Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system

Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system

Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.

CALCULATION OF THE EXCHANGE INTERACTION CONSTANT BETWEEN RARE-EARTH AND TRANSITION METAL SUBLATTICESIN R_2Fe_(17_x)Al_x(R=Tb, Gd AND Dy)COMPOUNDS

An approximate calculation of the exchange interaction constant J_(RT)between the rare-earth sublattice and the transition metal sublattice in R_2Fe_(17-x)Al_x (R= Tb,Gd, and Dy) compounds is given by the molecular-field model and the results of neutron diffraction.The calculated values, -J_(R,T)/k, for Dy_2Fe_(17-x)Al_x (x=5, 6, 7 and 8), Tb_2Fe_(10)Al_7,Gd_2Fe_(17-x)Al_x (x=7, 8) compounds are 8.62K, 8.64K, 9.52K, 10.34K and 10.66K, 10.65K, and 9.85K,respectively, they are in agreement with the experimental values, -J_(R,T)/k, of Dy_2Fe_(17-x)Al_x(x=5, 6, 7 and 8), Tb_2Fe_(10)Al_7 and Gd_2Fe_(17-x)Al_x (x=7, 8) compounds, which are 8.77K, 9.25K,10.1K, 10.9K and 10.35K, 10.1K, and 10.3K, respectively. The origins of the difference between thecalculated and the experimental results are discussed.

Magnetizations of Multisublattice Bilayer System

Magnetizations of four sublattice bilayer system have been systematically investigated by the use of effectivefield theory with self-spin correlations and differential operator technique. The effects of the crystal field, longitudinal magnetic field, and intra- and inter-monolayer interaction constants on magnetizations axe examined in detail. Some interesting results are obtained, which may potentially be related to experimental work.

Single-Parameter Quantum Pumping in Graphene Nanoribbons with Staggered Sublattice Potential

We present a theoretical study of quantum charge pumping in metallic armchair graphene nanoribbons using the Floquet Green function method. A central part of the ribbon acting as the scattering region is supposed to have staggered sublattiee potential to open a finite band gap. A single ae gate is asymmetrically applied to a part of the scattering region to drive the pumping. Corresponding to the gap edges, there are two pumped current peaks with opposite current directions, which can be reversed by changing the position of the ac gate relative to the scattering region. The effects of the parameters, such as the staggered sublattice potential, the driving frequency and the geometric parameters of the structure, on the pumping are discussed.

布尔代数的(∈,∈∨q)-Fuzzy子代数和(∈,∈∨q)-Fuzzy理想

引入了布尔代数的(∈,∈∨q)-Fuzzy子代数、(∈,∈∨q)-Fuzzy理想和(∈,∈∨q)-Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy子集是(∈,∈∨q)-Fuzzy子代数((∈,∈∨q)-Fuzzy理想)的充要条件,讨论了布尔代数的(∈,∈∨q)-Fuzzy子代数((∈,∈∨q)-Fuzzy理想)在布尔代数同态下的像和逆像,并证明了当I是布尔代数R的(∈,∈∨q)-Fuzzy真理想时,R/I是布尔代数。

L-fuzzy格及(λ,μ)-fuzzy凸子格

基于一般格上模糊(对偶)理想、模糊素理想和凸子格的一些性质,讨论了L-fuzzy格的一些基本性质,并给出了(λ,μ)-fuzzy子格,(λ,μ)-fuzzy理想(对偶理想)和(λ,μ)f-uzzy凸子格概念,建立了(λ,μ)-fuzzy凸子格与其水平子格之间的联系.

α-fuzzy子群

给出了一种新型的 fuzzy子群的定义 (称之为 α-fuzzy子群 ) ,它是 Rosenfeld的定义及 S.K.Bhakat和 P.Das定义的推广 .我们还给出了 α-fuzzy子群的等价定义 ,给出了正规 α-fuzzy子群的定义 ,研究了 α-fuzzy商群及 α-fuzzy子群的同态象性质 .

泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。

完备Brouwerian格上无限@-Fuzzy关系方程的极大解问题

在论域为无限集时讨论了完备Brouwerian格L上@ Fuzzy关系方程A@X=b(其中@表示inf α合成,A=(aij)I×J,I,J为无限指标集,b∈L),当b为完全交既约元时构造出了方程的极大解,当b有不可约完全交既分解时对方程的解集中的每一个解都找到了一个大于等于它的极大解.

格的L′-Fuzzy理想的代数性质

引入格 L 的 L′- Fuzzy理想、L′- Fuzzy素理想和 L′- Fuzzy同余理想等概念 ,讨论这些理想在Zadeh型映射下像的性质 。

区间集上非交换剩余格〈∈,∈∪Q〉-Fuzzy滤子的特征刻画

基于区间集思想与滤子理论,讨论区间集上非交换剩余格与区间集上非交换剩余格Fuzzy滤子,给出了区间集上非交换剩余格〈∈,∈∪Q〉-Fuzzy滤子的代数结构及若干等价性特征刻画的表示定理.

区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的构造

以区间集和滤子理论作为研究区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的工具,通过引入区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的概念,讨论了生成〈∈,∈■Q〉-fuzzy滤子的几种方法,彰显模糊逻辑推演系统被视为代数滤子的镜像.

(∈,∈∨q)-Fuzzy线性空间

提出了 (∈ ,∈∨q) -Fuzzy域及 (∈ ,∈∨q) -Fuzzy域上 (∈ ,∈∨q) -Fuzzy线性空间的概念 ,给出了一个Fuzzy集是 (∈ ,∈∨q) -Fuzzy线性空间的充分必要条件 ,讨论了 (∈ ,∈∨q)

凸子格格的数量研究

本文主要研究了经过序和、三角和运算后形成的新格的凸子格格数目同原来的有限格凸子格格数目之间的数量关系,并将其进行了推广。在此基础上,得到了有限格凸子格格数目同格自身结构的一些特殊关系。

几类一元模糊代数方程的可解性条件

在取Zadeh算子的模糊空间中讨论3类基本的一元模糊代数方程,给出这3类方程的可解性判别条件;证明第1类方程的解集构成取Zadeh算子模糊空间的凸子格;当方程中的蕴涵算子取→R蕴涵时,第2、3类模糊代数方程的解集构成取Zadeh算子模糊空间的凸子格.

格群的-Fuzzy子格群的等价刻画及应用

给出- Fuzzy子格群的的几种等价刻画 。

L-Fuzzy子格群的若干刻画

在 L是完全分配格时 ,讨论 L- Fuzzy子格群的一些特征性质。特别地 ,借助 L- Fuzzy集的几种水平截集给出它的若干刻画。最后给出这些刻画的一个应用。

格的L-fuzzy素理想

给出了格的L-fuzzy素理想的定义。借助于L-fuzzy集的水平截集,得到了L-fuzzy子格、格的L-fuzzy理想、格的L-fuzzy素理想的若干等价刻画,并研究了它们的运算性质。

(∈,∈∨q)-Fuzzy带算子环

进一步讨论了Fuzzy环理论，给出(∈，∈Vq)-Fuzzy带算子环、(∈，∈Vq)-Fuzzy带算理想和(∈，∈Vq)-Fuzzy带算商环的定义，同时讨论了他们的一些初等性质．