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”.

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.

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.

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.

Electromagnetic Interpretation of Fractional-Order Elements

Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Recently, the fundamentals of the conventional circuit theory were extended to include the new generalized elements and fractional-order elements. As is known to all, circuit theory is a limiting special case of electromagnetic field theory and the characterization of classical circuit elements can be given an elegant electromagnetic interpretation. In this paper, considering fractional-order time derivatives, an electromagnetic field interpretation of fractional-order elements: fractional-order inductor, fractional-order capacitor and fractional-order mutual inductor is presented, in terms of a quasi-static expansion of the fractional Maxwell’s equations. It shows that fractional-order elements can also be interpreted as a fractional electromagnetic system. As the element order equals to 1, the interpretation of fractional-order elements matches that of the classical circuit elements: L, C, and mutual inductor, respectively.

Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

Effects of Elemental Sulphur and Farmyard Manure on pH and Salinity of Calcareous Sandy Loam Soil and Some Nutrient Elements in Tomato Plant

The objective of this study was to evaluate the effects of elemental sulphur （S） and farmyard manure on soil pH, EC and N, S, P concentrations of tomato grown in a calcareous sandy loam soil. For this purpose, a pot experiment was conducted in greenhouse conditions. Sulphur was applied at 0, 50, 100, 150, 200, 400 mg kg~ and farmyard manure at 0, 3 ton da^-1 to the soil. Three weeks after applications, tomato seedlings were planted and 8 weeks later, the plants were harvested to determine N, S, P concentrations and dry matter yield. Soil pH and EC were determined in the soil samples taken at 3 different periods. Effects of sulphur and farmyard manure applications were not significant on N, P concentrations and dry matter yield of tomato plant. S concentration of tomato plant was increased by sulphur alone. Soil pH was decreased and soil EC was increased in both 2^nd and 3^rd soil sampling period by the sulphur applications. As a result of farmyard manure application, soil pH decreased in the 2^nd soil sampling period but increased in the 3^rd soil sampling period. Also, soil EC was significantly increased in 1^st and 3^rd soil sampling period. Farmyard manure had no significant effect on S supply to tomato plant. The N：S ratio of tomato plant was decreased by sulphur alone. However, the sulphur with farmyard manure applications decreased N：S ratio in lesser extend compared to the S applications.

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。

EXPLICIT ERROR ESTIMATE FOR THE NONCONFORMING WILSON'S ELEMENT

In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.

Evidence of fluid evolution of Baoshan Cu−Pb−Zn polymetallic deposit:Constraints from in-situ sulfur isotope and trace element compositions of pyrite

In-situ LA-ICP-MS and S isotopes of pyrite from the Baoshan Cu polymetallic deposit were conducted to investigate the ore-forming process and the enrichment mechanism of elements.Three generations of pyrite (Py Ⅰ,Py Ⅱ,and Py Ⅲ) in the skarn-type ores and pyrite in the carbonate-hosted sulfide ores from central,western,and northern(C_Py,W_Py,and N_Py) mining districts are selected for comparison.Compared with Py Ⅰ and Py Ⅲ,the contents of most elements in Py Ⅱ are apparently higher.The As and Se contents are high within a wide range and are decoupled in the growth band of the C_Py.The highest As,Se,and Pb contents were found in W_Py and N_Py.These results indicate the drastic changes in the temperature and fluid mixing during the mineralization.The occurrence of fluctuation and change in temperature and f(O_(2)) was triggered by intermittent pulses of magmatic-hydrothermal fluids,mixing with meteoric water,and water-rock interactions.The sulfur isotopes of all species of pyrite indicated the magmatic source.The change in the f(O_(2)) conditions caused slight differences in the sulfur isotope compositions.Consequently,a metallogenic model was proposed to explain the ore-forming processes.

Icariin upregulates phosphorylated cyclic adenosine monophosphate response element binding protein levels in the hippocampus of the senescence-accelerated mouse

At 8 weeks after intragastric administration of icariin to senescence-accelerated mice （P8 strain）, Morris water maze results showed that escape latency was shortened, and the number of platform crossings was increased. Immunohistochemical staining and western blot assay detected significantly increased levels of cyclic adenosine monophosphate response element binding protein These results suggest that icariin upregulates phosphorylated cyclic adenosine monophosphate response element binding protein levels and improves learning and memory functions in hippocampus of the senescence-accelerated mouse.

Acute duodenal Crohn's disease successfully managed with low-speed elemental diet infusion via nasogastric tube:A case report

Duodenal Crohn＇s disease is rare, and patients without obstruction are treated medically. We herein report one case whose duodenal Crohn＇s disease was successfully managed with low-speed elemental diet infusion through a nasogastric tube. A 28-year-old female developed acute duodenal Crohn＇s disease. Upper GI radiologic and endoscopic examinations showed a stricture in the duodenal bulb. Using the duodenal biopsy specimens, mucosal cytokine levels were measured; interleukin （IL）-1β, IL-6, IL-8, and tumor necrosis factor-α levels were remarkably elevated. For initial 2 wk, powdered mesalazine was orally given but it was not effective. For the next 2 wk, she was treated with low-speed elemental diet therapy using a commercially available ElentalTM, which was infused continuously through a nasogastric tube using an infusion pump. The tip of the nasogastric tube was placed at an immediate oral side of the pylorus. The infusion speed was 10 mL/h （usual speed, 100 mL/h）. After the 2-wk treatment, her symptoms were very much improved, and endoscopically, the duodenal stricture and inflammation improved. The duodenal mucosal cytokine levels remarkably decreased compared with those before the treatment. Although our experience was limited, lowspeed elemental diet infusion through a nasogastric tube may be a useful treatment for acute duodenal Crohn＇s disease.

On the Error Estimate of Adini's Element for the Second Order Problems

The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.

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.