Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

On the Randić Index of Acyclic Conjugated Molecules

The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))^−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given Mei Lu: Partially supported by NNSFC (No. 60172005) Lian-zhu Zhang: Partially supported by NNSFC (No. 10271105) Feng Tian: Partially supported by NNSFC (No. 10431020)     

Performance of quantitative analyses by liquid chromatography–electrospray ionisation tandem mass spectrometry: from external calibration to isotopomer-based exact matching

Liquid chromatography–tandem mass spectrometry (LC-MS/MS) is a versatile coupling system which combines both selectivity and sensitivity and certainty. Hence, it is generally considered as the most reliable technique to quantify chemical compounds in complex matrices. In the present paper, we evaluate the performance of LC-MS/MS methods for the quantification of 3-nitrotyrosine in human urine in order to point out its dependence on the design of the quantification method, and emphasize the role of matrix effects in the performance. We compare external and internal calibrations, isotope dilution and isotopomer-based exact matching. The role of both sample preparation and multiple transitions monitoring is particularly addressed.     

A universal constant for the convergence of Newton's method and an application to the classical homotopy method

We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth ₀=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method.     

基于高斯滤波和AKAZE-LATCH的图像匹配算法

针对图像匹配中AKAZE(Accelerated-KAZE)算法匹配精度较低以及计算复杂等问题,提出了一种基于高斯滤波和AKAZE-LATCH(AKAZE-Learned Arrangements of Three Patch Codes)算法相融合的图像匹配算法。首先,对输入图像进行高斯滤波预处理,去除高斯噪声等连续性噪声,并且保留图像的边缘信息。然后通过LATCH算法为AKAZE算法构建高效的二进制描述子,再通过KNN(K Nearest Neighbors)算法得到对应的匹配对。最后结合USAC(Universal RANSAC)去除误匹配对方法进行再次筛选,得到最终的匹配结果。经实验对比,所设计的算法相较于AKAZE算法匹配精度更高,且具有良好的鲁棒性和可靠性,可用于多数复杂场景下的图像匹配。     

基于sMLD特征的远红外航空图像配准算法

航空场景下的远红外图像迫切需要准确、鲁棒、快速的特征描述与自动配准方法。由于已有的多重线型描述符MLD特征存在“特征孤岛”和“尺度变换受限”的问题,因此针对远红外航空图像的配准问题,文章提出了一种聚合特征点以及线型描述符分段统计的特征描述方式,即sMLD特征。结合sMLD特征相互连接构成网状拓扑结构的特性,还提出了一种由粗到细的分支加速匹配算法RF-BA。其中,RF-BA粗匹配充分利用拓扑图的结构,通过局部寻优算法提高匹配的效率。RF-BA精匹配利用最小外接凸四边形原则和GMS校验原则,提升配准精度。实验结果表明,与已有的几种代表性配准方法相比,所提方法在配准精度和时间开销方面均具有更好的性能。     

Balancing MXene Surface Termination and Interlayer Spacing Enables Superior Microwave Absorption

Surface chemistry and interlayer engineering determines the electrical properties of 2D MXene. However, it remains challenging to regulate the surface and interfacial chemistry of MXene simultaneously. Herein, simultaneous modulation of Ti₃C₂T_x MXene surface termination and layer spacing by alkali treatment are achieved. The electrical and electromagnetic properties of Ti₃C₂T_x are investigated in detail with respect to KOH and ammonia concentration dependence. A high concentration of KOH caused the Ti₃C₂T_x layer spacing to expand to 13.7 Å and the surface O/F ratio to increase to 33.84. Because of its weaker ionization effect, ammonia provides finer tuning compared to the drastic intercalation of KOH with a thorough sweeping of the F-containing groups. Ti₃C₂T_x is enriched with conductive -OH termination after ammonia treatment, which achieves an effective balance with the increased interlayer resistance. Therefore, NH₃H₂O-Ti₃C₂T_x achieves broad-band impedance matching and exhibits an efficient microwave loss of −49.1 dB at a low thickness of 1.7 mm, with an effective frequency bandwidth of 3.9 GHz. The results herein optimize the electrical properties of Ti₃C₂T_x using surface and interfacial chemistry to achieve broad microwave absorption, providing a framework for enhancing the electromagnetic wave loss of intrinsic MXene.     

A matching game framework for users clustering and resource allocation with wireless power transfer in a CR-NOMA network

This paper investigates the resource allocation in a massively deployed user cognitive radio enabled non-orthogonal multiple access (CR-NOMA) network considering the downlink scenario. The system performance deteriorates with the number of users who are experiencing similar channel characteristics from the base station (BS) in NOMA. To address this challenge, we propose a framework for maximizing the system throughput that is based on one-to-one matching game theory integrated with the machine learning technique. The proposed approach is decomposed to solve users clustering and power allocation subproblems. The selection of optimal cluster heads (CHs) and their associated cluster members is based on Gale-Shapley matching game theoretical model with the application of Hungarian method. The CHs can harvest energy from the BS and transfer their surplus power to the primary user (PU) through wireless power transfer. In return, they are allowed to access the licensed band for secondary transmission. The power allocation to the users intended for power conservation at CHs is formulated as a probabilistic constraint, which is then solved by employing the support vector machine (SVM) algorithm. The simulation results demonstrate the efficacy of our proposed schemes that enable the CHs to transfer the residual power while ensuring maximum system throughput. The effects of different parameters on the performance are also studied.     

小型化L波段1 000 W GaN内匹配功率管研制

L波段功率单管有增大功率的需求,但会面临体积较大的问题。基于0.5μm工艺研发了GaN高电子迁移率晶体管(HEMT)管芯,单芯功率达到300 W。通过负载牵引仿真提取模型的输入、输出最佳阻抗点。用高介电常数薄膜电路设计L-C网络,拉高芯片的输入输出阻抗,并抵消虚部。用微带电路设计两级阻抗变换的宽带功率分配器及合路器电路,进行四胞管芯合成。内置稳定电路、栅极和漏极供电偏置电路,实现高度集成化、小型化,以及50Ω输入输出阻抗匹配。芯片总栅宽4×40 mm,在漏压50 V、脉宽40μs、占空比4%的测试条件下,在0.96 GHz到1.225 GHz的宽带频段内,输出功率为60 dBm到61.2 dBm,效率为57.9%到72%,饱和功率增益大于14 dB。