Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras

In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring $R$. It is proved that, if the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with zero center, then every triple derivation of $L$ is a derivation, and every triple derivation of the derivation algebra $Der (L)$ is an inner derivation. Let $L,~L^{'}$ be Lie superalgebras over a commutative ring $R$, the notion of triple homomorphism from $L$ to $L^{'}$ is introduced. We proved that, under certain assumptions, homomorphisms, anti-homomorphisms, and sums of homomorphisms and anti-homomorphisms are all triple homomorphisms.Comment: 12pages in Indagationes Mathematicae, 201

Linear-Combined-Code-Based Unambiguous Code Discriminator Design for Multipath Mitigation in GNSS Receivers

Unambiguous tracking and multipath mitigation for Binary Offset Carrier (BOC) signals are two important requirements of modern Global Navigation Satellite Systems (GNSS) receivers. A GNSS discriminator design method based on optimization technique is proposed in this paper to meet these requirements. Firstly, the discriminator structure based on a linear-combined code is given. Then the requirements of ideal discriminator function are converted into the mathematical constraints and the objective function to form a non-linear optimization problem. Finally, the problem is solved and the local code is generated according to the results. The theoretical analysis and simulation results indicate that the proposed method can completely remove the false lock points for BOC signals and provide superior multipath mitigation performance compared with traditional discriminator and high revolution correlator (HRC) technique. Moreover, the proposed discriminator is easy to implement for not increasing the number of correlators

Cross-Correlation-Function-Based Multipath Mitigation Method for Sine-BOC Signals

Global Navigation Satellite Systems (GNSS) positioning accuracy indoor and urban canyons environments are greatly affected by multipath due to distortions in its autocorrelation function. In this paper, a cross-correlation function between the received sine phased Binary Offset Carrier (sine-BOC) modulation signal and the local signal is studied firstly, and a new multipath mitigation method based on cross-correlation function for sine-BOC signal is proposed. This method is implemented to create a cross-correlation function by designing the modulated symbols of the local signal. The theoretical analysis and simulation results indicate that the proposed method exhibits better multipath mitigation performance compared with the traditional Double Delta Correlator (DDC) techniques, especially the medium/long delay multipath signals, and it is also convenient and flexible to implement by using only one correlator, which is the case of low-cost mass-market receivers

Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type), which has a long correlation length $\xi\sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure

Defect electrocatalytic mechanism: concept, topological structure and perspective

Carbon-based materials have been attracting intense interest for electrocatalysis due to their various merits, such as abundance, low cost, high conductivity and tunable molecular structures. However, to date, the electrochemical activities of these electrocatalysts are mainly attributed to different active dopants (e.g. N, B, P or S), leading to a common concept that heteroatom doping is essential for carbon-based electrocatalysts. Recently, we presented a new concept where the specific topological defects could activate the oxygen reduction reaction (ORR) and developed a facile method to create such unique defects. Subsequent research has extended this new mechanism to other reactions, such as the hydrogen and oxygen evolution reactions (HER and OER) and confirmed that heteroatom doping is not essential but that these defects can serve as actives sites for electrochemical reactions. This new theory then creates a new research direction in electrocatalysis. In this short review, we summarise the origin and presentation of the defect mechanism concept, the possible topological defect structures that are effective for electrochemical reactions, the formation of desirable defects, the challenges in the synthesis and characterization of typical defects and future research directions on the electrochemical defect mechanism

Credit Scoring with AHP and Fuzzy Comprehensive Evaluation Based on Behavioural Data from Weibo Platform

It is increasingly necessary to evaluate the customers\u27 credit. In the era of big data, Information on the Internet is commonly used to judge the credit worthiness of customers. Some users\u27 credit information is incomplete or unavailable, so credit managers cannot judge the true credit situation of these users. However, with the support of social data especially behavioural data and credit evaluation system, this problem can be effectively solved. This study used Weibo to obtain the behavioural data of Chinese users for credit evaluation. Two methods are used to calculate the credit scores of Weibo users, which are the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation methods. By analysing social processes and inviting experts to make decisions, we constructed a credit evaluation system to expose users\u27 behavioural characteristics. We found that the three key indexes determining the user’s social credit are personal identification, behavioural characteristics and interaction among friends. Then, AHP was used to determine the weight of each index. Finally, a static algorithm was proposed to compute the credit evaluation system of Weibo users using fuzzy comprehensive evaluation methods