Systematic {\em ab initio} study of the phase diagram of epitaxially strained SrTiO3_3

We use density-functional theory with the local-density approximation to study the structural and ferroelectric properties of SrTiO$_3$ under misfit strains. Both the antiferrodistortive (AFD) and ferroelectric (FE) instabilities are considered. The rotation of the oxygen octahedra and the movement of the atoms are fully relaxed within the constraint of a fixed in-plane lattice constant. We find a rich misfit strain-induced phase transition sequence and is obtained only when the AFD distortion is taken into account. We also find that compressive misfit strains induce ferroelectricity in the tetragonal low temperature phase only whilst tensile strains induce ferroelectricity in the orthorhombic phases only. The calculated FE polarization for both the tetragonal and orthorhombic phases increases monotonically with the magnitude of the strains. The AFD rotation angle of the oxygen octahedra in the tetragonal phase increases dramatically as the misfit strain goes from the tensile to compressive strain region whilst it decreases slightly in the orthorhombic (FO4) phase. This reveals why the polarization in the epitaxially strained SrTiO$_3$ would be larger when the tensile strain is applied, since the AFD distortion is found to reduce the FE instability and even to completely suppress it in the small strain region. Finally, our analysis of the average polar distortion and the charge density distribution suggests that both the Ti-O and Sr-O layers contribute significantly to the FE polarization

Efficient and Perfect domination on circular-arc graphs

Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$. An \emph{efficient dominating set} is a perfect dominating set $V'$ where $V'$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them

Estimation accuracy of high–low spread estimator

[[abstract]]In this paper we analyze the estimation accuracy of high–low spread estimator. It is found that the performance of high–low spread estimator depends on the size of the true spread, the level of transaction frequency, and the degree of volatility. Analyzing the probability of measurement error, it is shown that the high–low spread estimators have better performance when the size of the spread is even wider, when the level of transaction frequency is even higher, or when the degree of volatility is relatively lower.[[notice]]補正完畢[[incitationindex]]SSCI[[booktype]]紙本[[booktype]]電子

Strongly Regular Graphs as Laplacian Extremal Graphs

The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest eigenvalues, the minimum of second-smallest eigenvalues of Laplacian matrices and hence the maximum of Laplacian spreads among all simple connected graphs of fixed order, minimum degree, maximum degree, minimum size of common neighbors of two adjacent vertices and minimum size of common neighbors of two nonadjacent vertices. Some other extremal graphs are also provided.Comment: 11 pages, 4 figures, 1 tabl

Signals of New Gauge Bosons in Gauged Two Higgs Doublet Model

Recently a gauged two Higgs doublet model, in which the two Higgs doublets are embedded into the fundamental representation of an extra local $SU(2)_H$ group, is constructed. Both the new gauge bosons $Z^\prime$ and $W^{\prime (p,m)}$ are electrically neutral. While $Z^\prime$ can be singly produced at colliders, $W^{\prime (p,m)}$, which is heavier, must be pair produced. We explore the constraints of $Z^\prime$ using the current Drell-Yan type data from the Large Hadron Collider. Anticipating optimistically that $Z^\prime$ can be discovered via the clean Drell-Yan type signals at high luminosity upgrade of the collider, we explore the detectability of extra heavy fermions in the model via the two leptons/jets plus missing transverse energy signals from the exotic decay modes of $Z^\prime$. For the $W^{\prime (p,m)}$ pair production in a future 100 TeV proton-proton collider, we demonstrate certain kinematical distributions for the two/four leptons plus missing energy signals have distinguishable features from the Standard Model background. In addition, comparisons of these kinematical distributions between the gauged two Higgs doublet model and the littlest Higgs model with T-parity, the latter of which can give rise to the same signals with competitive if not larger cross sections, are also presented.Comment: 39 pages, 23 figures, 7 tables and two new appendixes, to appear in EPJ