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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]

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]

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]

Let G be a finite connected undirected graph and G⇀ a strong orientation of G. The diameter of G⇀, denoted by diam(G⇀), is the maximum directed distance between any two vertices of G⇀. The oriented diameter of G is defined as diam⇀(G)=min{diam(G⇀)∣G⇀is a strong orientation ofG}. In this paper, we show that diam⇀(G)≤⌈n∕2⌉ for any maximal outerplanar graph G of order n≥3, with four exceptions, and the upper bound is sharp. [ABSTRACT FROM AUTHOR]

For two given sets C1 and C2 of cycles, the Ramsey number R(C1,C2) is the smallest integer N such that for any graph G on N vertices, either G contains a cycle from C1 or G¯ contains a cycle from C2. In this paper, we determine all Ramsey numbers R(C1,C2), which confirms a conjecture due to Hansson, and extends the well‐known Ramsey numbers for two cycles. [ABSTRACT FROM AUTHOR]

Carbon fibre‐reinforced polymers (CFRPs) are now widely used for high‐performance fields such as aircraft structures. On average, these structural components are subjected with more than 108 cycles during their lifetime. To make full use of the mechanical performance of CFRP, the fatigue behaviour needs to be well studied. Nevertheless, at present, fatigue behaviour and failure mechanisms of CFRP under hygrothermal environment are not sufficiently investigated. To obtain comprehensive knowledge about fatigue behaviour and failure mechanisms of CFRP, hygrothermal tests and ultrasonic three‐point bending fatigue experiments are designed. Besides, a damage variable is proposed as the function of stiffness to evaluate the fatigue degradation of the composite. A nonlinear continuum damage mechanics (CDM) model is compared with three models and employed for fatigue damage evolution under cyclic loading. Compared with the other three models, the experimental results show a better consistency between the result of the CDM model and the measured damage. Meanwhile, the damage variable expresses the damage state of the composite effectively. The damage variable and the CDM model provide a reference for fatigue characterization analysis and further life prediction of CFRP. [ABSTRACT FROM AUTHOR]