分拆大偶数为两个几乎相等的素数之和

我们称n =p+q 为偶数n的最平衡哥德巴赫分拆 ,其中 p与 q均为奇素数 ,p≤ q且 |p - q|取可能的最小值。根据哥德巴赫猜想 ,对于每个大于或等于 6的偶数 ,必存在其最平衡哥德巴赫分拆。本文通过对 10 7以内的偶数进行的数值计算 ,进一步提出如下猜想 :由所有 (≥ 6的 )偶数之最平衡哥德巴赫分拆产生的三组比值 p/q ,p/n 以及 (n/2 -p) /n的均值 ,分别具有极限 1,1/2及 0。     

A Superlimiting Phased-Array Receiving System in a Two-Source Environment

The performance of a uniformly spaced phased-steered line array with element channel superlimiting is studied for far-field sources consisting of 1) two sinusoidal signals with different frequencies and angular locations, and 2) a sinusoid and a noise signal at different angular locations. Attention is focused on the nonlinear case where internal noise is negligible compared to both input signals. The analysis for the two-sinusoid case gives the precise frequencies, positions, and amplitudes of all apparent sources. In addition to the two active sources, the array output has an array of images arranged symmetrically in sine space about the larger input, at intervals equal to the spacing between the two active sources. For the case of a separated sinusoid and a noise source, the analysis shows that the angular positions and average powers of the array outputs duplicate the double-sinusoid results, but the images have noise-like spectra. The analyses are confirmed by experimental results obtained with a 60-element superlimiting X-band array.     

Fast Maximnurm Likelihood Joint Estimation of Frequency and Frequency Rate

A fast maximum likelihood algorithm is presented that jointly estimates the frequency and frequency rate of a sinusoid corrupted by additive Gaussian white noise. It consists of a coarse search and a fine search. First the two-dimensional frequency-frequency rate plane is subdivided into parallelograms whose size depends on the region of convergence of Newton's method used in maximizing the log-likelihood function (LLF). The size of the parallelogram is explicitly computed and is optimal for the method used. The coarse search consists of maximizing the LLF over the vertices of the parallelograms. Then starting at the vertex where the LLF attained its maximum, a two-dimensional Newton's method to find the absolute maximum of the LLF is implemented. This last step consists of the fine search. The rate of convergence of Newton's method is cubic, and is extremely fast. Furthermore Newton's method will converge after two iterations when the starting point used in the method lies within 75 percent of the distances defined by the parallelogram of convergence whose center coincides with the true values of frequency and frequency rate. In this case, the root mean square error (RMSEs) for frequency and frequency rate are practically equal to the Cramer-Rao bound at all signal-to-noise ratio (SNR)?15 dB. The frequency-frequency rate ambiguity function is shown to be even and its periodicities are extracted.     

Signal-to-Noise Ratio Calculations in Pulse and Pulse Doppler Radars

In low pulse-repetition frequency (PRF) pulse radars, signal-to-noise ratio (SNR) is usually calculated on a per pulse basis and this value is then multiplied by the number of pulses integrated to obtain the SNR for a given duration of target illumination. In high PRF pulse Doppler radars, SNR is usually calculated by using the centerline power of the transmitted signal spectrum as the target return power because the centerline is kept in the receiver and returns of the PRF lines are notched out [1]. We show here that both methods of SNR calculations are entirely equivalent for matched transmit-receive radar systems.     

A Study on Particle Filters for Single-Tone Frequency Tracking

In this paper, we present an online approach for frequency tracking of a noisy sinusoid using sequential Monte Carlo (SMC) methods, also known as particle filters (PFs). In addition, apart from employing the classical Cartesian formulation model, we also develop two alternative dynamical models, namely, nearly constant frequency (NCF) and Singer, which are adapted from the maneuvering target tracking discipline, to describe the evolution of time-varying frequencies, and investigate their fitness to the frequency tracking application. When compared with conventional techniques whose performance is restricted to linear Gaussian models and/or to slowly varying frequencies, PFs are more flexible to handle situations where these conditions are violated. Extensive evaluations on the proposed new models and PF tracking algorithms are conducted with different sets of frequency inputs and levels of signal-to-noise ratio (SNR). According to the computer simulation results, it is found that PFs under all investigated models consistently outperform and are less sensitive to SNR levels than the extended Kalman filter (EKF). Furthermore, the results suggest that while none of the models perfectly fits all types of frequency inputs, NCF model is more suitable for moderately varying frequencies, whereas the Singer is more suitable for rapidly changing frequencies.     

干摩擦对称黏滑响应的级数解及黏滑边界特性

针对航空发动机中的摩擦振动问题,给出了对称黏滑运动摩擦力的分段表达式.利用谐波平衡方法推导了具有偶数次黏着的黏滑运动的级数形式解析解,并基于该解析解给出了参数平面内的黏滑边界线方程.黏滑运动响应仅包含奇次谐波成分,在奇次分数倍频处存在超谐次共振.当频率比小于0.4时,黏滑边界线呈现凸凹交替特征,局部极小值位于各阶超谐次共振频率处.黏性阻尼增大能够缩小无黏着运动的参数范围,但在各阶超谐共振频率附近,黏性阻尼增大会扩大无黏着运动的参数区域.      

Hard-Limiter Output Autocorrelation Function: Gaussian & Sinusoidal Input

An expression is derived for the autocorrelation function of the output of a hard limiter whose input is stationary Gaussian noise with zero mean plus independent random-phase sinusoidal signal. The output spectrum may then be evaluated. This spectrum is extremely useful in understanding the properties of a filter-limit-filter-detect signal processor whose signal input is an actual sinusoid, or when a sinusoid is used as a test signal.     

基于ICA包络增强MEMD的滚动轴承故障诊断

针对多元经验模态分解(MEMD)存在模态混叠、带内噪声干扰导致轴承故障特征信息微弱难提取问题,提出了基于独立分量分析(ICA)包络增强MEMD的滚动轴承故障诊断。采用MEMD对多通道信号进行自适应分解,依据峭度和相关系数选取包含故障信息的本征模态函数(IMF);对所选取IMF分量的包络信号进行ICA分析,抑制模态混叠和削弱带内噪声;选取峭度最大的独立分量包络进行频谱分析,判断滚动轴承的运行状况。实测信号结果表明:ICA包络增强MEMD后包络谱中可以清楚地看到前6阶故障频率,故障特征频率误差小于1 Hz,其他方法只能看到2~3阶,且干扰频率成分较多。      

转子-电磁轴承系统动静件碰摩动力特性研究

对转子—磁轴承系统动静件间发生碰摩时的非线性动力学行为进行了研究,在考虑质量偏心的情况下建立了系统的数学模型,求解了系统的周期解,并结合分岔图、庞加莱映射和频谱分析研究了系统的动态特性,研究表明系统发生碰摩后,随着转速及偏心率的增加,转子运动中具有连续的周期分岔现象,并走向失稳,其频谱图中组合频率在奇数倍频附近发生了从右到左的频移现象。这些研究结果可用于控制碰摩后电磁轴承的稳定性,避免大事故的发生。其振动频率特征可判别磁轴承系统是否发生了碰摩故障。      

Sensitivity of Low Frequency Oscillations to Updated Solar Models

A large number of acoustic frequencies have already been detected, leading to a "seismic" model of the Sun rather close to the actual standard solar models. The core however is not yet well constrained by these observations and frequencies of low degree, low frequency modes which penetrate deeply into the solar core are needed. We present here a study on the sensitivity of low degree low frequency (50 - 900 μHz) modes to the structure of the solar interior, in order to help their detection and identification in the low frequency spectrum observed by SoHO experiments like VIRGO and GOLF. The frequencies of p and g modes have been computed for a set of solar models with updated physics (Morel et al., 1997). We analyze their sensitivity to solar parameters like age and metallicity, and to various physical processes, like convective core overshoot and mass loss during the beginning of solar evolution. This revised version was published online in June 2006 with corrections to the Cover Date.     

尾流撞击效应在低速轴流压气机中应用实验研究的初探

通过改变尾流撞击效应扰流耦合器的叶片数目来改变尾流撞击效应的激励频率,从而研究其对压气机稳态性能的影响。通过12组方案的实验,当尾流撞击频率为2 000 H z和4 000 H z时,对压气机失速裕度的改善最为明显,相对增量分别达到19.5%和15.2%;当尾流撞击频率为1 000 H z时压气机性能有所恶化。并得到转子的分离流特征频率约为2 000 H z。也就是说,激励频率为特征频率及其倍频时流场可获得最好的气动性能,而激励频率为特征频率的1/2时流场的损失最大。此外,初步讨论了尾流撞击效应作用机理及激励频率与性能提高的关系,这就为轴流压气机中两种流态转化的工程应用,特别是多级轴流压气机设计中的级间匹配问题提供了一个新的思路与途径。      

外激作用下自激热声系统的非线性动力学响应

在高温高压燃烧实验台上,以频率ff为78~716Hz,幅值A为0.026~0.629的外激信号激励有自激响应的同心分层旋流部分预混预蒸发火焰热声系统,研究其非线性动力学响应。结果表明:系统的自激频率fn为366.85Hz;当外激频率和自激频率的比值为1.022, 幅值A为0.629时,火焰主要被外激频率其谐波控制,其状态轨迹密集在很窄的封闭带中;当外激频率和自激频率的比值与A在其他的范围时,火焰不仅在ff和fn处响应,还在谐频、结合频和分频处响应。说明当外激幅值足够大并且外激频率靠近自激频率时,火焰发生锁相;当火焰未锁相时,出现了谐频、结合频以及分频的非线性响应,火焰准周期振荡。受迫范德波尔振荡器模型能够预测锁相、奇数谐频以及结合频2fn±ff。      

运行模态分析的频域空间域分解法及其应用

提出了一种基于频域空间域分解(Frequency and Spatial Domain Decomposition, FSDD)的运行模态分析方法。该法将同时具有输入和输出的试验模态分析的经典方法——复模态指示因子(Complex Mode Indicator Function, CMIF)法拓展到了仅有输出响应的运行状态模态分析。FSDD法采用奇异值分解将信号空间和噪声空间分离开来,把奇异值曲线作为模态指示的依据,以奇异值向量作为加权函数得到每一阶模态的增强功率谱(Power Spectrum Density, PSD),进而在频域内对增强PSD曲线进行最小二乘拟合以得到准确的模态频率和阻尼参数。采用了一个二层楼仿真算例和在欧洲广为人知的瑞士Z24公路大桥实测算例来验证FSDD算法。     

Spectrum management: a high stakes game

The optimal use of the frequency spectrum is an incredibly difficult but vital requirement to be achieved. Among the numerous services and applications which are requesting more frequencies, radar and telecommunications are certainly the most demanding. The purpose of this paper is to discuss several technical aspects contributing to the frequency management within the whole spectrum. To this effect it is proposed to analyse the following main aspects: first, a survey of the foreseeable evolution of telecommunications and radars mainly in terms of frequency band needs, radiated power density and waveforms; second, we will provide a comparative analysis of signals used in radars and telecommunications; finally, we propose a few necessary conditions to coordinate the operation of radars and telecommunications within the whole spectrum     

A Semi-Empirical Approach to the PLL Threshold

This correspondence considers the response of the PLL near threshold to an input consisting of a modulated carrier and white, Gaussian noise. For high input signal-to-noise power ratios ?, the output noise power is Gaussian with a parabolic spectrum. As ? is decreased, the PLL tends to lose lock which gives rise to impulses or ?spikes? in the output with a resulting white power spectrum. The additional output noise due to these ?spikes? causes a threshold in the output signal-to-noise ratio. Unfortunately the loss of lock rate in the PLL depends on the modulation as well as the noise power. A semiempirical approximate expression for the loss of lock rate as a function of the noise and sinusoidal frequency modulation is presented and is used to determine the optimum design procedure for PLL's to demodulate FM signals of varying modulation indexes, ?.     

主字母体制调制系数的选择

针对靶场安全控制系统主字母体制中主字母信号的调制系数选取范围问题,对主字母信号经FM (Fre-quency Modulation,调频)调制后的功率进行理论分析,选取一组频率组成主字母信号调制到中频.通过仿真得到数据曲线.同时将仿真参数移植到与工程设备相似的实验设备上,使用频谱仪进行实际测试,以测试数据拟合出曲线,该曲线符合理论分析及仿真曲线,即理论分析、仿真与设备测试结果一致.可以得出结论,在主字母体制信号可解调的条件下,调制系数与主字母信号经FM调制后的功率的关系函数为对数函数,从而可为工程参数的选择提供参考范围,有利于工程应用.     

The solar flare plasma: Observation and interpretation

In the past several years, X-ray observations of the Sun made from rockets and satellites have demonstrated the existence of high temperature (20 × 10⁶ – 100 × 10⁶ K), low density plasmas associated with solar flare phenomena. In the hard X-ray range ( < 1 ), spectra of the flaring plasma have been obtained using proportional and scintillation counter detectors. It is possible from these data to determine the evolution of the hard X-ray flare spectrum as the burst progresses; and by assuming either a non-thermal or thermal (Maxwellian) electron distribution function, characteristic plasma parameters such as emission measure and temperature (for a thermal interpretation) can be determined. Thermal interpretations of hard X-ray data require temperatures of 100 × 10⁶ K.In contrast, the soft X-ray flare spectrum (1 <<30 ) exhibits line emission from hydrogen-like and helium-like ions, e.g. Ne, Mg, Al, Si,... Fe, that indicates electron energies more characteristic of temperatures of 20 × 10⁶ K. Furthermore, line intensity ratios obtained during the course of an event show that the flare plasma can only be described satisfactorily by assuming a source composed of several different temperature regions; and that the emission measures and temperatures of these regions appear to change as the flare evolves. Temperatures are determined from line ratios of hydrogen-like to helium-like ions for a number of different elements, e.g., S, Si, and Mg, and from the slope of the X-ray continuum which is assumed to be due to free-free and free-bound emission. There is no obvious indication in soft X-ray flare spectra of non-thermal processes, although accurate continuum measurements are difficult with the data obtained to date because of higher order diffraction effects due to the use of crystal spectrometers.Soft X-ray flare spectra also show satellite lines of the hydrogen-like and helium-like ions, notably the 1s ²2s ² S-1s2s2p ² P transition of the lithium-like ion, and support the contention that in low density plasmas these lines are formed by dielectronic recombination to the helium-like ion. Also, series of allowed transitions of hydrogen-like and helium-like ions are strong, e.g., the Lyman series of S up to Lyman-, and ratios of the higher member lines to the Lyman- line can be compared with theoretical calculations of the relative line strengths obtained by assuming various processes of line formation.This review will discuss the X-ray spectrum of solar flares from 250 keV to 0.4 keV, but will be primarily concerned with the soft X-ray spectrum and the interpretation of emission lines and continuum features that lie in this spectral range.     

Instantaneous Frequency Estimation Using Adaptive Linear Predictor Weights

A computationally efficient scheme for estimating the digital instantaneous frequencies of narrowband inputs is introduced. The frequency estimates are obtained by searching for minima of the inverse input power spectrum. This spectrum is estimated at each input sample from the weights of an adaptive linear predictor which uses the LMS (least mean square) algorithm to update its weights. The related minima are sought via an iterative search algorithm, referred to as the iterative frequency estimator. This algorithm is computationally more efficient than available methods, and also provides a higher resolution. Simulation results are included; these include tracking of random message sequences in FM signals, and the formant frequency estimation of speech.     

传导干扰研究

传导发射是沿电源线或信号线传输的电磁发射,在低频范围内,传导发射是电磁干扰的主要形式。如不采取措施,几乎所有的电子、电气设备电源线的传导发射都得超标,若将这些设备安装在飞机上,它将严重地威胁着机上其他设备的正常工作。本文对各种脉冲波形的频谱进行了比较,并对整流器的谐波发射进行了分析,最后介绍了降低传导发射的设计方法。     

SAR resolution in the presence of phase errors

The author analyzes the effects of phase errors on synthetic aperture radar (SAR). The theory is applied to the following question: how does the achievable resolution vary with the carrier frequency when optimum quadratic focus and/or optimum processing interval (synthetic aperture length) are used? Numerous related results are given, so that much of the material is tutorial. For phase errors corresponding to uncompensated motion, the best achievable RMS resolution with any phase error spectrum satisfies the derived equation. For motion-induced phase errors it is seen that resolution improves with increasing carrier frequency when the first term in the expression applies (e.g. for phase errors concentrated at low frequencies) and resolution is independent of carrier frequency when R δ/v/v is the smaller term (e.g. with broad band or high frequency phase errors)