On the Erdos-Sos Conjecture for Graphs on n=k+4 Vertices

The Erd\H{o}s-S\'{o}s Conjecture states that if $G$ is a simple graph of order $n$ with average degree more than $k-2,$ then $G$ contains every tree of order $k$. In this paper, we prove that Erd\H{o}s-S\'{o}s Conjecture is true for $n=k+4$.Comment: 18 page

SU(3) trimer resonating-valence-bond state on the square lattice

We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.Comment: 6 pages, 6 figure

Recurrent Neural Networks For Accurate RSSI Indoor Localization

This paper proposes recurrent neuron networks (RNNs) for a fingerprinting indoor localization using WiFi. Instead of locating user's position one at a time as in the cases of conventional algorithms, our RNN solution aims at trajectory positioning and takes into account the relation among the received signal strength indicator (RSSI) measurements in a trajectory. Furthermore, a weighted average filter is proposed for both input RSSI data and sequential output locations to enhance the accuracy among the temporal fluctuations of RSSI. The results using different types of RNN including vanilla RNN, long short-term memory (LSTM), gated recurrent unit (GRU) and bidirectional LSTM (BiLSTM) are presented. On-site experiments demonstrate that the proposed structure achieves an average localization error of $0.75$ m with $80\%$ of the errors under $1$ m, which outperforms the conventional KNN algorithms and probabilistic algorithms by approximately $30\%$ under the same test environment.Comment: Received signal strength indicator (RSSI), WiFi indoor localization, recurrent neuron network (RNN), long shortterm memory (LSTM), fingerprint-based localizatio

Numerical Research About the Internal Flow of Steam-jet Vacuum Pump: Evaluation of Turbulence Models and Determination of the Shock-mixing Layer

AbstractSteam-jet vacuum pump is widely used in a range of applications. This paper evaluated the performance of four well-known turbulence models for predicting and understanding the internal flow of a steam-jet vacuum pump first. With the help of a commercial computational fluid dynamics (CFD) code ANSYS-Fluent 6.3, the simulation results obtained from the concerned turbulence models were compared with experimental values, the k-omega-SST model was chosen as a tool model for carrying out numerical simulations. Then, based on the simulation results obtained from specific operating conditions, a method for locating the shock-mixing layer was put forward. The shape of the shock-mixing layer shows that the secondary steam does not mix with the primary steam immediately after being induced into the mixing chamber of the pump; actually, they maintain their independence till the shocking position instead. After the shock happens, the shock-mixing layer disappear, the two fluid in the pump begin to mix with each other and discharge to the next stage with almost the same state. Based on the shape of the shock-mixing layer and the supersonic region of the secondary steam, a detailed analysis for the flow duct of the secondary steam was carried out. It is found that the throat of the secondary steam flow duct plays a crucial role in maintaining a stable operating state and the length of the throat reflects the back pressure endurance for the pump

Numerical analysis of an annular water-air jet pump with self-induced oscillation mixing chamber

This paper presents an improved annular water-air jet pump concept design through integrating a self-induced oscillation mixing chamber with the conventional annular jet pump (AJP). The internal flow characteristics for both conventional and improved AJP were numerically investigated and compared by a validated computational fluid dynamics model. The numerical comparison demonstrated an approximately 10% pumping performance increase compared with the conventional pump, which is mostly attributed to the improved mass and energy transfer along the oscillating phase interface. Furthermore, transient flow analysis was conducted to resolve the unsteady self-introduced oscillation. The results revealed the self-introduced oscillation induces a continuous break-up and formation of fresh water-air interfaces, which exhibits a periodic feature with a dominant frequency of 147 Hz for the current design under given operational conditions. This study contributes toward a better understanding of the internal annular water-air jet pump flow patterns, and also demonstrates the feasibility of incorporating self-introduced oscillation chamber into AJP design

TFN: An Interpretable Neural Network with Time-Frequency Transform Embedded for Intelligent Fault Diagnosis

Convolutional Neural Networks (CNNs) are widely used in fault diagnosis of mechanical systems due to their powerful feature extraction and classification capabilities. However, the CNN is a typical black-box model, and the mechanism of CNN's decision-making are not clear, which limits its application in high-reliability-required fault diagnosis scenarios. To tackle this issue, we propose a novel interpretable neural network termed as Time-Frequency Network (TFN), where the physically meaningful time-frequency transform (TFT) method is embedded into the traditional convolutional layer as an adaptive preprocessing layer. This preprocessing layer named as time-frequency convolutional (TFconv) layer, is constrained by a well-designed kernel function to extract fault-related time-frequency information. It not only improves the diagnostic performance but also reveals the logical foundation of the CNN prediction in the frequency domain. Different TFT methods correspond to different kernel functions of the TFconv layer. In this study, four typical TFT methods are considered to formulate the TFNs and their effectiveness and interpretability are proved through three mechanical fault diagnosis experiments. Experimental results also show that the proposed TFconv layer can be easily generalized to other CNNs with different depths. The code of TFN is available on https://github.com/ChenQian0618/TFN.Comment: 20 pages, 15 figures, 5 table