Search Results (5)

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the double covering of the general affine group $\overline{GA}(4,\mathbb{R})$. Then, by means of an appropriate decomposition of the metalinear double-covering group $\overline{SL}(5,\mathbb{R})$ with respect to the general linear double-covering group $\overline{GL}(4,\mathbb{R})$, one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations, allowing us to build the observables of the theory by means of the BRST algebra constructed using a $\overline{sa}(5,\mathbb{R})$ algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion. Full article

Prefabricated construction (PC) is considered to be a low-carbon construction method. Implementing prefabricated construction projects (PCPs) requires multiple industry organizations to participate and collaborate. As different PCPs are initiated and implemented, industry organizations will gradually gather into a complex and evolving collaborative network at the industry level based on specific collaboration relationships with different project backgrounds. The evolution of the collaborative network is related to how industry organizations interact with each other, and how PC-related knowledge and innovation has spread among organizations in the long term. However, the laws of network evolution and the micro effects that drive network evolution are still unknown. This study analyzes 236 prefabricated construction projects (PCPs) in Shanghai during 2015–2023, using the stochastic actor-oriented models (SAOM) method to explore how the macro structure of project-based inter-organizational collaborative networks for prefabricated construction (PC) technology implementation evolves over time, and how micro effects jointly support the evolution of the networks. The macro-level descriptive analysis of the network indicates that the collaborative network has become increasingly dense over time and continues to show a core–peripheral structure, with a small number of super-connected organizations. The micro-level SAOM analysis further reveals that the evolution of the collaborative network structure is driven by structure-based preferential attachment and geographic proximity effects, as well as attribute-based ownership similarity effect. This exploratory effort applies a network dynamics model to investigate the micro mechanism of the evolution of inter-organizational collaboration. The research results provide theoretical guidance and decision-making references for PC industry organizations to develop efficient network action strategies. In addition, it can help industry managers to formulate appropriate network management strategies. Full article

The hypercube $Q_n$ is one of the most popular interconnection networks with high symmetry. To reduce the diameter of $Q_n$, many variants of $Q_n$ have been proposed, such as the n-dimensional locally twisted cube $LT{Q}_n$. To further optimize the diameter of $LT{Q}_n$, the n-dimensional folded locally twisted cube $FLT{Q}_n$ is proposed, which is built based on $LT{Q}_n$ by adding $2^{n-1}$ complementary edges. Connectivity is an important indicator to measure the fault tolerance and reliability of a network. However, the connectivity has an obvious shortcoming, in that it assumes all the adjacent vertices of a vertex will fail at the same time. Super-connectivity is a more refined index to judge the fault tolerance of a network, which ensures that each vertex has at least one neighbor. In this paper, we show that the super-connectivity ${\kappa }^{\left(1\right)}\left(FLT{Q}_n\right)=2n$ for any integer $n\ge 6$, which is about twice $\kappa \left(FLT{Q}_n\right)$. Full article

This paper surveys recent progress in our search for an appropriate internal space algebra for the standard model (SM) of particle physics. After a brief review of the existing approaches, we start with the Clifford algebras involving operators of left multiplication by octonions. A central role is played by a distinguished complex structure that implements the splitting of the octonions $\mathbb{O}=\mathbb{C}\oplus {\mathbb{C}}^3$, which reflect the lepton-quark symmetry. Such a complex structure on the 32-dimensional space $\mathcal{S}$ of $C{\ell }_{10}$ Majorana spinors is generated by the $C{\ell }_6(\subset C{\ell }_{10})$ volume form, ${\omega }_6={\gamma }_1\cdots {\gamma }_6$, and is left invariant by the Pati–Salam subgroup of $Spin\left(10\right)$, $G_{\mathrm{PS}}=Spin\left(4\right)\times Spin\left(6\right)/{\mathbb{Z}}_2$. While the $Spin\left(10\right)$ invariant volume form ${\omega }_{10}={\gamma }_1\dots {\gamma }_{10}$ of $C{\ell }_{10}$ is known to split $\mathcal{S}$ on a complex basis into left and right chiral (semi)spinors, $\mathcal{P}=\frac{1}{2}(1-i{\omega }_6)$ is interpreted as the projector on the 16-dimensional particle subspace (which annihilates the antiparticles).The standard model gauge group appears as the subgroup of $G_{\mathrm{PS}}$ that preserves the sterile neutrino (which is identified with the Fock vacuum). The ${\mathbb{Z}}_2$-graded internal space algebra $\mathcal{A}$ is then included in the projected tensor product $\mathcal{A}\subset \mathcal{P}C{\ell }_{10}\mathcal{P}=C{\ell }_4\otimes C{\ell }_6^0$. The Higgs field appears as the scalar term of a superconnection, an element of the odd part $C{\ell }_4^1$ of the first factor. The fact that the projection of $C{\ell }_{10}$ only involves the even part $C{\ell }_6^0$ of the second factor guarantees that the color symmetry remains unbroken. As an application, we express the ratio $\frac{m_H}{m_W}$ of the Higgs to the W boson masses in terms of the cosine of the theoretical Weinberg angle. Full article

This paper presents an educational low-cost C-band frequency-modulated continuous wave (FMCW) radar system for use in indoor through-wall metal detection. Indoor remote-sensing applications, such as through-wall detection and positioning, are essential for the comprehensive realization of the internet of things or super-connected societies. The proposed system comprises a two-stage radio-frequency power amplifier, a voltage-controlled oscillator, circuits for frequency modulation and system synchronization, a mixer, a 3-dB power divider, a low-noise amplifier, and two cylindrical horn antennas (Tx/Rx antennas). The antenna yields gain values in the 6.8~7.8 range when operating in the 5.83~5.94 GHz frequency band. The backscattered Tx signal is sampled at 4.5 kHz using the Arduino UNO analog-to-digital converter. Thereafter, the sampled signal is transferred to the MATLAB platform and analyzed using a customized FMCW radar algorithm. The proposed system is built using commercial off-the-shelf components, and it can detect targets within a 56.3 m radius in indoor environments. In this study, the system could successfully detect targets through a 4 cm-thick ply board with a measurement accuracy of less than 10 cm. Full article