Low Energy Properties of the Random Spin-12 Ferromagnetic-Antiferromagnetic Heisenberg Chai

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Quantum spin liquid emerging in 2D correlated Dirac fermions

At sufficiently low temperatures, condensed-matter systems tend to develop order. A notable exception to this behaviour is the case of quantum spin liquids, in which quantum fluctuations prevent a transition to an ordered state down to the lowest temperatures. There have now been tentative observations of such states in some two-dimensional organic compounds, yet quantum spin liquids remain elusive in microscopic two-dimensional models that are relevant to experiments. Here we show, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence-bond liquid, akin to the one proposed for high-temperature superconductors: the possibility of unconventional superconductivity through doping therefore arises in our system. We foresee the experimental realization of this model system using ultra-cold atoms, or group IV elements arranged in honeycomb lattices.

低场核磁测水分分布参数设置

低场核磁测水分分布参数设置英文回答：To measure water distribution using low-field nuclear magnetic resonance (NMR), there are several parameters that need to be set appropriately. These parameters determine the sensitivity and accuracy of the NMR measurements. Here are some important considerations:1. Magnetic Field Strength: Low-field NMR typically operates at field strengths below 1 Tesla. The choice of field strength depends on the desired spatial resolution and the relaxation times of the water molecules in the sample. Higher field strengths provide better resolution but may require longer relaxation times for accurate measurements.2. Pulse Sequence: The pulse sequence determines the timing and duration of the radiofrequency pulses used to excite and detect the NMR signal. Common pulse sequencesinclude spin echo and inversion recovery. The choice of pulse sequence depends on the desired contrast and sensitivity for water detection.3. Echo Time (TE): The echo time is the time between the excitation pulse and the peak of the NMR signal. It affects the sensitivity to water and the ability to distinguish different water compartments. Short TE values are suitable for detecting free water, while longer TE values can detect bound or restricted water.4. Repetition Time (TR): The repetition time is the time between consecutive pulse sequences. It determines the recovery of the NMR signal and affects the contrast between different water compartments. Long TR values allow for better recovery of the signal and can enhance the detection of bound water.5. Number of Averages: The number of averages determines the signal-to-noise ratio of the NMR measurements. Increasing the number of averages improves the precision of the measurements but also increases theacquisition time. It is important to find a balance between signal quality and measurement time.6. Gradient Strength: Gradient pulses are used to encode spatial information in NMR measurements. The gradient strength affects the spatial resolution and the ability to distinguish different water compartments. Higher gradient strengths provide better resolution but may lead to increased susceptibility artifacts.7. Data Processing: After acquiring the NMR data, appropriate data processing techniques should be applied to extract the water distribution information. This may involve Fourier transformation, image reconstruction, and quantitative analysis.In summary, setting the parameters for low-field NMR measurements of water distribution involves considerations such as magnetic field strength, pulse sequence, echo time, repetition time, number of averages, gradient strength, and data processing techniques. By optimizing these parameters, accurate and sensitive measurements of water distributioncan be obtained.中文回答：低场核磁共振（NMR）测量水分分布时，需要设置几个参数以确保测量的灵敏度和准确性。

材料科学(10)12章-Electrical-Properties

Conduction & Electron Transport
• Metals (Conductors):
-- for metals, empty energy states are adjacent to filled states.
• thermal energy excites electrons into empty higher energy states.
Resistance (电阻), Resistivity (电阻率)
Resistance, R, depends on the intrinsic resistivity r of the material [W-m] and on the geometry (length L and area A through which the current passes): R = r L/A
filled band
The outmost band largely determines the electron band structures in solids (group of atoms bonding to each other)
Cu
filled band
Mg
In a metal, n is large. In an insulator, n is very, very small.
Classification of Materials
based on their electrical conductivity
Electrical conductivity varies between different materials by over 27 orders of magnitude, the greatest variation of any physical property.

稀疏距离扩展目标自适应检测及性能分析

第39卷第7期自动化学报Vol.39,No.7 2013年7月ACTA AUTOMATICA SINICA July,2013稀疏距离扩展目标自适应检测及性能分析魏广芬1苏峰2简涛2摘要在球不变随机向量杂波背景下,研究了稀疏距离扩展目标的自适应检测问题.基于有序检测理论,利用协方差矩阵估计方法,分析了自适应检测器(Adaptive detector,AD).其中,基于采样协方差矩阵(Sample covariance matrix,SCM)和归一化采样协方差矩阵(Normalized sample covariance matrix,NSCM),分别建立了AD-SCM和AD-NSCM检测器.从恒虚警率特性和检测性能综合来看,AD-NSCM的性能优于AD-SCM和已有的修正广义似然比检测器.最后,通过仿真实验验证了所提方法的有效性.关键词稀疏距离扩展目标,自适应检测,采样协方差矩阵,归一化采样协方差矩阵,有序统计量引用格式魏广芬,苏峰,简涛.稀疏距离扩展目标自适应检测及性能分析.自动化学报,2013,39(7):1126−1132DOI10.3724/SP.J.1004.2013.01126Sparsely Range-spread Target Detector and Performance AssessmentWEI Guang-Fen1SU Feng2JIAN Tao2Abstract In the background where the clutter is modeled as a spherically invariant random vector,the adaptive detection of sparsely range-spread targets is addressed.By exploiting the order statistics and the covariance matrix estimators,the adaptive detector(AD)is assessed.Herein,the detectors of AD-SCM and AD-NSCM are proposed based on the sample covariance matrix(SCM)and normalized sample covariance matrix(NSCM),respectively.In terms of constant false alarm rate properties and detection performance,the AD-NSCM outperforms the AD-SCM and the existing detector of modiﬁed generalized likelihood ratio.Finally,the performance assessment conducted by simulation conﬁrms the eﬀectiveness of the proposed detectors.Key words Sparsely range-spread target,adaptive detection(AD),sample covariance matrix(SCM),normalized sample covariance matrix(NSCM),order statisticsCitation Wei Guang-Fen,Su Feng,Jian Tao.Sparsely range-spread target detector and performance assessment.Acta Automatica Sinica,2013,39(7):1126−1132低分辨率雷达的目标尺寸小于距离分辨率,这种目标常称之为点目标[1].通过采用脉冲压缩技术,高分辨率雷达能够在空间上把一个目标分解成许多散射点[2−3],目标回波在雷达径向上的多个散射点分布在不同的距离分辨单元中,形成距离扩展目标[4].在许多情况下,距离扩展目标的散射点密度是稀疏的,可将这种目标简称为“稀疏距离扩展目标”.目前,高斯背景下的距离扩展目标检测已取得一定进收稿日期2011-12-28录用日期2012-08-27Manuscript received December28,2011;accepted August27, 2012国家自然科学基金(61174007,61102166),山东省优秀中青年科学家科研奖励基金(BS2010DX022)资助Supported by National Natural Science Foundation of China (61174007,61102166)and the Scientiﬁc Research Founda-tion for Outstanding Young Scientists of Shandong Province (BS2010DX022)本文责任编委韩崇昭Recommended by Associate Editor HAN Chong-Zhao1.山东工商学院信息与电子工程学院烟台2640052.海军航空工程学院信息融合技术研究所烟台2640011.School of Information and Electronics,Shandong Institute of Business and Technology,Yantai2640052.Research Insti-tute of Information Fusion,Naval Aeronautical and Astronauti-cal University,Yantai264001展,其中,针对估计参数空间过大的问题,文献[5]提出了一种无需辅助数据的检测器,简称为修正的广义似然比检验(Modiﬁed generalized likelihood ratio test,MGLRT)检测器,其在高斯背景下是有界恒虚警率(Constant false alarm rate,CFAR)的.但在高距离分辨率的条件下,背景杂波呈现出诸多的非高斯特性[1],高斯背景下获得的检测器已无法有效检测目标.在非高斯背景下,文献[6]研究了已知杂波协方差矩阵条件下的距离扩展目标检测;而通过利用不含目标信号的辅助数据,文献[7]和文献[8]分别针对距离扩展目标和距离–多普勒二维分布式目标展开了自适应检测研究.需要指出的是,以上自适应检测方法[7−8]都是基于辅助数据的.当无法获得满足条件的辅助数据时,实现非高斯背景下距离扩展目标的自适应检测具有重要意义.文献[9]基于迭代估计方法实现了自适应检测,但迭代估计计算量较大,如何在保证性能的同时减小计算量,也是值得探讨的问题.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1127稀疏距离扩展目标的散射点只占据目标距离扩展范围的一部分,与含纯杂波的距离分辨单元幅值相比,含目标散射点的距离分辨单元幅值明显更高,这就为实现目标的自适应检测提供了条件.本文针对非高斯杂波中的稀疏距离扩展目标检测问题,在不需要辅助数据的条件下,首先,采用有序统计检测理论和协方差矩阵估计方法,粗略估计目标散射点单元集合;然后,进一步利用适当估计方法获得协方差矩阵的精确估计,设计了自适应检测器(Adaptivedetector,AD),并通过仿真实验验证了检测器的有效性.1问题观测数据来源于N个阵元的线性阵列天线,需跨过K个可能存在目标的距离分辨单元z t,t=1,···,K,判决一个距离扩展目标的存在与否.假设可能的目标完全包含在这些数据中,并且忽略目标距离走动的问题.在杂波背景下,待解决的检测问题可由以下二元假设检验公式来表达.H0:z t=c t,t=1,···,KH1:z t=αt p+c t,t=1,···,K(1)其中,p=(1,e jφ,e j2φ,···,e j(N−1)φ)T/√N表示已知单位导向矢量,即p H p=1,这里(·)H表示共轭转置,φ表示相移常量,(·)T表示转置,αt,t=1,···,K是反映目标幅度的未知参数.非高斯杂波可用球不变随机向量建模[10],由于中心极限定理在较小区域的杂波范围内仍是有效的,球不变随机向量可以表示为两个分量的乘积:一个是反映受照区域反射率的时空“慢变化”纹理分量,另一个是变化“较快”的“散斑”高斯过程.那么,距离分辨单元t的N维杂波向量c t为c t=√τt·ηt,t=1,···,K(2)其中,ηt=(ηt(1),ηt(2),···,ηt(N))T是零均值协方差矩阵为Σ的复高斯随机向量,非负的纹理分量τt与ηt相互独立,其用来描述杂波功率在不同距离分辨单元间的起伏,且服从未知分布fτ.另外,杂波协方差矩阵结构Σ可以表示为Σ=E{ηt ηHt}(3)距离扩展目标完全包含在K个距离分辨单元的滑窗中,假设一个等效散射点最多只占据一个距离分辨单元,即目标等效散射点数目与其所占据的距离分辨单元数目是相等的.通常目标散射点是稀疏分布的,与含纯杂波的距离分辨单元相比,有散射点的距离分辨单元幅值往往更高.含目标等效散射点的距离分辨单元数目用h0表示,而其所对应的距离分辨单元下标用集合Θh表示.为了简化分析,假设h0是已知的,若其未知,可利用模型阶数选择方法获得合适的估计值[11].如前所述,对距离扩展目标的检测只需在距离分辨单元Θh内进行,式(1)表示的假设检验问题可以进一步表示为H0:z t=c t,t∈ΘhH1:z t=αt p+c t,t∈Θh(4)在分布fτ未知的条件下,距离分辨单元t的杂波是条件高斯的,其相应的方差为τt.由于幅度αt 未知而向量p已知,针对不同假设,观测向量z t的联合概率密度可表示为t∈Θhf(z t|τt,H0)=t∈Θh1πNτN t det(Σ)×exp[−1τtz HtΣ−1z t](5)t∈Θhf(z t|αt,τt,H1)=t∈Θh1πNτN t det(Σ)×exp−1τt(z t−αt p)HΣ−1(z t−αt p)(6)其中,det(·)表示方阵的行列式.2检测器实现在未知集合Θh的条件下,为了获得估计的参数集合ˆΘh,这里先假设已知矩阵Σ.由于未知参数α={αt|t∈Θh}和τ={τt|t∈Θh},可利用广义似然比检验(GLRT)原理进行检测器设计[12].在矩阵Σ已知的条件下,根据GLRT原理,对于似然比中的未知参数,可用最大似然(Maximum likelihood,ML)估计进行替换,即考虑如下二元判决:maxτmaxαt∈Θhf(z t|αt,τt,H1)maxτt∈Θhf(z t|τt,H0)H1><H0T0(7)在H1假设下求得αt的ML估计为[13]ˆαt=p HΣ−1z tp HΣ−1p(8)将ˆαt代入式(7)后,可进一步在不同假设条件下求得τt的ML估计:H0:ˆτt=1Nz HtΣ−1z t(9) H1:ˆτt=1N(z t−ˆαt p)HΣ−1(z t−ˆαt p)(10)1128自动化学报39卷将式(8)∼(10)代入式(7)中,可得自然对数形式的GLRT判决为λ1=−Nt∈Θh0ln1−|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)H1><H0T1(11)令w t=|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)(12)值得注意的是,w t的结构类似于一个归一化匹配滤波器(权向量为Σ−1p)[14].可以看出,式(12)的分子部分p HΣ−1z t等效于给定距离分辨单元观测z t经过匹配滤波后的结果[14].而分母部分的两项z HtΣ−1z t和p HΣ−1p起到了归一化处理的作用,因此,w t是距离单元观测z t经过匹配滤波后模平方的归一化,可以看作是距离单元观测经归一化匹配滤波后的能量.由于目标完全包含在K个单元的距离滑窗中,且距离扩展目标等效散射点所占据的距离分辨单元幅值往往大于纯杂波的距离分辨单元幅值,因此,可通过归一化能量w t,t=1,···,K中最大的h0个值来确定未知集合ˆΘh.实际应用中协方差矩阵结构Σ往往是未知的,为了确定集合ˆΘh,需先对协方差矩阵结构进行估计.如前所述,纹理分量τt的分布fτ是未知的,因此,协方差矩阵结构Σ的ML估计不能通过期望最大化得到[13].本文考虑两种协方差矩阵估计方法.一种是高斯背景下的经典采样协方差矩阵(Sample covariance matrix,SCM),其可以表示为ˆΣSCM =1RRr=1y r y Hr(13)其中,y r,r=1,···,R表示可用于估计的R个数据.当R≥N时,SCM是以概率为1非奇异的,同时也是正定Hermitian矩阵[12].另外,在非高斯背景下,也常常利用辅助数据获得归一化采样协方差矩阵(Normalized sample covariance matrix, NSCM),可以表示为ˆΣNSCM =1RRr=1Ny Hry ry r y Hr(14)与文献[9]类似,针对稀疏距离扩展目标的自适应检测,AD检测器的实现分为如下三个步骤.步骤1.基于SCM或NSCM方法,利用K个待检测单元的观测数据获得初步估计矩阵ˆΣ1,进一步将估计矩阵ˆΣ1代入式(12)中,可得到初步估计ˆw(1)t.对ˆw(1)t,t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(1)(1)≤···≤ˆw(1)(t)≤···≤ˆw(1)(K)≤1(15)步骤2.考虑有序序列的K−h0个最小值(即ˆw(1)(t),t=1,···,K−h0),并用Ωh表示相应距离分辨单元下标的集合.为了获得可逆的估计矩阵,需满足K−h0≥N.根据之前的分析,集合Ωh中的距离分辨单元极可能只包含纯杂波,故可以利用Ωh0对应的距离分辨单元观测值,精确估计矩阵Σ,并采用与初步估计中相同的估计方法(SCM或NSCM),进一步获得较为精确的协方差矩阵结构估计ˆΣ2.利用ˆΣ2代替式(12)中的未知矩阵Σ,得到w t的精确估计值用ˆw(2)(t)表示.对ˆw(2)(t),t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(2)(1)≤···≤ˆw(2)(t)≤···≤ˆw(2)(K)≤1(16)考虑有序序列的h0个最大值(即ˆw(2)(t),t=K−h0+1,···,K),并用ˆΘh表示相应距离分辨单元下标的集合.步骤3.将距离分辨单元下标的集合ˆΘh和协方差矩阵的精确估计ˆΣ2代入式(11)中,获得自适应检测器AD的检测统计量可以表示为λ2=−NKt=K−h0+1ln(1−ˆw(2)(t))=−Nt∈ˆΘhln[1−|p HˆΣ−12z t|2(z H tˆΣ−12z t)(p HˆΣ−12p)]H1><H0T2(17)需要说明的是,在存在目标散射点的情况下,步骤1的初步估计矩阵不可避免地引入了估计误差,虽然这种误差在步骤2中得到了一定的抑制,但它仍将影响后续精确估计矩阵的精度.在存在辅助数据的前提下,为了获得良好的检测性能,一般要求辅助数据个数不小于阵元数N的两倍[15].在待检测单元数K不变的情况下,可利用的纯杂波单元数(K−h0)将随着散射点个数的增加而减小,因此,此处需等价满足(K−h0)≥2N.进一步考虑到步骤1中散射点单元所引起的估计误差,实际应用中可能需要更大的(K−h0)/N值以弥补步骤1中导致的性能损失,具体取值将在接下来的性能评估中给出.由于采用不同的估计方法会获得不同的自适应检测器,在这里,我们分别将采用SCM和NSCM估计方法获得的相应检测器简称为AD-SCM和AD-NSCM.由于本文的自适应检测器中ˆΘh和ˆΣ2均受到协方差矩阵估计方法的影响,因此,有必要评估自适应距离扩展目标检测器的CFAR特性,这将在接下来的性能分析中进行.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1129 3性能评估本节对稀疏距离扩展目标自适应检测器AD-SCM和AD-NSCM进行了CFAR特性和检测性能评估,并与无需辅助数据的MGLRT检测器[5]进行了比较分析.利用Toeplitz矩阵对Σ进行建模,具体采用指数相关结构,在杂波一阶相关系数为γ的条件下,第m行第n列的矩阵元素为[Σ]m,n=γ|m−n|,1≤m,n≤N(18)利用Γ分布对纹理分量的分布fτ进行建模:fτ(x)=LbLΓ(L)x L−1e−(L b)x,x≥0(19)其中,Γ(·)是Gamma函数,均值b代表了平均杂波功率;参数L表示分布fτ的非高斯拖尾特征,具体来说,随着L的减小,函数fτ的拖尾将增大,而杂波的非高斯尖峰程度将增大.采用蒙特卡罗方法计算相应的检测概率P d和虚警概率P fa.根据前面的假设,在所有距离分辨单元均存在杂波的条件下,目标等效散射点只存在于h0个距离分辨单元中,且一个等效散射点最多只占据一个距离分辨单元.在所有K个距离分辨单元上,每个单元的目标或杂波的平均功率分别用σ2s 或σ2c表示.对于存在目标散射点的距离分辨单元(t∈Θh),用零均值独立复高斯变量对等效散射点建模,即目标散射点幅度在不同距离分辨单元间瑞利起伏;相应的方差表示为E{|αt|2}=εtσ2sK(εt表示单个散射点占目标总能量的比率).由|αt|2,t=1,···,K的独立性可知,检测性能与散射点在待检测单元中的位置无关.几种典型的散射点分布模型如表1所示.其中,Model 1中的目标能量等量分布在h0个距离分辨单元范围内;Model2∼4中某个距离分辨单元具有大部分能量,而剩下的能量在其余距离分辨单元中等量分布.Model5相当于点目标,是Model2∼4的极端特例.输入信杂比(Signal to clutter ratio,SCR)定义为K个距离分辨单元内的平均信杂比,即SCR=σ2sσ2cp HΣ−1p(20)为了便于CFAR特性评估,需针对杂波功率水平(对应于b)、尖峰程度(对应于L)和协方差矩阵结构(对应于γ)的不同情况,分析检测器的检测阈值与虚警概率间的关系.相关研究表明[9],在非高斯杂波下MGLRT是非CFAR的,即高斯背景下获得的MGLRT检测器不适用于非高斯背景.为了便于比较,在K=15,h0=3,N=2,L=0.1,1,γ=0,0.5,0.9和b=1,10条件下,图1和图2分别给出了AD-SCM和AD-NSCM的检测阈值(De-tection threshold)与虚警概率(False alarm prob-ability)的关系曲线.图1表明,AD-SCM检测器对杂波协方差矩阵结构和功率水平具有自适应性,但对杂波尖峰不具有适应能力.而图2说明,AD-NSCM对杂波尖峰和杂波功率水平具有CFAR特性,但其检测阈值仍受协方差矩阵结构的轻微影响.综合来看,AD-NSCM的检测阈值在不同杂波条件下的鲁棒性更好.图1K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-SCM的CFAR特性曲线Fig.1CFAR curves of AD-SCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3表1不同散射点分布模型的εt值Table1Values ofεt for typical scatters models目标距离分辨单元12···h0Model11h01h01h01h0Model20.50.5h0−10.5h0−10.5h0−1Model30.90.1h0−10.1h0−10.1h0−1Model40.990.01h0−10.01h0−10.01h0−1Model510001130自动化学报39卷图2K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-NSCM的CFAR特性曲线Fig.2CFAR curves of AD-NSCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3接下来分析AD检测器的检测性能.图3给出了MGLRT、AD-SCM和AD-NSCM的性能曲线.可以看出,AD-NSCM的检测性能最优,MGLRT 其次,而AD-SCM的检测性能最差.从以上分析综合来看,与MGLRT和AD-SCM相比,AD-NSCM 在CFAR特性和检测性能方面均具有一定的优势.下文将重点对AD-NSCM的检测性能展开分析.图3K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1时,MGLRT,AD-SCM和AD-NSCM的检测性能曲线Fig.3Detectability curves of MGLRT,AD-SCM and AD-NSCM for K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1首先,针对表1中5种不同模型,图4评估了散射点能量分布对AD-NSCM检测性能的影响.可以看出,随着距离分辨单元间散射点能量分布的均匀性增加,检测性能逐渐改善.为了便于分析,下文中主要针对Model1模型.另外,在不同的散射点密度条件下,图5分析了AD-NSCM检测性能.由图5可知,当h0<7时,协方差矩阵结构的估计误差较小,其对检测性能的影响也较小,当散射点数目增加时,检测器可利用的目标能量增大,AD-NSCM的检测性能得到一定的改善.当h0≥7时,协方差矩阵结构的估计误差影响较大,当散射点数目增加时,进行矩阵估计所用的观测数据量减少,估计矩阵的误差加大,导致较为严重的检测损失,且损失量高于增加散射点数目所获得的性能增益,并引起总检测性能的退化.综合来看,当h0<K/2时,AD-NSCM 的检测性能较好.图4K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1∼5对应的AD-NSCM检测性能曲线Fig.4Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1∼5图5K=15,N=2,L=1,γ=0.9,P fa=10−4,Model 1时,h0=2,4,6,7,8,10,12对应的AD-NSCM检测性能曲线Fig.5Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,P fa=10−4,Model1,h0=2,4,6,7,8,10,12在不同杂波尖峰条件下,图6给出了AD-NSCM检测性能.由图6可知,随着L的减小,杂波尖峰程度增大,AD-NSCM的检测性能有所改善.图7给出了不同杂波相关性对应的检测性能曲线.可以看出,杂波一阶相关系数的变化对检测性能几乎没有影响,说明AD-NSCM对杂波相关性7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1131的变化具有良好适应性.图8进一步分析了阵元数变化(N =2,4,6,8)对AD-NSCM 检测性能的影响.可以看出,在阵元数N ≤4的条件下,当N 增加时,检测性能有所提高;而在N >4的条件下,当N 增加时,检测性能反而有所下降.可能的原因是,当进行矩阵估计所用的观测数据量不变时(R =K −h 0=12),N 的增加会导致协方差矩阵维数变大,待估参量的数目增加,估计精度下降,并直接引起检测性能的退化.综合来看,当K −h 0≥3N 时,AD-NSCM 的检测性能较好.图6K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1时,L =0.5,1,2,10对应的AD-NSCM 检测性能曲线Fig.6Detectability curves of AD-NSCM for K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1,L =0.5,1,2,10图7K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1时,γ=0,0.5,0.9对应的AD-NSCM 检测性能曲线Fig.7Detectability curves of AD-NSCM for K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1,γ=0,0.5,0.94结论本文研究了非高斯杂波中的稀疏距离扩展目标检测问题.在不需要辅助数据的条件下,基于SCM 和NSCM 估计器,分别建立了AD-SCM 和AD-NSCM 检测器.从CFAR 特性和检测性能综合来看,AD-NSCM 的性能优于AD-SCM 和MGLRT.对于典型的非高斯杂波环境,随着杂波尖峰程度的增大,AD-NSCM 的检测性能得到提高,且其对杂波相关性的变化也具有良好适应性.另外,对于h 0<K/2的稀疏距离扩展目标,在K −h 0≥3N 条件下,AD-NSCM 能获得满意的检测性能.需要说明的是,与文献[9]中的检测器相比,AD-NSCM 虽然减小了计算量,但也牺牲了部分CFAR 特性.如何减小检测器对散射点信息的依赖性,是下一步需要研究的问题.图8K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1时,N =2,4,6,8对应的AD-NSCM 检测性能曲线Fig.8Detectability curves of AD-NSCM for K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1,N =2,4,6,8References1Zhou Yu,Zhang Lin-Rang,Liu Xin,Liu Nan.Adap-tive detection based on Bayesian approach in heteroge-neous environments.Acta Automatica Sinica ,2011,37(10):1206−1212(周宇,张林让,刘昕,刘楠.非均匀杂波环境下基于贝叶斯方法的自适应检测.自动化学报,2011,37(10):1206−1212)2He Chu,Liu Ming,Feng Qian,Deng Xin-Ping.PolIn-SAR image classiﬁcation based on compressed sensing and multi-scale pyramid.Acta Automatica Sinica ,2011,37(7):820−827(何楚,刘明,冯倩,邓新萍.基于多尺度压缩感知金字塔的极化干涉SAR 图像分类.自动化学报,2011,37(7):820−827)3Zhu Yi-Long,Fan Hong-Qi,Lu Zai-Qi,Fu Qiang.A radar target maneuver detection algorithm based on the one-dimensional high resolution Doppler proﬁle.Acta Automat-ica Sinica ,2011,37(8):901−914(祝依龙,范红旗,卢再奇,付强.基于高分辨一维多普勒像的雷达目标机动检测算法.自动化学报,2011,37(8):901−914)4Jian T,He Y,Su F,Qu C W,Ping D F.High resolu-tion radar target adaptive detector and performance assess-ment.Journal of Systems Engineering and Electronics ,2011,22(2):212−2185Gerlach K,Steiner M J.Adaptive detection of range dis-tributed targets.IEEE Transactions on Signal Processing ,1999,47(7):1844−18511132自动化学报39卷6Gerlach K.Spatially distributed target detection in non-Gaussian clutter.IEEE Transactions on Aerospace and Elec-tronic Systems,1999,35(3):926−9347Conte E,De Maio A,Ricci G.CFAR detection of distributed targets in non-Gaussian disturbance.IEEE Transactions on Aerospace and Electronic Systems,2002,38(2):612−6218Bon N,Khenchaf A,Garello R.GLRT subspace detection for range and Doppler distributed targets.IEEE Transac-tions on Aerospace and Electronic Systems,2008,44(2): 678−6969Jian Tao,Su Feng,He You,Li Bing-Rong,Gu Xue-Feng.Distributed target detection without secondary data.Acta Aeronautica et Astronautica Sinica,2011,32(8): 1542−1547(简涛,苏峰,何友,李炳荣,顾雪峰.无需辅助数据的分布式目标自适应检测器.航空学报,2011,32(8):1542−1547)10Jian T,He Y,Su F,Qu C W,Gu X F.Performance charac-terization of two adaptive range-spread target detectors for unwanted signal.In:Proceedings of the9th International Conference on Signal Processing.Beijing,China:IEEE, 2008.2326−232911Gini F,Bordoni F,Farina A.Multiple radar targets de-tection by exploiting induced amplitude modulation.IEEE Transactions on Signal Processing,2004,52(4):903−913 12Kay S M.Fundamentals of Statistical Signal Processing, vol.2:Detection Theory.New York:Prentice-Hall,1998.196−26013Kay S M.Fundamentals of Statistical Signal Processing, vol.1:Estimation Theory.New York:Prentice-Hall,1993.157−21814Kraut S,Scharf L L,McWhorter L T.Adaptive subspace detectors.IEEE Transactions on Signal Processing,2001, 49(1):1−1615Reed I S,Mallett J D,Brennan L E.Rapid convergence rate in adaptive arrays.IEEE Transactions on Aerospace and Electronic Systems,1974,10(6):853−863魏广芬博士,山东工商学院副教授.2005年获得大连理工大学机械电子工程专业工学博士学位.主要研究方向为传感器检测与信号处理理论及技术.本文通信作者.E-mail:*******************(WEI Guang-Fen Ph.D.,associateprofessor at Shandong Institute of Busi-ness and Technology.She received her Ph.D.degree from Dalian University of Technology in2005.Her research in-terest covers theory and technology of sensor detection and signal processing.Corresponding author of this paper.)苏峰博士,海军航空工程学院信息融合技术研究所讲师.主要研究方向为雷达信号检测与信号处理.E-mail:*****************(SU Feng Ph.D.,lecturer at NavalAeronautical and Astronautical Univer-sity.His research interest covers radarsignal detection and signal processing.)简涛博士,海军航空工程学院信息融合技术研究所讲师.主要研究方向为雷达信号检测与信号处理.E-mail:********************.cn(JIAN Tao Ph.D.,lecturer at NavalAeronautical and Astronautical Univer-sity.His research interest covers radarsignal detection and signal processing.)。

测绘工程专业英语翻译

测绘工程专业英语翻译各位读友大家好，此文档由网络收集而来，欢迎您下载，谢谢篇一：测绘工程专业英语课文翻译Unit 9 Basic Statistical Analysis of Random Errors （随机误差的统计学基本分析）Random errors are those variables that remain after mistakes are detected and eliminated and all systematic errors have been removed or corrected from the measured 后，并且所有系统误差被从测量值中移除或修正后，保留下的那些变量variable变量、变化n.）They are beyond the control of the the random errors are errors the occurrence of which does not follow a deterministic pattern.确定性的模式pattern而发生的误差）In mathematical statistics, they areconsidered as stochastic variables, and despite their irregular behavior, the study of random errors in any well-conducted measuring process or experiment has indicated that random errors follow the following empirical rules:mathematical statistics中，它们被当成随机变量stochastic variable，尽管它们的行为无规律，在任一正确的well-conducted原意为品行端正的，这里指测量实验和活动是无误的测量活动和实验中，对的随机误差的研究显示indicate随机误差遵循以下经验法则empirical⑴A random error will not exceed a certain amount.（随即误差不会超过一个确定的值）⑵Positive and negative random errors may occur at the same frequency.（正负误差出现的频率相同）⑶Errors that are small in magnitude are more likely to occur than those that are larger in magnitude.比数值大的误差出现可能性大be likely to 可能）⑷The mean of random errors tends to zero as the sample size tends to infinite.随机误差的平均值趋近于0）In mathematical statistics, random errors follow statistical behavioral laws such as the laws of 行为behavioral行为的规律，如概率法则）A characteristic theoretical pattern of error distribution occurs upon analysis of a large number of repeated measurements of a quantity, which conform to normal or Gaussian distribution.观测分析analysisn.中的误差分布的一个特征理论模式，遵照conform to遵照正态或高斯分布）在对一个量进行大量重复观测分析后，得到一个误差分布的理论特征——正态或高斯分布The plot of error sizes versus probabilities would approach a smooth curve of the characteristic bell-shape.与……相对概率的关系图，接近一条光滑的特有的characteristic特有的钟形曲线。

游戏道具和物品翻译

Armourer's ScrapImproves the quality of an armour增加装备质量(quality)值 1% 最高20%Blacksmith's WhetstoneImproves the quality of a weapon增加武器质量(quality)值 1% 最高20%Blessed OrbRandomises the numeric values of the implicit properties of an item 随机刷新固有属性的值（固有属性就是一个装备没有鉴定就显示的属性）Chaos OrbReforges a rare item with new random properties随机刷新黄色装备属性(很有用可以当货币换装备）Chromatic OrbReforges the colour of sockets on an item随机刷新装备上孔的颜色Divine OrbRandomises the numeric values of the random properties on an item 随机刷新装备非固有属性的值（就是属性种类不变，是指刷新数字）Exalted OrbEnchants a rare item with a new random property.增加黄色装备一个额外的属性Gemcutter's PrismImproves the quality of a gem增加技能石质量1% 最高20%（技能石有质量的话,会有新的属性.质量越高属性越高）Glassblower's BaubleImproves the quality of a flask.增加药剂质量2% 最高20%Jeweler's OrbReforges the number of sockets on an item随机刷新装备上孔的数量Mirror of KalandraCreates a mirrored copy of an item复制一件装备（非常稀少在下打没出过）Orb of AlchemyUpgrades a normal item to a rare item白装变黄装 (也是常用货币）Orb of AlterationReforges a magic item with new random properties.随机刷新蓝装属性Orb of AugmentationEnchants a magic item with a new random property增加蓝装一个额外属性Orb of ChanceUpgrades a normal item to a random rarity将一个白色的装备随机转化为蓝装或者黄装Orb of FusingReforges the links between sockets on an item随机连接装备上的孔 (这个消耗量巨大没存够前请误随便使用）Orb of RegretGrants a passive skill refund point洗天赋树点数 (一颗宝石洗一点)Orb of ScouringRemoves all properties from an item洗装备,使其变为白色.Orb of TransmutationUpgrades a normal item to a magic item白装变蓝装Regal OrbUpgrades a magic item to a rare item蓝装变黄装。

气体分子动理论(英文)

1
2
3
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S1
Ideal gas and the microscopic interpretation of
p and T
1.1 Microscopic properties of Ideal gas
Deﬁnition: ideal gas II All realistic gases can be regarded as ideal gas at suﬃciently low pressure and high temperature. Deﬁnition: ideal gas III From microscopic point of view, ideal gas means that ∙ The diameter of each molecule is negligible so that the molecules are considered to be pointlike particles. ∙ The molecules are considered to be noninteracting.
#» v #» v
Iv × Nv
Nv ∆V = 2 mv2 ∆S∆ t z V V
S1
Ideal gas and the microscopic interpretation of
p and T
{ The whole impulse on the wall of area ∆S during the time interval ∆ t ∑︁ Nv I= 2 mv2 ∆S∆ t z V moving to the wall | Finally we obtain the pressure ∑︁ Nv I p= = 2 mv2 z V ∆ t ∆S moving to the wall } Simplify the expression using the statistic postulate Nv ∑︁ 2 Nv 1 ∑︁ p= 2 mv2 = mv z z V V 2 all v all v

随机振动疲劳分析流程

随机振动疲劳分析流程Random vibration fatigue analysis is a critical process in engineering design and analysis. It involves predicting the life of a structure subjected to random vibrations, such as those experienced in vehicles, aircraft, and industrial machinery. This type of analysis is essential for ensuring the reliability and durability of components and systems under real-world operating conditions.随机振动疲劳分析是工程设计和分析中的一个关键步骤。

它涉及预测结构在随机振动下的寿命，例如车辆、飞机和工业机械中经历的振动。

这种分析对于确保组件和系统在实际运行条件下的可靠性和耐久性是至关重要的。

One of the main challenges in random vibration fatigue analysis is the uncertainty in the input loads. Unlike deterministic loading, which is well-defined and repeatable, random vibrations have unpredictable characteristics that make it difficult to accurately predict the fatigue life of a structure. This uncertainty requires the use of probabilistic methods and statistical tools to assess the effects of random loading on the structural integrity.随机振动疲劳分析中的主要挑战之一是输入载荷的不确定性。

光学中光滑的英文

光学中光滑的英文Title: The Optical Phenomenon of Surface SmoothnessLight, a fundamental aspect of our physical world, has fascinated scientists and philosophers for centuries. One of the intriguing phenomena associated with light is the concept of surface smoothness and its optical implications. In the realm of optics, the smoothness of a surface plays a crucial role in the behavior of light as it interacts with various materials and surfaces.At the most basic level, the smoothness of a surface can be described as the absence of significant irregularities or deviations from a perfectly flat or uniform surface. When light encounters a smooth surface, it interacts with the surface in a predictable manner, exhibiting specific optical properties that are distinct from those observed when light interacts with a rough or uneven surface.One of the primary consequences of surface smoothness in optics is the phenomenon of specular reflection. Specular reflection occurs when light is reflected off a smooth surface in a manner where the angle of reflection is equal to the angle of incidence. This type of reflection is often observed in everyday life, such as the reflection of lightoff a mirror or a still body of water. The smoothness of the surface is a critical factor in determining the quality and clarity of the reflected image, as any irregularities or imperfections on the surface can distort or scatter the reflected light.In contrast, when light encounters a rough or uneven surface, the reflection of light is diffuse, meaning that the light is scattered in multiple directions rather than being reflected in a single, predictable direction. This diffuse reflection is responsible for the appearance of many everyday objects, such as matte painted surfaces or rough-texturedmaterials, where the light is scattered in a more random and unpredictable manner.The smoothness of a surface can also influence the refractive properties of light as it passes through the material. Refraction is the bending of light as it transitions from one medium to another, such as from air to glass or water. When light passes through a smooth surface, the refraction is consistent and predictable, allowing for the precise control and manipulation of light beams. This property is essential in the design and manufacture of optical components, such as lenses and prisms, where the smooth surfaces are crucial for achieving desired optical outcomes.Furthermore, the smoothness of a surface can also impact the transmission of light through the material. In the case of transparent materials, such as glass or certain plastics, the smoothness of the surfaces can minimize the scatteringand absorption of light, allowing for efficient transmission and the preservation of image quality. This is particularly important in the design of optical devices, such as camera lenses, where the quality of the transmitted light is crucial for capturing high-resolution images.The importance of surface smoothness extends beyond the realm of optics and has significant implications in various scientific and technological fields. In the field of materials science, the smoothness of a surface can influence the adhesive properties, friction, and wear characteristics of a material. Smooth surfaces can exhibit reduced friction and improved resistance to wear, making them valuable in applications such as mechanical engineering, tribology, and surface coatings.In the semiconductor industry, the smoothness of surfaces is critical for the fabrication of high-performanceelectronic devices. The manufacturing of integrated circuitsand microchips requires the creation of extremely smooth surfaces, often at the nanoscale level, to ensure the accurate deposition of thin films and the precise patterning of features. Any irregularities or roughness on the surface can lead to defects and performance issues in the final devices.Moreover, the smoothness of surfaces plays a crucial role in the development of advanced materials and technologies, such as in the field of nanotechnology. The ability to engineer and control surface smoothness at the nanoscalelevel has opened up new possibilities for the creation of novel materials with unique optical, electronic, and mechanical properties. These materials find applications in areas like quantum computing, energy storage, and medical diagnostics.In conclusion, the optical phenomenon of surface smoothness is a multifaceted and profoundly important aspectof the study of light and its interactions with various materials. The smooth or rough nature of a surface can significantly impact the behavior of light, influencing phenomena such as reflection, refraction, and transmission. The understanding and optimization of surface smoothness have far-reaching implications in a wide range of scientific and technological fields, from optics and materials science to semiconductor fabrication and nanotechnology. As our understanding of the optical properties of smooth surfaces continues to evolve, the potential for innovativeapplications and groundbreaking discoveries in these fields remains vast and exciting.。

翻译

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马尔可夫《概率演算》

马尔可夫《概率演算》（中英文实用版）Title: Markov"s "Probability Calculus"Title: 马尔可夫《概率演算》In the world of mathematics, Andrey Markov"s work on "Probability Calculus" is highly regarded.His book, published in 1912, was one of the first to systematically study the theory of stochastic processes.在数学世界中，安德烈·马尔可夫关于《概率演算》的工作备受推崇。

他于1912年出版的书籍，是首批系统研究随机过程理论的著作之一。

Markov"s work was groundbreaking because it introduced the concept of a Markov chain, a mathematical system in which the future state of a process depends only on the current state and not on the sequence of events that preceded it.马尔可夫的工作之所以具有划时代意义，是因为他引入了马尔可夫链的概念，这是一种数学系统，其中过程的未来状态只取决于当前状态，而与之前事件的序列无关。

This idea was revolutionary because it provided a way to model and analyze complex systems that are influenced by random events.Today, Markov chains are used in a wide variety of fields, including physics, finance, economics, and computer science.这个想法之所以具有革命性，是因为它为建模和分析受随机事件影响复杂的系统提供了一种方法。

Topological low-energy modes in N=0 Landau levels of graphene a possibility of a quantum-li

a r X i v :0804.4762v 1 [c o n d -m a t .m e s -h a l l ] 30 A p r 2008Topological low-energy modes in N =0Landau levels of graphene:a possibility of a quantum-liquid ground stateYasuhiro Hatsugai a ,b ,1,Takahiro Fukui c and Hideo Aoki daInstitute of Physics,University of Tsukuba,Tennodai,Tukuba 305-8571Japan bDepartment of Applied Physics,University of Tokyo,Hongo,Tokyo 113-8656,Japan c Department.of Mathematical Sciences,Ibaraki University,Mito 310-8512,Japan d Department of Physics,University of Tokyo,Hongo,Tokyo 113-0033,Japan1.IntroductionGraphene,for which an unconventional quantum Hall eﬀect has recently been discovered,[1]is a pecu-liar condensed-matter realization of massless Dirac fermions.While the quantum Hall eﬀect is generally characterized by a topological (Chern)number,the pe-culiarity of Landau levels (LL)in graphene appears as existence of the exactly zero energy Landau level.We have established topological aspects in the graphene QHE[2],among which is a bulk-edge correspondence coming from the topological nature of bulk and edge states.All the topological features are intimately re-lated with the chiral (bipartite)symmetry of the hon-eycomb lattice,which,in addition to being responsibleral symmetry.In magneticﬁelds,the bond ordering acts to split the zero-energy Landau level of the Dirac fermions,which may be viewed as a kind of the Peierls instability since the one-particle density of states di-verges.2.Bond ordering and the split zero-energy Landau levelsWe now examine the above idea in the simplest man-ner,i.e.,we assume that the ordering is static and adopt a Hamiltonian that has the hopping t ij with a Kekul´e-type modulation,which represents,in a mean-ﬁeld sense,the bond ordering,say,originating from the electron-electron interaction.Weﬁrst take the case in which the ordering pattern has a translational symme-try as in Fig.1.The massless Dirac fermions then ac-quire a mass which opens a gap(Fig.2).As stressed the bond ordering does not destroy the chiral symmetry (although the size of the Brillouin zone is expanded), which implies that the particle-hole symmetry is pre-served as well for any(including random)ordering pat-terns.This contracts with other types of modulation (such as site dependent potentials)which break the chi-ral symmetry.Correspondingly,the zero-energy Lan-dau level in uniform magneticﬁelds,which is a special Landau level sitting right at the Dirac cone vertex,also splits into two[4].This implies that the bond ordering,which is here assumed,is expected to spontaneously induced in a self-consistent treatment as a kind of Peierls instability in the zero-energy LL[3].3.Topological states localized along domain boundaries as2D analogue of solitonsWe have seen that the bond ordering,when trans-lationally symmetric,splits the zero-energy Landau level accompanied by an energy gap at E=0.How-ever,there are a vast number of possible realizations of bond-ordering patterns that have no translational symmetry.Speciﬁcally,there is an important class of such states that consist of“domains”.Namely, there are three,equivalent‘Kekul´e patterns(diﬀer-ently colored in Fig.1),and there are a hugenumberFig.1.Kekul´e(static bond-ordering)patterns have three, equivalent realizations,where either the red,blue or green bonds are r(>1)times stronger than the others.The two arrows are unit vectors of the enlarged unit cell.(coloronline)Fig.2.(a)The band dispersion around E=0in graphene before(a)and after(b)a(static)bond ordering is intro-duced,as displayed in the folded Brillouin zone for r=1.2 here.of conﬁgurations where,e.g.,a bond-ordered phase with strong red bonds sits next to another phase with strong blue bonds(Fig.3).We can then expect that “boundary states”that are localized along the domain boundaries should appear as generalized boundarystates in graphene,which have topological origin and stability.[2]The situation reminds us of the well-known soliton modes across the diﬀerent conjugated patterns in1D polyacetylene.So the boundary states considered here is a2D extension of solitons which are topologically protected.The boundary states,whose energies reside in the gap of the split N=0Landau levels,still do not vi-olate the chiral symmetry.Physically the situation is similar to the appearance of the zero-mode edge states along the zig-zag edges in graphene in zero magnetic ﬁeld,which also have a topological origin.These loop-like boundary states(“strings”)may have diﬀerent re-alization in2D as further exempliﬁed in Fig.4.In each case topologically stable boundary states arise near the 2zero energy as displayed in Figs.3(b),4(b).Fig.3.(a)A bond ordering with straight domain bound-aries,where the red (blue)hopping is stronger than the others (by a factor of 1.2)in the left (right)domain.(b)The boundary state whose energy sits between the split N =0LL is shown with the charge density represented by yellow circles for the magnetic ﬂux of 1/6times the ﬂux quantum per hexagon.(color online)In reality the bond ordering conﬁguration can be dy-namical,which may be described in terms of the ﬂuctu-ating strings[3].We can then conjecture that the true state may possibly be a quantum liquid realized as a condensate of such “strings”.The physics may have an analogy with the “string net condensation”considered for spin models[5].A self-consistent treatment of the eﬀect of the electron-electron interaction will be given elsewhere[3].This work has been supported in part by Grants-in-Aid for Scientiﬁc Research on Priority Areas from MEXT,“Physics of new quantum phases in superclean materials”(Grant No.18043007)for YH,“Anoma-lous quantum materials”(No.16076203)for HA,and a Grant-in-Aid for Scientiﬁc Research (No.18540365)from JSPS forTF.Fig.4.A bond-ordering pattern with a closed-loop bound-ary,where the red (blue)hopping is stronger than the oth-ers (by a factor of 1.2)in the inner (outer)domain.(b)The boundary state shown as the charge density represented by yellow circles for the same magnetic ﬂux as in Fig.3.(color online)References[1]K.S.Novoselov et al.,Nature 438(2005)197;Y.Zhang et al.,ibid .438(2005)201;A.K.Geim and K.S.Novoselov,Nature Mater.6,183(2007).[2]Y.Hatsugai,T.Fukui and H.Aoki,Phys.Rev.B 74,205414(2006).[3]Y.Hatsugai,T.Fukui and H.Aoki,to be published.3[4]T.Nakajima and H.Aoki,in these proceedings,proposeanother mechanism for the splitting in a one-particlepicture.[5]M.A.Levin and X.G.Wen,Phys.Rev.B71,045110(2005).4。

random variable 的英文解释

random variable 的英文解释Random variables are an essential concept in probability theory and statistics, as they play a crucial role in modeling and analyzing uncertain phenomena. A random variable is a mathematical function that assigns a numerical value to each possible outcome of a random experiment. In other words, it is a variable that can take on different values with certain probabilities.The concept of a random variable is fundamental in many areas of study, including finance, engineering, biology, and social sciences, where researchers and analysts need to deal with uncertainty and make decisions based on probabilistic information. By understanding and working with random variables, we can gain insights into the behavior of complex systems, make more informed decisions, and better understand the world around us.One of the key characteristics of a random variable is its probability distribution, which describes the likelihood of the variable taking on different values. The probability distribution can be either discrete or continuous, depending on the nature of the random variable. Discrete random variables can only take on a finite or countable number of values, while continuous random variables can take onany value within a specified range.Discrete random variables are often used to model situations where the possible outcomes are distinct and countable, such as the number of heads in a series of coin flips or the number of defective items in a production process. In these cases, the probability distribution can be described by a probability mass function, which assigns a probability to each possible value of the random variable.Continuous random variables, on the other hand, are used to model situations where the possible outcomes are not discrete, such as the height of individuals in a population or the time it takes for a machine to break down. In these cases, the probability distribution can be described by a probability density function, which specifies the relative likelihood of the random variable taking on different values within a continuous range.One of the most important properties of random variables is their expected value, also known as the mean or average. The expected value represents the long-term average or typical value of the random variable, and it is calculated as the weighted average of all possible values, with the weights being the corresponding probabilities. The expected value is a crucial measure in decision-making, as it provides a way to quantify the central tendency of a random variable.Another important property of random variables is their variance, which measures the spread or dispersion of the values around the expected value. The variance reflects the degree of uncertainty or variability associated with the random variable, and it is calculated as the average of the squared deviations from the expected value. The square root of the variance, known as the standard deviation, is also a commonly used measure of variability.Random variables can also be classified based on their independence or dependence. Independent random variables are those whose values are not influenced by the values of other random variables, while dependent random variables are those whose values are related to the values of other random variables. Understanding the relationships between random variables is crucial in many applications, as it allows for more accurate modeling and better decision-making.In addition to these basic properties, random variables can also exhibit more complex characteristics, such as skewness (the asymmetry of the probability distribution) and kurtosis (the peakedness or "tailedness" of the distribution). These higher-order moments can provide additional insights into the behavior of the random variable and its potential impact on the system or process being studied.The concept of random variables is not only important in theoretical studies but also has numerous practical applications. In finance, for example, random variables are used to model stock prices, interest rates, and other financial variables, which are crucial for investment decisions and risk management. In engineering, random variables are used to model the reliability and performance of systems, such as the lifetime of electronic components or the strength of materials. In biology, random variables are used to model the genetic variations within a population or the spread of infectious diseases.In conclusion, random variables are a fundamental concept in probability theory and statistics, and they play a crucial role in modeling and analyzing uncertain phenomena. By understanding the properties and characteristics of random variables, researchers and analysts can make more informed decisions, gain deeper insights into complex systems, and better understand the world around us.。

大学英语六级改革适用(阅读)模拟试卷14(题后含答案及解析)

大学英语六级改革适用（阅读）模拟试卷14(题后含答案及解析) 题型有： 4. Reading ComprehensionPart III Reading ComprehensionSection BStartup Nuclear Energy Companies Augur Safer, Cheaper Atomic PowerA)Nothing captures how fashionable the startup has become quite like crowdfunding. The craze for raising contributions via websites like Kickstarter and Indiegogo is helping to launch companies from scooter manufacturers to lightbulb vendors to filmmakers. Now, even nuclear fusion is game.B)Yes, the Holy Grail of cheap, clean, safe, plentiful, low-carbon energy that has remained 40 years in the future since scientists proposed it over half a century ago has entered the crowd sourcing era. International government projects like ITER in France and the National Ignition Facility in California may have spent billions of dollars in pursuit of the technology, but that doesn’t mean there can’t be a little grassroots action, too.C)LPP Fusion, a tiny company based in Middlesex, N.J., launched in May an Indiegogo campaign to raise $200,000—loose change in this business—that it believes will help it reach a major fusion development milestone in a year and commercialize fusion reactors by 2020.D)LPP(it stands for “Lawrenceville Plasma Physics”)is representative of a new class of companies emerging to address the world’s energy crisis: Nuclear startups. Dozens of small new reactor companies are either chasing the elusive fusion dream or pursuing fission designs that trump those on the market today. All are promising to deliver a knock-out blow to the carbon-intensive fossil fuels that bedevil the world with environmental impact and volatile geopolitics and economics. Many of these innovative firms are positioning their reactors not just for electricity, but also to provide clean heat for high temperature industrial processes and for water desalination.E)While LPP might be the only crowdfunded member of the group, it is determined like its young peers to shake up the staid nuclear industry. Reactor designs have not fundamentally changed since utilities first connected fission machines to the grid in the 1950s, marking a conservatism that has mired nuclear in the era of black-and-white television while colourful possibilities abound. The startups aim to brighten the palette.F)For LPP, that would mean not only delivering fusion—melding atoms together rather than fission’ s waste-creating process of splitting them apart—but it would also eliminate the time-honoured need for costly turbines and generators. Nuclear power, including most fusion concepts, functions mechanically the same way fossil fuel plants do by creating heat to produce steam to drive a turbine. LPP is working on a type of fusion called “aneutronic”that emits charged particles for electricity.G)”The nuclear industry is stuck using the same method for making electricity that utilities have used since the days of Thomas Edison—generate heat to make steam to drive a turbine and generator,”says Eric Lerner, president of LPPFusion. “We can change all that. We can convert energy directly into electricity and slash costs.”H)First, he’ll need the $200,000 he seeks on Indiegogo(he has until July 5 to raise it), which would buy him some fancy new beryllium electrodes that would withstand rigors far better than the copper variety that LPP has been using. He hopes to install them by the end of this year in his experimental fusion reactor, which Lerner operates at the Friendly Storage premises in Middlesex, a place otherwise full of surplus boxes and furniture.I)Lerner is boldly confident that the beryllium would by the middle of next year enable his lab to overcome the problem that has vexed fusion projects forever: It would harness more energy out of its reactor than what goes into it. Additional financing might then rush in. LPP will need $50 million in total, virtually nothing next to the nearly $18 billion that ITER has budgeted for only the next 10 years of an expected 30 years of construction and development of a 20-story “tokamak” facility.J)With the financing, Lerner believes that by 2020 he could license the mass-production of small $300,000-to- $500,000 fusion machines—each the size of a one-car garage—with a capacity of 5 megawatts, enough to power 3,000 houses.K)If only he had the wherewithal of rival fusion startup Tri-Alpha Energy, which has rounded up over $140 million from Goldman Sachs, Microsoft co-founder Paul Allen, and Russian state-owned company Rusnano, among others. Like LPP, Irvine, Calif.-based Tri-Alpha hopes to develop an aneutronic machine that delivers electricity without using turbines.L)ITER and NIF, the government groups, are taking a more “conventional” fusion approach, aspiring to drive turbines with heat released by fusing isotopes of hydrogen.(In contrast, an aneutronic process tends to fuse standard hydrogen and boron.)So, too, are a number of startups that believe they can crack fusion long before the big science projects do by developing smaller machines(NIF’s facility is 3 football fields long and 10 stories tall)and deploying different technologies.M)”We liken it to the Human Genome Project or SpaceX, where large government programs were ultimately outrun by more nimble and more practical innovation in the private sector,”notes Nathan Gilliland, CEO of General Fusion near Vancouver, Canada. General Fusion has raised $32 million from sources including the Canadian oil company Cenovus and Jeff Bezos, Amazon’s chief executive.N)As intriguing as fusion is, there is probably more startup activity in fission, where novel approaches promise great improvements over the industry’s addiction to fissioning solid uranium fuel rods then cooling and moderating them with water.O)A host of startups are experimenting with different approaches including the use of liquid fuel, the use of solid fuel with different shapes(such as bricks or pebbles), and the use of alternative coolants and moderators such as salts and gases. Many of the designs draw on ideas that politics suppressed decades ago. Some, like Bill Gates-chaired TerraPower in Bellevue, Wash., are designing “fast reactors” that don’t moderate neutrons. Some envision using the element thorium instead of uranium.P)Between them, they portend leaps in safety, cut way down on nuclear waste, use “waste” as fuel, and minimize weapons proliferation risks, slash costs and tremendously boost efficiencies. Many fit the “small modular”forms that enables mass production and affordable incremental power.(Oregon startup NuScale Power recently secured $217 million in federal funds to develop a small but comparativelyconventional reactor.)Q)”There is a growing market pull for innovation in the nuclear space, so you ‘re beginning to see a blossoming of startup companies doing different things in nuclear,” says Simon Irish, CEO of startup Terrestrial Energy, Mississauga, Canada, which is developing a “molten salt” reactor(MSR)based on liquid fuel. In the U.S., Russ Wilcox, CEO of Cambridge, Mass.-based MSR developer Transatomic Power, implores the U.S. Nuclear Regulatory Commission to broaden its focus beyond conventional reactor safety, which he says “freezes progress”.R)Many observers believe that countries other than the U.S., such as Canada and China, will deploy first. Beijing is funding innovative Chinese fission projects, with collaboration from the U.S. DOE. Meanwhile, Western companies seek funds. Like Cenovus at General Fusion, more oil companies might pony up, because they want clean heat to process petroleum. As Fortune reported last month, a lack of industry funding appears to have slowed progress in DOE’s mission to develop an advanced reactor. LPP Fusion doesn’ t seem to be worried. For the young company, the next financing stage could simply be a matter of warming up the crowd.1．The aneutronic machine can generate electricity without the support of turbines.正确答案：K解析：题干意为无中子核聚变发电机不需要借助汽轮机也能发电。

能量的原理英语作文

能量的原理英语作文Title: The Principle of Energy。

Energy is an essential concept in physics, encompassing the capacity to do work or produce heat. Understanding the principles governing energy is crucial for comprehending various phenomena in the universe. In this essay, we will delve into the fundamental principles of energy.Firstly, it's imperative to grasp the principle of conservation of energy. This principle states that energy cannot be created or destroyed but can only be transformed from one form to another. It implies that the total energy of an isolated system remains constant over time, irrespective of the transformations it undergoes. This foundational concept, often summarized by the equation$ E_{\text{total}} = E_{\text{kinetic}} +E_{\text{potential}} + E_{\text{thermal}} + \ldots $, underscores the interconvertibility and persistence of energy.Next, let's explore the various forms of energy. Energy manifests in diverse forms, each with distinct characteristics and properties. Kinetic energy, for instance, is associated with the motion of an object and is given by the equation $ KE = \frac{1}{2}mv^2 $, where$ m $ represents mass and $ v $ denotes velocity. Potential energy, on the other hand, is stored energy attributed to an object's position or configurationrelative to its surroundings. It encompasses gravitational potential energy, elastic potential energy, and more.Moreover, energy exists in non-mechanical forms such as thermal, chemical, electrical, and nuclear energy. Thermal energy, often referred to as heat, results from the random motion of particles within a substance. Chemical energy is stored within the bonds of chemical compounds and is released during chemical reactions. Electrical energy arises from the movement of electrons in a conductor under the influence of an electric field. Nuclear energy originates from the nucleus of an atom and is released during nuclear reactions, such as fission and fusion.Furthermore, the law of entropy, a fundamentalprinciple of thermodynamics, governs the direction of energy transformations. According to this law, the entropy of an isolated system tends to increase over time, leading to a gradual dissipation of energy and a progression towards thermodynamic equilibrium. In essence, it underscores the irreversibility of certain processes and the tendency towards disorder in the universe.In addition, energy transfer mechanisms play a pivotal role in various natural phenomena and technological applications. Conduction, convection, and radiation are primary modes of heat transfer, elucidating how thermal energy propagates through different mediums. Likewise, electromagnetic waves facilitate the transfer of radiant energy across space, encompassing phenomena such as light, radio waves, and X-rays.Furthermore, energy conversion processes are ubiquitous in everyday life and industry. Power plants, for instance, harness various energy sources, such as fossil fuels,nuclear reactions, and renewable resources, to generate electricity. This process involves the conversion of chemical, nuclear, or mechanical energy into electrical energy, which powers homes, businesses, and infrastructure.In conclusion, the principle of energy encompasses fundamental concepts such as conservation, transformation, and transfer. From the conservation of energy to the laws of thermodynamics, these principles govern the behavior of energy in the universe. Understanding these principles not only elucidates natural phenomena but also underpins technological advancements and societal progress. As we continue to explore and harness the potential of energy,it's imperative to uphold these principles and strive for sustainable practices that preserve our planet's resources for future generations.。

降低地球磁场的方法

降低地球磁场的方法英文回答：To begin with, it is important to note that the Earth's magnetic field plays a crucial role in protecting our planet from harmful solar radiation and cosmic particles. However, if you are interested in discussing ways to reduce the strength of the Earth's magnetic field, I can provide some insights.One possible method to lower the Earth's magnetic field is through the use of large-scale electromagnetic devices. These devices would generate magnetic fields that counteract the Earth's field, effectively weakening it. However, implementing such a method would require significant technological advancements and would have numerous unforeseen consequences. Additionally, the energy requirements for such devices would be immense, making it an impractical solution.Another approach to reducing the Earth's magnetic field is through the manipulation of the Earth's core. TheEarth's magnetic field is generated by the motion of molten iron in the outer core. By altering the flow patterns of this molten iron, it may be possible to weaken the magnetic field. However, this method is highly theoretical and would require a deep understanding of the Earth's core dynamics, which is currently limited.It is worth mentioning that tampering with the Earth's magnetic field could have significant repercussions. The magnetic field plays a vital role in protecting the atmosphere from being stripped away by solar winds. Without a strong magnetic field, the Earth would be exposed to higher levels of radiation, leading to detrimental effects on both the environment and living organisms.In conclusion, while there may be theoretical methods to reduce the Earth's magnetic field, the practical implementation and potential consequences make it an unlikely and undesirable approach. It is crucial to understand and appreciate the importance of the Earth'smagnetic field in maintaining a habitable planet.中文回答：首先，需要注意到地球的磁场对于保护我们的星球免受太阳辐射和宇宙粒子的伤害起着至关重要的作用。

stablediffusion提示词格式

Stable DiffusionIntroductionIn the field of physics and chemistry, diffusion refers to the process by which molecules or particles spread out from an area of high concentration to an area of low concentration. This natural phenomenon plays a crucial role in various scientific and industrial applications, such as drug delivery systems, environmental pollution control, and material synthesis. However, in some cases, diffusion can become unstable and lead to unpredictable outcomes. This article will explore the concept of stable diffusion, its significance, and its applications.Understanding DiffusionDiffusion is driven by the random motion of particles due to their thermal energy. The particles move in a zigzag pattern known as Brownian motion. Over time, this random motion causes the particles to spread out evenly throughout the available space until they reach equilibrium.The rate of diffusion depends on several factors, including temperature, concentration gradient, and the properties of the diffusing substance and medium. In stable diffusion, these factors are carefully controlled to ensure a predictable and controlled spreading process.Significance of Stable DiffusionStable diffusion is essential for many scientific and industrial processes where precise control over particle distribution is required. By maintaining stable diffusion conditions, researchers can achieve uniform coating thicknesses in material synthesis processes or deliver drugs evenly throughout a patient’s body.Moreover, stable diffusion enables accurate modeling and simulation of various phenomena. For example, understanding how pollutants disperse in the air helps environmental scientists predict pollution levels and develop effective mitigation strategies.Applications of Stable DiffusionDrug Delivery SystemsStable diffusion plays a critical role in drug delivery systems. By controlling the release rate of drugs from carriers such as nanoparticles or patches, stable diffusion ensures that therapeutic compounds are delivered consistently over time. This controlled release mechanism improves efficacy and reduces potential side effects.Coating TechnologiesCoating technologies rely on stable diffusion to achieve uniform coating thicknesses on various surfaces. Whether it’s applying protective coatings on electronic devices or depositing thin films on solar panels, stable diffusion ensures even distribution of coating materials, resulting in improved performance and durability.Environmental Pollution ControlStable diffusion is vital in understanding and mitigating environmental pollution. By studying the dispersion of pollutants in air or water, scientists can develop models to predict pollution levels and design effective strategies for pollution control. Stable diffusion also allows for the controlled release of chemicals for environmental remediation purposes.Material SynthesisIn material synthesis processes, stable diffusion is crucial for achieving desired material properties. For instance, in the production of catalysts, controlling the diffusion of precursor molecules onto a substrate ensures uniform deposition and enhances catalytic activity. Stable diffusion is also employed in the growth of crystals withspecific structures and properties.Techniques for Achieving Stable DiffusionTo achieve stable diffusion, several techniques can be employed:Temperature ControlTemperature plays a significant role in determining the rate andstability of diffusion. By carefully controlling the temperature,researchers can optimize diffusion rates and prevent undesired fluctuations.Concentration Gradient ControlMaintaining a constant concentration gradient across the diffusing medium helps ensure stable diffusion. This can be achieved by adjusting the concentration of diffusing substances or using techniques such as membrane barriers to control their movement.Medium SelectionThe choice of medium can significantly impact diffusion stability. Factors such as viscosity, surface tension, and interaction with diffusing substances need to be considered when selecting an appropriate medium for stable diffusion.ConclusionStable diffusion is a fundamental process that underlies many scientific and industrial applications. By understanding how to achieve stable diffusion and controlling its parameters effectively, researchers can harness its potential for drug delivery systems, coating technologies, environmental pollution control, and material synthesis. The ability to maintain stable diffusion opens up new possibilities for innovation in various fields while ensuring predictable outcomes.。