关于Diophantine方程的解

对于正整数a ,设S(a)是Smarandache函数。证明了 :方程S(1·2 ) +S(2·3) +… +S(x(x +1) ) =S(x(x +1) (x +2 ) /3)仅有正整数解x =1。     

Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Ultra-Deep Optical Spectroscopy with PMAS. Using the Nod-and-Shuffle Technique

PMAS, the Potsdam Multi-Aperture Spectrophotometer, is a new integral field spectrograph in the optical, which is optimized for good transmission and high image quality from 350 nm to 1 μm. We present our plan to implement a CCD charge-shuffle mode to allow for beam switching with a very high degree of sky subtraction accuracy for faint object 3-D spectroscopy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electric Discharges in the Protoplanetary Nebula as a Source of Impulse Magnetic Fields to Promote Dust Aggregation

Lightning discharge generated in the protoplanetary nebula is viewed as a temporally isolated surge in the flow of electrically charged particles, similar to that of terrestrial lightning. If the current is intense enough, a powerful circular impulse magnetic field is generated around the instantaneous virtual electric conductor. Such magnetic field is capable of magnetizing dust grains containing ferromagnetic components present in its vicinity to their saturation levels. As a result, dust grains attract one another, forming the aggregates. This magnetically driven attraction suggests an important process possibly operational at an early stage of the planetary accretion. Based on both a classical model for electric conductor, and the theory of Lienard–Wiechert electromagnetic potentials, our calculations show that the magnetic impulse due to a discharge channel of a few cm in diameter transferring a charge of about 10⁴ electrons reaches as high as 10 T. At these magnetic fields, the ferromagnetic dust grains, and possibly the already-formed larger aggregates as well, are easily magnetized to the saturation levels, producing compact clusters exhibiting permanent magnetic moments.     

Invariance and scaling properties in the distributions of contributing area and energy in drainage basins

The cumulative probability distributions for stream order, stream length, contributing area, and energy dissipation per unit length of channel are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be related to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability distributions is able to fit the observed frequency distributions, and their deviations from straight lines in a log-log plot.     

对应分析在法国Douarnenez海湾拟庸鲽食性研究中的应用(Ⅱ)

２．４拟庸蝶食性的对应分析２．４．１观察量和变量的分组观察量（捕食鱼类）依不同季节（冬、夏季）、不同性别（雌雄性）和不同性成熟状态（幼鱼和成鱼）来分组，因此得到８（２３）个观察量。对应分析的变量（饵料）首先根据个体生态的不同分为６个类型：游走多毛类，隐居多毛类，双壳类，不大游动的甲壳类（端足目和等足目），爬行甲壳类（十足国短尾部）和棘皮动物。其他６个类型的饵料生物（类、纽虫类、小型游泳甲壳类、腔肠动物、鱼类及苔藓虫类顺在分组时剔除，其原因为它们的出现可能少了些。考虑到捕食鱼类和饵料双壳类贝壳厚度…     

数字水准仪标尺编码原理研究

数字水准仪的标尺编码规则直接影响其测量精度.基于现有几种数字水准仪标尺编码的特点,归纳出标尺条码的编码衡量指标:信息密度、分辨率和纠错能力.以条码的最大编码容量与单个码区长度之比值衡量其承载的信息密度;利用光学系统的点扩散函数研究条码图像的分辨率,即相邻边缘的相互影响,得出码元相邻边缘的间距相等时,影响最小的结论;用相关系数或编码所用函数本身的性质表征条码的纠错能力.依据编码指标建立一套新的标尺编码规则:以格雷码为数值码,固定宽度的码元为参考码,两者交替组合.分析表明,该种编码不但信息密度大,分辨率高,而且纠错能力强.     

On the perturbation of the anomalistic period of a highly eccentric orbit satellite due to the zonal harmonics

In this note a simple formula is given for the perturbation of the anomalistic period of a highly eccentric orbit due to the zonal harmonics. This perturbation depends essentially only on the semi-major axisa, the eccentricitye (or pericentre radius r =a(1-e)) and the latitude of the pericentre.     

Compositional variation in Hg-bearing sphalerite from the polymetallic Eskay Creek deposit, British Columbia, Canada

The Eskay Creek, British Columbia, Canada, is a polymetallic, gold- and silver-rich, volcanic-hosted, massive sulfide deposit. The ore in the deposit is divided into subzones distinguished by mineralogy, texture, grade and metallurgical characteristics. This study presents the results of a mineralogical examination of three composite field samples, with emphasis on the chemistry of sphalerite. Sphalerite is associated with variable amounts of Hg-tetrahedrite and cinnabar, and an array of sulfides, sulphosalts and non-opaque minerals. Electron micro probe analyses of sphalerite in the three composite samples reveal wide variations in compositions. The Hg content in sphalerite in the three samples varies between 0.08 and 16.35 wt%, whereas the Fe content ranges from 0.33 to 2.29 wt%. The chemical formula of the sphalerite shows the compositional range (Zn_0.89–0.98Hg_0.01–0.09.Fe_0.005–0.02)S. Sphalerite exhibits an almost perfect substitution of Hg and Zn, as shown by the negative covariance between them. Sphalerite with the highest Hg contents tends to have the lowest Fe concentrations. The highest Hg contents in sphalerite are recorded in the samples with the highest bulk Hg concentrations and with the highest cinnabar contents.

The compositional variations of sphalerite are important because they can be used in mapping ore forming fluids and indicate possible temporal variations. Second, determination of the compositional variation of the sphalerite in the mine has metallurgical implications because the mineral is an important Zn source. The mineralogical data indicate that non-physical processes (e.g. pyrometallurgy) must be used to separate Hg from Zn concentrates, with direct environmental implications, that is, release of metals, such as Hg, into the environment during mining and processing.