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。     

Zimbabwe: a country rich in geological history

A holiday in Zimbabwe provided the opportunity to examine some of the rocks, many of Archaean age, in one of the geologically most interesting parts of the world. Here, a great deal of the Earth's geological history can be unravelled.     

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.     

Crustal Melting in the Cordilleran Interior: The Mid-Cretaceous White Creek Batholith in the Southern Canadian Cordillera

The mid-Cretaceous White Creek batholith in southeast BritishColumbia is a zoned pluton ranging from quartz monzodioriteon the margin, to hornblende-and biotite-bearing granodioritetowards the interior of the batholith, which are in turn crosscutby two-mica granite. This range in rock type is similar to therange displayed by Mesozoic granitoid suites found in the Cordilleraninterior of western North America. The lithological zones inthe White Creek batholith correlate with distinet jumps in majorelement, trace element, and isotopic compositions, and indicatethat several pulses of magma were emplaced within the WhiteCreek magma chamber. The hornblende-and biotite-bearing granitoidsare metaluminous to weakly peraluminous, have strong light rareearth element (LREE) enrichment, and small negative Eu anomalies.These granitoids have initial _Sr ranging from +32 to +84 (⁸⁷Sr/⁸⁶SrTfrom 0.7069 to 0.7106), initial _Nd ranging from –5 to–10, and initial ²⁰⁶Pb/²⁰⁴Pb, ²⁰⁷Pb/²⁰⁴Pb, and ²⁰⁸Pb/²⁰⁴Pbranging from 18.3 to 18.7, 15.58 to 15.65, and 38.3 to 39.0,respectively. The two-mica granites and associated aplites arestrongly peraluminous, and show only moderate LREE enrichmentand strong negative Eu anomalies. These granites have _Sr rangingfrom +174 to + 436 (⁸⁷Sr/⁸⁶Sr_T from 0.7169 to 0.7354), _Nd rangingfrom –12 to –16, and more radiogenic initial Pbisotope ratios than the hornblende-and biotite-bearing granitoids. Oxygen, Sr, Pb, and Nd isotopes, REE modelling, and phase equilibriumconstraints are consistent with crustal anatexis of Precambrianbasement gneisses and Proterozoic metapelites exposed in southeastBritish Columbia, the product being the hornblende-biotite granitoidsand two-mica granites, respectively. The sequence of intrusionin the White Creek batholith constrains the melting sequence.A zone of anatexis proceeded upwards through the crust, firstmelting basement gneisses then melting overlying metapelites.A model for basaltic magmatic underplating as a primary causeof anatexis of the crust during the mid-Cretaceous magmaticepisode is difficult to reconcile with the absence of earlyCretaceous basalt in the southern Canadian Cordillera. A muchmore likely petrogenetic model is that crustal anatexis wasprobably a response to crustal thickening in association withterrane accretion and collision along the western margin ofthe North American continent.     

A Strontium and Neodymium Isotopic Investigation of the Fongen--Hyllingen Layered Intrusion, Norway

The Fongen—Hyllingen Intrusion, situated 60 km SE of Trondheim,Norway, is a synorogenic layered mafic intrusion of Caledonianage . The intrusion is divided into four evolutionary stages based on cryptic variations: StageI—a basal reversal; Stage II—unchanged mineral chemistryor slight normal evolution; Stage III—a gradual regression;Stage IV— a strong normal fractionation trend Magma replenishmentdominated during most of the crystallization, i.e. during StagesI, II and III Replenishing magma was more dense than resident,evolved magma, and continuing influx eventually caused a compositionallystratified magma column to form. Cryptic lateral variation isan important feature in the southern part of the complex andformed by in situ crystallization from a stratified magma alongan inclined floor, where modal layering formed parallel to thecrystallization front. Initial Sr- and Nd-isotopic ratios inthe cumulates vary as a result of assimilation of country rockand subsequent mixing between uncontaminated, replenishing magmaand contaminated, resident magma. The parental magma had a moderatelydepleted isotope composition, relative to Bulk Earth, with _Nd=584and Sr_i=070308, whereas the main contaminant was a partialmelt of metapelitic country rock with _Nd=-874 and Sr_i=07195(Sr_i is the initial ⁸⁷Sr/⁸⁶Sr). Sr_i in the analysed cumulatewhole-rock samples ranges from 070308 to 070535 and initial_Nd ranges from. 158 to 584. There is a strong correlationbetween mineralogical composition and isotopic trends in mostof the cumulates: the most primitive samples are the least contaminated,as reflected by relatively high ed and low Sr,, and more evolvedsamples have progressively lower eNi and higher Sry A gradualregression of several hundred metres thickness characterizesStage III; stratigraphically upwards mineral compositions becomemore primitive and isotope compositions more depleted (higher_Nd and lower Sr_i), implying a process of. progressive mixing-inof replenishing, primitive and uncontaminated magma. Magma influxin Stage III took place by fountaining, whereas magma additionwas more tranquil in the earlier stages. The fountaining influxentrained resident, relatively evolved and contaminated magma,resulting in a hybrid magma which ponded at the floor. Duringprolonged magma addition with concomitant crystallization, thelowermost magma layer was replaced by progressively more primitivehybrid magma, creating a gradual regression in the crystallizingcumulate sequence. A detailed two-dimensional study revealslateral variations in mineral compositions both at the baseand top of Stage III, whereas lateral variations in Sr- andNd-isotopic compositions are present at the top, but not atthe base. This implies that the lowest crystallizing part ofthe magma column was essentially isotopically homogeneous, butcompositionally stratified, before influx in Stage III. Isotopicgradients in the magma were strong close to the roof, wheremost of the assimilation occurred, and decreased downwards,merging into isotopically homogeneous magma. This stratifiedsystem was destroyed by turbulent mixing between replenishingand resident magma during fountaining influx in Stage III, anda new stratification was established with both an isotopic anda compositional gradient. After the final influx, crystallizationcontinued in an essentially closed system, in which the remainingmagma column eventually became homogenized, as magma layersmixed when their densities converged owing to release of buoyant,residual liquid during fractional crystallization. Corresponding author     

U-Pb Zircon Calendar for Namaquan (Grenville) Crustal Events in the Granulite-facies Terrane of the O'okiep Copper District of South Africa

The O'okiep Copper District is underlain by voluminous 1035–1210Ma granite gneiss and granite with remnants of metamorphosedsupracrustal rocks. This assemblage was intruded by the 1030Ma copper-bearing Koperberg Suite that includes jotunite, anorthosite,biotite diorite and hypersthene-bearing rocks ranging from leuconoriteto hypersthenite. New sensitive high-resolution ion microprobeage data demonstrate the presence of 1700–2000 Ma zirconas xenocrysts in all of the intrusive rocks, and as detritalzircon in the metasediments of the Khurisberg Subgroup. Thesedata are consistent with published Sm–Nd model ages ofc. 1700 Ma (T_CHUR) and c. 2000 Ma (T_DM) of many of the intrusivesthat support a major crust-forming event in Eburnian (Hudsonian)times. In addition, U–Th–Pb analyses of zirconsfrom all major rock units define two tectono-magmatic episodesof the Namaquan Orogeny: (1) the O'okiepian Episode (1180–1210Ma), represented by regional granite plutonism, notably theNababeep and Modderfontein Granite Gneisses and the Concordiaand Kweekfontein Granites that accompanied and outlasted (e.g.Kweekfontein Granite) regional tectonism [F₂(D₂)] and granulite-faciesmetamorphism (M₂); (2) the Klondikean Episode (1020–1040Ma), which includes the intrusion of the porphyritic RietbergGranite and of the Koperberg Suite that are devoid of regionalplanar or linear fabrics. Klondikean tectonism (D₃) is reflectedby major east–west-trending open folds [F₃(D_3a)], andby localized east–west-trending near-vertical ductilefolds [‘steep structures’; F₄(D_3b)] whose formationwas broadly coeval with the intrusion of the Koperberg Suite.A regional, largely thermal, amphibolite- to granulite-faciesmetamorphism (M₃) accompanied D₃. This study demonstrates, interalia, that the complete spectrum of rock-types of the KoperbergSuite, together with the Rietberg Granite, was intruded in ashort time-interval (<10 Myr) at c. 1030 Ma, and that therewere lengthy periods of about 150 Myr of tectonic quiescencewithin the Namaquan Orogeny: (1) between the O'okiepian andKlondikean Episodes; (2) from the end of the latter to the formalend of Namaquan Orogenesis 800–850 Ma ago. KEY WORDS: U–Pb, zircon; O'okiep, Namaqualand; granite plutonism; granulite facies; Koperberg Suite; Namaquan (Grenville) Orogeny     

MULTIVARIATE GEOMORPHIC ANALYSIS OF FOREST STREAMS: IMPLICATIONS FOR ASSESSMENT OF LAND USE IMPACTS ON CHANNEL CONDITION

Multivariate statistical analyses of geomorphic variables from 23 forest stream reaches in southeast Alaska result in successful discrimination between pristine streams and those disturbed by land management, specifically timber harvesting and associated road building. Results of discriminant function analysis indicate that a three-variable model discriminates 10 disturbed from 13 undisturbed reaches with 90 per cent and 92 per cent correct classification respectively. These variables are the total number of pools per reach, the ratio of mean residual pool depth to mean bankfull depth, and the ratio of critical shear stress of the median surface grain size to bankfull shear stress. The last variable can be dropped without a decrease in rate of correct classification; however, the resulting two-variable model may be less robust. Analysis of the distribution of channel units, including pool types, can also be used to discriminate disturbed from undisturbed reaches and is particularly useful for assessment of aquatic habitat condition. However, channel unit classification and inventory can be subject to considerable error and observer bias. Abundance of pool-related large woody debris is highly correlated with pool frequency and is an important factor determining channel morphology. Results of this study yield a much needed, objective, geomorphic discrimination of pristine and disturbed channel conditions, providing a reference standard for channel assessment and restoration efforts.