Nonemptiness of Approximate Subdifferentials of Midpoint δ-Convex Functions

ABSTRACT

For some given positive δ, a function f:D ? X → ? is called midpoint δ-convex if it satisfies the Jensen inequality f[(x ₀ + x ₁)/2] ≤ [f(x ₀) + f(x ₁)]/2 for all x ₀, x ₁ ∈ D satisfying ‖x ₁ ? x ₀‖ ≥ δ (Hu, Klee, and Larman, SIAM J. Control Optimiz. Vol. 27, 1989). In this paper, we show that, under some assumptions, the approximate subdifferentials of midpoint δ-convex functions are nonempty.     

A two-particle exchange interaction model

The magnetisation reversal of two interacting particles was investigated within a simple model describing exchange coupling of magnetically uniaxial single-domain particles. Depending on the interaction strength W, the reversal may be cooperative or non-cooperative. A non-collinear reversal mode is obtained even for two particles with parallel easy axes. The model yields different phenomena as observed in spring magnets such as recoil hysteresis in the second quadrant of the field-magnetisation-plane, caused by exchange bias, as well as the mentioned reversal-rotation mode. The Wohlfarth’s remanence analysis performed on aggregations of such pairs of interacting particles shows that the deviation δM(H_m) usually being considered as a hallmark of magnetic interaction vanishes for all maximum applied fields H_m not only at W=0, but also for sufficiently large values of W. Furthermore, this so-called δM-plot depends on whether the sample is ac-field or thermally demagnetised.     

Attainment and (sub)differentiability of the infimal convolution of a function and the square of the norm

Let X be a Banach space whose norm is simultaneously LUR and Gateaux (Fréchet) smooth. Under some assumptions, it is shown that the infimal convolution of a fairly general function on X and the square of the norm is generically strongly attained and hence is Gateaux (Fréchet) differentiable. This contains a result of S. Dutta on distance functions.     

Oxygen-permeable membranes based on partially B-site substituted BaFe1−yMyO3−δ (M=Cu or Ni)

We carried out the partial substitution of the B-site in BaFeO_3−δ perovskite with divalent cations to develop novel oxygen-permeable materials. We demonstrated that the partial substitution of Cu or Ni by more than 10% resulted in the stabilization of the cubic perovskite structure even at room temperature in a highly oxygen-permeable phase, as revealed by the X-ray diffraction (XRD) analysis. The Cu substitution was more effective for the stabilization, because the introduction of Cu in the lattice more effectively made the Goldschmidt tolerance factor (t) close to 1.0. Ni- and Cu-substituted BaFeO_3−δ membranes showed higher oxygen permeabilities than their parent BaFeO_3−δ membranes particularly at lower temperatures around 600-700 °C owing to the stabilization of the cubic phase. Among the fabricated membranes, a BaFe_0.85Cu_0.15O_3−δ membrane (1.0 mm thickness) showed the highest oxygen permeation flux (1.8 cm³ min⁻¹ cm⁻² at 930 °C) under an air/He gradient. The results indicated that Cu-substituted BaFeO_3-δ is promising as a material for Co-free membranes with high oxygen permeabilities.     

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.