ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

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.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

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.

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).

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.

The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.

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.

A Virtual Boundary Element Method for Three-Dimensional Inverse Heat Conduction Problems in Orthotropic Media

This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.

Ribbon Element on Co-Frobenius Quasitriangular Hopf Algebras

Let (H, R) be a co-Frobenius quasitriangular Hopf algebra with antipode S. Denote the set of group-like elements in H by G (H). In this paper, we find a necessary and sufficient condition for (H, R) to have a ribbon element. The condition gives a connection with the order of G (H) and the order of S2.

Variational Formulations Yielding High-Order Finite-Element Solutions in Smooth Domains without Curved Elements

One of the reasons for the great success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains. Nevertheless it is well-known that, for standard variational formulations, the optimal approximation properties known to hold for polytopic domains are lost, if meshes consisting of ordinary elements are still used in the case of curved domains. That is why method’s isoparametric version for meshes consisting of curved triangles or tetrahedra has been widely employed, especially in case Dirichlet boundary conditions are prescribed all over a curved boundary. However, besides geometric inconveniences, the isoparametric technique helplessly requires the manipulation of rational functions and the use of numerical integration. In this work we consider a simple alternative that bypasses these drawbacks, without eroding qualitative approximation properties. More specifically we work with a variational formulation leading to high order finite element methods based only on polynomial algebra, since they do not require the use of curved elements. Application of the new approach to Lagrange methods of arbitrary order illustrates its potential to take the best advantage of finite-element discretizations in the solution of wide classes of problems posed in curved domains.

A Determinant Criterion of Invertible Elements in Group Algebras

An embedding from a group algebra to a matrix algebra is given in this paper. By using it, a criterion for an invertible element in a group algebra is proven.

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.

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.

‘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.

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

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。

普通混凝土-高延性混凝土组合式机场道面结构应力响应分析

由于普通混凝土(Regular Concrete,RC)弯拉强度较低、韧性差、易开裂,用于机场道面易出现断板、脱空和开裂等病害;高延性混凝土(High Ductility Concrete,HDC)具有高强度、高韧性和高抗裂性能,因此提出一种新型普通混凝土-高延性混凝土(RC-HDC)组合式机场道面结构,设计了RC单层板、HDC单层板和RC-HDC组合板3种机场道面结构。考虑基层支撑、接缝传荷能力和复杂起落架作用,建立了三维刚性道面有限元模型,分析了不同飞机荷载、道面板结构、道面板厚度、基层厚度、基层模量和土基反应模量等因素下的道面板应力响应,并计算了不同飞行区等级下的道面板最小设计厚度。研究结果表明:HDC单层板和RC-HDC组合板的弯拉强度为20 MPa和18 MPa,分别是RC单层板的4倍和3.6倍;RC-HDC组合板能够发挥HDC高弯拉强度和RC高模量的优势;对于相同道面结构,单轴单轮起落架荷载作用下道面板应力最大,双轴双轮起落架作用下道面板应力最小;4C、4D、4E、4F飞行区等级下,RC-HDC组合板的最小设计厚度分别为RC单层板的38.6%、39.0%、39.9%、41.5%;采用RC-HDC组合板不仅可以大幅减小道面板厚度,而且具有较好的经济性。