in this context. BAU’s unique situation, with campuses in both urban and rural zones, presents distinct transportation challenges, particularly for those traveling between these areas. Through a comprehensive survey of students, faculty, and staff, this research explores differences in transportation modes, travel distances, durations, and patterns. Statistical techniques, including one-way analysis of variance (ANOVA), Chi-Squared, and McNemar-Bowker tests, reveal significant variations among traveler groups. The findings highlight specific needs, such as improvements in bus services, car-sharing programs, and parking facilities, essential for creating sustainable campus environments. By examining these travel behaviors, the study offers valuable insights into the complexities of campus transportation, contributing new perspectives to the field. The originality of this research lies in its focus on an underexplored area, providing a deeper understanding of how diverse university environments impact transportation choices. This work not only fills a critical void in campus transportation research but also offers practical recommendations for enhancing transportation systems in similar settings. Full article

It is crucial for both traffic management organisations and individual commuters to be able to forecast traffic flows accurately. Graph neural networks made great strides in this field owing to their exceptional capacity to capture spatial correlations. However, existing approaches predominantly focus on local geographic correlations, ignoring cross-region interdependencies in a global context, which is insufficient to extract comprehensive semantic relationships, thereby limiting prediction accuracy. Additionally, most GCN-based models rely on pre-defined graphs and unchanging adjacency matrices to reflect the spatial relationships among node features, neglecting the dynamics of spatio-temporal features and leading to challenges in capturing the complexity and dynamic spatial dependencies in traffic data. To tackle these issues, this paper puts forward a fresh approach: a new self-supervised dynamic spatio-temporal graph convolutional network (SDSC) for traffic flow forecasting. The proposed SDSC model is a hierarchically structured graph–neural architecture that is intended to augment the representation of dynamic traffic patterns through a self-supervised learning paradigm. Specifically, a dynamic graph is created using a combination of temporal, spatial, and traffic data; then, a regional graph is constructed based on geographic correlation using clustering to capture cross-regional interdependencies. In the feature learning module, spatio-temporal correlations in traffic data are subjected to recursive extraction using dynamic graph convolution facilitated by Recurrent Neural Networks (RNNs). Furthermore, self-supervised learning is embedded within the network training process as an auxiliary task, with the objective of enhancing the prediction task by optimising the mutual information of the learned features across the two graph networks. The superior performance of the proposed SDSC model in comparison with SOTA approaches was confirmed by comprehensive experiments conducted on real road datasets, PeMSD4 and PeMSD8. These findings validate the efficacy of dynamic graph modelling and self-supervision tasks in improving the precision of traffic flow prediction. Full article

The article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor Couveignes-Rostovtsev-Stolbunov (CRS) scheme on ordinary non-cyclic Edwards curves are reviewed. Lower estimates of the computational speed gains of the modified algorithms over the original ones are obtained. The most significant results were obtained by choosing classes of non-cyclic Edwards curves connected as quadratic twist pairs instead of cyclic complete Edwards curves, as well as the method of algorithm randomization as an alternative to “constant time CSIDH”. It is shown that in the CSIDH and Commutative Supersingular Isogeny Key Encapsulation (CSIKE) algorithms, there are two independent cryptosystems with the possibility of parallel computation, eliminating the threat of side-channel attacks. There are four such cryptosystems for the CRS scheme. Integral lower bound estimates of the performance gain of the modified CSIDH algorithm are obtained at 1.5 × 2⁹, and for the CRS scheme are 3 × 2⁹. Full article

Torque ripple in a brushless DC motor (BLDCM) seriously restricts its application in high-performance fields. This paper proposes a commutation torque ripple suppression strategy based on a Zeta converter. The expected output voltage of a Zeta converter that suppresses the commutation torque ripple is obtained, according to the effect of the duty ratio of the Zeta converter on the turn-off phase freewheeling duration and the turn-on phase rising duration, during commutation. Based on the analysis of the dynamic response of the Zeta converter, the Zeta converter is adjusted to ensure that the Zeta converter reaches stability in sufficient time. During the commutation, the output voltage of the Zeta converter is connected to the main circuit to reduce the torque ripple during commutation, and the expected regulated duty cycle of the Zeta converter during the next commutation is calculated to adjust the output voltage of the Zeta converter. Based on this analysis, the experimental results verify the effectiveness of the proposed method. Full article

The integrated gate-commutated thyristor (IGCT) has the advantages of high voltage, high current, high reliability, and low manufacturing costs and has the potential to replace thyristor devices in the field of high-voltage direct current (HVDC) transmission. Over time, the development and manufacture of IGCT devices, drivers, and valve bodies have gradually matured, but the modeling and control technology of HVDC systems based on IGCT needs further research. This review aims to discuss the research status of key technologies of HVDC system modeling and control based on the IGCT in recent years, including the development of HVDC systems and the application potential of the IGCT, the efficient simulation and modeling technology of the IGCT HVDC system, and the key problems of HVDC system control technology based on the IGCT. At the same time, according to the author’s point of view, the existing problems and difficulties are extracted, and the next development ideas are clarified. Full article

This paper presents a single-phase Full-Bridge (FB) inverter with a hybrid commutation technique designed to reduce the harmonic distortion caused by the loss of the controller capability around the zero-crossing point in the unipolar commutation region. The hybrid modulation changes from unipolar to bipolar commutation under the loss of the reference control, improving the robustness and efficiency of the method. The commutation technique improves the switching performance and reduces the switching losses. Simulation models are developed in MATLAB/Simulink R2023b to evaluate their performance under different operating conditions. The results show that the proposed commutation technique can achieve high efficiency, low total harmonic distortion (THD), and fast dynamic response. The experimental implementation of sliding mode control (SMC) implemented in an STM32 microcontroller confirms that the hybrid commutation technique can reduce the THD by 0.96 percentage points for local (off-grid) loads and up to 2.45 in an industrial grid-tie network, compared with unipolar commutation. These findings highlight the potential of the proposed modulation technique for applications like solar panels and offer crucial insights for ongoing research and development in this field. Full article

This article considers arrowhead and diagonal-plus-rank-one matrices in ${\mathbb{F}}^{n\times n}$ where $\mathbb{F}\in \{\mathbb{R},\mathbb{C},\mathbb{H}\}$ and where $\mathbb{H}$ is a noncommutative algebra of quaternions. We provide unified formulas for fast determinants and inverses for considered matrices. The formulas are unified in the sense that the same formula holds in both commutative and noncommutative associative fields or algebras, with noncommutative examples being matrices of quaternions and block matrices. Each formula requires $O\left(n\right)$ arithmetic operations, as does multiplication of such matrices with a vector. The formulas are efficiently implemented using the polymorphism or multiple-dispatch feature of the Julia programming language. Full article

In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the $\mathbb{SE}\left(3\right)$ group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the $\mathbb{SE}\left(3\right)$ group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker–Campbell–Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the $\mathbb{SE}\left(3\right)$ group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional $\mathbb{SE}\left(3\right)$ group-based model. Full article

Over the years, prime submodules and their generalizations have played a pivotal role in commutative algebra, garnering considerable attention from numerous researchers and scholars in the field. This papers presents a generalization of 1-absorbing primary ideals, namely the classical 1-absorbing primary submodules. Let ℜ be a commutative ring and M an ℜ-module. A proper submodule K of M is called a classical 1-absorbing primary submodule of M, if $xyz\eta \in K$ for some $\eta \in M$ and nonunits $x,y,z\in \Re$, then $xy\eta \in K$ or $z^t\eta \in K$ for some $t\ge 1$. In addition to providing various characterizations of classical 1-absorbing primary submodules, we examine relationships between classical 1-absorbing primary submodules and 1-absorbing primary submodules. We also explore the properties of classical 1-absorbing primary submodules under homomorphism in factor modules, the localization modules and Cartesian product of modules. Finally, we investigate this class of submodules in amalgamated duplication of modules. Full article

Mass-impregnated (MI) cables have been used for many years as cables in high-voltage direct current (HVDC) systems. In line commutated converter (LCC) HVDC systems, polarity reversal for power flow control can induce significant electrical stress on MI cables. Furthermore, the mass oil and kraft paper comprising the impregnated insulation have significantly different coefficients of thermal expansion. Load fluctuations in the cable lead to expansion and contraction of the mass, creating pressure within the insulation and causing redistribution of the impregnant. During this process, shrinkage cavities can form within the butt gaps. Since the dielectric strength of the cavities is lower than that of the surrounding impregnation, cavitation phenomena in impregnated paper insulation are considered a factor in degrading insulation performance. Consequently, this study analyzes the electrical conductivity of thermally aged materials and investigates the transient electric field characteristics within the cable. Additionally, it closely analyzes the formation and dissolution of cavities in MI cables during polarity reversal based on a numerical model of pressure behavior in porous media. The conductivity of the impregnated paper indicates that it has excellent resistance to thermal degradation. Simulation results for various load conditions highlight that the interval of load-off time and the magnitude of internal pressure significantly influence the cavitation phenomenon. Lastly, the study proposes stable system operation methods to prevent cavitation in MI cables. Full article

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde–de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, while using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. In addition, we provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, is specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication. Full article