Joint Source and Relay Precoding/Beamforming Algorithm for OFDM Multi-user Cooperative Relay Systems

In order to reduce the feedback load of multi-user orthogonal frequency division multiplexing （ OFDM ） -based wireless systems, a practiral limited bits feedback precoding algorithm is proposed with direct source-destination link based on amplify-and- forward cooperative relay network under frequency selective fading channels. Using joint minimum mean square error（MMSE） filter, the receiving decoding matrix is designed for each user in the paper. Source precoding （beamforming） matrix is optimized with convex function of weight mean square error （MSE）. Relay precoding matrix is obtained under MSE decomposition and convex optimization. The precoding matrix index is fed back for clustered subcarrier of OFDM with limited feedback. Then using interpolation algorithm, all precoding matrices are achieved at base station （BS） and relay nodes. Simulations indicate the effectiveness of the proposed limited feedback joint precoding and beam_formlng design. The proposed method can improve bit error rate （BER） performance and obtain better sum-rate performance in contrast to existing algorithms. It displays the BER performance is close to that of the unquantified precoding feedback method.     

Application of NIR spectroscopy for firmness evaluation of peaches

The use of near infrared （NIR） spectroscopy was proved to be a useful tool for quality analysis of fruits. A bifurcated fiber type NIR spectrometer, with a detection range of 800-2500 nm by InGaAs detector, was used to evaluate the firmness of peaches. Anisotropy of NIR spectra and firmness of peaches in relation to detecting positions of different parts （including three latitudes and three longitudes） were investigated. Both spectra absorbency and firmness of peach were influenced by longitudes （i, ii, iii） and latitudes （A, B, C）. For modeling, two thirds of the samples were used as the calibration set and the remaining one third were used as the validation or prediction set. Partial least square regression （PLSR） models for different longitude and latitude spectra and for the whole fruit show that collecting several NIR spectra from different longitudes and latitudes of a fruit for NIR calibration modeling can improve the modeling performance. In addition, proper spectra pretreatments like scattering correction or derivative also can enhance the modeling performance. The best results obtained in this study were from the holistic model with multiplicative scattering correction （MSC） pretreatment, with correlation coefficient of cross-validation γcv=0.864, root mean square error of cross-validation RMSECV=6.71 N, correlation coefficient of calibration r=0.948, root mean square error of calibration RMSEC=4.21 N and root mean square error of prediction RMSEP=5.42 N. The results of this study are useful for further research and application that when applying NIR spectroscopy for objectives with anisotropic differences, spectra and quality indices are necessarily measured from several parts of each object to improve the modeling performance.     

平面上随机微分方程的一个极限定理

考虑平面上的随机微分方程 {dXn（z）=fn（z,Xn（z））dz＋gn（z,Xn（z））dw（z） z∈R＋^2/δR＋^2 Xn（z）=Φn（z） z∈δR＋^2 讨论当系数和边界过程fn,gn,Φn分别趋于f,g,Φ时,对应解的收敛性。     

Simultaneous in-situ determination of U-Pb age and trace elements in zircon by LA-ICP-MS in 20 μm spot size

Simultaneous in-situ determination of U-Pb ages and 20 trace elements of three international zircon standards （91500, GJ1 and TEMORA 1） and one laboratory zircon standard （SK10-2） separated from Cenozoic fine-grained gabbro was carried out on quadrupole ICP-MS equipped with 193 nm excimer laser in 20 μm spot size. The weighted mean ^206Pb/^238U ages of 91500, GJ1 and TEMORA 1 are 1064.4±4.8 Ma （2σ）, 603.2±2.4 Ma （2σ） and 418.2±2.4 Ma （2σ）, respectively. The relative standard deviations （RSDs） of ^206Pb/^238U ages （2σ） are less than 2.2% for single measurements and 0.6% for weighted means. The obtained weighted mean ^206Pb/^238U ages of three standard zircons agree with the recommended values within 2σrerror. The weighted mean ^206Pb/^238U age of SK10-2 is 31.42=0.25 Ma （2σ） and the RSDs of ^206Pb/^238U ages （2σ） are between 2.4% and 5.7% for single measurements and less than 0.8% for weighted mean. The obtained weighted mean ^206Pb/^238U age is in good agreement with the age obtained by Yuan （2004）. Trace element concentrations of NIST612 and NIST614 obtained under the same LA-ICP-MS operating conditions agree with the recommended values within analytical error. The results indicate that it is possible to measure U-Pb age and trace elements simultaneously by LA-ICP-MS in a small spot size of 20μm.     

对超核∧∧^6He，∧^9Be，∧∧^10Be和∧^13C基态结构的研究

用集团模型和少体理论研究超核∧∧^6He，∧^9Be，∧∧^10Be和∧^13C的基态结合能．采用的α-α势符合低能α-α散射实验，∧-α势用∧-N势及α粒子密度分布函数得到的，∧-∧势通过拟合∧∧^10Be基态结合能的实验值而得到的，尝试在超核∧∧^6He，∧^9Be，∧∧^10Be和∧^13C中引入∧^5Be的结构，计算这四个超核的基态结合能，得到了一些合理的结果。     

基于数值与文本特征的LSTM股票价格预测研究

行为金融学理论指出，由社交媒体文本数据所折射出的投资者情绪在一定程度上影响着股票市场的波动。为了利用投资者情绪对股票市场作出更准确的预测，本文爬取2020年8月31日至2021年9月1日的沪深300指数股吧评论文本数据，使用基于融合基础情感词典和金融词典的分析方法将评论文本数据量化为投资者情绪指标，并利用长短期记忆（Long short-term memory,LSTM）神经网络构建了融合股票历史交易数据和基于股吧评论的投资者情绪指标的多特征预测模型。实验结果表明，基于数值和文本特征的LSTM股票价格预测模型的平均绝对误差（Mean absolute error,MAE）、均方根误差（Root mean squared error,RMSE）和均方误差（Mean square error,MSE）值较LSTM数值特征预测模型降低了18.84、15.79、1486.54。较GRU(Gated recurrent unit)数值文本特征模型，其MAE、RMSE、MSE值则降低了11.42、10.49、931.75。实验结果表明本文提出的方法可以有效预测股票价格指数。     

拟双曲轨道的强跟踪性

设M是一个紧致n维C^∞黎曼流形，f∈Diff（M），∧是f的闭不变集合，并且∧具有连续不变分解T∧M=E F，则对任意的ε〉o和λ∈（0，1），存在δ〉0，使得对f的任意λ-拟双曲强δ-伪轨{xi,ni}i=-∞^＋∞都存在一点x∈M，强ε-跟踪{xi,ni}i=-∞^＋∞。     

基于改进SEIR算法的疫情传播趋势检测方法

通过对传统SEIR(susceptible-exposed-infectious-removed)算法进行优化重建, 提出一种改进的SEIR算法. 该算法通过为感染率β添加衰减函数, 对数据拟合得到随时间增长而改变的β. 仿真实验结果表明, 该算法在测试集上的平均MSE（mean square error）只有0.11, 相比于目前已有的其他算法, 误差值显著降低.     

毫米波雷达数据驱动的桥梁挠度预测

为监测公路桥梁健康状况从而保证车辆行驶桥面的安全性,基于毫米波雷达监测的桥梁挠度数据,结合深度学习理论,提出了一种基于卷积神经网络（convolutional neural network, CNN）与门控制循环单元（gate recurrent unit, GRU）组合的桥梁挠度预测模型。首先,获取高速公路大桥高精度挠度数据,通过数据预处理,在保留原始数据特征的基础上,修复部分噪声数据;其次,将处理后的样本数据、时间步长和特征数的三维数据,以桥梁挠度数据序列构造的输入矩阵作为输入层,经过CNN-GRU组合模型的密集连接层后,输出预测桥梁挠度值。最后,选取具有代表性的监测点数据,利用均方根误差 (root mean square error, RMSE)、平均绝对误差 (mean absolute error, MAE)、平均百分比误差 (mean absolute percentage error, MAPE)进行预测效果验证。结果表明,CNN-GRU模型的精度更高：较于传统LSTM（long short-term memory）模型在RMSE上提升了59.65%,MAE提升了61.30%;较于CNN-LSTM模型在RMSE上提升了2.48%,MAE提升了4.87%。其对于桥梁挠度极值及趋势的判断基本准确,可以作为桥梁健康状况预测的科学依据。     

均方偏差分析的多态可变步长LMS算法

最小均方（least mean square,LMS）算法在时变信道的最小稳态均方偏差（mean square deviation,MSD）由输入功率、噪声功率、随机扰动信号功率以及滤波器长度共同决定。为达到系统中最小的MSD值,传统的LMS算法存在有迭代次数较多和收敛速度慢等问题,提出了一种多态可变步长最小均方（multi-state variable step size least mean square,MVSS-LMS）算法。该算法通过添加暂态递减步长作为过渡,实现以更快的收敛速度达到系统中最小的MSD值。理论分析与仿真结果表明,与目前最新的Prob-LMS算法相比,所提算法在时变信道以及突变信道都具有更快的收敛速度和更低的MSD值,且算法的复杂度更低。     

一类具有密度制约的捕食-食饵扩散模型的定性分析

研究了一类具有密度制约的捕食-食饵模型共存解的唯一性和渐近行为。利用不动点指数理论给出了共存解存在的充分条件。然后采用线性算子的扰动理论讨论了共存解的唯一性和稳定性。最后运用抛物方程的比较原理得到了系统的持久性和灭绝性条件,并通过数值模拟对其理论结果进行了验证。结果表明在一定条件下两物种共存且系统存在稳定的唯一共存解。     

最小Hellinger距离方法在扩散过程参数估计中的应用——基于转移密度的估计量

为了研究扩散过程的参数估计问题,本文基于最小Hellinger距离的定义给出了利用转移密度构造的参数估计量.首先定义了转移密度的非参数估计量并研究了它的性质(一致收敛性以及渐近正态性),然后通过最小化扩散过程的转移密度和该密度的一个非参数估计量之间的距离构造扩散过程的参数统计量,实现这一统计量的一致收敛性和渐近正态性.最后为了强调说明该方法的可行性,本文将这一方法应用于几何Brown运动和CEV模型这两个例子.     

一类具有功能反应的捕食者-食饵动力系统研究

讨论一类具有功能反应和非线性密度制约的捕食者-食饵扩散模型解的整体性态。通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性。     

密度与回归的随机窗宽核估计的渐近正态性

本文建立了密度和回归函数的随机窗宽核估计的渐近正态性,并给出了在回归函数最近邻估计场合的一个应用。     

具双密度制约和Non-Monotonic型功能反应的捕食系统的周期性与全局稳定性

利用比较原理和重合度理论与Lyapunov函数,研究了一类具有双密度制约和Non-Monotonic型功能性反应食饵-捕食者系统的持久性和全局周期解的存在性及其全局稳定性,得到了周期系统存在唯一全局渐近稳定的正周期解的充分条件.所得结论推广了已有的结果.     

食饵有病的生态-流行病模型的分析

在考虑捕食者捕食染病的食饵对自己不利作用和捕食者有密度制约的基础上,建立了食饵有病的生态流行病模型,得到系统平衡点局部渐近稳定的充分条件.讨论了系统的非负不变性和解的有界性,并在此基础上研究了边界平衡点的全局稳定性,得出平衡点全局稳定的充分条件.     

威布尔分布族参数的经验Bayes检验

在"线性损失"下,文章研究了威布尔分布族刻度参数经验Bayes(EB)检验问题,并利用概率密度函数的核估计,构造了刻度参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性,并获得了它的收敛速度,最后给出一个有关主要结果的例子。     

一维量子Euler-Poisson方程的解的渐近性

讨论了一类一维量子半导体方程,这类方程具有等熵Euler—Poisson方程的形式,并且动量方程有量子势力项和松弛项．当远场动量不一致和远场电场非零时,证明了一维量子Euler—Poisson方程的初值问题的解的渐近性．通过选择适当的修正函数和能量估计的方法,得到了上述初值问题的解在时间足够大时收敛到相应的稳态解．这个结果改进了前人的关于远场动量一致和零远场电场时解的渐近性的结果．     

基于残差的非线性自回归模型的拟合优度检验

时间序列模型中,考虑误差分布的拟合优度检验是很重要的．Lee和Na（2002）考虑了在线性自回归模型下,基于残差的Bickel—Rosenblatt检验问题．他们指出了在原假设条件下,检验统计量的极限分布与利用独立同分布观测值的经典Bickel—Rosenblatt检验相同．本文主要讨论无限阶的非线性自回归模型的基于残差的Bickel—Rosenblatt检验统计量的渐近性质．我们证明了在自回归函数未知的情况下,当满足一定条件时,检验统计量的渐近性质与基于真实误差的统计量的性质相同．     

Exotic structure of the third excited state in ^21Na

The probability of the last proton being out of the binding potential, P and the root-mean-square （rms） radius （〈r^2〉^1/2=of the third excited state in ^21Na are calculated by means of asymptotic normalization coefficient （ANC） method with the experimental date existing. The results are P=54.73% and 〈r^2〉^1/2=5.28 fm respectively. The P value and the contribution of the asymptotic part to the 〈r^2〉^1/2 are compared with those of several other low energy states in ^21Na. It is found that the valence particle in the third excited state has an obvious larger P than those of other states. The density distribution of the valence proton in this state is also compared with the nucleons in the nuclear core ^20Ne, and a far extended tail can be seen clearly. These results show that the third excited state in ^21Na is a proton halo state.