Regular Elements of the Semigroup <i>B</i>_X(<i>D</i>) Defined by Semilattices of the Class &Sigma;₂(<i>X</i>, 8) and Their Calculation Formulas

The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B X (D) which is defined by semilattices of the class Σ2 (X, 8).

Duo Property Applied to Powers and Regular Elements

The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called right exp-DR.We investigate the structures of group rings,right quotient rings,matrix rings and(skew)polynomial rings,through the study of right exp-DR rings.In addition,we provide a method of constructing finite non-abelian p-groups for any prime p.

Multiple-cell elements and regular multifractals

Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper： First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the con- struction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.

REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results.

The element-free Galerkin method of numerically solving a regularized long-wave equation

The element-free Galerkin （EFG） method is used in this paper to find the numerical solution to a regularized long-wave （RLW） equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.

BOUNDARY ELEMENT ANALYSIS OF CONTACT PROBLEMS USING ARTIFICIAL BOUNDARY NODE APPROACH

An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.

关于“on finite regular BCI-algebras”一文的注记

文〔1〕引入了正则BCI一代数(fegularBCI—algebra)的概念。得到了有限正则BCI一代数的若干性质。本文证明了正则BCI一代数与P一半单BCI一代数是完全一致的。从而文〔1〕的结果正是Abel群的结果,是P一半单BCI一代数的再陈述。

Globals of Completely Regular Monoids

An element of a semigroup S is called irreducible if it cannot be expressedas a product of two elements in S both distinct from itself. In this paper we showthat the class C of all completely regular monoids with irreducible identity elementssatises the strong isomorphism property and so it is globally determined.

A Numerical Approach to a Nonlinear and Degenerate Parabolic Problem by Regularization Scheme

In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both locally fast and slow diffusion (i.e. the diffusion coefficients may explode or vanish in some point). The main difficulty is that the true solution is typically lacking in regularity. Our numerical approach includes a regularization step and a standard discretization procedure by means of C0-piecewise linear finite elements in space and backward-differences in time. Within this frame work, we analyze the accuracy of the scheme by using an integral test function and obtain several error estimates in suitable norms.

保持等价关系的变换半群的一些结果

给出了保持等价关系的变换半群上的格林关系L,R,H和格林*-关系L^(*),R^(*),H^(*)相容的充要条件,刻画了这类半群的左(右,完全)正则性,得到了这类半群的全体幂等元(正则元,富足元)构成子半群的等价描述.

ON STRONGLY REGULAR RINGS

?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.

SUPERCONVERGENCE OF LEAST-SQUARES MIXED FINITE ELEMENTS FOR ELLIPTIC PROBLEMS ON TRIANGULATION

In this paper,we present the least-squares mixed finite element method and investigate superconvergence phenomena for the second order elliptic boundary-value problems over triangulations.On the basis of the L2-projection and some mixed finite element projections,we obtain the superconvergence result of least-squares mixed finite element solutions.This error estimate indicates an accuracy of O(h3/2)if the lowest order Raviart-Thomas elements are employed.

The Atomic Regular Polyhedron Electronic Shell

The periodic table of elements is arranged based on a series of regular polyhedron. The stability of inert gas atoms can be explained by the distribution of electrons, as well as their motion and magnetic force structure. A magnetic force regular octahedron is proposed. It is a unique configuration that best satisfies the convergence of electrons moving in the same direction within regular polyhedra. In the case of an electrostatic force crust, the formal electron spin accounts for the crusts intrinsic magnetic moment exceeding the speed of light. If one is to consider that the electron has a magnetic outer layer and an electrostatic inner layer, then the question can be solved and abovementioned inference can provide the basis for magnetic force and momentum for the regular octahedron model. The electron periphery has twenty-petal adsorptive substances;the existence of adsorptive substance causes the magnetic force greater than the electrostatic force. Each electronic shell in the regular polyhedron is in accordance with the electron configuration of periodic table of elements;the kinetic track of each electron is a surface of regular polyhedron. The magnetic properties of iron, cobalt, and nickel can be explained by the regular dodecahedron electronic shell of an atom. The electron orbit converged from reverse direction can explain diamond. The adsorptive substances found in atomic nuclei and electrons are defined as magnetic particles called magnetons. The thermodynamic magneton theory can be better explained when it is analyzed using principles of thermodynamics, superconductivity, viscosity, and even in the creation of glass. The structure of the light is a helical line.

‘渝城1号’核桃矿质元素周年吸收规律研究

以‘渝城1号’核桃为研究对象,通过测定不同生育期的主要器官样品的生物量和N,P,K,Ca,Mg质量分数,总结分析核桃对5种矿质元素的吸收规律.结果表明:①开花坐果以后,核桃干物质快速增加,增加的干物质主要累积在果实、根和茎中,并在果实膨大期后,果实中的干物质累积量显著高于其他器官;②从各器官矿质元素质量分数上看,茎、营养枝和果枝中的N,P,K质量分数在展叶抽梢期最高,茎和营养枝中的Ca质量分数在果实膨大期最高,营养枝和果枝中Mg质量分数在落叶期最高.③从各器官矿质元素的累积量看,开花坐果前,N,P,K在根部的累积量最高.开花坐果后,果实中N,P,K的累积量逐渐升高.整个生育期,Ca在根部中的累积量最高,而Mg在果实膨大期前以根部累积量最高,之后在果实中的累积量最高;④5个矿质元素中,核桃对N,K,Ca吸收量大于P和Mg,其中核桃对N,P吸收量最大的时间在开花坐果期,对K和Mg吸收量最大的时间在坐果初期,对Ca吸收量最大的时间在果实膨大期.因此,开花坐果期到果实膨大期是核桃施肥的关键时期,在该时期应及时补充相应的矿质元素,以实现核桃的科学高效施肥.

半群Р_(n)(r)的正则性

设Р_(n)是X_(n)={1,2,…,n}上的部分变换半群,对任意1≤r≤n-1,记X_(r)={1,…,r},令Р_(n)(r)={α∈Р_(n):X_(r)■dom(α),X_(r)α?X_(r)},则Р_(n)(r)是Р_(n)的子半群。考虑了半群Р_(n)(r)的正则元、左正则元、右正则元,以及这些元素之间的关系。此外,给出Р_(n)(r)是正则半群、左正则半群和右正则半群的充要条件。

300例射血分数保留心力衰竭患者的中医证候分布规律

目的基于射血分数保留心力衰竭(heart failure with preserved ejection fraction,HFpEF)基本证候要素的病证结合诊断标准分析HFpEF的证候特征及分布规律。方法纳入300例符合标准的HFpEF患者,收集证候诊断所需信息及相关临床资料,统计单个证素、证素组合的频数分布,并采用两步聚类法探讨主要证型的划分。结果(1)300例HFpEF患者单个证素的出现频率依次为:气虚(97.0%)、血瘀(92.7%)、水饮(79.7%)、痰浊(55.0%)、阴虚(44.7%)、阳虚(36.3%)。(2)同时具有4证素和5证素的患者最多,分别占39.0%和30.3%。(3)患者以虚实夹杂证(94.0%)为主,纯虚证(3.0%)和纯实证(3.0%)较少。(4)300例患者共出现15种证素组合,通过两步聚类可分为8类,每类患者均有气虚、血瘀。结论HFpEF的病机关键为气虚、血瘀、水饮,气虚是始动因素,气虚血瘀为基本证候,可分为气虚血瘀、气阴两虚血瘀、阳气亏虚血瘀和阴阳两虚血瘀4种证型。

中国锗矿成矿规律与开发利用现状

锗是一种银灰色性脆的金属,在地壳中的含量约为0.0007%,属于稀散元素,是制造红外光学仪器的关键材料,2018年被美国内政部列为35种关键性矿产之一。中国的锗资源储量占全球的41%,产量占全世界的71%,拥有类似于稀土的全球影响力。已查明资源储量的锗矿区主要分布在内蒙古和云南等14个省(自治区),其中约一半的查明锗资源储量与煤矿伴生,其余大部分与铅锌矿等有色金属矿产伴生。锗可以出现在不同时代的各种矿床当中,主要包括中低温热液型多金属矿床、含锗有机岩矿床和沉积改造型三大类型,以前二者为主,占所有锗矿资源量的64%。我国高品位的富锗煤矿是世界上少有的优质资源,但尚未得到充分的开发利用。国际上主要从煤灰残渣中回收,我国除了煤矿中回收锗(如云南的临沧含锗煤矿、内蒙的乌兰图嘎)之外,也从有色金属冶炼厂综合回收(如广西大厂、云南会泽)。

轴向运动正六边形板的自由振动

本文研究了在轴向运动激励下正六边形薄板的横向自由振动问题。应用Reddy三阶剪切变形板理论刻画板的力学状态,采用6节点三角形单元离散求解域,利用虚功原理建立系统的动力学有限元方程。数值算例选取2种典型布置形式,并分别考虑固支和简支2种边界条件。通过求解系统方程得到了前四阶固有频率,经与ANSYS计算结果对比,验证了本研究方法的准确性。研究发现,速度通过离心力和科氏力影响系统固有振动,且速度与各阶频率反相关。正六边形板的第二和第三阶振动分别有2种模态,速度为零时其固有频率相同,但随着速度的增大逐渐分离。本文揭示的若干动力学现象可为轴向运动正六边形薄板的设计和优化提供参考。

粤北棉花坑铀矿床热液蚀变与物质迁移研究

本文以粤北长江铀矿区棉花坑铀矿床的横向矿化蚀变剖面为研究对象,系统研究了代表性新鲜花岗岩、蚀变岩和矿石的主量、微量以及稀土元素地球化学特征,运用质量平衡计算方法探讨了各蚀变带组分的迁移规律,以期解决成矿物质来源、成矿流体来源及其性质等问题。结果表明,该矿化蚀变剖面具有明显的水平分带特征,可分为新鲜花岗岩带(Ⅴ带)、远矿碱交代蚀变带(Ⅳ带)、近矿绿泥石化蚀变带(Ⅲ带)、矿旁水云母化蚀变带(Ⅱ带)和矿化中心赤铁矿化蚀变带(Ⅰ带)。从侧缘碱交代带→矿化中心带,Si O2的带入率(0. 27%→0. 21%→0. 50%→0. 70%)整体上与U的带入率(4. 73%→8. 07%→39. 26%→98. 29%)呈正比,K^+与Na^+相互排斥呈现"钾钠不相容"现象,MgO与MnO呈现出"此消彼长"的迁移特征,是对流平衡迁移方式的表现。Th、Pb、Cs、Mo、As元素在矿化中心带的带入率最大,Ba、Sr、Co、V元素在矿化中心带迁出率最小,这对铀成矿(铀矿化)具有很好的指示作用。根据各蚀变带元素的含量、比值及迁移特征,结合前人的研究成果,认为矿床的成矿物质主要来源于赋矿围岩长江岩体,成矿流体在成分上富含挥发分和矿化剂(CO2、F、H2O等)、碱金属元素(K、Cs、Rb)和重稀土元素,性质上具相对高的氧逸度,其来源是地幔流体与经历了深循环大气降水的混合成因流体。挥发分和矿化剂(CO2、F、H2O等)的带入是矿床重要的矿质迁移机制,CO2的逸出伴随着氧化向还原过渡的环境是矿床重要的矿质沉淀机制。

轴向运动正三角形Mindlin板的自由振动

基于Mindlin板理论和有限元法研究了轴向运动正三角形板的自由振动问题.利用虚功原理推导轴向运动正三角形板横向自由振动的有限元方程,在三边简支边界条件下研究系统自由振动特性.算例部分,针对两种常见布置形式,首先求解板无轴向速度时的前四阶固有频率,并将其与ANSYS软件计算结果对比,证实了所给方法的准确性;随后重点探讨了速度和布置形式对前四阶固有频率的实部和虚部的影响.结果显示:速度与板受到的离心力与科氏力密切相关,在这两种力的共同作用下,速度越大,固有频率越小;第二阶振动对应不同的模态,低速时频率相同,高速时频率发散;布置形式对振动有一定影响.