The Mathematics of Harmony. Proclus’ Hypothesis and New View on Euclid’s Elements and History of Mathematics Starting since Euclid

We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid. According to Proclus, the main goal of Euclid, when writing the Elements, was to build a complete geometric theory of Platonic solids (Book XIII), associated in the ancient philosophy (Pythagoras, Plato) with the Universe harmony. To construct this theory, Euclid introduced in Book II the problem of dividing a segment into extreme and mean ratio (the “golden section”). It follows from Proclus’ hypothesis that Euclid’s Elements are the first attempt to create the “Mathematical Theory of the Universe Harmony”, based on Platonic solids and the “golden section”.

基于D-S证据理论的岩爆预测方法研究

为了有效预测岩爆,提出基于D-S证据理论的岩爆预测方法.首先,选取与岩爆发生相关的6个指标因素作为证据体,并通过模糊物元框架和正态型隶属度函数构建证据体的基本概率分配.然后,利用K均值将证据体分类,并提出簇内证据用传统方式融合而簇间证据用权重方式融合的组合融合规则,以减轻高冲突证据融合的不利影响.最后,将模型应用在秦岭终南山公路隧道2号竖井工程,且与经验方法对比.为了分析预测过程的不确定性和估计岩爆发生概率,采用蒙特卡洛模拟进行抽样仿真,并通过Spearman秩相关系数衡量输入指标的全局敏感性.研究结果表明:输入指标在不同的岩爆案例的影响程度差异较大且方向不同;5个岩爆案例的发生概率在40.8%~70.1%之间.该模型表现出优异的预测分类性能,可为深埋地下工程岩爆预测提供参考.

基于S-R和分解定理的二维几何非线性问题的虚单元法求解

应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。

Simultaneous nitrification and autotrophic denitrification in fluidized bed reactors using pyrite and elemental sulfur as electron donors

In this study, simultaneous nitrification and autotrophic denitrification (SNAD) with either elemental sulfur or pyrite were investigated in fluidized bed reactors in mesophilic conditions. The reactor performance was evaluated at different ammonium (12-40 mg/L of NH4+-N), nitrate (35-45 mg/L of NO3--N), and dissolved oxygen (DO) (0.1-1.5 mg/L) concentrations, with a hydraulic retention time of 12 h. The pyrite reactor supported the SNAD process with a maximum nitrogen removal efficiency of 139.5 mg/(L·d) when the DO concentration was in the range of 0.8-1.5 mg/L. This range, however, limited the denitrification efficiency of the reactor, which decreased from 90.0% ± 5.3% in phases II-V to 67.9% ± 7.2% in phases VI and VII. Sulfate precipitated as iron sulfate (FeSO4/Fe2(SO4)3) and sodium sulfate (Na2SO4) minerals during the experiment. The sulfur reactor did not respond well to nitrification with a low and unstable ammonium removal efficiency, while denitrification occurred with a nitrate removal efficiency of 97.8%. In the pyrite system, the nitrifying bacterium Nitrosomonas sp. was present, and its relative abundance increased from 0.1% to 1.1%, while the autotrophic denitrifying genera Terrimonas, Ferruginibacter, and Denitratimonas dominated the community. Thiobacillus, Sulfurovum, and Trichlorobacter were the most abundant genera in the sulfur reactor during the entire experiment.

Trace-element geochemistry and S–O isotopes in the fluorite-barite mineralization of Merguechoum,Moroccan eastern Meseta:insights into ore genesis to the Pangea rifting

The Merguechoum fluorite-barite mineralization,located in the Eastern Meseta of Morocco,is hosted in the Late Hercynian granite.The ore consists of fine crystals of fluorite 1,massive barite 1,euhedral crystals of fluorite 2,and barite 2 with calcite and minor quartz and sulfides.The Merguechoum ore deposits have never been investigated.This study was the first contribution that studied the genesis of fluorite and barite.The ore occurs as dissemination within granite intrusion and also fills the NE-SWtrending meter-sized fractures and faults.The values of the total Rare Earth Elements and Yttrium(REY)and the ratios of LREY/HREY,Y/Ho,Tb/Ca,and Tb/La indicate that the Merguechoum fluorite precipitated from hydrothermal fluids,likely basinal brines,which interacted with the Hercynian granite.The REY data indicate that the ore-forming fluids of the early stage have intensely interacted with the Hercynian granite compared to those of the late ore stage.The gradual decrease in the europium(Eu/Eu^(*)),yttrium(Y/Y^(*)),and cerium(Ce/Ce^(*))anomalies and a low concentration ofΣREY observed in the second ore stage compared to the first ore stage suggest an increase in p H and fO_(2)and by inference a decrease in temperature during the evolution of the hydrothermal system.This evolution could be explained by fluid mixing between the ascending basinal hydrothermal fluids and the diluted sulfate-rich meteoric water barite separates from selected samples reveal that the dissolved sulfates(SO_(4)^(2-))were derived from Permian–Triassic sulfates and/or coeval poreseawater sulfates.The proposed fluid mixing triggered the precipitation of an early-stage F-Ba assemblage followed by the second-stage F-Ba mineralization.Geologic fieldwork,REY inventories,and isotope data point to the ore genesis during the Permian–Triassic extensional tectonic activity concerning the Pangea rifting.This extensional tectonic environment is likely the driving force that mobilized a large amount of the ore-forming basinal brines along the available faults and fractures to the loci of ore deposition.

四川康定偏岩子造山型金矿床成因:石英微量元素和硫化物S同位素证据

大渡河金矿带是中国重要的金矿化富集区,发育一系列造山型金矿床。偏岩子金矿床位于大渡河南段的康定地区,矿体赋存于震旦系灯影组白云岩中。金成矿过程分为金-黄铁矿-石英阶段、金-氟镁石阶段、金-硫化物-氟镁石-石英阶段和黄铁矿-白云石-白云母阶段4个成矿阶段。通过石英中微量元素和硫化物S同位素的原位分析,旨在约束成矿流体性质、成矿物质来源和矿床成因。石英中Li,B,Na,Al,P和K相对富集,主要以Al^(3+)^(+)(Li^(+),Na^(+),K^(+),H^(+))Si^(4+)和Al^(3+)^(+)P 5^(+)2Si^(4+)的替换机制进入石英晶格。石英中Al与Li呈明显正相关关系,指示其形成温度较低。围岩中硫化物的δ^(34) S值介于-22.3‰~-13.1‰之间,表明S来源于海相硫酸盐的细菌还原作用;矿石中硫化物的δ^(34) S值范围为5.4‰~7.0‰,与交代岩石圈地幔的硫同位素值一致。综合矿床地质特征、石英微量元素和硫化物硫同位素组成,研究认为偏岩子属于造山型金矿床。成矿流体在上升过程中与赋矿白云岩接触,发生水-岩反应,导致自然金、含金硫化物、氟镁石和萤石的沉淀结晶。

小红石砬子铅锌(银)矿床成因:来自S-Pb同位素和元素特征的证据

小红石砬子铅锌(银)矿床是吉中-延边铜镍多金属成矿带中具有代表性的中型矿床,前人关于该矿床类型划分的观点有火山成因块状硫化物型(Volcanogenic Massive Sulfide,VMS)、中-低温热液脉型、喷流沉积-热液叠加改造型,这三种观点的争论严重制约了对该矿区及区域成矿和找矿的认识。本文选取该矿床中金属硫化物开展原位微量和S-Pb同位素分析,赋矿围岩开展全岩S同位素分析。闪锌矿Fe-Zn含量(4.48%~10.33%、53.67%~62.12%)与中温热液矿床一致(3.00%~10.00%、50.00%~60.00%,成矿温度约200℃),Zn/Cd比值(53.68~76.75)同样指示中低温成矿作用(高温:Zn/Cd>500;低温:Zn/Cd<250),Ga/Ge比值在lg(Ga/Ge)-T图解中,对应温度约为100~180℃,上述温度范围与前人测定的流体包裹体均一温度基本吻合(90~250℃)。闪锌矿Zn/Cd的比值(53.68~76.75)与Cd含量(7577×10-6~11266×10-6)特征与密西西比河谷型(Mississippi Valley-Type,MVT)矿床一致;黄铁矿Fe/S比值(0.76~1.29,平均值为0.89)接近典型MVT矿床的理论值(0.88)。金属硫化物δ34 S V-CDT值介于-9.6‰~-0.5‰之间,总体偏负;赋矿围岩δ34 S V-CDT值介于-8.5‰~4.2‰之间,两者重叠范围较大(主要集中于-9.0‰~-2.0‰),说明围岩提供了主要的还原硫,而古老基底可能提供了部分较轻的硫。金属硫化物Pb同位素比值为206 Pb/204 Pb=18.30~18.39、207 Pb/204 Pb=15.61~15.63、208 Pb/204 Pb=38.38~38.44,指示铅为混合来源,成矿物质可能主要来自上地壳和造山带,模式年龄计算显示上太古界乌拉山群变质岩可能为铅的初始来源。综上所述,小红石砬子铅锌(银)矿床地球化学特征与MVT型矿床基本一致,地质特征略有差别,因此推测其为类MVT型矿床。

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson＇s ratio（PR）are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials＇ auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.

Determination of 13 Trace Elements in Anshun Thorn Pear (Rosa roxburghii) and Golden Thorn Pear (Rosa sterilis S.D.Shi) by ICP-MS

[Objectives] This study was conducted to establish an analytical method for the establishment of 13 trace elements in Anshun thorn pear(Rosa roxburghii) and golden thorn pear(Rosa sterilis S. D. Shi). [Methods] Nitric acid was used as the digestion system for microwave digestion. Inductively coupled plasma mass spectrometry(ICP-MS) was used to determine the trace elements in thorn pear and golden thorn pear. [Results] Be, Ti, V, Cr, Mn, Co, Ni, As, Sr, Mo, Cd, Sb and Hg were determined by ICP-MS method in thorn pear and golden thorn pear. The correlation coefficients of the regression equations of the elements were higher than 0.996; the precision RSD was lower than 2.87%; and the recovery ranged from 94.3% to 109.8%. [Conclusions] The method has the advantages of high sensitivity, good accuracy and simultaneous detection of multiple elements, and provides a reference method and theoretical basis for determining trace elements in thorn pear and golden thorn pear and other fruits.

ESD保护电路在HDMI板级信号完整性中的影响分析及其布局优化研究

为了解决HDMI接入ESD保护电路后信号完整性受破坏等问题,从器件的空间布局对HDMI信号完整性影响进行研究分析,同时考虑了瞬态电压抑制(TVS)高频寄生参数的影响,搭建了ESD放电模型和TVS高频等效电路模型,并对其可靠性进行了验证。从差分器件接入信号线旋转角度和彼此间错开距离研究其对信号完整性的影响,设计了25套不同夹角和4套不同错开距离的板级模型,在不同特性的传输频率下进行S参数仿真,并从中选取出垂直型、水平型、错开型三种具有代表性的空间布局模型,利用有限元仿真得到差分信号线的S参数和眼图。仿真结果表明,垂直型排布相比于其他两种典型空间布局,回波损耗平均降低了248.1%,插入损耗平均降低了20.6%,眼图的眼宽和眼高在三种空间布局中最大。研究成果为PCB静电放电保护电路分析与设计提供了布局优化指导。

S对铸造高温合金K417G凝固行为的影响

在1340~1230℃采用等温凝固实验,研究了w[S]分别为0.0001%、0.0018%和0.0037%对K417G合金凝固特性的影响。结果表明,S降低合金的固相线温度,扩大固液两相区,当w[S]从0.0001%增加到0.0037%时,合金的固相线温度由1255℃降低至1245℃。在凝固过程中S元素偏析于液相,并在终凝区析出Y相,且S促进Al、Cr元素在固液界面处的富集。在相同等温温度下,S元素对MC碳化物和γ+γ’共晶的析出温度与形貌无明显影响,但S含量的增加促使MC碳化物、γ+γ’共晶和Y相数量的增加,且Y相的析出温度从1230℃提升至1240℃。

Representation of an Integer by a Quadratic Form through the Cornacchia Algorithm

Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.

Finite Element Analysis of the Base

This paper describes the structure of the base,on which two working arms are installed simultaneously.To ensure structura safety,the fatigue failure analysis and statics analysis are finished using the finite element method.The calculation can make sure that the structure of the base meets the design standard,and the material can be reduced one grade.

Determination of Inorganic Elements in Paris daliensis H.Li et V.G.Souku and Paris dulongensis H.Li et S.Kuritap by ICP-OES

[Objectives] To determine 29 kinds of inorganic elements in samples of Paris daliensis H.Li et V.G.Souku and P. dulongensis H.Li et S.Kuritap produced in different regions, and to measure the content of 10 key inorganic elements: chromium(Cr), manganese(Mn), iron(Fe), copper(Cu), mercury(Hg), zinc(Zn), arsenic(As), antimony(Sr), cadmium(Cd) and lead(Pb). [Methods] The wet digestion and technique of inductively coupled plasma optical emission spectrometry(ICP-OES) were employed. [Results] Under the experimental conditions, elements were not related to each other, and many kinds of elements could be measured at the same time; toxic and heavy metals in samples of P. daliensis H.Li et V.G.Souku and P. dulongensis H.Li et S.Kuritap did not exceed the limit; Hg was not detected in all samples. [Conclusions] This method is simple, easy to operate and reproducible. It can be used for the detection of inorganic elements in P. daliensis H.Li et V.G.Souku and P. dulongensis H.Li et S.Kuritap; the heavy metals and Hg of the rhizome meet the requirements of the limit of medicinal materials.

Ore Genesis for Stratiform Ore Bodies of the Dongfengnanshan Copper Polymetallic Deposit in the Yanbian Area, NE China:Constraints from LA-ICP-MS in situ Trace Elements and Sulfide S–Pb Isotopes

The Dongfengnanshan Cu polymetallic deposit is one representative deposit of the Tianbaoshan ore district in the Yanbian area, northeast(NE) China. There occur two types of ore bodies in this deposit, the stratiform ore bodies and veintype ones, controlled by the Early Permian strata and the Late Hercynian diorite intrusion, respectively. Due to the ambiguous genetic type of the stratiform ore bodies, there has been controversy on the relationship between them and veintype ore bodies. To determine the genetic type of stratiform ore bodies, laser ablation inductively coupled plasma mass spectrometry(LA-ICP-MS) in situ trace elements and S–Pb isotope analysis have been carried on the sulfides in the stratiform ore bodies. Compared with that in skarn, Mississippi Valley-type(MVT), and epithermal deposits, sphalerite samples in the stratiform ore bodies of the Dongfengnanshan deposit are significantly enriched in Fe, Mn, and In, while depleted in Ga, Ge, and Cd, which is similar to the sphalerite in volcanic-associated massive sulfide(VMS) deposits. Co/Ni ratio of pyrrhotites in the stratiform ore bodies is similar to that in VMS-type deposits. The concentrations of Zn and Cd of chalcopyrites are similar to those of recrystallized VMS-type deposits. These characteristics also reflect the intermediate ore-forming temperature of the stratiform ore bodies in this deposit. Sulfur isotope compositions of sulfides are similar to those of VMS-type deposits, reflecting that sulfur originated from the Permian Miaoling Formation. Lead isotope compositions indicate mixed-source for lead. Moreover, the comparison of the Dongfengnanshan stratiform ore bodies with some VMStype deposits in China and abroad, on the trace elements and S–Pb isotope characteristics of the sulfides reveals that the stratiform ore bodies of the Dongfengnanshan deposit belong to the VMS-type, and have closely genetic relationship with the early Permian marine volcanic sedimentary rocks.

Tragic Beauty of Faulkner’s Villain Characters

This paper applies the theory of“Sphinx Factor”to examine the characters such as Sutpen,Emily and Jason in Faulkner’s fiction who are filled with brutal elements.It is found that although these characters are generally considered evil,cruel and violent,they also possess tragic beauty.

Are spatial distributions of major elements in soil influenced by human landscapes?

The present study attempted to evaluate the influence of human activity on major elements （Na2O, MgO, A1203, SiO2, K2O, CaO, Fe203）, and to find a method to explore correlations between major elements and human disturbances, according to geospatial theories and methods. The study results indicate that landscapes influence major elements in diverse ways： Al2O3 is closely related to road and mine landscapes; strong relationships exist between MgO, Fe2O3, CaO, and SiO2 and roads; Na2O, SiO2, and Fe2O3 are unrelated to city landscapes; and Na2O is unrelated to road and mine landscapes.

Breakthrough in the China's Separation Technology for Extraction of Rare Earth Elements

Separation technology of rare earth elements （REEs）, as the critical step in the separation process, had long been fraught with technical difficulty. A research project conducted by Baotou Shibo Rare Earth Extraction ＆ Equipment Co. Ltd., Baotou REE Research Institute, and Baotou Steel ＆ REE Group Hi-Tech Co. Ltd （Inner Mongolia）, has successfully solved the problem using a centrifugal extractor and advanced techniques to achieve a key breakthrough.

Concentration of Platinum Group Elements during the Early Earth Evolution: A Review

Numerous unique geological processes [1] took place during the early Earth evolution;several of them, especially those occurring in the Hadean—Early Archean and later, are reflected in the modern geological (geophysical, geochemical, etc.) pattern. One such significant enigmatic feature is the preservation of extremely dense and heavy platinum group elements (PGEs): Pt, Pd, Rh, Ru, Ir, Os. Concentration of PGEs during this period could have taken place in two ways: 1) presence of particular matter capable of preserving PGEs near the earth's surface, 2) transportation of PGEs by magma flows from deep lithospheric (asthenospheric) layers (slabs) to the subsurface. Clearly, much of the dense and heavy PGEs did not sink through to the Earth’s mantle (core) at the time of the magma-ocean, and occur near Earth’s surface in abundances for formation of ore deposits with PGE concentrations found to be 2 - 3 orders of magnitude greater than those in their host media. Their enrichments are associated in numerous cases with such enigmatic phenomena as formation of anorthosites and anorthosite-bearing layered magmatic intrusions. PGE deposits and mineralization zones are also found in associations with chromitites, dunites and serpentinites. In this review, problems related to the initial concentration and preservation of PGEs, their association with anorthosites, and formation of layered intrusions are discussed in detail. The main aim of this article is analysis of the requirements—initial concentration and preservation of PGE and PGM (Platinum Group Minerals) during the early Earth evolution, as well as examination of the distribution behavior of some PGEs in different ore deposits and meteorites. It is supposed that meteoritic bombardment of Earth has played a significant role in formation of PGEs deposits. Some conclusions made in this article may be useful for developing and enhancing strategies of prospecting for PGEs deposits.

Evaluation of Serum Trace Elements and Vitamin Levels in Hashimoto’s Thyroiditis: Single Centre Experience from Turkey

Aim: To determine levels of serum trace elements and vitamins, and to find out possible correlations between these elements and vitamins with thyroid function tests and thyroid autoantibody levels in patients having Hashimoto’s thyroiditis (HT). Methods: The study included 51 premenauposal women with untreated HT, aged 18 to 56 years without any known chronic diseases or chronic medicine usage, and 27 healthy premenauposal women aged 19 to 42 years old. Trace elements (selenium, zinc, copper, iron levels) and vitamins [A, E, B12, 25-OH-D, 1,25(OH)2D and folic acid levels] were evaluated in patient and control groups. Results: Consequently, serum trace elements and vitamin B12 levels did not significantly differ in patients with HT and control group. Thyroid functioning tests and autoantibody levels did not show any correlation with the levels of trace elements, vitamin A, vitamin E and 25-OH vitamin D. A correlation was detected between vitamin B12 and Anti thyroid peroxidase levels. Conclusion: The negative correlation between vitamin B12 and Anti thyroid peroxidase levels may demonstrate the necessity to screen the patients with HT for atrophic gastritis. We believe that more comprehensive studies with larger sample sizes are needed in which patients are randomized according to their nutritional status.