Local density approximation study of transition andf-electron materials

The local density approximation (LDA) has been proved to be a powerful starting point for calculating electronic and structural properties for many real materials. We have studied the effects of particular forms of exchange-correlation potentials (the X{dollar}\alpha{dollar} and Hedin-Lundqvist form) upon the structural properties for the 3d Ti and 4d Zr using a highly accurate linearized augmented plane wave (LAPW) method. The calculated equilibrium volumes differ by 6-8% for these two forms (with X{dollar}\alpha{dollar} results in better agreement with experiment) with proportional differences in other structural properties, which we take to be an indication of the intrinsic reliability of the LDA. Considerable sensitivity in the calculated structural properties to the particular exchange-correlation potential (the X{dollar}\alpha{dollar}, Wigner, and Hedin-Lundqvist) was also found for the fcc and the high temperature bcc La. The calculation on SmS reveals that the LDA is inadequate for this very localized 4f electron system, while the LDA works fairly well for the chemically similar material LaS. For HgTe and HgSe, the fully occupied 5d electrons in Hg has been found to be important in determining the structural properties through the Hg d - chalcogen p interactions, however this p-d hybridization appears to be relatively unchanged through the various pressure induced phase transitions. We calculated the total energy of the seven layer slabs of Pd(111) surface as a function of the top layer spacing, the relaxation is found to be very small ({dollar}\u3c{dollar}1%)

Properties of Catlin's reduced graphs and supereulerian graphs

A graph $G$ is called collapsible if for every even subset $R\subseteq V(G)$, there is a spanning connected subgraph $H$ of $G$ such that $R$ is the set of vertices of odd degree in $H$. A graph is the reduction of $G$ if it is obtained from $G$ by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs $G$ of order $n$ with $d(u)+d(v)\ge 2(n/p-1)$ for any $uv\in E(G)$ where $p>0$ are given, we show how such graphs change if they have no spanning Eulerian subgraphs when $p$ is increased from $p=1$ to 10 then to $15$

Linear extension of the Erdos-Heilbronn conjecture

The famous Erdos-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdos-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements $a_1,...,a_n$ of F, the set {a_1x_1+...+a_nx_n: x_1,....,x_n are distinct elements of A} has cardinality at least min{p(F)-delta, n(|A|-n)+1}, where the additive order p(F) of the multiplicative identity of F is different from n+1, and delta=0,1 takes the value 1 if and only if n=2 and $a_1+a_2=0$. In this paper we prove this conjecture of Sun when $p(F)\geq n(3n-5)/2$. We also obtain a sharp lower bound for the cardinality of the restricted sumset {x_1+...+x_n: x_1\in A_1,...,x_n\in A_n, and P(x_1,...,x_n)\not=0}, where $A_1,...,A_n$ are finite subsets of a field F and $P(x_1,...,x_n)$ is a general polynomial over F

Alloying and Processing Effects on the Aqueous Corrosion Behavior of High-Entropy Alloys

The effects of metallurgical factors on the aqueous corrosion behavior of high-entropy alloys (HEAs) are reviewed in this article. Alloying (e.g., Al and Cu) and processing (e.g., heat treatments) effects on the aqueous corrosion behavior of HEAs, including passive film formation, galvanic corrosion, and pitting corrosion, are discussed in detail. Corrosion rates of HEAs are calculated using electrochemical measurements and the weight-loss method. Available experimental corrosion data of HEAs in two common solutions [sulfuric acid (0.5 M H$_{2}$SO$_{4}$) and salt water (3.5 weight percent, wt.%, NaCl)], such as the corrosion potential (E$_{corr}$), corrosion current density (i$_{corr}$), pitting potential (E$_{pit}$), and passive region (ΔE), are summarized and compared with conventional corrosion-resistant alloys. Possible directions of future work on the corrosion behavior of HEAs are suggested