On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

A New Spin Gapless Semiconductors Family: Quaternary Heusler Compounds

Using first-principles calculations, we investigate the band structures of a series of quaternary LiMgPdSn-type Heusler compounds. Our calculation results show that five compounds CoFeMnSi, CoFeCrAl, CoMnCrSi, CoFeVSi and FeMnCrSb possess unique electronic structures characterized by a half-metallic gap in one spin direction while a zero-width gap in the other spin direction showing spin gapless semiconducting behavior. We further analysis the electronic and magnetic properties of all quaternary Heusler alloys involved, and reveal a semi-empirical general rule (total valence electrons number being 26 or 28) for indentifying spin gapless semiconductors in Heusler compounds. The influences of lattice distortion and main-group element change have also been discussed.Comment: 20 pages, 5 figures, 1 supplementary file, submitted for publicatio

CP violation for neutral charmed meson decays to CP eigenstates

CP asymmetries for neutral charmed meson decays to CP eigenstates are carefully studied. The formulas and numerical results are presented. The impact on experiments is briefly discussed.Comment: 7 pages, 1 figure, 1 table, Revte

Crossover of magnetoresistance in the zerogap half-metallic Heusler alloy Fe2CoSi

This work reports on the band structure and magneto-transport investigations of the inverse Heusler compound Fe2CoSi. The first-principles calculations reveal that Fe2CoSi has a very peculiar band structure with a conducting property in the majority spin channel and a nearly zero bandgap in the minority spin channel. The synthesized Fe2CoSi sample shows a high-ordered inverse Heusler structure with a magnetic moment of 4.88 {\mu}B at 5 K and a high Curie temperature of 1038 K. With increasing temperature, a crossover from positive to negative magnetoresistance (MR) is observed. Complemented with the Hall effect measurements, we suggest the intriguing crossover of MR can be ascribed to the dominant spin carriers changing from the gapless minority spin channel to the majority spin channel at Fermi level.Comment: 16 pages, 5 figures, submitted for publicatio

The cholera epidemic in South Africa, 1980 - 1987 Epidemiological features

During the cholera epidemic in South Africa, 1980-1987, 25251 cases of cholera were bacteriologically proven. The case-fatality rate was 1,4%. Outbreaks occurred in the summer rainfall season. Age-specific aUack rates followed the pattern typically found during the 'epidemic phase' of the disease in most years. The vast majority of patients were black South Africans living in rural areas with an average annual rainfall in excess of 600 mm. The containment strategy employed is summarised. Despite the apparent eradication of the disease, it is strongly recommended that vigilance should be maintained and investigations of all possible sources of infection and all human contacts of any new proven case should be carried out speedily and thoroughly

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe