全能近似分析简介

根据无限的“无有终了”的事实，应当把无尽小数看作无穷数列简写，采用这种观点就可以得到实数的运算法则；如果用康托（Cantor，G）的“无限是现实的、完成了的、存在着的整体”的“实无限”观点就得不到这个法则．点是针对误差界的足够小，其中没有大小的点叫做理想点，有大小的点叫做近似点．理想点具有无法点出的性质．近似点的集合能够组成线段，但理想点的集合不能组成线段．绝对准确地讨论没有大小的理想瞬时上的速度没有实际意义，理想的瞬时速度依赖于近似瞬时的速度．对于点、线、面、实数、函数、导数、积分、积分变换、实数集等数学名词都需要提出近似、理想、全能近似三类技术术语，应用对立统一法则去阐述数学理论．     

Equimodular and linearity in modular spaces

In this paper, the concept of equimodular is introduced. It contains several generalizations of Mazur-Ulam's isometric theorem in modular spaces. Let X and Y be two real modular spaces and X with δ₁-midpoint shrinking whose modular ρ_X satisfies the Δ₂-condition. Assume that an operator T maps X onto Y in an δ₂-{t_i}-equimodular manner for all , where {t_i} is a null-sequence of nonnegative reals with the property that t₀=1, t₁?1/2, and t_i?t_i−1?2t_i for i?2. Then T is affine.     

稀土元素替代Y对YBa2Cu3O7-δ氧吸附性能的影响

用热重法研究了RBa2Cu3O7-δ(R=Gd、Er、Eu、Dy、Sm、Ho和Nd)及Y1-xLaxBa2Cu3O7-δ(x=0.1,0.5和1.0)共10种材料在高温下的氧吸附—脱附性能。结果表明,随着温度的升降循环,仅NdBa2Cu3O7-δ(R=Gd)和Y1-xLaxBa2Cu3O7-δ的氧吸附—脱附性能有较好的重复性,其余的6个样品的重复性都很差;并且这10种样品的质量变化率都没有YBCO的大。     

掺Pr的YBCO体系的EXAFS研究

通过对掺Pr的YBCO体系的EXAFS数据计算机分析发现:体系中的O的位置随Pr含量改变发生了变化。CuO₂平面曲折度增加,Cu-O链上的O更趋近于CuO₂面,Ba-O3间距增大。所有这些变化导致载流子浓度降低和载流子严重局域化,引起超导性发生变化。     

固相线下Pr1-xBa2-yCax+yCu3O7±δ体系的相关系和晶体结构

 利用X射线衍射分析和Rietveld结构精修的方法研究了固相线下Pr_1-xBa_2-yCa_x+yCu₃O_7±δ体系的相关系和晶体结构。研究表明：950 ℃、空气条件下，Pr_1-xBa_2-yCa_x+yCu₃O_7±δ（y=0）体系系列样品总是含有两相：Pr123（PrBa₂Cu₃O_7±δ）和BaCuO₂；而且，随Ca含量的增加，杂相BaCuO₂的含量也随之增加。Pr_1-xBa_2-yCa_x+yCu₃O_7±δ（x=0）体系y=0.1、0.2、0.3、0.4的样品都只含有Pr123单相；y=0.5的样品含有3相：Pr123、Ca₂CuO₃和Pr₄Ca₁₀Cu₂₄O₄₁。另外，Pr_1-xBa_2-yCa_x+yCu₃O_7±δ（x=0）系列样品（y=0.1、0.2、0.3、0.4）中Pr123相还发生了正交-四方晶系的结构转化。y=0.1和0.2的样品为正交晶系，晶胞参数分别为a=0.390 33(4)和0.389 36(1) nm，b=0.389 53(4)和0.387 73(1) nm，c=1.173 38(4) 和1.168 20(2) nm；y=0.3和0.4的样品为四方晶系，晶胞参数分别为a=b=0.387 80(0) 和0.387 67(0) nm，c=1.166 00(2) 和1.165 20(2) nm。在Pr123结构中，Ba离子可以被Pr离子代替，但不能被Ca离子所代替。Ca离子占据部分Pr离子的位置。在Pr_1-xBa_2-yCa_x+yCu₃O_7±δ（x=0）体系中Pr、Ba和Ca离子间的相互替代中，离子半径比化学性质起到了更大的作用。在950 ℃、空气条件下，Ca离子在Pr_1-xBa_2-yCa_x+yCu₃O_7±δ体系中的最大溶解量是当x=0时，y≤0.4。     

Effects of divalent impurities on the fluctuation conductivity of YBa2Cu3O7 single crystals

We have studied experimentally the in-plane fluctuation conductivity near the superconducting transition in single crystal samples of YBa₂Cu₃O₇, Y_0.98Ca_0.02Ba₂Cu₃O₇, YBa_1.9Sr_0.1Cu₃O₇ and YBa₂Cu_2.97Zn_0.03O₇. In order to test the stability of the observed fluctuation regimes, low magnetic fields were applied perpendicular to the Cu-O₂ atomic planes. When the transition is approached from above we first observe a three-dimensional (3D) Gaussian regime then a crossover to a genuine critical region where the exponent is consistent with the predictions of the 3D-XY-E universality class. Decreasing further the temperature towards T_c, our results systematically reveal the occurrence of a regime beyond 3D-XY characterized by a very small critical exponent. We propose that this regime is precursory to a weak first-order superconducting transition driven by antiferromagnetic excitations related to the pseudogap phenomenon. The dilution of divalent impurities in YBa₂Cu₃O₇ does not affect the stability of the fluctuation regime beyond 3D-XY and in the case of Ca doping a further approach towards the first-order behaviour is observed.     

Synthesis of 3-acetonyl- and 3-(2-oxoethyl)glutarates

Several synthetic routes to 3-acetonyl- and 3-(2-oxoethyl)glutarates 1-5 have been explored. The most advantageous involves, as the key steps, the conjugate addition of an appropriately substituted vinylmagnesium bromide to an alkylidenemalonic ester, a bis-homologation of the resulting diester and, finally, the reductive ozonolysis of the carbon-carbon double bond. The synthesis can be satisfactorily conducted in good overall yield on a multigram scale.     

基于量子限制的受主带间跃迁太赫兹探测器的制备与测量

使用分子束外延生长设备,在GaAs（100）衬底上生长了量子阱宽度为3 nm的GaAs/AlAs多量子阱样品,并在量子阱层中央进行了Be受主的δ-掺杂。根据量子限制受主从束缚态到非束缚态之间的跃迁,设计并制备了δ-掺杂Be受主GaAs/AlAs多量子阱太赫兹光探测器原型器件。在4.2 K温度下,分别对器件进行了太赫兹光电流谱和暗电流-电压曲线的测量。在6 V直流偏压下,空穴载流子沿量子阱层方向输运。当正入射激光频率为6.8 THz时,器件响应率为2×10^-4 V/W（2 μA/W）。通过器件的暗电流-电压曲线计算了器件全散粒噪声电流,在4.2 K、6 V直流偏压下,全散粒噪声电流为5.03 fA·Hz^-1/2。     

Spaces of holomorphic functions on non-balanced domains

This paper studies the coincidence of the _τω${\tau }_{\omega }$ and _τδ${\tau }_{\delta }$ topologies on the space of holomorphic functions defined on an open subset U   of a Banach space. Dineen and Mujica proved that _τω=_τδ${\tau }_{\omega }={\tau }_{\delta }$ when U   is a balanced open subset of a separable Banach space with the bounded approximation property. Here, we study the _τω=_τδ${\tau }_{\omega }={\tau }_{\delta }$ problem for several types of non-balanced domains U.