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Current transformers (CTs) are widely used for energy metering, relay protection, condition monitoring and control circuits. However, CT saturation may lead to non‐negligible measurement errors and relay malfunctions, posing a threat to the stability and security of the power grid. In order to address the problem of CT saturation, a novel measurement‐protection‐integrated current transformer (MPICT) is proposed. First, the working states of the MPICT are summarised and the approximate expressions for the steady‐state measuring characteristics, the transient response characteristics, and the measurement errors are derived from the equivalent circuit model. Then, the feasibility of the MPICT and the theoretical analyses are verified by the 3D FEM simulation imitating the presented MPICT excited by diverse currents. Finally, a down‐scale prototype is fabricated and a series of tests are conducted in the laboratory to validate the effectiveness of the equipment. The simulation and experimental results suggest that the output of the MPICT can accurately reconstruct the primary current waveform, even if the primary current contains decaying or constant DC component. [ABSTRACT FROM AUTHOR]

A graph G is a fractional $ (a,b,n) $ (a , b , n) -critical graph if removing any n vertices from G, the resulting subgraph still admits a fractional $ [a,b] $ [ a , b ] -factor. In this paper, we determine the exact tight isolated toughness bound for fractional $ (a,b,n) $ (a , b , n) -critical graphs. To be specific, a graph G is fractional $ (a,b,n) $ (a , b , n) -critical if $ \delta (G)\ge a+n $ δ (G) ≥ a + n and $ I(G)>a-1+\frac {n+1}{n_{a,b}} $ I (G) > a − 1 + n + 1 n a , b , where $ n_{a,b}\ge 2 $ n a , b ≥ 2 is an integer satisfies $ (n_{a,b}-1)a\le b\le n_{a,b}a-1 $ (n a , b − 1) a ≤ b ≤ n a , b a − 1. Furthermore, the sharpness of bounds is showcased by counterexamples. Our contribution improves a result from [W. Gao, W. Wang, and Y. Chen, Tight isolated toughness bound for fractional $ (k,n) $ (k , n) -critical graphs, Discrete Appl. Math. 322 (2022), 194–202] which established the tight isolated toughness bound for fractional $ (k,n) $ (k , n) -critical graphs. [ABSTRACT FROM AUTHOR]

Let G $G$ be a simple graph and λ(G) $\lambda (G)$ the spectral radius of G $G$. For k≥2 $k\ge 2$, a k $k$‐edge decomposition (H1,...,Hk) $({H}_{1},{\rm{\ldots }},{H}_{k})$ is k $k$ spanning subgraphs such that their edge sets form a k $k$‐partition of the edge set of G $G$. In this paper, we obtain some sharp lower and upper bounds for λ(H1)+⋯+λ(Hk) $\lambda ({H}_{1})+\,\cdots \,+\lambda ({H}_{k})$ in terms of the clique number of Hi ${H}_{i}$ and the size of G $G$, and discuss what k $k$‐edge decomposition (H1,...,Hk) $({H}_{1},{\rm{\ldots }},{H}_{k})$ can maximize λ(H1)+⋯+λ(Hk) $\lambda ({H}_{1})+\cdots \,+\lambda ({H}_{k})$ when G $G$ is a complete graph. These generalize some Nordhaus–Gaddum‐type results on spectral radius for k=2 $k=2$, due to Nosal, Hong and Shu, and Nikiforov. [ABSTRACT FROM AUTHOR]

In the networking designing phase, the network needs to be built according to certain indicators to ensure that the network has the ideal functions and can work smoothly. From a modeling perspective, each site in the network is represented by a vertex, channels between sites are represented by edges, and thus the entire network can be denoted as a graph. Problems in the network can be transformed into corresponding graph problems. In particular, the feasibility of data transmission can be transformed into the existence of fractional factors in network graph. This note gives an independent set neighborhood union condition for the existence of fractional factors in a special setting, and shows that the neighborhood union condition is sharp.

In data transmission networks, the availability of data transmission is equivalent to the existence of the fractional factor of the corresponding graph which is generated by the network. Research on the existence of fractional factors under specific network structures can help scientists design and construct networks with high data transmission rates. A graph G is named as an all fractional (g, f, n′, m)-critical deleted graph if the remaining subgraph keeps being an all fractional (g, f, m)-critical graph, despite experiencing the removal of arbitrary n′ vertices of G. In this paper, we study the relationship between neighborhood conditions and a graph to be all fractional (g, f, n′, m)-critical deleted. Two sufficient neighborhood conditions are determined, and furthermore we show that the conditions stated in the main results are sharp.

The Turán number ex(n,H) $\text{ex}(n,H)$ is the maximum number of edges in an H $H$‐free graph on n $n$ vertices. Let T $T$ be any tree. The odd‐ballooning of T $T$, denoted by To ${T}_{o}$, is a graph obtained by replacing each edge of T $T$ with an odd cycle containing the edge, and all new vertices of the odd cycles are distinct. In this paper, we determine the exact value of ex(n,To) $\text{ex}(n,{T}_{o})$ for sufficiently large n $n$ and To ${T}_{o}$ being good, which generalizes all the known results on ex(n,To) $\text{ex}(n,{T}_{o})$ for T $T$ being a star, due to Erdős, Füredi, Gould, and Gunderson (1995), Hou, Qiu, and Liu (2018), and Yuan (2018), and provides some counterexamples with chromatic number three to a conjecture of Keevash and Sudakov (2004), on the maximum number of edges not in any monochromatic copy of H $H$ in a 2‐edge‐coloring of a complete graph of order n $n$. [ABSTRACT FROM AUTHOR]

Recent studies have shown that there is a profound connection between the existence of H‐factors under attack circumstances and the parameters to measure the vulnerability of the network. The disadvantage of the previous theoretical conclusions is that the connectivity is often regarded as fixed, and the relationship between other network parameters and the H‐factor is explored. However, in a real situation, as the network structure changes, connectivity becomes a dynamically variational parameter, and its changing will affect other parameters to make corresponding changes. In this study, we treat all parameters as a complex system that restricts each other, consider their mutual constraints from a geometric point of view, and apply high‐dimensional surfaces to characterize their relationships. Seven network parameters including toughness and binding number are considered, and the concrete expression form of the surfaces in several specific settings are obtained. Furthermore, the local version for these seven network parameters are introduced. [ABSTRACT FROM AUTHOR]

Objective. This study aims to find the novel lncRNAs closely related to the progression of oral squamous cell carcinoma (OSCC) by comprehensively analyzing microarray. Methods. Chip dataset GSE84805 was downloaded from the Gene Expression Omnibus (GEO) database, lncRNA expression profiles of OSCC and paracancerous tissue were obtained, probes sequences reannotation was conducted, and differentially expressed lncRNAs (DELs) and differentially expressed genes (DEGs) were identified. Finally, these data were analyzed by constructing the lncRNA-function enrichment network. Results. We found that 465 lncRNAs are differentially expressed consisting of 193 upregulated lncRNAs and 272 downregulated lncRNAs. Meanwhile, 811 DEGs were identified with 498 upregulated genes and 313 downregulated genes. Analysis of the lncRNA-function enrichment network showed that these aberrant lncRNAs may be related to focal adhesion, inflammatory response pathway, cell cycle, matrix metalloproteinases, and other biological functions. Also, we found that some key lncRNAs such as LINC00152 and HOXA11-AS have been shown to play an important role in tumor proliferation and migration. Conclusion. The key lncRNAs may serve as potential molecular markers or therapeutic targets in OSCC formation and development. It can also help us to understand the molecular mechanism of occurrence and development in OSCC. [ABSTRACT FROM AUTHOR]