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Gauss Sum of Index 4:(2)Non-cyclic Case

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Acta Mathematica Sinica,English Series 2006年第3期22卷 833-844页

作者： Jing YANG Shi Xin LUO ke qin feng Department of Mathematical Science Tsinghua University

Assume that m ≥ 2, p is a prime number, （m,p（p - 1）） = 1,-1 not belong to 〈p〉 belong to （Z/mZ）^＊ and [（Z/mZ）^＊：〈p〉]=*** this paper, we calculate the value of Gauss sum G（X）=∑x∈F^＊x（x）ζp^T（x） over Fq,where q=p^f,f=φ（m）/4,x is a multiplicative character of Fq and T is the trace map from Fq to *** our assumptions,G（x） belongs to the decomposition field K of p in Q（ζm） and K is an imaginary quartic abelian unmber *** the Galois group Gal（K/Q） is cyclic,we have studied this cyclic case in anotyer paper：＂Gauss sums of index four：（1）cyclic case＂（accepted by Acta Mathematica Sinica,2003）.In this paper we deal with the non-cyclic case.

关键词： Gauss sum Stickelberger Theorem Davenport-Hawse formula class number of imaginary quadratic field

Gauss Sum of Index 4:(1)Cyclic Case

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1425-1434页

作者： ke qin feng Jing YANG Shi Xin LUO Department of Mathematical Science Tsinghua University Beijing 100084 P. R. China

Let p be a prime, m ≥ 2, and （m,p（p - 1）） = 1. In this paper, we will calculate explicitly the Gauss sum G（X） = ∑x∈F＊qX（x）ζ^Tp^（x） in the case of [（Z/mZ）＊：（p）] = 4, and -1 （不属于）（p）, wher... 详细信息

Let p be a prime, m ≥ 2, and （m,p（p - 1）） = 1. In this paper, we will calculate explicitly the Gauss sum G（X） = ∑x∈F＊qX（x）ζ^Tp^（x） in the case of [（Z/mZ）＊：（p）] = 4, and -1 （不属于）（p）, where q P^f, f =φ（m）/4, X is a multiplicative character of Fq with order m, and T is the trace map for Fq/Fp. Under the assumptions [（Z/mZ）＊：（p）] = 4 and 1（不属于）（p）, the decomposition field of p in the cyclotomic field Q（ζm） is an imaginary quartic （abelian） field. And G（X） is an integer in K. We deal with the case where K is cyclic in this oaDer and leave the non-cvclic case to the next paper.

关键词： Gauss sum Stickelberger theorem Davenport-Hasse formula cyclic quartic number field

Effect of sintering temperature on the microstructure and properties of foamed glass-ceramics prepared from high-titanium blast furnace slag and waste glass

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International Journal of Minerals,Metallurgy and Materials 2017年第8期24卷 931-936页

作者： Chang-hong Chen ke-qin feng Yu Zhou Hong-ling Zhou School of Manufacturing Science and Engineering Sichuan University

Foamed glass-ceramics were prepared via a single-step sintering method using high-titanium blast furnace slag and waste glass as the main raw materials The influence of sintering temperature(900–1060℃) on the microstructure and properties of foamed glass-ceramics was studied. The results show that the crystal shape changed from grainy to rod-shaped and finally turned to multiple shapes as the sintering temperature was increased from 900 to 1060℃. With increasing sintering temperature, the average pore size of the foamed glass-ceramics increased and subsequently decreased. By contrast, the compressive strength and the bulk density decreased and subsequently increased. An excessively high temperature, however, induced the coalescence of pores and decreased the compressive strength. The optimal properties, including the highest compressive strength(16.64 MPa) among the investigated samples and a relatively low bulk density(0.83 g/cm^3), were attained in the case of the foamed glass-ceramics sintered at 1000℃.

关键词： foamed glass-ceramics sintering temperature blast furnace slag waste glass crystallization

Influence of CeO_2 addition on the preparation of foamed glass-ceramics from high-titanium blast furnace slag

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International Journal of Minerals,Metallurgy and Materials 2018年第6期25卷 689-695页

作者： Hong-ling Zhou ke-qin feng Chang-hong Chen Zi-di Yan School of Manufacturing Science and Engineering Sichuan University

Foamed glass-ceramics doped with cerium oxide（CeO_2）were successfully prepared from high-titanium blast furnace slag by one-step *** influence of CeO_2 addition（1.5wt%–3.5wt%）on the crystalline phases,microstructure,and properties of foamed glass-ceramics was *** show that CeO_2 improves the stability of the glass phase and changes the two-dimensional crystallization mechanism into three-dimensional *** analysis indicates the presence of Ca（Mg,Fe）Si_2O_6 and Ca（Ti,Mg,Al）（Si,Al）_2O_（6 ）in all sintered *** with CeO_2,Ti CeO_4 precipitates,and crystallinity increases,leading to increased thickness of pore walls and uniform *** comprehensive properties of foamed glass-ceramics are better than that of samples without CeO_*** particular,the sample added with a suitable amount of CeO_2（2.5wt%）exhibits bulk density that is similar to and compressive strength（14.9 MPa）that is more than twice of foamed glass-ceramics without CeO_2.

关键词： foamed glass-ceramics cerium oxide blast furnace slag sintering crystallization

Influence of phosphorus on iron-based friction material prepared directly vanadium-bearing titanomagnetite concentrates

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Journal of Iron and Steel Research International 2021年第6期28卷 669-678页

作者： Yan-yan Zhang ke-qin feng Yue Shui Si-tan Chen Yan-fang Liu School of Mechanical Engineering Sichuan UniversityChengdu 610065SichuanChina

In situ selective carbothermic reactions and vacuum sintering were used to prepare iron-based friction material directly vanadium-bearing titanomagnetite *** of phosphorus addition(0.05–0.20 wt.%)on the microstructure and properties of iron-based friction material were *** results show that the addition of phosphorus improves the microstructure and properties of the material *** phosphorus addition increases to 0.15 wt.%,the sintering densification is promoted and the number of lamellar pearlites ***,the relative density,hardness and tribological properties of the material are greatly ***,the friction coefficient decreases 0.58 to 0.43,and the wear rate reduces 1.829×10^(–7) to 0.694×10^(–7)cm^(3)J^(-1).The dominant wear mechanism of the material changes severe abrasive wear to mild oxidation wear ***,when phosphorus addition exceeds 0.15 wt.%,the matrix continuity and tribological properties of the material are ***,the optimal addition of phosphorus in the iron-based friction material is 0.15 wt.%.

关键词： Vanadium-bearing titanomagnetite concentrate Iron-based friction material Tribological behavior Phosphorus

Influence of aluminium nitride as a foaming agent on the preparation of foam glass-ceramics from high-titanium blast furnace slag

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International Journal of Minerals,Metallurgy and Materials 2016年第5期23卷 595-600页

作者： Huan Shi ke-qin feng Hai-bo Wang Chang-hong Chen Hong-ling Zhou School of Manufacturing Science and Engineering Sichuan University Chengdu 610065 China School of Materials Engineering Panzhihua College Panzhihua 617000 China

To effectively reuse high-titanium blast furnace slag （TS）, foam glass-ceramics were successfully prepared by powder sintering at 1000℃. TS and waste glass were used as the main raw materials, aluminium nitride （AIN） as the foaming agent, and borax as the fluxing agent. The influence of the amount of A1N added （lwt%-5wt%） on the crystalline phases, microstructure, and properties of the produced foam glass-ceramics was studied. The results showed that the main crystal phases were perovskite, diopside, and augite. With increasing A1N content, a transformation from diopside to augite occurred and the crystallinity of the pyroxene phases slightly decreased. Initially, the aver- age pore size and porosity of the foam glass-ceramics increased and subsequently decreased; similarly, their bulk density and compressive strength decreased and subsequently increased. The optimal properties were obtained when the foam glass-ceramics were prepared by adding 4wt% AIN.

关键词： blast furnace slag aluminium nitride powder sintering foam glass-ceramics crystallization

Preparation of micro/nano-structured ceramic coatings on Ti6Al4V alloy by plasma electrolytic oxidation process

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Transactions of Nonferrous Metals Society of China 2019年第12期29卷 2546-2555页

作者： Da-jun ZHAI ke-qin feng School of Mechanical Engineering Sichuan UniversityChengdu 610065China Department of Materials Engineering Sichuan Engineering Technical CollegeDeyang 618000China Sichuan Laboratory of Engineering Aeronautical Materials Inspection and Die-forging Technology Deyang 618000China

In order to improve the osseointegration and antibacterial activity of titanium alloys,micro/nano-structured ceramic coatings doped with antibacterial element F were prepared by plasma electrolytic oxidation(PEO)process on Ti6Al4V alloy in NaF *** influence of NaF concentration(0.15-0.50 mol/L)on the PEO process,microstructure,phase composition,corrosion resistance and thickness of the coatings was investigated using scanning/transmission electron microscopy,energy dispersive spectroscopy,atomic force microscopy,X-ray diffractometer,and potentiodynamic *** results demonstrated that Ti6Al4V alloy had low PEO voltage(less than 200 V)in NaF electrolyte,which decreased further as the NaF concentration increased.A micro/nano-structured coating with 10-15μm pits and 200-800 nm pores was formed in NaF electrolyte;the morphology was different from the typical pancake structure obtained with other *** coating formed in NaF electrolyte had low surface roughness and was thin(<4μm).The NaF concentration had a small effect on the phase transition from metastable anatase phase to stable rutile phase,but greatly affected the corrosion *** general,as the NaF concentration increased,the surface roughness,phase(anatase and rutile)contents,corrosion resistance,and thickness of the coating first increased and then decreased,reaching the maximum values at 0.25 mol/L NaF.

关键词： plasma electrolytic oxidation Ti6Al4V alloy micro/nano structure NaF surface modification

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基于改进的SVM的短时交通流预测

煤炭技术 2012年第5期31卷 208-209页

作者：唐世星柯凤琴承德石油高等专科学校承德067000

在SVM预测模型中引入交叉验证和网格搜索算法,优化惩罚因子和核函数的参数,建立了改进的SVM预测模型,并应用于短时交通流预测进行实证分析。以某城市道路的实时数据来对模型进行验证,预测结果表明了模型的有效性。

关键词：交叉验证网格搜索惩罚因子短时交通流预测

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基于FCM算法的小脑基因模糊聚类分析

数学的实践与认识 2010年第12期40卷 74-79页

作者：唐世星陈军柯凤琴承德石油高等专科学校人事处河北承德067000 第三军医大学卫生统计学教研室重庆400038 承德石油高等专科学校汽车工程系河北承德067000

探讨基因表达数据的聚类分析方法,结合一种聚类结果的评判准则,应用于胎儿小脑基因表达数据,得到了最优的聚类结果,并做出了生物学解释.利用Matlab软件进行了仿真,利用模糊聚类Xie-Beni指数得到了最优聚类数,并把每一类对应的基因标号... 详细信息

探讨基因表达数据的聚类分析方法,结合一种聚类结果的评判准则,应用于胎儿小脑基因表达数据,得到了最优的聚类结果,并做出了生物学解释.利用Matlab软件进行了仿真,利用模糊聚类Xie-Beni指数得到了最优聚类数,并把每一类对应的基因标号输出到txt文件,最后进行生物学解释.得到的小脑基因最优聚类数为3类,与生物学意义比较吻合,各类中的基因功能接近.基于FCM算法的基因模糊聚类是有效的,结果具有一定生物学意义,能对生物学基因聚类有一定指导作用.

关键词： FCM算法基因表达聚类分析 Xie—Beni指数