我的数学研究与哲学思考

1951年暑假后,我进入大学本科数学系学习。但在一年后,我竟迷上了哲学,在我的哲学先师、革命家和马克思主义哲学家刘丹岩教授指导下,制订了自修哲学的计划。刘老师首先告戒我:“搞哲学,最好掌握或精通一门具体科学,无论是自然科学还是社会科学,否则容易成为空头哲学家”。因此,我没有放弃数学,而是利用三年的课余时间,修毕了大学本科哲学系的主要课程。1955年大学毕业后留校工作,还兼任哲学助教。1956年,还与一位老教师合作,共同为数学系、物理系高年级学生开设了《辩证唯物主义与历史唯物主义》课程。

超限数与自由度

超限数的研究是根据数学理论发展的需要提出来的,自从1883年德国数学家康托尔(1829—1920)建立集合论以来,集合论的思想和方法已经渗透到各个领域.在数学研究对象中,更多的是无穷集合,用什么样的数刻划无穷集合元素个数的无穷程度成了研究无穷集合的一个重要问题.十九世纪末期Cantor首先进行了超限数的研究,基本上解决了这一问题,使超限数的思想和方法成了今日数学的基础.几何学中又用自由度的概念刻划无穷集合元素个数的无穷程度.由此引起了本文对超限数与自由度的探讨.

The Structures of the AR Sequences of Tilted Algebras

In this paper,We give the forms of AR sequences of a tilted algebra with terms all belonging to x(A_T),or all belonging to y(A_T).The sink maps of a tilted algebra which end at the indecompos able projective modules and the source maps of starting at the indecomposable injective modules are also obtained.These results together with the connecting sequecnes given in [3] determine the AR quiver of the tilted algcbra,morever,this can be done directly from the AR quiver of the correspond ing hereditary algebra.

A case study on behaviors of composite soil nailed wall with bored piles in a deep excavation

A complete case of a deep excavation was explored. According to the practical working conditions, a 3D non-linear finite element procedure is used to simulate a deep excavation supported by the composite soil nailed wall with bored piles in soft soil. The modified cam clay model is employed as the constitutive relationship of the soil in the numerical simulation. Results from the numerical analysis are fitted well with the field data, which indicate that the research approach used is reliable. Based on the field data and numerical results of the deep excavation supported by four different patterns of the composite soil nailed wall, the significant corner effect is founded in the 3D deep excavation. If bored piles or soil anchors are considered in the composite soil nailed wall, they are beneficial to decreasing deformations and internal forces of bored piles, cement mixing piles, soil anchors, soil nailings and soil around the deep excavation. Besides, the effects due to bored piles are more significant than those deduced from soil anchors. All mentioned above prove that the composite soil nailed wall with bored piles is feasible in the deep excavation.

The Direct Product of Graded Finite Posets

A new concept Graded Finite Poset is proposed in this paper. Through discussing some basic properties of it, we come to that the direct product of graded finite posets is connected if and only if every graded finite poset is connected. The graded function of a graded finite poset is unique if and only if the graded finite poset is connected.

Effects of liquefaction-induced large lateral ground deformation on pile foundations

The pile-soil system interaction computational model in liquefaction-induced lateral spreading ground was established by the finite difference numerical method.Considering an elastic-plastic subgrade reaction method,numerical methods involving finite difference approach of pile in liquefaction-induced lateral spreading ground were derived and implemented into a finite difference program.Based on the monotonic loading tests on saturated sand after liquefaction,the liquefaction lateral deformation of the site where group piles are located was predicted.The effects of lateral ground deformation after liquefaction on a group of pile foundations were studied using the fmite difference program mentioned above,and the failure mechanism of group piles in liquefaction-induced lateral spreading ground was obtained.The applicability of the program was preliminarily verified.The results show that the bending moments at the interfaces between liquefied and non-liquefied soil layers are larger than those at the pile＇s top when the pile＇s top is embedded.The value of the additional static bending moment is larger than the peak dynamic bending moment during the earthquake,so in the pile foundation design,more than the superstructure＇s dynamics should be considered and the effect of lateral ground deformation on pile foundations cannot be neglected.

Mechanical analysis of fixed geosynthetic technique of GRPS embankment

To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed and introduced. Based on the discussion about the load transfer mechanism of FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of the FGT embankment were proposed. Two conditions, the pile cap and pile beam conditions are considered in the mechanical model. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and the soil strata. Then, the numerical procedure is programmed. Finally, a field test is conducted to verify the mechanical model and the calculated results are in good agreement with field measured data.

论二阶算术的理论解释

直观而言,自然数有无穷多个,每一个都可从初始元(设为0)出发,通过有限步后移而达到(有限可达性),自然数全体构成一个良序集。从结构的角度刻画自然数集所遇到的最大困难是如何既表征自然数集的无穷性又表征每一个自然数的有限可达性。

A numerical method for structural uncertainty response computation

A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.

DISTRIBUTION OF THE (0,∞) ACCUMULATIVE LINES OF MEROMORPHHIC FUNCTIONS

Suppose that f(z) is a meromorphic function of order and of lower order μin the plane. Let ρ be a positive number such that .(1) If f(l)(z) () has ρ() finite nonzero deficient values ai (i =1,…,p) with deficiencies δ(ai, f(l)), then f(z) has a (0, ∝) accumulative line of order inany angular domain whose vertex is at the origin and whose magnitude is larger than(2) If f(z) has only p ()(0, ∝) accumulative lines of order : arg z = θk (θ1<θ2…<θp<2π, θp+1 = θ1 + 2π), then , where , providedthat has a finite noasero deficient value.

Base force element method (BFEM) on complementary energy principle for linear elasticity problem

Using the concept of base forces as state variables,a new finite element method-the base force element method (BFEM) on complementary energy principle for linear elasticity problems is presented.Firstly,an explicit expression of compliance matrix for an element is derived through base forces by dyadic vectors.Then,the explicit control equations of finite element method of complementary energy principle are derived using Lagrange multiplier method.Thereafter,the base forces element procedure for linear elasticity is developed.Finally,several examples are analyzed to illustrate the reliability and accuracy of the formulation and the procedure.

Numerical analysis of wave hazards in a harbor

Resonance may occur when the periods of incoming waves are close to the eigen-periods of harbor basin.The amplified waves by resonance in harbor will induce serious wave hazards to harbor structures and vehicles in it.Through traditional theoretical approaches,the eigen-periods of harbor basin with regular shapes can be obtained.In our study,we proposed a numerical model to simulate the behavior characteristics of the harbor waves.A finite difference numerical model based on the shallow water equations(SWE) is developed to simulate incoming tsunami and tidal waves.By analyzing the time series data of water surface wave amplitude variations at selected synthetic observation locations,we estimate the wave height and arrival time in coastal area.Furthermore,we use frequency spectrum analysis to investigate the natural frequencies from the data recorded at the synthetic observation stations.