Research of optimization to solve nonlinear equation based on granular computing

In this article, a real number is defined as a granulation and the real space is transformed into real granu-lar space[1]. In the entironment, solution of nonlinear equation is denoted by granulation in real granular space. Hence,the research of whole optimization to solve nonlinear equation based on granular computing is proposed[2]. In classicalcase, we solve usually accurate solution of problems. If can't get accurate solution, also finding out an approximate solutionto close to accurate solution. But in real space, approximate solution to close to accurate solution is very vague concept. Inreal granular space, all of the approximate solutions to close to accurate solution are constructed a set, it is a granulation inreal granular space. Hence, this granulation is an accurate solution to solve problem in some sense, such, we avoid to sayvaguely "approximate solution to close to accurate solution". We introduce the concept of granulation in one dimension real space. Any positive real number a together with movinginfinite small distance ε will be constructed an interval [a-ε,a ε], we call it as granulation in real granular space, denotedby ε(a) or [a]. We will discuss related properties and operations[3] of the granulations. Let one dimension real space be R, where each real number a will be generated a granulation, hence we get a granularspace R* based on real space R. Obviously, R∈R*. Infinite small number in real space R is only O, and there are three in-finite small granulations in real number granular space R* : [0], [ε] and [-ε]. As the graph in Fig. 1 shows. In Fig. 1,[-ε] is a negative infinite small granulation,[ε] is a positive infinite small granulation,[0] is a infinite small granulation.[a] is a granulation of real number a generating, it could be denoted by interval [a-ε,a ε] in real space [3-5].Letf(x)=0 be a nonliner equation,its graph in interval[-3,10]id showed in Fig.2.Where -3≤x≤10 Relation ρ(f‖,ε)is defied is follows:(x1,x2)∈ p(f‖,ε)iff |f(x1)- f(x2)|<εWhere ε is any given small real number.We have five appoximate solution sets on the nonliner equation f(x)=0 by ρ(f‖,ε)∧|f(x)|[a,b]max,to denote by granulations[xi1 xi2/2],[xi3 xi4/2],[xi5 xi6/2],[xi7 xi8/2]and[xi9 xi10/2]respectively,where |f(x)|[a,b]max denotes local maximum on x ∈[a,b].This is whole optimum on nonliear equation in interval [-3,10].We will get best opmension solution on nonliner equation via computing f(x)to use the five solutions dented by grandlation in one dimension real granlar space[2,5].     

钼选别作业中粒度与回收率的关系

实验室筛析试验证明：辉钼矿在浮选过程中,原、尾矿的粒度分布及粒级金属分布规律有所改变;尾矿中的金属主要损失在粗粒级;＋0.2mm粒级回收率最低,-0.074mm至＋0.0385mm区间粒级回收率较好。由此指导生产,磨矿循环作业中应特别引起重视,在保证处理量的情况下,尽可能避免入选＋0.2mm以上粗颗粒,以保证选厂作业回收率。     

制备条件对拟薄水铝石晶粒度与孔结构的影响

采用反应结晶法,以偏铝酸钠、硫酸铝为原料,制备了一系列拟薄水铝石样品．用X射线衍射、氮吸附脱附、扫描电镜等方法分析了制备条件对拟薄水铝石晶粒度与孔结构的影响．实验结果表明：拟薄水铝石的平均晶粒度随pH值、温度及老化时间的增加而增加;较低pH值或温度下生成无定形凝胶,较高的pH值或温度下生成了薄水铝石或β-三水铝石;温度升高与老化时间增加可分别有利于大孔的形成与整体孔数量的增加;晶粒度较大的单一拟薄水铝石样品,其表面积与孔容也较大．在 pH 值为8.6、反应温度75,℃及老化时间2,h 的优化制备条件下,拟薄水铝石具有单一晶相,平均晶粒度为4.58,nm,比表面积为342,m2/g,孔容为0.533,cm3/g,平均孔径约为3,nm,形貌如绒毛球状．     

南京燕子矶下蜀黄土颗粒分形研究

根据分形理论,研究了南京燕子矶下蜀黄土粒度分形结构特征,发现在双时数坐标下粒径和粒度含量之间存在明显的线性关系,表明粒度组成具有分形结构.通过对燕子矾下蜀黄土颗粒分形的计算,发现其分维值介于2.4～2.6之间,随着黏粒含量的增大而增大,且与不均匀系数和曲率系数有良好的非线性关系.在此基础上,讨论了粒度分维所具有的工程地质意义.指出粒度分维揭示了不同土体工程地质性质差异的本质.可以作为土体分类的一个合理指标.     

Effects of the grain size distribution on magnetic properties of magnetite: constraints from micromagnetic modeling

Magnetite is the most important magnetic mineral in paleomagnetism. Its magnetic properties are controlled by many factors, such as grain size distribution, shape and interactions. Traditional rock magnetic experiments, however, have great difficulty in decoupling the effects of these parameters. In this study, we attempted to investigate the effects of grain size distribution on magnetic properties of magnetite powders by using a micromagnetic method. The particle geometries used in the micromagnetic model were based on the grain size distribution observed in a synthetic magnetite powder. The simulated hysteresis parameters agree well with the experimental measurements and provide clear microstructures of the magnetic remanence. Our results show that grain size plays a more important role in affecting hysteresis parameters of magnetite assemblages than shape under effects of interactions. Uniform or vortex superstates formed by two or more particles are found and display different stabilities of magnetic recording in assemblages. Some domain structures of single-domain （SD） particles are reversed as the applied field decreases to zero. Small pseudo-single-domain particles behave as SD structures and may dominate the magnetic recordings. In all, micromagnetic modeling of grain size distributions provide a better understanding of magnetic assemblages consisting of nanoscale particles.     

塔里木虎拉山地区上石炭统碎屑岩沉积环境

文章根据对塔里木北缘的虎拉山地区石炭纪碎屑岩粒度分析,对该地区砂岩的分选性、偏度及峰度等进行了分析,利用萨胡粒度判别函数识别了浊流和浅海沉积环境,并结合前人研究成果以及岩相特征,判别出虎拉山地区石炭纪浊流沉积广泛发育.     

散射法粒度分布测试中无约束反演的误差分析

激光散射法测量粒度分布技术近年来发展很快，其测量误差涉及散射理论及其反演计算，有关的理论研究还不充分。通过数值模拟，利用Chahine算法研究包含反演计算在内的系统误差。计算结果表明，光散射测量粒径不能通过简单的增加离散级数来提高测量精度，必须通过反演算法的改进来提高。     

鄂尔多斯盆地上三叠统延长组物源分析

根据重矿物组合、古流向和碎屑颗粒粒度等资料，对鄂尔多斯盆地上三叠统延长组物源区的母岩性质、物源方向及演变特征等进行了分析。结果表明：延长组沉积物主要来自两种类型的母岩，即深变质的结晶片岩和片麻岩、浅海相碎屑岩及碳酸盐岩；在延长组沉积早中期，主要物源来自北部和西南两个方向，而延长组沉积晚期，西南方向物源占优势，北部物源的影响明显减弱，而且物源南北分布特征明显。     

洞庭湖区防洪通信指挥决策系统的总体方案设想

根据洞庭湖区地理行政区划管理体制,提出了洞庭湖区通信指挥决策系统的设计目标和三级体系结构,并在此体系下的变粒度功能分布模式及系统的信息存储的合理分布准则：纵向信息流按递阶结构传递控制,横向信息源按类归口建库与维护;论述了系统开发所用的关键技术;给出了系统的逻辑体系结构、网络拓扑结构、逻辑功能结构和系统信息源分布结构视图;构造了一个层次分明、功能完备、控制有序的系统优化总体方案．     

信息系统的粒度熵及基于粒度熵的属性约简算法

针对完备信息系统中,知识随着知识中属性的逐渐增加或减少从而对论域产生不同粗细的划分进行研究,给出了一个新的度量--粒度熵,以度量知识随着属性的逐渐增加或减少对论域产生不同粗细划分时的分辨能力,并基于粒度熵设计了对信息系统进行属性约简的算法.